Write an equation of the line passing through the point (4, –3) that is perpendicular to the line y−3=−9 (x+4).

Answer:

y = 90°

Step-by-step explanation:

The left side base angle of the triangle and the angle of 110° form a straight angle and are supplementary, thus

base angle = 180° - 110° = 70°

The right base angle is also 70° , thus the triangle is isosceles

The line segment from the vertex is a perpendicular bisector, hence

y = 90°

Answer:

Step-by-step explanation:

The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve the equation, ax2 + bx + c = 0.

Answer:

We need to simplify the following expressio:

[tex]\frac{1}{2} x^{2}- 4x-\frac{2}{x}[/tex]

Multiply the whole expression by '2x':

[tex]x^{3}-8x^{2}-4[/tex]

The expression can't be more simplified.

Answer:

The value that best approximates the correlation coefficient is r=0.50

Step-by-step explanation:

we know that

The correlation coefficient r measures the strength and direction of a linear relationship between two variables. Are expressed as values between +1 and -1

Using a Excel tool (Correl function)

see the attached table

the correlation coefficient  is r=0.45

so

The value that best approximates the correlation coefficient is r=0.50

Answer:

91 campers can swim

Step-by-step explanation:

step 1

Find the number of campers

we know that

The ratio of counselors to campers at a camp is 1 : 9

so

by proportion

Find the number of campers if there are 13 counselors

Let

x-----> the number of campers

1/9=13/x

x=9*13=117 campers

step 2

How many campers can swim?

we know that

The ratio of campers who can swim to campers who cannot swim is 7 : 2

so

The ratio of total campers  to campers who can swim is 9 : 7

by proportion

Find how many campers can swim for a total of 117 campers

Let

x----> the number of campers that can swim

9/7=117/x

x=117*7/9

x=91 campers can swim

ANSWER

[tex]p + q= 7[/tex]

EXPLANATION

We determine the slope of each line using the slope formula;

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

The slope of BC is

[tex] = \frac{ q - 1}{9 - 6} [/tex]

[tex] \frac{ q - 1}{3} [/tex]

The slope of AB is

[tex] = \frac{1 - 4}{6 - p} [/tex]

[tex] = - \frac{3}{6 - p} [/tex]

The two lines are perpendicular so the product of their slopes is -1.

[tex] - \frac{3}{6 - p} \times \frac{ q - 1}{3} = - 1[/tex]

This implies that,

[tex]\frac{q - 1}{6 - p} = 1[/tex]

[tex]q - 1=6 - p[/tex]

[tex]q + p = 6 + 1[/tex]

[tex]p + q= 7[/tex]

.

Answer:

x > 3

Step-by-step explanation:

Given

2(4 + 2x) < 5x + 5 ← distribute left side

8 + 4x < 5x + 5 ( subtract 5 from both sides )

3 + 4x < 5x ( subtract 4x from both sides )

3 < x ⇒ x > 3

Answer:

C) none

Step-by-step explanation:

The two lines are parallel (have the same slope (x-coefficient), but different y-intercepts). They have no point in common, hence there is no solution to the system of equations.

___

Another way to think about this: subtract the first equation from the second. You get ...

0 = 1

There are no values of the variables that will make this be true, hence no solutions.

Answer:

The answer is y = 6/x ⇒ answer A

Step-by-step explanation:

* Lets revise what is the meaning of the inverse variation

- It is a mathematical relationship between two variables

- It can be expressed by an equation in which the product of two

 variables is equal to a constant

- If y is in inverse variation with x

∴ y ∝ 1/x

- Change this relation to equation

∴ y = k/x, where k is the constant of the variation

- We can write it by another way

∵ y ∝ 1/x

∴ y = k/x ⇒ by using cross multiplication

∴ yx = k

* Now lets solve the problem

∵ There is an inverse variation between the two variables x and y

∴ y ∝ 1/x

∴ y = k/x

- Look to the answer

# We will chose A because

∵ y = 6/x  ⇒ use the cross multiplication

∴ yx = 6 ⇒ and 6 is a constant

∴ k = 6

* The answer is y = 6/x

Answer:

Its subtract 12.

Step-by-step explanation:

The first question mark is positive 6.

6-12= -6

The second question mark is  -22.

Negative 10 minus 12 equals negative 22

Once you understand integers, it will be really easy. I was in 6th grade last year.

Answer:

SY=34, SK=21 and KY=13

Step-by-step explanation:

we have that

SY=SK+KY

substitute the given values

(36-x)=(13x-5)+(2x+9)

solve for x

36-x=15x+4

15x+x=36-4

16x=32

x=2

Find the value of SY

SY=(36-x)=36-2=34

Find the value of SK

SK=(13x-5)=13(2)-5=21

Find the value of KY

KY=(2x+9)=2(2)+9=13

To find the values of SK, KY, and SY, substitute the given expressions for x into the equations.

To find the values of SK, KY, and SY, we need to substitute the given expressions for x into the equations.

Therefore, SK = 86, KY = 23, and SY = 29.

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Answer:

B

Step-by-step explanation:

Adjusting entries for prepaid expenses are classified as a (D) deferral. They gradually recognize the cost as expense over the period of benefit. This involves decreasing the prepaid asset account and increasing the corresponding expense account.

Prepaid expenses are costs that have been paid in advance for services or goods that will be received in the future. In accounting, prepaid expenses are considered assets because they provide future economic benefits to the company. When adjusting entries for prepaid expenses, the necessary adjusting entry is a ( D) deferral.

This means that the initial payment is recorded in a prepaid asset account, and then as the expense is incurred over time, it is gradually recognized as an expense on the income statement. For example, if a company pays a year's worth of rent in advance, each month, a portion of that prepaid rent would be moved from the prepaid asset account to the rent expense account, reflecting the usage of the space.

An adjusting entry for a deferral decreases the prepaid asset account and increases the expense account. The goal of this type of entry is to apportion the expense to the periods in which the benefits from the prepaid cost are actually realized.

Answer:

The solution for k is the interval (-3.5,1.5)

Step-by-step explanation:

we have

[tex]k(x^{2}+1)=x^{2}+3x-3[/tex]

[tex]kx^{2}+k=x^{2}+3x-3[/tex]

[tex]x^{2}-kx^{2}+3x-3-k=0[/tex]

[tex]}[1-k]x^{2}+3x-(3+k)=0[/tex]

we know that

If the discriminant is greater than zero . then the quadratic equation has two real and distinct solutions

The discriminant is equal to

[tex]D=b^{2}-4ac[/tex]

In this problem we have

a=(1-k)

b=3

c=-(3+k)

substitute

[tex]D=3^{2}-4(1-k)(-3-k)\\ \\D=9-4(-3-k+3k+k^{2})\\ \\D=9+12+4k-12k-4k^{2}\\ \\D=21-8k-4k^{2}[/tex]

so

[tex]21-8k-4k^{2} > 0[/tex]

solve the quadratic equation by graphing

The solution for k is the interval (-3.5,1.5)

see the attached figure

The first option is the correct choice

Answer: its called an image

Step-by-step explanation:

This is because it the result of the reflection

The reflection of a figure is called an image.

A reflection is a transformation representing a flip of a figure.

An image formed by mirrors is due to the reflection of light originating from an object.

Image may be real or virtual, upright or inverted, and diminished or enlarged.

When we place an object in front of the mirror, we see the same object in the mirror. This image that appears to be behind the mirror is called the image.

Image is a visual or other representation of a real object; a graphic; a picture while reflection is the act of reflecting or the state of being reflected.

Whereas, The pre-image is the original appearance of a figure in a transformation operation.

The definition of a reflection is a thought or writing about something, particular in the past, or what one sees when looking into a mirror or body of water. An example of reflection is an article written by an author discussing how he feels he has grown in the past year in his writing style.

When a ray of light approaches a smooth polished surface and the light ray bounces back, it is called the reflection of light. The incident light ray that land on the surface is reflected off the surface. The ray that bounces back is called the reflected ray.

Hence, the reflection of a figure is called an image.

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Answer:

64

Step-by-step explanation:

We are dividing by 2 each time

1024 /2 = 512

512/2 = 256

256/2 =128

128/2 = 64

Answer:

The radius of the silo should be [tex]16\ ft[/tex]

Step-by-step explanation:

we know that

The volume of the grain silo is equal to the volume of the cylinder plus the volume of a hemisphere

[tex]V=\pi r^{2} h+\frac{4}{6}\pi r^{3}[/tex]

we have

[tex]V=35,500\pi\ ft^{3}[/tex]

[tex]h=4D=8r[/tex]

substitute the values and solve for r

[tex]35,500\pi=\pi r^{2} (8r)+\frac{4}{6}\pi r^{3}[/tex]

Simplify

[tex]35,500=r^{2} (8r)+\frac{4}{6}r^{3}[/tex]

[tex]35,500=8r^{3}+\frac{2}{3}r^{3}[/tex]

[tex]35,500=\frac{26}{3}r^{3}[/tex]

[tex]r^{3}=35,500*(3)/26[/tex]

[tex]r=16\ ft[/tex]

To find the radius of the silo, we need to calculate the volume of the cylinder and hemisphere components of the silo, and then set their sum equal to the desired volume of grain. By substituting the given relationship between the height and radius, we can express the volumes in terms of the radius, and solve for the value of r that satisfies the equation.

To find the radius of the silo, we can start by calculating the volume of the cylinder. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height. In this case, we are given that the height of the cylinder is 4 times the diameter of the base, so we can write h = 4r. The volume of the cylinder portion would then be V_cylinder = πr²(4r) = 4πr³.

The volume of the hemisphere on top can be calculated using the formula for the volume of a sphere, which is V = (4/3)πr³. Since the radius of the hemisphere is the same as the radius of the base of the cylinder, this volume would be V_hemisphere = (4/3)πr³.

The total volume of the silo is the sum of the cylinder volume and the hemisphere volume. So we have the equation V_total = V_cylinder + V_hemisphere = 4πr³ + (4/3)πr³ = (16/3)πr³. We know that the silo is to hold 35,500π cubic feet of grain, so we can set up the equation (16/3)πr³ = 35,500π and solve for r. Dividing both sides by (16/3)π, we get r³ = 35,500/((16/3)π), and taking the cube root of both sides, we find r = ∛(35,500/((16/3)π)). Evaluating this expression, we find that r ≈ 5.02 feet.

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Answer:

The number of roses is 16

The number of lilies is 8

The number of orchids is 21

Step-by-step explanation:

Let

x-----> the number of roses

y-----> the number of lilies

z-----> the number of orchids

we know that

x=2y ----> y=x/2 ----> equation A

z=x+5 ---> equation B

x+y+z=45 ----> equation C

substitute equation A and equation B in equation C and solve for x

x+(x/2)+(x+5)=45

(5/2)x=45-5

(5/2)x=40

x=40*2/5

x=16 roses

Find the value of y

y=x/2 ----> y=16/2=8 lilies

Find the value of z

z=x+5 -----> z=16+5=21 orchids

therefore

The number of roses is 16

The number of lilies is 8

The number of orchids is 21

Answer:

The maximum value of the equation is 1 less than the maximum value of the graph

Step-by-step explanation:

We have the equation [tex]y=-x^2+4x-8[/tex].

We can know that this graph will have a maximum value as this is a negative parabola.

In order to find the maximum value, we can use the equation [tex]x=\frac{-b}{2a}[/tex]

In our given equation:

a=-1

b=4

c=-8

Now we can plug in these values to the equation

[tex]x=\frac{-4}{-2} \\\\x=2[/tex]

Now we can plug the x value where the maximum occurs to find the max value of the equation

[tex]y=-(2)^2+4(2)-8\\\\y=-4+8-8\\\\y=-4[/tex]

This means that the maximum of this equation is -4.

The maximum of the graph is shown to be -3

This means that the maximum value of the equation is 1 less than the maximum value of the graph

Answer:

The maximum value of the equation is 1 less than the maximum value of the graph

Step-by-step explanation:

T*4 just go step by step

Answer:

It can't be A. since if you only look at managers, you are missing all the sales executives.

It may be C. this option is more random but doesn't guarantee that you will represent both groups of employee's. Also, each time you would conduct the survey, you will receive the exact same results since it is the same people. 

It isn't D. for the exact same reason as A. but you're missing managers now. 

Therefore the answer is B. Some managers and some sales executives selected at random. This way you get a sample from both categories, and within those groups, it is randomly selected.

 I hope this helps!

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Step-by-step explanation:

The generalization could be valid for a sample that accurately represents the entire employee population of Ashton's company.

This sample should be large enough to be statistically significant and should be selected randomly to avoid bias.

To calculate the sample size needed for a valid generalization, Ashton could use a confidence level and margin of error. Let's say he wants a 95% confidence level with a margin of error of 5%.

First, he needs to find the population size (total number of employees at the company). Let's assume there are 500 employees.

Next, he can use the formula for sample size calculation:

[tex]\[n = \frac{{Z^2 \cdot p \cdot (1-p)}}{{E^2}}\][/tex]

Where:

- (n) = sample size

-(Z) = Z-score corresponding to the desired confidence level (for 95% confidence level, Z = 1.96)

- (p) = estimated proportion of employees using cell phones primarily for business (from the survey data)

- (E) = margin of error (0.05 for 5%)

Let's say from the survey, Ashton found that 70% of employees use cell phones primarily for business.

Plugging in the values:

[tex]\[n = \frac{{1.96^2 \cdot 0.70 \cdot (1-0.70)}}{{0.05^2}}\][/tex]

[tex]\[n = \frac{{3.8416 \cdot 0.70 \cdot 0.30}}{{0.0025}}\][/tex]

[tex]\[n = \frac{{0.719856}}{{0.0025}}\][/tex]

[tex]\[n ≈ 287.94\][/tex]

So, Ashton would need a sample size of approximately 288 employees to make a valid generalization about the entire company.

To ensure the generalization is valid, Ashton needs to collect data from a sample that accurately represents the entire employee population. This sample should be large enough to be statistically significant and should be selected randomly to avoid bias.

Using statistical methods, Ashton can calculate the minimum sample size needed for a valid generalization. By setting a confidence level and margin of error, he can determine the sample size required to achieve a certain level of accuracy.

In this case, Ashton chose a 95% confidence level with a margin of error of 5%. He used a formula that takes into account the population size, estimated proportion of employees using cell phones primarily for business, and the margin of error.

After plugging in the values, he calculated that he would need a sample size of approximately 288 employees to make a valid generalization about the entire company.

So, for the conclusion that most employees at his company use cell phones primarily for business to be valid, Ashton should survey at least 288 randomly selected employees.

Complete question:

Ashton surveyed some of the employees at his company about their cell phone habits. From the data, he concluded that most employees at his company use cell phones primarily for business. For which sample could this generalization be valid?

Answer: [tex]x=\frac{23}{22}[/tex]≈[tex]1.04[/tex]

Step-by-step explanation:

You need to solve for the variable "x" to find its value.

To solve for "x" you need to apply the Division property of equality. This  states that:

[tex]If\ a=b\ then\ \frac{a}{c}=\frac{b}{c}[/tex]

Then, knowing this, you can divide both sides of the equation by 22. Therefore, you get that the value of "x" is the following:

[tex]\frac{22x}{22}=\frac{23}{22}[/tex]

[tex]x=\frac{23}{22}[/tex]

[tex]x[/tex]≈[tex]1.04[/tex]

the equation of the graph should be

f(x)= 1/2x -1

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (2, 0) ← 2 points on the line

m = [tex]\frac{0+1}{2-0}[/tex] = [tex]\frac{1}{2}[/tex]

Note the line crosses the y- axis at (0, - 1) ⇒ c = - 1

y = [tex]\frac{1}{2}[/tex] x - 1 ← in slope- intercept form

f(x) = [tex]\frac{1}{2}[/tex] x - 1 ← in functional notation

To find the answer for one cup of flour, divide the cups of sugar by the cups of flour. Here’s how it works.

Since we want the proportion for 1 cup of flour, we divide it by itself to get 1.

Thus, we need to have equal sides, so we divide the number of cups of sugar by the amount the cups of flour divided by.

So: 2.5/7.5=1/3

1 cup of flour is proportional to 1/3 cups of sugar.

Hope this helps!

The amount of sugar for 1 cup of flour can be determined through setting up and solving a proportion based on the given proportional relationship, though specific values are required. For example, if 3 cups of sugar are needed for 2 cups of flour, then 1.5 cups of sugar would be needed for 1 cup of flour.

Unfortunately, the specific values are not given in the question, but we can still explain how you would find the answer. In a proportional relationship, the ratios between the two quantities (in this case, sugar and flour) is constant. This means that if we know the amount of sugar used for a certain amount of flour, we can determine the amount of sugar used for 1 cup of flour by setting up an equation and solving for the unknown variable, provided we have the necessary data.

For example, if the relationship was such that for every 2 cups of flour, you used 3 cups of sugar, then the ratio of sugar to flour would be 3/2. To find out how much sugar you need for 1 cup of flour, you can create a proportion that reads 3/2 = x/1 and solve for x. In this case, x is the equivalent amount of sugar needed for 1 cup of flour.

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Answer:

can you make it more specific please?

Step-by-step explanation:

I honestly don't get what you're saying in what subject this is?

Step-by-step explanation:

The area is

[tex] {x}^{2} - 110x + 2800 \\ = {x}^{2} - 40x - 70x + 2800 \\ = x(x - 40) - 70(x - 40) \\ = (x - 40)(x - 70)[/tex]

Since the width is

[tex]x - 40 \: (feet)[/tex]

Then, the length will be

[tex]x - 70 \: (feet)[/tex]

Answer:

7 + (-2) is equivalent to 5

Step-by-step explanation:

Answer:

A fixed point equidistant from all points on the surface of the sphere

Step-by-step explanation:

we know that

The sphere is the set of all points in the space equidistant from a fixed point called the center of the sphere

therefore

The center of a sphere is a fixed point equidistant from all points on the surface of the sphere

In Geometry, the center of a sphere is: B. a fixed point equidistant from all points on the surface of the sphere.

A sphere can be defined as a round, three-dimensional solid geometric figure that has all its surface points (every point on its surface) at equal distances (equidistant) from the center.

In this context, we can infer and logically conclude that the center of a sphere simply refers to a fixed point that is equidistant or at equal distances from all points on the surface of the sphere.

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from 76 down to 60 is a 16 difference.

if we take 76 to be the 100%, what is 16 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 76&100\\ 16&x \end{array}\implies \cfrac{76}{16}=\cfrac{100}{x}\implies \cfrac{19}{4}=\cfrac{100}{x} \\\\\\ 19x=400\implies x=\cfrac{400}{19}\implies x\approx 21.05[/tex]

Answer

The price reduced by 21.05%

Explanation

•To determine the price decrease in dollars, subtract:

76 - 60 = 16

•The price decreased by 16 dollars as shown above.

•16 is what percent of 76?

So, to find that, set up an equation:

76x = 16

•Divide both sides by 76.

[tex]\frac{76x}{76} = x[/tex]

[tex]\frac{16}{76} = .21 or 21%[/tex]

x = .2105 or 21.05%

Answer: Yes

Step-by-step explanation:

3 * 2 = 6. So you can get 6 1/2 foot pieces out of 1 roll. She has 3 rolls. 6 * 3 = 18. 18 is more than 15.

Yes, She have enough ribbon to cut 15 pieces.

The fraction is numerical representation of the numbers in the form of numerator and denominator.

We have,

Total rolls of ribbon = 3

Length of one roll of ribbon = 3 feet,

So,

Total Length of 3 roll of ribbon = 3 * 3 = 9 feet

And,

Marita cutting rolls into [tex]\frac{1}{2}[/tex] foot pieces.

So,

1 roll cut into pieces [tex]= \frac{3}{\frac{1}{2} } = \frac{3*2}{1}[/tex] = 6 pieces,

So,

3 roll cut into pieces = 6 * 3 = 18 pieces,

i.e.

18 pieces of  [tex]\frac{1}{2}[/tex] foot ,

And she needs [tex]15\frac{1}{2}[/tex] pieces of ribbon,

And total pieces of ribbon are 18.

Hence, we can say that Yes, She have enough ribbon to cut 15 pieces.

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