Answers
5x = 3(x+4)
5x = 3x + 12
5x - 3x = 12
2x = 12
x = 6
answer
C. 6
Answer:
C. 6
Step-by-step explanation:
It is given that the rectangles in the figure are similar.
Thus, the corresponding sides of the two rectangles will be equal.
So, we get,
[tex]\frac{3}{x}=\frac{5}{x+4}[/tex]
i.e. [tex]3(x+4)=5x[/tex]
i.e. [tex]3x+12=5x[/tex]
i.e. [tex]2x=12[/tex]
i.e. x = 6.
Hence, the value of x is 6.
Related Questions
what is 69.12 rounded to the nearest tenth
Answers
A store manager orders T-shirts so that 15 out of every 35 are a medium. How many medium T shirts would you expect to find when there are 126 T shirts on a rack
Answers
use cross multiplication to get 35x=126(15)
35x=1890 x=1890/35
x=54
54 medium shirts
how many times larger is the value of the 5 in 95,284 than the value 5 in 8,521
Answers
the value of the 5 in 8,521 is 500
5000/500 = 10
so the value of the 5 in 95,824 is 10 times greater then the value of the 5 in 8,521
ms.nenadal write 2×7=7×2 on the board. do you agree or disagree? draw arrays to help explain your thinking
Answers
It's accurate to say that 2×7 is not equal to 7×2, and the arrays provide a clear visual explanation of this mathematical concept.
Ms. Nenadal wrote 2×7 on the board, which is not equivalent to 7×2. The order of multiplication, as represented by the commutative property, states that changing the order of the factors does not change the product. In this case, 2×7 means adding 2 seven times, while7×2 means adding 7 two times.
Let's draw arrays to illustrate the difference:
For 2×7:
If we represent this as an array, it would have 2 rows and 7 columns, indicating 2 groups of 7.
Array for 2 × 7:
| * * * * * * * |
| * * * * * * * |
For 7×2:
On the other hand, 7×2 would be represented by an array with 7 rows and 2 columns, indicating 7 groups of 2.
Array for 7 × 2:
| * * |
| * * |
| * * |
| * * |
| * * |
| * * |
| * * |
While the product is the same (14) for both, the grouping and arrangement differ. Therefore, it's accurate to say that 2×7 is not equal to 7×2, and the arrays provide a clear visual explanation of this mathematical concept.
Mr. Abernathy bought a selection of wrenches for his shop and paid $78. He bought the same number of $1.50 and $2.50 wrenches, and half of that number of $4 wrenches. The number of $3 wrenches is one more than the number of $4 wrenches. How many of each did he buy?
Answers
2x = # of $1.50 wrenches
2x = # of $2.50 wrenches
x+1 = # of $3 wrenches
x(4.00) + 2x(1.50) + 2x(2.50) + (x+1)(3.00) = $78
4x + 3x + 5x + 3x + 3 = 78
15x + 3 = 78
15x = 75
x = 5
Therefore, he has 5 $4 wrenches, 10 $1.50 wrenches, 10 $2.50 wrenches and 6 $3 wrenches.
Verify:
5($4) + 10($1.50) + 10($2.50) + 6($3) = $20 + $15 + $25 + $18 = $78
In this algebraic word problem, equations were set up based on the prices and relationships between the numbers of wrenches bought, leading to the discovery that Mr. Abernathy purchased 12 wrenches each at $1.50 and $2.50, 6 wrenches at $4, and 7 wrenches at $3 to make a total of $78.
Mr. Abernathy's allocation of his $78 budget on wrenches can be formulated as an algebraic word problem where we define the number of wrenches bought at each price point and the total cost. Let us denote x as the number of $1.50 wrenches and also the number of $2.50 wrenches, so the number of $4 wrenches is x/2 since it is half of that number.
The number of $3 wrenches is x/2 + 1 because it is one more than the number of $4 wrenches. The total amount spent can be expressed as the sum of the products of the numbers of wrenches and their respective prices, which must equal $78.
The equation for the total amount spent on wrenches is therefore:
1.50x + 2.50x + 4(x/2) + 3(x/2 + 1) = 78
Solving this equation for x gives us the number of $1.50 and $2.50 wrenches, and then we can infer the quantities of the $4 and $3 wrenches.
After simplifying the equation, we solve for x, and by plugging x back into the previous expressions, we find out that Mr. Abernathy bought 12 wrenches at $1.50 each, 12 wrenches at $2.50 each, 6 wrenches at $4 each, and 7 wrenches at $3 each.
what is the complement to a 32 angle
Answers
so if x and y are complentary then x+y=90
the complemnt to a 32 degree angle is
32+x=90
minus 32 both sides
x=58 degres
the complement is 58 degrees
Imagine a sphere. if the sphere is cut three times at right angles, the resulting pieces would be what fraction of the original sphere?
Answers
Solve the following system of equations.
4x + 5y = -2
4x + 3y = 10
x=?
y=?
Answers
There are many ways to solve this math problem in specific but i ll go for the smartest and simplest for you ..
4x + 5y = -2
4x + 3y = 10
4x = -5y -2
4x = -3y +10
-5y -2 = -3y +10
-12 = 2y
-6 = y
4x = -3y +10
4x = -3(-6) +10
4x = 18 + 10 = 28
x = 7
y = -6
The solution to the system of equations 4x + 5y = -2 and 4x + 3y = 10 is x = 7 and y = -6. This is done by using the elimination method.
Explanation:To solve this system of equations, you can use a method called elimination. The idea is to subtract the second equation from the first to eliminate one of the variables, allowing us to solve for the other.
Subtracting the second equation from the first gives you:
4x + 5y - (4x + 3y) = -2 - 10
This simplifies to: 2y = -12
So, y = -12 / 2 = -6
Then, substitute y = -6 into the first equation:
4x + 5(-6) = -2
This simplifies to 4x - 30 = -2, or 4x = 28
So, x = 28 / 4 = 7
So the solution to the system of equations is x =7, y = -6
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Which equation correctly applies the distributive property?
A.70+2.028=(70⋅2)+(70⋅0.02)+(70⋅0.008)
B.−2.5⋅0.6⋅5.8=−2.5⋅5.8⋅0.6
C. −1.5⋅(6⋅1.25)=(−1.5⋅6)⋅1.25
D.(0.7⋅0.7)+(0.7⋅0.9)+(0.7⋅0.2)=0.7⋅(0.7+0.9+0.2)
Answers
It's C.!!! hope this helps :D!
Find the area of the region bounded by the given curves. y = 9x2 ln(x), y = 36 ln(x)
Answers
find where they intersect
9x²ln(x)=36ln(x)
divide both sides by 9
x²ln(x)=4ln(x)
[tex]ln(x^{x^2})=ln(x^4)[/tex]
so
[tex]x^{x^2}=x^4[/tex]
so x=1 and and 2 (x can't be 0 or -2 because ln(0) and ln(-2) don't exist)
so intersect at x=1 and x=2
which is on top?
9(1.5)²ln(1.5)=20.25ln(1.5)
36ln(1.5)=36ln(1.5)
36ln(1.5) is on top
so
that will be
the area is
[tex] \int\limits^2_1 {36ln(x)-9x^2ln(x)} \, dx= [/tex]
[tex] [36x(ln(x)-1)-x^3(3ln(x)-1)]^2_1=[/tex]
[tex] 48ln(2)-29[/tex]
the area between the curves is 48ln(2)-29
The area of the region bounded by y = 9x2 ln(x) and y = 36 ln(x) is found by integrating the absolute difference of the two functions from x = 1 to x = 2, which yields ∫ from 1 to 2 (|36 ln(x) - 9x2 ln(x)|) dx.
Explanation:To find the area of the region bounded by the curves y = 9x2 ln(x) and y = 36 ln(x), you first need to find the points where they intersect. This means setting the two functions equal to each other and solving for x, i.e., 9x2 ln(x) = 36 ln(x).
This simplifies to x2 = 4 which yields two solutions x = 2 and x = -2. However, since the natural logarithm ln(x) is not defined for x < 0, we discard x = -2. So, the two curves intersect at x = 2.
The area between the curves from x = 1 to x = 2 is then obtained by integrating the absolute difference of the two functions from x = 1 to x = 2, which gives:
∫ from 1 to 2 (|36 ln(x) - 9x2 ln(x)|) dx. You can evaluate this integral with standard calculus techniques.
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At a harvest 16 ears of corn are being picked for every 18 peppers if 9 peppers have been picked how many ears of corn have been picked(I need the actual math)
Answers
x : 9
x = 8
Hope this helps!
Clarence solved the equation 3x + 15 = 33 and showed the following work. 3x + 15 = 33 3x + 15 - 15 = 33 3x = 33 = x = 11 Which of the following is true? x is 11. x should be 6. x should be 16. x should be 99.
Answers
3x = 33 - 15
3x = 18
x = 18/3
x = 6 <==
Answer:
x=6
Step-by-step explanation:
How to write 5x923 in expanded form
Answers
4000 + 600 + 10 + 5 is your answer
hope this helps
or if you want the equation
(900 + 20 + 3) x 5
hope this helps
4500 + 100 + 15 = 4615.
The selling price for a classic car is $14000, which is $2500 less than three times its original price. What was the original price of the car?
Answers
The original price of the car was $5,500, which is derived from the mathematical equation based on the given information in the question.
Explanation:The subject of this question is algebra, a branch of mathematics. The question gives us the selling price of a classic car and tells us that this price is $2500 less than three times its original price. We're asked to find the original price. Let’s denote the original price by x.
According to the problem, 3x (three times the original price) minus $2500 equals the selling price ($14,000). So, if we set this up as an equation, it looks like this: 3x - $2500 = $14,000.
To solve for x (the original price), we first need to add $2500 to both sides of our equation, giving us 3x = $16,500. Then, we divide each side by 3 to solve for x, arriving at x = $16,500 ÷ 3 = $5,500. Therefore, the original price of the car was $5,500.
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A bird of species A, when diving, can travel 6 times as fast as bird of species B top speed. if the total speeds for these to birds 231 miles per hour, find the fastest speed of the birds of species A and the fastest speed of the bird of species B
Answers
x=38mph b
6x=228mph a
Given the sets
U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
A = {0, 1, 4, 7, 9}, and B = {0, 4, 5, 6, 7}, use De Morgan's Laws to find the indicated set. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.)
(A' ∩ B)'
Answers
We used De Morgan's laws to find the complement of the set formed by the intersection of the complement of A and B. We first found the complement of A, then the intersection of this set with B, and finally took the complement of this new set.
Explanation:In set theory, De Morgan's laws relate the intersection and union of sets in a very elegant way. Here, (A' ∩ B)' represents the complement of the set formed by the intersection of the complement of A and B.
First, let's find A'. This is the set of all elements in U that are not in A. U = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } and A = { 0, 1, 4, 7, 9 } So, A' = { 2, 3, 5, 6, 8 }.
Now, let's find the intersection of A' and B, denoted by A' ∩ B. We have B = { 0, 4, 5, 6, 7 } so A' ∩ B = { 5, 6 }.
Finally, let's find the complement of this set, denoted by (A' ∩ B)'. This is the set of all elements in U that are not in A' ∩ B. So, (A' ∩ B)' = { 0, 1, 2, 3, 4, 7, 8, 9 }.
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Prime factorization practice all factors 1.- 25 2.- 49 3.- 7 4.- 13 5.- 24 6.- 48 7.- 168
Answers
For 1, from some guess and check we can figure out that 5*5=25. Since 5 is a prime number, that's it!
For 2, we can figure out that 7*7=49 and 7 is a prime number, so we're good there.
From 6, we can do some guess and check to figure out that 2*24=48, 2*12=24, 2*6=12, and 2*3=6, resulting in 2*2*2*2*3=48 since 2 and 3 are prime numbers. We found out, for example, to find 2*12 due to that if 2*24=48, 2*24 is our current factorization. By finding 2*12=24, we can switch it to 2*2*12
Jason's age is 1 2 of his brother's age. His brother's age can be represented by the expression 12a - 9. Write an expression that can be used to represent the sum of their ages. A) 12a - 5.5 B) 18a - 13.5 C) 18a + 21 Eliminate D) (12a-9) 2
Answers
Answer:
[tex]18a - 13.5[/tex]
Step-by-step explanation:
Jason's age is [tex]\frac{1}{2}[/tex] of his brother's age.
Brother age is [tex]12a-9[/tex]
Sum of their ages = Age of Jonson + age of his brother
Jonson's age = half of his brother age
[tex]Jonson's \ age=\frac{12a-9}{2}[/tex]
Sum of their ages =[tex]\frac{12a-9}{2}+12a-9[/tex]
Take common denominator 2
[tex]\frac{12a-9}{2}+\frac{24a-18}{2}[/tex]
[tex]\frac{36a-27}{2} [/tex]
[tex]18a - 13.5[/tex]
An open top box with a square base has a surface area of 100 square inches. express the volume of the box as a function of the length of the edge of the base. what is its domain?
Answers
The box has a base of area: [tex]a \cdot a = a^2 (square ft) [/tex],
and 4 lateral faces of area ah (square ft).
thus the total area of the box is [tex]a^2+4ah[/tex].
we can reduce the number of variables as follows:
[tex]a^2+4ah=100\\\\4ah=100-a^2\\\\h= \frac{100-a^2}{4a}= \frac{25}{a}- \frac{a}{4} [/tex]
The volume of the box is given by the function:
[tex]V(a)=a \cdot a \cdot (\frac{25}{a}- \frac{a}{4} )=25a- \frac{a^3}{4} [/tex].
To find the domain we solve
[tex]25a- \frac{a^3}{4} \ \textgreater \ 0\\\\a(25- ( \frac{a}{2} )^{2} )\ \textgreater \ 0\\\\a(5- \frac{a}{2})(5+ \frac{a}{2} )\ \textgreater \ 0[/tex]
the roots of the expression are 0, 10 and -10. Since the overall sign of the expression is negative, we have the following sign table:
++++++++++++(-10)----------(0)++++++++++(10)--------------------
thus the solution of the inequation is (-infinity, -10) union (0, 10)
but we have another condition: a>0, since each side must be positive.
combining these 2 conditions, we have the domain: (0, 10)
Answer: [tex]V(a)=25a- \frac{a^3}{4}[/tex], Domain (0, 10)
Given:
An open-top box with a square base has a surface area of 100 square inches.
Question:
Express the volume of the box as a function of the length of the edge of the base. What is its domain?The Process:
Let the length of the edge of the base = x Let height = hPart-1: The surface area
Let us arrange the equation to get the surface area of the box with a square base. Recall that the box is without a lid and its surface area is 100 square inches.
[tex]\boxed{ \ Surface \ area = area \ of \ base + (4 \times area \ of \ rectangle) \ }[/tex]
[tex]\boxed{ \ x^2 + (4 \cdot x \cdot h) = 100 \ }[/tex]
[tex]\boxed{ \ x^2 + 4xh = 100 \ }[/tex]
From the above equation, we set it again so that "xh" is the subject on the left.
Both sides are subtracted by x².
[tex]\boxed{ \ 4xh = 100 - x^2 \ }[/tex]
Both sides are divided by 4.
[tex]\boxed{ \ xh = \frac{100 - x^2}{4} \ }[/tex] ... (Equation-1)
That is the strategy we have prepared.
- - - - - - - - - -
Part-2: The volume
[tex]\boxed{ \ Volume \ of \ the \ box = length \times width \times height \ }[/tex]
[tex]\boxed{ \ Volume = x \cdot x \cdot h \ }[/tex]
[tex]\boxed{ \ Volume = x^2h \ }[/tex] ...(Equation-2)
Substitution Equation-1 into Equation-2.
[tex]\boxed{ \ Volume = x(xh) \ }[/tex]
[tex]\boxed{ \ Volume = x \bigg( \frac{100 - x^2}{4} \bigg) \ }[/tex]
[tex]\boxed{ \ Volume = \frac{100x - x^3}{4} \ }[/tex]
[tex]\boxed{ \ Volume = 25x - \frac{1}{4}x^3 \ }[/tex]
Thus, an expression of the volume of the box as a function of the length of the edge of the base is [tex]\boxed{\boxed{ \ Volume = 25x - \frac{1}{4}x^3 \ }}[/tex]
- - - - - - - - - -
Part-3: The domain of volume
The value of volume must always be positive, i.e., V > 0.
[tex]\boxed{ \ 25x - \frac{1}{4}x^3 > 0 \ }[/tex]
Both sides are multiplied by 4.
[tex]\boxed{ \ 100x - x^3 > 0 \ }[/tex]
Both sides are multiplied by -1, notice the change in the sign of the inequality.
[tex]\boxed{ \ x^3 - 100x < 0 \ }[/tex]
[tex]\boxed{ \ x(x^2 - 100) < 0 \ }[/tex]
[tex]\boxed{ \ x(x - 10)(x + 10) < 0 \ }[/tex]
We get [tex]\boxed{ \ x = 0, \ x = 10, \ and \ x = - 10 \ }[/tex].
Since the values of x cannot be negative, x = -10 are promptly rejected. For x = 0 can be used as one of the domain limits.Consider the test of signs:
x(x - 10) (x + 10) is negative to the left of x = 10, and positive to the right of x = 10 on the number line.
Examples of tests:
[tex]\boxed{ \ for \ x = 2 \rightarrow 2(2 - 10)(2 + 10) < 0 \ }[/tex][tex]\boxed{ \ for \ x = 11 \rightarrow 11(11 - 10)(11 + 10) > 0 \ }[/tex]Remember this form above, [tex]\boxed{\ x(x - 10)(x + 10) < 0 \ }[/tex], the value of the test result must be negative (because < 0).
Thus, the domain of the volume is [tex]\boxed{ \ 0 < x < 10 \ }[/tex] or [tex]\boxed{ \ (0, 10) \ }[/tex]
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In discus competition an athlete threw the discus 63.37meters 62.95 meters and 63.7meters order the distance from least to greatest
Answers
what is the slope of the line that passes through each pair of points A(-2, -4), B(2,4)
Answers
which of these is a geometric sequence?
Answers
1/4 * 2 = 1/2
1/2 * 2 = 1
1 * 2 = 2
2 * 2 = 4
so ur geometric sequence is : 1/4, 1/2, 1, 2, 4...with a common ratio of 2
Can someone help figure out how to solve this equation? Thank you!
There 20 people competing in a contest if first place earns $100, second place earns $50 and third place earns $25, How many ways can the three winners be selected?
Answers
The formula is given by:
[tex]^nC_r= \left(\begin{array}{ccc}n\\r\end{array}\right)= \frac{n!}{(n-r)!r!} [/tex]
Where:
'n' is the total population or sample population
'r' is the number of pick
We have:
n = 20
r = 3
Substitute these values into the formula we have
[tex]^{20}C_3= \frac{20!}{(20-3)!3!}=1140 [/tex]
Answer:
There are 1140 different ways of picking three winners out of 20 people
g(x) = x3 + 6x2 + 12x + 8
Determine the function’s value when x = −1.
Answers
rewrite vertically,then add
63,594+98,697+59,835
Answers
63594
98697
+59835
----------
222126
222126 is your answer
hope this helps
find the unit rate???
Answers
Final answer: 500 kilobytes per minute
Answer:
500 kilobytes/ 1 min
Step-by-step explanation:
2,500 kilobytes/ 5 min
2,500 divide by 5 = 500 kilobytes
500 kilobytes/ 1 min
Evaluate cosθ if sinθ = [tex]\frac{ \sqrt{5} }{3} [/tex]
Answers
[sqrt(5)]^2 + adj^2 = 3^2, or 5 + adj^2 = 3^2. Thus, 5 + adj^2 = 9. Solving for adj, we get adj = plus or minus 2.
The angle theta could be in either QI or QIII, because the sine is positive.
If the angle theta is in QI, the cosine of theta is -2/3; if in QIII, 2/3.
Rico is estimating 139 x 18 Find his mistake and correct it.
100 x 10 =1,000
Answers
Home this works
The large rectangle's dimensions are three times the dimensions of the small rectangle. It is #60
A.)
B.)
C.)
D.)
I need help please
Answers
B. Larger rectangle is 9 time bigger in area.
C. The answers are not the same because the scale factor is 3, then the perimeter of large rectangle would have a perimeter 3 times bigger than the small one. Also, the area would be found by taking the scale factor of 3 and squaring it 3^2=9 since it is a square unit.
D. What happens is that now we have a scale factor of 2 so the perimeter would be 2 times bigger for the larger rectangle and the area would be 2^2=4 times bigger than the small one.
The large rectangle's dimensions are 3 times the dimensions of the small rectangle. If the small rectangle's dimensions are W for width and L for length, then the large rectangle's dimensions are 3W and 3L.
Explanation:The subject of this question is Mathematics, specifically relating to geometry and ratios. You're asked to compare two rectangles: a large one and a small one. The large rectangle's dimensions (both the width and length) are three times the dimensions of the small rectangle. Let's assume the dimensions of the small rectangle are W (width) and L (length). Then, the dimensions of the large rectangle would be 3W and 3L, respectively. This is because the large rectangle is three times the size of the small rectangle in both width and length.
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Renee hiked for 3 and 3/ 4 miles. After resting, Renee hiked back along the same route for 2 and 1 /4 miles. How many more miles does Renee need to hike to return to the place where she started? Represent your answer as a simplified mixed number, if necessary.