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mario62 [17]
2 years ago
11

Two triangles have the same base lengths. One Triangle has the height that is 4 times the height of the other triangle. Are the

heights and the areas of the two triangles proportional?
Mathematics
1 answer:
Scrat [10]2 years ago
4 0

YES

  • Area of Triangle 1

Base=b

Height= h

Area 1=A1=1/2*b*h

  • Area of Triangle 2

Base=b

Height= 4h

Area of triangle 2=A2=1/2*b*4h

  • Comparing A1 and A2

A2/A1= (1/2*b*4h)/(1/2*b*h)

= (1/2*b*4h)/(1/2*b*h)

=4/1

Ratio of heights =h2/h1= 4/1

Ratio of areas =A2/A1= 4/1

They are proportional.

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3. Rewrite the expression as simply as you can:<br> 3x + 11y - 2x - 4y
vfiekz [6]

Answer:

x+7y

Step-by-step explanation:

First off, lets split the question into both x and y.

3x - 2x for the x

11y - 4y for the y

You can solve both of them to get x + 7y

3x - 2x = x

11y - 4y = 7y

Then, add them back up and get x + 7y

7 0
3 years ago
Read 2 more answers
Here is the next one
LenaWriter [7]

Answer:

3

Step-by-step explanation:

-2 + 40x + 62 = 180 They are same side interior angles and add to 180

solve for x

40x + 60 = 180

40x = 120

x=3

8 0
2 years ago
At the beach this weekend, the ratio of sandcastles to kites was 3 to 5. If there were 15 kites spotted, how many items were see
Gelneren [198K]

Answer: 24

Step-by-step explanation:

The ratio of sandcastles to kites was 3 to 5 so if 15 kites were spotted that meant that the 5 was multiplied by 3 so then we multiply the 3 by 3. Now there are 9 sandcastles and 15 kites so now we add 9 to 15 to figure out how many items were seen in all. Nine added to 15 equals 24 which means that 24 items were seen in total.

6 0
3 years ago
Jane is playing a game in which he spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a number
sleet_krkn [62]

Answer:

The expected value of playing the game is $0.75.

Step-by-step explanation:

The expected value of a random variable is the weighted average of the random variable.

The formula to compute the expected value of a random variable <em>X</em> is:

E(X)=\sum x\cdot P(X=x)

The random variable <em>X</em> in this case can be defined as the amount won in playing the game.

The probability distribution of <em>X</em> is as follows:

Number on spinner:   1           2           3          4           5              6

Amount earned (<em>X</em>):   $1        $4         $7        $10     -$8.75     -$8.75

Probability:                 1/6       1/6         1/6        1/6         1/6           1/6

Compute the expected value of <em>X</em> as follows:

E(X)=\sum x\cdot P(X=x)

         =(1\times \frac{1}{6})+(4\times \frac{1}{6})+(7\times \frac{1}{6})+(10\times \frac{1}{6})+(-8.75\times \frac{1}{6})+(-8.75\times \frac{1}{6})

         =\frac{1}{6}+\frac{4}{6}+\frac{7}{6}+\frac{10}{6}-\frac{8.75}{6}-\frac{8.75}{6}

         =\frac{1+4+7+10-8.75-8.75}{6}

         =0.75

Thus, the expected value of playing the game is $0.75.

5 0
3 years ago
Simplify: |3 – 10| – (12 / 4 + 2)^2<br> 0 - 32<br> O – 18<br> O3<br> 0 - 6
MakcuM [25]

Answer:

-18

Step-by-step explanation:

Simplify: |3 – 10| – (12 / 4 + 2)^2

|3 - 10| - (\frac{12}{4}  + 2)^2\\\\|-7|-(\frac{12}{4}  + 2)^2 < == absolute\ numbers\ are\ always\ positive\\\\7-(3+2)^2 < ==add\ numbers\ in\ parenthesis\\\\7-5^2 < ==square\ the\ number\ (5)\\\\7-25 < ==add\ numbers\\\\-18 < ==final\ answer

Hope this helps!

6 0
2 years ago
Read 2 more answers
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