Trina's car uses 12 gallons of gas to travel 144 miles. If she has 6 gallons of gas in the tank, how much more gas will she need to drive 240 miles?

The equation of the line is y=-1/5x+4/5.

Calculating m, the slope we subtract two of the points,

(-1, 1)

(4, 0)

This equals 0-1/4+1, which simplifies to -1/5

The slope is -1/5 and we can put that into the slope-intercept form along with a point to get b, the y-intercept.

So, y=-1/5x+b

Substituting x and y with a point.

1=-1/5(-1)+b

1=1/5+b

b=4/5

So, the equation is y=-1/5x+4/5.

The equation of a line is a single illustration of numerous points on the line. the general form of the equation of a line is of the form ax + via + c = zero and any factor on the road satisfies this equation. these two minimal requirements to shape the equation of a line are the slope of the road and a factor on the line.

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Answer:

19+d=234

Step-by-step explanation:

"increased by d" is addition. "is" is equal. So Putting these together it would be 19+d=234.

Hope this helped!

For this case we have that by definition, the discriminant of a quadratic equation [tex]ax ^ 2 + bx + c = 0[/tex], is given by:

[tex]d = b ^ 2-4 (a) (c)[/tex]

[tex]d> 0[/tex]: Two different real roots

[tex]d = 0[/tex]: Two equal real roots

[tex]d <0[/tex]: Two different complex roots

If we have [tex]9x ^ 2 + 12x + 4 = 0[/tex], then:

[tex]a = 9\\b = 12\\c = 4[/tex]

Substituting the values:

[tex]d = 12 ^ 2-4 (9) (4)\\d = 144-144\\d = 0[/tex]

Thus, we have two equal real roots.

ANswer:

We have two equal real roots.

Answer:

A

Step-by-step explanation:

y = log3(x) – 1

I don't know why but this is the correct answer.

[tex]y = \log_{3}x - 1[/tex] is the equation with real zeros corresponding to the x-intercepts of the graph.

According to the statement, we must find a function such that all values of [tex]x[/tex] so that [tex]y(x) = 0[/tex] and are the same of the graph. A quick approach consists in solving on each expression:

[tex]\log_{3}x-1 = 0[/tex]

[tex]\log_{3}x = 1[/tex]

[tex]x = 3[/tex]

[tex]3\cdot x - 3 = 0[/tex]

[tex]3\cdot x = 3[/tex]

[tex]x = 1[/tex]

[tex]-3\cdot (x-1) + 3 = 0[/tex]

[tex]-3\cdot x +6 = 0[/tex]

[tex]x = 2[/tex]

[tex]\log_{3}2x - 2 = 0[/tex]

[tex]\log_{3}2x = 2[/tex]

[tex]2\cdot x = 9[/tex]

[tex]x = \frac{9}{2}[/tex]

Hence, we conclude that [tex]y = \log_{3}x - 1[/tex] is the equation with real zeros corresponding to the x-intercepts of the graph. [tex]\blacksquare[/tex]

The graph is missing and all functions are poorly formatted. Correct statement is shown below:

Which equation has real zeros corresponding to the x-intercepts of the graph?

A. [tex]y = \log_{3} x - 1[/tex]

B. [tex]y = 3\cdot x -3[/tex]

C. [tex]y = -3\cdot (x-1) + 3[/tex]

D. [tex]y = \log_{3}2x -2[/tex]

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Answer:

true is the answer off this question

Answer:

True

Step-by-step explanation:

3n would mean 3 times n where 3 is the coefficient.

Answer: 47

Step-by-step explanation:

Answer:

47 is the answer

Step-by-step explanation:

The measure of angle b is 25°.

Solution:

Given data:

The "L" shape angle is a right angle.

Right angle is splitted by another line and two angles are formed.

One angle is 65° and the other angle is b.

Let us find the other angle b.

65° + m∠b = 90°

Subtract 65° from both sides of the equation.

m∠b = 90° – 65°

m∠b = 25°

Hence the measure of angle b is 25°.

Answer:

15/6 or 2.5

Step-by-step explanation:

Step 1:  Convert words into an expression

The value of 3over2 + 3over3 = ___.

3/2 + 3/3 = ?

Step 2:  Make common denominators

3/2 * 3/3 = 9/6

3/3 * 2/2 = 6/6

Step 3:  Add

9/6 + 6/6

15/6

Answer:  15/6 or 2.5

Answer:

The polygon has 9 sides

Step-by-step explanation:

we know that

A regular polygon has equal length sides and equal interior angles

step 1

Find the measure of the interior angle

Remember that

The interior angle plus the exterior angle must be equal to 180 degrees (form a linear pair)

Let

x ----> the measure of each interior angle in the regular polygon

so

[tex]x+40^o=180^o[/tex]

solve for x

[tex]x=180^o-40^o=140^o[/tex]

step 2

Find the number of sides of the regular polygon

we know that

The measure of each interior angle in a regular polygon is given by the formula

[tex]x=\frac{(n-2)180^o}{n}[/tex]

where

n is the number of sides of the polygon

substitute the given values

[tex]140^o=\frac{(n-2)180^o}{n}[/tex]

solve for n

[tex]140n=180n-360\\180n-140n=360\\40n=360\\n=9\ sides[/tex]

therefore

The polygon has 9 sides

Answer:

The equation of the line is y=1x and I will show you a picture of a graph with your points and a line of that equation.

Step-by-step explanation:

Answer:

59,000

Step-by-step explanation:

That is scientific notation, as used in a calculator, for example, to mean

5.9 * 10^4

5.9 * 10^4 = 5.9 * 10,000 = 59,000

Answer:

a) : (2,0), (3,0), (-5,0)

Step-by-step explanation:

(x - 2)(x - 3)(x + 5)=0 (y=0)

x-2=0, x-3=0, x+5=0

x=2, x=3, x=-5

x-intercepts: (2,0), (3,0), (-5,0)

Answer:

119

Step-by-step explanation:

Hope this helps! Brainliest is appreciated.

Answer:

8.166666666666666666666666666666666666666666

Step-by-step explanation:

Answer:

x=0 and y=2/3

Step-by-step explanation:

Multiply top equation by 2 -> 4x+6y=4

Cancel out the "6y"s by elimination -> 3x=0

Divide both sides by 3 -> x=0

Plug x=0 into x+6y=4 to get y -> 0+6y=4 -> 6y=4 -> y=4/6=2/3

So x=0 and y=2/3

Answer:

55

Step-by-step explanation:

For the mean you add together all of the values, and then divide the sum by the number of digits there are.

23+91+83+31+49+11+60+92 = 440

440/8 = 55

23 + 91 + 83 + 31 + 49 + 11 + 60 + 92 = 440/8 = 55

Mean: 55.

Answer:

Step-by-step explanation:

r=√((4-1)²+(2+2)²)=√(9+16)=5

area of circle=π r²=3.14×5²=78.50=78.5

The area of the circle is found by calculating the radius using the distance formula and then applying the formula A = πr². Using the common approximation of π as 3.14, the area is found to be approximately 78.5 square units when rounded to the nearest tenth.

The first step in finding the area of the circle is to determine its radius. The radius can be found by calculating the distance between the center of the circle, C (1, -2), and a point on the circle, (4, 2). Using the distance formula, we get the radius r = √((4-1)² + (2-(-2))²)} = √{(3)² + (4)²} = √{9 + 16} = √{25} = 5 units. Next, we use the formula for the area of a circle, which is A = πr². Substituting the radius in, we find A = π(5)² = 25π. The approximation on the circle for π is 3.14, thus the area of the circle is approximately A = 25 * 3.14 = 78.5 square units, which should be rounded to the nearest tenth.

It is also noteworthy that any approximation on the circle may vary slightly depending on the value chosen for π, but using 3.14 is commonly accepted for most calculations. So our final answer is, rounding to the nearest tenth, the area of the circle is approximately 78.5 square units.

Answer:

Step-by-step explanation:

As the two figure are the image and pre-image of a dilation.

Considering the left sided triangle is original and right sided triangle ( smaller one) is the image.

As one of the sides of the left triangle (original figure) is 4 in. And the corresponding length of the side on the right triangle (image of the figure) is 2 in.

It means the image of the side (2 in) is obtained when the side (4 in) of the original object is dilated by a scale factor of 1/2. In other words, the side of the image (2 in) is obtained multiplying the side (4 in) of original figure by 1/2. i.e. 4/2 = 2 in

Lets determine the missing side of the right side triangle by the same rule.

As the original object has one of the sides is 5 in and the corresponding side of the image has x in. As the original figure is dilated by a scale factor of 1/2. so the missing side of x will be: x = 5/2 = 2.5

So, the value of x will be 2.5

Similarly, the original object has one of the sides with length (y + 1 in). As the As the original figure is dilated by a scale factor of 1/2. As the corresponding length of the side of the image triangle is 3 in.

so

y + 1 = 2(3)         ∵ 3 in (image side) is multiplied by 2

y + 1 = 6

y = 6 - 1

y = 5

So, the value of y = 5

Therefore,

Answer:5.5

6

Step-by-step explanation:

To find the value of k that makes the equation true, we can start by expanding both sides of the equation. Then, rearrange the equation to isolate the terms with a on one side and the terms with b on the other side. Finally, solve for k to find the value that makes the equation true.

To find the value of k that makes the equation true, we can start by expanding both sides of the equation:

12a + 9b = k(2a + 32b)

12a + 9b = 2ka + 32kb

Next, we can rearrange the equation to isolate the terms with a on one side and the terms with b on the other side:

12a - 2ka = 32kb - 9b

This simplifies to:

(12 - 2k)a = (32k - 9)b

To make this equation true, the coefficient of a must be equal to the coefficient of b. Therefore, we can set up an equation:

12 - 2k = 32k - 9

Solving for k:

12 + 9 = 32k + 2k

21 = 34k

k = 21/34

Therefore, the value of k that makes the equation true is 21/34.

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We want to find the total capacity of the mug given that we know how much liquid there is in a 2/3 full mug.

We will find that the capacity of the mug is 1.25 cups.

We know that when the mug is 2/3 full, it has 5/6 cups.

Then if we define C as the total capacity of the mug, we can write:

(2/3)*C = 5/6 cups.

Now we can solve the above equation for C:

C = (3/2)*(5/6) cups = 1.25 cups.

The capacity of the mug is 1.25 cups.

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Answer:

Step-by-step explanation:

sodas ----x

hot dogs ---- y

x = 2y

x+y = 192

2y + y = 192

3y=192

y = 64

64 hotdogs and 128 sodas

Answer:

25%

Step-by-step explanation:

Sugar Syrup = 40 grams

10 grams / 40 grams = 1/4

1/4 = 25%

Answer:

40 grams of 25% sugar syrup

Step-by-step explanation:

Answer:

m= y/x

Step-by-step explanation:

The equation to find the slope (m) is to determine 2 points then divide the difference of y-coordinates with the x-coordinates.

The equation will look like this:

m= (y2-y1)/(x2-x1)  

When a function goes through the origin(0, 0), that means the line doesn't have c variable, the equation of the line will be as simple as y=mx

Then the equation to find the slope(m) will be:

y=mx

m=y/x

You can directly divide y-coordinate with x-coordinate to find the slope.

Answer:$1.33

Step-by-step explanation: What I did is I subtracted the 46 dollars in donations from the total they raised on day 1 to get the amount for just the cookies $150. Then I added the amount of the 2 total of cookies sold = 200. Then, I took the amount of cookies sold and divided it by the amount they made selling the cookies = 1.33. 200 ÷ 150 = 1.33

I hope this helps

Answer:

18 yards

Step-by-step explanation:

6+5+3+4= 18

Answer:

g(3)=34

Step-by-step explanation:

Just plug in 3 for x:

4(3)^2-3(3)+7

4(9)-9+7

36-9+7

27+7

34

So g(3)=34

Answer:

5/9 pounds or rounded 0.5555... pounds

Step-by-step explanation:

Step 1:  Make an equation

5 / 9 = x

Step 2:  Solve

5 / 9 = x

5/9 pounds or rounded 0.5555... pounds

Answer: 5/9 pounds or rounded 0.5555... pounds

Answer:

5/9 of a pound

Step-by-step explanation:

5 pounds of clay is divided into 9 equal pieces

5 ÷ 9

This can be written as a fraction

5/9

Each block weighs 5/9 of a pound

Hope this helps :)

Answer:

Joyce has total 62 colored beads.

Step-by-step explanation:

For making groups of 9, let the number of beads be x.

total beads = 9x + 8

For making groups of 8, let the number of beads be y.

total beads = 8y + 6

As the total number of beads in both cases are same so,

   9x + 8= 8y + 6

or, 9x-8y = -2

Now lets check the values through hit and trial;

First check; x=6, y=7

   9*6 - 8*7 = -2

or, 54- 56 = -2

or, -2 =-2

This satisfies our equation.

Hence; Total beads = 9*6 + 8 = 62

The total number of beads joyce had is 62.

Number of beads she have is 62 .

Step-by-step explanation:

Here we have , joyce has between 25 to 75 colored beads. when she makes them into groups of 9, 8 beads are left out. when she groups into groups of 8, We need to find how many beads are left . Let's solve this:

when she makes them into groups of 9, 8 beads are left out equation is

[tex]9x+8[/tex]

when she groups into groups of 8 , 6 beads are left out, equation is

[tex]8y+6[/tex]

Equating both equation's we get:

⇒ [tex]9x+8 = 8y+6[/tex]

⇒ [tex]9x-8y = -2[/tex]

By hit & trial method , we put x = 6 & y=7:

⇒ [tex]9(6)-8(7) = -2[/tex]

⇒ [tex]54-56= -2[/tex]

⇒ [tex]-2= -2[/tex]

Since , LHS = RHS x = 6 & y=7 satisfies the equation [tex]9x+8 = 8y+6[/tex] . So putting value of x=6 in [tex]9x+8[/tex] we get:

⇒ [tex]9x+8[/tex]

⇒ [tex]54+8[/tex]

⇒ [tex]62[/tex]

Therefore, Number of beads she have is 62 .

Answer:

500

Step-by-step explanation:

450/90 × x/100

how to solve x

100÷90=1.11111111111

1.11111111111×450

Answer:1 5/12

Step-by-step explanation:

3 4/6 - 2 1/4

Change to improper fraction we have

22/6 - 9/4

(2x22-3x9)/12

(44-27)/12

17/12=1 5/12

Answer:

1 5/12

Step-by-step explanation:

3 4/6 - 2 1/4

3 2/3 - 2 1/4

11/3 - 9/4

Lcm is 12

(11×4 - 9×3)/12

(44 - 27)/12

17/12

1 5/12