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3 years ago

Which of the following are true statements about the expression 12^5

Mathematics

1 answer:

Usimov [2.4K]3 years ago

4 0

12×12×12×12×12 is equivalent to 12^5 (a^b means a is to be written down B times all being multiplied.)

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Quadrilateral JKLM is graphed with vertices at J(-2,2), K(-1,-5), L(4,0), and M(3,7).

AveGali [126]

Answer:

Question (a)

Midpoint of a line segment:

$M=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

Given:

J = (-2, 2)
L = (4, 0)

$\implies \textsf{midpoint of }JL=\left(\dfrac{-2+4}{2},\dfrac{2+0}{2}\right)=(1,1)$

Given:

M = (3, 7)
K = (-1, -5)

$\implies \textsf{midpoint of }MK=\left(\dfrac{3-1}{2},\dfrac{7-5}{2}\right)=(1, 1)$

Question (b)

Find slopes (gradients) of JL and MK then compare. If the product of the slopes of JL and MK equal -1, then JL and MK are perpendicular.

$\textsf{slope }m=\dfrac{y_2-y_1}{x_2-x_1}$

Given:

J = (-2, 2)
L = (4, 0)

$\implies \textsf{slope of }JL=\dfrac{0-2}{4+2}=-\dfrac13$

Given:

M = (3, 7)
K = (-1, -5)

$\implies \textsf{slope of }MK=\dfrac{-5-7}{-1-3}=3$

$\textsf{slope of }JL \times \textsf{slope of }MK=-\dfrac13 \times3=-1$

Hence segments JL and MK are perpendicular

4 0

2 years ago

Liam is setting up folding chairs for a meeting. If he arranges the chairs in 8 rows of the same length, he has 9 chairs left ov

Mnenie [13.5K]

8x +9 = 6x + 21 where x = number of chairs in each row
2x=12
x=6

sub back into original equation 8 x 6 + 9 =57 chairs

4 0

3 years ago

You have 55,000 in your savings account that pays 2.5% annual interest and the inflation rate is 3.4%. How much buying power wil

diamong [38]

We solve the question as follows:
Simple interest=Principle×Rate×Time
Thus given:
p=$55000, R=2.5%, time= 1 year
thus
Interest=55000×0.025×1=$1375

To evaluate the amount required to keep up with the inflation, your interest rate should match the inflation rate otherwise prices are going up faster than the savings.
Required interest rate=55000×0.034×1=$1870

The buying power lost will be the difference between your required interest and actual interest.

Thus:
Buying power lost=1870-1375=$495

8 0

3 years ago

What’s the equation that is parallel line 3y-4x=6 please help for brainlist

iren2701 [21]

Answer:

y=3/4 x-6

Step-by-step explanation:

i passed this

6 0

3 years ago

An excavating company charges $300 an hour for the use of a backhoe and $500 an hour for the use of a bulldozer. (part of an hou

Fed [463]

We have that

Cost use of a backhoe----------------------$300 an hour

Estimate for equipment rental each week---------------------$18,400

Total hours operator per week--------------------------------------40

40*300=$12000---------------------it is the cost per week to use a backhoe

$12000<$18400 is ok

The maximum of hours that I can rent a backhoe are 40 hours, since it is the limit of the operator and it do not overcome the total budget

4 0

3 years ago