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2 years ago

For the following right triangle, find the side length x.

Mathematics

1 answer:

zalisa [80]2 years ago

4 0

Answer:

Step-by-step explanation:

We can use the Pythagorean Theorem to find the value of x,

The Pythagorean Theorem states that $a^2 + b^2=c^2$ , where a and b are the legs and c is the hypotenuse.

We already know a and b’s value so we can substitute inside the formula to find the length of the hypotenuse.

$24^2+7^2=c^2\\\\576+49=c^2\\\\625=c^2\\\\c=25$

Hope this helped!

You might be interested in

A heap of rubbish in the shape of a cube is being compacted into a smaller cube. Given that the volume decreases at a rate of 3

inna [77]

Answer:

-1/4 meter per minute

Step-by-step explanation:

Since, the volume of a cube,

$V=r^3$

Where, r is the edge of the cube,

Differentiating with respect to t ( time )

$\frac{dV}{dt}=3r^2\frac{dr}{dt}$

Given, $\frac{dV}{dt}=-3\text{ cubic meters per minute}$

Also, V = 8 ⇒ r = ∛8 = 2,

By substituting the values,

$-3=3(2)^2 \frac{dr}{dt}$

$-3=12\frac{dr}{dt}$

$\implies \frac{dr}{dt}=-\frac{3}{12}=-\frac{1}{4}$

Hence, the rate of change of an edge is -1/4 meter per minute.

4 0

2 years ago

f(x) = −16x2 + 24x + 16 Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points) Part B: Is the vertex

DerKrebs [107]

Answer:

see below

Step-by-step explanation:

f(x) = −16x^2 + 24x + 16

Set equal to zero to find the x intercepts

0 = −16x^2 + 24x + 16

Factor out -8

0 = -8(2x^2 -3x-2)

Factor

0 = -8(2x +1) (x-2)

Using the zero product property

2x+1 =0 x-2 =0

x = -1/2 x=2

The x intercepts are -1/2 ,2

Since the coefficient of x^2 is negative the graph will open down and the vertex will be a maximum

The x value of the maximum is 1/2 way between the zeros

(-1/2+2) /2 = 1.5/2 =.75

To find the y value substitute into the function

f(.75) = -8(2x +1) (x-2)

=-8(2*.75+1) (.75-2)

= -8(2.5)(-1.25)

=25

The vertex is at (.75, 25)

We have the zeros, and the vertex. We know the graph is symmetrical about the vertex

3 0

2 years ago

You have just received an inheritance of $28,000 and would like to invest it into an account. The bank offers two investment pla

grigory [225]

First we need to calculate annual withdrawal of each investment
The formula of the present value of an annuity ordinary is
Pv=pmt [(1-(1+r)^(-n))÷(r)]
Pv present value 28000
PMT annual withdrawal. ?
R interest rate
N time in years
Solve the formula for PMT
PMT=pv÷[(1-(1+r)^(-n))÷(r)]

Now solve for the first investment
PMT=28,000÷((1−(1+0.058)^(−4))
÷(0.058))=8,043.59
The return of this investment is
8,043.59×4years=32,174.36

Solve for the second investment
PMT=28,000÷((1−(1+0.07083)^(
−3))÷(0.07083))=10,685.63
The return of this investment is
10,685.63×3years=32,056.89

So from the return of the first investment and the second investment as you can see the first offer is the yield the highest return with the amount of 32,174.36

Answer d

Hope it helps!

6 0

2 years ago

Babe Ruth's 1931 salary was $80,000, Government statistics show a consumer price index of 15.2 for 1931 and 237 for 2015. Ruth's

Lady_Fox [76]

Answer:

Ruth's 1931 salary was equivalent to a 2015 salary of $1,247,368.

Step-by-step explanation:

This question can be solved by a rule of three.

Government statistics show a consumer price index of 15.2 for 1931 and 237 for 2015.

This means that $15.2 in 1931 is equivalent to $237 in 2015. So

$15.2 in 1931 - $237 in 2015

$80,000 in 1931 - $x in 2015

$15.2x = 237*80,000$

$x = \frac{237*80,000}{15.2}$

$x = 1,247,368$

Ruth's 1931 salary was equivalent to a 2015 salary of $1,247,368.

8 0

2 years ago

A contractor has submitted bids on three state jobs: an office building, a theater, and a parking garage. State rules do not all

german

Answer:

The following are the answer to this question:

Step-by-step explanation:

In the given question the numeric value is missing which is defined in the attached file please fine it.

Calculating the probability of the distribution for x:

$\to f(x) = 0.19\ for \ x=14\\\\\to f(x) = 0.29 \ for\ x=7\\\\\to f(x) = 0.38\ for \ x=1\\\\\to f(x)=0.14 \ for \ x=0\\$

The formula for calculating the mean value:

$\bold{ E(X)= x \times f(x)}$

$=14 \times 0.19+7 \times 0.29+1 \times 0.38+0\times 0.14\\\\=2.66 + 2.03+0.38+ 0\\\\=5.07$

$\bold{E(X^2) = x^2 \times f(x)}$

$=14^2 \times 0.19+7^2 \times 0.29+1^2 \times 0.38+0^2 \times 0.14 \\\\=196 \times 0.19+ 49 \times 0.29+1 \times 0.38+0 \times 0.14\\\\= 37.24+ 14.21+ 0.38+0 \\\\=51.83$

use formula for calculating the Variance:

$\to \bold{\text{Variance}= E(X^2) -[E(X)]^2}$

$= 51.83 - (5.07)^2\\\\= 51.83 - 25.70\\\\=26.13$

calculating the value of standard deivation:

Standard Deivation (SD) = $\sqrt{Variance}$

$= \sqrt{26.13} \\\\=5.111$

6 0

2 years ago