What is the solution of ?\(\frac{5}{2} x-7=\frac{3}{4} x+14\)
Answers
Combine the terms by multiplying into a single fraction.
\(\bf{\dfrac{5}{2}x-7=\dfrac{3}{4}x+14 }\)
Find the common denominator.
\(\bf{\dfrac{5x}{2}-7=\dfrac{3}{4}x+14 }\)
Combine fractions with the lowest common denominator.
\(\bf{\dfrac{5x(-7)}{2}=\dfrac{3}{4}x+14 }\)
Multiply the numbers.
\(\bf{\dfrac{5x-14}{2}=\dfrac{3}{4}x+14 }\)
Combine the multiplied terms into a single fraction
\(\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+14 }\)
Find the common denominator.
\(\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+\dfrac{4\cdot14}{4} }\)
Combine fractions with the lowest common denominator.
\(\bf{\dfrac{5x-14}{2}=\dfrac{3x+4\cdot14}{4} }\)
Multiply the numbers.
\(\bf{\dfrac{5x-14}{2}=\dfrac{3x+56}{4} }\)
Eliminate the denominators of the fractions.
\(\bf{4\cdot\dfrac{5x-14}{2}=4\cdot\dfrac{3x+56}{4} }\)
Cancel the multiplied terms that are in the denominator.
\(\bf{2(5x-14)=3x+56}\)
To distribute.
\(\bf{10x-28=3x+56 }\)
Add 28 to both sides.
\(\bf{10x-28+28=3x+56+28 }\)
Simplify
\(\bf{10x=3x+84 }\)
Subtract 3x from both sides.
\(\bf{10x-3x=3x+84-3x }\)
Simplify
\(\bf{7x=84 }\)
Divide both sides by the same factor.
\(\bf{x=\dfrac{84}{7} }\)
Simplify
\(\bf{x=12 \ \ \ === > \ \ \ Answer}\)
↓
VerificationLet x=12.
\(\bf{\dfrac{5}{2}\times12-7=\dfrac{3}{4}\times12+14 }\)\(\bf{\dfrac{5\times12}{2}-7=\dfrac{3}{4}\times12+14 }\)\(\bf{\dfrac{60}{2}-7=\dfrac{3}{4}\times12+14 }\)\(\bf{30-7=\dfrac{3}{4}\times12+14 }\)\(\bf{30-7=\dfrac{3\times12}{4}+14 }\)\(\bf{30-7=\dfrac{36}{4}+14 }\)\(\bf{30-7=9+14 }\)\(\bf{23=9+14 }\)\(\bf{23=23}\)Checked ✅
Related Questions
if the dilation of K(-2,4) equals K'(1,-2), the scale factor used for the dilation is
Answers
Answer:
-1/2
Step-by-step explanation:
We know
The dilation of K(-2,4) equals K'(1,-2)
To get from -2 to 1, we time -1/2
To get from 4 to -2, we time -1/2
So, the scale factor used for the dilation is -1/2
Find the limit of the difference quotients for f(x) = x2+2x+1 if a= -1
Answers
The limit of the difference quotients for f(x) = x^2 + 2x + 1 as x approaches -1 is indeterminate.
To find the limit of the difference quotients for the function f(x) = x^2 + 2x + 1 as x approaches -1, we need to evaluate the following expression:
lim(x→-1) [f(x) - f(-1)] / (x - (-1))
First, let's substitute the values into the expression:
lim(x→-1) \([(x^2 + 2x + 1) - (-1^2 + 2(-1) + 1)] / (x + 1)\)
Simplifying further:
lim(x→-1) \([(x^2 + 2x + 1) - (1 - 2 + 1)] / (x + 1)\)
lim(x→-1)\([x^2 + 2x + 1 - 0] / (x + 1)\)
lim(x→-1) \((x^2 + 2x + 1) / (x + 1)\)
Now, we can directly substitute x = -1 into the expression:
\((-1^2 + 2(-1) + 1) / (-1 + 1)\)
(1 - 2 + 1) / (0)
0 / 0
We have obtained an indeterminate form of 0/0. This indicates that we need to further simplify the expression or use other techniques, such as L'Hôpital's rule, to evaluate the limit. However, without additional information or simplification, we cannot determine the precise value of the limit at x = -1.
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Find the value of x and y.
60°
6
Answers
Answer:
b .
x = 3
y = 3\(\sqrt3\)
Step-by-step explanation:
Using the pythagorean identities for 30-60-90° triangle,
we know the ratio of the sides is x - x√3 - 2x
Since 2x = 6
Then smallest side is x (opposite ∠30°) = 6/2 = 3
The other side y , opposite ∠60° will be x√3 or 3√3.
9514 1404 393
Answer:
B. x = 3; y = 3√3
Step-by-step explanation:
You only need to use your sense of triangles to choose the correct answer:
x < y < 6
This relation fits only one answer choice:
x = 3, y = 3√3
_____
Additional comment
For multiple choice questions, it isn't always about working the problem. Usually, it is about knowing what the answer has to look like. The usual criteria are (a) is the answer true; (b) does the answer make sense in the context of the problem statement; (c) can you get this answer if you work the problem in detail. More often than not, the first two criteria will let you choose the correct answer without doing any detailed solving.
Sam Long anticipates he will need approximately $225,300 in 12 years to cover his 3-year-old daughter's college bills for a 4-year
degree.
How much would he have to invest today at an interest rate of 8% compounded semiannually?
Answers
The amount of principal for the given situation is $87,894.37
What is compound interest?
The interest that is paid on both the initial principal and the accumulated past interest is known as compound interest.
The principal, interest rate, and time period are used to calculate compound interest.
Given, compound amount (A) = $225,300
time period (t) = 12 years
interest rate (r) = 8% = 0.08
compounded semiannually (n) = 2
principal amount (P) =?
Then. the compound amount is given by
\(A = P(1 + \frac{r}{n} )^{nt}\)
or, \(225300 = P(1 + \frac{0.08}{2} )^{2*12}\)
or, \(P= 225300/(1+0.04)^{24}\)
or, P = 87,894.37
Hence, the amount of investment today is $87,894.37
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What is the answer?? 3(b-5)<-2b
Answers
Answer:
b < 3
Step-by-step explanation:
3 ( b - 5 ) < - 2b
3 ( b ) - 3 ( 5 ) < - 2b
3b - 15 < - 2b
3b + 2b < 15
5b < 15
b < 15/5
b < 3
3(b-5)<-2b
3b<-2b+5
Add the 2b over.
5b<5
Divide by 5.
b<1
Check by plugging in.
3(1-5)<-2(1)
3(-4)<-2
-12<-2
1 is a possibly solution to the inequality.
Y=2X squared -12 X +20 for quadratic formula
Answers
x = (12 ± √(-16)) / 4,The solutions would be complex numbers.
What is the quadratic formula?To solve quadratic equations of the form ax2 + bx + c = 0, use the quadratic formula. For this situation, your condition is as of now as a quadratic condition, with a = 2, b = - 12, and c = 20.
The quadratic formula is:
x = (-b ± √\((b^2 - 4ac)\)) / 2a
Plugging in the values for a, b, and c, we get:
x = (-(-12) ± √\(((-12)^2 - 4(2)(20)))\) / 2(2)
Simplifying the expression inside the square root:
x = (12 ± √\((144 - 160)\)) / 4
x = (12 ± √(-16)) / 4
Since the square foundation of a negative number is definitely not a genuine number, this condition has no genuine arrangements. Complex numbers would provide the answers.
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If a sweater costs $40.00 before the sale and $35.00 after the sale, what was the percent of decrease?
Answers
Answer:
%12.5
Step-by-step explanation:
Answer:
12%
Step-by-step explanation:
What is my perfect crime? I break into Tiffany's at midnight. Do I go for the vault? No, I go for the chandelier. It's priceless. As I'm taking it down, a woman catches me. She tells me to stop. It's her father's business. She's Tiffany. I say no. We make love all night. In the morning, the cops come and I escape in one of their uniforms. I tell her to meet me in Mexico, but I go to Canada. I don't trust her. Besides, I like the cold. Thirty years later, I get a postcard. I have a son and he's the chief of police. This is where the story gets interesting. I tell Tiffany to meet me in Paris by the Trocadero. She's been waiting for me all these years. She's never taken another lover. I don't care. I don't show up. I go to Berlin. That's where I stashed the chandelier.
Solve the following polynomial function. y=x^4−21x^2−100
Answers
Answer:
y= x⁴ -21x²-100
combine x's I think
x⁴= 1x? cuz if it's 1x⁴ that's 1x*1x*1x*1x = 1x
1x * -21x²
-21x * -21x = 441x
+1x = 442x
y= 442x -100
I'm not sure if I did that right
Solve the equation. Please help
Answers
\(\cfrac{2y}{3}-\cfrac{3}{4}=\cfrac{1}{12}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{2y}{3}-\cfrac{3}{4} \right)=12\left( \cfrac{1}{12} \right)}\implies 8y-9=1 \\\\\\ 8y=10\implies y=\cfrac{10}{8}\implies y=\cfrac{5}{4}\)
Step 1: Add 3/4 on both sides
We get
2y/3 = 1/12+3/4
We add fractions by calculating a common denominator, adjusting the numerators accordingly and adding them. See this in action below:
12 and 4 have a common multiple in 12 which will be our common denominator. Now, 1/12 does not need to be adjusted, but 3/4 becomes 3*3 / 3*4 = 9/12.
In total 1/12 + 9/12 = 10/12
So, we have 2y/3 = 10/12
Now we multiply both sides by 3, so that the 3 will cancel out the 3 in the denominator on the left side:
2y =30/12
Now we just need to divide by 2 and get the solution:
y = 15/12 = 3*5 / 3*4 = 5/4
Therefore the final answer is A:
The solution set is {5/4}
Round 765.2 to nearest hundreds
Answers
the sum of three consecutive even numbers is 114 what's the smallest of these numbers
Answers
Answer:
36
Step-by-step explanation:
consecutive even numbers are 2,4, 6...
Let the smallest of the 3 numbers be x.
2nd number= x+2
3rd number
=x+2+2
= x+4
sum of the 3 numbers= x +x+2 +x+4
114= 3x+6
3x= 114 -6 (-3 on both sides)
3x= 108 (simplify)
x= 108 ÷3
x= 36
Thus, the smallest number is 36.
Let's check!
36+38+40= 114 ✓
Solve the inequality.
x13
| + 9| < 15
1
x
Answers
Answer:
x < 18 and x > −72
Step-by-step explanation:
Chelsey put for $450 into an account with a simple interest rate of 2.5% when she withdrew the money she had earned a total of $67.50 in interest how long did she leave the money in the account
Answers
Answer:
5.66 years
Step-by-step explanation:
450 x 1.025^(n) = 450 + 67.50
450 x 1.025^(n) = 517.50
1.025^(n) =(517.50 / 450)
1.025^(n) = 1.15
n = ln(1.15) / ln(1.025)
n = 5.66
Answer:meep
Step-by-step explanation:
meep
The water usage at a car wash is modeled by the equation W(x) = 5x3 + 9x2 − 14x + 9, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours. Write a function, C(x), to model the water used by the car wash on a shorter day. C(x) = 5x3 + 7x2 − 14x − 6 C(x) = 4x3 + 7x2 − 14x + 6 C(x) = 4x3 + 7x2 − 14x − 6 C(x) = 5x3 + 7x2 − 14x + 6
Answers
W(x) - C(x) = 2(W(x) - C(x))
Solving this equation for C(x), we get:
C(x) = (W(x) - 2W(x))
= W(x)(1 - 2)
= (5x3 + 9x2 - 14x + 9)(1 - 2)
= (5x3 + 7x2 - 14x + 6)
Therefore, the function C(x) to model the water used by the car wash on a shorter day is:
C(x) = (5x3 + 7x2 - 14x + 6)
The points E, F, G and H all lie on the same line segment, in that order, such that the
ratio of EF FG: GH is equal to 1: 5:3. If EH
:
= 54, find EG.
Answers
The ratio of EG = 36.
Let's assign variables to the lengths of the line segments:
EF = x
FG = 5x
GH = 3x
We know that EH = EF + FG + GH.
Substituting the given values, we have:
54 = x + 5x + 3x
Combining like terms, we get:
54 = 9x
To isolate x, we divide both sides of the equation by 9:
54/9 = x
Simplifying, we find:
6 = x
EF = 6, FG = 5(6) = 30, and GH = 3(6) = 18.
Since EG is the sum of EF and FG, we can calculate it as follows:
EG = EF + FG = 6 + 30
= 36
EG = 36.
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a prime number that is between 48 and 58
Answers
Answer:
53 is prime. How are you in collage?
A prime number is a number that is only divisible by 1 and the number itself (examples include 3, 11, 19). The prime numbers between 40 and 60 are 41, 43, 47, 53, and 59.
if a/5=60/4 what is the value of a
Answers
Answer:
a = 75
Step-by-step explanation:
A boy gets #2.00 per week as pocket money. His sister gets only #1.60 per week
Find the ratio of the boy's allowance to his sister's. If his sister gets 20 k more per week,what will be the new ratio?
Answers
The Ratio of the boy's allowance to his sister's is 5 : 4.
The new Ratio is 1 : 10000.
What is definition of ratio?The quotient of two mathematical expressions, 1a. b: the proportion between two or more items in terms of quantity, amount, or size.What does the arithmetic term "ratio" mean?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, if there is 1 boy and 3 girls, you may express the ratio as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.To learn more about :Ratio
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;
y=x^2+20
determine if symmetric on the..
x axysis
y axysis
both
Answers
The graph of the equation defined by; y = f(x) = x² + 20 as represented in the task content is symmetrical about the y-axis.
To which axis is the graph of the equation given symmetrical about?It follows from the task content that the axis about which the given graph is symmetrical be determined as follows.
Since it follows that for a function to be symmetric about the y-axis;
f(-x) = f(x).
Therefore, we have;
f(-x) = (-x)² + 20.
f(-x) = x² + 20 = f(x).
Hence, the graph is symmetrical about the y-axis.
Also; Since; f(-x) = x² + 20 ≠ - f(x).
It follows that the graph is not symmetrical about the origin and hence, the graph is only symmetrical about the y-axis.
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Select from the drop-down menus to correctly complete the statement. The expressions 3.2^2−1 and 10−0.33⋅2 should be joined by Choose... to form an Choose... .
Answers
Answer:
D)
Can you please mark me as "Brainliest"
HELP PLEASE I NEED ANSWER NOW
Answers
Answer:B
Step-by-step explanation:
I think it should be B u= -1
5*Please answer this correctly very urgent!
Answers
Answer:
1 3/15 - 5/15
Step-by-step explanation:
Hope this helps. PS the / sign is supposed to be for the fraction.
Step-by-step explanation:
1 1/5 - 1/3 = 0.86
Hope I helped. The only way I know how to dot this is in decimal form sorry.
Higher Order Thinking Morgan read
a thermometer at 7:00 P.M. The
temperature was 16°C. This temperature
was 9°C less than the temperature at
2:00 P.M. The temperature at 2:00 P.M.
was 10°C higher than the temperature at
8:00 A.M. What was the temperature at
8:00 A.M.?
Answers
The temperature at 8:00 A.M. was 15°C.
Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.
We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C
3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.
Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C
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One leg of a 45°-45°-90° triangle is 9. Find the lengths of the other sides.
Answers
Answer:
9, 9√2
Step-by-step explanation:
The ratios of side lengths in a 45°-45°-90° triangle are ...
1 : 1 : √2
The other leg is the same as the first, and the hypotenuse is √2 times that.
The other sides are 9 and 9√2.
Create an expression that has the same value as (6x-4) + (x + 5).
Write the correct numbers from the list in the blank boxes. Each number
may be used once, more than once, or not at all.
Answers
Answer: 7x + 1
Step-by-step explanation:
(6x-4)+(x+5)
Step 1: Remove Parentheses:
6x-4+x+5
Step 2: Combine Like Terms:
7x +1
100 Points! Geometry question. Photo attached. Find x and y. Please show as much work as possible. Thank you!
Answers
The values of given x and y is,
x = 6 and y = 13/2
Since we know that,
Basic proportionality theorem,
The basic proportionality theory was developed by Thales, a great Greek mathematician; hence, it is also known as the Thales theorem. According to the great mathematician, the ratio of any two matching sides of any two equiangular triangles is always the same. The basic proportionality theorem (BPT) was suggested based on this premise.
Since we know that,
In the figure we that,
⇒ 2x + 1 = x +7
⇒ x = 6
Similarly
⇒ 3y - 8 = y +5
⇒ y = 13/2
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an Expression for difference of a number s and -6
Answers
After answering the given query, we can state that The expression for the difference between a number s and -6 is: s - (-6) or s + 6
what is expression ?In numbers, you can multiply, split, add, or take away. The following is how a phrase is made together: Numeric number, expression, and arithmetic operator The elements of a mathematical expression are integers, factors, and functions. It is feasible to use contrasting words and terms. Any mathematical declaration containing variables, integers, and a mathematical action between them is known as an expression, also known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the provided equation, which are all separated by the mathematical symbol +.
The expression for the difference between a number s and -6 is:
s - (-6)
or
s + 6
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Look at the image below thanks it’s a proof
Answers
The Complete statements are shown below.
What are property of parallel line?If the corresponding angles created by any two lines are equal, then the lines are said to be parallel.If the alternate internal angles created are equal, any two lines are considered to be parallel.If the alternate outside angles created are equal, any two lines are considered to be parallel.If the consecutive interior angles on the same side of the transversal are supplementary, any two lines are said to be parallel.Given:
we have AB || CD
We have to prove that ABCD is a parallelogram so that
So, <CBD = <ABD { alternate Interior angle}
AB|| CD (given)
<CDB = <ABD { alternate Interior angle}
BD = BD (Common)
So, ΔADB ≅ Δ CDB by ASA criteria
Then by CPCT
AB= DC and AD = BC and <BCD = <DAB
So, <CDA = <CDB+ <ADB and <ABC = <CDB+ <ADB by Add Angle postulate.
Then, by transitive property
<CDA = <ABC
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What is the reciprocal of 3 3/7?
Answers
Answer:
7/9
Step-by-step explanation:
We know that 3 3/7 is equal to 9/7 by multiplying, and recoprocal is just the inverse of the fraction. Inverse is just the fraction upside down.
9/7 upside down is 7/9.
Answer:
7/9
Step-by-step explanation:
i don't know
Graph the line.
y = -5x + 2
Answers
Answer:
Step-by-step explanation:
