Questions related on indices. ( I need a full explanations of how the answer is found. )
Answers
Answer:
(a) m = 10
(b) n = 160
Step-by-step explanation:
To rewrite the expression in the manner indicated, write an equation that sets the given expression equal to the desired expression. Then solve for the variable value. The distributive property and the usual rules of exponents apply.
The rules of exponents you can use here are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
a^0 = 1
__
(a) 2^101 +2^103 = m×2^100
2^(101-100) +2^(103-100) = m × 2^(100-100) . . . . . . . multiply by 2^(-100)
2^1 +2^3 = m
2 + 8 = m
m = 10
__
(b) 2^101 +2^103 = n×4^48
2^101 +2^103 = n×(2^2)^48 . . . . . substitute 4 = 2^2
2^101 +2^103 = n×2^96 . . . . . . . . simplify
2^5 +2^7 = n . . . . . . . . . . . . . . . . . as above, multiply by 2^(-96)
32 +128 = n
n = 160
_____
Additional comment
The rules of exponents tell you that ...
(m × 2^100) × 2^-100 = m × 2^(100 -100) = m × 2^0 = m
This is effectively the same as dividing by 2^100. You're doing the same thing you would do to solve any linear equation: divide by the coefficient of the variable.
Related Questions
name the three factors that determine simple interest
Answers
Step-by-step explanation:
We know , [tex] \boxed{ \sf{Interest = Principal \times Time \times Rate}}[/tex]
Looking at the formula of simple interest , the three factors that determine simple interest should be :
Principal : The money which is borrowed or deposited is called principal . It is denoted by ' P ' .Time : The duration of time for which principal is deposited or borrowed is termed as time period. It is denoted by ' T ' .Rate : The condition under which the interest is charged is called rate. It is denoted by ' R ' .Hope I helped !♡
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Determine the domain of the following graph:
Answers
Answer:
Domain: (-3, 7)
General Formulas and Concepts:
Algebra I
Domain is the set of x-values that can be inputted into function f(x)Step-by-step explanation:
According to the graph, the line's x-value span from -3 to 7. Since both are open dot, they are excluded from the domain:
(-3, 7) or -3 < x < 7
Find the area of the composite figure.
Answers
Answer:
i think 48
Step-by-step explanation:
Which relationships have a constant of proportionality equal to 25? Pick 2 answers
Answers
Answer:
B and C.
Step-by-step explanation:
If you divide the y value by the x value then it would be 25 for B and C. A and D do not work. A does not work because as you move along the graph 25 divided by 2 and anything higher is not 25. I hope this helps!!
Answer:
b and c
Step-by-step explanation:
because 75/3=25
125/5=25 and and you already have the graph!
Someone plz help me ASAP
Answers
Answer:
its 12
Step-by-step explanation:
in the bottom right of this question click the button that says brainliest please
Find the equation of the linear function represented by the table below in slope-intercept form.
Answers
Answer:
y=-5x+1
Step-by-step explanation:
First lets identify what slope intercept form looks like:
y=mx+b
m=slope
b=y-intercept
the y-intercept would be at (0,1)
choose 2 points from the graph and lets find the slope.
The formula for slope is:
[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1} }[/tex]
The points we will be using will be (1,-4) and (2,-9)
so -9 will be [tex]y_{2}[/tex] and -4 is [tex]y_{1}[/tex]
2 is [tex]x_{2\\}[/tex] and 1 is [tex]x_{1}[/tex]
set up the equation.
[tex]\frac{-9-(-4)}{2-1}[/tex]
[tex]\frac{-5}{1}[/tex]
m = -5
So the slope is -5 and the y-intercept is 1
[To find the y-intercept all you have to do is find what y is counting by. In this is would be -5. Go backwards one on the table so x is 0 and take away -5 and it will give you 1 which would be the intercept]
So the equation will be
y=-5x+1
Now when you want to solve it you plug in the x and y values for the table but it doesn't ask you to do that,
I've included a picture so you have a visual.
If you need further assistance, don't be afraid to reach out. Hope this helps!
Joshua has $400 in his account and withdraws $25 each month.
How much will be left in his account after 6 months? Would this be a discrete or continuous graph
Answers
Answer:
since he have 400 in his account
then for 6 months= 25×6=150
400-150= 250.
i think it will be a discrete graph
Find the slope of the line through each pair of points. (10.-12).(10,7)
Answers
Answer:
7-(-12)/10-10
19
I hope this is correct.
Answer:
slope is undefined
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (10, - 12) and (x₂, y₂ ) = (10, 7)
m = [tex]\frac{7+12}{10-10}[/tex] = [tex]\frac{19}{0}[/tex]
Since division by zero is undefined then the slope of the line is undefined
The diagonals of square LMNP intersect at K. Given that LK=3 and PN= 4.25
Answers
Answer:
Answer and steps in attachment
Step-by-step explanation:
What type of exponential function is f(x)=0.75(2.1)x
What is the function's percent rate of change?
Select from the drop-down menus to correctly complete each statement.
The function is an exponential_____ function.
The percent rate of change of the function is _____%.
Answers
Answer:
Growth
110%
Step-by-step explanation:
(What did Benjamin Franklin use to lighten the mood in Philadelphia where the Constitution was being written?)
Sense of humor.
Ice cream.
An air-cooling device he had invented.
Poetic readings.
Answers
Answer:
Ice cream
Step-by-step explanation:
During the 1787 convention in Philadelphia when the constitution was being formed by the founding fathers, their sessions would usually end in heated arguments and disagreements.
To calm the delegates after the draining sessions, Benjamin Franklin who was then mostly in his home and 81 years old at that time, came up with the idea of entertaining the delegates in his home with the cold cream. His idea was helpful in reducing tensions.
Answer:
An air cooling he has invented
Step-by-step explanation:
Please help.
Anna is currently 8 years older than her sister Taylor. In 4 years she will be 2 times as old as Taylor. Let x be Taylor’s current age and answer the question
How oldies Taylor (numerical form)
Answers
Answer:
Taylor is currently 12
Step-by-step explanation:
x = Taylor's current age
x + 8 = Anna's current age
in 4 years: x + 8 + 4 = 2x
12 = x
Answer:
If anna 8 yrs older and she will be 2 times older in 4 yrs then anna is 20
Taylor is currently 12
Step-by-step explanation:
in 4 years 24 will be anna
solve for a.
p + a + r = k
Answers
Answer:
Step-by-step explanation:
sqrt(p+a)=k-r
we raised to the power of 2 both sides
(p+a)=k^2-2kr+r^2
a=k^2+r^2-2kr-p
choice 2
Solve the equation 18t – 8 = 1 for t.
A.
B.
C.
D. 2
Answers
18t - 8 = 1
18t = 9
t = 1/2
Answer:
1/2
Step-by-step explanation:
youu didn't put all options but
18 × 1/2 or 0.5 = 9
9-1 = 1
A. Group of students were competing to raise money for a local animal shelter their goal was to raise $400 Philip raised 60% of the goal by himself how much money with the rest of the students need to raised
Answers
Answer:
$160
Step-by-step explanation:
remaining money= 40% x $400= 160
Answer:
see explanation
Step-by-step explanation:
100 percent -60 percent =40 percent
rest money =40 percent of $400
=40/100×$400
=$160.
: the rest many needed by the student is $160.
I need the answer so I can pass the first semester♀️
Answers
Answer:
Step-by-step explanation:
0.333333 = 1/3
can check through dividing 1 by 3
0.125 = 125/1000 = 25/200 = 5/40 = 1/8
0.166666 = 1/6
0.1 = 1/10
0.66666 = 2/3
0.2 = 2/10 = 1/5
0.75 = 75/100 = 15/20 = 3/4
What happens first when a star begins to run out of fuel?
The star’s core shrinks.
The star becomes a black hole.
The star becomes a white dwarf.
The star’s outer layer drifts away.
Answers
Answer:
a
Step-by-step explanation:
When a star begins to run out of fuel, the first thing that happens is that the star’s core shrinks.
Option A is the correct answer.
What is the star's core in an automobile?In the context of an automobile, the term "core" usually refers to a component of a vehicle's cooling system called the radiator core.
The radiator core is responsible for dissipating heat from the engine coolant by allowing air to flow through a series of metal fins attached to narrow tubes that carry the coolant.
We have,
When a star begins to run out of fuel, the first thing that happens is that the star’s core shrinks.
This is because the energy produced by nuclear fusion reactions in the core of the star is what keeps the star from collapsing under its own gravity.
As the fuel for these reactions runs out, the core of the star no longer has enough energy to counteract the force of gravity, causing it to shrink.
This in turn causes the outer layers of the star to expand, leading to the next stage in the star’s life cycle.
Thus,
The star’s core shrinks.
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Someone Please help me..What must the value of x be in order for the figures below to be similar?
Answers
Answer:
16 cm
Step-by-step explanation:
x+x
8+8
16 cm
therefore 16 cm must be the value of x be in order for the figures below to be similar
Question 1
Mallory is investigating transformations in the coordinate plane. She makes the claims shown in the options below.
Select each claim that is true for all points in the coordinate plane.
СА A reflection over the y-axis takes the point (x, y) to (-2,y)
De A reflection over the line y = -x takes the point (x, y) to (x, y).
С
A translation of 4 units down takes the point (x, y) to (x, y - 4)
A rotation of 180° clockwise about the origin takes the point (x, y) to (y. –x).
co
2021 Illuminate Education Inc
Answers
Answer: A and C
Step-by-step explanation:
Point A and C is true about the coordinate plane.
Given that, Mallory is investigating transformations in the coordinate plane.
What is coordinate plane?A coordinate plane is a two-dimensional plane formed by the intersection of a vertical line called the y-axis and a horizontal line called the x-axis. These are perpendicular lines that intersect each other at zero, and this point is called the origin.
A) A reflection over the y-axis takes the point (x, y) to (-x, y)
When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
B) A reflection over the line y = -x takes the point (x, y) to (x, y)
When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x).
C) A translation of 4 units down takes the point (x, y) to (x, y - 4)
For example, to translate a point 1 unit to the left and 4 units down, subtract 1 from the x -value and subtract 4 from the y -value.
D) A rotation of 180° clockwise about the origin takes the point (x, y) to (y, -x).
The rule for a rotation by 180° about the origin is (x, y) → (−x, −y).
Therefore, point A and C is true about the coordinate plane.
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Which of the following statement(s) describes the rate of change of f over the interval 1.5 ≤ x ≤ 3? Select all that apply.
The graph with the X-coordinate marks 0, 2, and 4. The Y-coordinate mark 0, 2, and 4. There is graph of absolute value function “f” which opens downwards. The function has a vertex at (1, 0). It passes through the points (1.5, 1) and (3, 4).
A. The rate of change is 12.
B. The rate of change is 2.
C. The rate of change is constant.
D. The rate of change is increasing.
Answers
Answer:
B. The rate of change is 2.
C. The rate of change is constant.
D. The rate of change is increasing.
Step-by-step explanation:
Rate of change over 1.5 ≤ x ≤ 3:
[tex] rate of change = \frac{f(b) - f(a)}{b - a} [/tex]
Where,
a = 1.5, f(a) = 1,
b = 3, f(b) = 4
Plug in the values:
[tex] rate of change = \frac{4 - 1}{3 - 1.5} = \frac{3}{1.5} = 2 [/tex]
✔️The rate of change = 2
✔️The rate of change is increasing because the value is a positive value.
✔️The rate of change is also constant over 1.5 ≤ x ≤ 3 since the line is straight.
The points on the interval of the absolute value function in the graph are on the same straight line.
The statements that describe the rate of change over the interval; 1.5 ≤ x ≤ 3 are;
B. The rate of change is 2C. The rate of change is constantReasons:
The given parameter of the graph of the f are;
The vertex of the function = (1, 0)
The straight line of the function f passes through the points (1.5, 1) and (3, 4)
Therefore;
[tex]\displaystyle The \ slope \ of \ the \ graph \ between \ (1.5, \, 1) \ and \ (3, \, 4) = \mathbf{\frac{4 - 1}{3 - 1.5} }= \frac{3}{1.5} =2[/tex]
The slope of the graph = The rate of change of the graph
Therefore;
The rate of change of the graph over the interval 1.5 ≤ x ≤ 3 is 2
The rate of change is 2Given that the graph is a straight line graph, we have;
The slope of the graph is constant, therefore;
The rate of change is constantLearn more about the graph of linear functions here:
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What is the slope? (10 points)
Answers
Is 4 acres for 800 plants a rate it unit rate?
Answers
Answer:
yes, put it in this perspective, for every 4 acres, 800 plant are planted
Step-by-step explanation:
Graph the line that has a slope of 6 and includes the point (0,4).
Answers
Answer:
The equation of the line with slope 6 and containing the point (0, 4) will be:
[tex]y = 6x+4[/tex]
The graph of the line y = 6x+4 is attached below.
Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
m is the slopeb is the y-interceptGiven
The slope m = 6The point (0, 4)The y-intercept can be determined by setting x = 0 and determining the corresponding value of y.
The point (0, 4) indicates that:
at x = 0, y = 4
Thus, the y-intercept b = 4
now substituting b = 4 and m = 6 in the slope-intercept form of the line equation
[tex]y = mx+b[/tex]
[tex]y = 6x+4[/tex]
Thus, the equation of the line with slope 6 and containing the point (0, 4) will be:
[tex]y = 6x+4[/tex]
The graph of the line y = 6x+4 is attached below.
Mrs Browns bill for servicing her car is £96 plus VAT. VAT is charged at 17.5%. What is her total bill?
Answers
_______________________________
T = V × P ÷ 100 + P= 17.5% × £96 ÷ 100 + £96= £112.8Mrs. Brown's Total Bill Is £112.8_______________________________
The total bill for servicing her car will be £112.8
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Mrs. Browns bill for servicing her car is £96 plus VAT.
And, VAT is charged at 17.5%.
Now,
Since, VAT is charged at 17.5%.
So, The VAT charge = 17.5% of £96
= 17.5 / 100 x £96
= £16.8
Hence, The total bill for servicing her car = £96 + £16.8
= £112.8
Thus, The total bill for servicing her car will be £112.8
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Please answer correctly !!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!
Answers
Answer:
RS = 11
Step-by-step explanation:
well from the mid-point theorem we have that
[tex]\triangle PRS \sim \triangle PNQ[/tex]
by a ratio of
[tex]1:2[/tex]
so
[tex]\frac{RS}{NQ}=\frac{1}{2}\\\\2[\frac{RS}{NQ}]=2[\frac{1}{2}]\\\\\frac{2RS}{NQ}=1\\\\NQ[\frac{2RS}{NQ}]=NQ[1]\\\\2RS=NQ[/tex]
and now we plug in
[tex]RS = 5x-39\\\\NQ = 4x-18[/tex]
[tex]2[5x-39]=4x-18\\\\10x-78=4x-18\\\\10x-4x=-18+78\\\\6x=60\\\\x=10[/tex]
so the length of RS is
[tex]RS = 5x-39\\\\RS = 5(10)-39\\\\RS=50-39\\\\RS=11[/tex]
Describe the transformations applied to the following function.
f(x)=x4→g(x)=(x+2)4−5
Answers
Step-by-step explanation:
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Elsa buys x pencils at 8 cents each and y pens at 12 cents
each.
What is the total cost?
Answers
Answer:
20 cents
Step-by-step explanation:
8+12=20 cents
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What is the ratio 15 girls to 6 boys in simplest form?
15:6
6 boys to 15 girls
5 boys to 2 girls
5 girls to 2 boys
Answers
Because it says that 15 girls on the top
Which expressions are equivalent to - 62+(-5.5) + 1.5z + 7y-3.5?
Select all that apply.
A. – 9+ 7y +4.52
B. -9+ 7y + (-4.52)
C. 7y-9-4.5z
D. - 4.52 + 7y-9
E. 7y +(-4.52) -5.5
Answers
Please answer and show your work its "Pythagorean Theorem Word Problems" the first one is answered to show how you will be answering it.
When you are answering each question mark it 2 to 9.
(8 questions)
Answers
Answer:
I hope the answers are right. Most of them should be though
Step-by-step explanation: