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3 years ago

How many solutions does this linear equation system have y=2/3x+2

Mathematics

1 answer:

Neko [114]3 years ago

3 0

Answer:

infinite many solutions

Step-by-step explanation:

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What is the perimeter of triangle DEF

LuckyWell [14K]

Remember that A squared plus B squared equals C squared.

Since sides F_D and D_E are both 3, the answer cannot be 4.2 or 2.4.

SO basically you just add 3 + 3 = (The side F_E, which you can get by putting numbers in the formula), you should get your answer.

3² + 3² = Line EF²
9 + 9 = Line EF²
18 = Line EF²
√18

You get the idea. Hope this helps!

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3 years ago

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Label the equations in number 5-7 as True or False:

kkurt [141]

Answer:

${ \rm{ {(7}^{1}) ^{9 } = 7 {}^{5} \times {7}^{5} : \: { \tt{ \red{false}}} }} \\{ \boxed{ \mathfrak{correction \dashrightarrow \: ( {7}^{1}) {}^{9} = {7}^{9} }}} \\ \\ { \rm{ \frac{ {y}^{13} }{ {( {y}^{2}) }^{6} } = {y}^{ - 10} \times {y}^{9} : \:{ \tt { \red{false}}}}} \\ { \boxed{ \mathfrak{correction \: \dashrightarrow \: { \rm{{y}^{1} }}}}} \\ \\ { \rm{ {b}^{4} \times {b}^{ - 6} = \frac{ {b}^{1} \times {b}^{3} }{ {b}^{6} } }} \: : \: { \tt{ \green{true}}}$

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2 years ago

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You’re baking a circular cake for a party. Your cake can be any size you want. What will the radius of your cake be and how many

REY [17]

What will the radius of your cake be?

This is a problem of geometry. Given that the cake is circular, the greater the cake the greater the radius of it. So, as shown in the figure 1, the radius will be the distance from the center to any extreme point of the circle.

How many slices will you be able to cut?

The total area of a circle is given by:

$A= \pi r^{2}$

We need to fin how many slices will be cut, so let's calculate the area of the circular sector which can be obtained simply applying rule of three, so:

$A_{cs}= \pi r^{2}( \frac{\theta}{2\pi})= \frac{r^{2}\theta}{2}$

Let's name n the number of slices, if we divide the total area by n this result, each area must equal, then:

$\frac{\pi r^{2}}{n}=\frac{r^{2}\theta}{n}$

Finally, we will be able to cut:

$n= \frac{2\pi}{\theta}$ Slices

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3 years ago

20 feet of ribbon, cutting ribbon into 7 1/2 inches or 6 3/4 inch lengths to make bracelets. Write an algebraic expression that

IRINA_888 [86]

<u>ANSWER: </u>

The algebraic expression for number of ribbons is $\frac{20 \text { feet }-\left\{\frac{20 \text { feet }}{x}\right\}}{x}$ and the algebraic expression for length of ribbon is $\frac{25 x}{3} \text { feet }$

<u>SOLUTION: </u>

Given, 20 feet of ribbon, cutting ribbon into $7\frac{1}{2}$ inches or $6\frac{3}{4}$ inch lengths to make bracelets.

Let us convert the mixed fraction to improper fractions.

$7 \frac{1}{2}=\frac{7 \times 2+1}{2}=\frac{15}{2} \text { and } 6 \frac{3}{4}=\frac{6 \times 4+3}{4}=\frac{27}{4}$

Let, the length of bracelets can be made be “x”

First we have to remove the excess length of ribbon and then we have to divide the remaining with length of bracelet we want.

$\text { number of ribbons }=\frac{\text { length of ribbon-excess ribbon.}}{\text {length of bracelet}}$

$\left.=\frac{20 \text { feet }-\left\{\frac{20 \text { feep }}{x}\right.}{x} \text { [we know that, }\{x\} \text { is fractional part of } x\right$ ]

So, the algebraic expression for number of ribbons is $\frac{20 \text { feet }-\left\{\frac{20 \text { feet }}{x}\right\}}{x}$

Now, let us find the algebraic expression for feet of ribbon to make 100 ribbons.

We have 100 bracelets of length x, then total length = 100 × x

length of ribbon = 100x inches

$\begin{array}{l}{=100 \mathrm{x} \times \frac{1}{12} \text { feet }} \\\\ {=\frac{25 x}{3} \text { feet }}\end{array}$

So, the algebraic expression for length of ribbon is $\frac{25 x}{3} \text { feet }$

Hence, the algebraic expression for number of ribbons is $\frac{20 \text { feet }-\left\{\frac{20 \text { feet }}{x}\right\}}{x}$ and the algebraic expression for length of ribbon is $\frac{25 x}{3} \text { feet }$

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3 years ago

How many garbage cans should be placed in each campground? Explain how you can use addition or multiplication to find the answer

Vikentia [17]

Answer:

Step-by-step explanation:

Multiplication

Ratio of Tables to garbage = 8:3

Small camp ground:

40 picnic tables and let x be the number of garbage cans

$\frac{8}{3}=\frac{40}{x}\\\\\frac{8*5}{3*5}=\frac{40}{x}\\\\\frac{40}{15}=\frac{40}{x}\\\\$

x = 15

Small campground with 40 picnic table needs 15 garbage cans

Large picnic ground:

120 picnic tables and let y be the number of garbage cans

$\frac{8}{3}=\frac{120}{y}\\\\\frac{8*15}{3*15}=\frac{120}{y}\\\\\frac{120}{45}=\frac{120}{y}$

y= 45

Big campground with 120 picnic table needs 45 garbage cans

3 0

2 years ago