Answers
Answer:
n = - 5
Step-by-step explanation:
Using the rules of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]
[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex]
Consider the left side
[tex]\frac{y^4.y^{n} }{y^2}[/tex]
= [tex]\frac{y^{4+n} }{y^2}[/tex]
= [tex]y^{4+n-2}[/tex]
= [tex]y^{2+n}[/tex], then
[tex]y^{2+n}[/tex] = [tex]y^{-3}[/tex]
Since the bases on both sides are the same, equate the exponents
2 + n = - 3 ( subtract 2 from both sides )
n = - 5
Related Questions
Find the coordinate of point X inside segment BE that is 1/2 (half) the
distance from B to E.
2
Answers
Answer:
Point D
Step-by-step explanation:
Half the distance between B and E is at -4. Point D is at -4, so point X is at point D.
if ABC~DEF and the perimeter of ABC is 4 times greater than the
perimeter of DEF, what is the relationship between the areas of the
triangles?
Answers
Answer:
The area of triangle ABC is 16 times larger than the area of triangle DEF
Step-by-step explanation:
Step 1: Re-state the input
Given two triangles ABC and DEF are similar with ratio k.
Step 2: Derive the information
Suppose that the triangle ABC is k times larger than triangle DEF.
=> It means that all sides and heights of triangle ABC are k times larger than corresponding sides and heights of triangle DEF.
For example:
AB = k x DE
AC = k x DF
BC = k x EF
=> AB + AC + BC = k x (DE + DF + EF)
=> Perimeter of triangle ABC is k times larger than perimeter of triangle DEF
Step 3: Solve the problem step-by-step
Suppose that AH is the height from vertex A to base BC of triangle ABC and DH' is the height from the vertex D to base EF of triangle DEF.
As the above assumption states:
AH = k x DH'
BC = k x EF
Multiply both sides of the two above equations:
=> AH x BC = DH x EF x k x k
Simplify k components:
=> AH x BC = DH x EF x k^2
Multiply (1/2) to both sides:
=> (1/2) x AH x BC = (1/2) x DH x EF x k^2
Apply the formula to calculate the area of a triangle:
=> Area of triangle ABC = Area of triangle DEF x k^2
In other words:
The area of triangle ABC is (k^2) times larger than area of triangle DEK.
Here, the perimeter of triangle ABC is 4 times larger than the perimeter of triangle DEF => k = 4
Step 4: Make the conclusion
=>The area of triangle ABC is (4^2 = 16) times larger than area of triangle DEK.
Hope this helps!
:)
Subtract negative 24 from 11.
Answers
Answer:
-35
Step-by-step explanation:
Answer:
35
Step-by-step explanation:
11-(-24)
35
brianliest please
provide the value of k:
(2x-1)(kx+1)=6x^2-x-1
Answers
Answer:
k = 3
Step-by-step explanation:
Expand the left side and compare the coefficients of like terms on both sides.
(2x - 1)(kx + 1) ← expand using FOIL
= 2kx² + 2x - kx - 1
Compare the coefficients of the x² term on both sides
2k = 6 ( divide both sides by 2 )
k = 3
Answer:
k= 6x-3/2x-1
Step-by-step explanation:
Jennifer is organising a street party. she needs to make 300 cakes. the recipe consist of : 50g icing, 150g butter, 120g caster sugar, 110g flour, 1 egg, 5h baking powder. this makes 12 cakes. how much of each ingredient will she need? kilograms.
Answers
Answer:
1.25 kg of icing sugar
3.75 kg of butter
3 kgs of caster sugar
2.75 kgs flour
25 eggs
125g baking powder
Step-by-step explanation:
300/12 x (weight of ingredient)
Answer:
1.25kg icing
3.75kg butter
3kg caster sugar
2.75kg flour
25 eggs
125g baking powder
Step-by-step explanation:
Above is 6 ingredients that is all part of your answer, but you show 300/12 as your first step in workings , the rest is multiplying by 25 as shown here.
300/12 = 25
25 x 50 = 1250g = 1.25kg
25 x 150 = 3750g = 3.75kg
25 x 120 = 3000g = 3kg
25 x 110 = 2750g = 2.75kg
25 eggs
25 x 5 = 125g
Misty, Tina and Jen walk into a store. The manager places his hand on Tina’s shoulder and tells her, “You didn’t win the door prize.” Then he looks at Jen and Misty and says, “But one of you did.” What is the probability that Jen has won?
A. 50%
B. 25%
C. 75%
D. 100%
Answers
Answer:
50%
Step-by-step explanation:
3 of them walk into a store, giving her a 33.333% chance of winning. By eliminating one, Tina may as well have never walked into the store, leaving Jen with a 50% chance.
Answer:
A.50%
Step-by-step explanation:
PLEASE HELP !!
Image attached
Answers
Answer:
C = 31.4 inches
Step-by-step explanation:
The circumference of a circle is found by
C = pi *d
C =3.14 * 10
C = 31.4 inches
Answer:
C = 31.4 inches
Step-by-step explanation:
To find the circumfrence
C = pixd
C =3.14x10
C = 31.4 inches
equivalent fractions for 5 out of 7
Answers
Answer:
There are 20 ways but I will give you 4 :)
1. Multiply the numerator and the denominator by 2:
5/7 x 2/2 = 10/14
2. Multiply the numerator and the denominator by 3:
5/7 x 3/3 = 15/21
3. Multiply the numerator and the denominator by 4:
5/7 x 4/4 = 20/28
4. Multiply the numerator and the denominator by 5:
5/7 x 5/5 = 25/35
Step-by-step explanation:
There you go!
The volume of a cone is 201.92 cubic units. If a cylinder has the same height and radius as a cone what is it’s volume in cubic units?
Answers
Answer:
Cone: 201.92=π×r^2×h×1/3
Cylinder: V=π×r^2×h
So you can see that there is No difference between the two equations except from the Factor 1/3. Without This Factor the volume of the cone would be three Times as big. Therefore, to calculate the Volume of the cylinder, you have do This:
201.92×3
Step-by-step explanation:
Answer:
Anwser is (B)
Step-by-step explanation:
Cone: 201.92=π×r^2×h×1/3
Cylinder: V=π×r^2×h
So you can see that there is No difference between the two equations except from the Factor 1/3. Without This Factor the volume of the cone would be three Times as big. Therefore, to calculate the Volume of the cylinder, you have do This:
Pleasee help I am being timed
Answers
Answer:
A: 33.5
B: 24.5
Step-by-step explanation:
Answer:add the cost for all the books for answer one and for number 2 subtract 9 from the total of answer 1.
Step-by-step explanation:
A rectangular prism has a width of 5 cm, a height of 8 cm and a depth of 2 cm. What is the volume of the
prism?
Answers
So the volume of the prism would be 80 cubic centimeters
the volume of the rectangular prism is 80 cubic centimeters.
The volume of a rectangular prism can be calculated by multiplying its length, width, and height. In this case, the width is 5 cm, the height is 8 cm, and the depth is 2 cm.
Volume = length × width × height
Substituting the given values into the formula:
Volume = 5 cm × 8 cm × 2 cm
Calculating the multiplication:
Volume = 80 cm³
Therefore, the volume of the rectangular prism is 80 cubic centimeters. This means that the prism can hold 80 units of a cubic centimeter, such as water or any other substance.
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During 14 spins, a spinner landed on blue 4 times. If you spin the spinner once, what is the experimental probability that it will land on blue?
Answers
Answer:
2/7
Step-by-step explanation:
Since 4 out of 14 times it landed on blue, it must have a 4/14 experimental probability of 4/14 for landing on blue. 4/14 simplifies to 2/7.
Find the area of the shaded triangle.
Answers
And then you have to divide 24 by 2, that way it would be easier for you to find the answer, so what is 24 divided by two,
It equals 12, so the answer is 12.
Please thank me and mark me as brainliest answer
The area of the shaded triangle would be 12 ft.
What is a triangle?A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
The area of the triangle is the product of half the base and the height of the triangle.
The area of the triangle = 1/2 x b x h
Area of a triangle is 1/2 x base x height.
The base of the shaded triangle is 3 ft. the height is 8 ft.
Area = 1/2 x 3 x 8
Area = 12 square feet.
so the answer is 12.
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350 people visited a zoo the zoo has four types of tickets the manager wants a sample of size 30, stratified by ticket type. how man teenagers should be in the sample *see attached*
Answers
Answer: 10
Step-by-step explanation:
Given the following :
Total number of visitors = 350
Sample size = 30
Number selected from each strata is given by:
(Strata size ÷ Total population) × sample size
From the cumulative frequency distribution :
Child - 90
Teen - (210 - 90) = 120
Adult - (350 - 210) = 140
Senior = 0
Strata size of teen = 120
Therefore, number of teen selected is ;
(120 ÷ 350) × 30
0.3428571 * 30 = 10.26 (10 visitors)
pls help........................
Answers
Answer:
30 in
Step-by-step explanation:
idk how to explain, so yea:)
If 153=2(z+z)n, then what’s is the value of 4nz+20
Answers
Answer: (-4, 6)
Step-by-step explanation:
for this question, we can use the substitution method. this is where we substitute the coordinates in the answer choices into the given system of inequalities or equations to determine which one is true.
1. (-4,6)
x + 4y > 12
-4 + 4(6) > 12
20 > 12 is true
now we can substitute the second inequality.
3(6) > -4 + 6
18 > 2 is true, therefore making this set of points true.
it may be helpful to substitute the rest of the values of x and y into the inequalities to verify your answers :
5 + 4(2) > 12
5 + 8 > 12
13> 12 is true
3(2) > 5 + 6
6 > 11 is not true
the rest of the answer choices are also not true.
I hope this helped you!
a cyclist rides his bike at a rate of 10 miles per hour. what is this rate in kilometers per hour? how many kilometers will the cyclist travel in 4 hours? in your computations assume that 1 mile is equal to 1.6 kilometers. DO NOT ROUND YOUR ANSWER
Answers
Answer:
64
Step-by-step explanation:
speed of cyclist = 10 miles per hour
given 1 mile is equal to 1.6 kilometres.
1*10 miles will be equal to 1.6*10 kilometres
thus , 10 mile is equal to 16 kilometres
using 16 km in place of 10 miles in 10 miles per hour
we have
speed of cyclist = 16 kilometres per hour
we know that distance = speed * time
speed is 16 kilometres per hour
time 4 hours
thus , distance = 16*4 kilometres= 64 kilometres.
cyclist will travel 64 kilometres in 4 hours.
What is the value of n?
1339
nº
142"
A. 470
B. 810
C 389
D. 850
Answers
Answer:
D
Step-by-step explanation:
The sum of all exterior angles of a triangle is 360° so n + 133 + 142 = 360 and n = 85°.
Answer:
it is 85
Step-by-step explanation:
133+142=275
360-275=85
which of the following describes the number 0.5? A. irrational, terminating decimal
B. Rational, repeating decimal
C. irrational, nonrepeating decimal
D. Rational, terminating decimal
Answers
Answer:
D
Step-by-step explanation:
0.5 can be written as a fraction and 0.5 doesn't repeat
The number 0.5 is rational and terminating decimal thus option (D) is correct.
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
As per the given number, 0.5
Since 0.5 = 5/10 here 5 and 10 both are integers thus it will be a rational number.
Now, 0.5 here the number after the decimal is only one 5 so it is finite thus it will be terminating decimal.
Hence "The number 0.5 is rational and terminating decimal".
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which equation represents the function on the graph?
Answers
Answer:
the answer would be c the
third option
Me. Parsons wants to build a new banister for the staircase shown. If the rise of the stairs of a building is 5 feet and the run is 12 feet, what will be the length of the new banister?
I need this to be explained
Answers
How far up a wall will an 11-meter ladder reach, if the foot of the ladder is 4 meters away from the base of the wall?
Answers
Answer: approximately 10.4 feet
Step-by-step explanation:
What is the equation of the line that contains (-5,1) and has a slope of 4
PLEASE HELP
Answers
Answer:
y=4x +21
Step-by-step explanation:
Question: Meghan has created a diagram of her city with her house, school, store, and gym identified. A. How far is it from the gym to the store? B. Meghan also wants to walk to get some exercise, rather than going to the gym. She decides to walk along arc AB. How far will she walk? Round to 3 decimal places.
Answers
Answer:
a). Distance between the gym and store 9.25 m
b). Meghan will walk 5.637 m along the arc AB.
Step-by-step explanation:
a). Theorem of intersecting chords inside the circle,
When two chords intersect each other in a circle multiplication of their segments are equal.
3×7 = 4a
a = [tex]\frac{21}{4}[/tex]
a = 5.25 m
Distance between the gym and store = 4 + 5.25
= 9.25 m
b). Length of an arc = [tex]\frac{\theta}{360}\times (2\pi r)[/tex]
[tex]\widehat{AB}[/tex] = [tex]\frac{64.6}{360}\times 2\pi (5)[/tex]
= [tex]\frac{646\pi }{360}[/tex]
= 5.6374 m
≈ 5.637 m
Therefore, Meghan will walk 5.637 m along the arc AB.
Two machines are printing shirts. The first machine can produce 2,520 shirts in 180
minutes. The second machine can produce 1,440 shirts in 120 minutes. If the two
machines work together, how long will it take them to produce 6,500 shirts? If necessary,
round your answer to the nearest whole number.
Answers
Answer:
250Min
Step-by-step explanation:
1st machine = 2520 divided by 180min =14shirts/min
2nd machine =1440 divided by 120min =12 shirts/min
14 shirts/min +12shirts/min =26shirts/min
6500 shirts divided by 26shirts/min =250min
The answer is 250 minutes.
What is the rounding of decimals?Rounding of decimals refer to the rounding of decimals to certain accuracy. Process of rounding of decimals ; put simply , if the last digit is less than 5, round the previous digit down. However, if it is greater than 5 then round the previous digit up.
Given, The first machine can produce 2,520 shirts in 180 minutes.
So, the first machine is making 2520 / 180 = 14 shirts per minute.
And The second machine can produce 1,440 shirts in 120 minutes.
So, the second machine is making 1440 / 120 = 12 shirts per minute.
If the both machines work together then both are making 14 + 12 = 26 shirts per minute.
To take them to produce 6500 shirts , both will take 6500 / 26 = 250 minutes .
Hence the answer is 250 minutes.
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8
If Zoey sells over 50 boxes of cookies, then she will win a prize.
Which of the following is the hypothesis in the statement above?
A.
she will not win a prize
B.
Zoey sells under 50 boxes of cookies
C.
she will win a prize
D.
Zoey sells over 50 boxes of cookies
Answers
Answer: Zoey sells over 50 boxes of cookies
Step-by-step explanation: The hypothesis is the “if” part in an if-then statement.
y= 3x+7
y = -2x - 3
Whats the x and y for the solution
Answers
Answer:
x=-2, y=1
Step-by-step explanation:
y=3x+7
y=-2x+3
Set the two equations equal to each other:
3x+7=-2x-3
Add 2x to both sides:
5x+7=-3
Subtract 7 from both sides:
5x=-10
Divide both sides by 5:
x=-2
Plug back into one of the original equations to find y:
y=3(-2)+7=-15+7=1
Hope this helps!
11. The chess club has 50 members. They want to raise $680 for a trip to a competition. The school will give $130. How much must each member pay?
Answers
Answer:
$11
Step-by-step explanation:
Total members = 50 , Raised amount = $680
If school gives $130 then all the 50 members will pay the remaining amount.
Remaining amount to be paid by the 50 members = $680 - $130 = $550
50 members = $550
1 member = $550/50
1 member = $ 11 ( Answer)
Draw the graph of y = 3x - 1
on the grid.
Answers
If OP=17 and QP=6, what is OQ? First, complete the Segment Addition Postulate for this problem.
OQ + QP= BLANK?
Fill in what you know and solve for OQ
OQ= BLANK?
Answers
Answers:
OQ + QP = OP
OQ = 11
============================================================
Explanation:
The smaller pieces OQ and QP glue together to form the larger segment OP. This is effectively what the Segment Addition Postulate says. This only works if all three points are on the same single line segment.
We know that OP is 17, so QP = 6 adds to the other unknown piece to get 17. The other piece must be 11 units long. Algebraically you could write,
OQ + QP = OP
OQ + 6 = 17
OQ + 6-6 = 17-6 ... subtracting 6 from both sides
OQ = 11
OQ is 11 if OP=17 and QP=6. This is obtained by using Segment Addition Postulate.
What is Segment Addition Postulate ?If Q is between O and P, then OQ + QP = OP.
Find OQ + QP and OQ:
Given, OP=17 and QP=6
According to Segment Addition Postulate,
OQ + QP = OP
OQ + 6 = 17
OQ= 17-6 =11
OQ = 11
∴ OQ + QP =17 and OQ = 11
Hence the value of OQ is 11 when OP is 17 and QP is 6.
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