Mathematics College

how can you write the expression with a rationalized denominator? √3/√4

Answers

Answer 1
Well √4 = 2

So √3 / √4 would be √3 / 2 so denominator is now rationalized.

Hope this helps.

Related Questions

Terry uses 3 cups of pumpkin seeds to decorate the tops of 12 loaves if bread. She puts an equal amount of seeds on each loaf. How many cups of pumpkin seeds does she put on each loaf of bread?

Answers

There are 3 cups of pumpkin seeds used every 12 loaves of bread. To find how much she puts on each single loaf, divide 3 by 12 and get your answer, 0.25. So she uses 0.25 cups of pumpkin seeds per loaf.

hey can you please help me posted picture of question

Answers

G(x) = x² is the parent square function.

It has its vertex at origin and opens upwards.

The given graph is obtained by shifting the graph of x² 2 units vertically down. This vertically translation can be expressed by subtracting 2 from the parent function.

So,

F(x) = G(x) - 2

F(x) = x² - 2

Thus the correct option is A

y = x3 - 3x On which intervals is this function increasing?

Answers

The function is increasing on the intervals
  x ∈ (-∞, -1) ∪ (1, ∞)

A line has a slope of 2 and a y intercept of (0,-4) what is the value of y when x=6

Answers

First we set up an equation with the givens (slope and y intercept):
y = 2x -4
next plug in 6 for x.
y = (2x6) - 4
y = 12 - 4

And this will give us the value of y: 8.
Final answer:

The question is about finding the y-value of a line when the x-value is given, knowing the slope and the y-intercept. By plugging the given slope, y-intercept and the provided x-value into the formula y = mx + b, we find that y equals 8 when x equals 6.

Explanation:

If we know the slope (m) of a line and the y-intercept (b), we can use the formula y = mx + b to calculate the y-value for any x-value. In the given question, the slope (m) is 2 and the y-intercept (b) is -4. If we want to find the y-value when x = 6, we can substitute these values into the formula:

y = 2*6 - 4

So, y = 12 - 4 = 8. Therefore, when x = 6, the value of y is 8.

Learn more about Line equation here:

https://brainly.com/question/21511618

#SPJ2

Factor \2x^2-11x+5=0

Answers

2x² - 11x + 5
2x² - x - 10x + 5
x(2x - 1) - 5(2x - 1)

(2x - 1)(x- 5) is your answer. 
Final answer:

The quadratic equation [tex]2x^2[/tex]-11x+5=0 is factored into (2x - 1)(x - 5), and it has solutions x = 0.5 and x = 5.

Explanation:

The question asks us to factor the quadratic equation[tex]2x^2[/tex]-11x+5=0. To do this, we need to find two numbers that multiply to give ac (where a is the coefficient of x^2 and c is the constant term) and add to give b (the coefficient of x). Here, ac is (2)(5)=10, and b is -11. The two numbers that satisfy this are -10 and -1 because -10 * -1 = 10 and -10 + -1 = -11.

We rewrite the middle term using these two numbers and then group the terms to factor by grouping:

[tex]2x^2[/tex]- 10x - x + 5 = 0
([tex]2x^2[/tex]- 10x) - (x - 5) = 0
2x(x - 5) - 1(x - 5) = 0
(2x - 1)(x - 5) = 0

The factored form of the quadratic equation is (2x - 1)(x - 5). Therefore, the solutions to the equation are x = 0.5 and x = 5, found by setting each factor equal to zero.

The graph of y=|x| is transformed as shown in the graph below. Which equation represents the transformed function?

Answers

The vertex of the graph y=|x| is at (0,0)

After transformation the vertex becomes at (-3,-2)
Apply axes transformation from (0,0) to (h,k)
So, the transformation rule is (x,y) → (x-h, y-k)
(h,k) will be equal (-3,-2)


∴ y=|x| ⇒ (y-(-2)) = |x-(-3)|
∴(y+2) = |x+3|
∴ y = |x+3|-2


So, the correct answer is option 2

we have that

the original function [tex]y=\left|x\right|[/tex] has the vertex at point [tex](0,0)[/tex]

The transformed function has the vertex at point [tex](-3,-2)[/tex]

so

the rule of the translation is equal to

[tex](x,y)------> (x-3,y-2)[/tex]

That means

The translation is [tex]3[/tex] units to the left and [tex]2[/tex] units down

therefore

the answer is

the transformed function is [tex]y=\left|x+3\right|-2[/tex]



Ben buys a car for $50,000. The value of the car decreases at a rate of 4% per year. How much will the car be worth in 3 years? A. $48,000 B. $44,237 C. $45,082 D. $43,270

Answers

Given that the value of $50000 car decreases by 4%  per year, the value after 3 years will be given by exponential form:
y=abˣ
where:
a=initial value
b=decreasing rate
x=time in years
from the information:
a=50000, b=0.96, x=3
thus
y=50000(0.96)³
simplifying we get:
y=$44, 236.8
~$44237

Answer:
B. $44,237

Given: KLMN is a trapezoid, KF =10 MF ║ LK AKLMF = AFMN Find: KN

Answers

The trapezoid is shown in the picture attached.

We know:
LK // MF
KF = 10
A(KLMF) = A(FMN)

Since LM // KF (because they are bases of the trapezoid) and LK // MF because is given in the hypothesis, KLMF is a parallelogram.
The area of a parallelogram is given by the base times the height.
A(KLMF) = b × h
               = 10 × h

The area of a triangle is given by the formula:
A(FMN) = (b × h) / 2
             = (FN × h) / 2

We know that the two areas are congruent, therefore:
A(KLMF) = A(FMN)
10 × h = FN × h / 2

The two "h" cancel out because they are the same and we can solve for FN:
10 = FN / 2
FN = 20

Now we can calculate:
KN = KF + FN = 10 + 20 = 30

Hence, KN is 30 units long.
Final answer:

In a trapezoid with parallel sides, if a pair of opposite sides are equal, then the other pair of opposite sides are also equal. Therefore, in the given trapezoid KLMN, KN is equal to AN + 10.

Explanation:

In the given trapezoid KLMN, the sides KF and LM are parallel. We are given that KF = 10 and AFMN = AKLMF. We need to find KN.

Since KF and LM are parallel, KF = LM. Therefore, LM = 10.

Since AFMN = AKLMF, we can say that AN = KL. So, AN + LM = KL + KF. Substituting the given values, we get AN + 10 = KL + 10. Therefore, AN = KL.

Hence, KN = KL + LM = AN + LM = AN + 10.

Therefore, KN = AN + 10.

To win at lotto in a certain state, one must correctly select 6 numbers from a collection of 50 numbers (one through 50). the order in which the selections is made does not matter. how many different selections are possible?

Answers

Asked and answered elsewhere.
https://brainly.com/question/10013755

We have been given that the order doesn't matter in the selection procedure. Hence, the case is of combination.

The formula for the combination is given by

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Now, in order to win at lotto, one must correctly select 6 numbers from a collection of 50 numbers. Thus, the required ways should be

[tex]^{50}C_6[/tex]

Using the above formula, the number of different selections are

[tex]^{50}C_6=\frac{50!}{6!(50-6)!}\\ \\ =\frac{50!}{6!44!}\\ \\ =\frac{44!\times 45\times 46\times 47 \times 48\times 49\times 50}{6!44!}\\ \\ =15890700[/tex]

Therefore, 15890700 different selections are possible.

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12.

Answers

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$450\\ P=\textit{original amount deposited}\to& \$3000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to &3 \end{cases} \\\\\\ 450=(3000)(r)(3)\implies \cfrac{450}{(3000)(3)}=r\implies \cfrac{1}{20}=r \\\\\\ 0.05=r\implies r\%=0.05\cdot 100\implies r=\stackrel{\%}{5}[/tex]

function that has the same domain as y=2√x

Answers

The rest of the question;
A.y= [tex] \sqrt{2x} [/tex]
B.y=[tex] \sqrt[3]{ x^{2} } [/tex]
C.y=[tex] \sqrt{x-2} [/tex]
D.y=[tex] \sqrt[3]{x-2} [/tex]
====================================================

We are given the function
y = 2 √x

The domain for the given function is this
{ x | x ≥ 0 }

The answer is A. y = √2x

In general any function that has a domain of x that is equal to or greater than 0. Some examples:
f(x) = √x  -  2
f(x) = 5 √x



Answer:

The answer is A. y = √2x

Step-by-step explanation:

Two thirds of the families in smithville own their own homes. The total number of home owning families there is 480. How many families live in smithville?

Answers

x- the total number of families in Smithville.
(2/3)x  - the number of home owning families.
At the same time,  the number of home owning families is 480.

(2/3)x=480
x=480*3/2=720.

720 families live in Smithville.

What is the equivalent of pi over 3 radians in degrees?

Answers

(π/3)x(180/π)=60 degrees

[tex] \frac{ \pi }{3} [/tex] is equivalent to 60°


hey can you please help me posted picture of question

Answers

The correct answer is D. Graph D

Find the Vertex of   y = 3x2+7x+2

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 3 , is positive (greater than zero). 

 Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions. 

 Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex. 

 For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -1.1667  

 Plugging into the parabola formula  -1.1667  for  x  we can calculate the  y -coordinate : 
  y = 3.0 * -1.17 * -1.17 + 7.0 * -1.17 + 2.0 
or   y = -2.083
Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = 3x2+7x+2
Axis of Symmetry (dashed)  {x}={-1.17} 
Vertex at  {x,y} = {-1.17,-2.08}  
 x -Intercepts (Roots) :
Root 1 at  {x,y} = {-2.00, 0.00} 
Root 2 at  {x,y} = {-0.33, 0.00} 

We can find the roots of the given equation to determine its graph.

3x²+7x+2=0

Solving using factorization.

3x²+6x+x+2=0

3x(x+2)+1(x+2)=0

(3x+1)(x+2)=0

This means the roots of the equation are x = -2 and x = -1/3

Now from the graphs determine which one has the roots at  these two points. We can observe that Graph D has the roots at x=-2 and x=-1/3

So the answer to this question is option D

The circle belowis centered at the point (-2 ,1) and has a radiusof length 3

Answers

Answer:
Option A, (x + 2)² + (y - 1) = 9

Explanation:
The equation form of a circle is (x - h)² + (y - k)² = r², where the center is ordered pair (h, k) and r represents the radius.

From the given information, the center is point (-2, 1) and the radius (r) is 3 units. With this, we can plug the information in and simplify:
(x - (-2))² + (y - (1))² = (3)²
(x + 2)² + (y - 1)² = 9

The equation for the given circle is (x + 2)² + (y - 1)² = 9

which transformations are needed to change the parent some function to the sine function below?

Answers

Beginning with the function y = sin x, which would have range from -1 to 1 and period of 2pi:
Vertical compression of 1/2 compresses the range from -1/2 to 1/2
Phase shift of pi/2 to the left
Horizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4pi
Vertical shift of 1 unit up moves the range to 1/2 to 3/2
So the first choice looks like a good answer.
The first choice is the answer:

Solution:
the function y = sin x, which would have range from -1 to 1 and period of 2pi:

So the answer would be:Vertical compression of 1/2 compresses the range from -1/2 to 1/2Phase shift of pi/2 to the leftHorizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4piVertical shift of 1 unit up moves the range to 1/2 to 3/2

Instructions:Select the correct answer from each drop-down menu. The range of all real numbers x such that 2x − 5 < 7 and 4x + 10 > 6 is . The range of all real numbers x such that 2x − 5 < 7 or 4x + 10 > 6 is

Answers

In order to find the rang, solve for the first inequality:

2x - 5< 7

2x <12

x < 6

Solve for the second inequality:

4x +10 > 6
4x > -4 
x > -1

Graph these two inequalities on a number line to see that their union is the complete number line. Note that for any number of x can either be greater than negative 1 or less than 6 and can be both.

so the answer is:

range of negative infinity to infinity. required to use parenthesis

(-∞, ∞)

Q # 15 in the diagrams a || b a. Use the fiagrama o answer the question(diagrama not to scale.)

Answers

The interior angel to ∠7 is the angel ∠4

because ∠7 + ∠4 = 180°

The correct choice is number 1
I’m pretty sure its <4 angle four...
///EAGLEPAW

fully expand the logarithm: log(x^3/z^5)

Answers

to expand this logarithm, we have to apply the rules. These rules are;

Log(A/B) = logA - LogB and Alogx=log(x∧A)

Log (x³/z∧5) = log (x³) - log z∧5
                    =3log x - 5log z
Using the following properties we can expand the given expression:

1) Quotient Rule of Logs:
Log(A/B) = Log A - Log B

2) Power Rule of Logs: 
[tex]Log(a)^{b}=b*Log(a) [/tex]

[tex]log( \frac{ x^{3} }{ z^{5} } ) \\ \\ =log( x^{3})-log( z^{5}) \\ \\ =3logx-5logz[/tex]

What is the number of social security credits a worker needs to earn over his or her working lifetime to collect Social security benefits?

Answers

According to the Social Security Administration website, the number of work credits you need to get benefits depends on when you were born.  If you were born in 1929 or afterward, you need 40 credits.  If you were born before 1929, you don't need 40: 39 credits are required if you were born in 1928, 38 credits if you were born in 1927, etc.

ln(x+2)-ln(4x+3)=ln(1/2*x)

Answers

ln(x+2)-ln(4x+3)=ln(1/2*x)

Using properties of  logarithms

[tex] \frac{ln(x+2)}{ln(4x+3)} = ln \frac{x}{2} \\ \\ \frac{x+2}{4x+3} = \frac{x}{2} \\ \\2(x+2)=x(4x+3) 2x+4=4x^2+3x \\ \\ 4 x^{2} +x-4=0 \\ \\ x= \frac{-b+/- \sqrt{b^{2}-4ac} }{2a} \\ \\ x= \frac{ -1+/-\sqrt{1+64} }{8} \\ \\ x_{1} = \frac{-1+ \sqrt{65} }{8} \\ \\ x_{2} = \frac{-1- \sqrt{65} }{8} Check: When you substitute x_{2} into \\ \\ ln(4x+3)=ln(4* \frac{-1- \sqrt{65} }{8} ) =ln( \frac{-1- \sqrt{65} }{2} ) you will get negative number under ln, that is impossible , [/tex]

so x2 is not a solution of this logarithmic equation.

Only x1 is a solution.


This is incredibly frustrating. PLEASE HELP ME

Answers

The correct option is: Option (C)

Explanation:
Given expression:
[tex]\sum_{i=1}^{25} 2^{2i}[/tex]

When i = 1: The answer is [tex]2^{2*1}[/tex] = 4
When i = 2: The answer is [tex]2^{2*2}[/tex] = 16
When i = 3: The answer is [tex]2^{2*3}[/tex] = 64
.
.
When i = 25: The answer is [tex]2^{2*25}[/tex] = [tex]2^{50}[/tex]

Which is the series mentioned in Option C

Chloe puts 4 soaps and two bottles of lotion in each gift basket. She has 127 soaps and 85 bottles of lotion. How many gift baskets can Chloe complete?

Answers

127/4 = 31.75 = 31
85/2 = 42.5 = 43

She can only make 31 full gift baskets with the amount of soap she has.

Therefore, Chloe can make 31 gift baskets.

A ball is thrown into the air with an upward velocity of 32 ft/s. Its height h in feet after t seconds is given by the function h = –16t2 + 32t + 6. a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. b. What is the ball’s maximum height? 1 s; 54 ft 2 s; 6 ft 2 s; 22 ft 1 s; 22 ft

Answers

For this case we have the following equation:
 h = -16t2 + 32t + 6
 Deriving we have:
 h '= -32t + 32
 Equaling to zero:
 -32t + 32 = 0
 We clear the time:
 t = 32/32
 t = 1 s
 We are now looking for the maximum height:
 h (1) = -16 * (1) ^ 2 + 32 * (1) + 6
 h (1) = 22 feet
 Answer:
 The ball reaches its maximum height in:
 t = 1 s
 The ball's maximum height is:
 h (1) = 22 feet
 option: 22 ft, 1 s

Answer: 22 ft, 1 s

Step-by-step explanation:

graph of this ellipse

x^2 + y^2 =1
_ _
4 16

Answers

check the picture below.

PLz help!

Write the equation of the line that passes through (3, −2) and has a slope of 4 in point-slope form. (2 points)


1 y + 2 = 4(x − 3)

2 y − 3 = 4(x + 2)

3 x − 3 = 4(y + 2)

4 x + 2 = 4(y − 3)

Answers

[tex]y+2=4(x-3)[/tex]

It's the first answer.
[tex]\text{Slope} = \dfrac{Y_2 - Y_1}{X_2 - X_1} [/tex]

Given that the slope = 4 and the coordinate is (3, -2),

[tex]4 = \dfrac{y + 2}{x + 3} [/tex]

[tex] y + 2 = 4(x - 3) [/tex]

Answer : y + 2 = 4(x - 3)  (Answer A)

What is the vertex of the quadratic function f(x) = (x - 8)(x - 2)

Answers

good day ~_~ /////////////

Answer: (5, -9)

What is the vertex of the quadratic function f(x) = (x – 8)(x – 2)?

on a game show that are 10 keys in the bag and three of the key start a car and contest in randomly choosing the key it doesn't not start the car she returned to the bag the host mixed up the back she randomly selects another key this key does not start the car either what is the probability of this no start no start outcome

Answers

What are the answers

Solve the equation 3x+5y=4
for y

Answers

Answer:

y = (4 -3x)/5

Step-by-step explanation:

Find the terms containing y. If they are all on one side of the equation (it is), then identify the terms not containing y. Subtract those. Then, divide by the coefficient of y.

3x +5y = 4

5y = 4 - 3x . . . . . non-y term subtracted

y = (4 -3x)/5 . . . . divide by the coefficient of y

_____

If you like, you can rearrange this to slope-intercept form:

... y = -3/5x +4/5

The net asset value of stock in a mutual fund had increased by $20 per share when an investor decided to redeem them. The investor had purchased 100 shares of the stock for $2,316 and redeemed them for $4,301. What can you conclude about the fund? a. The fund is a no-load fund. b. The offer price of the fund was $0.15 less than the net asset value when purchased. c. The offer price of the fund was $0.15 more than the net asset value when purchased. d. The offer price of the fund was $0.15 more than the net asset value when sold.

Answers

The correct answer is letter c. The offer price of the fund was $0.15 more than the net asset value when purchased.


Formula for calculating NAV:

Net Asset Value (NAV) = (Assets - Debts) / (Number of Outstanding Units)

The Net Asset Value (NAV) is the price in which you pay to buy a unit of mutual fund scheme when you invest.
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