Factoring binomials with the difference of squares

Answer:

6 cm

Step-by-step explanation:

Let each side of the equilateral triangle be a.

Given, area of an equilateral triangle = 9√3 cm2

Area of an equilateral triangle = (√3)/4 × (Side)²

=> (√3)/4 × a² = 9√3

[tex] {a}^{2} = \frac{9 \sqrt{3} }{ \frac{ \sqrt{3} }{4} } = \frac{9 \sqrt{3} }{ \sqrt{3} } \times 4 = 9 \times 4[/tex]

=> a² = 36

[tex] \sqrt{ {a}^{2} } = \sqrt{36} \\ a = (+ - )6[/tex]

∴ Side = 6 cm  [taking positive square root because side is always positive]

Answer:

22.5 degrees and 67.5 degrees

Step-by-step explanation:

complementary angles add up to 90°

x + 3x = 90°

4x = 90

90/4 = x

x = 22.5

The first angle is 22.5

The second angle is 3 times as much

22.5 x 3 = 67.5

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-Chetan K

Answer: First Choice. 5ft

Step-by-step explanation:

Here we need to know the idea of the Pythagorean theorem.

Since a building is straight, the base angle is a right angle, thus it would be a right triangle.

Pythagorean Theorem: a² + b² = c²

**NOTE** Please refer to the attachment below for the figure. (I drew it, so if it was not clear and understandable for you, please tell me.)

Solve:

Given information

a = 12 ft

c = 13 ft

b = unknow base length

Given formula for Pythagorean Theorem

a² + b² = c²

Substitute values into the formula

12² + b² = 13²

Simplify exponents

144 + b² = 169

Subtract 144 on both sides

144 + b² - 144= 169 - 144

b² = 25

Square root both sides

√b² = √25

[tex]\boxed{b=5}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

you have $ 8

Step-by-step explanation:

cheque wrote ,=$10

and he threw =$2

then total $ left will be $8

please mark me brainleast

By looking at the dot graph, we can see that the single dot above 12 in the Stony Brook graph, means that the ecologist find that in one of the 42 places measured in the Stony Brooks lake, the nitrate concentration was 12 mg/L

To understand this, first I want to give a brief explanation of how these graphs work.

You know that the ecologist did study the Nitrate pollution at 42 places in two lakes.

Each of these 42 places is represented with a dot in the corresponding graph.  Now looking at the graph, the position of the dots represents the nitrate concentration (you can see it in the horizontal axis) on one of these 42 places (42 dots for 42 places).

So, having a single dot above 12 in the Stony Brook graph, means that the ecologist find that in one of the 42 places measured in the Stony Brooks lake, the nitrate concentration was of 12 mg/L

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Answer:

-12

Ydbzushsbsksjsbsksudjeke

Step-by-step explanation:

Hi there!

According to the question;

nth term (tn) = 3n+8

a).

T1 = 3*1+8

= 11

b).

t7 = 3*7+8

= 29

c).

t14 = 3*14+8

= 50

Therefore, t1 = 11, t7 = 29, t14 = 50.

Hope it helps!

Answer:

11, 29, 50

Step-by-step explanation:

To find the appropriate term , substitute the term number into the rule, that is

(a) t₁ = 3(1) + 8 = 3 + 8 = 11

(b) t₇ = 3(7) + 8 = 21 + 8 = 29

(c) t₁₄ = 3(14) + 8 = 42 + 8 = 50

Rewrite the length as an improper fraction.

21 7/8 = 175/8

Write the quantity of stamps as a fraction: 25/1

Divide length by number of stamps:

175/8 / 25/1

When dividing by a fraction change the sign to multiplication and flip the second fraction over:

175/8 x 1/25.

Now multiply numerators and then denominators:

(175 x1) / (8x 25) = 175/200

Simplify to 7/8

Each stamp is 7/8 inches long

Answer:

set of even counting number is well-defined

Answer:

Juanita's cat is faster because it can run more blocks in a second

Step-by-step explanation:

Take the number of blocks and divide by the number of seconds

Jim:

4 blocks/ 15 seconds

.26666.... block per second

Juanita

3 blocks / 11 seconds

.2727...... blocks per second

Juanita's cat is faster because it can run more blocks in a second

Answer:

164

Step-by-step explanation:

in standard form CLXIV IS 164

Answer:

The answer Is A 1 1/5 < -2 2/5

Step-by-step explanation:

It says that this statement is true because 1 1/5 is to the left of -2 2/5 on the number line but it is actually to the right because -2 2/5 is negative while 1 1/5 is positive therefore making it larger and the correct statement would be that    1 1/5 > -2 2/5

Answer:

4x^2 -12x +9

now

4 x 9 = 36

first take out the LCM of 36

it will be

2 x 2 x 3 x 3

4x^2 -6x -6x +9

2x(2x-3) -3(2x-3)

(2x-3)(2x-3)

it is showing that

2x-3 is the length for part A

Answer:

55°

Step-by-step explanation:

Since two of the sides are the same length, that means ∠A and ∠B are the same.

All angles of a triangle add up to 180°

180 - 70 = 110

To find ∠A, we just divide 110 by 2

110 ÷ 2 = 55

Both ∠A and ∠B are 55°

Answer:

Associative property.

Step-by-step explanation:

[tex]assosiative \: property \\ for \: any \: nubers \: likeur \: question \: \\ didnt \: affect \: theanswer \\ thank \: you[/tex]

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Answer:

2nd option

Step-by-step explanation:

Given

c = 8πab ( isolate a by dividing both sides by 8πb

[tex]\frac{c}{8\pi b}[/tex] = a

Answer:

[tex]3(y + 2) - 5 = 22 \\ 3(y + 2) = 27 \\ (y + 2) = 9 \\ y = 9 - 2 \\ y = 7[/tex]

Answer: 7

Step-by-step explanation:

3y+6-5=22

3y+1=22

3y=22-1

y=21/3

y=7

The third answer

1 quarter, 6 dimes, 1 nickel, 7 pennies

Answer:

It doesn't say what to do with that 0.1 of a gallon. I would buy another gallon or dilute what I had so it came to exactly 9.1 gallons. In math, I suppose the answer is 9.

In reality it would be 10.

You have to choose.  What has been done with other questions like this.

Step-by-step explanation:

1 can covers 55 square feet.

h = 10

w1 = 10 feet

w2 = 10 feet

w3 = 15 feet

w4 = 15 feet

Total area = Area of wall 1 + wall 2 + wall 3 + wall 4

Total area = 10*10 + 10*10 + 10*15 + 10* 15

Total area = 100  + 100 + 150 + 150

Total area = 500  feet^2

1 gallon / 55 ft^2 = x / 500 ft^2          Cross multiply

55 * x = 500                                       Divide by 55

x = 500/55

x = 9.1 gallons.

In real life you would buy another gallon.

Answer:

A

Step-by-step explanation:

x^a/x^b=x^(a-b). General rule of exponents

We have that the distance around the park to the nearest yard,QM to the nearest yard and the Time of travel for man's jog is given respectively as

From the Question we are told that

[tex]PQ=(50-10)=40\\\\QR=(80-10)70[/tex]

Generally the equation for the Resultant PR is mathematically given as

[tex]PR=\sqrt{PQ^2+QR^2}\\\\PR=\sqrt{70^2+40^2}\\\\PR=80yd[/tex]

a)

Generally the equation for the Distance around they park is mathematically given as

[tex]X=PQ+QR+PR\\\\X=80+70+40\\\\[/tex]

[tex]X=190yd[/tex]

b)

Generally the equation for the Path QM is mathematically given as

From the diagram we see that

[tex]QM=PM=MR\\\\QM=\frac{80}{2}\\\\[/tex]

[tex]QM=40yd[/tex]

c)

From the question we are told

Average speed of [tex]150yd/m[/tex]

Total distance traveled

[tex]D_t=40+40+40+70+40\\\\D_t=230yd[/tex]

Therefore

Time

[tex]T=\frac{D_t}{V}\\\\T=\frac{230}{150}[/tex]

[tex]T=1.5minutes.[/tex]

in conclusion

The distance around the park to the nearest yard,QM to the nearest yard and the Time of travel for man's jog is given respectively as

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Answer:

27 square are there in the given figure

Answer:

Represents

Step-by-step explanation:

Going over the basic definition of polynomial, an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division, we can see that the expression is indeed a polynomial.

Answer:

112 guests

Step-by-step explanation:

I. If her total cost is 773$

When Total = DJ + Cake + Guest

            773 = 250 + 75 + 4(x)

            773 = 325 + 4(x)

            773 - 325 = 4(x)

            448 = 4x

               x = 448/4

               x = 112

That makes guests are 112

Step-by-step explanation:

y+x-2-6x = y-5x-2

2x+3-x-4 = x-1

5xy+4x-5xy-3 = x