The root of the equation is rational for any real value of a where a>0. if a=0, the equation has a single root which is real and rational.
What are roots?In mathematics, the number that results in the initial number when multiplied by itself is called the root. For instance, 7 is the square root of 49 since 77=49. Because 49 is created by multiplying 7 by itself twice in this instance, we refer to 7 as the square root of 49. Since 333=27, the cube root of 27 is 3.
According to question:The given equation is 2x + a(x-a) = 0. Simplifying, we get:
[tex]$\begin{align*}2x + ax - a^2 &= 0 \x(2+a) &= a^2 \x &= \frac{a^2}{2+a}\end{align*}[/tex]
Therefore, the root of the equation is [tex]\frac{a^2}{2+a}$[/tex].
To show that this root is rational for any real value of a where a>0, we need to show that [tex]\frac{a^2}{2+a}$[/tex] can be expressed as a ratio of two integers.
Let [tex]$p=a^2$[/tex] and q=2+a. Since a>0, we have p>0 and q>0. Therefore, [tex]\frac{p}{q}$[/tex] is a rational number.
Thus, the root of the equation is rational for any real value of a where a>0.
If a=0, the given equation becomes 2x=0, which has only one root, x=0. Therefore, if a=0, the equation has a single root which is real and rational.
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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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A volume is described as follows:1. the base is the region bounded by y=6−3/8 x^2 and y=02. every cross-section parallel to the x-axis is a triangle whose height and base are equal.Find the volume of this object.volume =
The volume of the object is 168.96 cubic units. The volume of the object can be found using the formula for volume of a solid with known cross-sections : [tex]V = ∫ A(x)dx[/tex], where [tex]A(x)[/tex] is the area of the cross-section at x.
In this case, the cross-sections are triangles with equal base and height. The area of a triangle is A = 1/2bh, so the area of the cross-section at x is [tex]A(x) = 1/2b^2.[/tex]
The base of the triangle is the distance between the two curves, which is [tex]6−3/8 x^2 - 0 = 6−3/8 x^2.[/tex] So the area of the cross-section is [tex]A(x) = 1/2(6−3/8 x^2)^2.[/tex]
Now we can find the volume by integrating the area function over the x-values of the base region. The base region is bounded by the curve [tex]y=6−3/8 x^2[/tex], so the x-values are the roots of this equation:
[tex]0 = 6−3/8 x^2 3/8 x^2 = 6 x^2 = 16 x = ±4[/tex]
So the volume is:
[tex]V = ∫[−4,4] 1/2(6−3/8 x^2)^2dx = 1/2 ∫[−4,4] (36 - 9/4 x^2 + 9/64 x^4)dx[/tex]
[tex]= 1/2 [(36x - 3/4 x^3 + 9/320 x^5)] from x=-4 to x=4 = 1/2 [(288 - 192 + 72.96) - (-288 + 192 - 72.96)] = 1/2 (576 - 384 + 145.92) = 1/2 (337.92)[/tex]
= 168.96 , So the volume of the object is 168.96 cubic units.
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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 grocer bought 200 eggs at the rate of RS 10 each. 20 eggs were broken and he sold the remaining eggs at 8% profit. Find the rate of selling price of each egg
The rate of the selling price of each egg is 6%
What is the selling price of a commodity?The selling price of a commodity is the price at which a seller offers a product or service for sale to a buyer. It is the amount of money that a buyer must pay to purchase the commodity from the seller.
To calculate the selling price of a commodity, a seller typically adds a markup to the cost of production, which includes the direct and indirect costs of producing the commodity, such as materials, labor, and overhead expenses.
The markup is usually expressed as a percentage of the cost of production, and it varies depending on the industry, product, and market conditions.
If 200 eggs were bought for Rs10 each, then all egg costs Rs2000.
20 broken eggs, remaining 180 eggs.
Based on these conditions, we can formulate an equation:
10 × (8% + 1) ÷ (200 - 20)
Simplify;
[tex]=\dfrac{10\times 1.08}{180}[/tex]
Eliminate the common factor;
[tex]=\dfrac{1.08}{18}[/tex]
[tex]=\dfrac{108}{1800}[/tex]
Calculate the product or quotient;
[tex]=\dfrac{6}{100}[/tex]
Rewrite the rate of the selling price as a percentage = 6%
Therefore, we can conclude that the rate of the selling price as a percentage is 6%.
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The balance on Ramon Felipe's credit card on January 13, his billing date, was $221. 33.
For the period ending February 13, Ramon had the following transactions to the right.
a) Find the average daily balance for the billing period.
b) Find the finance charge to be paid on February 13. Assume an interest rate of 1. 2% per
month
c) Find the balance due on February 13.
a) The average daily balance for the billing period is $285.29.
b) The finance charge to be paid on February 13 is $3.42.
c) The balance due on February 13 is $288.71.
To calculate the average daily balance, we need to determine the daily balances for each day in the billing period. To do this, we need to add the previous day's balance to any new charges and subtract any payments or credits.
Day Transaction Daily Balance
Jan 13 Starting balance $221.33
Jan 17 Charge of $50 $271.33
Jan 22 Payment of $100 $171.33
Feb 4 Charge of $100 $271.33
Feb 6 Charge of $100 $371.33
Feb 10 Payment of $100 $271.33
Feb 13 Finance charge $288.71
To calculate the average daily balance, we add up the daily balances and divide by the number of days in the billing period:
(221.33 * 4) + (271.33 * 5) + (371.33 * 3) + (288.71 * 1) / 13 = $285.29To calculate the finance charge, we multiply the average daily balance by the interest rate and the number of days in the billing period:
285.29 * 0.012 * 31 = $3.42To calculate the balance due on February 13, we add the finance charge to the average daily balance:
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In the triangle below,
x= [ ? ]°. Round to the nearest
tenth. 9 and 4
TRIGONOMETRY IS CONFUSING!!
Answer:
from the figure
tanx= p/b
or, tanx= 4/9
or, x=arctan(4/9)
or, x=23.49°
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.
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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HELP MEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
THANK YOUUUUUUUUU
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
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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URGENT PLEASE I FORGOT TO STUDY. Unit 1 lesson 11 quadratic functions and equations unit test connections academy. There's 20 questions! If you've already done this test please spare the answers
The two solutions of the equation x2 - 4x + 1 = 0 are x = 2 + √3 and x = 2 - √3.
A quadratic equation is an equation that can be written in the form ax2 + bx + c = 0, where a, b, and c are real numbers and a is not equal to 0. Solving a quadratic equation involves finding the value of x that makes the equation true. This can be done in multiple ways, but the most common method is to use the Quadratic Formula. The Quadratic Formula states that the roots (or solutions) of a quadratic equation can be found using the following formula:
x = [-b ± √(b2 - 4ac)]/2a
For example, consider the equation x2 - 4x + 1 = 0. In this equation, a = 1, b = -4, and c = 1. Plugging these values into the Quadratic Formula gives us:
x = [-(-4) ± √((-4)2 - 4(1)(1))]/2(1)
Simplifying this equation, we get:
x = [4 ± √(16 - 4)]/2
Finally, simplifying further yields the following two solutions:
x = (4 ± √12) /2
x = 2 ±√3
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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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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.
Write an equation for a line perpendicular to y=-4x-2 and
passing through the point (-12,2)
y= ?
show work pls
The equation of the line perpendicular to y = -4x - 2 and passing through (-12, 2) is y = 1/4x + 5.
Given that a line passes through (-12, 2) and is perpendicular to y = -4x - 2. We have to find the equation of this line. To find the equation of the line perpendicular to the given line, we need to know the slope of the line we want to find. The slope of the given line is -4. Since the lines are perpendicular, the slope of the line we want to find will be the negative reciprocal of -4, which is 1/4.
Thus, the equation of the line passing through (-12, 2) and is perpendicular to y = -4x - 2 is:y - 2 = 1/4(x + 12)Simplify by distributing the 1/4:y - 2 = 1/4x + 3
Add 2 to both sides: y = 1/4x + 5
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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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The base of a triangle is seven less than twice its height. If the area of the triangle is 102cm squared, find the length of the base.
Answer:
length of base = 17 cm
Step-by-step explanation:
Area of a triangle A = 1/2 bh where b = base h = height
We are given
b = 2h - 7
A = 102
or
2h = b + 7
h = (b+7) /2
use this in the equation for A
1/2 (b) (b+7)/2 = 102
1/4 x b(b+7) = 102
b(b+7) = 4 x 102
b² + 7 b = 408
b² + 7b - 408 = 0
This is a quadratic equation which can be solved by factoring or using the quadratic formula
We can factor b² + 7b - 408 as follows
Find factors u, v of -408 (one factor positive, the other negative)See which of these factors will add(or subtract) to 7Factors of -408 areCheck if b = 17 is correct
With b = 17
h = (b+7) /2
= (17 + 7)/2
= 24/2
= 12
Therefore A = 1/2 x 17 x 12
= 17 x 6
= 102
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
If 10% of a number equals 2, find 40% of that number.
Answer:
8
Step-by-step explanation:
40% is 4 times 10%, so the number is 4 times greater.
4 × 2 = 8
Answer: 8
Let's call the number we're trying to find "x".
We know that 10% of x is equal to 2.
So, we can set up the equation:
0.1x = 2
To solve for x, we can divide both sides by 0.1:
x = 2 ÷ 0.1
x = 20
Now that we know x is 20, we can find 40% of that number:
40% of 20 = 0.4 x 20 = 8
Therefore, 40% of that number is equal to 8.
Suppose SAT Writing scores are normally distributed with a mean of 491 and a standard deviation of 109. A university plans to admit students whose scores are in the top 30%. What is the minimum score required for admission? Round your answer to the nearest whole number, if necessary
Therefore, the minimum score required for the scholarship 652
We are told in the question that:
A university plans to award scholarships to students whose scores are in the top 30%.
The top 30% means
100 - 30% = 70%
This means the student must be in the 93rd percentile
We solve using the z-score formula.
z = (x-μ)/σ, where
x is the raw score?
μ is the population mean = 496
σ is the population standard deviation = 109
Z score for 93rd percentile = 1.476
1.476 = x - 491/109
Cross Multiply
1.476 × 109 = x - 491
160.884 = x - 491
x = 160.884 + 491
x = 651.884
Approximately to the nearest whole number = 652
Therefore, the minimum score required for the scholarship 652
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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:
Given that the system has a type 1 defect, what is the probability that it has a type 2 defect? (round your answer to four decimal places. )
The probability of having a type 2 defect given a type 1 defect is 0.6667, rounded to four decimal places.
The probability of having a type 2 defect given a type 1 defect is the conditional probability of having a type 2 defect given a type 1 defect divided by the probability . This can be expressed as P(type 2 defect|type 1 defect)/P(type 1 defect).
P(type 2 defect|type 1 defect) = 0.2
P(type 1 defect) = 0.3
Therefore,
P(type 2 defect|type 1 defect) / P(type 1 defect) = 0.2 / 0.3 = 0.6667
The probability of having a type 2 defect given a type 1 defect is 0.6667 and when rounded to four decimal places it is 0.6667.
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Which statement describes this mapping diagram?
A 10 is the output of two different inputs.
B This is not a function because one input has two different outputs.
C This is a function because every input has one output.
D The input 17 has two outputs, 0 and 2.
Therefore, the correct answer is B: "This is not a function because one input has two different outputs."
What is mapping diagram?A mapping diagram is a graphical representation of a function that shows how elements of one set are mapped or transformed into elements of another set. It consists of two columns or sets, the first one is the input set, and the second one is the output set. The mapping rule or function is applied to each element of the input set to obtain the corresponding element of the output set. The elements of the input set are typically represented as points or values on the left-hand side, while the corresponding elements of the output set are represented as points or values on the right-hand side. Mapping diagrams are often used to illustrate simple functions, such as those involving basic arithmetic operations or algebraic expressions. They can also be used to demonstrate the properties of more complex functions, such as those involving trigonometric or exponential functions.
Here,
A mapping diagram is a visual representation of a relation between two sets of numbers, where each input corresponds to an output. In this diagram, we can see that each input (represented in the left column) has only one corresponding output (represented in the right column), except for the number 10, which has two outputs, 3 and 7. This violates the definition of a function, which states that each input can have only one output.
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A piece of blue yarn 5 2/7 yards long a piece of pink yarn is 5 times as long as that. What is total length of the blue and pink yard
The total length of the blue and pink yarn is 31 5/7 yards
What is total length of the blue and pink yardThe blue yarn is given as
Blue = 5 2/7 yards
The length of the pink yarn is 5 times the length of the blue yarn:
So, we have
Length of pink yarn = 5 x 5 2/7 yards
Length of pink yarn = 26 3/7 yards
To find the total length of the blue and pink yarn, we can add their lengths:
Total length = Length of blue yarn + Length of pink yarn
Total length = 5 2/7 yards + 26 3/7 yards
The fractions have the same denominator
So, we have
Total length = 31 5/7
Therefore, the total length of the blue and pink yarn is 31 5/7 yards
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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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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
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]
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.
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.
whats the area of sector and length of arc
The area of the sector is π square meters.
Length of arc [tex]= (90/360)* 2π(2m) = πm[/tex]
What is Area of Sector?To find the area of the sector and the length of the arc, we need to use the formulas:
Area of sector = ( Θ/360 x π[tex]r^2[/tex]
Length of arc = (θ/360) x 2πr
Given radius (r) = 2m and angle (θ) = 90 degrees, we can plug these values into the formulas to get:
Area of sector = [tex](90/360) * \pi (2m)^2[/tex]
[tex]= (1/4) * \pi * 4m^2[/tex]
[tex]= \pi m^2[/tex]
Therefore, the area of the sector is π square meters.
Length of arc = (90/360) x 2π(2m)
= (1/4) x 4πm
= πm
Therefore, the length of the arc is π meters.
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