6. A gas tank holds 450 gal. when it is filled to the height of 12 ft. How many
gallons will it hold when it is filled to 5 ft.?

QUESTION 1

the solution is (-1,-5)

To verify the solution algebraically, we need to multiply the first equation with -1 and then sum them up

-y=5

y=3x-2

0=3x+3

3x=-3

x=-3/3

x=-1

Then, we use this value to find the other one

y=3x-2

y=3(-1)-2

y=-3-2

y=-5

Therefore, the solution is (-1,-5), which is the same showed graphically.

QUESTION 2.

Using the same process as we did in the QUESTION 1. The image attached shows both lines and the interception point which is the solution. So, the solution is (6,0).

To verify the solution algebraically, we must multiply the second equation by -6

x+6y=6

-6y=-2x+12

x=-2x+18

x+2x=18

x=18/3

x=6

Then, we use this value to find the other one

x+6y=6

6+6y=6

6y=6-6

y=0/6

y=6

Therefore, the solution is (6,0),

Answer:

1200 dollars

Step-by-step explanation:

x-0.16x=1008

.84x=1008

x=1200 dollars

Answer:

1.) Tan C = [tex]\frac{12}{5}[/tex]

2.) Sin Z = [tex]\frac{24}{26}[/tex] or [tex]\frac{12}{13}[/tex] if reduced

3.) Cos A = [tex]\frac{15}{17}[/tex]

4.) Cos A = [tex]\frac{12}{37}[/tex]

Step-by-step explanation:

Let's keep in mind that;

Sin = [tex]\frac{opposite}{hypotenuse}[/tex]

Cos = [tex]\frac{adjacent}{hypotenuse}[/tex]

Tan = [tex]\frac{opposite}{adjacent}[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

Let the goldfish be G.

• Let the betta fish be B.

Given the following data:

• Total number of fishes = 150 fishes.

• Ratio of G to B = 2:3

• Total ratio= 2 + 3 = 5

To calculate the number of goldfish that the pet store have:

What is ratio?

Ratio can be defined as an expression that is used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

Mathematically, the number of goldfish in the pet store is given by this expression:

2 G = x 150 5

G = 0.4 x 150

G = 60 fishes.

Answer:

C. m<1 = 82.5 m<2 = 97.5

Step-by-step explanation:

Answer:

1 and 25, 5 and 5

Step-by-step explanation:

because both 5×5=25 and 1×25=25 and 1×5=5 are all equal factor pairs of 25.

Answer:

2.08 %

Step-by-step explanation:

(36.75 - 36.00) / 36.00 = .0208  = 2.08 %

Let's see

Check coordinates

Find a

And

Put value from second one

Put in second one

So the equation is

Answer:

[tex]y=4(1.5)^x[/tex]

Step-by-step explanation:

General form of an exponential function: [tex]y=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Given ordered pairs:

(3, 13.5)  and  (5, 30.375)

As the y-values are increasing, the function is increasing, so b > 1

Input the given ordered pairs into the general form of the equation:

[tex]\implies ab^3=13.5[/tex]

[tex]\implies ab^5=30.375[/tex]

To find b, divide the second equation by the first:

[tex]\implies \dfrac{ab^5}{ab^3}=\dfrac{30.375}{13.5}[/tex]

[tex]\implies b^2=2.25[/tex]

[tex]\implies b=\pm \sqrt{2.25}[/tex]

[tex]\implies b= \pm 1.5[/tex]

As the function is increasing, b > 1:

⇒ b = 1.5  only

Substitute the found value of b into one of the equations and solve for a:

[tex]\implies a(1.5)^3=13.5[/tex]

[tex]\implies 3.375a=13.5[/tex]

[tex]\implies a=\dfrac{13.5}{3.375}[/tex]

[tex]\implies a=4[/tex]

Therefore, the final exponential equation is:

[tex]y=4(1.5)^x[/tex]

Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

See picture below for explanation:

Answer:

Acute triangle

Step-by-step explanation:

We will see that the cube must be 10.23 inches tall.

The volume of the cube must be equal to the volume of the 4 spheres. Remember that the volume of a sphere of radius R is:

V = (4/3)*3.14*R^3

In this case, the radius is 4 inches, so we can write:

V = (4/3)*3.14*(4 in)^3 = 267.95 in^3

Then the volume of the 4 spheres is:

4*267.95 in^3 = 1,071.79 in^3

The volume of a cube of side length S is given by:

V = S^3

Then we must have:

S^3 = 1,071.79 in^3

S = ∛(1,071.79 in^3) = 10.23 in

We conclude that the cube is 10.23 inches tall.

If you want to learn more about spheres, you can read:

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Answer:

C. m=1/2 and b=-4

Step-by-step explanation:

To get the slope-intercept notation, you have to convert Ax+By = C to y = mx + b. We can do that by simply moving y to the left side and the rest to the right, or simply use the formula of m = -A/B, b = C/B

We'll do both, they're the same really.

x-2y=8

x-8=2y

2y=x - 8

y = 1/2*x - 4

Alternatively

x-2y=8

A = 1

B = -2

C = 8

m = -(1/-2) = 1/2

b = 8/-2 = -4

Answer:

father = 32    s = 5 y/o

Step-by-step explanation:

f s = 160  ====>   s = 160/f

f+4 = 4 ( s+4)  

f + 4 = 4 (160/f +4)

f + 4 = 640/f + 16

f^2 + 4f = 640 + 16 f

f^2 -12f - 640 = 0      Use Quadratic formula to find  f =  32   then s = 5

In the research, the distribution is described by its shape. If there are more higher values than lower values, the distribution is skewed left.

It should be noted that when the distribution of data is skewed to the left, the mean is less than the median.

The distribution can be described by its center. If the distribution is skewed left or right, the median is an accurate measure of center.

The distribution can be described by its spread. If the data set does not have an outlier, the interquartile range is an accurate measure of spread.

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Answer:

left, median, and range or the IQR

Step-by-step explanation:

Answer:

2?

Step-by-step explanation:

Answer:

A = 12 ft

Step-by-step explanation:

Perimeter ( of SQUARE) B = 64

  then each side = 64/4 = 16

AREA of SQUARE C = 400

    side X side = 400

        then side = sqrt 400

Now use Pyhtagorean Theorem to find leg of right triangle that is

   side A  Side B  hypotenuse Side C

A^2 + 16^2 = (sqrt 400)^2

A^2 = 400 - 256

A^2 = 144       then A = 12  Ft

Answer:

A translation and then a reflection

Step-by-step explanation:

A translation of 5 to the left, and then a a reflection across the x axis.

Here,

8x + y = 23 - 10x - y = - 27

10(8x + y) = 23 × 10 8 (- 10x - y) = - 27 × 8

80x + 10y = 230 ---> (i) - 80x - 8y = - 216 ----> (ii)

(80x + 10y) - (-80x - 8y) = 230 - (-216)

=> 80x + 10y + 80x + 8y = 230 + 216

=> 10y + 8y = 446

=> 18y = 446

=> y = 446/18

=> y = 24.7

80x + 10y = 230

=> 80x + 10 × 24.7 = 230

=> 80x + 247 = 230

=> 80x = 230 - 247

=> 80x = -17

=> x = -17/80

=> x = - 0.21

x = -0.21 and y = 24.7

Answer:  I'm pretty sure the measure is 122 degrees

Step-by-step explanation:

Answer:

[tex] \sf \: \fbox{Option C) \: The salary of B is 6000₹}[/tex]

Step-by-step explanation:

Let the salary or A is x and salary of B is y.

now,

Condition one,The sum of 3/4th of A’s salary and 5/3rd of B’s salary is ₹16,000.

writing above statement in equation form,

[tex] \sf \frac{3x}{4} + \frac{5y}{3} = 16000[/tex]

Multiplying above equation with twelve,

[tex] \sf \frac{3x}{4} + \frac{5y}{3} = 16000 \\ \sf \frac{12 \times 3x}{4} + \frac{12 \times 5y}{3} = 16000 \times 12 \\ \sf \fbox{9x + 20y = 192000} \rightarrow eq. 1[/tex]

and condition two,

The difference of their salaries is ₹2000

[tex] \sf \: x - y = 2000[/tex]

Multiplying above equation with 20

[tex] \sf \fbox{\: 20x -20y = 40000} \rightarrow eq.2[/tex]

On adding equation 1 and equation 2,

[tex] \sf9x + \cancel{20y} = 192000 \\ \sf 20x - \cancel{20y} = 40000 \\ \hline \sf 29x + 0y = 232000 \\ \sf x = \frac{232000}{29} \\ \sf \: \fbox{x = 8000₹}[/tex]

Substituting the value of x in,

[tex] \sf \: x - y = 2000 \\ \sf \: 8000 - y = 2000 \\ \sf \: y = 8000 - 2000 \\ \sf \fbox{y = 6000₹}[/tex]

[tex] \sf \: \fbox{The salary of B is 6000₹}[/tex]

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The equation that models the number of female eastern bluebirds observed, b,  and t, the total number of eggs laid is t = 5b

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

y = mx +c

To find the slope of a line, we find the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.

Let we take:

b = the number of female eastern bluebirds observed

t = the total number of eggs laid

Since the relationship between b and t is forming a line, so it can be modeled by linear equation.

Here, we take 'b' as independent variable,  and the value of 't' depending on the value of 'b', and therefore, let the linear equation representing them is:

[tex]t = mb + c[/tex]

For this case, we see that as the number of female eastern bluebird is increased by 1, half of 10 units (which is 5 units) is increased in the total number of eggs laid.

Thus, as we increase 'b' by 1 unit, there is increase by 5 units in the value of 't'.

and therefore, we get: m = increment in dependent variable per unit increment in independent variable = 5

Thus, the equation is:

[tex]t = 5b + c[/tex]

At b = 1, the number of eggs laid is 5, or t = 5, therefore, putting these values in the equation, we get:

[tex]5 = 5(1) = c\\c = 5-5=0[/tex]

Thus, the relation between t and b is t = 5b + 0= 5b

Thus, the equation that models the number of female eastern bluebirds observed, b,  and t, the total number of eggs laid is t = 5b

Learn more about linear equations here:

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Answer:

0

Step-by-step explanation:

(x,y)      slope is change in y / change in x⇒  Δy/Δx

(6,2)

(-18,2)

Δy = 2-2 = 0

Δx = 6-(-18) = 24

because the y values are the same, when you subtract you a slope of 0/24 or just 0 a horizontal line (because y is always =2)

Answer:

56n thats what ben said

Step-by-step explanation:

hohoho corent answer

Answer:

1/3 or 33.3333...%

Step-by-step explanation:

My understanding of this situation is that each dial represents a number in the combination. In order for the combination to start with 8, the first dial needs to land on 8. Since there are three numbers on the dial, the probability that the combination starts with 8 is 1/3. Hope I helped :)

Answer:

-64

Step-by-step explanation:

-4x-4x-4

Answer:

(5) 122 feet

Step-by-step explanation:

Perimeter of fencing:

[tex]2((25 + 4 + 4) + (20 + 4 + 4))[/tex]

[tex]2(33 + 28) = 2(61) = 122[/tex]

Answer:

21.6666666667

If you have to round it up it is 22.

Step-by-step explanation:

If he runs 5 times a week and his route is 4 1/3 then he runs that five times a week you do 5x4 1/3 and that is how you get your answer

Answer:

Step-by-step explanation:

Beth's position over time is constant, which makes the problem a lot easier. You are asked for the rate of position versus time, so begin by doing that. Since the rate is constant, clearly from the table, you can take any two data points and take their ratio. Her rate would be 11 feet every 5 seconds, or equivalently 2.2 feet every second. To graph the data, put position on the y-axis and time on the x-axis. The slope will be 2.2 at every point along her bike ride.

Moving on to the third part. If Amy traveled at a rate of 75 feet every 30 seconds, then she would be traveling 2.5 feet every second. Amy's rate is larger than Beth's rate. Since the rate corresponds to the slope of the postion vs. time graph, Amy's graph will have a steeper incline since the slope is 2.5

Lets see

Answer:

thanks just needed points

Step-by-step explanation:

The mark up price of the shoe would increase the final price

The given parameters are:

The final price is calculated using:

Final = Cost * (1 + Mark up)

This gives

Final = 245* (1 + 5.75%)

Evaluate

Final = 259.0875

Hence, the final price of the shoe is $259.0875

In (a), we have:

Final = 259.0875

Given that the tax is 5 3/4%, the final price after tax would be

After tax = Final * (1 + Tax)

So, we have:

After tax = 259.0875 * (1 + 5 3/4%)

Evaluate

After tax = 273.98503125

Hence, the final price of the shoe after tax is $273.98503125

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