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natita [175]
3 years ago
11

Consider the figure below where l2 intersects l1 and m∠2=90°.

Mathematics
1 answer:
mina [271]3 years ago
3 0
Layla bu la 520 and glue 729
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What are the steps of factoring (5m-2)^2-(3m-4)^2 ?
Svetlanka [38]
We use the formula a^2 - b^2 = ( a - b )( a + b );
We have a = 5m - 2 and b = 3m - 4;
<span>(5m-2)^2-(3m-4)^2 = (5m - 2 -3m + 4) x (5m-2 + 3m - 4) = (2m + 2)(8m - 6) = 2(m +1) x 2(4m - 3) = 4(m+1)(4m-3);

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6 0
3 years ago
Select all of the potential solution(s) of the equation 2log5x = log54.
Vanyuwa [196]

Answer:

x = ±2

Step-by-step explanation:

A equation is given to us , which is ,

\longrightarrow 2log_5(x) = log_5 4

From <u>properties </u><u>of </u><u>logarithm </u>we know that ,

\longrightarrow alog\ m = log \ m^a

Applying this to LHS , we have ;

\longrightarrow log_5 x^2 = log_5 4

Now the bases of logarithm on LHS and RHS is same . On comparing , we have ;

\longrightarrow x^2 = 4

Put square root on both sides,

\longrightarrow x =\sqrt{4}

Simplify ,

\longrightarrow \underline{\underline{ x =\pm 2 }}

This is the required answer.

6 0
2 years ago
Suppose y varies directly with x. If y = -4 when x = 8, what is the equation of direct variation?
tresset_1 [31]

\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that }~~ \begin{cases} y=-4\\ x=8 \end{cases}\implies -4=k(8)\implies \cfrac{-4}{8}=k\implies -\cfrac{1}{2}=k \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-\cfrac{1}{2}x~\hfill

8 0
3 years ago
Read 2 more answers
How to work out 270 ÷ 30
tresset_1 [31]

Answer:

270 ÷ 30 = 9

Step-by-step explanation:

9x3=27

90x3 = 270

27 ÷ 3 = 9

270 ÷ 30 = 9

90 x 3 = 270

30 x 9  = 270

8 0
3 years ago
Last week’s and this week’s low temperatures are shown in the table below. Low Temperatures for 5 Days This Week and Last Week L
STatiana [176]

Question:

Temperatures for 5 Days This Week and Last Week

Low Temperatures This Week (Degrees Fahrenheit) 4 10 6 9 6 Low Temperatures Last Week (Degrees Fahrenheit) 13 9 5 8 5 Which measures of center or variability are greater than 5 degrees? Select three choices.

a) the mean of this week’s temperatures

b) the mean of last week’s temperatures

c) the range of this week’s temperatures

d)the mean absolute deviation of this week’s temperatures

e) the mean absolute deviation of last week’s temperatures

Answer:

a) the mean of this week’s temperatures

b) the mean of last week’s temperatures

c) the range of this week’s temperatures

Step-by-step explanation:

I would be verifying the options a, b, and c in my answer above through calculations which are shown below.

We were given the following data:

Low Temperatures This Week (Degrees Fahrenheit)

4, 10, 6, 9, 6

Low Temperatures Last Week (Degrees Fahrenheit)

13, 9, 5, 8, 5

We are to find which measures of center or variability are greater than 5 degrees.

Option a

The mean of this week’s temperatures

(4+ 10+ 6+9+ 6) °F ÷ 5 = 35 °F ÷5 = 7°F

Option a is correct because it measures of center or variability which is 7 °F is higher than 5°F

Option b

The mean of last week’s temperatures

(13+ 9 + 5 + 8 + 5) °F = 40°F ÷ 5 = 8°F

Option b is correct , because its measure of variability which is 8°F is greater than 5°F.

Option c

the range of this week’s temperatures

This week's temperature is given as

(4, 10, 6, 9, 6) °F

Range is defined as the difference between the highest number and the lowest number

Range of this week's temperature = (10 - 4) °F = 6°F

Hence Option c is correct because it measures of center or variability which is 6°F is greater than 5°F

From the above calculations we can accurately confirm that options a, b, and c are correct because the measures of their center or variability is greater than 5°F

3 0
3 years ago
Read 2 more answers
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