What is the factored form of this expression?
x²-81
Fill in the values for p and q to complete the factored form of the expression.
(x+p)(x+q)

Answer:

x = 22°, y = 70°

Step-by-step explanation:

Isosceles Triangles

The base angles of an isosceles triangle are those formed by the base and one leg of the triangle.

On the other side, the base angles theorem converse states if two angles in a triangle are congruent, then the sides opposite those angles are also congruent.

We are given an isosceles triangle with base angles 3x-11 and 2x+11. Applying the theorem as explained above:

3x - 11 = 2x + 11

Subtracting 2x:

x - 11 = 11

Adding 11:

x = 22

The base angles have a measure of

3x - 11 = 3*22 - 11 = 55°

Thus, the remaining angle of the triangle is:

y = 180° - 2*55° = 180° - 110° = 70°

x = 22°, y = 70°

Answer:

the height of the taller building is 14.47 m

Step-by-step explanation:

Given the data in the question as illustrated in the image below.

form the image; ( Triangle BDE )

we know that sin∅ i= opposite/hypotenuse

so; sin12° = BE / 21.5

BE = 21.5sin12°

BE = 4.47 m

since, EA = DC = 10 m

BA = BE + EA

BA = 4.47 m + 10 m

BA = 14.47 m

Therefore, the height of the taller building is 14.47 m

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9514 1404 393

Answer:

  26 square feet

Step-by-step explanation:

When two of the trapezoids are combined to make a parallelogram, the height remains the same (4 ft), but the width is the sum of the base lengths, 10 ft + 3 ft = 13 ft.

The area of the combined trapezoids is ...

  A = bh = (13 ft)(4 ft) = 52 ft^2

The area of one trapezoid is half that, so is ...

  A = (52 ft^2)/2 = 26 ft^2 . . . . area of the trapezoid

Answer:

–1.5, Negative one-half, 2.9, 3 and three-fourths, 4.6 AKA B

Step-by-step explanation:

common sense

Answer:

4.6 = b

Step-by-step explanation:

Answer: Tuesday

April 20,2021

Answer:

Step-by-step explanation:

Price:

Equations:

Multiply the first equation by 5 and the second equation by 2 and subtract to eliminate x:

Use the first equation to find x:

Iced tea costs $4.50 per gallon

Lemonade costs $4.75 per gallon

Answer:

C

Step-by-step explanation:

Got it right on ed 2021

Answer:

Hope this helps! :D

Answer:

x + 15

Step-by-step explanation:

N/A

Answer:

Step-by-step explanation:

if the bill was 51.48

and the tip        6.69

51.48/6.69=100/x where x= the % tip

x=(6.69*100)/51.48=13

x=13% tip

9514 1404 393

Answer:

  13%

Step-by-step explanation:

The tip percentage is the ratio of the tip to the bill, converted to a percent.

  tip/bill × 100%

  = $6.69/$51.48 × 100% ≈ 12.995% ≈ 13%

Claudia left a 13% tip.

Answer:

1. 45.76, 52.17, 54.2, 55.16, 56.78

2. 9.18, 9.2, 9.98, 10.54, 11.23

3. 0.01, 0.05, 0.067, 0.07, 0.09

4. 33.14, 33.15, 33.45, 33.52, 33.55

5. 3.45, 4.45, 4.9, 5.49, 6.5

Answer:

[tex]-(a+1\frac{3}{4}b)[/tex]

Step-by-step explanation:

Perimeter of a polygon = Sum of the measures of all sides of the polygon

For the given trapezoid,

Perimeter = [tex]1\frac{1}{2}a+1\frac{1}{2}b+1\frac{1}{2}a+2\frac{3}{4}b[/tex]

By combining similar terms,

Perimeter = [tex](1\frac{1}{2}+1\frac{1}{2})a+(1\frac{1}{2}+2\frac{3}{4})b[/tex]

                 = [tex](1+\frac{1}{2}+1+\frac{1}{2})a+(1+\frac{1}{2}+2+\frac{3}{4})b[/tex]

                 = (2 + 1)a + [tex](3+\frac{1}{2}+\frac{3}{4})b[/tex]

                 = 3a + [tex](3+\frac{2}{4}+ \frac{3}{4})b[/tex]

                 = 3a + [tex](3+\frac{5}{4})b[/tex]

                 = 3a + [tex](3+1+\frac{1}{4})b[/tex]

                 = 3a + [tex]4\frac{1}{4}b[/tex]

For rectangle,

Perimeter = 2(Length + Width)

                 = 2(2a + 3b)

Difference between the perimeter of trapezoid and rectangle,

= (3a + [tex]4\frac{1}{4}b[/tex]) - 2(2a + 3b)

= (3a - 4a) + ([tex]4\frac{1}{4}b[/tex] - 6b)

= -a + [tex](4+\frac{1}{4}-6)b[/tex]

= -a + [tex](\frac{1}{4}-2)b[/tex]

= -a + [tex](\frac{1}{4}-\frac{8}{4})b[/tex]

= -a - [tex]\frac{7}{4}b[/tex]

= [tex]-(a+1\frac{3}{4}b)[/tex]

Answer:

d ≈ 10.5

Step-by-step explanation:

The formula for the diagonal of a retangular prism (cuboid) is

[tex]d=\sqrt{l^2+w^2+h^2}[/tex]

1.) Plug in all the values for l, w, and h

[tex]d=\sqrt{5^2+6^2+7^2}[/tex]

2.) simplify by squaring the terms inside the square root

5 * 5 = 25

6 * 6 = 36

7 * 7 = 49

[tex]d=\sqrt{25+36+49}[/tex]

3.) Add the terms

[tex]d=\sqrt{110}[/tex]

4.) Simplify

[tex]d = 10.488[/tex]

5.) Round to one decimal place

d ≈ 10.5

Answer:

part A :BODMAS ( Bracket of Division Multiplication Addition Subtraction )

part b; Bracket (2+3.2) = - 2- 3.2

= 16- 2-3.2 +30-5

ADDITION:-3.2+30 = - 33.2

16-2(-33.2)30-5

14-33.2 +30-5

14-33.2 +25

-19.2+25

-44.2

Step-by-step explanation:

THE FOLLOWING EQUATION CAN ONLY BE SOLVED USING BODMAS

Answer:

The slope is -5/2 :)

Step-by-step explanation:

Answer:

The interest is $1050 and the amount is $8550.

Step-by-step explanation:

Answer: 12=4c

Step-by-step explanation:

The required simplified value of c in the given expression is c = 3.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

The equation is the values of two expressions that are equal.

Here,
From the figure, we have to balance the equation,
So,
12 = c +c +c +c
4c = 12
c = 3

Thus, the required simplified value of c in the given expression is c = 3.

Learn more about simplification here:

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Answer:

1

Step-by-step explanation:

In this figure, |v| represents the absolute value to 0. For example, |-3| would be 3 because it is 3 spaces from 0.

|10| - 3 × |-2| +5

10 - 3 * 2 + 5

10 - 6 + 5 ^ PEMDAS

-4 + 5

1

Answer:

4; 12 (refer to explanation)

Step-by-step explanation:

IF: 12 = total plants; 3 = amount of rows then,

12 ÷ 3 = 4

There are 4 plants per row.

IF: 12 = plants per row; 3 = amount of rows,

12 × 3 = 36 total plants; 12 plants in each row.

Answer:

x = 26°

Step-by-step explanation:

3x - 26° = 52°

3x - 26° + 26° = 52° + 26°

3x = 78°

3x : 3 = 78° : 3

x = 26°

Answer:

its the linear par postulate because it talks about linear pairs

Answer:

Linear Pair Postulate

Step-by-step explanation: Complements is wrong because we are not trying to prove that two angles of different figures are congruent and we are given two angles are added up to 180 not 90. Supplements is wrong because we arent trying to prove that two angles of different figures are congruent. Vertical Angles is wrong becuase we dont know if these angles are made by intersecting lines. Linear Pair Postulate states that hat two angles that form a linear pair are supplementary; that is, their measures add up to 180 degrees.

Answer:

Point-slope equation for the line is

[tex]y-2= -\frac {3}{2} (x -0)[/tex]

Step-by-step explanation:

Equation of straight line in slope intercept form is given as

[tex]y-y_1=m(x-x_1)[/tex]  ---------- (1)

Here

Slope            [tex]m=-\frac{3}{2}[/tex]  

Any Passing Point     [tex](x_1, y_1) = (0, 2)[/tex]

Substituting values in equation (1)

[tex]y-2= -\frac {3}{2} (x -0)[/tex]

Watch the letter order of the statement:

ΔABC ≅ ΔDEF

Where point:

A = D

B = E

C = F

Take any sides and use the corresponding labels correctly to make them congruent.

Let's say I take side AB.

ΔABC ≅ ΔDEF

Refer to the correspondence chart we did above ^^^. As you can see that AB is equal to DE. You can also see this by referring to the first two letters in the triangle statement.

One pair of congruent sides: AB ≅ DE

Now for the angles, it's basically the same concept.

I'll take angle ∠ABC or ∠B. (Note: Always refer to the middle letter when there is a three letter angle label like ∠ABC)

Refer to the chart and what do we see?

We see that:

∠ABC = ∠DEF

          or

∠B = ∠E

One pair of congruent angles: ∠ABC ≅ ∠DEF or ∠B ≅ ∠E

Note: you can also do this with any letter combination, order, etc. ONLY IF you can correctly order their corresponding points.

Answer:

140...........

Step-by-step explanation:

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Answer:

A nonagon is also called enneagon, which is derived from a Greek word called enneagonon, which means nine corners. The first use of the word nonagon dates back to the early 17th century, and has a Latin prefix (nona) and a Greek suffix (gon), making it a polygon with nine sides and nine angles.

Answer:

8.4 miles

Step-by-step explanation:

a mph in 45 min.

This means that she did 0.75 of a miles during that time.

When she bikes 4mph slower, she did 0.75a-4 which took her 70 minutes.

Now, V=d/t.

First equation: 0.75a=d/45

Second equation: (0.75a-4)=d/70

First equation: d=33.75a

Second equation: d=52.5a-280

Now, to put it all together: 52.5a-280=33.75a

18.75a=280

a= 14 14/15 mph

1 hour=60 min.

d=(0.75*14 14/15)/60

d=504/60

d=8.4 miles.

:)

Jasmine's grandma's home will be 504 miles away from her home.

The relation between distance[x] and time [t] is -

⇒ [x] = v [t]

where v is the velocity of body.

Given that;

Jasmine reached her grandma's house in 45 minutes. When she was biking back home in the evening it was foggy and she went 4 mph slower. The trip back took her 1 hour and 10 minutes.

Now, Let her grandma's home be [x] miles away form her house.

Assume that her velocity was [v] mph on her way to grandma's house.

So, We get;

⇒ 45 = x/v

⇒ x = 45v

And, Her velocity on her way back home would be [v - 4] mph

⇒ 70 = x/(v - 4)

⇒ x = 70(v - 4)

Equating both -

⇒ 45v = 70(v - 4)

⇒ 45v = 70v - 280

⇒ 70v - 45v = 280

⇒ 25v = 280

⇒ v = 11.2 mph

Hence, The value of [x] will be -

⇒ x = 45 x 11.2 = 504 miles

Thus, Jasmine's grandma's home will be 504 miles away from her home.

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Answer:

2 • 3 • 5

(30 is not a prime number.)

Answer:

Please check the expalantion.

Step-by-step explanation:

Let

Given that:

After reading two books, he has read 396000 words of text.

After five books, he has read 990000 words of text.

As the function is linear, so we take the points

Determining the slope between (2, 396000) and (5, 990000)

(x₁, y₁) = (2, 396000)

(x₂, y₂) = (5, 990000)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [990000 - 396000] / [5 - 2]

               = 594000 / 3  

               = 198000

Thus, the slope of the line = m = 198000

substituting the point (2, 396000) and m = 198000 in the slope-intercept form of the linear equation to determine the y-intercept

y = mx+b

396000 = 198000(2) + b

flipe the equation

198000(2) + b = 396000

396000 + b = 396000

subtracting 396000 from both sides

396000 + b - 396000 = 396000 - 396000

b = 0

now substituting b = 0 and m = 198000 in the slope-intercept form of the linear equation to determine the y-intercept

y = mx+b

y = 198000x + 0

y = 198000x

Therefore, a linear function in slope-intercept form to model his progress is:

y = 198000x

Part b)

How many books will he need to read to reach a total of 10,000,000 words?

As we have already determined a linear function in slope-intercept form to model his progress.

y = 198000x

substituting y = 10,000,000 in the equation

y = 198000x

10,000,000 =  198000x

flip the equation

198000x = 10,000,000

dividing the both equation by 198000

198000x/198000 = 10,000,000/198000

x = 50.5

Thus, Sonny will need to read 50.5 books to read to reach a total of 10,000,000 words.