Answer:
Therefore x = 1 is an extraneous solution.
Step-by-step explanation:
The solution to the equation StartFraction 1 Over x minus 1 EndFraction = StartFraction x minus 2 Over 2 x squared minus 2 EndFraction
[tex]\Rightarrow \frac{1}{x - 1} = \frac{x- 2}{2x^2-2} \hspace{0.3cm} \Rightarrow \hspace{0.3cm} 2x^2 - 2 = (x-1)(x-2)[/tex]
therefore [tex]2x^2 - 2 = x^2 - 3x + 2 \hspace{0.3cm} \Rightarrow \hspace{0.3cm} x^2 + 3x - 4 = 0[/tex]
therefore [tex]x^2 + 3x - 4 = 0 \hspace{0.3cm} \Rightarrow = \hspace{0.3cm} (x-1)(x+4) = 0 \\[/tex]
therefore x = 1 and x = -4 but we can see that if we place x = 1 in the original solution then [tex]\frac{1}{x-1} = \frac{1}{1-1} = \frac{1}{0}[/tex] which is indeterminate.
Therefore x = 1 is an extraneous solution.
Answer:
C. x = 1
Step-by-step explanation:
Which solution to the equation StartFraction 1 Over x minus 1 EndFraction = StartFraction x minus 2 Over 2 x squared minus 2 EndFraction is extraneous?
x = 1 and x = –4
neither x = 1 or x = –4
x = 1
x = –4
Question text
If x − 2 = 1/3, then what is the value of x to the power of 2 − 4x + 4?
Answer: 1/9
Step-by-step explanation:
it cost $45.75 for 5 apple pies. give the point of the unit rate
Area of a rectangle is 100 sq ft. The length is 10 ft longer than twice it’s width. What is the length and the width.
The length of the rectange is 20ft and width of the 5ft.
Step-by-step explanation:
Let us consider a rectangle and its area is known to be 100 sq ft.
We are given the information that the length of the rectangle is 10ft longer than twice its width.
⇒Length l = 2w+10.
Where w is the width of the rectangle.
The formula for area of the rectangle A = length × width.
A= (2w+10)×w.
100 = [tex]2w^2+10w[/tex].
0=[tex]2w^2+10w-100[/tex].
Thus it forms an quadratic equation we have to solve for the solution.
0=(2w-10)(w+10).
2w-10=0. w+10=0.
2w=10. w=-10. (negative value cannot be choosed.)
w=[tex](\frac{10}{2} )[/tex].
w=5ft.
Thus width is is 5 ft.
Length = 2(5)+10.
=10+10.
=20ft.
Thus the length is 20ft.
HELP NOW BRANLIEST AND 15 points
Answer: C A L C U L A T O R probably on calculator soup
Step-by-step explanation:
Answer:
look at the picture shown
the sum of two consecutive integers is one less than three times the smallest integer. find the two integers
Answer:
n + (n+1) = 3n -1
n = 2
the integers are 2 and 3
Step-by-step explanation:
Leah wrote 2 different fractions with the same denominator.Both fractions were less than 1. Can their sum equal 1? Can their sum be greater than 1? Explain.
Answer:
1. Yes
2. Yes
Step-by-step explanation:
Leah wrote 2 different fractions with the same denominator. Both fractions were less than 1.
1. Can their sum equal 1?
Let Leah fractions be [tex]\dfrac{6}{7}[/tex] and [tex]\dfrac{1}{7}.[/tex] Both these fractions have the same denominators and are less than 1. Find their sum:
[tex]\dfrac{6}{7}+\dfrac{1}{7}=\dfrac{7}{7}=1[/tex]
2. Can their sum be greater than 1?
Let Leah fractions be [tex]\dfrac{6}{7}[/tex] and [tex]\dfrac{5}{7}[/tex]. Both these fractions have the same denominators and are less than 1. Find their sum:
[tex]\dfrac{6}{7}+\dfrac{5}{7}=\dfrac{11}{7}=1\dfrac{4}{7}>1[/tex]
Two fractions with the same denominator can sum to 1 if their numerators add up to the denominator, or they can sum to more than 1 if their numerators together exceed the denominator. This is based on the concept of adding fractions where only the numerators are summed.
Leah wrote two different fractions with the same denominator, and both were less than 1. Can their sum equal 1? Can their sum be greater than 1? The answer to both questions depends on the value of the numerators. Fractions represent parts of a whole. For two fractions with the same denominator to have a sum of 1, the numerators must add up to the denominator. If their sum is greater than the denominator, then the total sum would be greater than 1.
For example, if we have fractions ½ and ¾, their sum is ½ + ¾ = ¾ which is less than 1. However, if we have ¾ and ¾, the sum equals 6/4, which reduces to 1½, a sum greater than 1.
In conclusion, two fractions with the same denominator and each less than 1 can sum to 1 if the numerators total the denominator, or can sum to greater than 1 if the numerators together exceed the denominator. An important aspect of adding fractions is that we only add the numerators and never the denominators.
The value of y varies directly as the square of x and y=36 when x=3. What is y when x=4?
Answer: y = 64
Step-by-step explanation:
y <> x² ----------------------- 1
y = kx² ----------------------- 2
36 = 3²k
36 = 9k
K = 36/9
= 4.
To find y when x = 4, we substitute for x in equation 2
y = kx²
y = 4²k
y = 16 x 4
y = 64
The value of y, which varies directly as the square of x, is determined by first identifying the constant of variation from the given values, in this case, y = 36 when x = 3. The constant is found to be 4. Using this constant (k), when x is 4, y will be 64.
Explanation:The value of y varies directly as the square of x, which is represented mathematically as y = kx², where k is the constant of variation. Using the given that y = 36 when x = 3, we can determine k by substituting these values into the equation. Thus, k = y/x² = 36/9 = 4. Now, having the value for k, we can find y when x = 4 by substituting these values into the equation: y = kx² = 4×16 = 64. Therefore, y equals 64 when x equals 4 in the given relation.
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if sin theta = cos theta then find the value of theta
Step-by-step explanation:
[tex] \because \sin \theta = \cos \theta \\ \\ \therefore \: \sin \theta = \sin(90 \degree - \theta) \\ \\ \therefore \: \theta = 90 \degree - \theta \\ \\ \therefore \: \theta + \theta= 90 \degree \\ \\ \therefore \: 2\theta = 90 \degree \\ \\\therefore \: \theta = \frac{90 \degree }{2} \\ \\ \huge \orange{\boxed{\therefore \: \theta = 45 \degree}}\\ \\[/tex]
The deepest part of a swimming pool is 12 feet deep the shallowest part of the pool is 3 feet deep. what is the ratio of the depth of the deepest part of the pool to the depth of the shallowest part of the pool?
Answer:
12 : 3
Step-by-step explanation:
You put the depth of the deep before the depth of the shallowness to get the ratio. The ratio could be written like,
12 : 3
12 / 3
12 to 3
Answer:
the answer to the question is 12:3
Four trucks were used to make deliveries. The drivers recorded the number of miles driven and the amount of gasoline
Which truck drove the fewest number of miles per gallon of gas?
Answer:
b
Step-by-step explanation:
Answer:
Truck D
Step-by-step explanation:
36:4 = 9 best mpg
On a certain hot summer's day, 391 people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $752.75. How many children and how many adults swam at the public pool that day?
Final answer:
there were 127 children and 264 adults.
Explanation:
To solve this problem, we use a system of equations. Let's denote the number of children as C and the number of adults as A. We know two facts: the total number of people is 391, and the total amount of money collected is $752.75. Therefore, we have the equations:
C + A = 3911.25C + 2.25A = 752.75To solve this system, we first multiply the first equation by 1.25 to align the coefficient of C with the second equation:
1.25(C + A) = 1.25(391)1.25C + 1.25A = 488.75Next, we subtract this result from the second equation to eliminate C, leaving an equation in terms of A only:
2.25A - 1.25A = 752.75 - 488.75
A = (264) / 1 = 264
Substituting the value of A into the first equation, we find the value of C:
C + 264 = 391
C = 127
Therefore, there were 127 children and 264 adults who swam at the public pool that day.
A patient’s weight is recorded as 75 kilograms. How many pounds does the patient weigh? Round your answer to the nearest pound.
answer: about 165 lbs
to go from kilograms to pounds, you multiply by 2.205 to get the approximate answer.
75x2.205≈165
brainliest and 100 pts!!!!!!!!!!!!!!!!!!!
Natalie's coach has a stopwatch that records times to the nearest thousandth of a second. Natalie ran a given distance in 25.453 seconds.
What is Natalie's time rounded to the nearest tenth of a second?
Enter your answer in the box.
___s
Answer:
25.5
Step-by-step explanation:
The table shows how a leading automobile dealer plans to spend its advertising dollars for this year. If this company plans to increase its budget by 5% next year, approximately how much will it spend on social media ads? Advertising Budget: $81,000 48.5% Television 23% Magazines 20% Newspapers 7% Radio 1% Billboards 0.5% Social Media $405 $20 $425 $4,250
Answer:
$425
Step-by-step explanation:
Answer:
the answer is c, $425
Step-by-step explanation:
just did the quiz
find the x-intercepts and y-intercepts of 10x+6y=-4
The x intercept is [tex](\frac{-2}{5}, 0)[/tex]
The y intercept is [tex](0, \frac{-2}{3})[/tex]
Solution:
Given equation is:
10x + 6y = -4
The x intercept is the point where the line crosses the x axis
The y intercept is the point where the line crosses the y axis
Find x intercept:
Substitute y = 0 in given equation
10x + 6(0) = -4
10x = -4
[tex]x = \frac{-4}{10}\\\\x = \frac{-2}{5}[/tex]
Thus the x intercept is [tex](\frac{-2}{5}, 0)[/tex]
Find y intercept:
Substitute x = 0 in given equation
10(0) + 6y = -4
[tex]6y = -4\\\\y = \frac{-4}{6}\\\\y = \frac{-2}{3}[/tex]
Thus the y intercept is [tex](0, \frac{-2}{3})[/tex]
Ella and her children went into a bakery and where they sell cookies for $0.50 each and brownies for $2.25 each. Ella has $15 to spend and must buy a minimum of 9 cookies and brownies altogether. If Ella decided to buy 5 cookies, determine the maximum number of brownies that she could buy. If there are no possible solutions, submit an empty answer.
Answer: 5 brownies
Step-by-step explanation:
cookies = 5 x $0.50 = $2.5
$15 - $2.5 = $12.5
$12.5 divided by $2.25 = $5.555
so at the most ella can buy 5 brownies if she buys 5 cookies
Answer:
If each cookie is .50 and she wants to buy 5 cookies @ .50= $2.50
Than subtract $2,50 from $15.00 (which she has to spend you have $12.50
Then divide 2.25 into $12.5 and you get an answer of 5 brownies with a $1.30 extra to spend
Step-by-step explanation:
Which of the following expressions are equivalent to -8 -(-1)-5
Answer:
Step-by-step explanation:
-8 -(-1)-5
Opening bracket
= -8 + 1 - 5
= -12
The student's expression -8 -(-1)-5 simplifies to -8 + 1 - 5, which is equal to -12 after performing the addition and subtraction sequentially.
The expression in question is -8 -(-1)-5. To solve this, we need to recognize that subtracting a negative number is the same as adding its positive equivalent. So, the expression simplifies to -8 + 1 - 5.
Now, we perform the addition and subtraction in the order they appear:
First, we add 1 to -8, which gives us -7.Then, we subtract 5 from -7, which gives us -12.Therefore, the expression -8 -(-1)-5 is equivalent to -12.
The soda can is a cylinder with a diameter of 2 inches and a height of 5 inches. What is the area
Answer:
?
Step-by-step explanation:
Fill in the table using this function rule. y=-3x+5
The missing values are 11, 8, 5 and 2 respectively.
The picture of the question in the attached figure
we have
y=-3x+5
Substitute the different values of x in the linear equation, to obtain the
different values of y in the table
For x-2-> y=-3(-2)+5=11
For x=-1-> y=-3(-1)+5=8
For x-0->9=-3(0)+5=5
For x-1->y=-3(1)+5=2
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Russell randomly surveys seventh-graders in his school and finds that 6 of 30 attend summer camp. If there are 200 seventh-graders in his school, about how many are expected to attend summer camp? Enter your answer in the box.
----------eighth -graders
Answer:
40
Step-by-step explanation:
6 of 30 is the ratio 6 to 30 or 6/30.
6/30 reduces to 1/5
The survey shows that 1/5 of the students attend summer camp.
1/5 of 200 = 1/5 * 200 = 40
Roxy has some necklaces. Kelly has 4 times more rings than Roxy. Together they have 35. How many necklaces does Roxy have?
Answer:
Roxy has 7 necklaces.
Step-by-step explanation:
35 = n + 4n
35 = 5n
5 = 5
n = 7
The problem is a simple algebra problem related to ratios. By setting up an equation according to the given information, we find that Roxy has 7 necklaces.
Explanation:This is a math problem concerning ratios and simple algebra. Let's denote the number of necklaces that Roxy has as R. Then, Kelly has 4 times more rings, which is 4R. Together they have 35. So, the equation can be set up as:
R + 4R = 35
Combine like terms, you get:
5R = 35
Then, you can solve for R by dividing both sides by 5:
R = 35/5 = 7
So, Roxy has 7 necklaces.
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Prime factor of 2080
Answer:
2 x 2 x 2 x 2 x 2 x 5 x 13
Step-by-step explanation:
The Prime Factorization is:
2 x 2 x 2 x 2 x 2 x 5 x 13
In Exponential Form:
25 x 51 x 131
CSV Format:
2, 2, 2, 2, 2, 5, 13
The prime factors of 2080 are 2, 2, 2, 2, 5, and 13.
Divide 2080 by the smallest prime number, which is 2:
2080 ÷ 2 = 1040
Continue dividing by 2:
1040 ÷ 2 = 520
Continue dividing by 2:
520 ÷ 2 = 260
Continue dividing by 2:
260 ÷ 2 = 130
Continue dividing by 2:
130 ÷ 2 = 65
Now, 65 is not divisible by 2.
Move to the next prime number, which is 5:
65 ÷ 5 = 13
13 is a prime number.
So, the prime factors of 2080 are 2, 2, 2, 2, 5, and 13. In exponential form, this can be written as 24 * 5 *13.
Kelly has a rock garden with a length of 6 feet. She constructs a scale model of the rock garden using
the scale 1 inch:2 feet.
What is the length of the garden in her model? Show your work, including your proportion.
If the width is 5 inches for the scale model and the scale is still 1 inch to 2 feet, will her scale
model drawing fit on a piece of paper that is 8.5 inches by 7 inches? Why or why not?
Answer:
Answer:
3 inches
It will fit in the paper.
Step-by-step explanation:
In the scale drawing the 2 feet original length is converted to 1 inch drawing length as Kelly constructs a scale model of the rock garden using the scale 1 inch : 2 feet.
Now the proportion is 1 inch : (2 × 12) inches = 1 : 24 {Since 1 foot is equivalent to 12 inches}
Now, maintaining that scale ratio the 6 feet original length of the garden will be converted to [tex]\frac{1}{24} \times (6 \times 12) = 3[/tex] inches in the drawing.
It is also given that the width of the garden in the scale model is 5 inches and the scale is still 1 inch : 2 feet.
Therefore, the dimensions of the garden in the model is 3 inches by 5 inches and this will fit on a piece of paper that is 8.5 inches by 7 inches. (Answer)
in Eduardo’s collection, the number of butterflies is 12 more than twice the number of moths. If there are x moths, write an expression to represent the number of butterflies he has.
Answer:
An expression to represent the number of butterflies he has is y = 12 + 2x
Step-by-step explanation:
Let the number of butterflies in Eduardo’s collection be y
Then according to the question
The number of moths = x
The number of butterflies y = 12 + twice the number of moths---------(1)
Twice the number of moths = [tex]2 \times \text{number of moths}[/tex]
Twice the number of moths = 2x -----------------------(2)
Substituting equation (2) in (1)
The number of butterflies y = 12 + 2x
Solve the equation for the variable
X/2+1=6
How many times does 7 go into 52
Answer:
7.43
Step-by-step explanation:
52/7 = 7.4285714...
that can be shortened to 7.43
7.43
Step-by-step explanation:
52/7 = 7.428
Consider the formula
d
=
m
V
d=
V
m
d, equals, start fraction, m, divided by, V, end fraction, where
d
dd represents density,
m
mm represents mass and has units of kilograms
(kg)
(kg)left parenthesis, start text, k, g, end text, right parenthesis, and V
Represents volume and has units of cubic meters
(m3)
(m
3
)start text, left parenthesis, m, end text, cubed, right parenthesis.
Select an appropriate measurement unit for density.
Option C:
[tex]$\frac{\text{kg}}{\text{m}^3}}[/tex]
Solution:
Given data:
[tex]$\text{d}=\frac{\text{m}}{\text{V}}[/tex]
where "d" represents density
"m" represents mass
"V" represents volume
The unit of mass is kilogram (kg).
The unit of volume is cubic metres [tex](\text{m}^3)[/tex].
To find an appropriate measurement unit for density:
[tex]$\text{d}=\frac{\text{m}}{\text{V}}[/tex]
Substitute kg and [tex](\text{m}^3)[/tex] in mass and volume respectively.
[tex]$\text{d}=\frac{\text{kg}}{\text{m}^3}}[/tex]
Option C is the correct answer.
An appropriate measurement unit for density is [tex]$\frac{\text{kg}}{\text{m}^3}}.[/tex]
Answer:
option b Kg/m3
Step-by-step explanation:
same as other answer
What is 3/4(121+8) in distributive property
Answer:
387/4
Step-by-step explanation:
121+8=129
3/4(129)=387/4
a reflection through what line will move P(-4, 5) to P'(4,5)?
r __________
Step-by-step explanation:
Reflection through y-axis.
Answer:wait
Step-by-step explanation:
What is 1/4 * 4x + 8