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2 years ago

5w-8/3 =4w+2 Please solve with steps

Mathematics

1 answer:

Natalka [10]2 years ago

4 0

Answer:

5w-8/3=4w+2

-8/3=-1w+2

-8=-1w+6

-14=-1w

14=w

Hope this helps, have a great day :)

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A 3 m spring requires 12 J to stretch to 3.1 m. How much work is required to stretch the spring to 3.2m?

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2 years ago

50 POINTS!!! In rectangle ABCD, AB = 6 cm, BC = 8 cm, and DE = DF. The area of triangle DEF is one-fourth the area of rectangle

aalyn [17]

Answer:

$EF=4\sqrt{3}$

Step-by-step explanation:

In rectangle ABCD, AB = 6, BC = 8, and DE = DF.

ΔDEF is one-fourth the area of rectangle ABCD.

We want to determine the length of EF.

First, we can find the area of the rectangle. Since the length AB and width BC measures 6 by 8, the area of the rectangle is:

$A_{\text{rect}}=8(6)=48\text{ cm}^2$

The area of the triangle is 1/4 of this. Therefore:

$\displaystyle A_{\text{tri}}=\frac{1}{4}(48)=12\text{ cm}^2$

The area of a triangle is half of its base times its height. The base and height of the triangle is DE and DF. Therefore:

$\displaystyle 12=\frac{1}{2}(DE)(DF)$

Since DE = DF:

$24=DF^2$

Thus:

$DF=\sqrt{24}=\sqrt{4\cdot 6}=2\sqrt{6}=DE$

Since ABCD is a rectangle, ∠D is a right angle. Then by the Pythagorean Theorem:

$(DE)^2+(DF)^2=(EF)^2$

Therefore:

$(2\sqrt6)^2+(2\sqrt6)^2=EF^2$

Square:

$24+24=EF^2$

Add:

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And finally, we can take the square root of both sides:

$EF=\sqrt{48}=\sqrt{16\cdot 3}=4\sqrt{3}$

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3 years ago

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

Mrs. Benson has graded 46 math assignments but has 80% of the assignments left to grade. Mrs. Benson has how many math assignmen

timofeeve [1]

Mrs. Benson has 184 math assignments left to grade.

<u>Step-by-step explanation:</u>

Here we have , Mrs. Benson has graded 46 math assignments but has 80% of the assignments left to grade.We need to find Mrs. Benson has how many math assignments left to grade. Let's find out:

Let total Number of math assignments be x , So According to question 46 math assignments are graded & 80% are left i.e.

⇒ $x = 46+\frac{80x}{100}$

⇒ $x -\frac{80x}{100}= 46$

⇒ $\frac{100x-80x}{100}= 46$

⇒ $\frac{20x}{100}= 46$

⇒ $\frac{x}{5}= 46$

⇒ $x=230$

Now , Assignments left to grade is :

⇒ $230-46$

⇒ $184$

Therefore , Mrs. Benson has 184 math assignments left to grade.

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3 years ago