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Inga [223]
3 years ago
5

A metal frame is constructed in the form of an isosceles trapezoid. Each base angle measures 80°, the length of the base is 7 fe

et, and each of the nonparallel sides is 5 feet long. Determine the length of a diagonal brace to the nearest whole number.
Mathematics
1 answer:
jonny [76]3 years ago
3 0
Height of a trapezoid:
h = 5 · sin 80° = 5 · 0.985 = 4.924
x = 5 · cos 80° = 5 · 0.17365 = 0.868
7 - x = 7 - 0.868 = 6.132
By the Pythagorean theorem:
d² = 6.132² + 4.924²
d² = 37.6 + 24.25
d² = 61.85
d = √61.85
d = 7.86 ≈ 8
Answer: The length of a diagonal brace is 8 feet.
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One serving of Gooey Gushers provides 12% of the daily value of vitamin C. Tim ate 312 servings of Gooey Gushers.
Studentka2010 [4]

Answer:

a) Given expression,

12% of 312

Since 100% of 312 = 312

⇒ 10% of 312 = 31.2,

⇒ 1% = 3.12

⇒ 2% = 2 × 3.12 = 6.24

So, 12% of 312 = 10% of 312 + 2% of 312

= 31.2 + 6.24

= 37.44

b) Given,

Total number of servings = 312,

The percentage of vitamin C in each serving = 12%,

Thus, the total amount of the vitamin C in 312 servings = 12% of 312

=\frac{12\times 312}{100}

=\frac{3744}{100}

= 37.44,

Hence, the question can be asked about the total amount of the vitamin C.

6 0
3 years ago
A woman is standing at the edge of a slow-moving river which is one mile wide, and she wishes to return to her campground on the
vesna_86 [32]

Answer:

the best option would be to swim

Step-by-step explanation:

Hello! To solve this problem we must follow the following steps.

1. remember the concept of uniform motion with constant speed, which establishes the following equation

t=\frac{X}{V}

where

t=time

x=distance

V=speed

2. Calculate the time it takes to swim and calculate the time it takes to walk

walking:

x=10mile

v=5milles/h

t=\frac{10}{5} =2h

swimming

x=1mile

v=3milles/h

t=\frac{1}{3} =0.3h

3. Compare both results and choose the one with the least time.

as you can see it takes less time swimming, so this would be the best way

7 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20-%208y%20%5Cgeqslant%2056" id="TexFormula1" title=" - 8y \geqslant 56" alt=" - 8y \geqslant
SCORPION-xisa [38]

Answer:

y ≤-7

Step-by-step explanation:

-8y ≥56

Divide each side by -8.  Remember to flip the inequality

-8y/-8 ≤56/-8

y ≤-7

8 0
3 years ago
At the same store, Peter bought 2 pairs of pants and 5 shirts for $61, and Jessica bought 3 pairs of pants and 4 shirts for $67.
svetlana [45]

Hey there!!

Given :

The total cost for 2 pairs of pants and 5 shirts is $61.

The total cost for 3 pairs of paints and 4 shirts is $67.

<em>Let's take the cost for each pair of paints as 'p' and the cost for each shirt as 's'. </em>

Now, let's get these into an equation.

<em>Peter's equation</em> :

... 2p + 5s = 61

<em>Jessica's equation : </em>

...3p + 4s = 67

......................................................................................................

2p + 5s = 61 --- (1)

3p + 4s = 67 --- (2)

Multiply the first equation with 3 and the second equation with 2.

6p + 15s = 183

6p + 8s = 134

S<em>ubtract both the equations - </em>

... 7s = 49

Divide both sides with 7.

... s = 7

<u><em>Hence, the cost of each shirt is $7. </em></u>

Hope my answer helps!!


6 0
4 years ago
RS= 4y+2, ST = 3y+8, and RT = 38 what is the value of y
emmainna [20.7K]

Answer:

y = 4

Step-by-step explanation:

Given that,

RS= 4y+2, ST = 3y+8, and RT = 38

We need to find the value of y.

As,

RT = RS+ST

Put all the values,

38 = 4y+2+3y+8

38-2-8 = 4y+3y

28 = 7y

y = 4

So, the value of y is equal to 4.

7 0
3 years ago
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