PLEASE HELP ME ASAP!!!! WILL GIVE BRAINLIEST!!!!!!! 50 POINTS!!!!!!
Provide a proof to the following theorem.

Given: <1 is congruent to <2 and <3 and <4 are supplementary.

Prove: a is parallel to c
You may label any of the other angles if needed.
Provide a proof of the situation described above.
The proof may be either a paragraph proof, a two-column proof, or a flow chart proof.

Answer:

$722.40

Step-by-step explanation:

2.8% x 4300 = 120.4

120.4 x 6 = 722.40

Answer:

Step-by-step explanation:

8. The volume of the rocket = the volume of the cone + the volume of the cylinder.

The volume of the cone is = [tex]\frac{1}{3} \pi \times radius^{2} (height) = \frac{1}{3} \pi \times 3^{2} \times5 = 15\pi[/tex] [tex]inch^{3}[/tex].

The volume of the cylinder is [tex]\pi \times radius^{2} \times height = \pi \times 3^{2} \times 10 = 90\pi[/tex] [tex]inch^{3}[/tex].

The total volume is [tex]15\pi + 90\pi = 105\pi inch^{3}[/tex].

9. Matt made the error in calculating the volume.

The diameter of the spherical ball is given by 15 centimeter.

The volume of a spherical ball is calculated by the formula [tex]\frac{4}{3} \pi \times radius^{3}[/tex].

Matt put the diameter of the spherical ball instead of its radius.

Answer:

$500

Step-by-step explanation:

We are given;

We are supposed to determine the amount spent on food;

Therefore;

Amount on gas and hotel room = 3/5 × $2500

                                                     = $ 1500

Thus;

Remaining amount = $2500 - $1500

                                = $1000

But;

1/2 of the remainder was spent for the food

Thus;

Amount on food = 1/2 × $1000

                           = $500

Hence, the family spent $500 on food

Ricky jogged 6 miles on tuesday and 6 miles on friday

Solution:

Given that,

Rick jogged the same distance on tuesday and friday

Let "x" be the distance jooged on each tuesday and friday

He also jogged for 8 miles on sunday

Total of 20 miles for the week

Therefore, we frame a equation as,

total distance jogged = miles jogged on tuesday + miles jogged on friday + miles jogged on sunday

20 = x + x + 8

20 = 2x + 8

2x = 20 - 8

2x = 12

x = 6

Thus Ricky jogged 6 miles on tuesday and 6 miles on friday

Final answer:

Rick jogged 6 miles each day on Tuesday and Friday. This was found by solving the equation 2x + 8 = 20, where 2x represents the total distance for Tuesday and Friday, and 8 miles is the distance for Sunday.

Explanation:

Rick jogged the same distance on Tuesday and Friday, and 8 miles on Sunday for a total of 20 miles for the week. Since Rick jogged the same distance on both Tuesday and Friday, we can let the distance he jogged on each of those days be represented by the variable x. The total distance jogged over these three days (Tuesday, Friday, and Sunday) can be represented by the equation 2x + 8 = 20.

To solve for x, first subtract 8 from both sides of the equation to isolate the variable:

2x + 8 - 8 = 20 - 8

2x = 12

Then, divide both sides by 2 to get the value of x:

2x / 2 = 12 / 2

x = 6

The distance Rick jogged on Tuesday and Friday was therefore 6 miles each day.

x + y = 12

Equation 2: Difference:

x - y = 4

Solution:

x + y = 12

x - y = 4

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

Add the two equations together:

2x = 16

Divide both sides by 2:

x = 8

Solve for y:

Use equation 1 substituting for x:

x + y = 12

8 + y = 12

Subtract 8 from both sides:

y = 4

Answer:

one number is 8 and the other number is 4.

8 + 4 = 12

8 - 4 = 4

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The numbers are 8 and 4.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Let the two numbers be M and N.

Now,

The sum is 12 and their difference is 4.

This can be written as,

M + N = 12 _____(1)

M - N = 4 _______(2)

From (1) we get,

M = 12 - N ______(3)

Putting (3) in (2) we get,

M - N = 4

12 - N - N = 4

12 - 2N = 4

Add 2N on both sides.

12 = 4 + 2N

Subtract 4 on both sides.

12 - 4 = 2N

8 = 2N

Divide 2 on both sides.

N = 8/2

N = 4

Now,

Put N = 4 on (3).

M = 12 - 4

M = 8

We can cross-check.

M + N = 12

8 + 4 = 12

12 = 12

M - N = 4

8 - 4 = 4

4 = 4

Proved.

Thus,

The numbers are 8 and 4.

Learn more about expressions here:

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Answer:

A Factor can be explained as combination of the numerator and denominator by which the demo is decided by the numerator

Answer:

factor a number means to break it up into numbers that can be multiplied together to get the original number. EXAMPLES: 6 = 3 x 2 so, factors of 6 are 3 and 2 9 = 3 x 3 so, factors of 9 are 3 and 3 Sometimes, numbers can be factored into different combinations.

Step-by-step explanation:

Answer:

Therefore the coordinates of C is

C(4,9).

Step-by-step explanation:

Given:

Point A , B , and C are Collinear.

i.e A-B-C is a Straight Line

AB : BC = 1 : 1

i.e B is the Mid Point of AC.

And Point A , B and C lie on the Same Line

point A( x₁ , y₁) ≡ ( 0 ,-9)

point B( x , y) ≡ (2 , 0)

To Find:

point C( x₂ , y₂) ≡ ?

Solution:

B is the Mid Point of AC. Hence by Mid point Formula,

[tex]Mid\ point(AC)=(\dfrac{x_{1}+x_{2} }{2}, \dfrac{y_{1}+y_{2} }{2})[/tex]

Substituting the values we get

[tex]B(2,0)=(\dfrac{0+x_{2} }{2}, \dfrac{-9+y_{2} }{2})[/tex]

Substituting x and y value we get

[tex]2=\dfrac{0+x_{2} }{2}\\and\\0=\dfrac{-9+y_{2} }{2}[/tex]

[tex]x_{2}=4\\and\\y_{2}=9[/tex]

Therefore the coordinates of C is

C(4,9).

Answer:

[tex]5s^2 +13s-10[/tex]

Step-by-step explanation:

Given the expression

[tex]5s(3+s)-(2s+10)[/tex]

First, use distributive property:

[tex]5s(3+s)=5s\cdot 3+5s\cdot s=15s+5s^2\\ \\-(2s+10)=(-1)\cdot (2s+10)=(-1)\cdot 2s+(-1)\cdot 10=-2s-10[/tex]

Now, the given expression is equivalent to the following expression:

[tex]15s+5s^2-2s-10[/tex]

Rewrite this expression using commutative property:

[tex]5s^2+15s-2s-10\\ \\=5s^2 +13s-10 \ [\text{Add the like terms}][/tex]

Answer:

Step-by-step explanation:

Answer:

= 8a/b + 6b/a

look at the phot below for more details.

:)

Answer:

0

Step-by-step explanation:

Answer:

701 revolutions

Step-by-step explanation:

Given: Length= 2.5 m

            Radius= 1.5 m

            Area covered by roller= 16500 m²

Now, finding the Lateral surface area of cylinder to know area covered by roller in one revolution of cylindrical roller.

Remember; Lateral surface area of an object is the measurement of the area of all sides excluding area of base and its top.

Formula; Lateral surface area of cylinder= [tex]2\pi rh[/tex]

Considering, π= 3.14

⇒ lateral surface area of cylinder= [tex]2\times 3.14\times 1.5\times 2.5[/tex]

⇒ lateral surface area of cylinder= [tex]23.55 \ m^{2}[/tex]

∴ Area covered by cylindrical roller in one revolution is 23.55 m²

Next finding total number of revolution to cover 16500 m² area.

Total number of revolution= [tex]\frac{16500}{23.55} = 700.6369 \approx 701[/tex]

Hence, Cyindrical roller make 701 revolution to cover 16500 m² area.

The number of revolutions a cylindrical roller makes can be determined by first finding the area it covers in one revolution (using the formula for the surface area of a cylinder) and then dividing the total area covered by this. The formula to calculate the surface area of a cylinder is 2πrh, where r is the radius and h is the length of the cylinder.

First, we need to find the surface area of the roller. The surface area of a cylinder can be calculated using the formula: 2πrh, where r is the radius and h is the height (or in this case, the length of the roller). Here, r = 1.5m and h = 2.5m, so the surface area that the roller covers in one revolution is 2π(1.5m)(2.5m) = 11.25π m².

The roller covers an area of 16500 m², so to find out how many revolutions it makes, we divide the total area by the area covered in one revolution. That is, 16500m² / 11.25π m². After carrying out the division, we get the number of revolutions the roller makes. This will give us the desired answer.

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Answer:

DC = 4.5

Step-by-step explanation:

Since DC is on AC it is a segment bisector.

This divides AC exactly in half.

AC = 9 / 2  = 4.5

DC = 4.5

Answer:

The ratio of AC to CB is 1.677 to  5.03

Step-by-step explanation:

Step 1: Finding the distance of AC

By using distance formula

[tex]AC = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

Substituting the values

[tex]AC = \sqrt{(1.5 -0)^2 + (0.75 -0)^2}[/tex]

[tex]AC = \sqrt{(1.5 )^2 + (0.75)^2}[/tex]

[tex]AC = \sqrt{2.25 +0.5625 }[/tex]

[tex]AC = \sqrt{2.8125 }[/tex]

AC= 1.677

Step 2: Finding the distance of CB

[tex]CB = \sqrt{(6 - 1.5)^2 + (3 - 0.75)^2}[/tex]

Substituting the values

[tex]CB = \sqrt{(4.5)^2 + (2.25)^2}[/tex]

[tex]CB = \sqrt{(20.25) + (5.0625)}[/tex]

[tex]CB = \sqrt{25.3125}[/tex]

CB = 5.03

The Ratio is   1.677 to  5.03

[tex]4NO+6H_{2} O\Leftrightarrow4 NH _{3}+5O_{2}[/tex]

Step-by-step explanation:

[tex]NO+H_{2} O\rightarrow NH _{3}+O_{2}[/tex]

[tex]4NO+6H_{2} O\Leftrightarrow4 NH _{3}+5O_{2}[/tex]

Answer:

1) The simplified radical form is  [tex]\sqrt{36x^2}=6x[/tex]

2) The simplified radical form is  [tex]\sqrt{72x^3}=6x\sqrt{2x}[/tex]

3) The simplified radical form is  [tex]\sqrt{15x^8}=\sqrt{15}x^4[/tex]

4) The simplified radical form is  [tex]\sqrt{36x^7}=6x^3\sqrt{x}[/tex]

Step-by-step explanation:

1) Given expression is [tex]\sqrt{36x^2}[/tex]

To find the simplified radical form of the given expression :

[tex]\sqrt{36x^2}[/tex]

[tex]=\sqrt{36\times x^2}[/tex]

[tex]=\sqrt{36}\times \sqrt{x^2}[/tex]

[tex]=\sqrt{6\times 6}\times \sqrt{x\times x}[/tex]

[tex]=6\times x[/tex]

[tex]\sqrt{36x^2}=6x[/tex]

Therefore the simplified radical form is  [tex]\sqrt{36x^2}=6x[/tex]

2)Given expression is [tex]\sqrt{72x^3}[/tex]

To find the simplified radical form of the given expression :

[tex]\sqrt{72x^3}[/tex]

[tex]=\sqrt{72\times x^3}[/tex]

[tex]=\sqrt{72}\times \sqrt{x^3}[/tex]

[tex]=\sqrt{9\times 8}\times \sqrt{x\times x\times x}[/tex]

[tex]=\sqrt{9}\times \sqrt{8}\times x\sqrt{x}[/tex]

[tex]=3\times 2\sqrt{2}\times x\sqrt{x}[/tex]

[tex]\sqrt{72x^3}=6x\sqrt{2x}[/tex]

Therefore the simplified radical form is  [tex]\sqrt{72x^3}=6x\sqrt{2x}[/tex]

3) Given expression is [tex]\sqrt{15x^8}[/tex]

To find the simplified radical form of the given expression :

[tex]\sqrt{15x^8}[/tex]

[tex]=\sqrt{15\times x^8}[/tex]

[tex]=\sqrt{15}\times \sqrt{x^8}[/tex]

[tex]=\sqrt{5\times 3}\times \sqrt{x^4\times x^4}[/tex]

[tex]=\sqrt{15}\times x^4[/tex]

[tex]\sqrt{15x^8}=\sqrt{15}x^4[/tex]

Therefore the simplified radical form is  [tex]\sqrt{15x^8}=\sqrt{15}x^4[/tex]

4) Given expression is [tex]\sqrt{36x^7}[/tex]

To find the simplified radical form of the given expression :

[tex]\sqrt{36x^7}[/tex]

[tex]=\sqrt{36\times x^7}[/tex]

[tex]=\sqrt{36}\times \sqrt{x^7}[/tex]

[tex]=\sqrt{6\times 6}\times \sqrt{x^3\times x^3\times x}[/tex]

[tex]=6\times x^3\sqrt{x}[/tex]

[tex]\sqrt{36x^7}=6x^3\sqrt{x}[/tex]

Therefore the simplified radical form is  [tex]\sqrt{36x^7}=6x^3\sqrt{x}[/tex]

Answer:

Step-by-step explanation:

so John (lol...who names a snake John)....ok...so at 5 months he was 4 ft...and at 6 months, he was 4'2....means he is growing at a rate of 2 inches per month. So if he continues to grow at 2 inches per month, then this is linear...but if he doesn't, its not linear.

So from 6 months to 1 year, is a period of 6 months...and if he grows at 2 inches per month, in 6 months he should have grown (6 * 2) = 12 inches.

4'2" + 12 inches = 4 ft 14 inches = 5 ft 2 inches......but he is not 5'2" at age 1, he is only 5 ft.....so NO, this is NOT linear.

Answer: -1

Step-by-step explanation:

i^42

(i^2)^21 ( NOTE i^2 = -1 )

(-1)^21

-1 ( -1^odd number is -1 )

Answer:

(x/2)*4=3

= x*4/2=3

2x=3

x=1.5

Check:

4*(1.5)/2

=6/2

=3

Answer:

3/8

Step-by-step explanation:

The product of the fraction numbers 5/4 and 3/10 in the simplified form will be 3/8.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The fraction numbers are given below.

5/4 and 3/10

Then the product of the fraction numbers 5/4 and 3/10 is given as,

⇒ 5/4 x 3/10

⇒ 15 / 40

⇒ 3/8

The product of the fraction numbers 5/4 and 3/10 in the simplified form will be 3/8.

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Answer:

Simplified: 10x-55

Step-by-step explanation:

Distribute the five into the parenthesis..

(5)2x- (5)11

Then, multiply.

10x-55

10x-55 is the simplified version by the distributive property.

Answer:

10x - 55

Step-by-step explanation:

5(2x-11)

5*2x=10x

5*11

10x-55

Answer:

X = 0.75

Step-by-step explanation:

0.25[2.5x + 1.5(X-4)]= -X

0.25[2.5x + 1.5x - 6] = -x

0.25[4x -6] = -x

1x + x = 1.5

2x = 1.5

x = 1.5/2

x = 0.75

Answer:

number of sodas sold = 105

number of hot dogs sold = 61

Step-by-step explanation:

i) Let the number of sodas sold be = x

ii) Let the number of hot dogs sold be = y

iii) It is given that the total number of hot dogs and sodas sold = 166

Therefore we can say that x + y = 166

iv) It also given that the number of sodas sold was 44 more than the number of hot dogs sold

Therefore we can say that x = y + 44

v) Substituting the value of x from iv) in the equation in iii) we get

    (y + 44) + y  = 166 ⇒    2y + 44 = 166    ⇒   2y = 122  ∴ y = 61

   Therefore the number of hot dogs sold = 61

vi) Substituting the value of y from v) in iv) we get

            x = y + 44    ⇒    x = 61 + 44   ∴ x = 105

     Therefore the number of sodas sold = 105

Answer:

the ratio of part time workers to total workers are 12/30

Answer:

2 3

4 5

(2x+3)(4x-5)

Step-by-step explanation:

Ur welcome

For this case we must simplify the following expression:

[tex]\frac {3- \frac {2} {a}} {5+ \frac {3} {a}}[/tex]

So, we have:

[tex]\frac {\frac {3a-2} {a}} {\frac {5a + 3} {a}} =[/tex]

We apply double C:

[tex]\frac {a (3a-2)} {a (5a + 3)} =[/tex]

We simplify:

[tex]\frac {3a-2} {5a + 3}[/tex]

Answer:

The simplified expression is:

[tex]\frac {3a-2} {5a + 3}[/tex]

The expression for the number of words Craig types in m minutes is 20 words/minute × m minutes. This equation can be used to calculate how many words Craig can type in any given number of minutes.

If Craig types at a speed of 20 words per minute, to find the expression for the number of words he types in m minutes, you would use the simple formula of rate times time. The rate is the number of words per minute, and the time is how many minutes he is typing. Therefore, the expression would be:

20 words/minute × m minutes = number of words Craig can type in m minutes.

To find out if Craig can type more than 200 words, you can set m to a value greater than 10, since 20 words/minute for 10 minutes would result in 200 words exactly (20 × 10 = 200).

x + 5y = -9

8x - 10y = 28

Set y equal

-2y - 10y = 18

8x - 10y = 28

Subtract from one another

-10x = -10

Divide

x = 1

Plug x in one of the equations and solve

x + 5y = -9

1 + 5y = -9

5y = -10

y = -2

Answer

(1,-2)

Hope this helps! ;)

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x+5y=-9\\8x-10y=28&\text{divide both sides by 2}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}x+5y=-9\\4x-5y=14\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad5x=5\qquad\text{divide both sides by 5}\\.\qquad\boxed{x=1}\\\\\text{Put it to the first equation}\\\\1+5y=-9\qquad\text{subtract 1 from both sides}\\5y=-10\qquad\text{divide both sides by 5}\\\boxed{y=-2}[/tex]

Answer:

It has 2 solutions

Step-by-step explanation:

Solution 1

-17(y - 2) = -17y + 64 - 17(y - 2)

Solution 2

-17y + 64 - 17(y - 2) = -17y + 64

-17(y - 2) = -17y + 64

-17y  + 34 = -17y + 64

-17y + 17y = 64 - 34

0 = 30 (incorrect)

this system has NO SOLUTIONS

The expression (4r+6)÷2 can be used to represent the number of females on a team if r is used to represent the number of female team members. Otherwise, it represents what the variable r represents.

The expression (4r+6)÷2 represents an algebraic equation where r is a variable. If r is representing the number of female team members in a sport, then the value for r can be inserted into the equation to find the total. For instance if r=5, representing 5 female team members, the equation would then be (4*5+6) ÷2 = (20+6) ÷ 2 = 26 ÷ 2 = 13.

However, it's important to note that this equation does not inherently represent the number of females on a team. The value it represents is dependent on what the variable r is representing. If r represents something different, then the result would represent that different thing. Thus, the equation can only represent the number of females on a team if r is used to represent that.

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