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svetoff [14.1K]
3 years ago
7

The fence is 106 meters long. Each section of fence is 3 meters long. How many sections were needed to complete the fence?

Mathematics
1 answer:
denis23 [38]3 years ago
4 0
Answer: approximately 35
explanation:
divide 106 by 3 = 35.33
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By what percent will the product of two numbers decrease if one of them is decreased by 25% and the other one is decreased by 50
olchik [2.2K]
Well, let's say the numbers are "a" and "b"

so a * b = ab

ok... now, if we reduce "a" by 25%, that means the new size is just 75% of the old one, how much is 75% of a? well, (75/100) * a, or 0.75a

now let's reduce "b" by 50%, that means the new size is 50% or half,  how much is 50% of b? well (50/100)*b, or 0.5b

\bf \begin{cases}
a\cdot b\implies  ab\\
0.75a\cdot 0.5b\\
\qquad 0.75\cdot 0.5ab\\
\qquad 0.375ab
\end{cases}

now, the new size of "ab" is just 0.375ab... well, let's revert the decimal format by simply multiplying by 100

0.375 * 100, is 37.5%

the new size of "ab" is just 37.5% of the original "ab"

it decreased by 100 - 37.5 or 62.5%
5 0
4 years ago
The coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .
daser333 [38]

Answer: The correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

Explanation:

It is given that  coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .

The distance formula for two points is given below,

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

DE=\sqrt{(2+2)^2+(4-5)^2}=\sqrt{17}

EF=\sqrt{(0-2)^2+(0-4)^2}=\sqrt{20}

FG=\sqrt{(-4-0)^2+(1-0)^2}=\sqrt{17}

DG=\sqrt{(-4+2)^2+(1-5)^2}=\sqrt{20}

Slope formula,

m=\frac{y_2-y_1}{x_2-x_1}

Slope of DE,

m_1=\frac{4-5}{2+2}= \frac{-1}{4}

Slope of EF,

m_2=\frac{0-4}{0-2}= 2

Slope of FG,

m_3=\frac{1-0}{-4-0}= \frac{-1}{4}

Slope of DG,

m_4=\frac{1-5}{-4+2}= 2

The slope of opposite sides are equal, it means the opposite sides are parallel.

All four sides do not have the same length. It means it is not a rhombus.

From the figure it is noticed that the opposite sides are parallel.

Therefore, the correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

3 0
4 years ago
Read 2 more answers
The rule T 5, -0.5° Ro, 1800(x, ) is applied to FGH to
Yuki888 [10]

Answer:

Step-by-step explanation:

Given rule for the multiple translations is,

T_{5,-0.5}.R_{0.180^{\circ}}(x,y)

Apply the rule R_{0,180^{\circ}} first.

(x, y) → (-x, -y)

This rule illustrates a rotation of the triangle FGH by 180° about the origin,

Vertices of ΔFGH are,

F → (1, 1)

G → (4, 5)

H → (5, 1)

After rotation vertices of the image triangle are,

F' → (-1, -1)

G' → (-4, -5)

H' → (-5, -1)

Further apply the rule,

T_{5,-0.5}

(x, y) → (x + 5, y - 0.5)

By this rule of translation,

F'(-1, -1) → F"{(-1 + 5), (-1 - 0.5)}

            → F"(4, -1.5)

G'(-4, -5) → G"[(-4 + 5), (-5 - 0.5)]

              → G"(1, -5.5)

H'(-5, -1) → H"[(-5 + 5), (-1 -0.5)]

             → H"(0, -1.5)

8 0
3 years ago
What is the solution to y=3x-1 ?
Iteru [2.4K]

I'm ASSUMING that we're talking about Three Ordered Ordered Pair Solutions.

If so, the answer is (0,−1),(1,2),(2,5).


8 0
3 years ago
Read 2 more answers
Simplify (12a5−6a−10a3)−(10a−2a5−14a4) . Write the answer in standard form
almond37 [142]

Answer:

=14a^5+14a^4-10a^3-16a

Step-by-step explanation:

\left(12a^5-6a-10a^3\right)-\left(10a-2a^5-14a^4\right)\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=12a^5-6a-10a^3-\left(10a-2a^5-14a^4\right)\\-\left(10a-2a^5-14a^4\right):\quad -10a+2a^5+14a^4\\-\left(10a-2a^5-14a^4\right)\\\mathrm{Distribute\:parentheses}\\=-\left(10a\right)-\left(-2a^5\right)-\left(-14a^4\right)\\Apply\:minus-plus\:rules\\-\left(-a\right)=a,\:\:\:-\left(a\right)=-a\\=-10a+2a^5+14a^4\\=12a^5-6a-10a^3-10a+2a^5+14a^4

\mathrm{Simplify}\:12a^5-6a-10a^3-10a+2a^5+14a^4:\quad 14a^5+14a^4-10a^3-16a12a^5-6a-10a^3-10a+2a^5+14a^4\\Group\:like\:terms\\=12a^5+2a^5+14a^4-10a^3-6a-10a\\\mathrm{Add\:similar\:elements:}\:12a^5+2a^5=14a^5\\=14a^5+14a^4-10a^3-6a-10a\\\mathrm{Add\:similar\:elements:}\:-6a-10a=-16a\\=14a^5+14a^4-10a^3-16a

4 0
3 years ago
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