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3 years ago

An isosceles triangle has a perimeter of 36 inches. Its base is 2

Mathematics

1 answer:

astra-53 [7]3 years ago

3 0

The lengths of the sides of the triangle are 8, 8, 20

Explanation:

Given that the perimeter of an isosceles triangle is 36 inches.

The base of the triangle is $2\frac{1}{2}$ times longer than each of its legs.

We need to determine the lengths of the sides of the triangle.

Lengths of the sides:

Let x denote the lengths of the sides of the triangle.

The base of the triangle is given by

$2\frac{1}{2}x=\frac{5}{2}x=2.5x$

Perimeter of the isosceles triangle = Sum of the three sides of the triangle.

Thus, we have,

$36=x+x+2.5x$

$36=4.5x$

$8=x$

Thus, the length of the sides of the isosceles triangle is 8 inches.

Base of the triangle = $2.5(8)=20 \ inches$

Hence, the three sides of the isosceles triangle are 8, 8, 20

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Which of the following graphs of exponential functions corresponds to a geometric sequence with a first term of 4 and a ratio of

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Answer: graph E.

A geometric sequence can be written as:

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where:

a₁ = first term = 4

r = ratio = 0.5

Substituting the numbers, we have:

$a_{n} = 4 \cdot (\frac{1}{2})^{n-1}$

or else

$f(x) = 4 \cdot (\frac{1}{2})^{x - 1}$

This is an exponential function with base less than 1. Therefore, we can exclude graph C (which depicts a linear function), and graphs A and D (which depict an exponential function with base greater than 1).

In order to choose between graph B and E, let's evaluate the function in two different points:

$f(1) = 4 \cdot (\frac{1}{2})^{1 - 1} = 4$

$f(2) = 4 \cdot (\frac{1}{2})^{2 - 1} = 4 \cdot \frac{1}{2} = 2$

Therefore, we need to look for the graph passing through the points (1, 4) and (2, 2). That is graph E.

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Explain how to use the combine values strategy to find 223-119

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223
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Two girls scout troops are completing a wilderness campouts. The blue troops hikes 2/3 mile every 1/2 hour. The yellow troop hik

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Answer:

Yellow troop will complete the hike faster than blue troop

Blue troop hikes 1.33 miles in 1 hour

Yellow troop hikes 2.25 miles in 1 hour

Missing portion:

Since the final statement is missing, so we will find how much distance can the troops travels in 1 hour and which troop can complete the hike faster.

Step-by-step explanation:

As given in the statement:

Blue troops travels $\frac{2}{3}$ miles ever $\frac{1}{2}$ hour:

$\frac{1}{2}$ hr = $\frac{2}{3}$ miles

1 hr = $\frac{(2)2}{3}$

1 hr= $\frac{4}{3}$ miles = 1.33 miles

Blue troop hikes 1.33 miles in 1 hour

Yellow troops travels $\frac{3}{4}$ miles ever $\frac{1}{3}$ hour:

$\frac{1}{3}$ hr= $\frac{3}{4}$ miles

1 hr = $\frac{(3) 3}{4}$ miles

1 hr = $\frac{9}{4}$ miles =2.25 miles

Yellow troop hikes 2.25 miles in 1 hour

Yellow troop will complete the hike faster than blue troop

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One day is what percent of one week?

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Answer:

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Step-by-step explanation:

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What is the most precise name for a quadrilateral with the following vertices:

lozanna [386]

Answer:

The most precise name for a quadrilateral ABCD is a parallelogram

Step-by-step explanation:

we have

A(2,3) B(7,2) C(6,-1) D(1,0)

Plot the quadrilateral'

using a graphing tool

The quadrilateral ABCD in the attached figure

Verify the length of the sides

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find distance AB

A(2,3) B(7,2)

substitute

$d=\sqrt{(2-3)^{2}+(7-2)^{2}}$

$d=\sqrt{(-1)^{2}+(5)^{2}}$

$d_A_B=\sqrt{26}\ units$

step 2

Find distance BC

B(7,2) C(6,-1)

substitute

$d=\sqrt{(-1-2)^{2}+(6-7)^{2}}$

$d=\sqrt{(-3)^{2}+(-1)^{2}}$

$d_B_C=\sqrt{10}\ units$

step 3

Find distance CD

C(6,-1) D(1,0)

substitute

$d=\sqrt{(0+1)^{2}+(1-6)^{2}}$

$d=\sqrt{(1)^{2}+(-5)^{2}}$

$d_C_D=\sqrt{26}\ units$

step 4

Find distance AD

A(2,3) D(1,0)

substitute

$d=\sqrt{(0-3)^{2}+(1-2)^{2}}$

$d=\sqrt{(-3)^{2}+(-1)^{2}}$

$d_A_D=\sqrt{10}\ units$

step 5

Compare the length sides

AB=CD

BC=AD

Opposite sides are congruent

Verify the slope of the sides

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

step 1

Find slope AB

A(2,3) B(7,2)

substitute

$m=\frac{2-3}{7-2}$

$m=\frac{-1}{5}$

$m_A_B=-\frac{1}{5}$

step 2

Find slope BC

B(7,2) C(6,-1)

substitute

$m=\frac{-1-2}{6-7}$

$m=\frac{-3}{-1}$

$m_B_C=3$

step 3

Find slope CD

C(6,-1) D(1,0)

substitute

$m=\frac{0+1}{1-6}$

$m=\frac{1}{-5}$

$m_C_D=-\frac{1}{5}$

step 4

Find slope AD

A(2,3) D(1,0)

substitute

$m=\frac{0-3}{1-2}$

$m=\frac{-3}{-1}$

$m_A_D=3$

step 5

Compare the slopes

$m_A_B=m_C_D$

$m_B_C=m_A_D$

The slope of the opposite sides are equal, that means, opposite sides are parallel

The slopes of consecutive sides are not opposite reciprocal, that means, consecutive sides are not perpendicular

therefore

The most precise name for a quadrilateral ABCD is a parallelogram

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3 years ago