Two tankers contain 850 litres and 680 litres of kerosene oil respectively. find the maximum capacity of a container which can measure the kerosene oil of both the tankers when used an exact number of times

The slope of the line that passes through the points (-9, 0) and (−17,4) is -2

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.

The formula to calculate slope is -

m = x2 - x1 / y2 - y1

(-9, 0) and (−17,4)

m = -17 + 9 / 4 - 0

m = -8/4

m = -2

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The solution to the expansion of each polynomial is;

1. (x + 9)(x² - 9x + 81) = x³ + 729

2. (y² - 7)(y⁴ - 7y² + 49) = y⁶ − 14y⁴ + 98y² - 343

3. (x² - 5)(x⁴ + 5x² + 25) = x⁶ - 125

4. (8x - 9y)(64x² + 72xy + 81y²) = 512x³ - 729y³

5. (10m - 11) (100m² + 110m + 121) = ​1000m³ - 1331

1) We want to expand the polynomial;

(x + 9)(x² - 9x + 81)

= x³ + 729

2) We want to expand the polynomial;

(y² - 7)(y⁴ - 7y² + 49)

Multiplying out gives;

y⁶ −7y⁴ + 49y² −7y⁴ + 49y² - 343

Combining like terms gives;

y⁶ − 14y⁴ + 98y² - 343

3) We want to expand the polynomial;

(x² - 5)(x⁴ + 5x² + 25)

Multiplying out gives;

x⁶ - 125

4) We want to expand the polynomial;

(8x - 9y)(64x² + 72xy + 81y²)

Multiplying out gives;

512x³ - 729y³

5) We want to expand the polynomial;

(10m - 11)(100m² + 110m + 121)

Multiplying out gives;

1000m³ - 1331

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Answer:

k = -4

Step-by-step explanation:

8 = 2k - 8 - 6k

Collect like terms

8 = -4k - 8

Add 4k to both sides (nice to have variable on left, constants on right)

8 + 4k = -8

Subtract 8 from both sides

4k = -16

Divide both sides by 4

k = -4

Thus, 36° is the smaller angle and 144° is the greater angle.

For instance, the complement angle of 130° and the angle of 50° is 180°. Complementary angles add up to 90 degrees. When the two extra angles are combined, they create a straight line and an angle. The two angles that complement one another do not necessarily need to be close to one another, it should be emphasised. As a result, two angles may be supplementary if their sum is 180 degrees. The study of various shapes is one of the main areas of mathematics.

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Answer:

Step-by-step explanation:

Answer:

0.153 or 15.3%

Step-by-step explanation:

Subtract save percentage last season from save percentage this season:

0.738 - 0.585 = 0.153

Convert the decimal answer to a percent

0.153 x 100% = 15.3%

Step-by-step explanation:

5/8 = y/3

(5/8) times 3 = 15/8

y=15/8

or

y = 1 and 7 over 8

or y = 1.875

Answer:

2 1/3 :)

Step-by-step explanation:

Answer:

g(-6) = -6

g(0) = 5

g(7) = 8

h(-6) = 10

h(0) = -1

h(7) = -4

Step-by-step explanation:

g(x) = (1/3) f(x)

g(-6) = (1/3)(-18) = -6

g(0) = (1/3)(15) = 5

g(7) = (1/3) (24) = 8

h(x) = -g (x) + 4

h(-6) = -(-6) + 4 = 10

h(0) = -(5) + 4 = -1

h(7) = -(8) + 4 = -4

I hope this helps!

Answer:

$45

Step-by-step explanation:

100% = $75

100% - 40% = 60% (discounted price)

60% = 0.6

0.6 x 75 = 45

60% = $45 (discounted price)

Answer:

5

Step-by-step explanation:

Answer:

7.8

-7.9

-17.40

1. 5.6

-2. 17.18

-5. 7.12

.8 15.22

Step-by-step explanation:

The statement that a function is decreasing on an interval if the output values decrease as the input values decrease is FALSE.

A decreasing function refers to a function where the value of the output moves in a different direction from the value of the input.

For instance, in a decreasing function, the value of the output would decrease when the value of the input increases.

In conclusion, it is false that a function is decreasing if the output and the input are both decreasing.

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Answer:

∉

Step-by-step explanation:

10 is not a member of the set {6, 8, 13, 14} and ∉ is used to represent "not a member of"

Answer:

B ( if you talking about Mathematics enhancement )

Step-by-step explanation:

First one make the statement true but ( 6, 8, 13 ,14 ) didn't related to 10 According to a pattern

Answer:

see explanation

Step-by-step explanation:

f(x) × g(x)

= 3x(4x - 1) ← distribute parenthesis by 3x

= 12x² - 3x

when x =  1 , then

= 12(1)² - 3(1) = 12(1) - 3 = 12 - 3 = 9

Answer:

-1

Step-by-step explanation:

Tn = a+(n-1)d (general formula)

Tn = 8-n (given formula)

T9 =8-9

T9=-1

Answer:

C. 73.5lbs

Step-by-step explanation:

The quadratic equation to model the graph is y = x² - 6 · x + 14.

The picture presents us the graph of a parabola, whose algebraic expression is a quadratic equation. In accordance with fundamental theorem of algebra, a quadratic equation can be derived by knowing three distinct points on Cartesian plane.

If we know that (x, y) = (0, 14), (x, y) = (3, 5) and (x, y) = (6, 14), then the coefficients of the quadratic equation in standard form:

14 = c                                       (1)

5 = 9 · a + 3 · b + c                  (2)

14 = 36 · a + 6 · b + c              (3)

The solution of the system of linear equations is (a, b, c) = (1, - 6, 14). Hence, the quadratic equation to model the graph is y = x² - 6 · x + 14.

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Answer:

Step-by-step explanation:

{(0, 2), (1, –1), (2, 3), (3, –2)}

Answer:basically, x never reats with a different y

(x,y)

A is a fn of x since x never repeats

B is a fn of x since x never repeats

C is a fn of x since x never repeats

D is not since we have (1,2) and (1,-2) so this is the answer

Step-by-step explanation:

The degree of the polynomial formed is 6.

The degree of a polynomial is the highest degree of the variables present with non-zero coefficients.

For example the polynomial has three 7x³y²+9xy+4 terms. The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5, which is the highest degree of any term.

Now the given functions are:

[tex]f(x)=x^3[/tex] ,g(x)=3x²-1 and h(x)=2x

Now we have to find (f ° g° h)(x). Let us first find (g°h)(x).

(g°h)(x) is equal to g[h(x)]

=g[2x+5]

=3(2x+5)²-1

=3(4x²+20x+25)-1

=12x²+60x+74

Now we find (f ° g° h)(x)

(f ° g° h)(x)=f[g(2x+5)]

f[g(2x+5)]=f(12x²+60x+74)

f(12x²+60x+74)=(12x²+60x+74)³

Now we have to simplify the expression:

(12x²+60x+74)³

=[tex]1728x^6+25920x^5+161568x^4+535680x^3+996336x^2+985680x+405224[/tex]

The largest degree of the variable x in the polynomial is 6.

hence the degree of [f o go h](x) is 6.

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Answer: she could buy 10 cookies.

Step-by-step explanation:

In order to figure out how many cookies she can buy just do 20÷2.

Answer: 1:8

Step-by-step explanation:

13 tables

104 chairs

Ratio: 13:104

divide both sides by 13

13:104 = 1:8

[tex]\displaystyle\\Answer: \frac{400}{93}\approx4.3[/tex]

Step-by-step explanation:

[tex]\displaystyle\\4:0.93=\\\\\frac{4}{0.93 }=\\\\\frac{4}{\frac{93}{100} } \\\\\frac{4*100}{93} \\\\\frac{400}{93} \approx\\\\4.3[/tex]

The third angle of 16 degrees and 102 degrees is 62 degrees.

The third angle of 119 degrees and 23 degrees is 38 degrees.

The third angle of 28 degrees and 87 degrees is 65 degrees.

The third angle of 96 degrees and 51 degrees is 33 degrees.

A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees

In order to determine the missing angle, subtract the sum of the two given angles from 180.

180 - (16 + 102) = 62

180 - (119 + 23) = 38

180 - (28 + 87) = 65

180 - (96 + 51) = 33

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Answer: −8n+3+n+11

Add the terms

−7n+3+11

Solution

−7n+14

Step-by-step explanation: hope this helps

the area covered by the light of the lighthouse is given by: A = πx²

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

Area of a circle having r as radius = πr²

Given: The revolving light beam that extends to the pier.

Let the distance to the pier x.

Typically, the rotating beam rotates 360 degrees.

Therefore, Its motion is circular.

The mathematical formula for the area that the light covers is: A = πx²

Hence, the area covered by the light of the lighthouse is given by: A = πx²

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Answer:

Step-by-step explanation:

(x+4) = -6

x + 4 + 6 = -6 + 6

x = 10

The greatest possible value of A + B is 600000.

The smallest possible value of A + B is 600000.

The greatest possible value of A - B is 0.

It should be noted that from the information, A and B are integers.

A = 300,000 to the nearest 100,000

B = 300,000 to the nearest 10,000

Therefore, the greatest possible value of A + B will be:

= 300,000 + 300,000

= 600000.

The smallest possible value of A + B is also, 600000.

The greatest possible value of A - B will be:

= 300,000 - 300,000

= 0.

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