Answer:
The vertices of the image are D' (40, 20), E' (10, 30), F' (15, 5)
Step-by-step explanation:
If the point (x, y) dilated by a scale factor k using the origin as a center of dilation, then its image is (kx, ky)
Let us use this rule to solve our question
∵ The vertices of ΔDEF are D (8, 4), E (2, 6), and F (3, 1)
∵ ΔDEF dilated by a scale factor 5
∴ k = 5
∵ The origin as the center of dilation
→ That means, multiply the coordinates of every point by 5
∴ D' = (8 × 5, 4 × 5)
∴ D' = (40, 20)
∴ E' = (2 × 5, 6 × 5)
∴ E' = (10, 30)
∴ F' = (3 × 5, 1 × 5)
∴ D' = (15, 5)
∴ The vertices of the image are D' (40, 20), E' (10, 30), F' (15, 5)
A and B can do a piece of work in 12 days; B and C can do it in 15 days while C and A can finish it in 20 days. In how many days will A, B and C finish it, working together? In how many days will each of them finish it working alone?
Answer:
It takes A 30 days to finish the work aloneIt takes B 20 days to finish the work aloneIt takes C 60 days to finish the work aloneWorking together, it takes them 10 days to finish the workStep-by-step explanation:
Given;
[tex]\frac{1}{A} + \frac{1}{B} =\frac{1}{12} \\\\\frac{1}{B} + \frac{1}{C} = \frac{1}{15}\\\\\frac{1}{A} + \frac{1}{C} = \frac{1}{20}\\\\[/tex]
From given equations above;
[tex]\frac{1}{A} +\frac{1}{B} = \frac{1}{12}\\\\But, \frac{1}{B} =\frac{1}{15} -\frac{1}{C}\\\\ \frac{1}{A} +\frac{1}{15} -\frac{1}{C}= \frac{1}{12}\\\\Also, \frac{1}{C} = \frac{1}{20} -\frac{1}{A} \\\\ \frac{1}{A} +\frac{1}{15} -(\frac{1}{20} -\frac{1}{A})= \frac{1}{12}\\\\ \frac{1}{A} +\frac{1}{15} -\frac{1}{20} +\frac{1}{A}= \frac{1}{12}\\\\ \frac{1}{A} +\frac{1}{A} = \frac{1}{12} +\frac{1}{20}-\frac{1}{15}\\\\\frac{2}{A} = \frac{300+ 180-240}{3600} \\\\\frac{2}{A} =\frac{240}{3600}\\\\[/tex]
[tex]\frac{2}{A} = \frac{1}{15} \\\\A = 30 \ days[/tex]
solve for B;
[tex]\frac{1}{A} + \frac{1}{B} = \frac{1}{12}\\\\ \frac{1}{B} = \frac{1}{12} - \frac{1}{A} \\\\ \frac{1}{B} = \frac{1}{12} - \frac{1}{30}\\\\ \frac{1}{B} =\frac{5-2}{60} \\\\ \frac{1}{B} =\frac{3}{60}\\\\B = 20 \ days[/tex]
Solve for C;
[tex]\frac{1}{C} =\frac{1}{20} -\frac{1}{A}\\\\ \frac{1}{C} = \frac{1}{20} -\frac{1}{30}\\\\ \frac{1}{C} =\frac{3-2}{60} \\\\ \frac{1}{C} =\frac{1}{60}\\\\C = 60 \ days[/tex]
When they work together;
[tex]\frac{1}{A} +\frac{1}{B} +\frac{1}{C} =\frac{1}{y} \\\\\frac{1}{30} +\frac{1}{20} +\frac{1}{60} = \frac{1}{y}\\\\\frac{2+ 3+ 1}{60} =\frac{1}{y}\\\\\frac{6}{60} =\frac{1}{y}\\\\y = 10\ days[/tex]
An ant crawls 10 centimeters down into an ant hole. It then crawls 2 centimeters up to the queen’s nest. How many centimeters does the ant have to crawl in order to get out of the ant hole? (Hint: Draw a diagram to help you out)
pLS ANSWER IM IN 7TH GRADE MOST OF YOU SHOULD KNOW THIS
Answer:
8
Step-by-step explanation:
10 down plus 2 up equals 8
Question 2
8 pts
You buy a bike for $200 and a skateboard for $30. What is the total cost if the tax rate is
8.25%? Round your answer to the nearest hundredth.
I
Answer:
$248.98
Step-by-step explanation:
200 + 30 = 230.
8.25% of 230 is 18.975, rounded to $18.98.
230 + 18.98 = 248.98.
4a I do not understand the process
Answer:
9/40
Step-by-step explanation:
He needs 5/8, he already has 2/5, so still needed is 5/8-2/5.
To add or subtract fractions, the denominators must be equal.
Simplest approach is to multiply them. 8 times 5 is 40, so 40 is the new denominator we need for both fractions.
So first we convert 5/8 to 25/40.
Then we convert 2/5 to 16/40.
Now we can subtract them:
25/40 - 16/40 = 9/40.
9/40 cannot be simplified so this is the final answer.
There are some basic rules you need to know to work with fractions. If above work is too fast, comment below for deeper explanation.
What is the x- intercept of the line that represents y=-4x+12
Answer:
3,0
for steps
Step-by-step explanation:
math
way
On a coordinate plane, how are the locations of the points (5 , -7) and (-5 , 7) related?
A.
reflection across the y-axis
B.
reflection across the x-axis
C.
locations unrelated
D.
reflection across both axes
Answer:
its c or d but i think c
Step-by-step explanation:
PLEASE HELP!!!!!!!!!
Identify the type for each triangle.
(Please do not answer if you do not know so the right people get the points)
Answer:
1. isosceles
2. obtuse
3. isosceles
4. right triangle
5. right isosceles triangle
6. obtuse isosceles triangle
Which ratio is equal to 27:817 OA 1:9 OB. 2:9 Oc. 3:9 OD. 3:27 O E 9:12
Answer:
54 : 1634
Step-by-step explanation:
Divide 350rs in 3:4 ratio
plzzz fast
Part B
Choose the inequality that compares the numbers
Choose
Choose
0.25
I'm sorry but this question is very confusing but I believe you want me to choose 0.25?
<3 Enjoy,
Dea
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
65/2
Step-by-step explanation:
3 1/4= 13/4
13/4(10)=65/2
Answer:
32 1/2
Step-by-step explanation:
first, convert both numbers into improper fractions. (10/1 and 13/4) then multiply the numerators to get 130 and the denominators to get 4. You get 130/4. Simplified, that would be 65/2 and as a mixed number, it would be 32 and 1/2.
HELP!!!!!!!!!!!!!!! Together, two clerks can count a certain number of coins in 7.5 minutes. If one clerk, working alone, takes 8 minutes longer than the other needs to do the same job working alone, how long does each clerk need to count the coins when alone?
Answer:2 minutes each
Step-by-step explanation:
 write an expression equivalent to 9X +14
Answer:
The correct answer is 9x+14
Step-by-step explanation:
Let's simplify step-by-step.
9x+14
There are no like terms.
Hey I need help ASAP!
Identify the function shown in this graph
Answer:
The answer is B.
y=-5x + 3
Step-by-step explanation:
Hope this helps
4. What is the value of -24 + 6?
Answer:-18
Step-by-step explanation:
Answer:
-18
Step-by-step explanation:
Please give brainliest!
what is the cost of 1 pound of pears?
Answer:
2.8
Step-by-step explanation:
Answer:
$1.75
Step-by-step explanation:
If a circle has a diameter of 30 meters, which expression gives its area in
square meters?
A. 30•n
B. 30^2•n
C. 15^2•n
D. 15•n
Answer:
C. 15²π
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Diameter: d = 2rArea of a Circle: A = πr²Step-by-step explanation:
Step 1: Define
d = 30 m
Step 2: Find Area
Substitute [D]: 30 m = 2rIsolate r: 15 m = rRewrite: r = 15 mSubstitute [AC]: A = π(15 m)²Rearrange: A = 15²πWhat number makes the sentence true?
15 – 7 = 3+1
Answer:
4
Step-by-step explanation:
Although you didn't give me any answers to go with your problem, I am assuming that since 15-7 is 8, and 3 + 1 = 4, the answer should be 4. Now regarding if it is times, it would be x2. Because for times 2 would be 8. Overall the answer should be 4.
Write the following quadratic equation in equivalent factored form by filling in the blanks. x^2+3x-40 (x - __ )(x + __ )
Answer:
(x-5)(x+8)
Step-by-step explanation:
what is 5 - 3x + x - 32 in a simplified expression?
Answer:
-27-2x
Step-by-step explanation:
5-3x+x-32
(collect like terms)
5-32-3x+x
-27-2xLet's simplify step-by-step.
5−3x+x−32
=5+−3x+x+−32
Combine Like Terms:
=5+−3x+x+−32
=(−3x+x)+(5+−32)
=−2x+−27
Answer:
=−2x−27
What is the value of x?
(57-5)
Your answer:
x = 15
x = 13
x = 60
ox=37
pls helpppppo
Answer:
x = 13
Step-by-step explanation:
All triangles equal 180 degrees
Since this is an equilateral triangle, all angles have the same measurement
180 degrees divided by 3 angles = 60 degrees per angle
Make an equation based on the info given:
60 = 5x - 5
Solve:
*add 5 to both sides*
65 = 5x
*divide both sides by 5*
13 = x
Which pair of events are independent of each other?
A.
getting an even number on the first and second roll of the die
B.
selecting an ace from a deck of cards, and then drawing another ace without replacing the first
C.
drawing a ball from a bag, and then drawing another ball without replacing the first
D.
drawing a red paperclip from a bag of paperclips, and then drawing another red paperclip without replacing the first
PLZ HELP AND HURRY
Answer:
A
Step-by-step explanation:
The other 3 pairs are all dependent because you have to take into account when you are choosing a card, ball, or paperclip for a second time, that you already got rid of one of the items, so it is less likely to draw a duplicate.
Sorry if that doesn't make sense lol
−8x+6−2=−12
what is x?
Answer: x=2
Step-by-step explanation:
have a good day! :)
plz give me brainliest
Answer:
(f+g)(x) = f(x) +g(x)
= (7x^3 −2x−12) +(−3x^3 -8x^2 +10x)
= x^3(7 -3) +x^2(-8) +x(-2+10) +(-12)
= 4x^3 -8x^2 +8x -12
Corresponds to selection C.
Step-by-step explanation:
The graph shows the heigh if a tree ever time. What can you reduce the rate of change to be from 2years to 4years
Answer:
the question sounds confusing but I believe you would reduce the time or the x value so that the years are reduced.
Jesse plays basketball for his high school team. In his last 12 twelve games he scored the following points: 18, 22, 19, 15, 24, 22, 18, 15, 10, 14, 18, 10. Barbara plays basketball for her high school team. In her last 10 games she scored the following points: 15, 12, 12, 16, 18, 22, 16, 20, 20, 14. Determine which player had the largest range of points scored? What is the difference is the range of points between the two players?
In the form of a paragraph, explain in complete sentences the steps necessary to compute the range of the points, which team player had the largest range of points and include the final answer in your explanation. Complete your work in the space provided.
Answer:
Jesse has the largest range. To find the range you have to take the greatest value and the lowest value to find the range. Jesse's largest value is 24 points while his lowest is 10 points making his range 14 points. Barbara's highest value is 22 points while her lowest is 12 points making her range 10 points.
Step-by-step explanation:
24-10=14 Jesse
22-12=10 Barbara
In a lab, 30% acid solution is being mixed with a 5% acid solution to create a 10% acid solution. What is the ratio of the amount of the 30% solution used to create the 10% solution?
Answer:
1:4
Step-by-step explanation:
The hemmings borrowed $3 000 for home improvements. They repaid the loan and $600 in simple interest four years later. What simple annual interest rate did they pay
Answer:
5%
Step-by-step explanation:
Given that:
Principal = $3000
Simple Interest paid = $600
Period = 4 years
Simple interest = principal * rate * time
$600 = $3000 * rate * 4
$600 = $12000 * rate
Rate = $600 /$12000
Rate = 0.05
Hence, simple interest rate paid = (0.05 * 100%) = 5%
What are the correct answers?
5. What is the length of the unknown leg?
Answer: a = 8
Step-by-step explanation:
a² + b² = c²
a² + 6² = 10²
a² + 36 = 100
a² = 100 - 36
a² = 64
a = √64
a = 8
What can you do if your struggling in Volume in Math?
Answer:
Study Harder
Step-by-step explanation: