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2 years ago

A speed walker covered 4 1/2 mi in 3/4 hour. How far will he walk in 3/4 hour if he walks?

Mathematics

1 answer:

Nezavi [6.7K]2 years ago

7 0

Given:

Consider the complete question is "A speed walker covered $4\dfrac{1}{4}$ mi in $\dfrac{3}{4}$ hour. How far will he walk in 3/4 hours if he walks twice as fast?"

A speed walker covered $4\dfrac{1}{4}$ mi in $\dfrac{3}{4}$ hour.

To find:

Distance covered by him if in 3/4 hour if he walks twice as fast.

Solution:

We have,

$Distance=4\dfrac{1}{2}=\dfrac{9}{2}$

It means a speed walker covered $\dfrac{9}{2}$ mi in $\dfrac{3}{4}$ hour.

If the speed is twice then he can cover double distance is same time.

Distance covered by him if in 3/4 hour if he walks twice as fast is

$2\times \dfrac{9}{2}=9$

Therefore, distance covered by him is 9 mi.

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The height of a triangle is 7 ft more than its base. If the area of the triangle is 30 ft2, what is the length of the base?

SSSSS [86.1K]

Answer:

see below

Step-by-step explanation: 5 27 7 16

area = 1/2 bh

height of a triangle is 7 ft more than its base

base = b

height = b + 7

area = 30

area = 1/2 b(h)

30 = 1/2 b(b + 7)

30 = 0.5(b²+ 7b)

30 = 1/2 b²+ 3.5b solve for b

1/2 b²+ 3.5b = 30

1/2 b²+ 3.5b - 30 = 0

b²+ 7b - 60 = 0 factor

(b +12)(b - 5) = 0 when b = -12 or 5 base length can't be negative

b = base = 5

area = 1/2 bh 1/2×2(9) = 9

area = 1/2 bh 1/2×5(12) = 60

area = 1/2 bh 1/2×9(16) = 56

area = 1/2 bh 1/2×12(19) = 114

5 0

2 years ago

Find the area of a square with the sides 24feet ,27ft.18feet and 30feet

34kurt

Well, this question isn't really fair, considering that those sides aren't possible to make a square since a square has 4 congruent sides.

5 0

3 years ago

1. Wendy wants to find the width, AB, of a river. She walks along the edge of the river 300 ft and marks point C. Then she walks

Ierofanga [76]

It can be deduced that the triangles are similar because the three internal angles are equal for both triangles.

<h3>How to solve the triangle?</h3>

It should be noted that the triangles are similar because the three internal angles are equal.

In this case, the ratio of the corresponding sides are equal and the corresponding angles are congruent.

The width of the river will be:

300/80 = AB/50

AB = (300 × 50)/80

AB = 187.50 feet.

Learn more about triangles on:

brainly.com/question/17335144

7 0

2 years ago

Jaden is flying a kite and let’s off 275 feet of string. If the kite is 150 feet above ground and assuming the string is straigh

vivado [14]

Answer:

≈ 33°

Step-by-step explanation:

So, first, you can draw a visual. Refer to the image attached below:

Using this info, you can use trigonometric ratios. Recall that:

tangent = opposite side/adjacent side

sine = opposite side/ hypotenuse

cosine = adjacent side/hypotenuse

You can clearly see that you have an opposite side and a given hypotenuse. This means we'll be using sine.

So:

$sinX = \frac{150}{275}$

However, we're not trying to find sinX, we're trying to find X.

So we would have to use inverse sine, which would then be:

$X = sin-1 (\frac{150}{275} )$

Put this into your calculator, and:

X ≈ 33.05573115...

3 0

2 years ago

What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?

Trava [24]

Answer:

$\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}$

Step-by-step explanation:

The explicit formula for a geometric sequence:

$a_n=a_1r^{n-1}$

$a_n$ - n-th term

$a_1$ - first term

$r$ - common ratio

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}$

We have

$a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...$

The common ratio:

$r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}$

<h2>It's not a geometric sequence.</h2>

If $a_3=-\dfrac{1}{16}$ then the common ratio is $r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}$

Put to the explicit formula:

$a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}$

Put $a_n=\dfrac{1}{1024}$ and solve for <em>n </em>:

$-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1$

$\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6$

5 0

3 years ago