David drives 210 miles a week for work. He fills his petrol tank twice a week. Each fill up is for 42 litres. Assuming he uses all of the petrol each week and only uses the car to travel to and from work, what is the mileage per litre of his car?

Final answer:

To find f(g(x)), substitute g(x) into f(x) and simplify the expression to get the final answer. The final answer to the question would be as f(g(x)) = 8x⁴ - 32x³ + 32x² + 3

Explanation:

To find the value of f(g(x)) the following steps to be followed where the value of f(x) be substituted in g(x).

f(x) = 2x² + 3; g(x) = −2x² + 4x

Find f(g(x)) by substituting g(x) into f(x): f(g(x)) = 2(-2x² + 4x)² + 3

Simplify the expression: f(g(x)) = 2(4x⁴ - 16x³ + 16x²) + 3

Final answer after expansion: f(g(x)) = 8x⁴ - 32x³ + 32x² + 3

Answer:

12 feet.

Step-by-step explanation:

A roller coaster climbs the height on first hill = 84 feet.

Then drops down = 60 feet.

Height gained by the roller coaster =  84 - 60

                                                         = 24 feet

On other hill roller coaster climbs = 32 feet

Height gained by the roller coaster = 24 + 32 = 56 feet.

It drops again to the height = 44 feet

So the final height at the second hill = 56 - 44

                                                            = 12 feet

Therefore, height of roller coaster on the second hill is 12 feet.

sandbox 1 area = 5*5 = 25 square m

sandbox 2

25=w*(3w+1)=

3w^2+w-25=0

w=2.7248 (round to 2.72 m)

2.72*3=8.16+1 = 9.16

Longest side = 9.16 meters

Answer:

C.) 9.16 meters

Step-by-step explanation:

We are given that the two sandboxes have same area and the equation is given by 25 = w*(3w+1).

Now, we simplify this equation in order to find the value of unknown variable 'w'.

i.e. 25 = 3[tex]w^{2}[/tex]+w

i.e. 3[tex]w^{2}[/tex]+w-25=0

The two factors of this quadratic equation are w=2.72 and w= -3.05.

But, as 'w' represents the length of the box, so it cannot be negative.

Therefore, w = 2.72

So, the longest side of the box is (3w+1) = 3*2.72+1 = 9.16 meter

Hence, the length of longest side to the nearest hundredth is 9.16 meter.

Which best describes the diameter of a circle?

Statements

A. The distance from the center to any point of the circle

This statement describes the radius of the circle

B. The length of a chord that contains the center of the circle

This statement describes the diameter of the circle

C. The distance around the circle

This statement describes the circumference of the circle

D. The length of a chord that does not contain the center of the circle

This statement describes a line segment linking any two points on a circle that does not contain the center of the circle

therefore

the answer is the option

B. The length of a chord that contains the center of the circle

The correct answer is:

B) The length of a chord that contains the center of the circle

Explanation:

A chord is a segment that goes across a circle, with both endpoints on the circle.

A diameter goes through the center of a circle and has both endpoints on the circle; this makes it a chord that goes through the center.

For a Polynominal 3x^4+4x^2-9x^-?+2 the missing part is mathematically given as

3x^4+4x^2-9x^-(-9)+2

-9, Option C is correct

Polynomials are summations of elements of the format of kxn, having k as any digit and n is +ve integer

Generally, the expression for the Polynominal  is mathematically given as

3x^4+4x^2-9x^-?+2

In conclusion, the Polynominal must have all positive exponents, hence the value must be negative to give a positive exponent

Hence, -9 is correct

Read more about Polynomial

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Answer:

A. It has two complex roots.

Step-by-step explanation:

We are given that

Discriminant of an equation =negative

We have to find which is  true about the equation .

Let quadratic equation

[tex]ax^2+bx+c=0[/tex]

Discriminant=[tex]D=b^2-4ac[/tex]

If D < 0 , then the equation has complex roots.

Therefore, if the discriminant of an equation is negative then the equation has two complex roots.

Answer:A. It has two complex roots.

The given equation is:

p(x) = x^2 + ax - b

We write this in terms of y:

y = x^2 + ax – b

To solve for the values of the constants a and b, we are given the following conditions:

When x = 6, y = -9

When x = 1, y = 16

From these conditions, we can formulate two equation by substituting the values of y:

-9 = 6^2 + a(6) – b

6a = b – 45                           ---> 1

16 = 1^2 + a(1) – b

a = b + 15                             ---> 2

Combining equations 1 and 2:

6 (b + 15) = b – 45

6b + 90 = b – 45

5b = -135

b = -27

calculating for a using equation 1:

a = b + 15

a = -27 + 15

a = -12

Answers:

a = -12

b = -27

f(x) = x-3

g(x) = 2f(x)

g(2)  = 2(2-3) = 2 * -1 = -2

1 cup = 0.25 quarts

52 *0.25 = 13 quarts

13 is the answer HOPE THAT HELPS

Answer:

It will cost approximately $71.360.

Step-by-step explanation:

Given,

The dimension of the concrete is 17 ft by 17 ft by 2 in.

1 ft = 12 inches ⇒ 2 inches = 1/12 × 2 = 1/6 ft.

Thus, the dimension of the concrete is 17 ft by 17 ft by 1/6 ft.

Now, the volume of the concrete = 17 × 17 × 1/6

[tex]=\frac{289}{6}\text{ cubic ft}[/tex]

We know that,

1 cubic yard = 27 cubic feet

[tex]\implies 1 \text{ cubic feet}=\frac{1}{27}\text{ cubic yards}[/tex]

[tex]\implies \frac{289}{6}\text{ cubic ft}=\frac{289}{6}\times \frac{1}{27} = \frac{289}{162}\text{ cubic yards}[/tex]

Since,  the concrete costs $40.00 per cubic yard.

Hence, the total cost of concrete = [tex]\frac{289}{162}\times 40=\frac{11560}{162}=\$71.3580247\approx \$71.360[/tex]

The total cost of concrete is,

C = $71.4

We have to give that,

Dimensions of the concrete are,

17 ft by 17 ft by 2 in.

And, the concrete costs $40.00 per cubic yard.

Since we know that,

1 feet = 12 inches

Hence,

2 inches = 2/12 = 1/6 feet

Thus, the dimension of the concrete is 17 ft by 17 ft by 1/6 ft.

So, the Volume of the concrete,

V = 17 x 17 x 1/6

V = 48.2 cubic feet

Here, 1 cubic yard = 27 cubic feet

And, the concrete costs $40.00 per cubic yard.

Hence, the total cost of concrete is,

C = 48.2 × 40 / 27

C = $71.4

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Final answer:

By applying the Pythagorean theorem and comparing the square of the longest side to the sum of the squares of the other two sides, it is determined that a triangle with sides of 9, 10, and 12 is an acute triangle since 144 is less than 181.

Explanation:

To determine whether a triangle with side lengths of 9, 10, and 12 is acute, obtuse, or right, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the lengths of the other two sides. If this condition is met, the triangle is right-angled. If the square of the longest side is greater than the sum of the squares of the other two sides, the triangle is obtuse. Conversely, if the square of the longest side is less than the sum of the squares of the other two sides, the triangle is acute.

For this triangle, the side lengths squared are:

Adding the squares of the two shorter sides: 81 + 100 = 181.

Since 144 < 181, the square of the longest side (12²) is less than the sum of the squares of the other two sides, indicating that this triangle is acute.

The sum of 7 and 9 is:

7 + 9 = 16

The sum which is 16 is greater than 12. Therefore we add 3 to the sum:

16 + 3 = 19

Therefore the correct answer to this problem is 19.

44 x 4 = 176

44 x 7 =308

44 x 8 = 352

44 x 28 =1232

 none of those will =432

 are you sure you have the right numbers?

(44)x=432

x=432/44 = 9.8181