In order to solve this problem, we the cost of both to equal each other, so we need to set up two expressions that will equal each other.
Let t = time in months.
The cost of Fab Pool can be represented by the expression 35t + 50
The cost of Perfect Pools can be represented by the expression by 40t + 35.
Now that we have the cost for each, we need to find when they are the same, so we set the expressions equal to each other.
35t + 50 = 40t + 35
Now we solve like a regular equation
50 = 5t + 35
15 = 5t
t = 3
At three months, the cleaning costs will be the same.
Hey there!!
Fab pool service costs $35 per month, this is a variable, the number of month could change and $50 for equipment. And perfect pools cost $40( a variable ) and $35 for equipment.
Let's take the number of month as 'm'.
The question asks us to find the number of months at which both of these costs become equal.
As the question states, we will have to equate both the sums or the values.
Total cost = Cost for month + Cost for equipment.
Fab pool :
Cost per month = $35
Cost for equipment = $50
Total cost = 35 × ( the number of months ) + 50
Perfect pools :
Cost for month = $40
Cost for equipment = $35
Total cost = 40 × ( the number of months ) + 35
We have taken the number of months as 'm'.
Now, plugging in the values :
Fab pools : 35m + 50
Perfect pools : 40m + 35
Equating this :
... 35m + 50 = 40m + 35
Subtracting 35m on both sides :
... 50 = 5m + 35
Subtracting 35 on both sides:
... 15 = 5m
Dividing by 5 on both sides :
... m = 3
Hence, the number of months is 3.
Hope it helps!!
Find the area of an equilateral triangle with sides of length 8
Answer:
Your answer is 16√3 units2
Step-by-step explanation:
a triangle has sides of length 4,3, and 5. is it a right triangle? explain
Yes. Notice that the Pythagorean Theorem applies here. 3^2 + 4^2 = 5^2, so this triangle is a right triangle.
the ordered pairs (0, 1), (3' 2), (3, 5), and (5, 4) are on the graph of a relation between x and y. which of the following statements is true?
A: x is a function of y
B: y is a function of x
C: the relation passed the vertical line test
D: the domain of the relation is {1, 2, -5, 4}
Your answer is C.The relation passed the vertical line test.
Helppppppppppppppppppppp!!!!!!!!!!!!!!!!!ME
Answer:
23
Step-by-step explanation:
The notation (f∘g)(1) means f(g(1)). We can first find g(1), then use that value as the argument to the f function.
g(1) = 2·1-6 = -4
f(-4) = -4(-4)+7 = 16+7 = 23
Line segment of length k is divided into 3 equal parts. What is distance between midpoints of first and third segments?
A) 2k/3 B) k C) k/6 D) 2k
Line segment of length k is divided into 3 equal parts.
so first segment is 0-k/3 and third segment is 2/3k-k
so mid-pt of 1st = k/6 and 3rd = 5/6k
so the distance in between = 5/6k-k/6 = 4/6k = 2/3k
ans is A
The distance between the midpoints of the first segment and the third segment is 2k/3. Hence, option A is the right choice.
What is the mid-point of a line segment?The mid-point of a line segment is the point from which the distance to both ends of the line segment is equal.
How to solve the question?In the question, we are given a line segment of length k units, which is divided into 3 equal parts.
We are asked to find the distance between the midpoints of the first and third segments.
Firstly, we divide the line segment at points k/3 and 2k/3, to get three equal parts of lengths k/3 each.
Now, the mid-point of the first segment = (0 + k/3)/2 = k/6.
The mid-point of the third segment = (2k/3 + k)/2 = 5k/6
Therefore, the distance between the midpoints of the first segment and the third segment is (5k/6 - k/6) = 4k/6 = 2k/3. Hence, option A is the right choice.
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989 times 49 the answer is
you can use a calculator and plug n 989x49 which equals 48461
989 times 49 is 48461
Hope this helps :)
Need help on this one please answer asap
For what value of k will the relation S = {(2k+3, 1), (3k−1, −2)} not be a function?
The relation will not be a function if the to ordered pairs have the same first value. That will happen when
... 2k+3 = 3k-1
... 4 = k . . . . . . add 1-2k
The relation will not be a function when k=4.
How do i find the domain and the range of the function ????
Note that the graph shows 8 dots with associated x-values 1 through 8. The domain is the set of integers {1, 2, 3, 4, 5, 6, 7, 8}. The range is the set of all y-values associated with this domain, a bit harder to read off the graph. One by one, I will approximate the y-value associated with each x value and present these 8 y-values as the range: {7.5, 9, 12, 15. 18, 22, 23}.
A manufacturer of sunglasses currently sells one type for $15/pair. The price p and the demand x are related by x=9500-250p.
A) at this price, is the demand inelastic or elastic.
B) should the price be increased or decreased to increase revenue?
A) The price elasticity of demand is given by
... Ed = (dx/dp)·(p/x)
... = -250·(15/(9500-250·15)) ≈ -0.652
B) This value has a magnitude less than 1, so price can be increased to increase revenue.
_____
The price at which Ed has a magnitude of 1 is ...
... 250p/(9500 -250p) = 1
... 250p = 9500 -250p
... 500p = 9500
... p = 9500/500 = 19
Revenue will increase as price increases up to $19 per pair.
A ________ is a transformation that changes the size but not the shape of an image.
A.) rotation
B.) translation
C.) dilation
D.) reflection
C.) Dilation changes the size
A car rental company charges a daily rate of $21 plus $0.30 per mile for a certain car. Suppose that you rent that car for a day and your bill (before taxes) is $123. How many miles did you drive?
340 miles because you do 123-21 divided by 0.30.
I'm so smart!! :D
What is the length of DC? (picture)
DC = [tex]\frac{5}{2}[/tex] = 2.5
since the triangles are similar then the ratios of corresponding sides are equal
[tex]\frac{AC}{AD}[/tex] = [tex]\frac{BC}{DE}[/tex]
[tex]\frac{7.5+DC}{7.5}[/tex] = [tex]\frac{8}{6}[/tex] (cross-multiply )
45 + 6DC = 60
6DC = 60 - 45 = 15 ( divide both sides by 6 )
DC = [tex]\frac{5}{2}[/tex]
Please help!
Approximate the solution to the graphed system. Explain how you got your answer.
EASY BRAINLIEST!
Mia plans to build a fence to divide her rectangular garden into two triangular areas. Use the diagram to find the length of fence she will need to divide the garden. Round up to the nearest hundredth.
Mia will need a fence that is meters long.
The length of fence she will need to divide the garden is 9.22 m.
RectangleRectangle is a quadrilateral (has four sides and four angles) in which both sides are parallel and opposite to each other.
Pythagoras theorem is used to show the relationship between the sides of a right angled triangle.
From the diagram, let x represent the length of the fence, hence using Pythagoras:
x² = 6² + 7²x = 9.22 mThe length of fence she will need to divide the garden is 9.22 m.
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A and B received a total of $210,000 from a deceased relative's estate. They decided to put away $50,000 in a trust for their child and divide the remainder into ¼ for B and ¾ for A. How much will A receive?
Initial amount: $210,000
Setting aside: $50,000
Remaining: $160,000
3/4 of remaining amount: 160,000 times 0.75 = $120,000
1/4 of remaining amount: 160,000 times 0.25 = $40,000
After joining two pieces of a picture frame together a frame maker checks her work by measuring the diagonal. The sides of the frame form a right angle and the measurements are as follows: a=12in. and b=5in.
Find the zeros for:
f(x)=x^4+x^3+4x^2
(Please show work)
View the image to see how I solved this problem.
There is an obvious factor of x², so we can reduce this to the problem of finding zeros of a quadratic by factoring that out. Then, we can determine the zeros of the quadratic factor to complete the finding of zeros for the function.
A factor of x² can be factored out, leaving ...
... f(x) = x²(x² +x +4)
The latter factor has only complex zeros. It can be rewritten by completing the square.
... x² +x +4 = (x² +x +1/4) +(3 3/4) = (x +1/2)² +(3 3/4)
So, the real zeros are where x² = 0, at x = 0. The complex zeros are where the above expression is zero, ...
... (x +0.5)² +3.75 = 0
... (x +0.5)² = -3.75
... x + 0.5 = √-3.75 = ±0.5i√15
... x = -0.5(1 ±i√15)
The function zeros are 0 (multiplicity 2) and -0.5±0.5i√15.
PLS HELP Will give Brainliest!
Five hot dogs and four hamburgers cost $12. Four hotdogs and five hamburgers cost 12.75. How much does one hot dog and one hamburger cost?
If you add the two purchases, you find 9 hotdogs and 9 hamburgers cost 24.75. One hotdog and one hamburger will cost 1/9 of that total, or 2.75.
... One hotdog and one hamburger costs $2.75.
_____
This is what your question asks. Usually, we want to know the individual costs of the items. If we multiply this total by 5, then we have the cost of 5 hotdogs and 5 hamburgers: 13.75. This $1.75 more than the cost of 5 hotdogs and 4 hamburgers, so the cost of a hamburger must be $1.75
... One hotdog costs $1.00
... One hamburger costs $1.75
Find the values of x for which f(x)=g(x) (f)x=x^2-7x+3 g(x)=-3x+8
x = 5 or x = - 1
equate f(x) and g(x)
x² - 7x + 3 = - 3x + 8 ( subtract (- 3x + 8 ) from both sides )
x² - 4x - 5 = 0 ← in standard form
(x - 5)(x + 1) = 0
equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 1 = 0 ⇒ x = - 1
Michael got 28 out of 33 points on his math test what percent of the questions did he get correct round your answer to the nearest whole number show your work will mark brainiest
28/33 × 100% = 0.84848... × 100% ≈ 85%
Michael got about 85% of the available points.
_____
Since we're not told the number of points per question, we don't actually have enough information to answer the question.
To find out the percentage of correct answers, divide the number of correct answers by the total number of questions and multiply by 100. Michael got 85% of the questions correct on his math test.
Explanation:To find out what percent of the questions Michael answered correctly, we need to divide the number of correct answers by the total number of questions and multiply by 100.
Here's the step-by-step calculation:
Divide the number of correct answers (28) by the total number of questions (33). The result is approximately 0.848. Multiply the result by 100 to get the result as a percent. The answer is approximately 84.8%. But, we need to round this to the nearest whole number. We round 84.8% up to 85%, because 0.8 is more than half of 1 (0.5).
So, Michael got 85% of the questions correct on his math test.
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Please help, It's geometry
A plot of the points shows you the triangle is an acute triangle.
_____
All angles are less than 90°.
Tony and Mario went to the store to buy school supplies. Tony bought 3 packs of pencils for $4 each and a pencil box for $7. Mario bought 4 binders for $6 each and used a coupon for $6 off . Who spent more money ?
Tony because he spent $19 while Mario spent $18. To explain, you would multiply 3 by $4 because Tony bought 3 of the $4 packs of pencils. Therefore, he would have spent $12. In addition, add $7 to $12, you get $19. On the other hand, Mario bout 4 of the $6 binders. That would mean he spent $24 on binders However, he had a $6 coupon which means he can take $6 off the total price of $24. That would mean subtracting $6 from $24. That would get Mario $18
For what values of x does the function y=2x+13 take on a positive value? a negative value?
Final answer:
The function y=2x+13 takes on a positive value for x > -6.5 and a negative value for x < -6.5.
Explanation:
The function y=2x+13 represents a linear equation. To find the values of x for which the function takes on a positive value, we need to solve the inequality 2x+13 > 0.
Subtracting 13 from both sides gives 2x > -13.
Dividing both sides by 2, we get x > -6.5.
Therefore, for x values greater than -6.5, the function will be positive.
To find the values of x for which the function takes on a negative value, we need to solve the inequality 2x+13 < 0. Subtracting 13 from both sides gives 2x < -13.
Dividing both sides by 2 and flipping the inequality sign, we get x < -6.5.
Therefore, for x values less than -6.5, the function will be negative.
what is the solution set for the open sentence with the given replacement set x2 +12 = 8x, 2 4 5 8
Answer:
2
Step-by-step explanation:
Given the points M(-7,-4),N(-3,-3) O(-4,-7) and P(-8,-8). Determine the type of quadrilateral by using coordinate geometry
Try this solution (see the attachment, there is not the only way).
The short explanation: the target - to prove, PN≠OM; PN⊥OM; point S is midpoint of OM&PN, - the properties of rhombus.
solve each given equation and show your work. tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction or neither.
20-4x=12-x+8-3x
5x+4x-3= 24+8x
5x+6=2x+6+3x-15
(A) Subtracting the right side from both sides, we get ...
... (20 -4x) -(12 -x +8 -3x) = 0
... (20 -12 -8) +x(-4 +1 +3) = 0
... 0 = 0 . . . . . true for all values of x (infinite solutions)
(B) Subtracting the right side from both sides, we get ...
... (5x +4x -3) -(24 +8x) = 0
... x(5 +4 -8) +(-3 -24) = 0
... x -27 = 0
... x = 27 . . . . . . (one solution)
(C) Subtracting the right side from both sides, we get ...
... (5x +6) -(2x +6 +3x -15) = 0
... x(5 -2 -3) +(6 -6 +15) = 0
... 15 = 0 . . . . . . . not true for any value of x (no solutions)
if you know the order from least to greatest of 5 negative rational numbers how can you use the information to order the absolute value of those numbers from least greatest
Consider the ordering
... -2 < -1
Now consider the ordering of their absolute values:
... 1 < 2
_____
Hopefully, you see that changing the sign reflects the sequence across the origin, so that the ordering is reversed when the signs are changed.
Help ASAP plsssssssssss
Substitute the value of the variable into the expression and simplify.
1. 24
2. 17
258,197-64,500 (show me how to round this and I will give brainliest!)
There are a variety of methods of performing this subtraction, and corresponding different methods of regrouping.
If you're taught (as I was) to do the subtraction right-to-left, then the first regrouping you need to do is when you try to subtract 500 from 100. You must regroup the 8 thousands and 1 hundred to 7 thousands and 11 hundreds. Then, when you subtract 5 hundreds, you end with 7 thousands and 6 hundreds.
The next regrouping you need to do is when you try to subtract 6 ten-thousands from 5 ten-thousands. You must regroup the 2 hundred-thousands and 5 ten-thousands to 1 hundred-thousand and 15 ten-thousands. Then, when you subtract 6 ten-thousands, you end with 1 hundred-thousand and 9 ten-thousands.
The end result is
... 258,197 - 64,500 = 193,697
_____
If you use an abacus or soroban or similar tool to help you keep track of the numbers, you were likely taught to do the subtraction left-to-right. In this case, the first regrouping comes when you want to subtract 6 ten-thousands. Practitioners of this method know that -6 = -10 +4, so the number represented on the tool becomes (2-1) hundred-thousands and (5+4) ten-thousands plus the rest of the initial number, or 198,197 after subtracting the 6 ten-thousands.
The subtraction proceeds until you find you need to subtract 500 from 100. At this point, the tool is representing the partial result as 194,197. Again, if you practice this method, you know that -5 = -10 +5, so you reduce the thousands digit by 1 (to 3) and add 5 to the hundreds digit to get 193,697.
_____
An attempt is made to show the regroupings in the attachment. In each case there are two of them. However, working left-to-right, the result of the first subtraction of 6 ten-thousands is 19 ten-thousands, so you never actually write down anything else. Of course, if you're using an abacus or soroban, you don't write down anything—you simply change the position of the beads on the tool.