A student is given this proof.
Given: AOM DON
Prove: CON~ BOM
ZAOM ZDON
given
ZBOM DON
vertical angles
theorem
ZAOM ZBOM
transitive
property of
congruence
ZAOM ZCON
vertical angles
theorem
ZCON BOM
transitive
property of
congruence
The student says that the proof shows that AOM BOM because they
are vertical angles.
Which statement best corrects the student's interpretation?

The lengths of the other two sides is 6 inches each.

The perimeter of any figure is sum of all the sides of the figure.

Here, we are given that the area of a triangle is 18 inches. Also, in the figure, we can see that the 3 sides of the triangle are-

6 inches, s inches and s inches.

Therefore, the perimeter of the given triangle will be-

Perimeter = 6 + s + s

⇒ 18 = 6 + s + s

Thus, the equation to find the lengths of the two sides is-

18 = 6 + 2s

18 - 6 = 2s

12 = 2s

2s = 12

s = 12/ 2

s = 6

Thus, the lengths of the other two sides is 6 inches.

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In the graph we have a parabola, and its equation is y = (x - 2)^2 - 3

In the graph, we can see a parabola.

We only need to identify 3 parts, which are the two x-intercepts (if it has) and the y-intercept.

Remember that if the vertex and the y-intercept. Remember that if the vertex is (h, k) and the leading coefficient is a, then we can write the equation as:

y = a*(x - h)^2 + k

In the image we can see that the vertex is (2, -3), then:

y = a*(x - 2)^2 - 3

And the y-intercept is y = 1, then if we evaluate in x = 0 we should get y = 1, replacing that we get:

1 = a*(0 - 2)^2 - 3

1 = a*4 - 3

1 + 3 = a*4

4/4 = a = 1

Then the quadratic equation is y = (x - 2)^2 - 3

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We get the values of RS and RT as 6 and 17 respectively after solving the equations.

We are given the equations:

RS = 2x - 8

ST = 11

RT = x + 10

Now, we know that:

RS + ST = RT.

Substituting the values, we get that:

2 x - 8 + 11 = x + 10

2 x + 3 = x + 10

2 x - x = 10 - 3

x = 7

Now substituting it to find RS and RT:

RS = 2 x - 8

RS = 2 ( 7 ) - 8

RS = 14 - 8

RS = 6

RT = x + 10

RT = 7 + 10

RT = 17

Therefore, we get the values of RS and RT as 6 and 17 respectively after solving the equations.

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The required number is 2001.

To solve this problem we need to know the concept of rounding off.

Rounding off a number means making the value of number equal to the nearest tens place.

When we round off 45 we will get 50; when we round off 44 we get 40.

So, if a number has 5 at its unit place then it will be rounded off to the tens place which is ahead of 5 and if a number is less than 5 then it is rounded off to the tens place before that number.

Here it is asked to find the least whole number that rounds off to 2000 when rounded off to nearest hundred which will be 2001.

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Answer :  7.5 ft

Step-by-step explanation:

when the length of the shadow is 8ft, the actual height of the man = 5ft

8:5

let the giraffe be 'x' ft tall.

if the length of the shadow is 12ft, actual height = x ft

12:x

8:5 x 12:x

[tex]\frac{8}{5}[/tex] × [tex]\frac{12}{x}[/tex]

x= [tex]\frac{15}{2}[/tex]

x=7.5 ft

Therefore, the giraffe is 7.5ft tall.

Answer:

[tex]7.5\; {\rm ft}[/tex].

Step-by-step explanation:

The height of objects nearby under the sun are approximately proportional to the length of their shadows.

In other words, if the man and the giraffe are near each other and under the sun:

[tex]\begin{aligned} \frac{\text{height of man}}{\text{length of shadow of man}} = \frac{\text{height of giraffe}}{\text{length of shadow of giraffe}}\end{aligned}[/tex].

Given that:

Rearrange the equation to find [tex](\text{height of giraffe})[/tex]:

[tex]\begin{aligned} (\text{height of giraffe}) &= (\text{length of shadow of giraffe})\times \frac{\text{height of man}}{\text{length of shadow of man}} \\ &= 12\; {\rm ft} \times \frac{5\; {\rm ft}}{8\; {\rm ft}} \\ &= 7.5\; {\rm ft}\end{aligned}[/tex].

Answer:

7 + 2 + 4 = 13 km
13 km x 0.62 = 8.06
The answer is about 8.06 miles

Step-by-step explanation:

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!

The number in each of the set of blank boxes is 10

From the first number set of stamps, we see that the sum of each row is;

5 + 5 + 5 + 5 = 20

There are four rows. Thus;

Total sum of set of stamps = 20 + 20 + 20 + 20

Total sum of set of stamps = 80

Now, for the blank set of stamps, we see that there are 8 boxes which are al equal. Now, for this 8 boxes t have same sum as that of the initial set of stamps, it means they must sum up to 80.

If the number in each box is x, then;

8x = 80

x = 80/8

x = 10

Thus, the number in each of the set of blank boxes is 10

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Answer:

$29.77

Step-by-step explanation:

First, divide 429 by 33 to find how many gallons that she's paying for, then multiply that by $2.29 to find the answer.

The cost for Carmen to drive 429 miles is $29.77.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Given that,

Distance car travels per gallon = 33 miles per gallon

Cost of gasoline per gallon = $2.29 per gallon.

33 miles can be travelled with 1 gallon of gasoline.

1 mile can be travelled with 1/33 gallon of gasoline.

429 miles can be travelled with 429/33 = 13 gallon of gasoline.

Amount of gasoline needed for 429 miles = 13 gallon.

Cost of gasoline for 1 gallon = $2.29

Cost of gasoline for 13 gallon = 13 × $2.29 = $29.77

Hence it will cost $29.77 for her to drive 429 miles.

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Answer:

2n-67

Step-by-step explanation:

Twice a number means 'multiply by 2' so we can write 2 x n. We can also write this in a simpler form- 2n

'67 decreased' means minus 67 off your answer so therefore the answer must be:

2n-67

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nina can swim 8/7 laps in one minute

given that

nina can swim 4 laps in 7/2 minutes

we have to calculate that how many laps can nina swim in 1 minute

then 4 laps= 7/2 minutes

then 4*2 /7 =1 minute

           8/7=1 minute

  thus nina can swim 8/7 laps in one minute

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Answer:

[tex]-\frac{47}{64}[/tex] or [tex]\frac{1}{2}^{3} -6/\sqrt{64}[/tex]

Step-by-step explanation:

Answer:

F=9/5c+32

Step-by-step explanation:

Multiply both sides by 9/5 to cancel out the 5/9 on the right side of the equation. This gives you:

9/5C = F-32

C=F−32

Then add 32 to both sides, giving you:

9/5C + 32 = F

C+32=F

Thus, you have:

F= 9/5C + 32F=

5

9

C+32

Answer:

[tex]F= \frac{9}{5}C + 32[/tex]

Step-by-step explanation:

Multiply both sides by 9/5 to cancel out the 5/9 on the right side of the equation. This gives you:

[tex]\frac{9}{5}C = F-32[/tex]

Then add 32 to both sides, giving you:

[tex]\frac{9}{5}C + 32 = F[/tex]

Thus, you have:

[tex]F= \frac{9}{5}C + 32[/tex]

Answer:

3080983

Step-by-step explanation:

ihhueuhreuhefhuuufehuefefeh

After simplification of the given expression, 6a + (-12b) - 9b + 8a the value is (B) 14a - 21b.

So, 6a + (-12b) - 9b + 8a:

Therefore, after simplification of the given expression, 6a + (-12b) - 9b + 8a the value is (B) 14a - 21b.

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The correct question is given below:
Simplify 6a+ (-12b) - 9b+8a

A. 2a + 3b

B. 14a-21b

C. 2a-21b

D. 14a + 3b

Answer:

-44

Step-by-step explanation:

2 x 4 + 3 - 8 ÷ 1 x 6 + 4 - 11=-44

Hope this helps!

Answer:

-44

Step-by-step explanation:

This is probably what steps your friend took, or something similar.

5x+4x-68 = 34-8x

9x = 34-8x-68

9x = -8x-34

9x+8x = -34

17x = -34

x = -34/17

x = -2

However, the error is when they subtracted 68 from both sides (line 2).

Instead, they should have added 68 to each side to undo the -68 on the left hand side.

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

Here's what the steps should look like (one variation of it anyway)

5x+4x-68 = 34-8x

9x = 34-8x+68

9x = -8x+102

9x+8x = 102

17x = 102

x = 102/17

x = 6 is the correct value of x

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

Check:

5x+4x-68 = 34-8x

5*6+4*6-68 = 34-8*6

30+24-68 = 34-48

54-68 = 34-48

-14 = -14

We get the same thing on both sides after replacing each x with 6, so it confirms x = 6 is the solution.

If you were to try x = -2, then you would end up with -86 = 50 which is a false statement. So that rules out x = -2 as a solution.

Answer: 6

Step-by-step explanation:

Answer:

GCF = 2

Step-by-step explanation:

The order from least to greatest of the numbers will be B. one eighth, 0.4, seventy five percent, seven fifths.

It should be noted that 7/5 = 1.4

It should be noted that 1/8 = 0.125

It should be noted that 75% = 0.75

Therefore, the ordering of the numbers from least to greatest will be one eighth, 0.4, seventy five percent, seven fifths.

In conclusion, the correct option is B.

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Answer:

b

Step-by-step explanation:

Answer:

y2-y1/x2-x1

-8--3/0-2

Step-by-step explanation:

-8+3/-2=-5/-2=5/2

The value 8 x 10^5 is 200 times greater than 4 x 10^3

The standard scientific notation is expressed as A * 10^n

where

A is the values between 1 and 10

n is any integer

In order to determine how many times larger is 8 x 10^5 than 4 x 10^3, we will take the ratio;

Ratio = 8 x 10^5/4 * 10^3

Ratio = 8/4 * 10^5/10^3

Ratio = 2 * 10^2

Ratio = 200

Hence the value 8 x 10^5 is 200 times greater than 4 x 10^3

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       A parallel equation (when graphed) will have the same slope, but a different y-intercept.

       As long as you keep y = -[tex]\frac{5}{2}[/tex]x + b, you can input anything for b to solve this question.

       Given:

y = -[tex]\frac{5}{2}[/tex]x - 5

       Equation of a parallel line:

y = -[tex]\frac{5}{2}[/tex]x + 6, y = -[tex]\frac{5}{2}[/tex]x + 1,356, y = -[tex]\frac{5}{2}[/tex]x - 8, etc

     Example answer you can use:

             y = -[tex]\frac{5}{2}[/tex]x - 8

Using the Pythagorean theorem, the missing sides are:

1. 5

2. 13

3. √15

4. 3

The Pythagorean theorem is given as: c² = a² + b², where c is the longest side and a and b are the other two legs.

1. Missing side = √(3² + 4²) [Pythagorean theorem]

Missing side = 5

2. Missing side = √(12² + 5²) [Pythagorean theorem]

Missing side = 13

3. Missing side = √(4² - 1²) [Pythagorean theorem]

Missing side = √15

4. Missing side = √((√10)² - 1²) [Pythagorean theorem]

Missing side = √(10 - 1) = √9

Missing side = 3

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Answer:

{a, c, e, f, g}

Step-by-step explanation:

[tex]B'=\{a,b,c,d,e,f,g\}-\{a,b,c,d\}=\{e,f,g\} \\ \\ A \cup B=\{a,c,e,f,g\}[/tex]

The speed of the faster cyclist is 30 mph.

Two cyclists, distance = 90 miles.

let the speed of one cyclist is = x and

let the speed of the other cyclist = 2x

time after which both the cyclists will meet = 3 hours.

Since they are travelling towards each other the effective speed = 2x ₊ x

= 3x

we know that time = distance/speed

3 = 90/3x

3x = 30

x = 10 mph speed of one cyclist.

speed of the other cyclist will be 3x = 3 × 10 = 30 mph

The speed of the fastest cyclist is 30 mph.

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The number of nails in each box is: 1300, 1400, 600, 1200, and 500

Given 5000 nails in five boxes.

Let X denote the universal set.

Then n(X) = 5000.

Let A denote the first box,

B denote the second box,

C denote the third box,

D denote the fourth box, and

E denotes the fifth box.

The first and second boxes have 2700 nails altogether.

⇒n(A ∪ B) = 2700

The second and third boxes have 2000 nails altogether.

⇒n(B ∪ C) = 2000

The third and fourth boxes have 1800 nails altogether.

⇒n(C ∪ D) = 1800

The fourth and fifth boxes have 1700 nails altogether.

⇒n(D ∪ E) = 1700

We need to find out how many nails are there in each box.

That is to find out: n(A), n(B), n(C), n(D), and n(E).

Note that all these five sets are disjoint. This means that the intersection is empty.

n(A ∪ B ∪ C ∪ D) = n(A ∪ B) + n(C ∪ D) = 2700 + 1800 = 4500

n(E) = n(X) - n(A ∪ B ∪ C ∪ D) = 5000 - 4500 = 500

n(D) = n(D ∪ E) - n(E) = 1700 - 500 = 1200

n(C) = n(C ∪ D) - n(D) = 1800 - 1200 = 600

n(B) = n(B U C) - n(C) = 2000 - 600 = 1400

n(A) = n(A U B) - n(B) = 2700 - 1400 = 1300

Therefore, the number of nails in each box is 1300, 1400, 600, 1200, and 500.

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Rene's limeade has a weaker flavor as calculated by division of fractions.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.

Concentration of Jaylan's limeade [tex]=\frac{3}{4} \div\frac{1}{5} = \frac{15}{4} =3.75[/tex]

Therefore as calculated by division of fractions, concentration of Jaylan's limeade is 3.75 cups of water for 1 cup of lime juice.

Concentration of Rene's Limeade[tex]=\frac{2}{3} \div\frac{1}{6} = \frac{12}{3} =4[/tex]

Therefore as calculated by division of fractions, concentration of Rene's limeade is 4 cups of water for 1 cup of lime juice.

Hence Rene's limeade has a weaker flavor as calculated by division of fractions.

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Answer:

19 cm.

Step-by-step explanation:

Area = h(a + b)/2

where h = height, and a and b are parallel sides,

145 = 10(10 + b)/2

290 = 100 + 10b

10b = 190

b  = 19 cm.

Answer:

the answer is 16 feet

Step-by-step explanation: