The base of a 50-ft ladder that is leaning against a building is placed 35 ft away from the bottom of a building. What angle does the ladder make with the ground?
The ladder makes a _______° angle with the ground. Round your answer to the nearest degree.

Answer:

one solution

Step-by-step explanation:

Given

3(x - 2) = 22 - x ← distribute parenthesis on left side

3x - 6 = 22 - x ( add x to both sides )

4x - 6 = 22 ( add 6 to both sides )

4x = 28 ( divide both sides by 4 )

x = 7

An equation can either have a solution, no solution or infinite many solutions

The equation has one solution.

The equation is given as:

[tex]\mathbf{3(x - 2) = 22 - x}[/tex]

Open bracket

[tex]\mathbf{3x - 6 = 22 - x}[/tex]

Collect like terms

[tex]\mathbf{3x + x = 6 + 22}[/tex]

Evaluate like terms

[tex]\mathbf{4x = 28}[/tex]

Divide both sided by 4

[tex]\mathbf{x = 7}[/tex]

The above equation is true for x = 7

This means that: the equation has one solution.

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Answer:

c) Quadratic Formula

It asked for width to length, so it is really important to put the width on top and the length on bottom.

46mm

_____

84mm

Reduce the fraction, if you can use a calculator you do not need to show this part.

46/2

____

84/2

Answer:

the correct one is 1. 16x - 12(1 + 2x) + 4

Step-by-step explanation:

16x−12−24x+4 is equivalent to 8x-8

1.  16x - 12(1 + 2x) + 4 is equivalent to 8x-8

2.  40x-16 is equivalent to 8(5x−2)

3.  4 - 12 + (2x - 3x) is equivalent to −x−8

4.   -8(x+1) is equivalent to −8x−8

Answer:

$4.20

Step-by-step explanation:

you first do 1.75 divided by 5 which gives you .35

so you do .35 times 12 which gives you 4.2

The price of a 12-minute phone call is  $4.2.

We have given that,

The price of a 5-minute phone call is $1.75.

We have to determine, the price of a 12-minute phone call.

A price is the (usually not negative) quantity of payment or compensation given by one party to another in return for goods or services.

We first 1.75 divided by 5 which gives you .35

That is,

[tex]\frac{1.75}{5} =0.35[/tex]

[tex](0.35)( 4)=4.2[/tex]

0 .35 times 12 which gives  $4.2.

Therefore the price of a 12-minute phone call is  $4.2.

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Answer:

111 cars

Step-by-step explanation:

30% of 78 is

78×30%=78×0.3=23.4

Cars needed to sell

78+23.4=111.4

Unless we can't have 0.4 of a car, we need to round that number, so 111.4≈111

The number of cars the dealership need to sell in May to reach their goal is 101.4 cars.

Given the following data:

To find the number of cars the dealership need to sell to reach their goal:

Mathematically, percentage increase is given by the formula:

[tex]Perecent\;increase = \frac{New\;value - Old\;value}{Old\;value} \times 100[/tex]

Substituting the given parameters into the formula, we have;

[tex]30 = \frac{New\;value -78}{78}\times 100\\\\2340=100New\;value -7800\\\\100New\;value = 7800+2340\\\\100New\;value=10140\\\\New\;value=\frac{10140}{100}[/tex]

New value = 101.4 cars

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Answer:

C

Step-by-step explanation:

If there are 45 balloons total, and there are more balloons, you will know that the blue balloons will have a higher ratio. The answer is C. 5:4.

Answer:

5: 4

Step-by-step explanation:

Answer:

the correct answer is b .

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area of polygon = area of square + area of triangle

Square:

Side = 12 cm

Area of square  = side *side

                          = 12 * 12

                          = 144 sq.cm

Triangle:

base (b) = 12 cm

Height h = 19 cm

[tex]Area =\frac{1}{2}bh\\\\=\frac{1}{2}*12*19\\[/tex]

= 6 * 19

= 114 sq.cm

Area of polygon = 144 + 114 = 258 square cm

Answer:

21.35 [tex]ft^{3}[/tex]

Step-by-step explanation:

It is given that the box is a triangular prism.

Side of Base of prism = 7 ft

Height of Base of prism = 6.1 ft

Area of a triangle is given as:

[tex]B = \dfrac{1}{2} \times \text {Base} \times \text{Height}[/tex]

[tex]\Rightarrow \dfrac{1}{2} \times 7 \times 6.1\\\Rightarrow 21.35\ ft^{2}[/tex]

Volume of a prism is:

[tex]V = B \times h[/tex]

B is the area of base of prism

h is the height of prism

Here, h = 1 foot

So, V = 21.35 [tex]\times[/tex] 1

Volume of prism is = 21.35 [tex]ft^{3}[/tex]

Sand required to fill the triangular prism shape box is 21.35 [tex]ft^{3}[/tex].

Answer:

m∠ ABF = 130°, m∠ ABD = 50°, m∠ EBC = 70°, m∠ FBC = 50°, m ∠ DBG = 45°

Step-by-step explanation:

Take a look at the picture below;

Answer:

The answer is A. log(8/7)

Step-by-step explanation:

Answer:

maybe the fourth one....

Answer:

5 x 18 = 5 x 2 x 9

5 x 18 = 90

Step-by-step explanation:

For the first equation, notice that 18 is broken into 9 and an unknown.

This can be written as:

18 ÷ 9 = ?

Well, 18 divided by 9 equals 2.

18 ÷ 9 = 2

We can use this to answer the second equation.

Instead of trying to multiply 5 and 18, multiply 5 and 2 first.

5 x 18 = 5 x 2 x 9

5 x 18 = 10 x 9

Now, just multiply 10 and 9.

5 x 18 = 10 x 9

5 x 18 = 90

Therefore, the product of 5 and 18 is 80.

Answer:

The zeros are x = 1 and x = 3

In the picture attached, the graph of the function is shown. The zeros are those points where h(x) intersect x-axis.

Step-by-step explanation:

Given the expression:

x² - 4x + 3

Rewrite -4x term:

x² - x - 3x + 3

Take x as common factor in the first terms, and -3 in the last terms:

x(x - 1) - 3(x - 1)

Take (x - 1) as common factor:

h(x) = (x - 1)(x - 3)

Answer:

(x - 3)^2 + (y - 5)^2 = (√89)^2

Step-by-step explanation:

Well if you estimate, you can see that the circle touches one point at (-5, 0) and the center is at about (3, 5).

The standard equation for the circle is (x - h)^2 + (y - k)^2 = r^2 where (h, k) is the center.

So, you can start by plugging in the center. (x - 3)^2 + (y - 5)^2 = r^2

Now, all you have to do is find the radius.

You can do this by connecting the point (-5, 0) to the center.

You will have to use the distance formula:

√(-5 - 3)^2 + (0 - 5)^2 = √64 + 25 = √89

The final equation will be (x - 3)^2 + (y - 5)^2 = (√89)^2

This is the general idea, but my answer may not be correct, so check my steps.

Answer:

The volume of the cone is:

Step-by-step explanation:

You should know that the volume of a straight circular cone is equal to:

Where:

r = radius.

h = height.

Since the radius and diameter are not provided in the exercise but the circumference, the circumference formula should be used and the diameter must be cleared:

When clearing you get:

By replacing the data you get:

Since the radius is equal to half the diameter, then the diameter is equal to 2,385 inches, now having the value of radius we proceed to replace in the volume formula:

Answer:

112.8 in  

Step-by-step explanation:

Answer:

120 cm^2

Step-by-step explanation:

area of a rhombus is pq/2

that means that the product of the two diagonals divided by 2 is the area of the rhombus.

so that means one diagonal is 24 and one is 10, (we are given what half of both diagonals are so just multiply by 2)

now put it in the formula

24x10 = 240

now divide by 2

240/2 = 120

check again with google if u disagree

Answer:

D. 114ft2

Step-by-step explanation:

So i checked the question online and i believe the part "a scale where 12 inch corresponds to 6 feet" should be "a scale where 1/2 inch corresponds to 6 feet"

In that case, a scale where 1/2 inch corresponds to 6 feet means

scale = 1inch to 12 feet

On the floor plan, Alexis' room is 1in by 1in

-> in reality, alexis' room is 12ft by 12ft

-> a scale where 1/2 inch corresponds to 6 feet

Answer: $9362.36

Step-by-step explanation:

A = P(1 + r/n)^nt

After 18 years, this investment will be worth of  $9,379.45.

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.

Compound interest is calculated by multiplying the initial principal amount (P) by one plus the annual interest rate (R) raised to the number of compound periods (nt) minus one. That means, CI = P[(1 + R)ⁿˣ – 1] Here,

P = Initial amount

R = Annual rate of interest as a percentage

n = Number of compounding periods in a given time

Given,  Five thousand dollars is invested at an interest rate of 3.5% compounded quarterly.

From the above formula of compound interest

Total amount  A = P(1 + r/n)^nt

In our case

p = 5000

r = 3.5%

t = 18 years

Thus,

Total amount = 5000( 1 + 3.5%)^18

Total amount = $9,379.45

therefore, this investment will be worth $9,379.45 after 18 years.

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Answer:

What needs to be answered? There's no question.

Step-by-step explanation:

Answer:

210

Step-by-step explanation:

This is the problem of combination.

Number of ways of choosing x thing out n different thing is given by

[tex]{n \choose x} = n!/x!(n-x)![/tex]

___________________________________________

The number of bridesmaids = 10

number of bridesmaids, bride can choose = 4

Thus, Number of ways of choosing 4 bridesmaids thing out 10 bridesmaids  is given by

[tex]{10 \choose 4} = 10!/4!(10-4)! = 10!/4!6!\\=> 10*9*8*7*6!/4*3*2*1 *6! = 5*3*2*7 = 210[/tex]

Thus,  in 210  ways can she choose 4 bridesmaids.

Answer:          210

Step-by-step explanation:

Answer:

the answer is (1,5,6,35) or (1.5,-2,33

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

6x + 7 = 67

Subtract 7 from each side

6x + 7-7 = 67-7

6x = 60

Divide each side by 6

6x/6 = 60/6

x = 10

Answer:

10

Step-by-step explanation:

1) 6x = 67 - 7

2) 6x = 60

3) x = 60/6

4) x = 10

Please mark me as brainliest...it would mean a lot

Answer:

17,148.58

Step-by-step explanation:

[tex] \frac{4}{3} \times \pi \times {r}^{3} \\ = \frac{4}{3} \times 3.14 \times 16 \times 16 \times 16 \\ = 17,148.58[/tex]

Answer:

37

Step-by-step explanation:

[tex]f(4)=2(4)^2-3=\\\\2(16)-3=\\\\32-3=\\\\29\\\\g(29)=29+8=\\\\\boxed{37}[/tex]

Hope this helps!

Answer:

idk

Step-by-step explanation:

Answer:

Yeah it's D

Step-by-step explanation:

Answer:

[tex]a^{8} b^{8}[/tex]

Step-by-step explanation:

First, remember that [tex]x^{a} *x^{b} =x^{a+b}[/tex]

[tex]a^{5+3} b^{3+5}[/tex]

Simplify (5+3 and 3+5)

[tex]a^{8} b^{8}[/tex]

Hope this helped! :]

Answer:

Step-by-step explanation:

hello :

(a^5b^3)(a^3b^5)=a^8b^8=(ab)^8

Answer:

4 feet or 3.5 feet

Step-by-step explanation:

if 12 inches equals a foot then you divide 42 by 12

which gives you 3.5