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2 years ago

14

Which expressions are equivalent? Select Equivalent or Not equivalent for each pair of expressions. 3(a−b) and 3a−3b 2a(2+b) and

4ab

2 answers:

Lapatulllka [165]2 years ago

5 0

The first one is <span>Equivalent and the second is nonequivalent</span>

zysi [14]2 years ago

5 0

i just took the test, the first one is equivalent and the second one is not.

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Point E is the midpoint of AB and point F is the midpoint

GREYUIT [131]

The options are;

1) AB is bisected by CD

2) CD is bisected by AB

3) AE = 1/2 AB

4) EF = 1/2 ED

5) FD= EB

6) CE + EF = FD

Answer:

Options 1, 3 & 6 are correct

Step-by-step explanation:

We are told that Point E is the midpoint of AB. Thus, any line that passes through point E will bisect AB into two equal parts.

The only line passing through point E is line CD.

Thus, we can say that line AB is bisected by pine CD. - - - (1)

Also, since E is midpoint of Line AB, it means that;

AE = EB

Thus, AE = EB = ½AB - - - (2)

Also, we are told that F is the mid-point of CD.

Thus;

CF = FD

Point E lies between C and F.

Thus;

CE + EF = CF

Since CF =FD

Thus;

CE + EF = FD - - - (3)

5 0

3 years ago

Which of the following rational functions is graphed below?

Shalnov [3]

You didn’t put your whole question so I can’t help sorry :(((((((((((

4 0

2 years ago

Find the unit vector in the direction of u = (-3,2).

DENIUS [597]

$\bf \textit{unit vector for }(a,b)\implies \left( \cfrac{a}{\sqrt{a^2+b^2}}~~,~~\cfrac{b}{\sqrt{a^2+b^2}} \right)\\\\
-------------------------------\\\\
(-3,2)\qquad \stackrel{unit~vector}{\implies }\qquad \left( \cfrac{-3}{\sqrt{(-3)^2+2^2}}~~,~~\cfrac{2}{\sqrt{(-3)^2+2^2}} \right)
\\\\\\
\left( -\cfrac{3}{\sqrt{13}}~~,~~ \cfrac{2}{\sqrt{13}}\right)\\\\
-------------------------------$

$\bf \textit{and now let's \underline{rationalize} the denominator for each}
\\\\\\
-\cfrac{3}{\sqrt{13}}\cdot \cfrac{\sqrt{13}}{\sqrt{13}}\implies -\cfrac{3\sqrt{13}}{13} \qquad \qquad \qquad \qquad \cfrac{2}{\sqrt{13}}\cdot \cfrac{\sqrt{13}}{\sqrt{13}}\implies \cfrac{2\sqrt{13}}{13}
\\\\\\
\textit{and written in \underline{ai+bj form}}\qquad -\cfrac{3\sqrt{13}}{13}i~~~~+~~~~\cfrac{2\sqrt{13}}{13}j$

7 0

3 years ago

Youssef can either way from his home to his workplace or ride his bicycle. he walks at a pace of 1 block per min, but he can tra

alex41 [277]

Youssef lives 15 blocks away from his work

<em><u>Solution:</u></em>

Given that Youssef can either way from his home to his workplace or ride his bicycle

Let "x" be number of blocks away from work Youssef works

<u><em>Case 1: walking</em></u>

He walks at a pace of 1 block per min

Therefore,

1 block = 1 minute

Thus to cross "x" blocks he takes "x" minutes

<em><u>Case 2: Bicycle</u></em>

He can travel 1 block in 20 sec on his bicycle

We know that,

To convert seconds to minute, divide the time value by 60

$\rightarrow 20 seconds = \frac{20}{60} minutes = \frac{1}{3} minutes$

Thus he takes 1/3 minutes for 1 block

So to cross "x" blocks he will take $\frac{x}{3}$ minutes

Given that it takes youssef 10 min longer to walk to work than to ride his bike

This means difference between time taken to cross "x" blocks by walking and ride by bicycle is 10 minutes

$\rightarrow x - \frac{x}{3} = 10\\\\\rightarrow \frac{3x - x}{3} = 10\\\\\rightarrow \frac{2x}{3} = 10\\\\\rightarrow x = \frac{30}{2}\\\\\rightarrow x = 15$

Thus he lives 15 blocks away from his work

4 0

3 years ago

Find the total surface area of the figure below:

kow [346]

Answer:

95

Step-by-step explanation:

Formula -

Triangle Area - 1/2bh

Square - l x w

Triangle - 5 x 7 = 35/2 = 17.5

Since there are four triangle, we will multiply 17.5 x 4 which is equal to 70

Square - 5 x 5 = 25

Now we add both 70 and 25 which is 95

So the total surface area is 95

8 0

2 years ago

Read 2 more answers