Evaluate the expression given the replacement values.

8x−2y for x=4 and y=−7.
10xy

Answer:

a. lines intersecting at a single point

b. one solution

Step-by-step explanation:

a. The equations can be rewritten as:

y = -5x+23 and y = -1/6x+1

Comparing the equations with standard equation: y=mx+c, where m is the gradient of the line formed by the linear equation.

Since the gradient of the lines are different then the lines cannot be parallel and will intersent at one point.

b. The equation will have one solution as below.

The equations can be rewritten as:

5x+y=23

5x+30y=30

Subtracting both equation will result in,

29y=7

=> y=7/29

Hence x= 660/29

As per the given confidence interval, the population mean remodeling costs for the two types of projects is -1.6

Confidence interval

The  range of values that's likely to include a population value with a certain degree of confidence is known as confidence interval.

Given,

A certain association provided data on the cost of the most popular home remodeling projects.

Here we need to find the the population mean remodeling costs for the two types of projects.

Here we will find the point estimate of the difference between the population mean remodeling costs for the two types of projects using an equation,

=> X1​ − X2​

In order to calculate the sample mean we will use equation,

=> X = ∑x/n

Now, we have to substitute values we get,

=> X1 ​= 21.2

=> X2 ​= 22.8

Here X1 refers the sample mean remodeling costs for the kitchen and X2​refers the sample mean remodeling cost for the master bedroom.

Therefore, the point estimate of the difference between the population mean remodeling costs for the two types of projects are,

=> X1 ​− X2​ ​= −1.6

Therefore, we estimate that the remodeling master bedroom has the mean costs of 1.6 greater than mean remodeling costs for the kitchen.

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Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

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Answer:

1) 1,-4

2)-3.5,-5

3) 2.5,-1

4)0,1

5)-2,-3.5

6)4,2

7)-0.5,0

8)-1.5,.05

Step-by-step explanation:

hopes this helps

The angles are formed by a transversal and two parallel lines in the figure. By applying congruent angles and vertical opposite angle property, ∠1 ≅∠3 ≅ ∠5 ≅ ∠7; ∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8. Therefore option B is correct.

Congruent angles are identical to each other and have the same measure. The angles formed by the transversal in corresponding corners are called corresponding angles and they are congruent.

Therefore, ∠1 ≅ ∠5, ∠3 ≅ ∠7----------(1)

At a vertex if two angles are opposite to each other, then they are vertically opposite angles, they are equal and congruent to each other.

Therefore, ∠1 ≅ ∠3, ∠5 ≅ ∠7----------(2)

Combining (1) and (2), we get:

∠1 ≅∠3 ≅ ∠5 ≅ ∠7
Similarly we can find,

∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8.

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Answer:

5.7... I belive

Step-by-step explanation:

hope this helps :3

if it did pls mark brainliest

Were you not given a diagram?

Answer:

1/6

Step-by-step explanation:

1 x 1/6 = 1/6

Any number multiplied with one is that number itself.

1/6

Step-by-step explanation: Anything multiplied by 1 equals itself, therefore, the answer is 1/6. Hope this helps, and please give me Brainliest! :)

Step-by-step explanation:

The problem asks to calculate the integral by using area of geometric shapes, but it is possible to integrate using trig substitution.

∫₀³ √(9 − x²) dx

If x = 3 sin u, then dx = 3 cos u du.

When x = 0, u = 0.  When x = 3, u = π/2.

∫₀ᵖⁱ`² √(9 − 9 sin²u) (3 cos u du)

∫₀ᵖⁱ`² 3 √(1 − sin²u) (3 cos u du)

∫₀ᵖⁱ`² 3 cos u (3 cos u du)

∫₀ᵖⁱ`² 9 cos²u du

Use power reduction formula.

9/2 ∫₀ᵖⁱ`² (cos(2u) + 1) du

9/2 ∫₀ᵖⁱ`² cos(2u) du + 9/2 ∫₀ᵖⁱ`² du

9/4 ∫₀ᵖⁱ`² 2 cos(2u) du + 9/2 ∫₀ᵖⁱ`² du

[ 9/4 sin(2u) + 9/2 u ] |₀ᵖⁱ`²

[ 9/4 sin(π) + 9/2 (π/2) ] − [ 9/4 sin(0) + 9/2 (0) ]

9π/4

Using geometry instead, the function is the top half of a circle centered at the origin with a radius of 3.  The limits are 0 ≤ x ≤ 3, so we're looking at the first quadrant only.  So the area is:

A = πr² / 4

A = π (3)² / 4

A = 9π/4

Answer:

9π/4

Step-by-step explanation:

Consider this approach.

We have a circle, rather a semicircle, covering quadrants I and II. This is as it is simply the 'upper part of the circle.' Now then we have our limits from 0 to 3, and therefore our radius will be 3, as the difference between 0 and 3 on the coordinate is 3. Well then the shaded region for consideration here would be the area under the curve of the circle in the first quadrant, as remember our limits are from 0 to 3 (positive).

What would be the area of this shaded region? Consider the area formula πr^2. If radius = 3, area = π(3)^2 = 9π. The shaded region is only 1/4ths of the whole circle, so the area would be 9π/4. Done!

Check:

y = √9 - x^2,

y^2 = 9 - x^2,

x^2 + y^2 = 0,

x^2 + y^2 = 3^2

As you can see this is a circle equation, where radius = 3, centered at (0,0). Respectively √9 - x^2 is our upper semicircle.

Answer:

Step-by-step explanation:

We can use the formula for a confidence interval for the population mean:

CI = x¯¯¯ ± z*(σ/sqrt(n))

where:

x¯¯¯ is the sample mean, which is 81.

σ is the population standard deviation, which is 11.8 (assuming the sample is drawn from a normally distributed population).

n is the sample size, which is 175.

z is the z-score corresponding to the desired level of confidence, which is 2.33 for a 98% confidence level.

Substituting the known values, we get:

CI = 81 ± 2.33*(11.8/sqrt(175))

Calculating this expression, we get:

CI ≈ (79, 83)

Therefore, a 98% confidence interval for the population mean is approximately (79, 83).

Therefore, the answer is (B) (79, 83).

The probability that the newspaper Mario buys has reviewed both performances, given that he buys the first newspaper, is 0.72 or 72%.

a) Let's assume the probability of the first newspaper reviewing his performance is 2/7 and the probability of the second newspaper reviewing his performance is 5/7. The probability of both papers reviewing his performance is (2/7) * (5/7) = 10/49.

b)Since Clarissa buys both newspapers, there are two scenarios: either the first newspaper reviews her performance and the second one doesn't, or the second newspaper reviews her performance and the first one doesn't. The probability of only one paper reviewing her performance is 2 * (3/7) * (4/7) = 24/49.

c) If Mario buys one newspaper at random, there is a 2/7 chance that he buys the first newspaper and a 5/7 chance that he buys the second newspaper. Since each newspaper has reviewed one performance, the probability that the newspaper he buys has reviewed both performances is (2/7) * (5/7) = 10/49.

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Based on the information provided, the total length of the worms would be 6 1/2 inches.

The graph presented shows the length of the worms Abe measured, based on the graph we know that the shortest worm was 2.125 inches, while the longest worm was 2.875 inches. Using this information, let's now add the three shortest worms together:

2.125  inches + 2.125  inches + 2.25 inches = 6.5 inches in total, which can be expressed ad 6 1/2.

Based on this, the total length of the three shortest worms would be 6 1/2.

Note: This question is incomplete; here is the complete question:

Abe measured the lengths of several worms. He made this line plot to display his measurements. Abe laid the three shortest worms together end to end. What is the total length of these three worms?

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The length of the radius of the circle is √61.

Here there are two endpoints of the circle (-7,-4) and (3,8)

To find the distance between the two points we have a formula:

Distance = \(\sqrt{(x_{2} -x_{1} ^{2} + (y_{2} - y_{1})^{2} }\)

So here we have

(\(x_{1} , y_{1}\)) = (-7, -4)

(\(x_{2} , y_{2}\)) = ( 3,8)

Putting the value we have,

=\(\sqrt{(3-(-4))^{2} + (8-(-7))^{2} }\)

=\(\sqrt{10^{2} + 12^{2} }\)

=√244

=2√61

The diameter is 2√61

radius = diameter/2

            = 2√61/2

            = √61

Therefore the length of the radius of a circle is √61.

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Answer:

(−∞,∞)

Step-by-step explanation:

Since |x−5| is always positive and −2 is negative, |x−5| is always greater than −2, so the inequality is always true.

All real numbers

So, the answer is (−∞,∞)

Answer:

A or 53 squared

Step-by-step explanation:

Answer:

d is great than -3

Step-by-step explanation:

because negative numbers are less than whole numbers

The dot product of vectors a and b is option D. 30.

To find the dot product of two vectors, you need to multiply their corresponding components and then sum the results.

Let's calculate the dot product of vectors a = <5, 2> and b = <4, 5>:

a • b = (5 x 4) + (2 x 5)

= 20 + 10

= 30

Therefore, the dot product of vectors a and b is 30.

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Answer:

22/100 which reduces to 11/50

Step-by-step explanation:

78/100 correct

100/100 - 78/100 = 22/100 or 11/50

1) {(-1,8),(0, 15),(1,-4), (2, 0)}

It is a function as there is not any pair of points which have the x-coordinate and different y-coordinates.

2. {(-5,2), (5,2), (0, -3), (3,-8); 3) (-2, 7), (6,2), (-2,-3), (0, 9)}

It is not a function as there is a pair of

Answer:

-------------------------------

As per given drawing PQ is the segment bisector of XY.

The point W is the midpoint of XY. As per property of midpoint, XW and WY have equal length.

XW = 13 units, hence:

We need to know about writing equations given conditions to solve this problem. The equation for C1 is C1=0.27t and for C2 is C2=34.95+0.12t , the number of talk minutes that would produce the same cost for both plans is 233.

For writing equations for a variable given certain conditions we need to first assume the unknown variable to be x or something. Here in this question we know that the phone plans charge a particular cost for every minute, we have to assume the number of talk minutes to be t, so the total cost for the talk minutes can be calculated by multiplying the number of minutes to the cost per minute, if there is any additional constant charge then we add the cost to the equation which will give us the final cost equation.

For C1, it charges 27 cents for a minute, so the equation for C1 is

C1=0.27t [1 cent =$0.01]

For C2, it charges $34.95 monthly fee which is constant and 12 cents per minute.

C2=34.95+0.12t

To find the number of talk minutes that produce same cost we have to equate the two equations

0.27t=34.95+0.12t

0.15t=34.95

t=233

Therefore the equation for C1 is C1=0.27t and for C2=34.95+0.12t and the number of talk minutes that produce the same cost is 233.

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Answer: A triangle that only has two congruent sides is called an isosceles triangle. Two equal sides and two equal angles.

Answer:

d) 1/12

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

The experimental probability was 7/20 since she got a 6 7 out of 20 times

Multiply by the number of rolls

7/20 * 100

7* 100/20

7 *5

35

She should get a 6 around 35 times

A vector (u) with magnitude 4 in the opposite direction as v =⟨−2,3⟩ is u = ⟨-2/√13, 3/√13⟩.

A vector in the opposite direction of a given vector can be found by multiplying that vector by -1. The magnitude of a vector is the length of the vector and it can be found by using the Pythagorean theorem on the coordinates of the vector.

The magnitude of the vector v = ⟨-2,3⟩ is:

|v| = √(-2)^2 + 3^2 = √4 + 9 = √13

To find a vector with magnitude 4 in the opposite direction as v, we can first normalize the vector v by dividing it by its magnitude,

then multiply it by 4:

u = (-1) * (1/|v|) * v

= (-1) * (1/√13) * ⟨-2,3⟩

= ⟨2/√13, -3/√13⟩

So, a vector (u) with magnitude 4 in the opposite direction as v =⟨−2,3⟩ is u = ⟨2/√13, -3/√13⟩

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Answer:

Yes

Step-by-step explanation:

Calculate the missing angles in both triangles.

The sum of interior angles in a triangle add to 180.

E = 180 - 110 - 28 = 42

T = 180 - 28 - 42 = 110

They have all the same angles so are similar.

The calculated area of the composite figure is 85 cm².

From the question, we have the following parameters that can be used in our computation:

The composite figure (see attachment)

Where, we have

Rectangle:

Area = length × width.

Therefore, the area of the rectangle is 10 cm × 6 cm = 60 cm².

Triangle:

Area = (1/2) × base × height.

Therefore, the area of the triangle is (1/2) × 5 cm × 10 cm = 25 cm².

To find the total area of the composite figure, we add the areas of the rectangle and the triangle:

Total Area = Area of Rectangle + Area of Triangle

= 60 cm² + 25 cm²

= 85 cm².

Therefore, the area of the composite figure is 85 cm².

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Answer:

Step-by-step explanation:

Hopefully this is right.

Area = r²

Which is pi times the the radius squared

The radius is 2, so 2² is 4, So we multiply 3.14, which is pi, by 4.

Multiply 3.14 by 4, and the answer is 12.56, the question says round to the nearest tenth, so the final answer will be 12.6

My math teacher back in 7th grade gave us this sentence to help us memorize the equations.

Cherry Pie Delicious (C=d), Apple Pie Are Too (A=r²)

Do the same with the other two questions, and the answer for question two will be 3.14, rounded to the nearest tenth will be 3.1

Hope this helps!

For a circle with a radius of 2, the area can be calculated using the formula:

Area = π x r^2

where π is approximately 3.14 and r is the radius.

Plugging in the values, we get:

Area = 3.14 x 2^2

Area = 3.14 x 4

Area = 12.56

Rounding to the nearest tenth, we get:

Area ≈ 12.6

Therefore, the area of the circle with radius 2 is approximately 12.6.

For a circle with a radius of 1, the area can be calculated using the same formula:

Area = π x r^2

Plugging in the values, we get:

Area = 3.14 x 1^2

Area = 3.14

Rounding to the nearest tenth, we get:

Area ≈ 3.1

Therefore, the area of the circle with radius 1 is approximately 3.1.