A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground.
The angle made by the ladder with the ground is
degrees, and the length of the ladder is
inches.

Answer:

x = -26

Step-by-step explanation:

[tex](f-g)(x)=\frac{4}{x-3}-\frac{3}{x+5}=\frac{3}{x^2 +2x-15} \\ \\ \frac{4(x+5)-3(x-3)}{x^2 +2x-15} \\ \\ =\frac{4x+20-3x+9}{x^2 +2x-15}=\frac{3}{x^2 +2x-15} \\ \\ \frac{x+29}{x^2 +2x-15}=\frac{3}{x^2+2x-15} \\ \\ x+29=3 \\ \\ x=-26[/tex]

This is in the domain of the equation, and is thus a solution.

Answer:

y=2x+6

Step-by-step explanation:

First find the gradient of the perpendicular line. We can do this by turing the given gradient into a negative reciprocal.

-1/2 -> 2 (new gradient)

substitute new gradient into y=mx+c as well as the values for x and y from the given coordinate (-2,2)

y=mx+c

2=2(-2)+c

then solve for c

2=-4+c

c=6

therefore the formula for the line is y=2x+6

Answer:

D

Step-by-step explanation:

Applying the distance formula root square x2-x1 +y2-y1

then

let the (x1,y1 )=(2,2)

(x2,y2)=(-2,6)

The area of the rectangle whose diagonal is twice its width is (x²√3)/4  square units.

The area of rectangle is defined by the product of its length and width. Mathematically-

Area [A] = Length [L] x Width [W]

Given is a rectangle whose diagonal is twice as long as it's width. From this, we can write -

Width = w

Length of diagonal = x = 2w

Assume that the length of the rectangle is L. Using the Pythagoras theorem in the triangle ΔABC, we get -

AC² = AB² + BC²

x² = L² + w²

(2w)² = L² + w²

4w² = L² + w²

L² = 3w²

L = w√3

Now, the width of rectangle is 'w' and its length is 'w√3'. Its area will be-

Area = length x width

A = w√3 × w

A = w²√3

Now, length of diagonal → x = 2w. So, we can write -

w = x/2

Therefore, the area will be -

A = (x/2)²√3 = (x²√3)/4

Therefore, the area of the rectangle whose diagonal is twice its width is (x²√3)/4  square units.

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We have that [tex]g(t)=-t+5[/tex], and we are asked to evaluate [tex]g(-15)[/tex] . In notation of functions like this, the number inside the parentheses is the value of the variable.  Or, to be more clear, this is essentially telling us that [tex]t=-15[/tex] for our expression [tex]g(t) = -t+5[/tex].  So we can evaluate it as follows:

[tex]g(-15) = -15 + 5 = -10[/tex]

Based on the histogram above, the class width is equal to 4.

Based on the histogram above, the sample size is equal to 37.

In a frequency distribution table, a class width can be defined as the difference between the upper (maximum) and lower (minimum) boundaries of any class in a data set. This ultimately implies that, all classes must all have the same width in a frequency distribution table.

Mathematically, the class width of a data set can be calculated by using this formula:

Class width = (max - min)/n

Where:

In this context, the class width of this histogram can be calculated as follows;

Class width = max - min

Class width = 5 - 1

Class width = 4.

Furthermore, the sample size can be computed by adding all the frequencies of the corresponding rectangular bars of the histogram as follows;

Sample size = 6 + 10 + 4 + 2 + 7 + 8

Sample size = 37.

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Answer:

e=mc2

Step-by-step explanation:

69 ballz = 43= e=mc2

Answer:

F. 70

Step-by-step explanation:

[tex]{ \tt{(6x + 4) = (5x + 15)}}[/tex]

[Alternate angles]

[tex]{ \tt{(6x - 5x) = (15 - 4)}} \\ { \tt{x = 11}}[/tex]

Therefore;

[tex]{ \tt{angle = 6(11) + 4}} \\ = 66 + 4 \\ = 70 \degree[/tex]

The products of the matrices are

        [-4     19]

ST =  [8   -21]      

and

        [-12      -8]

TS = [-25      -10]

The matrices are given as

      [4      1]

S =  [-3   -2]

      [0      4]

T =  [-4   3]

The product of the matrices is then calculated as

        [4 * 0 + 1 * -4      4 * 4 + 1 * 3]      

ST =  [-3 * 0 - 2 * -4   -3 * 4 - 3 * 3]      

Evaluate the sum or difference of products

So, we have

        [-4     19]

ST =  [8   -21]      

Also, we have

        [0 * 4 + 4 * -3      0 * 1 + 4 * -2]      

TS = [-4 * 4 + 3 * -3      -4 * 1 + 3 * -2]      

Evaluate the sum or difference of products

So, we have

        [-12      -8]

TS = [-25      -10]

Hence, the products of the matrices are

        [-4     19]

ST =  [8   -21]      

and

        [-12      -8]

TS = [-25      -10]

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Answer:

  A  irrational

  B  real

Step-by-step explanation:

Given the value π/7, you want to classify it as whole, integer, real, and/or irrational.

Any number that does not have an imaginary part is a real number. Real numbers include integers, whole numbers, and natural numbers, none of which have any fractional part.

Any ratio of integers (with a non-zero denominator) is a rational number. All other real numbers are irrational numbers. Pi (π) is an irrational number.

When rational numbers are written as decimal numbers, their fractional part will either terminate or repeat. When the fractional part of a decimal number does not terminate or repeat, but continues indefinitely, the number is irrational.

As we said, pi is an irrational number. Multiplying it by a rational number (1/7) does not change its classification.

  π/7 is irrational and real

Answer:

y = 3x + 14

See the work below.

Step-by-step explanation:

Answer: 30

Step-by-step explanation:

Think of each number in the ratio of 2:5 as a group. Each group has to be the same. 2 groups of boys : 5 groups of girls. There are 12 boys on the bus. So the 12 boys are split into 2 groups. 12/2=6. 6 boys are in each group. Since we now know that each group had 6 kids we just need to find the number of girls. There are 5 groups of 6 girls. 5x6=30. There are 30 girls on the bus.

The book in real life is 7 times larger than the one on the website. When you divide 10.5/1.5 you get 7. So multiplying 3 by 7 will get you 21.

Therefore, the real book is 21 inches tall

Answer:they will both negative because the rules are  -x,-y

Step-by-step explanation:

Answer:

Step-by-step explanation:

1:4 Ratio on zebras to monkeys.

Can be expressed 1x:4x

7 zebras total.

7 x 4 = 28

7 x 1 = 7

(28 + 7 = 35).

So, there for a ratio of 1:4 equals 28 monkeys and 7 zebras leaving a total of 35 monkeys and zebras together.

Answer: See below

Step-by-step explanation:

a. 3(4)= 12

b. 4+11+(-4)

   =15+(-4)

Answer=11

c. 3.2(2)= 6.4

d. I (-2)+(-2)+(-2) I=  6

e. I 2(-7.5) I = 15

f. [tex]10\frac{1}{5}[/tex](-5)= -51

The exact value that is 98% of 2330 is 2283

The value is 98% of 2330

98% of 2330 is 98/100×2330=2283.4≅2283

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Answer:

I think it's c I haven't done those formulas in while

Answer:

Step-by-step explanation:

64 pi cm2

Answer:

201.1 = 8^2 pi cm2 = 64 pi cm2

Step-by-step explanation:

The area of a circle with a radius 8 is 201.1

Hope it helps!!!

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Hello...! :)

Very easy, we must eliminate the Parentheses and then we must use the Law of Signs and in this case we will use this which is:

[tex]\green{\underline{\blue{\bold{Law\: of \: signs:}}}} [/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - × + = - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \times + = + \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \times - = + \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \times - = - [/tex]

Once we know we must add but since we know that it is a minus sign (-) we will add it as if it were a simple sum but the minus sign just stays there

We start to solve:

[tex] \: \: \: \: \: \: \sf \red{(-10) } \pink+ \blue{ ( -2 ) } \purple+ \green{( -7 )}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \red{-10} \blue{ -2 } \green{-7}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \blue{-12} \green{ -7}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \green{-19}[/tex]

And in conclusion, the result of our problem is 19

¿Doubts? in the comments Greetings :D

The required step of indirect proving is to assume AABC is an acute triangle. Option B is correct.

Given that,
AABC is not an acute triangle.

What is the first step of indirectly proving this statement is to be determined.

The angle can be defined as the one line inclined over another line.

Here,
Indirect proving implies proving with contradictions,
So in order to prove AABC is not an acute triangle, we have first assumed that AABC is an acute triangle.

Thus, the required step of indirect proving is to assume AABC is an acute triangle. Option B is correct.

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Given, 5m+n = 10

5m = 10-n

[tex]m = \frac{10 - n}{5} [/tex]

Hope this helps :)

Answer:

5m = 10- n

m = (10 - n) /5

I used bracket around 10-n because they're both being divided by 5.

If the revenues and expenses of Up-in-the-Air Travel Service for the year ended April 30, 20Y7, follow: Fees earned $742,000, Office expense 308,000. The income statement has a net loss of: $66,000.

Income statement for the year ended April 30, 20Y7

Revenue:

Fees earned $742,000

Expenses:

Office expense $308,000

Miscellaneous expense $10,000

Wages expense $490,000

Total expenses $808,000

Net loss $66,000

($742,000-$808,000)

Therefore if the revenues and expenses of Up-in-the-Air Travel Service for the year ended April 30, 20Y7, follow: Fees earned $742,000, Office expense 308,000. The income statement has a net loss of: $66,000.

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The greatest number of groups that can be formed is 7.

It should be noted that there are 56 dancers wearing green outfits and 42 dancers wearing yellow outfits.

The greatest number of groups that can be formed will the highest common factor between the numbers.

It should be noted that the highest common factor between 42 and 56 is 7.

Therefore, the greatest number of groups that can be formed is 7.

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Answer:

Use the Pythagorean theorem

Step-by-step explanation:

Answer: debit Cash for​ $8,500, debit Accumulated Depreciation− Truck for​ $50,000, credit Truck for​ $56,000, and credit Gain on Disposal for​ $2,500.

Answer:

no

Step-by-step explanation:

it would have to be 8.55 to be rounded up not 8.549... there is a rule of if it is 4 and lower go down and if 5 and higher go up