What is the x-value of the solution to the system of equations?
5x + 4y = 8
2x – 3y = 17
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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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The first option is the correct choice

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

Answer: 9(9-4xy)

Step-by-step explanation:

You can factor out the 9, as 9*9 = 81 and 9*4 = 36.

So dividing both terms, you get 9(9-4xy)

T*4 just go step by step

Answer:

[tex]\large\boxed{C.\ (x^2-1)-5(x-1)}[/tex]

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)\\\\p(x)=x^2-1,\ q(x)=5(x-1)\\\\(p-q)(x)=(x^2-1)-5(x-1)[/tex]

Answer:

See picture attached below

Step-by-step explanation:

We can easily find the answer to your question, if we plot the equation with a graphing calculator or any plotting tool.

The equation is

y = 3 cos (θ + 20) - 4

See attached picture below

phase_shift = 20

max_amplitude = -1

min_amplitude = -7

Period = 2π

Answer:

Answer: [tex]x=76\°[/tex]

Step-by-step explanation:

By definition the angle formed by the intersection of two chords inside a circle is:

[tex]Angle\ formed\ by\ two\ Chords=\frac{sum\ of\ intercepted\ Arcs}{2}[/tex]

You can observe in the figure that  the angle formed by the intersection of the two chords measures 94°, and the intercepteed arcs are: x° and 112°.

Therefore, you need to substitute these values into the formula and solve for "x to find its value. Then:

[tex]94\°=\frac{x+112\°}{2}\\\\(94\°)(2)=x+112\°\\\\188\°-112\°=x\\\\x=76\°[/tex]

Answer:

The definition of present value is the current value of a future sum of money.

Choice A

Step-by-step explanation:

Present value (PV) is the current value of a future streams of cash flows or sum of money at a given expected rate of return by the investor. Future payment streams are discounted at the rate of return. The present value increases with the decrease in the rate of return or the discount rate and vice versa.

Option A is correct,  the definition of present value is the current value of a future sum of money.

Present value refers to the concept of determining the value of a future sum of money in terms of its current worth.

It takes into account factors such as the time value of money and discounting to calculate the value of future cash flows in today's terms.

By discounting future cash flows, the present value represents the amount of money that would need to be invested or received today to achieve the same value as the future sum of money.

Hence, the definition of present value of the current value of a future sum of money.

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ANSWER

[tex]y = - \frac{1}{3} x -\frac{4}{3} [/tex]

EXPLANATION

The given line is

[tex]y = 3x + 3[/tex]

The given point is

[tex](-1,-1)[/tex]

The slope of the given line is

[tex]m = 3[/tex]

We found this by comparing

[tex]y = 3x + 3[/tex]

to

[tex]y = mx + b[/tex]

If two lines are perpendicular, then one is the negative reciprocal of the other.

Hence the slope of the required line is

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

Using the point-slope formula or otherwise, we can find the required equation.

[tex]y-y_1=m(x-x_1)[/tex]

We substitute the slope and point to get:

[tex]y + 1 = - \frac{1}{3} (x + 1)[/tex]

[tex]y = - \frac{1}{3} x -\frac{4}{3} [/tex]

Answer: -1 1/2 < -1/4

Explanation: Since the number is negative, -1 1/2 is further to the left on the number line, meaning it has less value.

The relationship between -1 1/2 and -1/4 can be expressed as an inequality. In this case, -1 1/2 is less than -1/4, so the inequality is -1 1/2 < -1/4.

The relationship between -1 1/2 and -1/4 may be written as an inequality. Remember, an inequality indicates that one number is larger or smaller than another. In this case, it shows which negative number, either -1 1/2 or -1/4, is larger. On the number line, a negative number situated to the right is larger than a number situated to the left. So, in terms of value, -1/4 is larger than -1 1/2 as it's less negative. This can be written as:

-1 1/2 < -1/4

.

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Answer:

4.75

Step-by-step explanation:

Given

f(x)=  (x^2-1)/(x-4)

The average rate of change for the interval a≤x≤b is given by:

Rate of change=  (f(b)-f(a))/(b-a)

In our question,

a=2

and

b=6

So,

f(2)=  ((2)^2-1)/(2-4)

=(4-1)/(-2)

= -3/2

And

f(6)=  ((6)^2-1)/(6-4)

=(36-1)/2

=  35/2

Rate of change=  ( 35/2-(-3/2))/(6-2)

=(35/2+3/2)/(6-2)

=  ((35+3)/2)/4

=(38/2)/4

=19/4

=4.75

The average rate of change is 4.75 ..

Answer:

Average rate of change =4.75.

Step-by-step explanation:

Given function is [tex]f\left(x\right)=\frac{x^2-1}{x-4}[/tex].

Now we need to find the average rate of change of f(x) for [tex]2\le x\le6[/tex].

So plug these values into average rate of change  (ARC) formula.

[tex]ARC=\frac{f\left(b\right)-f\left(a\right)}{b-a}[/tex]

[tex]ARC=\frac{f\left(6\right)-f\left(2\right)}{6-2}[/tex]

[tex]ARC=\frac{\frac{6^2-1}{6-4}-\frac{2^2-1}{2-4}}{4}[/tex]

[tex]ARC=\frac{\frac{36-1}{6-4}-\frac{4-1}{2-4}}{4}[/tex]

[tex]ARC=\frac{17.5-\left(-1.5\right)}{4}[/tex]

[tex]ARC=\frac{19}{4}[/tex]

[tex]ARC=4.75[/tex]

So the final answer is average rate of change =4.75.

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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Answer:

b = -12/5

Step-by-step explanation:

5(b+6) = 18

5b + 30 = 18

5b = -12

b = -12/5

Answer:

b = -2.4

Step-by-step explanation:

5 ( b + 6 ) = 18

→ Expand brackets

5 b + 30 = 18

→ - 30 from both sides to isolate 5 b

5 b = - 12

→ ÷ Divide both sides 5 to isolate b

b = -2.4

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:

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:

The recursively-defined function to describe this situation is:

Step-by-step explanation:

To solve the number of birds that there will be after three years, you must recognize that the function f(0) means the number of birds at time zero, in which the birds are complete (that is, the 14,000 birds), by their part, following the equation provided below we have the following calculation:

So:

Therefore, the final number of birds after three years in decline is 10206.

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

The answer to this question is 2.

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:

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:

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:

Option D. angle S apostrophe

Step-by-step explanation:

we know that

The transformation of the figure is a translation

The rule of the translation is

(x,y)-----> (x-3,y-7)

That means ----> left 3 units and down 7 units

Remember that a translation does not modify the internal angles of the figure as neither the length of their sides

so

∠S=∠S'

Answer:

6.4

Step-by-step explanation:

8.9 - 2.5 = 6.4

8 - 2 = 6

9 - 5 = 4

there you have it your answer 6.4

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?

The distance from New York to Hartford represents 48% of the distance from New York to Boston.

To find the percentage of the distance from New York to Boston that is the distance from New York to Hartford, we need to calculate the ratio of the two distances. First, divide the distance from New York to Hartford (120 miles) by the distance from New York to Boston (250 miles):

120 / 250 = 0.48

Convert the ratio to a percentage by multiplying by 100:

0.48 * 100 = 48%

Therefore, the distance from New York to Hartford represents 48% of the distance from New York to Boston.

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Answer:

648 sq units

Step-by-step explanation:

Area of the base= 12×12= 144 sq. units

Perimeter of the base=4×12= 48

Total surface area= 1/2×48×21 + 144

=648 sq units

ANSWER

648 square units.

EXPLANATION

The surface area of the regular pyramid is the area of the base plus the area of the 4 triangular faces.

We use the formula;

[tex]S.A = {l}^{2} + 4 \times \frac{1}{2} bh[/tex]

where l=12 units is the length of the square base and h=21 units is the vertical height of the triangular faces.

We substitute the values to get;

[tex]S.A = 12^{2} + 4 \times \frac{1}{2} \times 12 \times 21[/tex]

[tex]S.A = 144+ 504[/tex]

[tex]S.A =648 {units}^{2} [/tex]

Answer:

x = 2

Step-by-step explanation:

A vertical line has the equation x = a.  This line passes through points with x-coordinate of 2, so the equation is x = 2.

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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