Answer:
[tex]x = 9[/tex]
Step-by-step explanation:
Assume EFGH and JKLM are rectangles
JKLM appears to be the smaller of both.
So:
[tex]EF = n * JK[/tex] and [tex]GH = n * LM[/tex]
Where n is the scale of dilation
The area of EFGH is:
[tex]Area = EF * GH[/tex] ----- (1)
Substitute [tex]EF = n * JK[/tex] and [tex]GH = n * LM[/tex]
[tex]Area = n*JK * n*LM[/tex]
[tex]Area = n^2*JK * LM[/tex]
So, we have:
[tex]Area = EF * GH[/tex] and [tex]Area = n^2*JK * LM[/tex]
[tex]EF * GH = 2x + 9[/tex] --- Given
[tex]JK * LM = 2x - 6[/tex] --- Given
So:
[tex]Area = EF * GH[/tex] and [tex]Area = n^2*JK * LM[/tex]
[tex]Area = 2x + 9[/tex] and [tex]Area = n^2 * (2x - 6)[/tex]
Equate bot areas
[tex]2x + 9 = n^2*(2x - 6)[/tex]
Make n^2 the subject
[tex]n^2 = \frac{2x + 9}{2x - 6}[/tex]
The perimeter (P) of EFGH is:
[tex]P = 2*(EF + GH)[/tex] ----- (1)
Substitute [tex]EF = n * JK[/tex] and [tex]GH = n * LM[/tex]
[tex]P = 2*(n*JK + n*LM)[/tex]
[tex]P = 2n*(JK + LM)[/tex]
So, we have:
[tex]P = 2*(EF + GH)[/tex] and [tex]P = 2n*(JK + LM)[/tex]
[tex]2*(EF + GH) = x + 3[/tex] --- Given
[tex]2*(JK + LM) = x - 1[/tex] --- Given
So:
[tex]P = 2*(EF + GH)[/tex] and [tex]P = 2n*(JK + LM)[/tex]
[tex]P =x + 3[/tex] and [tex]P = n *(x - 1)[/tex]
Equate bot perimeters
[tex]x + 3 = n(x - 1)[/tex]
Make n the subject
[tex]n =\frac{x + 3}{x - 1}[/tex]
Square both sides
[tex]n^2 =\frac{(x + 3)^2}{(x - 1)^2}[/tex]
Recall that: [tex]n^2 = \frac{2x + 9}{2x - 6}[/tex]
So, we have:
[tex]\frac{(x + 3)^2}{(x - 1)^2} = \frac{2x + 9}{2x - 6}[/tex]
Evaluate all squares
[tex]\frac{x^2 + 6x +9}{x^2 - 2x + 1} = \frac{2x + 9}{2x - 6}[/tex]
Cross multiply
[tex](x^2 + 6x +9)(2x - 6) = (x^2 - 2x + 1)(2x + 9)[/tex]
Open brackets
[tex]2x^3 +12x^2 + 18x - 6x^2 -36x -54 = 2x^3 - 4x^2 + 2x + 9x^2 - 18x +9[/tex]
Subtract 2x^3 from both sides
[tex]12x^2 + 18x - 6x^2 -36x -54 = - 4x^2 + 2x + 9x^2 - 18x +9[/tex]
Collect like terms
[tex]12x^2 - 6x^2 + 18x -36x -54 = - 4x^2 + 9x^2+ 2x - 18x +9[/tex]
[tex]6x^2 - 18x -54 = 5x^2- 16x +9[/tex]
Collect like terms
[tex]6x^2 -5x^2 - 18x +16x -54 -9= 0[/tex]
[tex]x^2 -2x -63= 0[/tex]
Expand
[tex]x^2 +7x - 9x - 63 = 0[/tex]
Factorize
[tex]x(x +7) - 9(x + 7) = 0[/tex]
[tex](x -9) (x + 7) = 0[/tex]
[tex]x = 9\ or\ -7[/tex]
x can not be negative.
So: [tex]x = 9[/tex]
what is the value of w
I think its 2..........
Sue has 18 sweets.
Tony also has 18 sweets.
Sue gives Tony x sweets.
Tony then eats half of his sweets.
Write expressions for the number of sweets Sue and Tony now have.
Answer:
Sue = 18-x
Tony = (18+x)/2
Step-by-step explanation:
Sue donates x amount of sweets
Tony receives x amount of sweets then eats half of them.
Plsss help this is hard for me
Can someone please help me with math.
Answer:
13.C
14.C
Step-by-step explanation:
Hello There!
For 13
The question is asking, which percentage would Darian most likely receive if he had studied for 9 hours.
The line of best fit would be used to determine the percentage he would most likely score based on the amount of hours he studied
Looking at the line of best fit we notice that at 9 hours Darian would most likely score a 78% on the test
Thus the answer is C
For 14
The question want you to find the graph that has a constant rate of change and has a y intercept of (0,0) so essentially
The question is asking "which graph best represents a proportional relationship."
If a relation is proportional it would have a straight line and it would go through the origin (0,0)
Looking at C we notice that the line is straight ( meaning it has a constant rate of change) and it also goes through the origin therefore C is your answer
Is it, A, B, C, Or D?
Answer:
C
Step-by-step explanation:
6(2m+5n)
12m+30n
Jacob had multiplied 6 to 2m right which is 12m but multiplied 6 and 5n wrong as he thought it was 11n yet it is 30n.
Andy buys a new car for $23,540. He estimates that the new car will decrease in value by about 5% each year. Which of the following functions best models this situation?
f(x)=23,540(1.05)xf of x is equal to 23 comma 540 times 1 point 0 5 to the x th power
f(x)=23,540(0.95)xf of x is equal to 23 comma 540 times 0 point 9 5 to the x th power
f(x)=−23,540(1.05)xf of x is equal to negative 23 comma 540 times 1 point 0 5 to the x th power
f(x)=−23,540(0.95)x
The function that best models the situation is f(x) = 23540(0.95)ˣ, where x is the number of years.
What is function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given that, Andy buys a new car for $23,540. He estimates that the new car will decrease in value by about 5% each year.
The depreciation rate =
A = P(1-r)ⁿ
Where, A = amount final
P = initial amount
r = rate and n = number of the years
Therefore,
The depreciation rate =
f(x) = 23540(1-0.05)ˣ
f(x) = 23540(0.95)ˣ
Hence, the function that best models the situation is f(x) = 23540(0.95)ˣ, where x is the number of years.
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Its due today plz help me out
Find the value of X?
Answer:
168
Step-by-step explanation:
the angles of a hexagon should add us to 720, subtract all teh given angles from the total and you find x.
which of the following equations is quadratic?
A. x( x² + 1) = 0
B. 5(4x + 2) = 3
C. (x + 3)(x + 4) = 5
I need help with this math problem on get more math the photo is at the top
Answer:
30
Step-by-step explanation:
6x5=30 Just took the test and got 100%
50 points! Look at the picture attached. I will mark brainliest
Answer:
Step-by-step explanation:
The small triangle is similar to the triangular face. Its side edges are half the length of the side edges of the face, so its base is half the length of the face.
2*58 ft = 116 ft
The length of the base of the pyramid is 116 ft.
need answers asap pls bae<3
ill mark you the whatever if you answer bae
Answer: Justin is shown in 15 pictures with friends, 6 with family, and 8 with only him
Step-by-step explanation: Hope this helps :)
A ship travels 200 km west from port and then 240 km due south before it is disabled. Illustrate this in a vector diagram. Use trigonometry to find the course that a rescue ship must take from port in order to reach the disabled ship.
The course that a rescue ship must take from port in order to reach the disabled ship is 312.4 km at a direction of 50.2⁰.
Sketch of the ship's motionThe sketch of the journey of the ship can be used to determine the course that a rescue ship must take from port in order to reach the disabled ship.
<-------- 200 km-------
|
| 240 km
↓
Displacement of the shipThe displacement of the ship from the initial position is calculated as follows;
d² = 200² + 240²
d² = 97,600
d = √97,600
d = 312.4 km
Direction of the displacementtanθ = 240/200
tanθ = 1.2
θ = tan⁻¹(1.2)
θ = 50.2⁰
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what does -5 3/4 -3 1/2 equal
Answer:
Step-by-step explanation:
-9 1/4 is the aswer
3) Slope = 4, passing through (-1,5)
Slope
13.2 inches is 27.5% of what number?
Answer:
48
My explanations is:
13.2:27.5*100 =
(13.2*100):27.5 =
1320:27.5 = 48
Part 1:
Worst Buy, a local electronics store, advertises a sale price of 25% off all televisions 42" or bigger. Model the sales price (original price minus discount) of those televisions, y, as a function of the regular price of the tv, x.
Part 2:
If the regular price of a 60" television is $1000, use the equation you came up with in part 1 to find the sales price of the item.
Answer:
Part 1 : y = 0.75x
Part 2 : $750
Step-by-step explanation:
Part 1
Worst Buy, a local electronics store, advertises a sale price of 25% off all televisions 42" or bigger. Model the sales price (original price minus discount) of those televisions, y, as a function of the regular price of the tv, x.
Let y be the sales price of the tv and x its regular price. Since its sales price = regular price - discount, and our discount is 25% of the sales price, that is 0.25x, we have
sales price = regular price - discount
y = x - 0.25x
y = 0.75x
Part 2: If the regular price of a 60" television is $1000, use the equation you came up with in part 1 to find the sales price of the item
Since the sales price, y = 0.75x,and x = regular price = $1000,
substituting x into y, we have
y = 0.75x
y = 0.75($1000)
y = $750
C'mon people! For the function g(x) = 2x2 – 19, what is the difference quotient?
A. 2h; h ≠ 0
B. 2x + 2h; h ≠ 0
C. 4x + 2h; h ≠ 0
D. 4x + 2h – 19; h ≠ 0
Answer:
C. 4x + 2h; h ≠ 0
Step-by-step explanation:
Step-by-step explanation:
A 2-column table with 6 rows. Column 1 is labeled x with entries 1.99, 1.999, 1.9999, 2.0001, 2.001, 2.01. Column 2 is labeled f (x) with entries 0.505, negative 0.827, 0.306, negative 0.306, 0.827, negative 0.506.
Find Limit of f (x) as x approaches 2 f(x), if it exists.
2
0.3
0
DNE
please help asap.1-5.
PLS HELP ASAP IN LIKE 1 MINUTE
A shopping bag contains 18 red potatoes and 12 white potatoes. You choose one potato from the bag without looking. Calculate P(~white potato).
Answer:
2/5
Step-by-step explanation:
Red potato: 18
White potato: 12
Combined: 30
Probability of white potato:
12/30
2/5
solve 3(2x + 1) in standard form
Answer:
3(2x+1)= 6x+3
Step-by-step explanation:
Since all you do is multiply 3 and 2x and 3 and 1 which is 6x+3
Find the length of side x in the simplest radical form with a rational denominator.
Answer:4.243
Step-by-step explanation:https://www.omnicalculator.com/math/right-triangle-side-angle?c=USD&v=given:0,angle_beta1:45!deg,b1:3!inch
JLK ~ PQR Find the value of x.
Answer:
12
Step-by-step explanation:
if their similar then find the proportion with a cross multiplication equation
x/36 = 13/39
x*39 = 36*13
39x = 468
x = 468/39
x = 12
Answer:
x = 12
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{JL}{PQ}[/tex] = [tex]\frac{JK}{PR}[/tex] , substitute values
[tex]\frac{x}{36}[/tex] = [tex]\frac{15}{45}[/tex] = [tex]\frac{1}{3}[/tex] ( cross- multiply )
3x = 36 ( divide both sides by 3 )
x = 12
If x and y vary inversely and x = 1 when y = 11, find x when y = 5.5.
Answer:
x = 2.
Step-by-step explanation:
y = k/x
11 = k/1
so k = 11
y = 11/x
When y = 5.5:
5.5 = 11/ x
x = 11/5.5
= 2.
The values of x and y vary inversely, if the value of y is 5.5 then the value of x will be equal to 2.
What is an arithmetic operation?The four fundamental operations of arithmetic are addition, subtracting, multiplying, and dividing two or more numbers. Included is the study of integers, especially the order of operations, which is essential for all other aspects of mathematics, notably algebra, information management, and geometry.
As per the information provided in the question,
y = k/x
11 = k/1
k = 11
y = 11/x
If y = 5.5,
5.5 = 11/ x
x = 11/5.5
x = 2.
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The Adams family bought a small piece of land in the hill country. The plot is in the shape of a rectangle and measures about 50 yards by 41 yards. What is the area of the plot?
Given:
The dimensions of a rectangular plot are 50 yards by 41 yards.
To find:
The area of the plot.
Solution:
We know that, the area of a rectangle is
[tex]Area=Length\times width[/tex]
So, the area of the rectangular plot is:
[tex]Area=50\times 41[/tex]
[tex]Area=2050[/tex]
Therefore, the area of the rectangular plot is 2050 square yards.
pleae answer this fast asap
Answer:
I think its (2, 1) .
Step-by-step explanation:
the 2 represents the x axis
the 1 represents the y axis
Wilson's brother earns $185 each month working an after-school job. What is the total amount of money he will earn after
working for 12 months?
Alex, x, saved 30 dollars and Ethan saved 1
3
more than that.
Ethan saved _______________ dollars
6=x/4
I really need help with this
Answer:
x=24
Step-by-step explanation:
City A: {2, 2.5, 4, 4.5, 3, 2.5} City B: {6, 4, 1.5, 3.5, 2, 4} (c) What is the median for each city? Show your work. City A: City B:
Answer:
to find the median you have to put the set in order and find the middle number (ex: 1,2,3,4,5,6,7,8,9 the median of this would be 5)
Step-by-step explanation:
City A: 2,2.5,2.5,3,4,4.5
The median has 2 number so you'd add them up and divide by 2.
2.5 + 3 = 5.5
5.5/2= 2.75
i dont know if you need it as a fraction
City B: 1.5,2,3.5,4,4,6
3.5+4 = 7.5
7.5/2 = 3.75
Median for city A: 2.75
Median for city B: 3.75
A teacher wants to determine how to sit 30 students in a classroom.
What simulation can be used determine where the students sit?
A
A coin is used and assigned for every two students.
B
A six-sided number cube and every 6 students are assigned
a side.
С
A random number generator where each student is assigned a number.
D
A standard deck of cards is used and students are assigned to the cards.
Answer:
I think C. because that will be easier and less chaotic