Answer:
see explanation
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
(1)
[tex]10^{8}[/tex] = 100,000,000 ( with b = 10 and n = 8 )
[tex]log_{10}[/tex] (100,000,000) = 8
(2)
[tex]10^{-4}[/tex] = 0.0001 ( with b = 10 and n = - 4 )
[tex]log_{10}[/tex] (0.0001) = - 4
Find the future value of 1000 at 7 % interest compounded annually for 10 years.
Answer:
1967.15
Step-by-step explanation:
1000 x 1.07^10 = 1967.15
The future value of 1000 with annual compounding for 10 years is $1967.15.
The formula for calculating with annual compounding is:
FV = P (1 + r)^n
FV = Future value P = the amount deposited R = interest rate N = number of years1000 x (1.07)^10 = $1967.15
To learn more about future value, please check: https://brainly.com/question/18760477
Find the equation of the function of the specified type that is the best fit for the given data
f(x)=x^2-7 and h(x)=7x-5, then f(h(2))= ?
==================================================
Work Shown:
h(x) = 7x-5
h(2) = 7(2)-5
h(2) = 14-5
h(2) = 9
f(h(2)) = f(9)
f(x) = x^2-7
f(9) = 9^2-7
f(9) = 81-7
f(9) = 74
f(h(2)) = 74
-----------
Here's a slightly alternative approach:
f(x) = x^2 - 7
f(h(x)) = ( h(x) )^2 - 7
f(h(x)) = ( 7x-5 )^2 - 7
f(h(2)) = ( 7*2-5 )^2 - 7
f(h(2)) = ( 14-5 )^2 - 7
f(h(2)) = ( 9 )^2 - 7
f(h(2)) = 81 - 7
f(h(2)) = 74
8. What are the solutions to this system
of equations?
3x + y = -1
2x + y=0
Identify the Nature of the Solution, Show
all work below.
-
Answer:
Below in bold.
Step-by-step explanation:
3x + y = -1
2x + y=0
Subtract to eliminate y:
3x - 2x + y - y = -1 - 0
x = -1
So, substituting for x in the first equation;
3(-1) + y = -1
y - 3 = -1
y = 2.
The solution is the ordered pair (-1, 2).
The system is a pair of straight lines which intersect at the point (-1, 2).
How do you turn a 5:1 ratio into a fraction
Answer:
[tex]\frac{5}{1}[/tex] is the same as 5:1
50pt Which of the following are maximum and minimum points of the function y=sin(x+ π)?
Answer:
none of the above
Maximum (3π/2, 1); Minimum (π/2, -1)
Step-by-step explanation:
The sine function is shifted left 1/2 cycle by the addition of π to x in the argument. That basically inverts the function, so it is equivalent to ...
y = -sin(x)
This has a minimum of -1 at π/2, and a maximum of +1 at 3π/2. This does not match any of the offered answer choices.
__
You might want to discuss this question with your teacher.
Answer:
The correct answer is C!
Step-by-step explanation:
The dude that said there’s no answer doesn’t know what he’s talking about.
Calculate the sum of integers x satisfying 15 ⋮ x and x < 0
Answer:
radius of the curve=r=150m
coefficient of friction=\muμ =0.6
As car is avoid skidding
\begin{gathered}\\ \sf\hookrightarrow \dfrac{mv^2}{r}=\mu mg\end{gathered}
↪
r
mv
2
=μmg
Cancel m
\begin{gathered}\\ \sf\hookrightarrow \dfrac{v^2}{r}=\mu g\end{gathered}
↪
r
v
2
=μg
\begin{gathered}\\ \sf\hookrightarrow v^2=\mu rg\end{gathered}
↪v
2
=μrg
\begin{gathered}\\ \sf\hookrightarrow v^2=0.6(10)(150)\end{gathered}
↪v
2
=0.6(10)(150)
\begin{gathered}\\ \sf\hookrightarrow v^2=60(150)\end{gathered}
↪v
2
=60(150)
\begin{gathered}\\ \sf\hookrightarrow v^2=900\end{gathered}
↪v
2
=900
\begin{gathered}\\ \sf\hookrightarrow v=30ms^{-1}\end{gathered}
↪v=30ms
−1
i really need help, does anyone know these
Answer: If angle A is congruent to angle E
Which of the following quadrants of the standard (x,y) coordinate plane contain points on the graph of the equation 6x – 3y = –9 ?
A. l and lll only
B. l, ll and lll only
C. l, ll and IV only
D. I, II and IV only
E. II, IIIand IV
Using linear function concepts, it is found that the correct option is:
B. l, ll and lll only
A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope.b is the y-intercept.If the slope is positive.
The function goes through quadrants I and III.If the intercept is positive, it also goes through quadrant II.If the intercept is negative, it also goes through quadrant IV.If the slope is negative:
The function goes through quadrants II and IV.If the intercept is positive, it also goes through quadrant I.If the intercept is negative, it also goes through quadrant III.In this problem, the equation is:
[tex]6x - 3y = - 9[/tex]
Placing it into the standard format:
[tex]3y = 6x + 9[/tex]
[tex]y = \frac{6}{3}x + \frac{9}{3}[/tex]
[tex]y = 2x + 3[/tex]
Both slope and intercept are positive, hence, quadrants I, II and III, option B.
You can learn more about linear functions at https://brainly.com/question/16302622
Which answer best describes the complex zeros of the polynomial function?
f(x) = 13 - 22 + 6x - 6
The function has two real zeros and one nonreal zero. The graph of the function intersects the x-axis at exactly one
location.
The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly two
locations.
The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly one
location.
The function has three real zeros. The graph of the function intersects the x-axis at exactly three locations.
Answer:
The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly one
location.
-16-|-2-4|+7 please solve this for me and explain. i would really appreciate it.
Answer:
-15
Step-by-step explanation:
-16 -|-6| +7
-16 - 6 + 7
= - 15
Absolute value is just taking the positive value of a number.
Step-by-step explanation:
-16-(-2-4)+7=
-16-(-6)+7=
-16+6+7=
-16+13=
-3
Simplify the linear expression. −4x+5(−5x−1) Enter your answer in the box.
Answer:
-29x - 5
Step-by-step explanation:
-4x - 25x - 5 = -29x - 5
Answer:
- 29x - 5
Step-by-step explanation:
- 4x + 5(- 5x - 1) ← distribute the parenthesis by 5
= - 4x - 25x - 5 ← collect like terms
= - 29x - 5
I am doing Khan Academy and I'm stuck on a question that said " What is another way to make 4.65 ? "
I learned it at school but I still need help on that Question.
Answer:
[tex]\frac{465}{100}[/tex] or [tex]\frac{93}{20}[/tex]
Step-by-step explanation:
You can always just multiply the by 100/100 to get any number into a fraction form. I am not sure if this is what you were asking, but here you go. Then you can simplify to get 93/20.
4781/32 without a decimal
Answer:
149(13/32)
Step-by-step explanation:
4781/32 and then take the remainder to make it an improper fraction
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region y=4x^2, y=x^2 + 3
Answer:
Step-by-step explanation:
integrate with respect to x
Area is symmetric so will be twice the integral from zero to 1
( I cannot seem to figure out how to make the lower limit negative in this editor)
[tex]A = 2\int\limits^1_0 {(x^2 + 3) - 4x^2} \, dx[/tex])
[tex]A = 2\int\limits^1_0 {-3x^2 + 3} \, dx[/tex]
[tex]A = 6\int\limits^1_0 {-x^2 + 1} \, dx[/tex]
A = 6(-⅓x³ + x)[tex]\left \| {{x=1} \atop {x=0}} \right.[/tex]
A = 6((-⅓(1)³ + (1)) - (-⅓(0)³ + (0)))
A = 6(⅔)
A = 4 units²
1 2/5m-3/5(2/3m+1)pls help
Answer: (10m-3)/5
Step-by-step explanation:
Convert 1 2/5 into an improper fraction
Simplify 5+25+2 to 7
Simplify 2/3m to 2m/3
Simplify 7/5m to 7m/5
Expand and remove the parenthesis
Collect the like terms
Simplify
what does the E stand for in PEMDAS?
Answer:
Exponents
Step-by-step explanation:
Parentheses
Exponents and roots
Multiplication
Division
Addition
Subtraction
What is the slope of the line containing (-3, 1) and (1, -2)?
Answer:
C is the answer
Step-by-step explanation:
Answer: The answer is C, -3/4.
Explanation: First graph the points, then add the straight line through them and to find the slope you do rise/run, formula being y2-y1/x2-x1. This means putting the second y value minus the first y value and dividing that by the second x value minus the first x value. Then simplify.
The scale on a map is 2 in. =250 miles. If Toledo and Kansas City are 2.25 in. How far are they apart in real life?
Answer:
281.25 miles
Step-by-step explanation:
2=250
1=125
0.5=62.5
0.25=31.25
250+31.25=281.25
Mrs. Montgomery earns a 6.5% commission on her total sales. Last month, she had sales of $55,780. How much commission did Mrs. Montgomery earn last month?
Answer:
3625.7
Step-by-step explanation:
hope that will help goodbye
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Step-by-step explanation:
.....................
help , I have like no clue on what I'm doing
Answer:
Step-by-step explanation:
Linear equations can have the form y = mx + b
where m is the slope of the line and equals Δy/Δx
and b is the y intercept.
Just for fun, let's choose the first and last sets of data points.
Δy = (275 - 135) = 140
Δx = (5 - 1) = 4
so slope m = 140/4 = 35 and the units on the slope would be $/month
Answer:
The slope of the line is 35
Step-by-step explanation:
We'll select [tex](1,135)[/tex] and [tex](2,170)[/tex] for this problem.
The slope is defined as the rate of change. Its formula is [tex]Slope=m=\frac{Rise}{Run}=\frac{y_2-y_1}{x_2-x_1}[/tex] where our two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
Therefore, we have [tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{170-135}{2-1}=\frac{35}{1}=35[/tex] as our slope.
50, 60, 72, ...
Find the 8th term.
Solve for q using both equation 1 and 2 question in pic
Answer:
p=1/8 q=3/4
Step-by-step explanation:
-2p+7q=5
-6p+35q=51/2
cancel out a variable
(-5)(-2p+7q=5)
-6p+35q=51/2
10p-35q=-25
-6p+35q=51/2 =
4p=1/2
4p/4=1/2 /4
p=1/8
substitute p=1/8 into one of the equation to find q
-2p+7q=5
-2(1/8)+7q=5
-1/4+7q=5
7q=5+1/4
7q=21/4
q= 21/4 /7
q=3/4
How many times do 5 go into 32
Answer:
6 times or 6.4
Quantity is proportional of 40/8
An eight-person relay team completed a race in 96.8 seconds. On average, what was each runner's time?
Answer:
12.1
Step-by-step explanation:
Answer:
12.1 Seconds
Step-by-step explanation:
96.8/8=12.1
help me plssssssssssssss
multipley by 2, to get the answer
4. The function y=-0.12x + 0.4 represents the percent y in decimal form of
battery power remaining x hours after turning on the laptop.
The slope is BLANK. This means the power is BLANK
by BLANK % per hour.
Please fill in blanks tysm
Answer:
Slope=0.12 power is down by 28%
Step-by-step explanation:
:)
1/2x + 4 = 10
solve the following equation algebratically. Show the work to support the answer.
Answer:
(1/2)x + 4 - 4 = 10 - 4
2(1/2)x = 6 * 2
x = 12