The expression 5⁻¹³× 5⁵ × 2⁵ can be rewritten as 5⁻⁸ × 2⁵.
What is Exponentiation?Exponentiation is the method of writing a number in terms of powers. This method is usually useful for writing larger numbers in an understandable and effective way.
For a number x, suppose x can be written as aᵇ, here 'a' is called the base and 'b' is called the exponent.
We have to write the expression 5⁻¹³× 5⁵ × 2⁵ in a form where each base comes only once.
This can be solved using one of the basic property of exponents as stated below:
xᵃ × xᵇ = xᵃ⁺ᵇ
That is, upon multiplying two exponents with the same base value, we can combine it and add the exponent values.
∴ 5⁻¹³× 5⁵ can be rewritten as 5⁻⁸.
So 5⁻¹³× 5⁵ × 2⁵ = 5⁻⁸ × 2⁵.
Hence the expression 5⁻¹³× 5⁵ × 2⁵ can be rewritten as 5⁻⁸ × 2⁵ where each base comes only once.
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You lose track of how many 2-point baskets and 3-point baskets a team makes in a basketball game. The team misses all the 1-point baskets and still scores 54 points. The equation 2x+3y=54$ models the total points scored, where x is the number of 2-point baskets made and y is the number of 3-point baskets made. a. Find and interpret the intercepts.
Answer:
x-intercept: 27, the number of 2-pointers if no 3-pointersy-intercept: 18, the number of 3-pointers if no 2-pointersStep-by-step explanation:
Each intercept is found by setting the other variable to zero and solving for the variable value of interest.
2x +3y = 54
x-intercept:
2x = 54
x = 27
y-intercept:
3y = 54
y = 18
__
By definition, the intercept values are the values that satisfy the equation when the other variable is zero.
x-intercept: To score 54 points, the team would have to make 27 2-point baskets if no 3-point baskets were made.
y-intercept: To score 54 points, the team would have to make 18 3-point baskets if no 2-point baskets were made.
HELP PLEASE !!!!!!!!!!!
[] The equation on the left, 292 [tex]\frac{1}{2}[/tex] = 18 * 6 [tex]\frac{1}{2}[/tex] * h
-> Volume is length times width times height. When we plug in all the values we have to solve for h (height) we get this equation.
[] The height is 2.5 inches
-> We will solve the equation above.
-> Multiply 18 by 6 and a half = 117
-> Divide 292 and a half by 117 = 2.5
-> The height is 2.5 inches or 2 [tex]\frac{1}{2}[/tex]inches
292 [tex]\frac{1}{2}[/tex] = 18 * 6 [tex]\frac{1}{2}[/tex] * h
292 [tex]\frac{1}{2}[/tex] = 117h
[tex]\frac{292 \frac{1}{2} }{117}[/tex]= [tex]\frac{117h}{117}[/tex]
2.5 = 1h
h = 2.5 inches
Plz Plz answer this!!!!! You’ll get brainliest if ur right and ull get 15 points Plz plz plz plz plz plz plz plz plz plz plz plz plz plz plz
Answer:
the last one
Step-by-step explanation:
thanks again everyone
Answer:
5 gallons
conversion:
2 cups → 1 pint2 pints → 1 quart 4 quarts → 1 gallonwe have here total 80 cups.
2 cups → 1 pint80 cups → 40 pints
Then convert it into quartz
2 pints → 1 quart40 pints → 20 quartz
Then convert quartz into gallons
4 quarts → 1 gallon20 quartz → 5 gallons
Josiah wants to ride his bicycle 42.5 miles this week. He has already ridden 18 miles.
If he rides for 5 more days, what is the average number of miles he would have to ride
each day to meet his goal?
Hello there! Allow me to help you!
|| ▼ Answer ▼ ||
4.9 miles
|| ✪ Solution ✪ ||
Step 1:
In this question, we are given the following:
Josiah wants to ride his bicycle 42.5 miles this week.
He has already ridden 18 miles. If he rides for 5 more days,
what is the average number of miles he would have to ride each day to meet his goal?
Step 2:
The details of the solution are as follows:
Total distance = 42. 5 miles
Distance ridden = 16 miles
Number of days left = 5 days
Let the number of miles that'll be ridden for each day be represented by x.
Hence, we have that,
[tex]5x+18=42.5[/tex]
[tex]5x=42.5-18[/tex]
[tex]5x=24.5[/tex]
Divide both sides by 5 we have that,
[tex]x=\frac{24.5}{5}[/tex]
[tex]x=4.9[/tex]
CONCLUSION:
The average number of miles he would have to ride each day to meet his goal = 4.9 miles
Hope this helps!
If you have any questions please ask.
The required average miles for him to ride for 5 days is 4.9 miles per day.
Given that,
Josiah wants to ride his bicycle 42.5 miles this week. He has already ridden 18 miles.
he rides for 5 more days, what is the average number of miles he would have to ride each day to meet his goal is to be determined
The average of the values is the ratio of the total sum of values to the number of values.
Here,
Josiah wants to ride his bicycle for a total of 42.5 miles,
he rides for 18 miles by now,
Remaining miles to ride = 42.5 - 18 = 24.5 miles
For 5 day is must ride for average = 24.5 / 5 = 4.9 miles per day.
Thus, the required average miles for him to ride for 5 days is 4.9 miles per day.
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x^3 + 3x^2 -10x factor polynomial and find zero
Answer:
x(x - 2)(x + 5)x = 0, x = 2, x = -5Step-by-step explanation:
x^3 + 3x^2 - 10x
~Factor
x(x - 2)(x + 5)
Solve for the zero.
x(x - 2)(x + 5) = 0
We know that; x = 0, x - 2 = 0, and x + 5 = 0
x = 0
x - 2 = 0
x = 2
x + 5 = 0
x = -5
Best of Luck!
Here we are provided with an polynomial of degree 3 and we have to factorise it first and then we have to compute it's zeroes.
Given Polynomial:
x³ + 3x² - 10xTaking common x from all the 3 terms,
➝ x(x² + 3x - 10)
Factorising through Middle term factorisation,
➝ x(x² + 5x - 2x - 10)
➝ x{x(x + 5) - 2(x + 5)}
➝ x(x - 2)(x + 5)
Hence, Factorised !!
Now equating to 0 to find the zeroes of the poly.
➝ x(x - 2)(x + 5) = 0
That means,
x = 0x - 2 = 0x + 5 = 0So, the zeroes of the polynomial is 0, 2 or -5
And we are done....
Carry On Learning [tex]![/tex]
Brainliest if correct
Answer:
[tex]\frac{5}{10}, \frac{4}{10}, \frac{1}{10}[/tex] are the numbers you need
Step-by-step explanation:
The least common denominator of those two numbers is 10.
[tex]\frac{1}{2} * \frac{5}{5} = \frac{5}{10} \\\\\frac{2}{5} * \frac{2}{2} = \frac{4}{10} \\\\\frac{5}{10} - \frac{4}{10} = \frac{1}{10}[/tex]
I hope this helps! Have a lovely day! :)
Please help asap! I will gave brainlest!
Step-by-step explanation:
[tex] \tan(x) \csc {}^{2} (x) - \tan(x) [/tex]
[tex] \tan(x) ( \csc {}^{2} (x) - 1)[/tex]
[tex] \tan(x) ( \cot {}^{2} (x) [/tex]
[tex] = \tan(x) \cot(x) \cot(x) [/tex]
[tex]1 \cot(x) [/tex]
[tex] = \cot(x) [/tex]
A home run is hit in such a way that the baseball just clears a wall 15.0 m high, located
152 m from home plate. The ball is hit at an angle of 34.0° to the horizontal, and air
resistance is negligible. Assume that the ball is hit at a height of 1.00 m above the
ground. Use significant figures in your final answer and show your work.
a. Find the initial speed of the ball. {8 Points}
Hang on I am figuring it out
A bee population is measured each week and the
results are plotted on the graph. What is the bee
population when it is first measured?
Answer:
500 bees
Step-by-step explanation:
The initial value is the y-intercept, where a point crosses the y-axis when x=0.
(0, x) = (0, 500)
Hope this makes sense :]
There are 500 bees in the population when it is first measured.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
Every week, a bee population is counted, and the findings are illustrated on the given graph.
According to the given graph, the initial value is the y-intercept, where a point intersects the y-axis when x = 0.
(0, x) = (0, 500)
This means the bee population is 500 when it is first measured.
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The lid of a box is 43 cm² an area the volume of the box is 420 cm3 what is the height of the box?
Answer: 9.77 cm
Step-by-step explanation:
The volume of the box is length x width x height (V = l*w*h). The area of the lid of the box is the length x width (A = l*w). So, to find the height, you can change the equation to volume / (length x width) = height (V/(l*w) = h). Divide the volume by the area (420/43), to get the answer of 9.77 cm.
True or false 49 is a irrational number
Answer:
FalseStep-by-step explanation:
49 is a rational number.
Hope this helps:)
Find the perimeter of a triangle with sides measuring 10 inches, 14 inches and 15 inches
Answer:
39
Step-by-step explanation:
Answer:
39 inches
Step-by-step explanation:
Perimeter is found by adding the sides of the object together.
10in. + 14in. + 15in. = 39in.
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Are these two figures similar? Explain.
Answer
YES
Step-by-step explanation:
yes, because one of their sides are equivalent.
What is this answer and how?
What is 0.801 in words?
Answer:
How to Write Out Number 0.801 in Words: eight hundred one thousandths in (US) American English, Number Converted (Spelled Out) to Words.
help pleas Given that f(x)=x^2+3x−7, g(x)=3x+5, and h(x)=2x^2−4, find each of the following. Solve each of the problems showing work.
f(g(x))
h(g(x))
(h−f)(x)
(f+g)(x)
Answer:
check below!given functions:
[tex]\sf f(x)=x^2+3x-7[/tex]
[tex]\sf g(x)=3x+5[/tex]
[tex]\sf h(x)=2x^2-4[/tex]
solving steps:
(a)
[tex]\sf f(g(x))[/tex]
[tex]\sf \sf f(3x+5)[/tex]
[tex]\sf (3x+5)^2 + 3(3x+5)-7[/tex]
[tex]\sf 9x^2+30x+25+9x+15-7[/tex]
[tex]\sf 9x^2+39x+33[/tex]
(b)
[tex]\sf h(g(x))[/tex]
[tex]\sf h(3x+5)[/tex]
[tex]\sf 2(3x+5)^2-4[/tex]
[tex]\sf 18x^2+60x+50-4[/tex]
[tex]\sf 18x^2+60x+46[/tex]
(c)
[tex]\sf (h-f)(x)[/tex]
[tex]\sf 2x^2-4-(x^2+3x-7)[/tex]
[tex]\sf 2x^2-4-x^2-3x+7[/tex]
[tex]\sf x^2-3x+3[/tex]
(d)
[tex]\sf (f+g)(x)[/tex]
[tex]\sf x^2 + 3x -7 +3x+5[/tex]
[tex]\sf x^2+6x-2[/tex]
tHanks again everyone
Let's solve
[tex]\\ \rm\rightarrowtail x+2<-3[/tex]
[tex]\\ \rm\rightarrowtail x<-3-2[/tex]
[tex]\\ \rm\rightarrowtail x<-5[/tex]
So
there is a open dot present over -5Less than means left side onwardsOption B
the cost of computer was rs 65000 the price of computer was depreciated 12% compounded yearly how much amount was depreciated in 2 years?find it
Answer:
50336
Step-by-step explanation:
The cost deprecates by 12% each year. If we have to find how much it deprecated for 2 years, we will have to calculate how much is 12% of the current price, subtract it, then find how much is 12% equal to again and subtract it once again. Not sure if that's the smartest way to do it though.
Anyway, we have
65000, 12% of 65000 is equal to (65000 * 12) / 100 = 650 * 12 = 7800
After the first year, the price will be:
65000 - 7800 = 57200
Now we do the same thing:
12% of 57200 = 57200 * 12% = 57200 * 12/100 = 57200 / 1 * 12/100 = (57200 * 12) / 100 * 1 = 572 * 12 / 1 = 572 * 12 = 6864
After the second year the price will be:
57200 - 6864 = 50336
Sally puts $200.00 in a bank account. Each year the account earns 8% simple interest. How much interest will be earned in three years? A $16.00 B $24.00 C $48.00 D $160.00
Answer:
D
Step-by-step explanation:
Errors in the programming language Python can be broadly classified into two types, syntax errors, and logical errors. When writing a program the first time, the probability for syntax errors to arise is 0.3, that for logical errors is 0.5, and that for both errors to occur is 0.1.(a) Find the probability that no syntax errors occur.(b) Find the probability that no errors occur.(c) Find the probability that errors of any type occur.(d) The programmer found a syntax error in the code. What is the probability that there are also logical errors based on this finding?(e) Are the events of having syntax errors and logical errors independent? Also, explain why.
Answer:
Step-by-step explanation:
a( Pr(no syntax error) = 1-Pr(syntax error arises)
Pr(no syntax error) = 1 -0.3
Pr(no syntax error) = 0.7
b) Pr(no error occurred) = 1-Pr(both error occurred)
Pr(no error occurred) = 1-0.1
Pr(no error occurred) = 0.9
c) Pr(any type of error occurred) = Pr(syntax error occur)+Pr(logical)
Pr(any type of error occurred) = 0.5+0.3 = 0.8
d) Pr(syntax and logical) = Pr(syntax occur)+Pr(logical or syntax occur)
= 0.3+0.1
= 0.4
e) Independent event are events that occurs at the same time. The occurrence of one does not affect the other.
Pr(logical and syntax) = pr(syntax)×pr(logical)
Given
pr(syntax)×pr(logical) = 0.3×0.5 = 0.15
From the question, Pr(logical and syntax) = Pr(both error occurred) = 0.1
Since Pr(logical and syntax) ≠ pr(syntax)×pr(logical), this means that the errors are not independent
A circle has a diameter that measures 20 inches. What is the area of the circle to the nearest 10th? Used 3.14 for pi
Answer:
A≈314.16
Step-by-step explanation:
a circle's diameter is 2 x radius
20/2 = radius
Area formula: A=πr^2
A=π 10^2
A≈314.16
1
9. Adam had 183 pieces of gum. He gave of the pieces to his sister. How many
3
pieces of gum does Adam have left?
Hi!
Your answer will be: 180.Reason being: 183-3=180. Also, 180+3=183.
Hope this helps!
Yours Truly,
~~~PicklePoppers~~~
10. Solve for x. Round to the nearest degree.
Answer:
x = 28°
Given:
opposite: 15hypotenuse: 32using sine rule:
[tex]\hookrightarrow \sf sin(x) = \dfrac{opposite}{hypotenuse}[/tex]
[tex]\hookrightarrow \sf sin(x) = \dfrac{15}{32}[/tex]
[tex]\hookrightarrow \sf x = sin^{-1}(\dfrac{15}{32})[/tex]
[tex]\hookrightarrow \sf x = 28^{\circ \:}[/tex]
[tex]\\ \rm\Rrightarrow sinX=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\\ \rm\Rrightarrow sinX=\dfrac{15}{32}[/tex]
[tex]\\ \rm\Rrightarrow sinX=0.47[/tex]
[tex]\\ \rm\Rrightarrow X=sin^{-1}(0.47)[/tex]
[tex]\\ \rm\Rrightarrow X=28.03[/tex]
7. The graph was made to compare the costs of renting copy machines
from Ames Business Product to those from Beck's Office Supply. What
information is given by the point of intersection of the two lines? *
The information given by the point of intersection of the two lines is (d) the number of copies for which the total cost per month is the same for both companies
How to interpret the point of intersectionThe point of intersection is the equilibrium point of both companies.
This means that, the point represents where the number of copies and the total cost per month for both companies is equal
Hence, the information given by the point of intersection of the two lines is (d)
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The cost of an air conditioner is $
130
. The cost to run the air conditioner is $
0.25
per minute for the first
400
minutes. Write the function that models the total cost of running the air conditioner for the first
400
minutes and determine the key features of the function.
Function:
Domain:
Range:
y−
intercept:
x−
intercept(s):
A function that models the total cost of running the air conditioner for the first 400 minutes is [tex]T=130 +0.25m[/tex].
Let the number of minutes be m.Let the total cost be T.Given the following data:
Cost of air conditioner = $130Running cost = $0.25 per minuteTime = 400 minutes.To write a function that models the total cost of running the air conditioner for the first 400 minutes:
How to solve a word problem.First of all, we would write an equation to models the total cost of running the air conditioner for the first 400 minutes:
For the total time:
[tex]0.25m[/tex]
For the total cost:
[tex]T=130 +0.25m[/tex]
For the domain:
The value of m is the domain and it can be chosen from 0 to 130.
Domain (m) = [0, 130].
For the range:
A range represents the minimum and maximum value of a data set.
Thus, the value of T would be between 130 and 230.
Range = [130, 230].
For the intercept:
when x = 0, we have:
[tex]y=130 +0.25(0)[/tex]
y = 130.
Intercept = [0, 130]
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Assessment Unit #1B
(FIF.2) Dora said that the mapping below does not represent a function because each value in the
domain is paired with the same value in the range. Explain the error in Dora's reasoning. (1 point)
6
-1
12
0.5
3
Answer:
i have no idea i think its 0.5 or 12
Step-by-step explanation:
An object starts from rest and accelerates at a rate of 3.0 meters per second2 for 6.0 seconds. The velocity of the object at the end of this time is
a= v-u/t
3 = v-0/6
3 = v/6
v=18 m/s
Which two fixed points define the shape of an ellipse?
A. Center and focus
B. Focus and directrix
C. Two foci
D. Vertex and focus
Animals help ⚠️BLANK⚠️ flowers when eating it and depositing the seeds in a different area?
FILL IN THE BLANK PLEASE
Answer:
Animals help pollinate flowers by eating them and depositing the seeds in different areas.