Operations with Radical ExpressionsThis is a new topic that I’ve never done before so I’m not sure where to start
Answers
We need to simplify the expression:
\(-2\sqrt[]{20}-2\sqrt[]{24}-2\sqrt[]{24}\)We can start by grouping the second and third terms since they have the same factor:
\(-2\sqrt[]{24}-2\sqrt[]{24}=(-2-2)\sqrt[]{24}=-4\sqrt[]{24}\)Then, we need to simplify:
\(-2\sqrt[]{20}-4\sqrt[]{24}\)Now, we can factor the number inside each square root:
\(\begin{gathered} 20=2\cdot2\cdot5=2^2\cdot5 \\ \\ 24=2\cdot2\cdot2\cdot3=2^2\cdot6 \end{gathered}\)And we can use the following properties:
\(\begin{gathered} \sqrt[]{a.b}=\sqrt[]{a}\cdot\sqrt[]{b} \\ \\ \sqrt[]{n^{2}}=n,\text{ for }n\ge0 \end{gathered}\)Then, we obtain:
\(\begin{gathered} \sqrt[]{20}=\sqrt[]{2^2\cdot5}=\sqrt[]{2^{2}}\cdot\sqrt[]{5}=2\sqrt[]{5} \\ \\ \sqrt[]{24}=\sqrt[]{2^2\cdot6}=\sqrt[]{2^{2}}\cdot\sqrt[]{6}=2\sqrt[]{6} \end{gathered}\)Using the above results in the expression, we find:
\(-2\sqrt[]{20}-4\sqrt[]{24}=-2\cdot2\sqrt[]{5}-4\cdot2\sqrt[]{6}=-4\sqrt[]{5}-4\cdot2\sqrt[]{6}\)Since both terms have the factor -4, we can group it to obtain:
\(-4(\sqrt[]{5}+2\sqrt[]{6})\)Therefore, a way to simplify the given expression is by writing it as:
\(-4(\sqrt[]{5}+2\sqrt[]{6})\)Related Questions
Pre-calculus please help and please explain
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x
f(x)= 4/x and g(x)= 4/x
Answers
We have to make sure the functions are simplified into just x to verify that they are inverses. To do this, we have to compose the functions into each other.
f(g(x)) = 4/(4/x)
The 4's cancel out and you're left with just x
f(g(x)) = x
Let's compose f(x) into g(x) now.
g(f(x)) = 4/(4/x)
The 4's cancel out and you're left with just x
Since both functions are equal to x after composing them into each other, we can confirm that they are indeed inverses of each other.
4x-5 2x+7 Find the value of x
answers should be from
27
37
47
57
Answers
4x - 5 = 2x + 7
First, let's simplify the equation by combining like terms:
4x - 2x = 7 + 5
2x = 12
Next, divide both sides of the equation by 2 to solve for x:
x = 12 / 2
x = 6
Therefore, the value of x that satisfies the equation is 6. None of the provided answer options (27, 37, 47, 57) are equal to 6.
What is 36,666 less 75,002
Answers
Answer:
38336
Step-by-step explanation:
75002 - 36666 = 38336
Solve the inequality -3 < 3/2(2-x)<5
Answers
Answer:
Step-by-step explanation:
12. How many planes are shown in the figure?
Your answer
Answers
Answer:
Six planes
Step-by-step explanation:
A plane is defined by the three different points on the same surface.
So the planes given in the picture are,
Plane A or plane MSR
Plane PWM
Plane QTS
Plane WTS
Plane QPN
Plane PQT
Therefore, six faces of the given polygon will define the six planes.
The IQ scores and science test scores of fourth grade students is given by the line of best fit ŷ = −20.3 + 0.7489s, where ŷ is the predicted science score and s is the IQ score. An actual science test score for a student is 52.6 with an IQ of 100.
Find and interpret the residual.
−1.99; The line of best fit underpredicts the student's science test score.
1.99; The line of best fit overpredicts the student's science test score.
1.99; The line of best fit underpredicts the student's science test score.
−1.99; The line of best fit overpredicts the student's science test score.
Answers
-19.99; The line of best fit underpredicts the student's science test score.
So correct option is A.
What do you mean by prediction?A prediction is an estimation or forecast about future events or conditions, based on past data and trends, current information, and/or mathematical models. Predictions can be made in various fields, such as finance, weather, sports, social sciences, and natural sciences. The accuracy of predictions depends on many factors, including the quality of the data used, the assumptions made, the complexity of the system being analyzed, and the reliability of the methods used. Predictions are not always accurate and are often subject to revision as new information becomes available.
The predicted science score for the student with IQ 100 can be calculated using the line of best fit:
ŷ = −20.3 + 0.7489 * 100 = 71.59
The residual is the difference between the actual science test score and the predicted science score:
residual = actual score - predicted score = 52.6 - 71.59 = -19.99
So the line of best fit underpredicts the student's science test score by 19.99 points.
Therefore, the residual is:
-19.99; The line of best fit underpredicts the student's science test score.
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Circle A has a radius of 5 units. Circle B has a radius of 3 inches. Which best represents the area of the figure below?
Answers
Since the formula is (5x5)3.14+(3x3)3.14≈107
Rewrite 2/3 : 1/15 as a unit rate
Answers
Answer: 10:1
Step-by-step explanation:
I don’t know. I took my math exam and got the wrong answer, this is the correct one. i hope i helped someone :)
2/3 : 1/15 as a unit rate is \(10:1\) .
What is a unit rate?A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
According to the question
\(\frac{2}{3} : \frac{1}{15}\) as a unit rate
As, unit rate is having denominator = 1
So,
\(\frac{2}{3} : \frac{1}{15}\)
= \(\frac{2}{1} : \frac{1}{5}\)
= \(10:1\)
Hence, 2/3 : 1/15 as a unit rate is \(10:1\) .
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What is the range of f?
O -15≤x≤35
Oy > 15
Oy> 35
O all real numbers
Answers
The possible values for the range of f(x) are given by:
y > 15.y > 35.all real numbers.What is the range of a function f(x)?The range of a function f(x) is the set that contains all possible output values for the function. Looking at the graph of the function, the range is composed by the values of y.
In this problem, the function is not given, so I can't give you an exact answer, but since the range is composed by the values of y, the first option is not possible, and the possible values for the range of f(x) are given by:
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Marcus was interested in whether the frequency that students check emails impacts their grades in the class. He categorized students into three groups. Those who checked email daily, those who checked email at least 2x a week (but not every day), and those who checked email less than 2x a week. Below are the GPAs for the students he studied. Conduct the steps of hypothesis testing on these data.
Table of data: GPAs for students separated by how often they check their email
Daily 2x a week Less than 2x a week
3.6 3.5 2.9
3.5 3.4 3.0
3.7 3.2 3.2
4.0 3.2 2.7
Answers
The steps to conduct the steps of hypothesis testing on these data are:
State the null hypothesis (H0) as well as the alternative hypothesis (H1):Select the significance level (alpha): Select the right test statistic:Formulate the decision rule:Compute the test statistic as well as the p-value:Decide on a decision.What is the hypothesis?The hypothesis will be:
H0: Email frequency does not affect grades.H1: Email frequency affects grades.Since we are comparing (GPAs) of three groups (students who check e-mail day by day, students who check mail at least 2x a week, and students who check mail less than 2x a week), one can be able to make use of one-way analysis of variance (ANOVA) as the fitting test measurement.
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Two positive numbers are in the ratio 2 : 3. Find the numbers if (a) their sum is 55 and (b) their product is 384.
Answers
say the numbers are "a" and "b", we know that they're in the ratio of 2:3, or namely that
\(\stackrel{\textit{in the ratio of 2 to 3}}{a~:~b\qquad \qquad 2:3}\qquad \qquad \implies \qquad \cfrac{a}{b}=\cfrac{2}{3}\implies \cfrac{3a}{2}=b \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{their sum is 55}}{a + b = 55}\implies a + \cfrac{3a}{2}=55\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( a + \cfrac{3a}{2} \right)=2(55)} \\\\\\ 2a+3a=110\implies 5a=110\implies a = \cfrac{110}{2}\implies \boxed{a = 22}\)
\(\stackrel{\textit{we know that}}{\cfrac{3a}{2}=b}\implies \cfrac{3(22)}{2}=b\implies \boxed{33=b} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{their product is 384}}{ab=384}\implies a\left( \cfrac{3a}{2} \right)=384\implies \cfrac{3a^2}{2}=384\implies 3a^2=768 \\\\\\ a^2=\cfrac{768}{3}\implies a^2=256\implies a=\sqrt{256}\implies \boxed{a=16} \\\\\\ \stackrel{\textit{we know that}}{\cfrac{3a}{2}=b}\implies \cfrac{3(16)}{2}=b\implies \boxed{24=b}\)
The positive numbers for both the parts are obtained as 22,33 and 16,24 respectively.
How to write a linear equation?A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.
(a) As per the question, the numbers can be considered as 2x and 3x respectively.
Then, the equation for their sum can be written as follows,
3x + 2x = 55
⇒ 5x = 55
⇒ x = 11
The numbers are obtained as 2 × 11 = 22 and 3 × 11 = 33.
(b) Similarly, the equation for the product of numbers can be written as,
3x × 2x = 384
⇒ 6x² = 384
⇒ x² = 64
⇒ x = 8
The numbers are obtained as 2× 8 = 16 and 3 × 8 = 24.
The required number for both the cases are 22,33 and 16,24 respectively.
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mathmatically indication example with solution
Answers
A mathematically indication example would be to solve the equation 3x + 2 = 14 for the value of x. The solution would be 4.
How to solve the equation ?Looking for a mathematically indication example, we can consider a simple mathematical equation with one variable and solve it.
The equation would be 3 x + 2 = 14.
So we can solve for the equation to be :
3x + 2 - 2 = 14 - 2
3x = 12
3 x / 3 = 12 / 3
x = 4
In conclusion, the mathematically indication example would be 3x + 2 = 14 and the value of x would be 4.
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Which of the following is the point-slope form of the equation with slope 3 that goes through the point (4,2)?
Answers
Answer:
y–y1 =m (X–X1)
y–2=3(x–4)
y=3x–10
the soccer team manager plans to have 2 gallons of water for every 4 players on the team during practice. determine whether the statements about ratios are true or false.
A. The team manager needs 1 gallon of water for every 1 player
` true or false
B. The ratio of number of players to gallons of water is 2:1
` true or false
C. The team manager ould need 4 gallons of water for 10 players
` true or false
D. For 30 players, the team manager would need 15 gallons of water ` true or false
Answers
Answer:
A.=False
B.=True
C.=False
D.=True
Step-by-step explanation:
The original ration is 2 gallons of water for 4 players.
Each player requires 1/2 gallon of water.
To get the amount of water needed multiply 1/2 by the amount of players.
1*(1/2) does not equal 1
2*(1/2) equals 1
10*(1/2) does not equal 4
30*(1/2) equals 15
please help me with this sum
Answers
Hello there!
4,968:8=621
3,960:6=660
2,728:4=682
1,584:2=792
2,527:7=361
2,586:3=862
4,205:5=841
8,550:9=950
2,200:4=550
1,923:3=641
Hope this helps you!
~Just a joyful teen
\(SilentNature\\(GraceRosalia)\)
bodmass
-3[2/6+8{-9/3(8-5*3)-6}]
Answers
9514 1404 393
Answer:
-361
Step-by-step explanation:
Your calculator can tell you the result. It is -361.
Start with the inner parentheses and work outward. Do multiplication and division in the order shown, left to right, before addition or subtraction.
-3[2/6+8{-9/3(8-5*3)-6}]
= -3[2/6+8{-9/3(8-15)-6}]
= -3[2/6+8{-9/3(-7)-6}]
= -3[2/6+8{-3(-7)-6}]
= -3[2/6+8{21-6}]
= -3[2/6+8{15}]
= -3[1/3+8{15}]
= -3[1/3+120]
= -3[361/3]
= -361
![bodmass-3[2/6+8{-9/3(8-5*3)-6}]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/JvDTbuj3vjL83osTliC1Q0nbOaMQa0mK.png)
Solve this system of equations for x using the addition method. (Must show steps of addition method to get credit. Do not solve using the substitution method. )
Answers
hi
here is the answer
i hope it helps
good luck:))
What is the measure of each exterior angle of the right triangle?
x =
y =
z =
Answers
Answer:
x = 90
y = 134
z = 136
Step-by-step explanation:
Sum of interior angles of a triangle are 180
Linear angles are 180
So 180 - 90 = 90
180 - 44 = 136
180 - 90-44 = 46
180 - 46 = 134
What is the measure of angle x?
Enter your answer in the box.
+
1470
x =
1 2 3 4 5 6 7
5.
Answers
Answer:
x=43 degrees
Step-by-step explanation:
Subtract 47 from 90 to get the angle next to 47 degrees which is 43 degrees and x is also 43 degrees because they form vertical angles with each other
An energy bar company manufactures peanut butter and chocolate bars.
Peanut butter bars cost 25¢ per lb.
The chocolate bars cost 30¢ per lb.
The company sold 260 lbs of bars for $71.
How many of the bars sold were peanut butter?
Answers
Answer:
sold 120 chocolate bars
sold 140 peanut butter bars
Step-by-step explanation:
x = peanut butter bars
y = chocolate bars
x + y = 260, total lbs
0.25x + 0.30y = 71, money
solve double variable equation
multiply -4 on both sides for 2nd equation
-x + -1.2y = -284
add both equations together
-0.2y = -24
y = 120
x = 260 - 120
x = 140
sold 120 chocolate bars
sold 140 peanut butter bars
Please help I can’t figure it out
Answers
well, let's first off find out how many actually do favor it in the first place.
\(\stackrel{total}{4000}\cdot \cfrac{3}{8}\implies \stackrel{seniors}{\text{\LARGE 1500}}\hspace{12em}\stackrel{total}{4000}-1500=\stackrel{not~seniors}{\text{\LARGE 2500}} \\\\[-0.35em] ~\dotfill\)
\(\stackrel{seniors}{\text{\LARGE 1500}}\cdot \cfrac{1}{6}\implies \stackrel{in~favor}{\text{\LARGE 250}}\hspace{11em} \stackrel{not~seniors}{\text{\LARGE 2500}}\cdot \cfrac{3}{5}\implies \stackrel{in~favor}{\text{\LARGE 1500}} \\\\[-0.35em] ~\dotfill\\\\ 250+1500\implies \stackrel{in~favor}{\text{\LARGE 1750}}\hspace{15em}\boxed{\underset{\textit{do not favor it}}{\stackrel{4000~~ - ~~1750}{\text{\LARGE 2250}}}}\)
have a good day..?.......
Answers
Answer:
Thank you......
Step-by-step explanation:
Same to you.....
youuu toooooooooooo let gooooooo
2
Linda paid $5.50 for 4 pounds of
strawberries. How much did she pay
per pound of strawberries?
Answers
She paid $1.375 per pound of strawberries.
What is the unit rate?
When expressed rate as a fraction, a unit rate has a denominator of 1.
Since 4 pounds cost $5.50, 1 pound of strawberries will cost 5.50/ 4 ≈ $1.375.
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Gameron wants to measure a poster frame, but he only has a sheet of
paper that is 8 1/2 by 11 inches
a.
He lays the long edge of the paper along the long edge of the frame several times
and finds the frame is 4 papers long. How long is this in inches?
In feet?
b.
He lays the short edge of the paper along the short edge of the frame several times
and finds the frame is 3 papers wide. How long is this in inches?
In feet?
plsss help!
Answers
The measure of the frame in feet of the length and width are 3.667 feet and 2.125 feet respectively.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: The measure of the frame is 8.5 inches and 11 inches
a) if the frame is 4 papers long then we have the length of the frame as
11×4=44 inches (since he lays the paper along the edge of frame)
We know 1 inch= 0.0833 foot
Thus 44 inches= 3.66667 foot
b) Again if he lays the paper along the short edge than the width of the frame is 3×8.5=25.5 inches
∴25.5 inches= 2.125 feet
Hence, The measure of the frame in feet of the length and width are 3.667 feet and 2.125 feet respectively.
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A quadratic function has roots of 2 and - 5, and passes through the points (3,24) and (1, -18).
Determine an equation for the function in factored form.
Answers
Answer: y + 4 = (x - 3)2, y = (x - 1)(x - 5
Step-by-step explanatin
In this lesson, you will see some advantages of a third form called factored form. Below are graphs of three equations
What is (x³-8x² + 6x +41) ÷ (x-4)
Answers
Step 1: Write the dividend and divisor:
\(\sf\:\frac{{x^3 - 8x^2 + 6x + 41}}{{x - 4}} \\ \)
Step 2: Divide the first term of the dividend by the first term of the divisor:
\(\sf\:\frac{{x^3}}{{x}} = x^2 \\ \)
Step 3: Multiply the divisor (x - 4) by the result (x^2):
\(\sf\:(x - 4) \cdot (x^2) = x^3 - 4x^2 \\ \)
Step 4: Subtract the result from the original dividend:
\(\sf\:(x^3 - 8x^2 + 6x + 41) - (x^3 - 4x^2) = -4x^2 + 6x + 41 \\ \)
Step 5: Bring down the next term from the dividend:
\(\sf\:\frac{{-4x^2 + 6x + 41}}{{x - 4}} \\ \)
Step 6: Repeat steps 2-5 with the new dividend:
\(\sf\:\frac{{-4x^2}}{{x}} = -4x \\ \)
\(\sf\:(x - 4) \cdot (-4x) = -4x^2 + 16x \\ \)
\(\sf\:(-4x^2 + 6x + 41) - (-4x^2 + 16x) = -10x + 41 \\ \)
Step 7: Bring down the next term from the dividend:
\(\sf\:\frac{{-10x + 41}}{{x - 4}} \\ \)
Step 8: Repeat steps 2-5 with the new dividend:
\(\sf\:\frac{{-10x}}{{x}} = -10 \\ \)
\(\sf\:(x - 4) \cdot (-10) = -10x + 40 \\ \)
\(\sf\:(-10x + 41) - (-10x + 40) = 1 \\ \)
Step 9: There are no more terms to bring down, so the division is complete.
Step 10: Write the final result:
The quotient is \(\sf\:x^2 - 4x - 10\\\) and the remainder is 1.
Therefore, the division of \(\sf\:(x^3 - 8x^2 + 6x + 41) by (x - 4) \\\) is:
\(\sf\:(x^3 - 8x^2 + 6x + 41) ÷ (x - 4) \\ \) \(\sf\:= x^2 - 4x - 10 + \frac{{1}}{{x - 4}} \\ \)
There are 65 people coming to your party and each person will need one cup. How many packages of cups should you buy if one package contains 3 cups?
ANWSER:
STEP BY STEP EXAMPLE:
Answers
Answer: 22
Step-by-step explanation: 65 divided by 3 is 22
Answer:
21or22
Step-by-step explanation:
65/3
at a university, 75%, or 1,014, of first-year students take a maths course. How many first-year students are there at the university?
A. s/1,014 = 75/100 ; 76 students
B. s/1,014 = 75/100 ; 761 students
C. 1,014/s = 75/100 ; 1,352
D. 1,014/s = 75/100 ; 714
help me pls!?
Answers
Answer:
C
Step-by-step explanation:
1014=0.75s
1014/0.75=s is the same as 1014/s=0.75
There are 4 pink, 5 yellow, 2 violet and 3 gray marbles
in a hat. You pick 2 marbles from the hat. Marbles are
NOT returned to the hat.
P(pink, then violet)
P(gray, then gray)
P(not yellow, not yellow)
P(yellow, not yellow)
Answers
================================================
Work Shown for problem 1
P(pink, then violet) = P(pink)*P(violet given 1st was pink)
= (4/14)*(2/13)
= 8/182
= 4/91
------------------------------
Work Shown for problem 2
P(gray, then gray)
= P(gray)*P(gray given 1st was gray)
= (3/14)*(2/13)
= 6/182
= 3/91
-------------------------------
Work Shown for problem 3
P(not yellow, not yellow)
= P(not yellow)*P(not yellow given 1st was not yellow)
= (9/14)*(8/13)
= 72/182
= 36/91
-------------------------------
Work Shown for problem 4
P(yellow, not yellow)
= P(yellow)*P(not yellow given 1st was yellow)
= (5/14)*(9/13)
= 45/182
if you vertically compress the quadratic parent function f(x)=x by multiplying by 1/2 what is the equation of the new function
Answers
Answer:
The equation of the new function if you vertically compress the quadratic parent function f(x)=x by multiplying by 1/2 is f(x)=1/2x. This can be obtained by simply multiplying both sides of the equation f(x)=x with 1/2. Therefore, the equation of the new function is f(x)=1/2x.