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3 years ago

Tom drives at a constant rate of 40 miles per hour for 3 hours. How far

Mathematics

1 answer:

Gnom [1K]3 years ago

8 0

Answer:

120 miles

Step-by-step explanation:

40×3=120

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What is the volume of the box if it is scaled down by a factor of 1/10?

Natalka [10]

Answer:

8.4in²

Step-by-step explanation:

We are given the dimensions of a box as :

7in = Height

6in = Length

2in = Width

The volume of a box = Length × Width × Height

Volume of a box = 7in × 6in × 2in

= 84in²

We are also told in the question to find the volume of the box if it is scaled down by a factor of 1/10

Hence,the new volume = 84in² × 1/10

= 8.4in²

Therefore, the volume of the box if it is scaled down by a factor of 1/10 is 8.4in²

8 0

3 years ago

What is the inverse of the function f(x)=3^x

Leokris [45]

Answer:

$f^{-1}(x) = \log_3(x)$

Step-by-step explanation:

The inverse operation for an exponential ( $a^x$ ) is the logarithm: $\log_a(x)$ .

8 0

2 years ago

PLs help 50 PTS!!!!! PLEASE ILL GIVE BRAINLIEST!!!!!

Nookie1986 [14]

Answer:

$\large\boxed{y=\dfrac{1}{4}x^2-x-4}$

Step-by-step explanation:

The equation of a parabola in vertex form:

$y=a(x-h)^2+k$

(h, k) - vertex

The focus is

$\left(h,\ k+\dfrac{1}{4a}\right)$

We have the vertex (2, -5) and the focus (2, -4).

Calculate the value of a using $k+\dfrac{1}{4a}$

k = -5

$-5+\dfrac{1}{4a}=-4$ add 5 to both sides

$\dfrac{1}{4a}=1$ multiply both sides by 4

$4\!\!\!\!\diagup^1\cdot\dfrac{1}{4\!\!\!\!\diagup_1a}=4$

$\dfrac{1}{a}=4\to a=\dfrac{1}{4}$

Substitute

$a=\dfrac{1}{4},\ h=2,\ k=-5$

to the vertex form of an equation of a parabola:

$y=\dfrac{1}{4}(x-2)^2-5$

The standard form:

$y=ax^2+bx+c$

Convert using

$(a-b)^2=a^2-2ab+b^2$

$y=\dfrac{1}{4}(x^2-2(x)(2)+2^2)-5\\\\y=\dfrac{1}{4}(x^2-4x+4)-5$

use the distributive property: a(b+c)=ab+ac

$y=\left(\dfrac{1}{4}\right)(x^2)+\left(\dfrac{1}{4}\right)(-4x)+\left(\dfrac{1}{4}\right)(4)-5\\\\y=\dfrac{1}{4}x^2-x+1-5\\\\y=\dfrac{1}{4}x^2-x-4$

3 0

3 years ago

Let $ 500 be paid at the end of each quarter for 5 years. If the interest is earned rate of 13%, compounded quarterly, find the

kap26 [50]

Answer:

Future value of annuity (FV) = $13,782.12 (Approx)

Step-by-step explanation:

Given:

Periodic payment p = $500

Interest rate r = 13% = 13%/4 = 0.0325 (Quarterly)

Number of period n = 5 x 4 = 20 quarter

Find:

Future value of annuity (FV)

Computation:

$Future\ value\ of\ annuity\ (FV)=p[\frac{(1+r)^n-1}{r} ] \\\\Future\ value\ of\ annuity\ (FV)=500[\frac{(1+0.0325)^{20}-1}{0.0325} ] \\\\Future\ value\ of\ annuity\ (FV)=13,782.1219 \\\\$

Future value of annuity (FV) = $13,782.12 (Approx)

7 0

2 years ago

PARALLEL LINES Find x and y.

Georgia [21]

4x = (130 - 2x) so x = 65/3

(3y + 40) + (130 -2x) = 180 because the angles are supplementary

plug in x

3y + 40 + 130 - 2(65/3) = 180

so 3y = 95/3

therefore y = 95/6

3 0

1 year ago

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