Ryan is traveling by car for his vacation. The first day, he travels 80 miles in 2 hours. The second day, he travels 100 miles in 3 hours. Is this a proportional relationship?

Answer:

x = 2.6, x = -1.6

Step-by-step explanation:

If we compare the graph to points (-1, 2) and (2, 2) [see blue lines on attachment], we can determine that the scale of the y-axis is 1 square per 1 unit.  (This is different from the scale of x-axis, which is 2 squares per unit).

Therefore, to use the graph to estimate the x-value when y = 4, count 4 square up the y-axis from 0, then trace along the horizontal line until you meet the curve.  Then trace down to the x-axis and read the values of x. (shown by the red lines on the attachment).

So the approximate value of x is -1.6 and 2.6 when y = 4.

The actual answer can be calculated as follows:

   x² - x = 4

⇒ x² - x - 4 = 0

Use the quadratic formula:

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\implies x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(1)(-4)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{1\pm\sqrt{17}}{2}[/tex]

[tex]\implies x=2.6,x= -1.6 \sf \ (1 \ dp)[/tex]

Answer:

x=-1.56,2.56

Answer:

38.5

D

Step-by-step explanation:

5.5x7=38.5

m<ABC=m<A'B'C'

Observe both triangles

<ABC=<A'B'C'

The value of k in the function f(x) = 2x-k is 6.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

f(x) = 2x + 4

f(x) = 2x-k

Now,

To shift a linear function to the right, we subtract a constant from the input variable x. For example, f (x) = 2x + 4 shifts to the right by 2 units when it is replaced with f (x) = 2 (x - 2) + 4.

In this case, f (x) = 2x + 4 shifts six units to the right when it is replaced with f (x) = 2 (x - k) + 4. To find the value of k, we can equate the expressions inside the parentheses and solve for k:

x - k = x - 6 k = 6

Therefore, by the given functions the answer will be 6.

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Answer:

0.02 tons per cubic foot

Step-by-step explanation:

delt math

The density of the material is, 106.36 tons per cubic foot.

Density is the mass of a material substance per unit volume.

d = M/V, where d is density, M is mass, and V is volume, is the formula for density.

Grams per cubic centimeter are a typical unit of measurement for density.

Given, The density of a certain material is such that it weighs 1 pound for every 3.5 cups.

Therefore, d = 1/3.5 per cubic cup.

d = 0.29 pounds per cubic cup.

Now, We know 1 ton is equal to 2000 pounds and 1 foot is equal to 119688.

Therefore, The density of the material per cubic foot is,

= 119688/(2000×0.29) tons per cubic foot.

= 106.36 tons per cubic foot.

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The probability of Kayla scoring above 70% on exactly three out of the four tests is 8.64%.

Given that the probability Kayla will score above 70% on a mathematics test is 0.60, and Kayla will take four tests this semester, and we want to find the probability she will score above 70% on exactly three out of the four tests, to determine what is the probability of Kayla scoring above 70% on exactly three out of the four tests, the following calculation must be performed:

Therefore, the probability of Kayla scoring above 70% on exactly three out of the four tests is 8.64%.

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Answer:

No

Step-by-step explanation:

(2,-2)

2 is the x coordinate

-2 is the y coordinate

3x - y = 4

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

6 + 2 = 8, not 4

Hope this helps :)

Have a nice day!

Answer:

No, it is not in the line.

Step-by-step explanation:

Let's plug the coordinates of the point and find out

[tex]3(2) -(-2) = 4\\6+2 = 8\ne 4[/tex]

Answer:

There are 30 apples left!

Step-by-step explanation:

81-

51

-----

30

Using an exponential function, the recursive formula that describes the fraction of contaminants still remaining in the liquid sample after passing through n filters is given by:

[tex]A[n] = (0.052)^n[/tex]

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, considering an initial fraction of A(0) = 100% = 1, the decay rate is of r = 0.948, hence the formula is:

[tex]A[n} = (1 - r)^n[/tex]

[tex]A[n] = (0.052)^n[/tex]

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Answer:

4(x+5)

Step-by-step explanation:

Answer:1.694

Step-by-step explanation:

You take away the decimal from 3.54 and make the 6 the same number place

Ex. 1 ÷ 1.20

1=100

1.20=120

600 ÷ 354 = 1.694

Answer:

-19x

Step-by-step explanation:

to make this equation easier, remove the variables (-8-11) which equals -19. You can then say the answer is -19x

Answer:

1,2,4

Step-by-step explanation:

all are positive intergers

[tex] - 6 \leqslant x \leqslant 6[/tex]

[tex] - 5 \leqslant y \leqslant 5[/tex]

Answer:

D  5y + 29x = 500

Step-by-step explanation:

Slope-intercept form of a linear equation:  y = mx + b

(where m is the slope/rate of change, and b is the y-intercept)

Given:  

⇒ when x = 0, y = 100

Therefore,  b = 100

Given:

Note that the water is decreasing in volume as time goes by.  Therefore, the rate of change is negative, so m = -5.8

Inputting these values into the equation gives:

y = -5.8x + 100

Multiply the equation by 5:

5y = -29x + 500

Rearrange:

5y + 29x = 500

Therefore, D is the solution.

Answer:

x = 3,75

Step-by-step explanation:

x/3 = 15/12

x/3 = 5/4

4x = 3 × 5

4x = 15

x = 15/4

x = 3,75

Answer:

Step-by-step explanation:

Answer:

The inverse is  5±sqrt(x+25)

Step-by-step explanation:

y = x^2 - 10x

To find the inverse, exchange x and y and solve for y

x = y^2 -10y

Complete the square

x+25 = y^2 -10y +25

x+25 = (y-5)^2

Take the square root of each side

±sqrt(x+25) = y-5

Add 5 to each side

5±sqrt(x+25) = y

The inverse is  5±sqrt(x+25)

Answer:

[tex]y=\pm\sqrt{x+25}+5[/tex]

Step-by-step explanation:

Given function:

[tex]y=x^2-10x[/tex]

Rearrange to make [tex]x[/tex] the subject.

First, complete the square by adding 25 to both sides and factoring:

[tex]y+25=x^2-10x+25[/tex]

[tex]y+25=(x-5)^2[/tex]

Square root both sides:

[tex]\pm\sqrt{y+25}=x-5[/tex]

Add 5 to both sides:

[tex]x=\pm\sqrt{y+25}+5[/tex]

Finally, swap [tex]x[/tex] and [tex]y[/tex] (since the inverse of a function is its reflection in the line [tex]y = x[/tex])

[tex]y=\pm\sqrt{x+25}+5[/tex]

Answer:

39%

Step-by-step explanation:

[tex]\frac{3471}{8900}[/tex] converted to a percentage = 39%, or 0.39 in decimal form.

Answer:

The area is 155 ft.

Step-by-step explanation:

To find the area if a trapezoid, you have to add the number on top( in this case 13 ft) and then add that with the bottom number(18 ft.) Then, you take that answer and divide it by 2. After that, multiply it with the height(10.) Thus, the answer is 155 ft.

The computation of triangle ABC and ACD which are both isosceles shows that the value of x will be 36°.

It should be noted that the sum of angles in a triangle is 180°. In this situation two of the three angles have been given.

Therefore, the value of the third angle will be:

86° + 58° + x = 180°

144° + x = 180°

x = 180° - 144°

x = 36°

In conclusion, x is 36°.

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Answer:

y=-1.25x+45

Step-by-step explanation:

pick 2 points

(4,40) and (8, 35)

use y-y1=m(x-x1)

m=(35-40)/(8-4)=-1.25

y-40=-1.25(x-4)

y=-1.25x+5+40

y=-1.25x+45

Answer:

8.5

Step-by-step explanation:

because the hundredths place is not above 5

Answer:

N=21

Step-by-step explanation:

20-3+12/6x2=N

20-3+2x2=N

20-3+4=N

21=N

N=21

Answer:

p=4a

Step-by-step explanation:

Answer:

B no wrok needed

Step-by-step explanation: