Identify the vertex of each graph. Tell whether it is a minimum or a maximum.

Answer:   x + 4

                5x

Step-by-step explanation:

The first one is "x + 4" because you are adding 4 to the 1st number

The second one is "5x" because you are multiplying 5 to the 2nd number.

Solution:

Given system of equations are:

[tex]\frac{1}{4}x + \frac{1}{8}y =2 ---------- eqn\ 1\\\\\frac{1}{3}x + \frac{1}{2}y = 4 -------------- eqn\ 2[/tex]

We have to find value of y

From eqn 1,

[tex]\frac{1}{4}x + \frac{1}{8}y =2 \\\\2x + y = 2 \times 8\\\\2x + y = 16 ---- eqn\ 3[/tex]

From eqn 2,

[tex]\frac{1}{3}x + \frac{1}{2}y = 4\\\\2x + 3y = 4 \times 6\\\\2x + 3y = 24 ------ eqn\ 4[/tex]

Subtract eqn 3 from eqn 4

2x + 3y = 24

2x + y = 16

( - ) -----------------

2y = 8

y = 4

Thus value of y is 4

Answer:

[tex]f(g( - 4)) = 196[/tex]

Step-by-step explanation:

The functions are;

[tex]f(x) = {x}^{2} [/tex]

and

[tex]g(x) = 3x - 2[/tex]

We want to find

[tex]f(g( - 4))[/tex]

First we find g(-4) to get:

[tex]g( - 4) = 3 \times - 4 - 2[/tex]

[tex]g( - 4) = - 12- 2[/tex]

[tex]g( - 4) = - 14[/tex]

Now

[tex]f(g( - 4)) = f( - 14)[/tex]

This implies that,

[tex]f(g( - 4)) = {( - 14)}^{2} [/tex]

[tex]f(g( - 4)) = {( - 14)} \times - 14[/tex]

[tex]f(g( - 4)) = 196[/tex]

First, subtract 24 from 31.

31 - 24 = 7

Now divide 7 by 2.

7 ÷ 2 = 3.5

Plug 3.5 into the equation to check.

24 + (3.5 × 2) = 31

x = 3.5

Answer:

x = -10/7

Step-by-step explanation:

Step 1:  Combine like terms

4 - 6 + 2x - 9x - 8

-7x - 10

Step 2:  Solve for x

-7x - 10 = 0

-7x - 10 + 10 = 0 + 10

-7x / -7 = 10 / -7

x = 10/-7

Answer:  x = -10/7

Answer:

I believe it would be a chemical change as there would be no way to reverse it

Answer:

The slope of the equation is:   [tex]m=\frac{2}{3}x[/tex]

Step-by-step explanation:

Given the equation

[tex]y=\frac{2}{3}x-1[/tex]

As the equation in slope intercept form

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

Here:

Comparing the equation in slope intercept form

[tex]y=\frac{2}{3}x-1[/tex]

so

[tex]m=\frac{2}{3}x[/tex]

Therefore, the slope of the equation is:   [tex]m=\frac{2}{3}x[/tex]

Answer:

Vertical translations would affect the horizontal asymptote.

the total cost of a $76.01 item is $81.14 .

Step-by-step explanation:

Here we have ,  sales tax is six 3/4% . We need to find that what is the total cost of a $76.01 item .Let's find out:

Sales tax is actually the extra money we need to give apart from actual cost of item which is given to government or concerned authority .

Tax is 6(3/4)% of cost price i.e.

[tex]Tax = \frac{cost-price(6\frac{3}{4})}{100}[/tex]

⇒ [tex]Tax = \frac{cost-price(6\frac{3}{4})}{100}[/tex]

⇒ [tex]Tax = \frac{(76.01)(6.75)}{100}[/tex]

⇒ [tex]Tax = \frac{513.06}{100}[/tex]

⇒ [tex]Tax = 5.13[/tex]

So, total cost = $76.01 + $5.13

total cost = $81.14

Therefore, the total cost of a $76.01 item is $81.14 .

Answer:

X = 4

Step-by-step explanation:

Solve for x.

-3x + 4 = -8

Make sure to subtract both sides.

-3x (+4 -4) = -8 - 4

-3x= -12

Divide by -3 on both sides.

-3x/-3 = -12/-3

Answer:

4

Step-by-step explanation:

-3x + 4 = -8

Subtract 4 from both sides

-3x + 4 - 4 = -8 - 4

-3x = -12

Divide both sides by by -3

x = -12/-3

x = 4

Answer: OPTION A.

Step-by-step explanation:

A dilation is defined as a transformation in which the Image (The figure obtained after the transformation) and the Pre-Image (The original figure before the transformation) have the same shape, but they have different sizes.

In this case you know that the dilation is centered at the origin and the scale factor is:

[tex]k=0.5[/tex]

Therefore, the rule is the following:

[tex]Q(kx,ky)[/tex]

You can identify in the figure attached that the point Q is:

[tex]Q(1,5)[/tex]

Therefore, you must multiply its coordinates by the scale factor 0.5 in order to get its Image Q'. This is:

[tex]Q'=(1*0.5,5*0.5)\\\\Q'=(0.5.2.5)[/tex]

Final answer:

The image of point Q for a dilation with a scale factor of 0.5 and center (0,0) is (option A) (0.5, 2.5).

Explanation:

To find the image of point Q, we need to apply the dilation equation: (x', y') = (k * x, k * y), where (x, y) are the coordinates of the original point and k is the scale factor.

In this case, the center of dilation is (0, 0) and the scale factor is 0.5. So, for point Q which has coordinates (x, y), the image coordinates (x', y') will be:

(x', y') = (0.5 * x, 0.5 * y)

Therefore, the image of point Q will be (option A) (0.5, 2.5).

Answer: 150 miles

Step-by-step explanation:

The distance between Chicago and Indianapolis is approximately 150 miles.

To find the distance between Chicago and Indianapolis using their latitude and longitude coordinates, we can apply the Pythagorean theorem. The distance between two points on the Earth's surface can be approximated by considering the Earth as a flat plane, which is reasonable for relatively short distances like the one between these two cities.

The difference in latitude (north-south distance) between Chicago and Indianapolis is:

[tex]\[ 42N - 40N = 2N \][/tex]

The difference in longitude (east-west distance) between the two cities is  [tex]\[ 86W - 88W = 2W \][/tex]

Since each degree is approximately 53 miles, we can calculate the north-south distance and the east-west distance:

North-south distance in miles:

[tex]\[ 2N \times 53 \text{ miles/degree} = 106 \text{ miles} \][/tex]

East-west distance in miles:

[tex]\[ 2W \times 53 \text{ miles/degree} = 106 \text{ miles} \][/tex]

Now, we can use the Pythagorean theorem to find the straight-line distance (the hypotenuse of the right triangle formed by the north-south and east-west distances):

Let [tex]\( d \)[/tex] be the distance between the two cities, then:

[tex]\[ d^2 = (106 \text{ miles})^2 + (106 \text{ miles})^2 \] \\[/tex]

[tex]\[ d^2 = 11236 \text{ miles}^2 + 11236 \text{ miles}^2 \] \\[/tex]

[tex]\[ d^2 = 22472 \text{ miles}^2 \] \\[/tex]

[tex]\[ d = \sqrt{22472 \text{ miles}^2} \] \\[/tex]

[tex]\[ d \approx 150 \text{ miles} \][/tex]

Answer:

x = 12; y = 60

Step-by-step explanation:

The opposite sides of a parallelogram are always equal, so x+3 = 15, making x = 12

The opposite angles of a parallelogram are always equal, making y = 60

Answer:

y=-3/2x+5

Step-by-step explanation:

3x + 2y = -4

2y=-4-3x /:2

y=-4/2-3x/2

y=-3/2x-2

Slope=-3/2(=m) , because this line is parallel slope is the same, then

y-y1=m(x-x1) ,where

A(4,-1).... x1 =4, y1 =-1

y-(-1)=-3/2(x-4)

y+1=-3/2x+3/2*4

y+1=-3/2x+6

y=-3/2x+6-1

y=-3/2x+5

Final answer:

The quadratic equation in standard form is t² + 14.3t - 20 = 0. It can be solved using the quadratic formula.

Explanation:

The quadratic equation in standard form that represents the given table is:

t² + 14.3t - 20 = 0

Where t represents the variable and the constants are a = 1.00, b = 14.3, and c = -20.0. The solutions to this equation can be found using the quadratic formula:

t = (-b ± √(b² - 4ac)) / (2a)

Without knowing the type of triangle or the values of the angles, we can only provide a possible range of values for side AC of triangle ABC, which is between 9 inches (in case of an acute triangle) and 47 inches (in case of an obtuse or right angled triangle). For accurate calculation, more detail is necessary.

The question pertains to determining the length of the side AC in a triangle ABC. Given are the lengths AB and BC so without additional details such as the angle values or the nature of the triangle, we cannot definitively determine the length of side AC. Such a calculation usually requires the use of trigonometric calculations or the Pythagorean theorem which applies only to right triangles. However, we can establish a range for the possible length of side AC.

If the triangle ABC is obtuse or a right triangle with the right angle at point B, the length of AC (AB+BC) could be up to 47 inches (19 inches + 28 inches). On the other hand, if it is an acute triangle, the length of AC (BC-AB) would be a minimum of 9 inches (28 inches - 19 inches). Please provide more details or check if it's a right triangle for a more specific calculation.

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The correct option is D (52 inches) satisfies all conditions of the triangle inequality theorem.

To determine which length of side AC could form a triangle with sides AB = 19 inches and BC = 28 inches, we apply the triangle inequality theorem:

1. Triangle Inequality Theorem:

  - For any triangle with sides [tex]\( a \), \( b \),[/tex] and [tex]\( c \)[/tex]:

    - [tex]\( a + b > c \)[/tex]

    - [tex]\( a + c > b \)[/tex]

    - [tex]\( b + c > a \)[/tex]

2. Checking the options:

  - Option A: 42 inches

    - [tex]\( 19 + 42 = 61 > 28 \)[/tex]

    - [tex]\( 19 + 28 = 47 > 42 \)[/tex]

    - [tex]\( 42 + 28 = 70 > 19 \)[/tex]

    - Valid

  - Option B: 7 inches

    - [tex]\( 19 + 7 = 26 < 28 \)[/tex]

    - Invalid (Does not satisfy [tex]\( AB + AC > BC \)[/tex])

  - Option C: 49 inches

    - [tex]\( 19 + 49 = 68 > 28 \)[/tex]

    - [tex]\( 19 + 28 = 47 < 49 \)[/tex]

    - Invalid (Does not satisfy [tex]\( AB + BC > AC \)[/tex])

  - Option D: 52 inches

    - [tex]\( 19 + 52 = 71 > 28 \)[/tex]

    - [tex]\( 19 + 28 = 47 < 52 \)[/tex]

    - [tex]\( 52 + 28 = 80 > 19 \)[/tex] Valid

3. Conclusion:

  - The lengths of side AC that satisfy the triangle inequality theorem and can form a triangle with sides AB = 19 inches and BC = 28 inches are 42 inches and 52 inches.

The complete question is:

In triangle ABC, the length of side AB is 19 inches and the length of side BC is 28 inches. Which of the following could be the length of side AC? A. 42 inches B. 7 inches C. 49 inches D. 52

The length around the rug is the circumference.

The formula is C = 2 x PI x r

C = 2 x 3.14 x 5 = 31.4 feet

For this case we must find the perimeter of the circular carpet.

By definition, the perimeter of a circle is given by:

[tex]P = 2 \pi * r[/tex]

Where:

r: It is the radius of the circle

According to the statement we have:

[tex]r = 5 \ ft[/tex]

Substituting:

[tex]P = 2 * 3.14 * 5\\P = 2 * 3.14 * 5\\P = 31.4 \ ft[/tex]

So, you need[tex]31.4 \ ft[/tex]

Answer:

[tex]31.4 \ ft[/tex]

The type of transformation that moves P (3,-7) to P'' (3,7) is a reflection. The point has been flipped over the x-axis.

The type of transformation which moves point

P (3,-7)

to

P'' (3,7)

is a

reflection

. It appears that point P has simply been flipped over the x-axis. The x-coordinate remains unchanged at 3, but the y-coordinate has been reflected to the opposite side of the x-axis, changing it from -7 to 7. So, a reflection over the x-axis is the correct transformation in this case. The transformation that moves point P (3,-7) to P'' (3,7) is a reflection over the x-axis. When a point is reflected in the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. In this case, when the y-coordinate of P changes from -7 to 7, it means that P was reflected over the x-axis.

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Answer:

345.

Step-by-step explanation:

Just divide 407.10 by 1.18 and you'll get your answer.

The greatest number of DVDs that Tony can pack in each box is 6, which is the greatest common divisor of 12, 24, and 30.

To find the greatest number of DVDs that Tony can pack in each box, we need to determine the greatest common divisor (GCD) of the quantities of each type of DVD. The GCD is the largest number that can evenly divide all the given numbers without leaving a remainder. The numbers of DVDs are 12 (comedy), 24 (animated), and 30 (musical).

Here are the steps to find the GCD:

Thus, the greatest number of DVDs Tony can pack in each box is 6.

Answer:

48 yards

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=7.6\ yd\\\pi=3.14[/tex]

substitute

[tex]C=2(3.14)(7.6)=48\ yd[/tex]

Answer: 48 yards

Step-by-step explanation:

The circumference of a circle can be calculated with the following formula:

[tex]C=2\pi r[/tex]

Where "C" is the circumference of the circle and "r" is the radius of the circle.

In this case you know that the radius of the circular track is the following:

[tex]r=7.6\ yd[/tex]

Knowing tha radius, you can substitute it into the formula (According to the information given in the exercise, you need to use [tex]\pi =3.14[/tex])

[tex]C=2(3.14)(7.6\ yd)[/tex]

Finally, you need to evaluate.

Therefore, you get that the whole yards of fencing that they need to purchase to enclose the track is:

[tex]C\approx48\ yd[/tex]

Answer:

Kevin needs 96 points on his last test to raise his mean test score to 90 points.

Step-by-step explanation:

we know that

The mean score is the total of all scores divided by the total number of tests.

Let

x_1 ----> the score in the first math test

x_2 ----> the score in the second math test

x_3 ----> the score in the third math test

x_4 ----> the score in the fourth math test

we have

After taking the first 3 tests, his mean test score is 88 points

so

[tex]\frac{x_1+x_2+x_3}{3} =88[/tex]

[tex]x_1+x_2+x_3=264[/tex] ----> equation A

How many points does he need on his last test to raise his mean test score to 90 points?

so

[tex]\frac{x_1+x_2+x_3+x_4}{4} =90[/tex]

[tex]x_1+x_2+x_3+x_4=360[/tex] ----> equation B

substitute equation A in equation B

[tex]264 + x_4 = 360[/tex]

solve for x_4

[tex]x_4 = 360-264[/tex]

[tex]x_4 = 96[/tex]

Therefore

Kevin needs 96 points on his last test to raise his mean test score to 90 points.

Answer:

the answer is d.) the runner stopped

Step-by-step explanation:

because the distance is staying the same but the time is changing wich means the runner isn't moving for a period of time.

Answer:2

Step-by-step explanation:

Log49 7=Log49/Log7=2Log7/Log7

=2

Answer:

0.33333333333

Step-by-step explanation:

Typing 1/3 in a calculator gives 0.333333333333

Answer:

Its a

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Just did it

Answer:

The distribution positively skewed

Step-by-step explanation:

We have the mean of a distribution to be 276, while the median is 231.

When compare the mean and median,

we gave

276>231

Since the mean is greater than the median, the distribution is skewed to the right.

In other words, the the distribution is positively skewed.

Answer:

Positively skewed

Step-by-step explanation:

Answer:  See Below

Step-by-step explanation:

(b) Make a table of white ovals and black ovals.  You will notice that

white starts with 3 and adds 3 to each design → 3 + 3(d - 1) = 3d

black starts with 4 and adds 4 to each design → 4 + 4(d - 1) = 4d

[tex]\begin{array}{c|c|c}\underline{\text{Design \#}}&\underline{\text{white ovals}}&\underline{\text{black ovals}}\\1&3&4\\2&6&8\\3&9&12\\4&3(4)=12&4(4)=16\\5&3(5)=15&4(5)=20\\6&3(6)=18&4(6)=24\\\cdot&\cdot&\cdot\\\cdot&\cdot&\cdot\\\cdot&\cdot&\cdot\\n&3n&4n\end{array}[/tex]

white ovals when design = 30   --->    3d = 3(30) = 90

black ovals when design = 100   --->   4d = 4(100) = 400

white ovals when design = 50   --->   3d = 3(50) = 150

black ovals when design = 50   --->   4d = 4(50) = 200

                                                                  TOTAL = 350

**********************************************************************************

(c) Make a table of rods and squares.  You will notice that

rods start with 19 and add 12 to each design → 19 + 12(d - 1) = 12d - 7

squares start with 6 and add 4 to each design → 6 + 4(d - 1) = 4d + 2

[tex]\begin{array}{c|c|c}\underline{\text{Design \#}}&\underline{\qquad \text{rods}\qquad }&\underline{\qquad \text{squares}\qquad }\\1&19&6\\2&31&10\\3&43&14\\4&12(4)-7=55&4(4)+2=18\\5&12(5)-7=67&4(5)+2=22\\6&12(6)-7=79&4(6)+2=26\\\cdot&\cdot&\cdot\\\cdot&\cdot&\cdot\\\cdot&\cdot&\cdot\\n&12n-7&4n+2\end{array}[/tex]

rods when design = 15   --->    12d - 7 = 12(15) - 7 = 173

squares when design = 15   --->   4d + 2 = 4(15) + 2 = 62

The missing length x is 99 m.

Solution:

Given polygons are similar.

If two triangles are similar, then the corresponding sides are in proportion.

[tex]$\Rightarrow\frac{81}{18}=\frac{x}{22}[/tex]

Multiply by 22 on both sides, we get

[tex]$\Rightarrow\frac{81}{18}\times 22=\frac{x}{22}\times 22[/tex]

[tex]$\Rightarrow\frac{9}{2}\times 22=x[/tex]

⇒ 9 × 11 = x

⇒ 99 = x

Switch the sides.

⇒ x = 99

The missing length x is 99 m.

Answer:

Note from question, Let K be any integer.  Integer = 1

θ = πk

  θ = 3.142 * 1

  θ = 3.142 in three decimal places

θ = sin⁻¹ (2/3) + 2kπ

   θ = sin⁻¹0.667 + 2*1*3.142

   θ = 0.718 + 6.284

   θ = 7.002 in three decimal places

∴ 7.002 , 3.142

Step-by-step explanation:

Considering the equation

3 tan(θ) sin(θ) − 2 tan(θ) = 0

The objective is to solve the equation.

First solve the equation in one period.

3 tan(θ) sin(θ) − 2 tan(θ) = 0

( 3sinθ − 2 ) tanθ = 0

Therefore, 3sinθ − 2 = 0    also   tanθ = 0

            =>  sinθ = 2/3        ,        tanθ = 0

Pick the right equation.

tanθ = 0

    θ = tan⁻¹ 0

    θ = 0

Using the unit circle, the period of tangent functions is π

Then the general solution of the equation is θ = 0 + πk ==> θ = πk

Pick the left equation.

3sinθ − 2 = 0

3sinθ = 2

sinθ = 2/3

    θ = sin⁻¹ (2/3)

As the sine function has period 2π

Then the general solution is θ = sin⁻¹ (2/3) + 2kπ