What is the missing justification?

transitive property
reflexive property
symmetric property
substitution property

Answer:

A ≈ 21.22 m²

Step-by-step explanation:

The area (A) of a triangle using Heron's formula is

A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

where s is the semi perimeter and a, b, c the sides of the triangle.

Here the perimeter of the equilateral triangle is 21 m , then

a = b = c = 21 ÷ 3 = 7 m

s = 21 ÷ 2 = 10.5

Then

A = [tex]\sqrt{10.5(10.5-7)(10.5-7)(10.5-7)}[/tex]

   = [tex]\sqrt{10.5(3.5)(3.5)(3.5)}[/tex]

   = [tex]\sqrt{450.1875}[/tex]

   ≈ 21.22 m² ( to 2 dec. places )

Step-by-step explanation:

2y³z²

2(-1)³(3)²

=2(-1)(9)

=-18

Answer: 13

Step-by-step explanation:

Take 7 to the other side and divide 91 by 7, the answer will be 13.

Answer:

D because even though the flat fee is 150 paying 5$ a hour it will cost less

Answer:

[tex] x = \frac {30}{r} + 2 [/tex]

Step-by-step explanation:

Given the following data;

To find how many times greater is the S.A compared to the area, we would have to divide the surface area (S.A) of the cylinder by the area of circle.

Let the unknown variable be x.

[tex] x = \frac {30 \pi r + 2 \pi r^{2}}{\pi r^{2}} [/tex]

Factorizing the numerator, we have;

[tex] x = \frac {\pi r(30 + 2r)}{\pi r^{2}} [/tex]

Dividing both sides by πr, we have;

[tex] x = \frac {30 + 2r}{r} [/tex]

Simplifying further, we would have;

[tex] x = \frac {30}{r} + 2 [/tex]

Answer:

B

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a, b ] = [ 1, 3 ] , then

f(3) = 18 ← value of y when x = 3

f(1) = 2 ← value of y when x = 1

Then

average rate of change = [tex]\frac{18-2}{3-1}[/tex] = [tex]\frac{16}{2}[/tex] = 8 → B

Answer: -2/7

|3x - 2| - 4x = 4

1) (3х - 2) - 4х = 4, if 3x - 2 >= 0

2) -(3x - 2) - 4x = 4, if 3x - 2 < 0

1)

3х - 4х = 4 + 2

-x = 6

x = -6

3х - 2 >= 0

3х >= 2

x >= 2/3 - wrong

2)

-3х + 2 - 4х = 4

-7х = 2

x = -2/7

3x-2<0

3x<2

3(-2/7)<2-right

Answer:

since Sal washed 5 cars in 50 minutes, we can express his time as follow:

[tex] \frac{5 \: cars}{50 \: minutes} [/tex]

simplifying it by diving by 5, we get:

[tex] \frac{1 \: car}{10 \: minutes} [/tex]

Thus the rate will be 10 minutes per car (10 min/car)

Answer:

10 mins / car

Step-by-step explanation:

50 / 5 = 10

BECAUSE ACCORDING TO THE PERIMETER (TRIANGLE ) FORMULA = B * H / 2.

B = BASE.

H = HEIGHT.

THE HEIGHT IS A VARIABLE VLAUE NEEDED IN ORDER TO ONTINUE TO SOLVE AND EVENTUALLY LEADING TO THE ANSWER (TRIANGLE PERIMETER.

Answer:

0

Step-by-step explanation:

r=5

So

=5⁴-5(5)³-4(5)²+5(5)+75

=5⁴-5(125)-4(25)+5(5)+75

=625-625-100+25+75

=0

Answer:

-------------

[tex]36x^3,\:22x^2,\:4xy[/tex]

Factor 36x³

Factor 22x²

Factor 4xy

Common factor

---------------------

[tex]36x^3-22x^2-12x[/tex]

Factor 36x³

Factor 22x²

Factor 12x

Common factor

OAmalOHopeO

Answer:

y = -3/4x + 3

Step-by-step explanation:

Answer: A) 87

The median value is the second quartile (Q₂), which is 87.

Answer:

A: 87

Step-by-step explanation:

Sorry for this very late response. But if anyone is not sure if answer A is correct, it is. I can confirm this because I just took the test. I hope I could help! (:

Answer:

3300cm²

Step-by-step explanation:

30cm+30cm=60cm 60cm is the lengh of the whole joint structure.We will put it in the equation as "a".

heigh stays the same(10cm) because the pieces are not stacked one on top of the other.They are joined on their sides.We will put it as "c".

Widht also stays the same.its 15 cm and we will put it as letter "b".

So

a=60cm

b=15cm

c=10cm

We need to calculate the surface area of the entire joint structure.

1.First thing to do is to calculate the top part which is:

a*b=15*60=900cm²

2.The bootom side is the same 900cm².

3.The front side is:

a*c=60*10=600cm²

4.The back side is the same as front so it is 600cm².

5.The left side is:

c*b=10*15=150cm²

6.The right side is the same as the left and it is 150cm²

Now we just add it up.

S(surface)=900*2+600*2+150*2=3300cm²

If you want the whole exercise in one equation:

S=2*(a*b)+2*(a*c)+2*(b*c)

Answer:

8x^2-1+3^2

Step-by-step explanation:

Answer Should be 45

Answered by Gauthmath must click thanks and mark brainliest

Answer:

1. -18x+6

multiply everything inside with the number outside the bracket

2. -18x-6

same as number one

3. 18x-12

same as number one

4. -18x-6

same as number one

for 5 I can't see it well but it should be similar

you just need to substitute what's outside the bracket to what Is inside the bracket

Answer: -6 (3x+1)

Step-by-step explanation:

Factor the polynomial -18x-6−18x−6 by it's GCF: -6−6

Answer:

864

Step-by-step explanation:

A=6a^2=6·12^2=864

Answer:

864 in^2

Step-by-step explanation:

2(144+144+144) = 2(432) = 864 in^2.

Hope this helped!

Answer:

-2/25

Step-by-step explanation:

Use the slope formula: rise/run to find the slope

Answer:

slope = - [tex]\frac{2}{25}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 20, 18) and (x₂, y₂ ) = (30, 14)

m = [tex]\frac{14-18}{30-(-20)}[/tex] = [tex]\frac{-4}{30+20}[/tex] = [tex]\frac{-4}{50}[/tex] = - [tex]\frac{2}{25}[/tex]

Answer:

x=[tex]\frac{3}{2}[/tex] and x=[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

[tex]\sqrt{36x^2-60x+25}=4[/tex]

=> [tex]\sqrt{36x^2-60x+25}^{2} =4^{2}[/tex]

=> [tex]{36x^2-60x+25}=16[/tex]

=> [tex]36x^2-60x+25-16=16-16[/tex]

=> [tex]36x^2-60x+9=0[/tex]

=> [tex]x_{1,\:2}=\frac{-\left(-60\right)\pm \sqrt{\left(-60\right)^2-4\cdot \:36\cdot \:9}}{2\cdot \:36}\\\\\sqrt{\left(-60\right)^2-4\cdot \:36\cdot \:9}=48[/tex]

=> [tex]x_{1,\:2}=\frac{-\left(-60\right)\pm \:48}{2\cdot \:36}[/tex]

=>[tex]x_{1} = \frac{-\left(-60\right)+48}{2\cdot \:36}\\\\x_{1}=\frac{60+48}{2\cdot \:36}\\\\x_{1}=\frac{108}{72} \\\\\\x_{1}=\frac{3}{2}\\[/tex]

=> [tex]x_{2}=\frac{-\left(-60\right)-48}{2\cdot \:36}\\\\x_{2} =\frac{60-48}{2\cdot \:36}\\\\x_{2}=\frac{12}{2\cdot \:36}\\\\\x_{2}=\frac{12}{72}\\\\x_{2}=\frac{1}{6}[/tex]

Answer:

Step-by-step explanation:

Distance traveled in [tex]1\frac{4}{5}[/tex] hours = [tex]\frac{3}{10}[/tex]

Distance traveled in 1 hour = [tex]\frac{3}{10}[/tex] ÷ [tex]1\frac{4}{5}[/tex]

          [tex]=\frac{3}{10}[/tex] ÷ [tex]\frac{9}{5}[/tex]

          [tex]= \frac{3}{10}*\frac{5}{9}\\\\=\frac{1}{2}*\frac{1}{3}\\\\=\frac{1}{6}[/tex]

distance traveled in 3 1/5 hours = [tex]\frac{1}{6}*3\frac{1}{5}[/tex]

 =[tex]=\frac{1}{6}*\frac{8}{5}\\\\=\frac{1}{3}*\frac{4}{5}\\\\=\frac{4}{15}[/tex]

Answer:

C. 2.

Step-by-step explanation:

The graph descends from the left  so the coefficient of the leading term is negative. It is also a cubic equation with zeros of -20, about 6.5 and about 13. so we can write the equation as below.  The last 2 values can only be guessed because the x axis only shows values which are multiples of 5.

f(x) = a(x + 20)(x - 6.5)(x - 13)   where a is  a negative constant.

(This is only an approximation).

By the Remainder theorem, when the expression is divided by (x + 10):

f(-10) = -20 so we have

-20 = a (-10 + 20)(-10-6.5)(-10 - 13)

(10)(-16.5)(-23)a = -20

a = -20 / (10)(-16.5)(-23)

a = -0.0053

When  the equation is divided by (x - 10) then f(10)  is the remainder so substituting we have as the remainder:

-0.0053(10+20)(10-6.5)(10 -13)

-0.0053 * 30 * 3.5 * -3

= 1.7 approximately.

Looks like the answer is 2.

Answer:

(1, 2)

Step-by-step explanation:

Given the equation of the lines x + 2y = 5 and 2x - 3y = -4

First we need to make x the subject of the formulas

For x+2y = 5

x = 5 - 2y ... 1

For 2x - 3y = -4

2x = -4+3y

x = (-4+3y)/2 ... 2

Equate 1 and 2

5 - 2y =  (-4+3y)/2

2(5-2y) = -4+3y

10 - 4y = -4+3y

-4 -3y = -4-10

-7y = -14

y = 14/7

y = 2

Substitute y = 2 into 1

x = 5 = 2y

x = 5 - 2(2)

x = 5 - 4

x = 1

Hence the point where the lines meet will be at (1, 2)

Answer:

Area=9:25 Volume=81:625

Step-by-step explanation:

Should be squared, might be wrong.

Answer: [tex]\large \boldsymbol {C) \ AB=\sqrt{41} }[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

The cos of an angle is the adjacent / hypotenuse.

In this case the adjacent and hypotenuse are the same length so the answer is 1 in some form.

You are going left when you talk about 180 degrees. So the adjacent = - 1

The answer you want is -1 / 1

Cos(180) = - 1

Answer:

C. Complex

Step-by-step explanation:

A complex number consists of a real part (-4.8) and an imaginary part (56i)

Answer:

Step-by-step explanation:

Let y is the required number.

a/c to question,

y² + greatest three digit prime number + smallest two digit prime number = 32²

we know, greatest three digit prime number = 997

smallest two digit prime number = 11

now, y² + 997 + 11 = 32²

or, y² + 1008 = 1024

or, y² = 1024 - 1008

or, y² = 16

or, y = 4

hence, required number number is one digit even number e.g., y = 4

Hope this answer helps you :)

Have a great day

Mark brainliest

This are a few of Rational numbers are not whole numbers: 8,−3,32,7−5.

Step-by-step explanation: Hope this helps

Answer:

Thamkhao

Step-by-step explanation: