Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. When graphed, the function gives a line
with a slope of 5.7. See the figure below.
With 46 gallons of fuel in its tank, the airplane has a weight of 2162.2 pounds. What is the weight of the plane with 18 gallons of fuel in its tank?

Answer:

Steps to find LCM

Find the prime factorization of 150

150 = 2 × 3 × 5 × 5

Find the prime factorization of 225

225 = 3 × 3 × 5 × 5

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

LCM = 2 × 3 × 3 × 5 × 5

LCM = 450

HCF of 150 and 225 by Prime Factorization

HCF of 150 and 225 by Listing the Common Factors

Method 1: Find HCF of 150 and 225 by Prime Factorization

Represent 8 and 14 as a product of its prime factors.

Prime factorization of 150 is 2 × 3 × 5 × 5

Prime factorization of 225 is 3 × 3 × 5 × 5

The common factor in the prime factorization of 150 and 225 are 3, 5, and 5.

HCF is the product of the factors that are common to each of the given numbers.

So, HCF of 150 and 225 is 3 × 5 × 5 = 75

Method 2: Find HCF of 150 and 225 by Listing the Common Factors

The factors of 150 and 225 are shown below.

Step-by-step explanation:

Hope it is helpful.....

Answer:

The amount is 5,955.08

Step-by-step explanation:

Here, we want to calculate compound interest

We can find this by using the compound interest formula

A = P( 1 + r/n)^nt

A is amount

P

is the principal = 5,000

r is the interest rate = 6% = 6/100 = 0.06

n is the number of times per year in which the interest is compounded = 1

t is the number of years = 3

Substituting these values;

A = 5,000(1 + 0.06/1)^3(1)

A = 5000(1.06)^3

A = 5,955.08

(-5,0)

Step-by-step explanation:

Numbers that lie on the x and y axis

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Answer:

40 [tex]\frac{5}{8}[/tex] [tex]cm^{3}[/tex]

Step-by-step explanation:

The figure is a rectangular prism, so the formula would be Volume = length x width x height.

length =  6 [tex]\frac{1}{2}[/tex] cm

width  =  2 [tex]\frac{1}{2}[/tex] cm

height  =  2 [tex]\frac{1}{2}[/tex] cm

If you plug everything you have in the problem into the volume equation, you would get : Volume = 6 [tex]\frac{1}{2}[/tex] cm x 2 [tex]\frac{1}{2}[/tex] cm x 2 [tex]\frac{1}{2}[/tex] cm.

Without a calculator, I would first turn the mixed numbers into improper fractions.

Volume = [tex]\frac{13}{2}[/tex] x  [tex]\frac{5}{2}[/tex] x  [tex]\frac{5}{2}[/tex]

When you multiply everything together you should get [tex]\frac{325}{8}[/tex].

As a mixed number, that would be 40 [tex]\frac{5}{8}[/tex] [tex]cm^{3}[/tex].

Answer:

The excluded value is x = 5/6

Step-by-step explanation:

Here, we want to calculate the excluded value

The excluded value is simply the value of x that will make the denominator of the fraction equals zero

We have this as;

6x -5 = 0

6x = 5

x = 5/6

Answer:

90 feet

Step-by-step explanation:

Answer:

Step-by-step explanation:

(2,4) is point lying on the line represented by 5x + 2y  = 18.

They are not intercepts.

x-intercept is point where the line crosses the x-axis and so, y-co ordinate at x-intercept is 0.

y-intercept is point where the line crosses they-axis and so,x-co ordinate at y-intercept is 0.

5x + 2y = 18

To find x-intercept, put y = 0 in the equation

           5x = 18

             x = 18/5

             x = 3.6

To find y-intercept, put x = 0 in the equation

          2y = 18

             y = 18/2

             y = 9

x-intercept : (3.6 , 0)

y-intercept :(0, 9)

Answer:

180 degrees in either direction

Step-by-step explanation:

picture it on a piece of paper, if you turn it once, the image becomes longer vertically, but if you flip it again, it looks like it does originally. If this is confusing, actually draw it and see how many times you need to rotate the page to make it look identical to the one you posted. 1 turn = 90 degrees.

Answer:

[tex]p^{4} s^{5} y^{-7} z^{-1}[/tex]

Step-by-step explanation:

[tex]\frac{1}{y^{7} } = y^{-7}[/tex]

[tex]\frac{1}{z} = z^{-1}[/tex]

Answer:

3.) it is a quadratic

4.) it is an absolute function

Step-by-step explanation:

3 has an exponent

4 has absolute values in it

Answer:

Step-by-step explanation:

Use the identity: a² - b² = (a + b)(a- b)

4 - 9w² = 2² - (3w²)

            = (2 + 3w)(2 - 3w)

Answer:

(-2,-3)

Step-by-step explanation:

A=(8,-5)

M=(3,-4)

The difference between them is that m is 5 to the left and 1 up. We need to do the same thing to find B.

B=(-2,-3)

Answer:

The first triangle can be solved using the triangle sum theorem.

There is a vertical angle, so 75 is the angle at the bottom left. 45 is also a vertical angle. Now we have 75+45+x=180, where x is the missing angle. x is 60.

A straight line = 180 degrees, so 60+79+y, where y is unknown, is equal to 180. y is 41. Now use the triangle sum theorem for the triangle to the right. 41+68+z, where z is unknown, = 180. Z is 71.

Now the last part is to find the question mark. A straight line is 180 degrees, so  71+"?" is 180. Simplify to find that "?" is 109.

Answer:

D. 157.5

Step-by-step explanation:

Formual for sum of interior angles

(n-2)*180

so 14*180=2520

but that is the sum

divide that by 16 (2520/16) = 157.5

Answer: 9 kilograms

Step-by-step explanation:

9 kilograms is larger because the kilogram, or kilogramme, is the base unit of weight in the Metric system. It is the approximate weight of a cube of water 10 centimeters on a side. While a gram is a unit of weight equal to 1/1000th of a kilogram. A gram is the approximate weight of a cubic centimeter of water.

Answer:

slope is 2

y-intercept is 3

equation y=2x+3

Step-by-step explanation:

Answer:

slope=4/2 or 2

y-intercept=3

equation=y=2x+3

the slope would be 4/2 because if you do the triangle method you see that the vertical distance of y is 4 and the horizontal distance of x is 2 so that gives you 4/2 the y intercept is where the line starts at 0 which you can see is 3. if the equation is y=mx+b you plug in the slope which is 4/2 or 2 and plug in the y-intercept which is 3 which gives you y=2x+3

At value of x=4

A pair of numbers that describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines  are called coordinates. General form of coordinate is (x, y)

From the graph we can see , coordinates of that point where both the lines are intersecting is (4, -3)

Because x coordinate is = 4

and y coordinate is = -3

At the value of x=4, the two lines intersect each other

Learn more about coordinate system :

https://brainly.com/question/4726772?referrer=searchResults

#SPJ2

Answer:

7.5

Step-by-step explanation:

Divide 3 by 2/5

3 divided by 2/5 = 7.5

Answer:

7.5

Step-by-step explanation:

when you do 2/5 it = 0.4 then you do 3/0.4 and you get 7.5

Answer:C

Step-by-step explenation: m=134kg,h=72m,g=10m/s

PE=mgh

PE=(134kg)(10m/s^2)(72m)

PE=964800J

Answer:

The answer is going to be C.

Step-by-step explanation:

To help you in the future with any question like this one, you can always use Desmos Calculator.

Answer:

x = 98

Step-by-step explanation:

If angle D is the center then

x + 4 = 2 × (x - 47)

x + 4 = 2x - 94

4 + 94 = 2x - x

98 = x

Answer:

20 292 02 202 202

Step-by-step explanation:

Answer:

60 miles

Step-by-step explanation:

1 hour=60 miles

1 hour=60 miles

Answer:

7/10

Step-by-step explana

7/10 was the answer

Answer:

7/10

Step-by-step explanation:

Answer:

Here is the answer bro

Answer:

the first one should be (0,-5)

the second should be (-2,1)

Step-by-step explanation:

You substitute the given value of y into your equation. 6x-y=5

6x-(-6x-5)=5

x=0

y=-6 * 0-5

y=-5

(x,y)=(0,-5)

AND

7x-6(4x+9)=-20

x=-2

y=4x(-2)+9

y=1

(-2,1)

hope this helps!