4) Let the polynomial function of degree 4 that has roots 3, 2, 2+ i as its roots be p(x).
So, the required polynomial function is:
p(x)=(x−3)(x−2)(x−(2+i))(x−(2−i))
= (x−3)(x−2)(x^2−(2+i)x−(2−i)x+(2−i)(2+i))
= (x−3)(x−2)(x^2−2x−ix+ix+4)
= (x−3)(x−2)(x^2−2x+4)
= x^4−9x^3+28x^2−36x+24
Thus, the polynomial function of degree 4 that has real coefficients and has 3, 2 and 2+ i as some of its roots is x^4−9x^3+28x^2−36x+24.
Given: x^3−2x^2+36x−72=0 and 6i is a zero of this polynomial function.
So, we can write it as:
x^3−2x^2+36x−72= (x−6i)(x−(−6i))(x−6)
= (x−6i)(x+6i)(x−6)
As this polynomial function has real coefficients, so the imaginary roots occur in conjugate pairs.
Thus, the remaining zeros are:
−6i (as 6i is a zero, so −6i is also a zero due to conjugate pair of complex roots) and 6 (as 6i is one factor of the polynomial function, so x−6i will be its conjugate factor, which will be x+6i. And, the remaining factor will be x−6)
Therefore, the remaining zeros of x^3−2x^2+36x−72 polynomial function are −6i and 6.
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A factory produces 10,000 computer monitors per day. The manager of the factory claims that fewer than 750 defective computer monitors are produced each day. In a random sample of 290 computer monitors, there are 9 defective computer monitors. Determine whether the manager's claim is likely to be true. Explain
The manager's claim that fewer than 750 damaged computer displays are produced daily is accurate, thus yes. A hypothesis theory can help us with this.
We need to conduct a hypothesis test to establish whether the manager's assertion is likely to be accurate. The null hypothesis, labelled H0, is that the fraction of damaged computer displays manufactured each day is 750/10,000 = 0.075. The proportion being less than 0.075 is the alternative hypothesis, labelled Ha.
The test statistic, which gauges how far the sample proportion deviates from the null hypothesis proportion assuming the null hypothesis is true, can be calculated using the sample data. Here is how the test statistic is computed:
p is the sample proportion of faulty, and z = (p - p0) / (p0(1-p0)/n) computer monitors, n is the sample size, and p0 is the null hypothesis proportion.
In this instance, n = 290, p = 9/290 = 0.031, and p0 = 0.075.
These variables are plugged in, and the result is: z = (0.031 - 0.075) / (0.075(1-0.075)/290) -4.50
The test statistic reveals how far the sample percentage deviates from the null hypothesis proportion by how many standard deviations. The test statistic's absolute value should be higher if there is more evidence arguing against the null hypothesis.
The likelihood of seeing a test statistic that is as extreme or more extreme than the one we computed assuming the null hypothesis is true is known as the p-value, and it may be determined using a conventional normal distribution. As the alternative hypothesis in this situation is that, we are interested in the left tail of the distribution. The proportion is lower than the proportion under the null hypothesis.
The p-value, which can be calculated or calculated using statistical tools, is about 0.000003. Due to the extremely low p-value, it is extremely unlikely that the sample proportion will be as extreme as or more extreme than 0.031, if the null hypothesis is correct.
The maximum probability of rejecting the null hypothesis when it is true is called the significance level, and it is typically used to compare the p-value to. The usual ranges for are 0.05 and 0.01. We reject the null hypothesis and come to the conclusion that there is evidence against it if the p-value is less than. If not, we are unable to reject the null hypothesis and come to the conclusion that there is insufficient evidence. to dismiss it.
If we apply = 0.05 in this instance, the p-value is significantly lower than. As a result, we reject the null hypothesis and come to the conclusion that there is evidence to support a daily production rate of fewer than 0.075 defective computer displays. The manager's assertion that fewer than 750 damaged computer displays are manufactured each day is in conflict with this.
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Nick and his family travel by train to new york the clocks show 6:15 they left the station and arrived in new york at 10:30how long was the train ride
The train ride duration was 4 hours and 15 minutes.
To find the duration of the train ride, we need to subtract the departure time from the arrival time.
First, let's convert the departure and arrival times to a 24-hour clock format for easier calculation.
6:15 PM in 24-hour clock format is 18:15.
10:30 PM in 24-hour clock format is 22:30.
To find the duration, we subtract the departure time from the arrival time:
22:30 - 18:15 = 4 hours and 15 minutes
Therefore, the train ride duration was 4 hours and 15 minutes.
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the distribution of scores on a standardized aptitude test is approximately normal with a mean of and a standard deviation of . what is the minimum score needed to be in the top on this test? carry your intermediate computations to at least four decimal places, and round your answer to the nearest integer.
The minimum score needed to be in the top 5% on this standardized aptitude test is 7. The distribution of scores on a standardized aptitude test is approximately normal with a mean of and a standard deviation of. What is the minimum score needed to be in the top on this test?
In statistics, we assume that the distribution of scores on a standardized aptitude test is approximately normal with a mean of µ and a standard deviation of σ, where µ and σ are the parameters of the normal distribution. To calculate the minimum score needed to be in the top 5%, we must first determine the z-score corresponding to the top 5%.It is known that the area to the left of z is 0.95, which corresponds to the top 5%.
To find the z-score that corresponds to the 95th percentile, we can use a standard normal distribution table, such as the one found in most statistics textbooks or online. The table gives the z-score that corresponds to the given area to the left of the mean.Using the standard normal distribution table, we find that the z-score corresponding to the top 5% is approximately 1.645. This means that the score needed to be in the top 5% is 1.645 standard deviations above the mean. We can calculate this score using the formula:X = µ + zσwhere X is the score we are trying to find, µ is the mean, z is the z-score corresponding to the top 5%, and σ is the standard deviation. Substituting the values we know into this formula:X = + 1.645 × = + 6.58. Rounding to the nearest integer, we get X = 7.
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Please help, I’ve tried multiple times to answer and I still don’t know.
The slant height of given square pyramid is √45 inch.
What is the square pyramid?A square pyramid is a geometric solid that has a square base and four triangular faces that meet at a common vertex. It belongs to the family of pyramids, which are three-dimensional shapes that have a palled the apex.
With the help of the Pythagoras theorem, we can find out the slant height of pyramid using the formula:
[tex]s^{2} =H^{2} +(\frac{a}{2} )^{2}[/tex]
Here, height of square pyramid is H.
take an equilateral triangle, where a triangle has all sides are equal.
so, the height of the triangle (h) = [tex]\sqrt{a^{2} + (\frac{a}{2}) ^{2} }[/tex] = [tex]\sqrt{6^{2} + (\frac{6}{2}) ^{2} }[/tex] = √45 inch
the height of the square pyramid (H) is:
[tex]H^{2} + (\frac{a}{2}) ^{2} } = h^{2}[/tex]
[tex]H^{2} = (\sqrt{45} )^{2} - (\frac{6}{2}) ^{2} }[/tex]
H = 6 inch
The slant height of pyramid using the formula:
[tex]s^{2} =6^{2} +(\frac{6}{2} )^{2}[/tex] = 36 + 9 = 45
s = √45 inch
Therefore, the slant height of given square pyramid is √45 inch.
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What is the area of the trapezoid?
Answer:
160
Step-by-step explanation:
area of trapezoid = 1/2 (base 1+base 2) x height.
24+8=32
32x10=320
320x1/2=160.
160.
The scale shown is not balanced. Drag base ten blocks to the box to show the amount that x needs to be to balance the scale.
The amount that x = 153 needs to be to balance the scale. Thus,we would need to drag, One block from A, 5 columns of blocks form B and 3 blocks from C to balance the scale.
What is a Scale?a scale is a device used to measure the weight or mass of an object by comparing it to a known reference weight or mass. It works by using the principle of equilibrium, where the weight on one side is balanced by an equivalent weight on the other side. This allows for accurate measurement of the weight or mass of an object.
This is sometimes represented in math as an equation.
We have an equation given in the above image:
221 = x + 68; to find the required blocks to balance the scale, we must find x.
To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 68 from both sides:
221 - 68 = x + 68 - 68
153 = x
Therefore, x = 153.
Since each Set "A" is a block of 100 Units, Set "B" is a block of 10 Units, and Set "C" is a Unit, we would need to drag, One block from A, 5 columns of blocks form B and 3 blocks from C to balance the scale.
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Full Question;
The scale shown is not balanced. Drag base ten blocks to the box to show the amount that x needs to be to balance the scale. See the attached image.
Helppppp meeeeeeee plsssss
Tim makes a lemon meringue pie
in a pie pan that is 9" in diameter.
What is the area of Tim's pie?
Answer:
Step-by-step explanation:
[tex]4.5^{2}[/tex] x [tex]pie[/tex] =63.6[tex]cm^{2}[/tex]
Answer:
20.25pi or about 63.62
Step-by-step explanation:
the formula for area of a circle is pi*r^2.
since the diameter is 9, the radius is half of that, which is 4.5
then, plugging this into our formula, we get 20.25pi. this rounds to 63.62.
The amount of time it takes p people to paint d doors varies directly with the number of doors and inversely with the number of people. Four people can paint 10 doors in 2 hours. How many people will it take to paint 25 doors in 5 hours?
4
5
10
20
Answer:
4 people
Step-by-step explanation:
We are given that The amount of time it takes p people to paint d doors varies directly with the number of doors inversely with the number of people.
Let constant of proportionality be k
There are 4 people , 10 doors and 2 hours.
Since we are given that time varies directly with no. of doors and inversely with no. of people.
[tex]2=k\times\frac{10}{4}[/tex]
[tex]\frac{2\times4}{10}=k[/tex]
[tex]\frac{8}{10}=k[/tex]
[tex]\frac{4}{5}=k[/tex]
Now we are supposed to find that How many people will it take to paint 25 doors in 5 hours.
⇒ [tex]5=k\times\frac{25}{d}[/tex]
⇒ [tex]5=\frac{4}{5} \times\frac{25}{d}[/tex]
⇒ [tex]d=\frac{4}{5} \times\frac{25}{5}[/tex]
⇒ [tex]d=4[/tex]
Hence it will take 4 people to paint 25 doors in 5 hours.
Pete and Mike were competing at soccer to see who could score the most number of goals in total. In today's match, Pete managed to score 4 goals, and Pete and Mike's scores were in the ratio of 1 : 2. Before today's match, the scores for Pete and Mike were in the ratio of 1 : 3. Mike did not manage to score any goal today. How many goals did Mike score in total?
Answer:
1x + 4 : 2x = 1 : 2
We can cross-multiply to get:
2(1x + 4) = 1(2x)
2x + 8 = 2x
8 = 2x - 2x
8 = 0
This is not possible, so our assumption that Pete and Mike's scores before today's match were 1x and 3x respectively must be incorrect.
Let's try a different assumption. Let's assume that before today's match, Pete and Mike's scores were 2x and 6x respectively. After today's match, Pete scored 4 goals, so his total score is now 2x + 4. We also know that Pete and Mike's scores were in the ratio of 1:2 after today's match. Therefore, we can write:
2x + 4 : 2(6x) = 1 : 2
We can simplify this to:
2x + 4 : 12x = 1 : 2
We can cross-multiply to get:
2(2x + 4) = 1(12x)
4x + 8 = 12x
8 = 12x - 4x
8 = 8x
x = 1
Therefore, before today's match, Pete and Mike's scores were 2 and 6 respectively. After today's match, Pete's score is 2 + 4 = 6. Since Pete and Mike's scores were in the ratio of 1:2 after today's match, Mike's score must be twice that of Pete's score, which is 2 x 2 = 4.
Therefore, Mike's total score is 6 + 4 = 10. Mike scored a total of 10 goals.
What are the coordinates of X′ for the image of △TUX after dilation with center at (0, 0) and scale factor 4, then applying (x, y) ⟶ (x − 3, y + 1), given T(−7, −6), U(−8, 3), X(2, 1)?
Reason:
The point X is located at (2,1)
We'll apply the scale factor to quadruple each coordinate to get (8,4)
Then apply the translation rule to shift 3 units left and 1 unit up.
[tex](\text{x},\text{y})\to(\text{x}-3,\text{y}+1)\\\\(8,4)\to(8-3,4+1)\\\\(8,4)\to(5,5)\\\\[/tex]
You receive a brochure from a large university. The brochure indicates that the mean class size for full-time is fewer than 33 students. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each. The results are shown in the table below. At α = 0.01, can you support the university's claim?
36 27 32 36 35 41 28 25 32
27 33 36 30 29 27 28 30 28
Find the P-value.
I disregard the null hypothesis & come to the conclusion supports the assertion that the mean classroom sizes for full-time is lower than [tex]33[/tex] pupils but since p-value [tex](0.033)[/tex] falls short of significance threshold [tex]=0.01[/tex].
What in mathematics is a value?Depending about where it is in the number, each digit has a different value, which is referred to as value. We estimate it by reducing the place value by the face value of the digit. Worth is the product of will get and face value.
What does five mean in math?Place value refers to how much a digit is worth in relation to where it is in a number, such as the ones, tens, thousands, and so on. For instance, 5 in 3458 has a placement value of 5 tens, and 50.
X bar [tex]= (36+27+32+36+35+41+28+25+32+27+33+36+30+29+27+28+30+28)/18 = 31.39[/tex]
s [tex]= \sqrt{(((36-31.39)^2 + (27-31.39)^2 + ... + (28-31.39)^2)/17)} = 4.84[/tex]
We can support the university's claim. The P-value is approximately [tex]0.033[/tex]
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High school geometry
The answer of the question based on the volume of prism is given below, the volume of the prism is 48 cubic units.
What is Pythagorean Theorem?The Pythagorean Theorem is fundamental theorem in mathematics that relates to three sides of right-angled triangle. It states that in any right-angled triangle, square of length of the hypotenuse (the longest side) is equal to sum of squares of lengths of other two sides.
we know that the area of the base is given by:
Area of base = (1/2) * base * height
where base = 4 and height = 3 (using the Pythagorean Theorem).
Therefore, Area of base = (1/2) * 4 * 3 = 6 square units.
The height of the prism is given as 8 units.
Hence, the volume of the prism is given by:
Volume = Area of base * height
= 6 * 8
= 48 cubic units.
Therefore, the volume of the prism is 48 cubic units.
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Mr.Alvarez has 25 students and his students collected 150 canned goods. Ms. Jensen has 28 students and her students collected 154 canned goods. Mrs. Saunders has 27 students and her students collected 162 canned goods are the ratios of canned goods per student equivalent between any or all of the classes? Explain your reasoning.
Answer:
Alvarez = Saunders ≠ Jensen
Step-by-step explanation:
You want to know if any or all of the classes collected the same number of canned goods per student when the numbers were ...
Alvarez: 150 cans, 25 studentsJensen: 154 cans, 28 studentsSaunders: 162 cans, 27 studentsCanned goods per studentThe metric "canned goods per student" is computed by dividing the number of canned goods by the number of students. These values might best be compared as decimal numbers.
The attached calculator screen shows this calculation.
The classes of Mr. Alvarez and Mrs. Saunders had equivalent ratios of canned goods per student: 6. Ms. Jensen's class had a ratio of 5.5 canned goods per student, so was not equivalent to the other two.
Answer:
Mr. Alvarez's and Mrs. Saunders's classes have equivalent ratios. While Ms. Jensen's class has a different ratio.Step-by-step explanation:
We can find out if the ratios of canned goods per student are the same for any or all of the classes by calculating the ratio of canned goods per student for each class.
Mr. Alvarez's class collected 150 canned goods with 25 students, giving a ratio of 6 canned goods per student. Ms. Jensen's class collected 154 canned goods with 28 students, giving a ratio of 5.5 canned goods per student. Mrs. Saunders's class collected 162 canned goods with 27 students, giving a ratio of 6 canned goods per student.Therefore, the ratios of canned goods per student are not the same for all the classes. However, Mr. Alvarez's and Mrs. Saunders's classes have equivalent ratios, indicating that each student, on average, collected the same number of canned goods in these two classes. In contrast, Ms. Jensen's class has a different ratio, indicating that, on average, her students collected a different number of canned goods per student compared to the other two classes.
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PLEASE HELP DUE IN 10 MINS!!
WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST
The solution of the equation is as follows:
[tex]\frac{8^{x} }{2^{y} } = 2^{12}[/tex]
Therefore, the answer is A.
How to solve an exponential expression?The equation 3x - y = 12. Let's find the value of [tex]\frac{8^{x} }{2^{y} }[/tex] as follows:
Let's apply the exponential law to solve the expression as follows:
Therefore, when dividing exponential values with the same base, we have to subtract the exponents.
Hence,
[tex]\frac{a^{x} }{a^{y} } = a^{x-y}[/tex]
Therefore,
[tex]8^{x} = 2^{3x}[/tex]
Hence,
[tex]\frac{8^{x} }{2^{y} } = \frac{2^{3x} }{2^{y} }[/tex]
Applying the law,
[tex]\frac{8^{x} }{2^{y} } = \frac{2^{3x} }{2^{y} } = 2^{3x - y}[/tex]
Using substitution,
3x - y = 12
Therefore,
[tex]\frac{8^{x} }{2^{y} } = \frac{2^{3x} }{2^{y} } = 2^{3x - y} = 2^{12}[/tex]
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how do i convert 5/34 to a improper fraction.
Answer: You cannot
Step-by-step explanation:
5/34 is considered a proper fraction, it is impossible to convert it into an improper fraction.
Please help me with my math!
The equation of the quadratic function with four times the maximum width, with a maximum of 3 and an axis of symmetry of x = -2 is given as follows:
y = -4(x + 2)² - 3.
How to define the quadratic function given it's vertex?The quadratic function of vertex(h,k) is given by the rule presented as follows:
y = a(x - h)² + k
In which:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.The width is four times the normal width and the function has a maximum, hence the leading coefficient is given as follows:
a = -4.
Considering the axis of symmetry and the maximum, the parameters h and k are given as follows:
h = -2, k = 3.
Hence the function is defined as follows:
y = -4(x + 2)² - 3.
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A vendor pays a rock band 13
of the total profit from T-shirts and sweatshirts sold at every concert. The vendor paid the rock band $726 after the last concert. If the profit from T-shirts sales was $1,632, what was the profit from sweatshirt sales?
If the profit from T-shirts sales was $1,632, and the vendor pays the rock bands 1/3 of the total profit from T-shirts and sweatshirts sales at every concert, proportionately, the profit from the sweatshirt sales alone is $546.
What is proportion?Proportion describes the equation of two ratios.
In this situation, when we equate the proportion or fraction of the share of profit paid to the band to the actual profit paid, we can find the total profit realized from the concert sales.
The fractional share of the total profit from T-shirts and sweatshirts paid to the rock band = 1/3
The total amount paid to the rock band after the last concert = $726
The profit from T-shirts sales = $1,632
Proportionately, the total profit from the sales of T-shirts and sweatshirts = $2,178 ($726 x 3)
The profit from sweatshirt sales is the difference between the total profits and the profit from T-shirt sales.
= $546 ($2,178 - $1,632)
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A debit of $10 on a number line
The set of integers that represents a debit of $10 and a credit of $6 would be option 1. {-10, 6}.
Define integerAn integer is a mathematical object that represents a whole number, either positive, negative or zero, without any decimal or fractional part. Integers include the natural numbers (1, 2, 3, ...), their negative counterparts (-1, -2, -3, ...) and the number zero (0).
In this case, a debit of $10 means that $10 has been spent or taken out of the account, which is represented by the negative integer -10. A credit of $6 means that $6 has been added to the account, which is represented by the positive integer 6.
Therefore, the set {-10, 6} represents a debit of $10 and a credit of $6.
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The complete question is:
Which set of integers represents a debit of $10 on a number line, and the credit of $6?
(-10,6)(-10,-6)(10,6)(10,-6)On #4 I need help please, I am in middle school so I have Homework on Friday so yeah
Answer:
enjoy your weekend bud , both answers and solutions ares given , if you didn't understand anything lmk with a message and ill be happy to explain
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Answer:
n=1,-2
L=2,3
m=5,0
Step-by-step explanation:
if that's in point not coordinates
check after me i might be wrong
According to the information that comes with a certain prescription drug, when taking this drug, there is a 20% chance of experiencing dizziness (D) and a 40% chance of experiencing headaches (H). The information also states that there is a 15% chance of experiencing both side effects
0.55 = 55% probability of experiencing neither of the side effects.
In a Venn probability, two non-independent events are related with each other, as are their probabilities.
Venn diagrams are diagrams used to visually describe sets, relationships between sets, and operations carried out on them. John Venn (1834–1883) invented the Venn diagram, which makes use of circles (overlapping, intersecting, and non–intersecting) to show the relationship between sets. A Venn diagram can also be referred to as a set diagram or a logic diagram that illustrates various set operations including the intersection, union, and difference of sets. Subsets of a set are also represented using it.
The "or probability" is given by:
P(A∪B)=P(A)+P(B)-P(A∩B)
P(N)=0.2 , P(D)=0.4 and P(N∩D)=0.15
The "at least one" probability is:
0.2+0.4-0.15=0.45
Hence, the "neither" probability is:
1-0.45=0.55
0.55 = 55% probability of experiencing neither of the side effects.
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Help :''( pls help, ppls! 50 pts. each answer :'(
Answer:
I think its C
Step-by-step explanation:
Answer:32
Step-by-step explanation:
Prompt The depression datanle is available in the Data section below. We will analyze the data to answer the 1st research question: Which of the drugs (if either) was more successful in preventing the recurrence of depression relative to the placebo? In the previous lab preparation activity, we determined that we will analyze the data using a two-way table and conditional percentages.
Using a two-way table and conditional percentages, the depression datanle available in the Data section below should be used.
The depression datanle should be analyzed using a two-way table and conditional percentages, to answer the research question: "Which of the drugs (if either) was more successful in preventing the recurrence of depression relative to the placebo?"
The table should show the number of patients who took the drugs and those who took the placebo, and the number of patients who had a recurrence of depression and those who didn't have a recurrence of depression after taking the drugs or placebo, respectively.Then, conditional percentages should be calculated for each group of patients who took the drugs and those who took the placebo.
These conditional percentages should be calculated by dividing the number of patients who didn't have a recurrence of depression by the total number of patients who took the drugs or placebo for each group. Finally, the percentage difference should be calculated between the two conditional percentages for the drug and placebo groups. The group with the highest percentage difference is the one that was more successful in preventing the recurrence of depression relative to the placebo.
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What is the measure of KJL?
Answer:
25°
Step-by-step explanation:
Triangles have a total count of 180°. Seeing that angle K has a measure of 130°, we know that the other two sides must be equal to 50°. However, if ∠KJL = 50°, then ∠KLJ would be 0°, which is impossible.
Question 4 Solve. Be sure to check for any extraneous solutions 2ln(x)=ln(4)+ln(16)
The solution is x = 8.
The solution to the equation 2ln(x) = ln(4) + ln(16) should be determined, taking into account any extraneous solutions. The steps to accomplish this are as follows:2ln(x) = ln(4) + ln(16)ln(x^2) = ln(4*16)ln(x^2) = ln(64)By taking the exponential of both sides, this expression can be resolved.x^2 = 64x = ±8Since the natural logarithm is only defined for positive numbers, only the positive value of x is taken into account. Therefore, the solution is x = 8.The process of checking for extraneous solutions involves substituting the answer obtained into the original equation and evaluating it to see whether it is accurate or not.2ln(8) = ln(4) + ln(16)The above equation can be simplified to become: ln(64) = ln(64)The answer is consistent. As a result, the solution is accurate and does not include any extraneous values. The solution is x = 8.
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For what value of 0 does sin20 = cos (0 +30)?
For cos(0) to be equal to 0.392, sin(20) must be equal to cos(0 + 30).
We can use the trigonometric identities to simplify the expression cos(0 + 30):
cos(0 + 30) = cos(0)cos(30) - sin(0)sin(30)
Since sin(0) = 0 and cos(30) = √3/2, we have:
cos(0 + 30) = cos(0)√3/2
We can then rearrange this equation to get:
sin(20) = cos(0)√3/2
To solve for cos(0), we can divide both sides by √3/2:
cos(0) = sin(20) / (√3/2)
Using the values of sin(20) ≈ 0.34 and √3/2 ≈ 0.866, we can calculate:
cos(0) ≈ 0.34 / 0.866 ≈ 0.392
Therefore, for cos(0) to be equal to 0.392, sin(20) must be equal to cos(0 + 30).
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have tiled my square bathroom wall with congruent square tiles. all the tiles are red, except those along the two diagonals, which are all blue (i.e. the corners are blue and all the tiles along the diagonals between each pair of opposite corners are blue). if i used 121 blue tiles, how many red ones did i use?
You can use 3599 red tiles. If you have used 121 blue tiles.
To begin, find out how many total tiles are in the square by squaring the number of tiles along one side. Then subtract the number of tiles in the two diagonals of the square, which are all blue, to get the number of red tiles. Let us try to solve the problem. Given that the tiles are square and congruent, they must have identical dimensions. Let us assume that the length of one side of the square tile is x.
Therefore, the length of each side of the square can be determined by dividing the number of tiles by the length of the side of the square. The total number of tiles in the square can be calculated by squaring the number of tiles along one side. Consider the following equation: Let x be the length of each side of the square tile.
Then, the total number of tiles that make up the square can be determined using the following equation:
Total number of tiles in square = [tex]x^2[/tex]
We know that all the tiles are congruent squares, except those that are blue, which are located on the two diagonals. This means that there are 2 diagonals of blue tiles, and the remaining tiles are red. To determine the number of blue tiles in the two diagonals, use the following formula:
Length of diagonal = √2 x side length
Since the diagonals pass through opposite corners of the square, they must be equal in length. The total number of blue tiles, 121, is equal to twice the number of blue tiles in one diagonal. Use the following formula to determine the number of blue tiles in one diagonal: 121 / 2 = 60.5 The answer is rounded up to 61.
Using the Pythagorean Theorem, the length of the diagonal of each blue tile can be calculated. The following equation can be used: Side of square = x
Length of diagonal of one blue tile = x√2
The number of blue tiles in one diagonal is the length of the diagonal divided by the length of the diagonal of one blue tile. This can be expressed as a formula:x / (x√2) = number of blue tiles in one diagonal
Simplify the formula:
x / (x√2) = number of blue tiles in one diagonal
Multiply both sides by √2 and simplify:(√2 / 2) = number of blue tiles in one diagonal
This indicates that each diagonal has a total of 61 blue tiles. Because the two diagonals have a total of 122 blue tiles, the number of red tiles is equal to the total number of tiles minus the total number of blue tiles. The following equation can be used to calculate the number of red tiles:([tex]x^2[/tex]) - 122 = number of red tiles
Substitute 61 for x: [tex](61)^2[/tex] - 122 = 3721 - 122 = 3599.
To know more about tiles problems: https://brainly.com/question/499197
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Please answer 10 questions in this and get 55 points
Answer:
Step-by-step explanation:
1. 7pq
2. 9-x^2=(3-x)(3+x)
3. 6z^2
4. i
5. x^2 + xy + 2y^2
6. i:2^3 ii:(x+5)^2 V:(6-7)(6+7) iiii: 4b(b-a) v again: n/a
19:300
Shelby multiplies 7,358. 9 by a power of 10 and gets the product
73. 589. Select all possible factors.
(A) 1/100 "fraction"
(B) 1/10 "Fraction"
(C) 1
(D) 0. 1
(E) 0. 01
(F) 0. 1
Answer:
A and E
Step-by-step explanation:
A. 7,358.9 is 7.3589 x 10³
B. 73. 589 is 7.3589 x 10¹
For A which is 10³ to reduce to 10¹, you need to multiply by a fraction
To reduce 3 to 1, you need to deduct 2 (10¹¯³ = 10¯²)
10¹/ 10³ = 10/1000 = 1/100 which can also be written as 0.01