Find The Value Of X.

An equation for the total cars and trucks for dealership A is: x + y = 164.

An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.

The number of cars that dealership A sold is: 98 cars.

The number of trucks that dealership B sold is: 66 trucks.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:

Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;

x + y = 164.

Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;

2x + 0.5y = 229.

By solving the systems of linear equations simultaneously, we have:

2x + 0.5(164 - x) = 229

1.5x + 82 = 229

x = 98 cars.

For the y-value, we have;

2(98) + 0.5y = 229

0.5y = 229 - 196

y = 33/0.5

y = 66 trucks.

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Answer:

The circle has an area of about 1385 square mm.

Step-by-step explanation:

Let's recall that circles have an area that can be found with the following formula:

\(A=\pi r^{2}\)

where r is the radius of the circle.

Now, focus your eyes on the circle. We are shown that the diameter of this circle is 42 mm, but we only want the radius. Since the radius is half the diameter, the radius is 21 mm. Now, we can solve for the area of the circle.

\(A=\pi (21)^2\\A=441\pi \\A=1385.44236...\)

So, to the nearest whole number, the area of the circle is 1385 square mm.

9514 1404 393

Answer:

  A(x) = 20000(0.88)^x

Step-by-step explanation:

The general form of these exponential equations is ...

  A(x) = a·b^x

where 'a' is the initial value, and b is the annual growth factor. x is the elapsed time in years.

The growth factor is ...

  growth factor = 1 + growth rate

Here, the growth rate per year is -12%, so the growth factor is ...

  b = 1 -12% = 88% = 0.88

Of course, the initial value is a=20,000, so the equation is ...

  A(x) = 20000(0.88)^x

Answer:

z > -4/5

Step-by-step explanation:

-9 - (2z - 7) > -2z - 6 - 5z

Get rid of the parenthesis

-9 - 2z + 7 > -2z - 6 - 5z

Combine like terms:

       -2 - 2z > -7z - 6

       +2       >       +2

Add 2 to both sides.

 -2z > -7z - 4

 +7z > +7z

Add 7 to both sides.

5z > -4

Divide both sides by 5 to get z.

z > -4/5

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

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The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.

Let's assume the length of the rectangle is 'l' and the width is 'w'.

From the given data, we know that each gate is 4 m wide.

Therefore, the width of the rectangle is:

Width = w + (4 m + 4 m) = w + 8 m

The perimeter of the rectangle is:

P = 2l + 2(w + 8 m) = 2l + 2w + 16 m

Now, we need to subtract the combined length of the two gates from the perimeter:

P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m

So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

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Answer:

The area is changing at the point of  \(\mathbf{61200 m^2/year}\)

Step-by-step explanation:

From the given information:

Let's recall from our previous knowledge that the formula for finding the area of a rectangle = L × w

where;

L = length and w = width of the rectangle

Suppose the Length L is twice the width w

Then L = 2w --- (1)

From The area of a rectangle

A = L  × w

A = 2w  × w

A = 2w²

Taking the above differentiating with respect to time

\(\dfrac{dA}{dt }= 4w \times \dfrac{dw}{dt} --- (2)\)

At the time t

\(\dfrac{dw}{dt}= 34 m \ per \ year ; w = 450 \ m\)

Replacing the values back into equation 2, we get:

\(\dfrac{dA}{dt }= 4 \times 450 \times 34\)

\(\mathbf{\dfrac{dA}{dt }= 61200 m^2/year}\)

Answer: -6, -3, 0

Step-by-step explanation:

Because it’s right :)

Answer:

A, C, E

Step-by-step explanation:

-6, -3, 0

Answer:

Y = -0.3587+0.09118X

92 %

Step-by-step explanation:

Using technology to fit the data between the variables, test score and hours of sleep; we obtain the linear model :

Ŷ = -0.3587+0.09118X

Where, x = test score ; y = hours of sleep

To obtain the test score of a student who sleep foe 8 hours using the model :

Y = 8

Ŷ = -0.3587+0.09118X

8 = -0.3587+0.09118X

8 + 0.3587 =0.09118X

8.3587 = 0.09118X

X = 8.3587 / 0.09118

X = 91.672515

X = 92 ( approximately)

Solving for N is an illustration of subject of formula, and the equation of N is N = 1 + (S - A)/D

The equation of S is given as:

S = A+(N-1) D

Subtract A from both sides

S - A = (N-1) D

Divide both sides by D

(S - A)/D = N-1

Add 1 to both sides of the equation

N = 1 + (S - A)/D

Hence, the equation of N is N = 1 + (S - A)/D

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Answer:

The answer is (C) 326.92

Step-by-step explanation:

784.065 - 457.15 is 326.915.

When simplified, the answer is 326.92.

Answer:

336

Step-by-step explanation:

Using the inverse of the function from the table, the value of f⁻¹(4) is 107/3

The inverse of a function is a new function that "undoes" the original function. It reverses the mapping of inputs and outputs, allowing you to find the original input value when you know the output value.

In this problem, we have to use the table to find the original function which is f(x) and use it to find the inverse of the function;

Taking two points from the table;

m = y₂ - y₁ / x₂ - x₁

m = 0 - (-3) / -9 - (-11)

m = 3 / 20

Using the slope and one point on the table;

y = mx + x

-3 = 3/20(-11) + c

-3 = -1.65 + c

c = -3 + 1.65

c = -1.35

Putting the slope and y - intercept together;

y = 3/20x - 1.35

y = 3/20x - 27/20

f(x) = 3/20x - 27/20

Taking the inverse of the function;

f⁻¹(x) = (20x + 27)/3

To find the value of f⁻¹(4), we just need to substituting the value of x in the function;

f⁻¹(4) = (20(4) + 27)/3

f⁻¹(4) = 107/3

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Answer:

3×2×1

Step-by-step explanation:

that is the answer

Answer:

see explanation

Step-by-step explanation:

The definition of factorial ! is

n! = n(n - 1)(n - 2) ...... × 3 × 2 × 1 , then

3! = 3 × 2 × 1

= 6

Answer:

NO

Step-by-step explanation:

I've already told you, it is closer to 1 than 1.25

Based on the line of best fit given in the scatter plot, the predicted value of y for an x value of 5 is: D. 0.5.

The line of best fit of a scatter plot is a straight line that shows a trend of the association between two variables which can be used for making predictions.

In the scatter plot given, when x = 5, the expected value of y is predicted to be: D. 0.5.

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1.The slope -intercept form of the function is  y = 7x

2.The slope -intercept form of the function is y = x - 8

3.The slope -intercept form of the function is y = -2x +9

4.The slope -intercept form of the function is \(y = \frac{1}{3}x+9\)

5.The slope -intercept form of the function is  y = 0.5x - 1.5

6.The slope -intercept form of the function is   y = 3x - 12

How is the slope -intercept form calculated?

1. The slope -intercept form of the equation of the function is  y = 7x

Slope = m

\(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{0+7}{0+1} \\\\m= 7\)

Substituting point (-1,-7)  and m in the slope-intercept form of the equation,

y = mx+ c   ----(1)

-7 = 7(-1) + c

c = 7 -7

c = 0

Substituting m and c in  (1)

y = 7x

2. The slope -intercept form of the equation of the function is y = x - 8

Slope = m

\(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{-8+17}{0+9} \\\\m= \frac{9}{9} =1\)

Substituting point (-9,-17)  and m in the slope-intercept form of the equation,

y = mx+ c   ----(1)

-17 = (-9) + c

c = -17 +9

c = -8

Substituting m and c in  (1)

y = x - 8

3. The slope -intercept form of the equation of the function is y = -2x +9

Slope = m

\(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{5-9}{2-0} \\\\m= \frac{-4}{2} =-2\)

Substituting point (0,9)  and m in the slope-intercept form of the equation,

y = mx+ c   ----(1)

9 =  -2 (0) + c

c = 9

Substituting m and c in  (1)

y = -2x +9

4.The slope -intercept form of the equation of the function is  \(y = \frac{1}{3}x+9\)

Slope = m

\(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{8-7}{-3+6} \\\\m= \frac{1}{3}\)

Substituting point (0,9)  and m in the slope-intercept form of the equation,

y = mx+ c   ----(1)

9 =  1/3 (0) + c

c = 9

Substituting m and c in  (1)

\(y = \frac{1}{3}x+9\)

5. The slope -intercept form of the equation of the function is

y = 0.5x - 1.5

Slope = m

\(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{1-0.5}{5-4} \\\\m= \frac{0.5}{1}= 0.5\)

Substituting point (5,1)  and m in the slope-intercept form of the equation,

y = mx+ c   ----(1)

1 =0.5 (5) + c

1 -2.5 = c

c = - 1.5

Substituting m and c in  (1)

y = 0.5x - 1.5

6. The slope -intercept form of the equation of the function is y = 3x - 12

Slope = m

\(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{9-3}{7-5} \\\\m= \frac{6}{2}\\\\m= 3\)

Substituting point (5,3)  and m in the slope-intercept form of the equation,

y = mx+ c   ----(1)

3 =3(5) + c

3 -15 = c

c = - 12

Substituting m and c in  (1)

y = 3x - 12

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the fraction of the class that did not participate in any of these activities is 1 - n * (151/60).

What is the fraction?

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing a numerator(upper value) and denominator(lower value).

Let's call the number of students in the class "n".

2/3 of the class played in the band, so:

n * 2/3 participated in the band

1/6 of the class sang in the chorus, so:

n * 1/6 participated in the chorus

1/10 of the class played football, so:

n * 1/10 played football

1/60 of the class played basketball, so:

n * 1/60 played basketball

The fraction of the class that participated in one of these activities is the sum of these fractions:

n * (2/3 + 1/6 + 1/10 + 1/60) = n * (7/6 + 1/10 + 1/60)

So, the fraction of the class that did not participate in any of these activities is:

1 - n * (7/6 + 1/10 + 1/60) = 1 - (7/6 + 1/10 + 1/60) * n = 1 - n * (151/60)

Therefore, the fraction of the class that did not participate in any of these activities is 1 - n * (151/60).

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Answer:

yoooo it equals 1

Step-by-step explanation:

The coordinate of the point on the directed line segment from (- 10, 2) to (-3,-5) will be;

⇒ (x , y) = (- 6, - 2)

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

The two points are;

(- 10, 2) and (- 3, 5)

And, The partitions the segment into a ratio of 4 to 3.

Now,

Since, We know that;

The The coordinate of the point on the directed line segment from

(x₁, y₁) to (x₂, y₂) that partitions the segment into a ratio of m₁ to m₂ will be;

⇒ x = (m₁ x₂ + m₂ x₁) / (m₁ + m₂)

⇒ y = (m₁ y₂ + m₂ y₁) / (m₁ + m₂)

Hence, The coordinate of the point on the directed line segment from

(- 10, 2) to (-3,-5) will be;

x = (4×-3 + 3×-10) / (4 + 3)

x = (-12 - 30) / 7

x = - 42/7

x = - 6

And,

y = (4×-5 + 3×2) / (4 + 3)

y = (-20 + 6) / 7

y = - 14/7

y = - 2

Thus, The coordinate of the point on the directed line segment from

(- 10, 2) to (-3,-5) will be;

⇒ (x , y) = (- 6, - 2)

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Answer:

The last option: 3 x (7 + 2) = (3 x 7) + (3 x 2)

Step-by-step explanation:

There is addition on the inside, and you are distributing the multiplication from the outside.

Answer:

X= 52

2X+24 =128

Step-by-step explanation:

128+52= 180

Answer:

15 pounds

Step-by-step explanation:

hope that help

Answer:

Compound interest is the interest imposed on a loan or deposit amount.

The most commonly used concept in our daily existence is compound interest.

The compound interest for an amount depends on both Principal and interest gained over periods.

Formula to calculate compound interest.

\({ \boxed{ \rm{C.I = P \bigg(1 + \dfrac{r}{n} \bigg) ^{nt} - P}}}\)

Here,

P is Principal

r is rate of interest

t is total time span.

n is number of times interest got compounded annually.

The total cost, in dollars, before taxes Addition

Given that

To find

So, according to the question

we have,

A store has a buy-one-get-one-half-off sale on laundry detergent, When we buy 1 bottle then we will get half of bottle free and we are buying 2 bottles so we just have to pay the price of one and half bottles only.

So, we can say that

   Total cost of 2 bottle laundry detergent = regular price of 1 bottle laundry detergent + regular price of \(\frac{1}{2}\) bottle laundry detergent

       = 2.60 + \(\frac{1}{2}\)× 2.60

       = 2.60 + 1.30

       = $3.90

Answer:

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The transformations that compares the functions y = 1/x and y = 5/(x + 6) are

What are transformations?

Transformations are mathematical operations that are performed to change the shape or value of a graph, function or image.

Since we have the functions

We want to see how the graphs of

We proceed as folows.

Looking at the functions

We compare the transformations and see that

So, the functions compare by

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Answer:

The answer is below

Step-by-step explanation:

a) Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It states that the square of the hypotenuse is equal to the sum of the square of the legs of the triangle.

Let x be the length of the hypotenuse, using Pythagoras:

x² = 25² + 25²

x² = 1250

x = 35 (to the nearest whole number)

b) Using sine rule:

\(\frac{x}{sin(90)} =\frac{25}{sin(45)} \\\\x=\frac{25}{sin(45)} *sin(90)\\\\x=35(to \ nearest\ whole\ number)\)

The counting process was an essential component in evaluating the results and drawing conclusions based on the data gathered.

Hi! Bob and Aniyah's apples were counted by a designated individual, likely a teacher, supervisor, or event organizer, who was responsible for ensuring the accuracy and fairness of the counting process.

This person utilized their organizational skills and attention to detail to effectively tally the number of apples collected by both Bob and Aniyah.

By doing so, they were able to determine the final count, which was then used to either compare the performance of the two individuals or contribute to a larger total for a specific event or purpose.

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Answer:

The amount of discount would be$1.20

The amount they pay would be $10.80

Step-by-step explanation:

Answer:

To factor −5x2 + 10x, we can first factor out the common factor of −5x from both terms, which gives:

−5x(x - 2)

Therefore, the factored form of −5x2 + 10x is −5x(x - 2).