Two cars are traveling in the same direction. the first car is going 40 mi/h and the second car is going 55 mi/h. the first car has a 120 mile head start. which equation could you solve to find how many hours it will take for the second car to catch up to the first car?

x is the independent variable and H(x) is the dependent variable

A dependent variable is a variable whose value depends upon independent variables.

An independent variable is a variable that does not depend on any other variable for its value.

For example, in an expression, y = 3x + 2, x is an independent and y is a dependent variable because y depends on x for its value

Given: H(x) = 3+0.5x

Therefore, x is the independent variable and H(x) is the dependent variable because it is a function of x

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Part 1: The total length of the rectangle; 20 + x (Expression).

Part 2: The total width of the rectangle; 16 + x (Expression).

Part 3: The total area of the pool along with walkway; (20 + x)(16 + x).

The data for the question is given as-

The expressions for the given cases are-

Part 1: The total length of the rectangle;

The total length of the rectangle = 10 + 10 + x

The total length of the rectangle = 20 + x (Expression)

Considering; 10 + 10 > 8 + 8

Part 2: The total width of the rectangle;

The total width of the rectangle = 8 + 8 + x

The total width of the rectangle = 16 + x (Expression)

Part 3: The total area of the pool along with walkway.

Area = length x breadth

Area = (20 + x)(16 + x).

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Answer:

The two numbers are [tex]3[/tex] and [tex]-16[/tex].

Step-by-step explanation:

Two numbers that, when multiplied, result in a product of [tex]-48[/tex]:

[tex]x \cdot y = -48[/tex]

Same two numbers when added get a sum of [tex]-13[/tex]:

[tex]x + y = -13[/tex]

Solve for x in the summation identity:

[tex]y = -13 - x[/tex]

Plug the value back into the product identity and solve for [tex]x[/tex]:

[tex]x \cdot (-13-x) = -48\\-13x - x^2 = - 48\\x^2 + 13x = 48\\x^2 + 13x - 48 = 0\\(x-3)(x+16) = 0[/tex]

The roots we found for [tex]x[/tex] were:

[tex]x = 3\\x = -16[/tex]

Our two numbers are [tex]3[/tex] and [tex]-16[/tex]. We can test this:

[tex]3 + (-16) = -13\\3 * -16 = -48[/tex]

Answer:

Read the given problem, look at the given figure of intersecting lines, and identify the angle given and the unknown angles.

Step-by-step explanation:

The runners whose speeds are in a proportional relationship with each other:

the running speed of Liam, Taylor, Ashley, Nathan, Juan are equal (0.0016) whereas the running speed  of Sarah and Katie are equal.

In this question, we have been given the data for the distance and amount of time each person ran one Saturday morning.

We need to select all the runners whose speeds are in a proportional relationship with each other.

We find the speed using formula, speed = distance / time

Name         Time (seconds)           Distance (miles)              Speed(mps)

Liam                   306.6                           0.5                      0.5/306.6 = 0.0016    

Taylor                756.36                          1.2                      1.2/756.36 = 0.0016

Sarah                 504.35                         0.7                     0.7/504.35 = 0.0014

Ashley               459.9                          0.75                    0.75/459.9 = 0.0016

Connor              600.5                              1                          1/600.5 = 0.0017

Nathan               942.75                         1.5                     1.5/942.75 = 0.0016

Juan                   827.82                         1.35                  1.35/827.82 = 0.0016

Katie                   429.48                          0.6                   0.6/429.48 = 0.0014

Therefore, the runners whose speeds are in a proportional relationship with each other:

the running speed of Liam, Taylor, Ashley, Nathan, Juan are equal (0.0016) whereas the running speed  of Sarah and Katie are equal.

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The equation for the linear equation parallel to BC is:

y = (2/3)*x - 19/3

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

slope = (y2 - y1)/(x2 - x1)

And two lines are parallel if both lines have the same slope and different y-intercept.

So if we want to et a line parallel to BC whose endpoints are (1, 3) and ( 4, 5), the slope should be:

slope = (5 - 3)/(4 - 1) = 2/3

So our line is like:

y = (2/3)*x + b

And this must pass through (2, -5)

Replacing these values we get:

-5 = (2/3)*2 + b

-5 - 4/3 = b

-15/3 - 4/3 = b

-19/3  =b

Then the linear equation is:

y = (2/3)*x - 19/3

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Answer: 7/6

Step-by-step explanation:

Ok so first we must take these fractions and make them have a common denominator. The best way to do this is to take 2/3 and multiply the numerator and denominator by 8 giving us 16/24. Next take 4/8 and multiply the numerator and denominator by 3 giving us 12/24. Now we have both a common denominator. Now we add the numerators of both (16+12) to get 28/24 but now we have an improper fraction divide the numerator and denominator by 4 to get us 7/6.

Hope this Helps :)

In the expression, 8 + x squared minus 4 x cubed + 5 x + 2 x squared.

2x^2 and x^2 are the like terms

The given expression is 8 + x squared minus 4 x cubed + 5 x + 2 x squared

This is rewritten as

8 + x^2 - 4x^3 + 5x + 2x^2

The terms in the expression are grouped as

constant terms: 8

terms with x variable : 5x

terms with x^2 variables: 2x^2 and x^2

terms with x^3 variables: 4x^3

Like terms refers to terms that are similar either as a constants or have same variables

Hence the like terms in the expression is 2x^2 and x^2

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The equation of line with a slope of -5 and which passes through point (-2, 8) is 5x + y = -2.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the data in the question;

Point (-2,8)

First, we determine the y-intercept 'b'. Plug the coordinates and slope into the equation of line formula and solve for b.

y = mx + b

8 = (-5)(-2) + b

8 = 10 + b

b = 8 - 10

b = -2

Now, plug values of slope m and y-intercept b into y = mx + b to determine the equation of the line.

y = mx + b

y = (-5)x + (-2)

y = -5x - 2

Convert to standard form; Ax + Bx = C

y = -5x - 2

Reorder the equation

5x + y = - 2

Therefore, the equation of the line is 5x + y = - 2.

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Answer:

I do not see the original triangle, but you would take the original and move it one unit to the left and 5 units up.

Step-by-step explanation:

For example, if the three vertices (corners) of the triangle were points:

(0,0), (1,5) and (-2,3).

Point (0,0) would move to (-1, 5)  0-1 and 0+5

Point (1,5) would move to (0, 10)

Point (-2,3) would move to (-3, 8)

Answer:

To graph the image of the triangle after the transformation, we first need to have the coordinates of the vertices of the original triangle. Once we have those coordinates, we can apply the transformation to each vertex to obtain the coordinates of the corresponding vertex in the transformed image. Then, we can plot the three transformed vertices to obtain the image of the triangle.

Let's say the original triangle has vertices A, B, and C with coordinates A(x1, y1), B(x2, y2), and C(x3, y3), respectively.

To obtain the transformed coordinates of A, we apply the transformation rule (x, y) → (x - 1, y + 5) to the coordinates of A:

A' = (x1 - 1, y1 + 5)

Similarly, we can obtain the transformed coordinates of B and C:

B' = (x2 - 1, y2 + 5)

C' = (x3 - 1, y3 + 5)

Now that we have the transformed coordinates of the three vertices, we can plot them to obtain the image of the triangle.

Here's an example:

Suppose the original triangle has vertices A(2, 4), B(5, 6), and C(7, 3). Applying the transformation rule (x, y) → (x - 1, y + 5) to each vertex gives us:

A' = (2 - 1, 4 + 5) = (1, 9)

B' = (5 - 1, 6 + 5) = (4, 11)

C' = (7 - 1, 3 + 5) = (6, 8)

Plotting these three points gives us the image of the triangle after the transformation:

Before transformation:

B (5, 6)

/ \

/ \

A (2, 4) C (7, 3)

After transformation:

B' (4, 11)

/ \

/ \

A' (1, 9) C' (6, 8)

Here's what the image of the transformed triangle would look like on a graph:

|

|

C' | B'

|

---------|--------

|

A' |

|

Answer: M = 1876 - 30n  will give the amount of Money (M) remaining after n months of withdrawing exactly $30 per month, PROVIDED NOTHING ELSE IS EVER ADDED TO OR WITHDRAWN FROM THE ACCOUNT.  (Not very realistic.)

Use n=6 to provide the balance after 6 months.

Step-by-step explanation:

Answer:

10y+3x^2+3x^2y

Step-by-step explanation:

^2 means square

2^2 is 4 and different variable cannot be added.

Answer:

x < 10 - 2y

Step-by-step explanation:

Answer:

Step-by-step explanation:

Para determinar el porcentaje, tenemos que dividir el valor por el valor total y luego multiplicar el resultado por 100.

Neither.

Parallel lines (when the line continues), never intersects. Perpendicular lines intersect and create a 90 degree angle.

The angle created by the lines intersect but do not create a 90 degree angle.

Answer:

a = 6.63 cm

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ (12)² = a² + (10)²

→ 144 = a² + 100

→ a² = 144 - 100

→ a = √44

→ [ a = 6.63 cm ]

Hence, value of a is 6.63 cm.

In the simple linear regression equation , the term b0 represents b) Estimated intercept

The expected mean value of Y when all X=0 is the intercept, also referred to as the constant. Create a regression equation with X as the only predictor to begin. The expected mean value of Y at that value is the intercept in the event that X occasionally equals 0. When x is 0, the projected value for y—the intercept of the regression line—is simply 0. A line's slope and intercept can be expressed in terms of the equation y = slope x x + intercept. The Value of Interception The point where the function crosses the y-axis is known as the intercept and is frequently denoted as a constant. In some analyses, removing the intercept and reducing the regression line to Y = bX + error causes the regression model to only become significant.

Given,

In the simple linear regression equation , the term b0 represents:

b) Estimated intercept

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Answer:

[tex]4 \frac{23}{40}\; \rm miles[/tex]

Step-by-step explanation:

To find how many more miles Ada lives from her grandmother's house than her aunt's house, we need to subtract the distance to her aunt's house from the distance to her grandmother's house.

Ada lives 17 3/8 miles from her grandmother's house.

Ada lives 12 4/5 miles from her aunt's house.

Convert both mixed numbers into improper fractions by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:

[tex]17 \frac{3}{8}=\dfrac{17 \cdot 8+3}{8}=\dfrac{139}{8}[/tex]

[tex]12 \frac{4}{5}=\dfrac{12 \cdot 5+4}{5}=\dfrac{64}{5}[/tex]

As both improper fractions have a different denominator, we need to change both fractions into equivalent fractions with the same denominator. To do this, find the least common multiple (LCM) of the denominators, 8 and 5.

The LCM of 8 and 5 is 40. Therefore, convert the fractions into their equivalent fractions (with 40 as their denominator) by multiplying the numerator and denominator by the same number:

[tex]\dfrac{139}{8}=\dfrac{139 \cdot 5}{8 \cdot 5}=\dfrac{695}{40}[/tex]

[tex]\dfrac{64}{5}=\dfrac{64 \cdot 8}{5 \cdot 8}=\dfrac{512}{40}[/tex]

Now the fractions have the same denominator, we can carry out the subtraction by simply subtracting the numerators:

[tex]\dfrac{695}{40}-\dfrac{512}{40}=\dfrac{695-512}{40}=\dfrac{183}{40}[/tex]

Finally, convert the improper fraction into a mixed number by dividing the numerator by the denominator:

[tex]183 \div 40=4\;\rm remainder \;23[/tex]

The mixed number answer is the whole number and the remainder divided by the denominator:

[tex]4 \frac{23}{40}[/tex]

Therefore, Ada lives 4 23/40 miles more from her grandmother's house than her aunt's house.

El interés junto con el préstamo de $ 200,000 tiene un monto de $ 8,080.

En este problema tenemos el caso de una persona que pide prestado $ 200,000 a una tasa de interés anual de 36 %, cuyo pago se realiza tras un plazo de dos años de realizarse el préstamo. Asumimos, que la deuda se genera por interés compuesto, esto es, un interés acumulativo. El interés compuesto es descrito mediante la siguiente fórmula:

I = C' · [(1 + r / 100)ⁿ - 1]

Donde:

Si sabemos que C' = 200,000, r = 36 y n = 2, entonces el interés a pagar al final del plazo es:

I = 200,000 · [(1 + 2 / 100)² - 1]

I = 8080

El interés a pagar es $ 8080, además del préstamo de $ 200,000.

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The mean number of new subscribers per month during that year is 242000.

A mean simply means the average of the numbers given.

The number of cable television subscribers increased from about 1 151 000 in 2002 to about 1 393 000 in 2003.

The mean number of new subscribers will be:

= Change in numbers / Number of years

= (1393000 - 1151000) / 1

= 242000 / 1

= 242000

Therefore, the mean is 242000.

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Original equation (1/2) + (1/2x) = (x² -7x +10)/4x is equivalent to the proportion (x+1)/2x = (x² -7x +10)/4x.

As given in the question,

Given equation is :

Original equation (1/2) + (1/2x) = (x² -7x +10)/4x

Simplify the original equation to get the equivalent equation

Least common multiple is 2 and 2x is equal to 2x

Original equation (1/2) + (1/2x) = (x² -7x +10)/4x is Equivalent to the proportion is given by:

( x + 1) / 2x = (x² -7x +10)/4x

Therefore, original equation (1/2) + (1/2x) = (x² -7x +10)/4x is equivalent to the proportion (x+1)/2x = (x² -7x +10)/4x.

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Answer:

6 pizzas

Step-by-step explanation:

12.99 times 3 which is the 3 pitchers of soda is 38.97

38.97 subtracted from 75 which is our total amount is 36.03

36.03 which is what we have left divided by 6 since each pizza is 6$ is 6.

Answer:

3.24759526401

Step-by-step explanation:

divide that

Step-by-step explanation:

the standard form is

f(x) = y = a(x - h)² + k

(h, k) are the vertex coordinates. here (-2, -9).

a is the stretch factor.

since the parabola opens upwards, a is positive.

so, we see already :

y = a(x + 2)² - 9

to get a we need an additional point on the curve. we see e.g. (1, 0) :

0 = a(1 + 2)² - 9 = a×3² - 9 = 9a - 9

9a = 9

a = 1

so, our standard form is

f(x) = (x + 2)² - 9

Answer:

C

Step-by-step explanation:

C has a directly proportional relationship. 27 glasses are in 9 cases, and 81 glasses are in 27 cases. Directly proportional since 9×3=27 (cases) and 27×3=81 (glasses)

The equivalent linear equation in standard form is 4x + 3y = 5

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

Points = (-7, 11) and (8, –9)

Point-slope form is y - 11 = -4/3(x + 7).

Recall that the point-slope form is y - 11 = -4/3(x + 7).

So, we have

y - 11 = -4/3(x + 7).

Multiply through both sides by 3

This gives

3y - 33 = -4(x + 7).

Open the brackets

3y - 33 = -4x - 28

Evaluate the like terms

3y = -4x +  5

Add 4x to both sides

4x + 3y = 5

Hence, the equation is 4x + 3y = 5

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Answer:

(x+8)(x-9)

Step-by-step explanation:

1. Use the sum-product pattern

x²-x-72

x²+8x-9x-72

2. Find the common factor from the 2 pairs

x²+8x-9x-72

x(x+8)-9(x+8)

3. Rewrite in factored form

x(x+8)-9(x+8)

(x-9)(x+8)

Solution to problem: (x-9)(x+8)