Li Juan solves the equation below by first squaring both sides of the equation.
13 - 2w = w + 6
What extraneous solution does Li Juan obtain?
will give 36 points HURRY PLEASE
Answer:
Step-by-step explanation:
(13-2w)^2 = 169 - 52w + 4w^2
(w+6)^2 = w^2 + 12w + 36
Setting them equal:
169 - 52w + 4w^2 = w^2 + 12w + 36
3w^2 - 64w + 133 = 0
Using the quadratic formula, we get
x = (64 +/- sqrt(64^2 - 4*3*133))/6
64^2-12*133 = 2500. sqrt(2500) = 50.
x = (64 +/- 50)/6.
x = 19 or 14/6 = 7/3.
Solving the original equation:
7 = 3w.
w = 7/3.
Therefore 19 is extraneous.
x = 19 is the extraneous solution Li Juan obtained.
The given equation is 13 - 2w = w + 6.
We need to solve the equation by squaring both sides of the equation.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, 13 - 2w = w + 6 squaring both sides of the equation.
That is, (13-2w)²= 169 - 52w + 4w²
(w+6)²= w²+ 12w + 36
Setting them equal, we get
169 - 52w + 4w² = w² + 12w + 36
⇒3w²- 64w + 133 = 0
Now, using the quadratic formula, we get
x = (64±√(64² - 4×3×133))/6
⇒x = (64±√2500)/6.
⇒x = (64±√50)/6.
⇒x = 19 or 14/6 = 7/3.
Solving the original equation, we get
7 = 3w⇒w = 7/3
Therefore, x = 19 is the extraneous solution Li Juan obtained.
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Find the sum.
4/5r+10/3r
Answer:
i hope this helps
Step-by-step explanation:
Evaluate 7j+5−8k j=0.5 k=0.25,
Answer:
Evaluate 7j+5-8k when j=0.5 and k=0.25 Get the answers you need, now!
2 answers
Step-by-step explanation:
Answer:
6.5
Step-by-step explanation:
(7*0.5)+(5)-(8*0.25)
PEMDAS
Multiply 7 and 0.5= 3.5
Multiply 8 and 0.25= 2
3.5+5-2
Add 3.5 and 5= 8.5
Subtract 8.5 and 2= 6.5
Please help!! I'll give brainleist
Jordan works for a landscape company during his summer vacation. He is paid $12 per hour for mowing lawns and $14 per hour for planting gardens. He can work a maximum of 40 hours per week, and would like to earn at least $250 this week. If m represents the number of hours mowing lawns and g represents the number of hours planting gardens, write a system of inequalities that could represent the given conditions.
Answer:
m + g < 40
12m + 14g > 250
Step-by-step explanation:
Given : Jordan is paid $12 per hour for mowing lawns and $14 per hour for planting gardens.
Let m represents the number of hours mowing lawns and g represents the number of hours planting gardens.
He can work a maximum of 40 hours per week, and would like to earn at least $250 this week.
Then, the system of the inequality becomes
m + g < 40
12m + 14g > 250
Hereee +13 points + the star
Find the zeros of the quadratic function
Step-by-step explanation:
the answer of the question above is
a=0
b=6
c=4
Cynthia invests some money in a bank which pays
5% compound interest per year.
She wants it to be worth over £8000 at the end of 3 years.
What is the smallest amount, to the nearest pound, she can invest?
Answer: £6910.7
Step-by-step explanation:
Given
Rate [tex]R=5\ \%[/tex]
Amount [tex]A=[/tex]£[tex]8000[/tex]
Time [tex]T=3\ years[/tex]
In compound interest, the Amount is given by
[tex]A=P[1+\frac{R}{100}]^T[/tex]
[tex]8000=P[1+\frac{5}{100}]^3[/tex]
[tex]P=\dfrac{8000}{1.1576}[/tex]
[tex]P=[/tex]£[tex]6910.7[/tex]
What is the interquartile range of the date shown in the box plot
Answer: 14
Step-by-step explanation: To find the Interquartile Range (IQR) you need to subtract points Q1 from Q3. The ends of the box are the Q1 and Q3 points.
Q3 = 80
Q1 = 66
80-66= 14
Y= -0.5x+5 3x+5y=2 what’s the answer
Answer:
x = -46
Step-by-step explanation:
Y= -0.5x+5
3x+5y=2 [replace the "y" in this problem with the what "y" equals above]
3x + 5( -0.5x + 5) = 2
3x + -2.5x + 25 = 2
0.5x = -23
x = -46
Under what conditions is a trinomial said to be completely factored?
Answer:
We say that a polynomial is factored completely when we can't factor it any more. Here are some suggestions that you should follow to make sure that you factor completely: Factor all common monomials first. Identify special products such as difference of squares or the square of a binomial.
Step-by-step explanation:
can you mark brainliest yes thanks you the best
(8x + 31) (16x - 9) whats the value of x?
Answer:
31
Step-by-step explanation:
31 weather hgrfgrrv rtgfrh rtbffh thgg thgt
Answer:
31
Step-by-step explanation:
Both numbers are greater than -15 and less than 5. One number is 6 greater than the other.
Answer:
-14 -8
Step-by-step explanation:
Answer
-14,-8
i did this on ttm and got it correct
there are 63 students on the bus with a ratio of 2 girls to 5 boys. How many boys are on the bus?
45
18
7
35
Answer:
45
Step-by-step explanation:
2x+5x=63
7x=63
x=9
number of boys =5×9=45
10 less than a number squared is 71
"Which expression stands for "32 more than a number d"?"
A: 32d
B: 32 - d
C: 32 + d
D: 32 ÷ d
I really need help on this question! It's really confusing
Answer:
32+d
Step-by-step explanation:
because it's asking for 32 added on to whatever d is
example
if d=5 it would be asking what's 32 +5
Use the expression 4/3 plus 8 -9/y to find an example of each kind of the expression
Answer:
The answer is:
Quotient: 9/y
Sum: 4(3) +8
Variable is: y
Step-by-step explanation:
A quotient is the result of a division problem.
The expression 9/y represents a quotient.
A sum is the result of an addition problem.
The 4(3) + 8 represents a sum.
A variable is a letter that stands for an unknown quantity.
Y is a variable
I hope this helped you out!! :D
Answer:
Quptient: 9/y
Sum: [tex]4^{3}[/tex]+8
Variable: 7
Step-by-step explanation:
A quotient is the result of a division problem.
the expression 9/y represents a quotient
A sum of an addition problem.
The expression [tex]4^{3}[/tex]+ 8 represents a sum.
A variable is a letter that statnds for a unknown quatily
y is a variable.
The correct answers are:
Kind of expressions: Example:
Quptient: 9/y
Sum: [tex]4^{3}[/tex]+8
Variable: 7
what is the solution to the equation? t-15=76
Answer:
t=91
Step-by-step explanation:
✨Help please it’s emergency I will mark you as brainlist ✨
Answer:
I believe the answer is A
Step-by-step explanation:
p\left(x\right)=x^{3}+6x^{2}+5x-12
Answer:[tex]P\left(x\right)=x^{3}+6x^{2}+5x-12[/tex]
Step-by-step explanation:
That is what she means! I don't know what you're asking but this may help the people that want to answer this question. :)
Two bags contain marbles. Bag A contains 112 marbles, and Bag B contains 140 marbles. What percent fewer marbles does Bag A have than Bag B?
Answer:
20%
Step-by-step explanation:
sorry if i am wrong
Evaluate the following expression.
Answer:
3
Step-by-step explanation:
2 + (9/ 3) ^ 2 / 9
2 + 3^2/9
2 + 3*3 / 9
2 + 9/9
2 + 1
3
Hope this helped!
Answer:
11
Step-by-step explanation:
Following the order as set out in PEMDAS ( parenthesis, exponents, multiplication, division, addition, subtraction )
evaluating parenthesis gives
2 + [tex]3^{4}[/tex] ÷ 9 ← evaluate exponent
= 2 + 81 ÷ 9 ← evaluate division
= 2 + 9 ← evaluate addition
= 11
Mr. Brown made 5 trips to the sushi bar. On his first trip, he got 14 pieces of sushi. On his second trip, he got 12 pieces of sushi. On his third trip, he got 22 pieces of sushi. On his fourth trip he got 8 pieces of sushi. On his final trip, he got 24 pieces of sushi. What was the average (use the mean) number of pieces of sushi he got on each trip to the sushi bar?
Answer: 16 pieces.
Step-by-step explanation:
Suppose that we have a set with N numbers
{x₁, x₂, x₃, ..., xₙ}
The mean of this set is calculated as:
M = (x₁ + x₂ + x₃ + ... + xₙ)/N
In this case, our set is:
{14, 12, 22, 8, 24}
So we have N = 5.
The mean of this set will be:
M = (14 + 12 + 22 + 8 + 24)/5 = 16
The average/mean number of pieces of sushi he got on each trip is 16 pieces.
help plz !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
h=2
Step-by-step explanation:
What is the volume of a rectangular prism that is 1 1/2 inches by 2 1/4 inches by 4 inches? Show your reasoning
help please someone
The volume of the rectangular prism is given by the equation
A = 13 1/2 inches³
What is the Volume of a Rectangle?
The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
Let the volume of the rectangular prism be represented as A
Now , the equation will be
The length of the rectangular prism L = 1 1/2 inches
The length of the rectangular prism L = 1.5 inches
The width of the rectangular prism L = 2 1/4 inches
The width of the rectangular prism L = 2.25 inches
The height of the rectangular prism L = 4 inches
So , the volume of the rectangular prism A = Length x Width x Height
Substituting the values in the equation , we get
The volume of the rectangular prism A = 1.5 x 2.25 x 4
On simplifying the equation , we get
The volume of the rectangular prism A = 13.5 inches³
Hence , the volume of rectangular prism is 13.5 inches³
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Peggy was taking a timed 50-question test. She was able to correctly answer 60% of the questions but had to skip the rest. How many questions did Peggy answer correctly?
Answer:
30 questions
Step-by-step explanation:
60% or 0.60 x 50 questions = 30
Find an expression which represents the sum of (9x+4y) and (-6x+4y) in simplest terms.
Answer:
54x+16y
Step-by-step explanation: u have insta
Ok the answer Is 3x+8y trust me it'll save you in algebra
Find the slope given the points (-2,-9) and (-1,-3).
will give brainliest!!!!
Answer:
The slope is 6
Step-by-step explanation:
Y2-Y1 / X2-X1
-3-(-9) / -1-(-2)
6
Answer:
m = 6
Step-by-step explanation:
slope (m) = rise / run
rise = y2 - y1 = -3 - (-9) = 6
run = x2 - x1 = -1 - (-2) = 1
slope = 6/1 = 6
What is the slope of the line?
Answer:
zero slope
Step-by-step explanation:
the equation of line r is y= -7/2x + 3. line s is parallel to line r. what is the slope of line s?
Answer:
m = -7/2
Step-by-step explanation:
If two lines are parallel, they have the same slope. The slope of r is -7/2 (y=mx+b), so the slope of r is also -7/2.
30 points!!!! ASAP
Triangle ABC is transformed to triangle A′B′C′, as shown below:
A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair 3, 0, B at ordered pair 4, negative 2, C at ordered pair 1, negative 3. A triangle A prime B prime C prime has A prime at ordered pair negative 3, 0, B prime at ordered pair negative 4, negative 2, C prime at ordered pair negative1, negative 3.
Which equation shows the correct relationship between the measures of the angles of the two triangles?
The measure of angle ABC = The measure of angle B prime C prime A prime
The measure of angle ABC = The measure of angle C prime A prime B
The measure of angle BCA = The measure of angle C prime A prime B prime
The measure of angle BCA = The measure of angle B prime C prime A prime
Answer:
D
Step-by-step explanation:
Answer:
The measure of angle BCA = The measure of angle B prime C prime A prime