To get rid of radicals in the denominator of a fraction, you should rationalize the denominator by multiplying the fraction by a helpful form of _____.A.the denominatorB.xC.1D.the numerator
Answers
Given:
To get rid of radicals in the denominator of a fraction
Required:
you should rationalize the denominator by multiplying the fraction by what
Explanation:
In fraction, a number is said to be a quotient, in which the numerator is divided by the denominator.
there are three types of fraction
1. Proper fraction
2. Improper fraction
3. Mixed
Final answer:
But to get rid of radival in the denominator of a fraction, you should rationalize the denimonator by multiplying the fraction with 1
Related Questions
Use substitution to solve each system of equations.y + 1/2x = 34y + 2x = 6
Answers
Answer:
No solution
Explanation:Given the system of eqations:
[tex]\begin{gathered} y+\frac{1}{2}x=3 \\ 4y+2x=6 \end{gathered}[/tex]From the second equation, find x.
[tex]\begin{gathered} 2x=6-4y \\ x=\frac{6-4y}{2} \\ =3-2y \end{gathered}[/tex]Substitute the obtained value of x into the first equation.
[tex]\begin{gathered} y+\frac{1}{2}(3-2y)=3 \\ y+\frac{3}{2}-y=3 \\ \frac{3}{2}=3 \end{gathered}[/tex]which isnotpossible. So, no solution exists.
Decide whether the given orderd pair is a solution to the stystem of equations?I don’t know how to to the bottom equation.
Answers
Given:
[tex]\begin{gathered} y=2x-6 \\ x+y=8 \end{gathered}[/tex]solve the equation for x and y then
[tex]\begin{gathered} x+y=8 \\ \text{put the value of y} \\ x+2x-6=8 \\ 3x=8+6 \\ 3x=14 \\ x=\frac{14}{3} \end{gathered}[/tex]so value of y is:
[tex]undefined[/tex]60% of the
students take the
bus. If there were
120 students on the
busses, how many
total students are
there?
Answers
Answer:
168
Step-by-step explanation:
60%=120
40% of 120
10%12
10%12
10%12
10%12
12×4=48
120+48=168
Find the inverse of the function. g(x)= -5x – 20/7
Answers
Given the function:
[tex]g(x)=\frac{-5x-20}{7}[/tex]To find the inverse function, let us first write it as:
[tex]y=\frac{-5x-20}{7}[/tex]Make x the subject of the equation
[tex]\begin{gathered} -5x-20=7y \\ -5x=7y+20 \\ x=\frac{-7y-20}{5} \end{gathered}[/tex]Replace x by y, and y by x to obtain the inverse function
[tex]y=\frac{-7x-20}{5}[/tex]Where
[tex]y=g^{-1}(x)[/tex]In how many months were there more than two days with thunderstorms? 1 3 5 7
Answers
To find how many months have more than 2 days look at the heights
of the bars
You need to count the bars which height more than 2
There are 5 bars that have a height of more than 2
The answer is 5
Can someone please help me with my math ;( ?
Answers
Step 1:
copy and complete the table below by inputting the data provided.
The marginal frequency numbers are the numbers at the edges of the table except for the number at the bottom right-most corner.
B) Marginal relative frequency is the ratio of the sum of the joint relative frequency in a row or column and the total number of data values
Hence,
[tex]\text{ the lowest marginal frequency }=\frac{107}{232}=0.461[/tex]Joint relative frequency the ratio of the frequency in a particular category and the total number of data values
Therefore,
[tex]\text{ the largest joint frequency }=\frac{63}{111}=0.568[/tex]C)For the circled number, the preferred style is Gothic given that the member is male and the percentage is 0.57
D) The total number of males surveyed = 111
the total number of members surveyed = 232
Hence, the percentage of the total number of choir students surveyed that were males are:
[tex]\frac{111}{232}=0.48[/tex]12 more than the product of 5 and a number x
Answers
Answer: (5*x) + 12 or 5x + 12
Step-by-step explanation: differant sites let you do it defferent ways but if the multipaction sign in an "x" I would do the 2nd one :) Hope it's right, have a great day!
Solve for h by using the inverse (opposite) operations. −5.3+h5=−19.4
Answers
Given:
The given term is -5.3+h/5=-19.4.
The objective is to find the value of h using inverse operation.
Inverse operation states that, if a term is in addition operation with another term, then it will change to subtraction operation while shifting to other side of the equation.
If a term is in multiplication operation, then it change to division operation while shifting to other side of the equation.
The value of h can be calculated as,
[tex]\begin{gathered} -5.3+\frac{h}{5}=-19.4 \\ \frac{h}{5}=-19.4+5.3 \\ \frac{h}{5}=-14.1 \\ h=-14.1(5) \\ h=-70.5 \end{gathered}[/tex]Thus, the value of h is -70.5.
Hence, option (c) is the correct answer.
1) P(A) = 0.6 P(B) = 0.45 P(A and B) = ? O 0.35 0.65 O 0.75 O 0.27
Answers
We are given the following probabilities:
[tex]\begin{gathered} P(A)=0.6 \\ P(B)=0.45 \end{gathered}[/tex]We are to find P(A and B), to do that we will use the following relationship:
[tex]P(\text{AandB)=P(A) x P(B)}[/tex]Replacing we get:
[tex]P(AandB)=0.6\times0.45[/tex]Solving the operations:
[tex]P(\text{AandB)}=0.27[/tex]Therefore, the probability of A and B is 0.27.
true or false18. In the circle: x^2+(y-2)^2=12, the radius is 12
Answers
The general equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h,k) is the center and r is the radius of the circle.
Comparing the given equation of a circle and the above general equation we get:
[tex]r^2=12[/tex]Then, the radius of this circle is:
[tex]r=\sqrt[]{12}[/tex]In conclusion, the sentence is false.
c. If x= 3 is specifically a hole (removable discontinuity) of f(x), then what would be true about g(3) and h(3)? Explain your reasoning.
Answers
Solution
We have the following function given:
f(x)= g(x)/h(x)
We have a point of discontinuity on x=3
c. If x= 3 is specifically a hole (removable discontinuity) of f(x), then what would be true about g(3) and h(3)? Explain your reasoning.
For this case we can conclude that g(3)/h(3) is not defined since f(3) is not defined for the function and that means that the function is not fully connected on x=3
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. The volleyball team and the wrestling team at Brookfield High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $2 per car. In addition, they have already brought in $92 from past fundraisers. The wrestling team has raised $16 in the past, and they are making $4 per car today. After washing a certain number of cars together, each team will have raised the same amount in total. What will that total be? How many cars will that take?
Answers
Data:
Volleyball team: V
Wrestling team: W
x: number of cars
V: $2 per car. Initial $92
W: $4 per car. Initial $16
You have the next equations:
[tex]\begin{gathered} V=2x+92 \\ W=4x+16 \end{gathered}[/tex]To find the total amount you have the next equation:
As each team have raised the same amount:
[tex]\begin{gathered} V=W \\ \\ 2x+92=4x+16 \end{gathered}[/tex]You solve x to find the number of cars each team wash in total:
[tex]\begin{gathered} 2x-4x+92=4x-4x+16 \\ -2x+92=16 \\ \\ -2x+92-92=16-92 \\ -2x=-76 \\ \\ \frac{-2}{-2}x=\frac{-76}{-2} \\ x=38 \end{gathered}[/tex]You use that value of x to find the final amount of each team:
[tex]\begin{gathered} V=2(38)+92=76+92=168 \\ \\ W=4(38)+12=152+12=168 \end{gathered}[/tex]Then, (the total of each team is $168) Total $336, (each team wash 38 cars) The total number of cars 76a jacket at Rick's clothing store originally costs $27 the store is having a 45% off sale on all of its merchandise what is the sale price of the jacket
Answers
Let:
Op = Original price
Sp = Sale price
r = Discount
Express the discount percentage as a decimal:
45% = 45/100 = 0.45
The sale price will be given by:
[tex]\begin{gathered} Sp=Op-0.45Op \\ where \\ Op=27 \\ so\colon \\ Sp=27-12.5 \\ Sp=14.85 \end{gathered}[/tex]$14.85
Jake, Becky, and Max are meeting at Charley's Pizza for dinner and then plan to go
pizza place,
each one of them has a different coupbn. They decide to use the coupon that will give them the best deal. movie. When they arrive. the
Jake's coupon is $19.99 for a pizza and pasta meal deal, Becky's
of the menu price; and Max's coupon is for three mediun
coupon is for two large one topping pizas-each at ]
one-topping pizzas - each at -off the menu price. Accordling
to the menu, a medium one-topping pizza is $8.99, and
large one-topping pizza $14.89. They also spend $1.25
for sodas and $5.00 on the tip. At the movie theater. Max has › coupon that's good for ãoff a third movie ticket when
you purchase two other movie tickets at the regular price.
The regular price of each movie ticket is $9.80.
Although Jake, Becky, and Max plan to split the cost of the pizza and movie, they decide that with the coupons, it's just
easier if one of them pays at each place. So, the friends agree that Jake will pay for the pizza and Becky will pay for the
movies. At the end of the night, they'll figure out how much Max owes
both Jake and Becky.
After all costs
split evenly, how much will each person contribute?
between $14 and $15
• between $15 and $16
• between $16 and $17
O between $17 and $18
Answers
Answer:
$16 and $17
Step-by-step explanation:
f(x) = -x2 + 7x - 13 Find f(-3)
Answers
Given the function :
[tex]f(x)=-x^2+7x-13[/tex]To find f(-3) , substitute with x = -3 , into the given function:
So,
[tex]\begin{gathered} f(-3)=-(-3)^2+7\cdot-3-13 \\ \\ f(-3)=-9-21-13 \\ \\ f(-3)=-43 \end{gathered}[/tex]
which equation shows x^2+6x-4=0 rewritten by completing the squarea) (x+3)^2=36b) (x+3)^2=4c) (x+3)^2=9d) (x+3)^2=13
Answers
Solution
Step 1
Write the equation:
[tex]x^2\text{ + 6x - 4 = 0}[/tex]Step 2:
Rewrite the equation:
[tex]x^2\text{ + 6x = 4}[/tex]Step 3
[tex]\begin{gathered} Add\text{ }\frac{b^2}{4a\text{ }}\text{ to both sides to get a perfect square.} \\ \text{a = 1, b = 6} \\ \frac{b^2}{4a}\text{ = }\frac{6^2}{4\times1}\text{ = }\frac{36}{4}\text{ = 9} \end{gathered}[/tex][tex]\begin{gathered} x^2\text{ + 6x + 9 = 4 + 9} \\ Add\text{ similar terms:} \\ (x\text{ + 3\rparen}^2\text{ = 13} \end{gathered}[/tex]Final answer
[tex]d)\text{ \lparen x + 3\rparen}^2\text{ = 13}[/tex]For the following figure, complete the statement for the specified pointsRS.199Points RT, S, and areboth collinear and coplanarcolinearcoplanarneither col near nor coplanar
Answers
From the figure, we can see that point R, T, S, Q are not on the same plane. Thus we can say they are neither colli coplanar
Match the steps to put them in the correct order of something. You will not use all of the options.
Answers
SOLUTION
[tex]\begin{gathered} Given \\ 2h+9=21 \end{gathered}[/tex][tex]\begin{gathered} Step\text{ 1:} \\ Subtract\text{ 9 from both sides} \\ 2h+9-9=21-9 \\ 2h=12 \end{gathered}[/tex][tex]\begin{gathered} Step\text{ }2: \\ Divide\text{ both sides by 2} \\ \frac{2h}{2}=\frac{12}{2} \\ h=6 \end{gathered}[/tex][tex]\begin{gathered} Final\text{ answer:} \\ h=6 \end{gathered}[/tex]Solve the equation for A: 2*Cos A + 2 = 3.
Answers
Answer:
A=60 degrees
Explanation:
Given the equation:
[tex]2\cos A+2=3[/tex]Subtract 2 from both sides of the equation.
[tex]\begin{gathered} 2\cos A+2-2=3-2 \\ 2\cos A=1 \end{gathered}[/tex]Divide both sides by 2:
[tex]\begin{gathered} \frac{2\cos A}{2}=\frac{1}{2} \\ \cos A=\frac{1}{2} \end{gathered}[/tex]Finally, solve for A.
[tex]\begin{gathered} A=\arccos (\frac{1}{2}) \\ A=60\degree \end{gathered}[/tex]Simplify this expression. Assume that x is nonzero.– 11.7X<-11.x?(Type exponential notation with positive exponents.)
Answers
If two numbers have the same base ( the number below the exponent) then the multiplication of the two of them is the number with the same base but with the sum of its exponents (rule of exponents)
[tex]x^{-11}\cdot x^7=x^{-11+7}=x^{-4}[/tex]On the other hand, if a number is to the power a negative number, it means that it is the reciprocal elevated to the number, in this case
[tex]x^{-4}=(\frac{1}{x})^4[/tex]what digit is in the
Answers
The number given in the statement is
2.113 pints.
To write in word form,
Two and one hundred thirteen thousandths.
As in the number from last we have thousand , hundred, tens and ones.
So, we can write the given number in word form.
Two and one hundred thirteen thousandths.
Hence the correct option is c.
What is the remainder when j(x)=x4+2x3−5x2+2x+4 is divided by x+3
Answers
From the problem, we have a function :
[tex]j(x)=x^4+2x^3-5x^2+2x+4[/tex]The remainder when j(x) is divided by x + 3 is the value of the function when x = -3
x = -3 comes from :
x + 3 = 0
x = -3
Substitute x = -3 to the function,
[tex]\begin{gathered} j(-3)=(-3)^4+2(-3)^3-5(-3)^2+2(-3)+4 \\ j(-3)=81-54-45-6+4 \\ j(-3)=-20 \end{gathered}[/tex]The answer is -20
directly as Vi and inversely as y°. If: = 61 when = 36 and y = 9, find a if r = 64 and y = 6. (Round off your answer to the nearest hundredth.)
Answers
Given: z directly varies as √x and inversely varies as y³
when x = 36 and y = 9 then z = 61
To find:
when x = 64 and y = 6 then z = ?
explanation:
z ∝ √x / y³
z = k √x / y³
when x = 36 and y = 9 then z = 61
[tex]z=\text{ }\frac{k\text{ }\sqrt{x}}{y^3}[/tex][tex]\begin{gathered} 61=\frac{k\text{ * }\sqrt{36}}{9^3} \\ 61=\frac{k*6}{729} \\ k=\frac{61*729}{6}=\frac{61*243}{2}=\frac{14823}{2} \end{gathered}[/tex]when x = 64 and y = 6
[tex]z=\text{ }\frac{14823}{2}*\frac{\sqrt{64}}{6^3}=\frac{14823*8}{2*216}=\frac{4941*4}{72}=\frac{4941}{18}=274.5[/tex]the value of z = 274.5
final answer:
z = 274.5 ≈ 300 when rounded off to the nearest hundredth
Use the properties of exponents to simplify. Express all answers using positive exponents.each)35x10 over 5x^5
Answers
Consider the given expression,
[tex]\frac{35x^{10}}{5x^5}[/tex]Consider the property,
[tex]\frac{x^m}{x^n}=x^{m-n}[/tex]Then the given expression can be simplified as follows,
[tex]\begin{gathered} \frac{35x^{10}}{5x^5} \\ =\frac{35}{5}\times\frac{x^{10}}{x^5} \\ =7\times x^{10-5} \\ =7\times x^5 \\ =7x^5 \end{gathered}[/tex]Thus, the given expression is simplified as,
[tex]\frac{35x^{10}}{5x^5}=7x^5[/tex]X= 7 4. Find the equation of a line passing through (5, -6) perpendicular (b) 3x + 5y = (d) 7x - 12y (f) x = 7 (a) 2x + y = 12 (c) x + 3y = 8 (e) 2y = 5 Find the equation of the line connecting the points of intersect (a) S x + y = 4 S 3x - y = 12 (b) Sy= and 2x=6 = -6 X=
Answers
Given data:
The first set of equations are x+y=4, and x=6.
The second set of equations are 3x-y=12 and y=-6.
The point of intersection of first set of te equations is,
6+y=4
y=-2
The first point is (6, -2).
The point of intersection of second set of te equations is,
3x-(-6)=12
3x+6=12
3x=6
x=2
The second point is (2, -6).
The equation of the line passing through (6, -2) and (2, -6) is,
[tex]\begin{gathered} y-(-2)=\frac{-6-(-2)}{2-6}(x-6) \\ y+2=\frac{-6+2}{-4}(x-6) \\ y+2=x-6 \\ y=x-8 \end{gathered}[/tex]Thus, the required equation of the line is y=x-8.
Jada and Priya are trying to solve the equation 2/3 + x = 4 Jada says I think we should multiply each side by 3/2 because that is the reciprocal of 2/3 Priya since I think we should add -2/3 to each side because that is the opposite of 2/3
Answers
The equation they are trying to solve is
[tex]\frac{2}{3}+x=4[/tex]In order to solve this equation, they need to add -2/3 on each side (the opposite of 2/3).
[tex]\begin{gathered} \frac{2}{3}-\frac{2}{3}+x=4-\frac{2}{3} \\ x=4-\frac{2}{3} \end{gathered}[/tex]Hence, Priya is correct because they need to use the opposite of 2/3, not the reciprocal.
An equation that can be solved using Jada's strategy is
[tex]\frac{2}{3}x=4[/tex]This equation would need to use a reciprocal, as Jada said.
Which expression is equivalent to 1-51 +131? —8 ООО O2 o 8
Answers
Theg given expression : |-5|+|3|
Since modulus is express as |-a|=a and |a|=a
[tex]undefined[/tex]You invested $28,000 in two accounts paying 7% and 9% annual interest, respectively. If the total interest earned for the year was $2180, how much was invested at each rate?
Answers
We are given the following information:
total of $28,000 invested in 2 accounts
7% and 9% interest rates for each account
total interest was $2,180
We are asked to calculate the amount invested at each rate.
To do this, let us first identify our variable and what it stands for. Let us use the variable x to represent the amount invest at 7%. That leaves us t
What is the greatest common factor of 48x^2?and 32x^3?A. 16x^2B. 96x^3C. 8x^2D. 16x
Answers
greatest common factor (GCF) of 2 algebraic terms is the largest monomial that evenly divides the two expressions.
We have
[tex]\begin{gathered} 48x^2 \\ \text{and} \\ 32x^3 \end{gathered}[/tex]There are two parts, the numbers and variables.
From the numbers, the largest number we can divide 48 and 32 by is:
16
From the variables, the largest factor is x^2
Putting them together, we can say the GCF is:
[tex]16x^2[/tex]Correct Answer: A
A student is taking a test in which items of type A are worth 8 points and items of type B are worth 12 points. It takes 3 min to complete each item of type A and 6 min to complete each item of type B. The total time allowed is 60 min and Anna answers exactly 16 questions. How many questions of each type did she complete? Assuming that all her answers were correct, what was her score? She completed questions of type A.
Answers
Type A questions are worth 8 points each.
Type B questions are worth 12 points each.
it takes 3 minutes to answer a Type A question
it takes 6 minutes to answer a Type B question.
total time allowed = 60 minutes
She answered a total of 16 questions.
let
number of question answer on type A = x
number of question answered on type B = y
Therefore,
3x + 6y = 60
x + y = 16
then,
[tex]\begin{gathered} 3x+6y=60 \\ x+y=16 \\ x=16-y \\ 3(16-y)+6y=60 \\ 48-3y+6y=60 \\ 3y=60-48 \\ 3y=12 \\ y=\frac{12}{3} \\ y=4 \\ x=16-4 \\ x=12 \end{gathered}[/tex]She answered 12 questions on type A and 4 questions on type B.
If all her answer is correct her score can be computed below
[tex]undefined[/tex]