The equation of the tangent to the circle at point A is 6x + 7y - 93 = 0
How do we solve for the equation of the tangent to the circle?The equation of a circle in standard form is (x-h)² + (y-k)² = r²,
(h,k) is the center of the circle
r is the radius.
The radius formula ⇒ √((x₂ - x₁)² + (y₂ - y₁)²).
Here,
x₁ = -1, y₁ = 2 (center of the circle),
x₂ = 5, y₂ = 9 (point A on the circle).
∴
r = √((5 - (-1))² + (9 - 2)²) = √(36 + 49) = √85.
Now, we have the equation of the circle: (x - (-1))² + (y - 2)² = 85, or (x + 1)² + (y - 2)² = 85.
The slope of the radius from the center of the circle to point A ⇒ (y₂ - y₁) / (x₂ - x₁)
= (9 - 2) / (5 - (-1)) = 7/6.
tangent line is the negative reciprocal of the slope of the radius, ∴ -6/7.
The equation of a line in point-slope form is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.
The slope of the tangent line (m) is -6/7 and it passes through point A(5,9). Substituting these values in, it becomes
y - 9 = -6/7 (x - 5).
Multiplying every term by 7 to clear out the fraction and to have the equation in the ax + by + c = 0 form, we get:
7y - 63 = -6x + 30,
or
6x + 7y - 93 = 0.
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Graph the line with y-intercept 4 and slope 2.
Answer is in the file atttached.
I have a problem at 4'o clock on the given attachment picture please check it out
Answer:
4
Step-by-step explanation:
You want the product of terms (n+1)/n for integers n from 1 to 3.
ProductWhen there are only 3 terms, we can write out the product:
(1 +1)/1 × (2 +1)/2 × (3 +1)/3 = 2 × 3/2 × 4/3 = 4
The product is 4.
__
Additional comment
You will notice the first term has a denominator of 1. In each pair of terms, the numerator of a term cancels the denominator of the next term. This means the product of k terms will always be (k+1). For 3 terms, the product is 3+1 = 4.
Apparently, the answer in each case is the hour number.
<95141404393>
the next 3 terms of 10,13,17,238
If you spin the spinner 90 times, what is the best prediction possible for the number of times
it will not land on yellow?
times
Submit
Answer:
Assuming the spinner has 6 equal sectors of different colors, and yellow is only one of those colors, we can say that the probability of the spinner not landing on yellow is 5/6 or approximately 0.8333.
To predict the number of times the spinner will not land on yellow out of 90 spins, we can multiply the probability by the total number of spins:
0.8333 x 90 = 74.997 or approximately 75
Therefore, the best prediction possible for the number of times the spinner will not land on yellow out of 90 spins is 75 times.
How do -3.8 and -4 1/2 compare
Answer:
-3.8 > -4.5
Step-by-step explanation:
Convert the fraction to decimal and then compare.
[tex]\sf -4\dfrac{1}{2}=\dfrac{-9}{2}[/tex]
= -4.5
Now compare (-3.8) & (-4.5)
-3.8 > -4.5
An oven used 7.31 units of electricity over
4 hours.
What is the rate of electricity usage for this
oven in units per hour?
Give your answer to 1 d.p.
The rate of electricity usage for the oven is 1.8275 units per hour.
What is the rate of electricity usage for the oven?The electricity consumption represents the amount of electrical energy that has been consumed over a specific time in units of Wh (or kWh),
To get rate of electricity usage for the oven in units per hour, we will divide the total electricity used by the number of hours.
Data:
Electricity used: 7.31 units
Time: 4 hours
Rate of electricity usage = Electricity used / Time
Rate of electricity usage = 7.31 units / 4 hours
Rate of electricity usage = 1.8275 units per hour.
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What is the area of a rectangle whose width is n feet and who’s length is 2 feet more than 3 times it’s width in terms of n?
Answer: The length of the rectangle is given as "2 feet more than 3 times its width."
Let's break it down step by step:
The width of the rectangle is n feet.Three times the width is 3n.Two feet more than 3 times the width is 3n + 2.
The formula for the area of a rectangle is length multiplied by width. So, in terms of n, the area of the rectangle would be:
Area = Length × Width
= (3n + 2) × n
= 3n^2 + 2n
Therefore, the area of the rectangle, in terms of n, is 3n^2 + 2n.
What is the equation of a circle, if the end points of its
longest chord are (4, -3) and (-2,5)?
Answer:
The answer is D, the last one.
Help me pls….. I’m confused on this!!!!!
A truck is being filled with cube-shaped packages that have side lengths of foot, the volume of the part of the truck that is being filled is 34,808 cubic feet.
To discover the finest range of applications that may in shape in the truck, we want to calculate the volume of the truck and divide it by using the quantity of every cube-formed bundle.
The quantity of the truck is given with the aid of the method:
Volume = Length x Width x Height
Volume = 8 ft x 61 ft x 71 ft
Volume = 34,808 cubic toes
The volume of every cube-shaped bundle is given with the aid of the method:
Volume = Side [tex]Length^3[/tex]
Volume = 1 [tex]ft^3[/tex]
Number of packages = Volume of truck / Volume of each package
Number of packages = 34,808 ft^3 / 1 ft^3
Number of packages = 34,808
Thus, the greatest number of packages that can fit in the truck is 34,808.
Volume of the part of the truck being filled = Number of packages x Volume of each package
Volume of the part of the truck being filled = 34,808 x 1 ft^3
Volume of the part of the truck being filled = 34,808 ft^3
Thus, the volume of the part of the truck that is being filled is 34,808 cubic feet.
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line p is parallel to line q and both these lines are intersected by transversal t show workkkkkk
The value of x is equal to 10 degrees.
What is the Alternate Interior Angles Theorem?In Mathematics and Geometry, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent:
By applying the alternate interior angles theorem to parallel lines p and q, we have the following congruent angles:
(5x - 65) = (x - 25)
5x - x = 65 - 25
4x = 40
x = 40/4
x = 10 degrees.
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Johnson Industries purchased a metal-working lathe for $38,000. This item will be used for business 90% of the time. Accountants elected to take a $18,000 section 179 deduction and utilize the special depreciation allowance of 50%.
Prepare a depreciation schedule (in $) using MACRS.
Round all dollar amounts to the nearest cent.
The depreciation schedule (in dollars) using MACRS for the metal-working lathe is as follows:
Year 1: $1,429.00
Year 2: $2,449.00
Year 3: $1,749.00
Year 4: $1,249.00
Year 5: $893.00
Year 6: $892.00
Year 7: $893.00
What is the MACRS depreciation schedule?The depreciation schedule using the Modified Accelerated Cost Recovery System (MACRS) is prepared as follows:
Given data:
Purchase cost of the metal-working lathe: $38,000
Business use percentage: 90%
Section 179 deduction: $18,000
Special depreciation allowance: 50%
Depreciable basis = Purchase cost - Section 179 deduction
Depreciable basis = $38,000 - $18,000 = $20,000
Special depreciation allowance = $20,000 * 50%
Special depreciation allowance = $10,000
Adjusted depreciable basis = $20,000 - $10,000
Adjusted depreciable basis = $10,000
The recovery period for a metal-working lathe is 7 years.
Using MACRS, the depreciation rates for a 7-year recovery period are as follows:
Year 1: 14.29%
Year 2: 24.49%
Year 3: 17.49%
Year 4: 12.49%
Year 5: 8.93%
Year 6: 8.92%
Year 7: 8.93%
Annual depreciation expense = Adjusted depreciable basis * Depreciation rateYear 1:
Depreciation expense = $10,000 * 14.29% = $1,429.00
Year 2:
Depreciation expense = $10,000 * 24.49% = $2,449.00
Year 3:
Depreciation expense = $10,000 * 17.49% = $1,749.00
Year 4:
Depreciation expense = $10,000 * 12.49% = $1,249.00
Year 5:
Depreciation expense = $10,000 * 8.93% = $893.00
Year 6:
Depreciation expense = $10,000 * 8.92% = $892.00
Year 7:
Depreciation expense = $10,000 * 8.93% = $893.00
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Solve 5(2x – 3) = x – 15 + 9x for x. Question 7 options: A) Infinitely many solutions B) –18∕5 C) 0 D) –12∕5
Step-by-step explanation:
5(2x – 3) = x – 15 + 9x
10x - 15 = x - 15 + 9x
10x - 9x - x = -15 + 15
0 = 0
Answer = A) Infinity many solutions
1. A research poll was conducted to investigate opinions about global warming. The respondents (1 point)
who answered yes when asked if there is solid evidence that the Earth is getting warmer were
then asked to select a cause of global warming. The results were arranged between male and
female responses. Using a 0.05 significance level, a test statistic of 0.792 and a critical value of
5.991 are found. Test the claim that the gender of the respondent is independent of the choice
for the cause of global warming. State the initial and final conclusion
OReject the null hypothesis; there is not sufficient evidence to warrant rejection of the claim that the
gender of the respondent is independent of the choice for the cause of global warming.
OReject the null hypothesis; there is sufficient evidence to warrant rejection of the claim that the gender
of the respondent is independent of the choice for the cause of global warming.
Fail to reject the null hypothesis; there is not sufficient evidence to warrant rejection of the claim that
the gender of the respondent is independent of the choice for the cause of global warming.
OFail to reject the null hypothesis; there is sufficient evidence to warrant rejection of the claim that the
gender of the respondent is independent of the choice for the cause of global warming.
The initial and final conclusion would be Fail to reject the null hypothesis; there is not sufficient evidence to warrant rejection of the claim that the gender of the respondent is independent of the choice for the cause of global warming. Option C
Why does it fail to reject the null hypothesis?The initial hypothesis is that the gender of the respondent is independent of the choice for the cause of global warming.
The alternative hypothesis is that the gender of the respondent is dependent on the choice for the cause of global warming.
The test statistic of 0.792 is less than the critical value of 5.991. Therefore, we do not reject the null hypothesis.
Looking at the statistic that has been provided, we do not have enough evidence to conclude that the gender of the respondent is related to the choice of the cause of global warming at the 0.05 significance level.
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All of the pairs of corresponding angles and sides in ΔCAT and ΔDOG are congruent. Based on this information, which of the following is a true statement?
A true statement based on the given information is that ΔCAT and ΔDOG are similar triangles, meaning their corresponding angles are congruent and their corresponding sides are in proportion.
If all pairs of corresponding angles and sides in triangles ΔCAT and ΔDOG are congruent, it implies that the two triangles are similar. In similar triangles, the corresponding angles are congruent, and the corresponding sides are in proportion.
Based on this information, the following true statement can be made:
The ratio of the lengths of the corresponding sides in ΔCAT and ΔDOG is equal.
For example, if the corresponding sides are CA and DO, the ratio CA/DO will be equal to the ratio of the lengths of the other corresponding sides.
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Pls help me with this asap
Container #1 is the only one large enough to hold the contents of a one liter bottle of soft drink.
Container #1: The volume formula for a cylinder is V = πr²h, where r is the radius and h is the height.
Radius (r) = 8 cm / 2 = 4 cm
Height (h) = 19 cm
So, V1 = π(4 cm)²(19 cm)
≈ 3032.07 cm³
Container #2:
Radius (r) = 5 cm
Height (h) = 12 cm
Using the formula:
V2 = π(5 cm)²(12 cm)
≈ 942.48 cm³
Container #3:
Diameter (d) = 12 cm
Radius (r) = 12 cm / 2 = 6 cm
Height (h) = 10 cm
V3 = π(6 cm)²(10 cm)
≈ 1130.97 cm³
Now, Comparing the volumes:
V1 ≈ 3032 cm³
V2 ≈ 942 cm³
V3 ≈ 1131 cm³
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what is greatest common factor of -x^2+6x-19
The greatest common factor of -x^2 + 6x - 19 is 1.
To find the greatest common factor (GCF) of the polynomial [tex]-x^2 + 6x - 19,[/tex] we need to factorize the polynomial and identify the common factors among its terms.
First, let's examine the polynomial and see if we can factor it further:
[tex]-x^2 + 6x - 19[/tex]
The polynomial does not appear to have any common factors among its terms.
It cannot be factored using simple integer factors.
In this case, we can say that the GCF of the given polynomial is 1.
It is important to note that the GCF represents the highest degree of common factors that can be factored out from all terms of a polynomial. In this particular case, the polynomial does not possess any common factors that can be factored out.
It's worth mentioning that this polynomial is already in its simplest form and cannot be factored further.
However, if the polynomial had common factors that could be factored out, such as common binomial factors or other mathematical patterns, the GCF would differ from 1.
But in this case, the polynomial does not exhibit any common factors beyond 1.
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Please actually help me I really need it
Area of shape 1:
Area of triangle = 1/2 × b × h
Area of triangle = 1/2 × 6 × 8
Area of triangle = 24 cm²
Area of shape 2:
Area of Semicircle = πr²/2
Radius of Semicircle = Diameter / 2
Radius of Semicircle = 3 cm
Then,
Area of semicircle = π(3)²
Area of semicircle = 9π cm²
Total Area = Area of semicircle + Area of triangle
Total Area = (24 + 9π) cm²
Total Area = 52.27 cm² .
Hence Total area of the figure combining triangle and semicircle is 52.27 cm².
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A rectangular prism measures 3 ft by 6 ft by 5 ft. If the dimensions of the box were all quadrupled, how would the surface area of the box change?
1.The new surface area would be 16 times the original surface area.
2.The new surface area would be quadruple the original surface area.
3.The surface area would not change.
4.The new surface area would be 12 times the original surface area.
To determine how the surface area of a rectangular prism changes when all dimensions are quadrupled, we need to compare the original surface area to the new surface area.
The original surface area of the rectangular prism is given by:
SA_original = 2lw + 2lh + 2wh
where l, w, and h represent the length, width, and height of the prism, respectively.
In this case, the dimensions of the original box are:
Length (l) = 3 ft
Width (w) = 6 ft
Height (h) = 5 ft
Substituting these values into the formula, we have:
SA_original = 2(3)(6) + 2(3)(5) + 2(6)(5)
= 36 + 30 + 60
= 126 square feet
Now, if we quadruple all the dimensions of the box, the new dimensions would be:
Length (l_new) = 4(3) = 12 ft
Width (w_new) = 4(6) = 24 ft
Height (h_new) = 4(5) = 20 ft
The new surface area of the enlarged box is given by:
SA_new = 2(l_new)(w_new) + 2(l_new)(h_new) + 2(w_new)(h_new)
= 2(12)(24) + 2(12)(20) + 2(24)(20)
= 576 + 480 + 960
= 2016 square feet
Comparing the original surface area (SA_original = 126 sq ft) to the new surface area (SA_new = 2016 sq ft), we can see that SA_new is 16 times greater than SA_original.
Therefore, the correct answer is:
1. The new surface area would be 16 times the original surface area.
Which statement correctly explains the association of the scatter plot? Since the Y values increase as the X values increase the Scatter plot shows a positive association. Sense to Weibo use decrease as the X values increase the scatter plot shows a positive association.
The statement "Since the y-values decrease as the x-values increase, the scatter plot shows a negative association" correctly explains the association of the scatter plot.
From the plot, we see that:
Any time the Y value decreases, it will be a negative valueAny time the X value decreases, it will be a negative valueA scatter pIot is a type of graph that shows the reIationship between two variables. The variabIes are plotted on the x-axis and y-axis, and each data point is represented by a dot. The pattern of the dots can be used to infer the reIationship between the variables.
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A dinner theater has fixed costs of $1,000 per day. It costs the dinner theater $10 per person for food and a
ticket to the dinner theater costs $30. How many tickets does the dinner theater have to sell in order to break
even?
50 tickets
O 10 tickets
O 100 tickets
O20 tickets
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer: is X = 5 within the diagram.
I need help bro how do you find the median, perp bisector, altitude, and angle bisector of a triangle? I need to know this for my final
You can determine the median of a triangle by looking out for the point that is 2/3 of the distance tht connects from the vertices, to midpoint and oposite sides.
The perpendicular bisector is determined by measuring the point that is equidistant from the segment.
How to find the altitude and angle bisectorThe altitude of a triangle can be found by measiring the height of the triangle's extension that could be inside or outside the triangle. In obtsue triangles, this altitude is commonly found outside the triangle.
Also, the angle bisector of a triangle is the point that is equidistant from the angles sides. These descriptions can help in analyzing a trinagle.
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This number pattern -1:5 ;x; 35 ; ...
Is a quadratic number pattern.
a) Calculate x
b) Hence, or otherwise, determine the nth term of the sequence.
This sequence 4;9; x; 37; .... is a quadratic sequence.
a) Calculate x
b) Hence, or otherwise, determine the nth term of the sequence.
Answer:
[tex]\textsf{a)} \quad x = 17[/tex]
[tex]\textsf{b)} \quad T_n=3n^2-3n-1[/tex]
[tex]\textsf{a)} \quad x = 20[/tex]
[tex]\textsf{b)} \quad T_n=3n^2-4n+5[/tex]
Step-by-step explanation:
Given quadratic number pattern:
-1, 5, x, 35, ...To find the equation for the nth term, we can use the general form of a quadratic equation:
[tex]\boxed{T_n=an^2 + bn + c}[/tex]
where n is the position of the term.
Let's substitute the values of T₁, T₂ and T₄ into the quadratic equation: to create three equations:
[tex]\begin{aligned}T_1=a(1)^2+b(1)+c&=-1\\a+b+c&=-1\end{aligned}[/tex]
[tex]\begin{aligned}T_2=a(2)^2+b(2)+c&=5\\4a+2b+c&=5\end{aligned}[/tex]
[tex]\begin{aligned}T_4=a(4)^2+b(4)+c&=35\\16a+4b+c&=35\end{aligned}[/tex]
Rearrange the first equation to isolate c:
[tex]c=-a-b-1[/tex]
Substitute this into the second and third equations:
[tex]\begin{aligned}4a+2b+(-a-b-1)&=5\\3a+b&=6\end{ailgned}[/tex]
[tex]\begin{aligned}16a+4b+(-a-b-1)&=35\\15a+3b&=36\end{ailgned}[/tex]
Solve the equations simultaneously by rearranged the first equation to isolate b and substituting this into the second equation and solving for a:
[tex]b=-3a+6[/tex]
[tex]\begin{aligned}15a+3(-3a+6)&=36 \\15a-9a+18&=36\\6a&=18\\a&=3 \end{aligned}[/tex]
Substitute the found value of a into the equation for b and solve for b:
[tex]\begin{aligned}b&=-3a+6\\&=-3(3)+6\\&=-9+6\\&=-3\end{aligned}[/tex]
Finally, substitute the found values of a and b into the equation for c and solve for c:
[tex]\begin{aligned}c&=-a-b-1\\&=-3-(-3)-1\\&=-3+3-1\\&=-1\end{aligned}[/tex]
Therefore, the equation for the nth term is:
[tex]\boxed{T_n=3n^2-3n-1}[/tex]
The value of x is the 3rd term. Therefore, to find the value of x, substitute n = 3 into the equation for the nth term:
[tex]\begin{aligned}T_3&=3(3)^2-3(3)-1\\&=3(9)-3(3)-1\\&=27-9-1\\&=18-1\\&=17\end{aligned}[/tex]
Therefore, the value of x is 17.
[tex]\hrulefill[/tex]
Given quadratic number pattern:
4, 9, x, 37, ...To find the equation for the nth term, we can use the general form of a quadratic equation:
[tex]\boxed{T_n=an^2 + bn + c}[/tex]
where n is the position of the term.
Let's substitute the values of T₁, T₂ and T₄ into the quadratic equation: to create three equations:
[tex]\begin{aligned}T_1=a(1)^2+b(1)+c&=4\\a+b+c&=4\end{aligned}[/tex]
[tex]\begin{aligned}T_2=a(2)^2+b(2)+c&=9\\4a+2b+c&=9\end{aligned}[/tex]
[tex]\begin{aligned}T_4=a(4)^2+b(4)+c&=37\\16a+4b+c&=37\end{aligned}[/tex]
Rearrange the first equation to isolate c:
[tex]c=-a-b+4[/tex]
Substitute this into the second and third equations:
[tex]\begin{aligned}4a+2b+(-a-b+4)&=9\\3a+b&=5\end{ailgned}[/tex]
[tex]\begin{aligned}16a+4b+(-a-b+4)&=37\\15a+3b&=33\end{ailgned}[/tex]
Solve the equations simultaneously by rearranged the first equation to isolate b and substituting this into the second equation and solving for a:
[tex]b=-3a+5[/tex]
[tex]\begin{aligned}15a+3(-3a+5)&=33 \\15a-9a+15&=33\\6a&=18\\a&=3 \end{aligned}[/tex]
Substitute the found value of a into the equation for b and solve for b:
[tex]\begin{aligned}b&=-3a+5\\&=-3(3)+5\\&=-9+5\\&=-4\end{aligned}[/tex]
Finally, substitute the found values of a and b into the equation for c and solve for c:
[tex]\begin{aligned}c&=-a-b+4\\&=-3-(-4)+4\\&=-3+4+4\\&=5\end{aligned}[/tex]
Therefore, the equation for the nth term is:
[tex]\boxed{T_n=3n^2-4n+5}[/tex]
The value of x is the 3rd term. Therefore, to find the value of x, substitute n = 3 into the equation for the nth term:
[tex]\begin{aligned}T_3&=3(3)^2-4(3)+5\\&=3(9)-4(3)+5\\&=27-12+5\\&=15+5\\&=20\end{aligned}[/tex]
Therefore, the value of x is 20.
100 Points! Geometry question. Photo attached. Find x and y. Please show as much work as possible. Thank you!
The values of given x and y is,
x = 6 and y = 13/2
Since we know that,
Basic proportionality theorem,
The basic proportionality theory was developed by Thales, a great Greek mathematician; hence, it is also known as the Thales theorem. According to the great mathematician, the ratio of any two matching sides of any two equiangular triangles is always the same. The basic proportionality theorem (BPT) was suggested based on this premise.
Since we know that,
In the figure we that,
⇒ 2x + 1 = x +7
⇒ x = 6
Similarly
⇒ 3y - 8 = y +5
⇒ y = 13/2
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2. The table includes results from polygraph experiments. In each case, it was known if the
subject lied or did not lie, so the table indicates when the polygraph test was correct. Find the
test statistic needed to test the claim that whether a subject lies or does not lie is independent of
the polygraph test indication.
Polygraph test indicated
that the subject lied.
Polygraph test indicated
that the subject did not lie.
025.571
Did the Subject Actually Lie?
No (did not lie) Yes (lied)
15
32
42
9
(1 poir
We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.
How to explain the hypothesisThe test statistic needed to test the claim that whether a subject lies or does not lie is independent of the polygraph test indication is the chi-square statistic.
In this case, the grand total is 90. The row totals are 57 and 33, and the column totals are 42 and 48. The expected frequencies are as follows:
The chi-square statistic is calculated as 0.177. The p-value for the chi-square statistic is calculated using a chi-square table. The degrees of freedom for the chi-square table are the number of rows minus 1, multiplied by the number of columns minus 1.
Since the p-value is greater than 0.05, we fail to reject the null hypothesis. We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.
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which quadratic equation has the roots 3 + i and 3 - i
The quadratic equation that has the roots 3 + i and 3 - i is x² - 6x + 10 = 0.
The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.
The roots of the quadratic equation are the values of x that make the equation equal to zero.
Therefore, if a quadratic equation has the roots 3 + i and 3 - i, it can be written in the factored form as (x - (3 + i))(x - (3 - i)) = 0. Expanding this product yields x² - (3 + i + 3 - i)x + (3 + i)(3 - i) = 0.
Simplifying this expression further results in the quadratic equation x² - 6x + 10 = 0.
The quadratic equation that has the roots 3 + i and 3 - i is x² - 6x + 10 = 0.
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which expression is equivalent to the expression below? -2(5+7x) + 5(x+5) A. 15+9x B. 15 -9x C.35+40x D .35-40x
The expression -2(5 + 7x) + 5(x + 5) is equivalent to the expression -9x + 15. So, the answer is option B: 15 - 9x.
To simplify the expression -2(5 + 7x) + 5(x + 5), we can distribute the coefficients and simplify further.
Starting with the expression -2(5 + 7x):
-2(5 + 7x) = -2 × 5 - 2 × 7x
= -10 - 14x
= -14x - 10
Now let's simplify the expression 5(x + 5):
5(x + 5) = 5 × x + 5× 5
= 5x + 25
Finally, combining the two simplified expressions:
-14x - 10 + 5x + 25
Combining like terms:
(-14x + 5x) + (-10 + 25)
-9x + 15
Therefore, the expression -2(5 + 7x) + 5(x + 5) is equivalent to the expression -9x + 15.
So, the answer is option B: 15 - 9x.
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I need help solving these problems please.
Answer: i dont know what this is but i do believe its the second one
Step-by-step explanation:
A ballroom dance couple has learned 8 different routines and is going to perform 6 of them at a local competition. How many different ways could they arrange their performance?
The ballroom dance couple can arrange their performance in 28 different ways by selecting 6 routines out of the 8 they have learned.
To solve this problem
The idea of combinations can be used.
The number of ways to select k items from a set of n items is given by the formula for combinations:
C(n, k) = n! / (k! * (n - k)!)
In this case, n = 8 (the total number of routines they have learned) and k = 6 (the number of routines they will perform).
Using the formula, we can calculate:
C(8, 6) = 8! / (6! * (8 - 6)!)
= 8! / (6! * 2!)
The factorial function is represented in this case by the exclamation symbol (!).
The sum of all positive integers from 1 to n is the factorial of the number n.
Calculating the factorials involved:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
2! = 2 * 1 = 2
Plugging in these values:
C(8, 6) = 40,320 / (720 * 2)
= 40,320 / 1,440
= 28
Therefore, the ballroom dance couple can arrange their performance in 28 different ways by selecting 6 routines out of the 8 they have learned.
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Plant cells and animal cells were observed under a microscope. The characteristics of two cells are listed below.
Cell X: Has chloroplast
Cell Y: Does not have a cell wall
Which statement about the two cells is correct?
Cell X has a cell membrane.
Cell X has a small vacuole.
Cell Y has a large vacuole.
Cell Y has chloroplast.
PLEASE HELP!!!
The correct statement about the two cells is:Cell Y has a large vacuole.
Cell X is described as having chloroplast, which is an organelle found in plant cells and is responsible for photosynthesis. This indicates that Cell X is a plant cell. Since the presence of chloroplast is mentioned specifically for Cell X and not for Cell Y, it implies that Cell Y is an animal cell, as animal cells do not contain chloroplasts.
Cell X having a cell membrane is not stated explicitly, and it is a characteristic shared by both plant and animal cells. Therefore, we cannot conclude whether Cell X has a cell membrane or not based on the given information.
The statement Cell X has a small vacuole is not mentioned in the provided characteristics, so we cannot determine the size of the vacuole in Cell X.
On the other hand, Cell Y not having a cell wall is mentioned, which is a characteristic specific to animal cells.Cell Y does not have a cell wall.
The correct statement based on the given information is that Cell Y has a large vacuole, while the other statements cannot be determined from the provided characteristics.
The correct statement about the two cells is: Cell Y has a large vacuole.
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