A gas tank has a leak. Each hour it loses 3 gallons of gas. Write the equation that represents how much gas, g , the tank loses over h hours.

Answer:

✅ triangle

✅ pentagon

✅ hexagon

✅ trapezoid

❌ octagon

Step-by-step explanation:

The value of "a" is 2.

To find the value of "a," we can use the formula for the equation of a line, which is y = mx + b.

First, we need to find the slope, represented by "m," using the given points (-1, -5) and (4, 5). The slope formula is (y2 - y1) / (x2 - x1).

Substituting the coordinates, we have:

m = (5 - (-5)) / (4 - (-1))
m = 10 / 5
m = 2

Now that we have the slope, we can substitute it into the equation of the line with the point (a, 1):

1 = 2a + b

To solve for "a," we need to find the value of "b." We can substitute one of the given points into the equation and solve for "b."

Using (-1, -5):

-5 = 2(-1) + b
-5 = -2 + b
b = -3

Now we can substitute the values of "b" and "a" into the equation:

1 = 2a - 3

To isolate "a," we add 3 to both sides:

1 + 3 = 2a
4 = 2a

Dividing both sides by 2, we find:

2 = a

Therefore, the value of "a" is 2.

The correct answer is:

7.8 × 10⁷

Explanation:

To write a number in scientific notation, we want the decimal behind the first non-zero digit in the number. The first non-zero digit in 78 is 7; this means we want 7.8. In order to have the decimal point behind the 7, we need to move the decimal 7 places. This is the exponent of 10 in our scientific notation, which gives us

7.8 × 10⁷

Answer

It is 2 scoops

Step-by-step explanation:

3⁄8 x 1⁄4 = 3⁄32 quart

3⁄4 ÷ 3⁄32 = 8 scoops

Answer: [tex]1x^2+4x+3[/tex]

Step-by-step explanation: Given expression (x^3-x^2-17x-15)/(x-5).

We need to divide it x^3-x^2-17x-15 by x-5 using synthetic division .

In order to solve by synthetic division, we would write all the coefficients of given divisor polynomial:

And we divide them by 5 using synthetic division method.

             ______________          

      5    |     1   -1   -17   -15                       Getting first number down.

            |           5   20   -15                      Multiplying each down number by

           - - - - - - - - - - - - - - - -                    divisor 5.

                  1    4      3       0                     5×1=5  , 5×2=20, 5×2=15

                                                   Subtracting those products from coefficients.

Now, writing the final polynomial degree 1 less than 3, that is 2.

So, [tex]1x^2+4x+3[/tex] would be our quotient.                    

x = 24
y = 18
Length of Major Axis = a
Length of Minor Axis = b

Center (0, 0):

h = 0
k = 0

a = 1/2 x
a = 1/2 *(24)
a = 12
b = 1/2 y
b =1/2 (18)
b = 9
So, Equation of Ellipse:

General : (x - h)² / a² + (y - k)² / b² = 1

(x - 0)² / (12)² + (y - 0)² / (9)² = 1

x² / 144 + y² / 81 = 1


Focus = c:
        _____
c = √a² - b²
        _______
c = √(12)² - (9)²
        ______
c = √144 - 81 = sqrt63 = 7.9372

Focus : ( -7.9372, 0) and ( 7.9372, 0)

The correct answer is: a. 7.94 ft

Step 1

To find the distance from the center of the board to the foci of the ellipse that will result in the largest possible elliptical tabletop, we can use the formula:

[tex]\[ c = \sqrt{a^2 - b^2} \][/tex]

where:

- a is half the length of the major axis (which is half of the longer side of the rectangle)

- b is half the length of the minor axis (which is half of the shorter side of the rectangle)

Step 2

Given that the rectangle is 18 feet by 24 feet, [tex]\( a = \frac{24}{2} = 12 \)[/tex] feet and [tex]\( b = \frac{18}{2} = 9 \)[/tex] feet.

Step 2

Now, we can substitute these values into the formula:

[tex]\[ c = \sqrt{12^2 - 9^2} \]\[ c = \sqrt{144 - 81} \]\[ c = \sqrt{63} \][/tex]

Taking the square root of 63 gives us approximately 7.94 feet.

The average fuel efficiency rating, calculated by adding the mpg ratings and dividing by five, is 32.418 mpg, rounded to the nearest hundredth as 32.42 mpg. The answer is D. 32.42 mpg.

To find the average fuel efficiency rating of the top five models, we need to calculate the mean mpg rating. To do this, we add up all the mpg ratings and then divide by the number of models:

Add the fuel efficiency ratings together: 26.3 + 28.95 + 33.6 + 35 + 38.24.

The sum is 162.09 mpg.

Divide this sum by the number of cars, which is 5: 162.09 ÷ 5.

The average is 32.418 mpg.

To record the average to the appropriate degree of precision, we consider the place values of the original data provided. The given ratings include mpg values recorded to the nearest hundredth, as in 28.95 mpg and 38.24 mpg. This means the average should also be recorded to the nearest hundredth: 32.42 mpg. Therefore, the correct answer is D. 32.42 mpg.

Answer:

4 inches

Step-by-step explanation:

1 foot = 12 inches

45 feet --- 6 inches

From this we can conclude that the scale of the Blueprint is:

1 foot in actual = 1/90 foot on blueprint

If the girder is actually 30 feet long, then

30 feet --- (1/90*30*12) inches

30 feet --- 4 inches

divide completions by percentage

345 / 0.60 = 575 pass attempts

Answer:

An equivalent expression to 54+18x, using the distributive property is 18(3+x)

Step-by-step explanation:

In the problem we have the binomial (54+18x), and we are asked to use the distributive property, this means that we can find a factor wich is distributed in both terms of the binomial.

We know that any number, or in this case any polinomial (or binomial), can be multiplied times 1 and will stay the same number, and we only need to write this 1 in a way that could resolve our problem, in particular we can say that

[tex]1=\frac{18}{18}[/tex]

then we can distribute the denominator, so we calculate:

[tex](54+18x)=1(54+18x)=\frac{18}{18}(54+18x)=18(\frac{54}{18}+\frac{18x}{18})=18(3+x)[/tex]

And the equivalent expression to (54+18x) is 18(3+x).

1 mile = 5280 feet

 5280 * 2/3 =

5280 *2 = 10560

10560/3 = 3520

 it is 3520 feet long

In a standard deck of cards, there are a total number of 52 different card. From those 52 cards, 4 cards are numbered as five. Therefore the probability of selecting a card of five is:

Probability = 4 / 52 = 1 / 13

Assuming that no replacement is made, so the probability changes with each draw, since the total number of cards decreases from 52 to 51 to 50 and so on. Therefore this is not a simple event.

Answer:

D. [tex]6\pi\text{ cm}[/tex].

Step-by-step explanation:

We are asked to find the circumference of a a circle with a diameter of 6 cm.

We will use circumference of circle to solve our given problem.

[tex]C=\pi\cdot D[/tex], where,

C = Circumference of circle,

D = Diameter of circle,

Upon substituting [tex]D=6\text{ cm}[/tex] in above formula we will get,

[tex]C=\pi\cdot 6\text{ cm}[/tex]

[tex]C=6\pi\text{ cm}[/tex]

Therefore, circumference of our given circle would be [tex]6\pi\text{ cm}[/tex] and option D is the correct choice.

Solution:

The points at which Raquel Darts hit the coordinate grid having center at the origin are  (–5, 0), (1, –3), (4, 5), (–8, –6), (0, 2), and (9, 6).

As we can see that not all points are collinear.

As line of best fit is the the line which passes through some points , may be not through the single point, or all the points.

Plotting all the options on coordinate grid i.e on a scatter plot and then determining , the  line of best fit of the darts is

y= 0.6 x + 0.6 →→Option (A), the reason being it passes through a point (9,6).

Answer:

Look at the below steps.  

Step-by-step explanation:

We have been given two intersecting lines:

The given angles are vertically opposite angles:

[tex]2x+6=96[/tex]

On simplification we get:

[tex]2x=90[/tex]

On further simplification we get:

[tex]x=\frac{90}{2}[/tex]

[tex]x=45[/tex]

Hence proved that x=45.