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2 years ago

H(x) = ax^2 +1 Find the value of a when h(-2) = 21.

Mathematics

1 answer:

blagie [28]2 years ago

4 0

Answer:

$a = 5$

Step-by-step explanation:

Solving $h(-2) = 21$ :

$h(-2) = 21 \\ a(-2)^2 +1 = 21 \\ a(4) +1 = 21 \\ 4a +1 = 21 \\ 4a +1 -1 = 21 -1 \\ 4a = 20 \\ \frac{4a}{4} = \frac{20}{4} \\ a = 5$

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A circular pond 24 yd in

Schach [20]

Answer:

The walk will cost $8164.

Step-by-step explanation:

Given:

Diameter of the circular pond (D) = 24 yd

Width of the gravel path (x) = 2 yd

Cost per yard of the path = $50

Now, radius of the circular pond is half of the diameter and is given as:

$Radius,R=\frac{D}{2}=\frac{24}{2}=12\ yd$

Now, area of the pond is given as:

$A_{pond}=\pi R^2=3.14\times (12)^2=3.14\times 144=452.16\ yd^2$

Area of the complete path including the pond area is given as:

$A_{outer}=\pi(R+x)^2=3.14\times(12+2)^2=3.14\times196=615.44\ yd^2$

Now, area of the gravel path can be obtained by subtracting the pond area from the total outer area. This gives,

$A_{path}=A_{outer}-A_{pond}\\\\A_{path}=615.44-452.16=163.28\ yd^2$

Now, using unitary method,

Cost of 1 square yard of path = $50

∴ Cost of 163.28 square yard of path = 50 × 163.28 = $8164

Hence, the walk will cost $8164.

5 0

3 years ago

Read 2 more answers

Where is the opposite of −10 located on a number line? A) to the left of 0 B) to the right of 0 C) to the right of 12 D) to the

aalyn [17]

Answer:

B. to the right of 0

Step-by-step explanation:

the opposite of -10 would be 10 and out of all the answer choices the number 10 only fits into B.

6 0

2 years ago

Read 2 more answers

I need help with Multiplication Properties of Exponents desperately!! I've tried to solve both problems repeatedly and I cannot

Yuliya22 [10]

Answer:

1) x= -36.

2) x = 0.

Step-by-step explanation:

1) Taking the 3rd power to both sides and using the following exponent law:

$\left(a^b\right)^c = a^{bc}$

we get:

$\left(\left(m^{x}\right)^{\frac{1}{3}}\right)^3 = \left(m^{-12}\right)^3 \\ m^x = m^{-36}$

So this tells us that x = -36.

2) We can distribute the power inside every term. So the left side becomes:

$\left(3x^3y^x\right)^3 = 3^3\left(x^3)^3y^{3x} = 27x^9y^{3x}$

Now, the trick here is to remember that $y^0 = 1$ , so replacing 1 with $y^0$ , which then gives us:

$27x^9y^{3x} = 27x^9y^{0}$ , telling us that 3x = 0 and thus, x = 0.

7 0

3 years ago

¿Se puede distribuir el exponente de una suma o una resta? ¿Y la raiz?

azamat

Si se puede distribuir el exponente de una suma porque si 2+3 elevado al 2 entonces el Raiz seria cuadrada de 19

6 0

2 years ago

30 feet is to 40 feet as 12 feet is to 16 feet

astraxan [27]

Answer:

I don't know what to do but

30 feet is to 40 feet is plus 10, 12 feet is to 16 feet is plus 4. I think if this wrong I am so sorry

Step-by-step explanation:

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2 years ago