Use the diagram above to answer the questions.
a. What are the coordinates of point N? (1 pt.)
b.
Use the Pythagorean Theorem to find the length of
segment PQ. (2 pts)

Answer:

x^2 +3x -4 = 0  --> (x +4)(x -1) = 0

Step-by-step explanation:

Let's find A and B such that

A*B = - 4    and  A+B = 3

Numbers are:

A = +4  and  B = -1

The factoring equation is y = (x + A)(x + B)

In this specific case: y = (x +4)(x -1)

Solutions to the quadratic equation require

y = (x +4)(x -1) = 0

and hence

x +4 = 0  --> x = -4

x - 1 = 0 -->  x= +1

The amount of money does Liam need to put in the simple interest account to earn  $750 in interest, is $6250.

Simple interest is the amount charged on the principal amount with a fixed rate of interest for a time period. Simple interest calculated only on the principal amount.

The formula for the simple interest can be given as,

[tex]I=\dfrac{Prt}{100}[/tex]

Here, (I) is the interest amount earned on the principal amount of (P) with the rate of (r) in the time period of (t).

Liam wants to put some money in a simple interest account. He pays R=6% interest annually for t=2 years. Liam would like to earn I=$750 in interest.

Put the values in the formula,

[tex]750=\dfrac{P\times6\times2}{100}\\P=\dfrac{750\times100}{6\times2}\\P=6250[/tex]

Thus, the amount of money does Liam need to put in the simple interest account to earn  $750 in interest, is $6250.

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The amount of money does Liam need to put in the simple interest account to earn  $750 in interest, is $6250.

What is simple interest?

Simple interest is the amount charged on the principal amount with a fixed rate of interest for a time period. Simple interest calculated only on the principal amount.

The formula for the simple interest can be given as,

Answer: $6,250

Step By Step: Here, (I) is the interest amount earned on the principal amount of (P) with the rate of (r) in the time period of (t).

Liam wants to put some money in a simple interest account. He pays R=6% interest annually for t=2 years. Liam would like to earn I=$750 in interest.

Put the values in the formula,

Thus, the amount of money does Liam need to put in the simple interest account to earn  $750 in interest, is $6250.

Answer:

300

Step-by-step explanation:

Let y = unknown number

30% of y = 90

⇒ 0.3 × y = 90

⇒ y = 90 ÷ 0.3

⇒ y = 300

Answer: B. hours

Step-by-step explanation:

    Let us closely look at the varible t it gives, the one we are looking at units for. "t stands for the amount of time the workers have left to clean the windows"

         "t stands for the amount of time ..."

    The only unit they give that represents time is hours, meaning the answer to your question is:

     B. hours

The ladder makes an angle 30 degrees with the ground

Data;

Length of the ladder (hypothenuse) = 30 ft

height of the wall (opposite) = 15 ft

When the ladder reclines on the wall, it forms a right-angle triangle and we can solve it.

Using SOHCAHTOA,

We have the value of hypothenuse and opposite and we can use the sine angle of this triangle.

The ladder makes an angle 30 degrees with the ground.

Learn more on trigonometric ratio here;

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Step-by-step explanation:

Answer:

x = 6.40

Step-by-step explanation:

The formula to find the area of the rectangle is :

Area = Length × Width

Given that,

Area ⇒ 50

Length ⇒ ( 2x - 5 )

Width ⇒ x

So now we can write an expression like this.

Area = Length × Width

50  = x ( 2x - 5 )

And now we can solve for x.

Let us solve now by using the completing square method.

x ( 2x - 5 ) = 50

2x² - 5x = 50

First divide the whole equation by 2.

x² - 2.5 = 25

x² - 2.5 + 1.5625 = 25 + 1.5625

( x - 1.25 )² = 26.5625

x - 1.25 = ±√26.5625

x  - 1.25 = ±5.1538

So,

x = + 5.1538 + 1.25                           or        x = - 5.1538 + 1.25

x = 6.40                                                       x = -3.90

As we cannot get a negative number as a value for length,

x = 6.40

Answer:

[-5, 4) ∪ (4, ∞)

Step-by-step explanation:

Given functions:

[tex]f(x)=\dfrac{1}{x-3}[/tex]

[tex]g(x)=\sqrt{x+5}[/tex]

Composite function:

[tex]\begin{aligned}(f\:o\:g)(x)&=f[g(x)]\\ & =\dfrac{1}{\sqrt{x+5}-3} \end{aligned}[/tex]

Domain: input values (x-values)

For [tex](f\:o\:g)(x)[/tex] to be defined:

[tex]x+5\geq 0 \implies x\geq -5[/tex]

[tex]\sqrt{x+5}\neq 3 \implies x\neq 4[/tex]

Therefore, [tex]-5\leq x < 4[/tex]  and  [tex]x > 4[/tex]

⇒  [-5, 4) ∪ (4, ∞)

Answer:

No.

Step-by-step explanation:

The maximum that can be earned is $720, which results from walking 60 dogs at $12 per walk.

Answer:

Different

Step-by-step explanation:

Diversity is a noun that means the state or fact of being diverse; difference; unlikeliness. Variety; multiformity. A state of difference.

6 x 13^2=1,014

A=1,014 in

The surface area of the cube is 1,014 square in

Answer:

3

Step-by-step explanation:

Use the formula:

The slope equation using the equation of line is given as, y = mx + b, here, m is the slope and b is the y-intercept.

choose any 2 rows and plot them into the formula.

(-2)-1/(-2)-(-1) = 3

Answer: 3 or C

Step-by-step explanation:

Answer:

7.8 rounding up to 8

Step-by-step explanation:

Answer: The answer is 120

Step-by-step explanation:

5x4x3=60   6x4x5+120 divided by 2= 60

                               60+60= 120

Solution:

Your problem → x + 45 = 97x

x+45=97x

⇒-96x+45=0

⇒96x=45

⇒x=45/96

⇒x=15/32

Answer:

177 600 000 is the answer

Answer:

[tex]408cmx^{2}[/tex]

Step-by-step explanation:

A=2(wl+hl+hw)=2·(2·6+24·6+24·2)= 408cm²

length= 6

width= 2

height= 24

the area if the box.

[tex]a = lwh[/tex]

[tex]a = 2(wl + hl + hw)[/tex]

[tex]a = 2 \times (2.6 + 24.6 \times + 24.2)[/tex]

[tex]a = 408 {cm}^{2} [/tex]

therefore, the area of the box is 408 square centimeters.

Answer:

X=37.56

Step-by-step explanation:

Answer:

discount: 30% sale price: $98

Step-by-step explanation:

Simply multiply 140 by 70%(0.7) to get 98

Answer:

√41

Step-by-step explanation:

Pythagorean Theorem:

a^2+b^2=c^2

4^2+5^2=c^2

16+25=c^2

41=c^2

√41=c

Answer:

A fully functioning forest has a great capacity to regenerate. But exhaustive hunting of tropical rainforest wildlifecan reduce those species necessary to forest continuance and regeneration. For example, in Central Africa, theloss of species like gorillas, chimps, and elephants undercuts the seed dispersal and slows the recovery.

Step-by-step explanation:

a. The least amount as indicated in the box plot is: 10

b. Median amount of snowfall is: 20

c. Data is concentrated at the third quartile

The median of a data in a box plot is the value indicated by the vertical line that divides the box.

a. The least amount is the minimum value which is at the extreme end of the whisker to your left = 10

b. Median amount of snowfall is the value indicated by the vertical line = 20

c. The largest section is the third quarter, so the data is most concentrated within the third quarter.

Learn more about median in a box plot on:

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Answer:

I think that it is the one on the bottom left

Step-by-step explanation:

I am so sorry if it is wrong he he

Answer:

7,24,20

Step-by-step explanation:

The perimeter is simply the lengths of the sides, added up
n+4n-4+4n-8=9n-12=51 cm
9n=51+12
9n=63
n=7

plug in 7 for n to get:
7,4*7-4,4*7-8
or
7,24,20

Answer:

12 miles per hour.

Step-by-step explanation:

1. If you pick 5 hours, then you will noticed that the graph shows you 60 miles.

2. Find the unit rate.

5 hours = 60  miles

1 hour = x miles

x= 60 ÷ 5

x= 12 miles per hour

Answer:

B

Step-by-step explanation:

because the angles 1 and 7 are alternate and equal , we can conclude that p and q are parralel

Answer:

74

Step-by-step explanation:

By average definition:

(74 + 67 +73 +x) / 4 = 72

Multiply by 4

(74 + 67 +73 +x)  = 288

shift the first three terms on the right side

x = 288 -74 -67 -73 =  74

Answer:

A. (2, 0)

Step-by-step explanation:

The function crosses the x-axis at point (2,0). Therefore, that is the x-intercept.

hope this helps :)