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2 years ago

Determine whether the triangles are similar. or not.

Mathematics

1 answer:

galina1969 [7]2 years ago

7 0

Answer:

A. similar, AA

Step-by-step explanation:

Angles F and H are given as congruent in the figure.

From the figure, we see that angles EGF and JGH are congruent since they are vertical angles.

We have two angles of one trianfgle congruent to two angles of the other triangle.

The triangles are similar by AA Similarity.

Answer: A. similar, AA

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The length of a rectangular painting is 3 inches longer than its width. If the diagonal is 15 inches long, what is the length of

vladimir2022 [97]

A^2+b^2= 15^2

b=a-3

Use substitution
a^2+(a-3)^2= 225
a^2+a^2-6a+9=225
2a^2-6a=-216
2a^2-6a+216=0

2(a^2-3a+108)
2(a-12)(a+9)

(a-12)=0
a=12
(a+9)=0
a=-9
A is -9 or 12, but since an object can't have a negative length or width, a must be 12.

Plug this value of a in.
b=(12)-3
b=9

Final answer: Length=9, width=12

8 0

3 years ago

Read 2 more answers

Noah ran around the track two times. How far did he run in feet? Round your answer to the nearest whole number.

AfilCa [17]

Answer:

237 feet

Step-by-step explanation:

take the circumference (5), square it, and multiply it by pi. Then add 40 for the distance of the two sides. Multiply your answer by two to find the distance for twice around

8 0

3 years ago

Which graph represents the function f(x)=0.2x+3?

g100num [7]

Answer:

The top right

Step-by-step explanation:

The y intercept is = 0.2^(0) + 3 = 1+3 = 4

Now let considered some point

Let x = 3

0.2^(3) + 3 = 3.008

Let x = 10000

0.2^(10000) + 3 = 3.00032

As we can see, it approaching 3 so the top right is correct

3 0

3 years ago

Which statement is not true about the data shown by the box-and-whisker plot below?

Tom [10]

Answer: The data point 25 lies in the first quartile of the date

Step-by-step explanation: The data point 25 is not in the data set.

7 0

3 years ago

An island is 1 mi due north of its closest point along a straight shoreline. A visitor is staying at a cabin on the shore that i

Elanso [62]

Answer:

The visitor should run approximately 14.96 mile to minimize the time it takes to reach the island

Step-by-step explanation:

From the question, we have;

The distance of the island from the shoreline = 1 mile

The distance the person is staying from the point on the shoreline = 15 mile

The rate at which the visitor runs = 6 mph

The rate at which the visitor swims = 2.5 mph

Let 'x' represent the distance the person runs, we have;

The distance to swim = $\sqrt{(15-x)^2+1^2}$

The total time, 't', is given as follows;

$t = \dfrac{x}{6} +\dfrac{\sqrt{(15-x)^2+1^2}}{2.5}$

The minimum value of 't' is found by differentiating with an online tool, as follows;

$\dfrac{dt}{dx} = \dfrac{d\left(\dfrac{x}{6} +\dfrac{\sqrt{(15-x)^2+1^2}}{2.5}\right)}{dx} = \dfrac{1}{6} -\dfrac{6 - 0.4\cdot x}{\sqrt{x^2-30\cdot x +226} }$

At the maximum/minimum point, we have;

$\dfrac{1}{6} -\dfrac{6 - 0.4\cdot x}{\sqrt{x^2-30\cdot x +226} } = 0$

Simplifying, with a graphing calculator, we get;

-4.72·x² + 142·x - 1,070 = 0

From which we also get x ≈ 15.04 and x ≈ 0.64956

x ≈ 15.04 mile

Therefore, given that 15.04 mi is 0.04 mi after the point, the distance he should run = 15 mi - 0.04 mi ≈ 14.96 mi

$t = \dfrac{14.96}{6} +\dfrac{\sqrt{(15-14.96)^2+1^2}}{2.5} \approx 2..89$

Therefore, the distance to run, x ≈ 14.96 mile

6 0

3 years ago