(02.01, 02.02 HC)Vanessa and William are stuck simplifying radical expressions. Vanessa has to simplifyx3William has to simplify 15xx.x4. Usingx6full sentences, describe how to fully simplify Vanessa and William's expressions. Describe if Vanessa and William started with equivalentexpressions or if they started with expressions that are not
Answers
ANSWER:
[tex]\begin{gathered} \text{ The Vanness expression is simplified by subtracting the exponents, and we obtain the following:} \\ \\ \frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}=x^{\frac{1}{2}} \\ \\ \text{ The Williams expression is simplified by adding the exponents, and we obtain the following:} \\ \\ \sqrt[16]{x\cdot\:x^3\cdot\:x^4}=x^{\frac{1}{2}} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have that the given expression is the following:
[tex]\frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}[/tex]The other expression is the following:
[tex]\sqrt[16]{x\cdot \:x^3\cdot \:x^4}[/tex]We simplify in each case:
[tex]\begin{gathered} \text{ The Vanness expression is simplified by subtracting the exponents, and we obtain the following:} \\ \\ \frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}=x^{\frac{4}{3}-\frac{5}{6}}=x^{\frac{1}{2}} \\ \\ \text{ The Williams expression is simplified by adding the exponents, and we obtain the following:} \\ \\ \sqrt[16]{x\cdot\:x^3\cdot\:x^4}=\sqrt[16]{x^{1+3+4}}=\sqrt[16]{x^8}=x^{\frac{8}{16}}=x^{\frac{1}{2}} \end{gathered}[/tex]This means that the expressions are equal
Related Questions
A collection of black cats and crows has a total of 99 heads and legs between them. There
are twice as many crows as there are cats. How many of each is there?
Answers
Answer:
Crow=
50×2
100 leg.
cat=
49×4
196 leg.
Use the sequence below to complete each task. 972, 324, 108, ... a. Identify the common ratio (r). b. Write an equation to represent the sequence. C. Find the 6th term (ac)
Answers
(a),
The common ratio between the terms is
[tex]\frac{972}{324}=\frac{324}{108}=3[/tex](b).
The common ratio found in (a) tells us that every next number is found by dividing the previous number by 3; therefore, the equation for a_n the nth term will be
[tex]a_n=\frac{972}{3^n}[/tex](c).
The sixth term will be at n = 6. Putting n = 6 into the equation in (b) gets us
[tex]a_6=\frac{972}{3^6}=\frac{4}{3}[/tex]Your test in math class has problems with 2 points (x) and problems worth 4 points (y). Altogether, the test has 100 points. Write an equation that represents the total points on the test, including the 2-point and 4-point problems.
____________x + _____________y = ___________(total points)
If you answer 30 2-point questions and 8 4-point questions correctly, what will your score be?
Answers
The equation that represents the total points on the test, including the 2-point and 4-point problems is 2x + 4y = 100
How to illustrate the equation?From the information, the test in math class has problems with 2 points (x) and problems worth 4 points (y) and the test has 100 points. The equation to illustrate this will be:
2x + 4y = 100
When one answers 30 2-point questions and 8 4-point questions correctly, the score will be:
= 2x + 4y
= 2(30) + 4(8)
= 60 + 32
= 92
The score is 92 points.
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HELP!! This is due soon!
Answers
From the given quadratic equation, we have that:
The maximum height is of 600 feet.The ball hits the ground after 8.9 seconds.What is the vertex of a quadratic equation?A quadratic equation is modeled by the following rule:
y = ax^2 + bx + c
The vertex has these following coordinates.
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that the vertex can represent either a maximum or a minimum point, as follows::
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.For this problem, the function is:
h(t) = -16t² + 160t + 200.
Then the coefficients are:
a = -16, b = 160, c = 200.
And the maximum height, in feet, will be of:
[tex]y_v = -\frac{160^2 - 4(-16)(200)}{4(-16)} = 600[/tex]
When does the ball hits the ground?The ball hits the ground for the positive root when h(t) = 0, hence after 8.9 seconds.
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Determine the value of the trigonometric ratio.
Answers
Given,
The measure of side YZ is 21.
The measure of side XY is 20.
The measure of side XZ is 29.
Required:
The value of tanX.
The trigonometric ratio is calculated as,
[tex]tan\theta=\frac{side\text{ opposite to }\theta}{side\text{ adjacent of }\theta}[/tex]Substituting the values,
[tex]\begin{gathered} tanX=\frac{YZ}{XY} \\ tanX=\frac{21}{20} \end{gathered}[/tex]ence, the value of tanX is 21/290.
Gwen spent $12.50 to purchase 5 bracelets. Each 4.
bracelet costs the same amount. What is the unit rate
for each bracelet?
Answers
Answer:
simply divide 12.50 by 5. Therefore each bracelet costs $2.05 : 2$ and 5 cents.
Step-by-step explanation:
The cost of each bracelet will be $2.5.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The cost of 5 bracelets = $12.50
Now,
Since, The cost of 5 bracelets = $12.50
So, The cost of 1 bracelets = $12.50 ÷ 5
= $2.5
Thus, The cost of each bracelet will be $2.5.
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12. A company has bought 3.4 acres of land out of the 4
acres of land that it plans to buy. What percent of the land
has the company already bought? Solve the problem with a
math drawing or a percent table, or both, explaining your
reasoning.
Answers
Answer:
I think about 3.4/4=.85 or 85% of acreage was bought.
Step-by-step explanation:
Please help me solve this
Answers
(a) 291/2020
Divide the total for the 10-14 year column by the total.(b) 77/465
There are 465 people from the east, 77 of which were loyal for 10 to 14 years(c) 437/1010
There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.(d) 145/376
376 people are from the West, (45+100)=145 of which are at least 10.(e) 32/157
157 people were loyal for less than a year, 32 of which were from the East.(f) 53/157
157 people were loyal for less than a year, 53 of which were from the South.(g) 433/465
465-32=433 people were loyal for at least 1 year out of the 465 people from the East.(h) 335/376
376-41=355 people were loyal for at least 1 year out of the 376 people from the West.A 35 foot ladder is set against the side of a house so that it reaches up 21 feet. If Elijah
grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the
side of the house will the ladder reach now? (The answer is not 17 ft.) Round to the
nearest tenth
Answers
Answer:
14.2 feet
Step-by-step explanation:
Use the Pythagorean Theorem to solve both parts.
Part 1.
35 is the hypotenuse and 21 is a leg.
[tex]a^{2} +b^{2} =c^{2} \\a^{2} +21^{2} =35^2\\a^2 + 441 = 1225\\a^2 +441-441=1225-441\\a^2 =784\\\sqrt{a^2} =\sqrt{784} \\a = 28 feet[/tex]
28 feet represents how far the base of the ladder is from the house.
Part 2.
Now move the ladder 4 feet farther from the house. 28 + 4 = 32 ft.
Now you have a leg that is 32 feet and the hypotenuse is still 35 feet. Solve for the other leg.
[tex]a^{2} +b^{2} =c^{2} \\a^{2} +32^{2} =35^2\\a^2 + 1024 = 1225\\a^2 +1024-1024=1225-1024\\a^2 =201\\\sqrt{a^2} =\sqrt{201} \\a = 14.177 feet[/tex]
Round to the nearest tenth and you have 14.2 feet
When Ms. Paul bought a new office phone, she borrowed $1,200 at a rate of 18% for 9 months. How much interest did she pay?
Answers
Assuming simple interest, the formula to calculate the interest Ms. Paul paid is:
[tex]Interest=Principal\times Rate\times Time[/tex]In the problem, here are the given information:
Principal (Money borrowed) = $1,200
Rate = 18% or 0.18 in decimal form
Time = 9 months or 0.75 year.
(Take note that the time in the formula is measured in years.)
Let's plug in the given information to the interest formula above.
[tex]Interest=1,200\times0.18\times0.75[/tex]Then, solve.
[tex]Interest=162[/tex]Therefore, Ms. Paul paid interest of $162.
Please
50 POINTS! BRAINLIEST!
The graphs of the conics intersect at two points.
x² + y² = 4
x^2/4 - y^2/9 =1
What are the coordinates of these points of intersection?
Enter your answer by filling in the boxes.
and
( , ) and ( , )
Answers
In linear equation, The co - ordinates of these points of intersection are ( -2,0) ( 2, 0) .
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an uncertain variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.x² + y² = 4 ..........1
x²/4 - y²/9 = 1
⇒ 9x² - 4y² = 36 ..........2
multiply equation (1) is multiply by 9
9 x² + 9y² = 36 ..............3
equation (3) - (2)
13y² = 0
y = 0
put y =0 in equation 1
x² + 0 = 4
x = ± 2
The co - ordinates of these points of intersection are ( -2,0) ( 2, 0) .
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What value(s) of x in the relation below would create a set of ordered pairs that is not a function? Justify your answer. {(0,5) (1,5) (2, 6) (x, 7)}
Answers
First, let's see the points on the coordinate plane:
Now, let's remember that a function has every element of it's domain related with only one element from it's image.
Therefore, x = 2 would create a set of ordered pairs that is not a function. Let's see it in the plane:
As we can see, x = 2 has two values on the image: f(2) = 6 and f(2) = 7, and this never can happen in a function.
In a promotion for a local
Subway, every 5th customer will
get a free sandwich and every
3rd customer will get a free
drink. Which customer will be
the first person to get a free
sandwich and drink?
Answers
Answer:
15th customer
Step-by-step explanation:
to find the answer to this, you have to find the least common multiple(I think that’s what it is called). In this case, in order to find it, you can just multiply 5*3 to get 15 for the answer
It takes 3 1/5 teaspoons
of strawberry syrup
to make 1 3/4
strawberry
milkshakes. How
many teaspoons of
syrup would it take to
make just one
strawberry
milkshake?
Answers
The quantity of teaspoons of syrup it would take to make just one strawberry milkshake is 1 29/35 teaspoons
RatioThis is the number which gives the comparison between two quantities. The ratio of teaspoons of strawberry to make strawberry milkshake is the comparison between the two quantities.
It takes 3 1/5 teaspoons of strawberry syrup to make 1 3/4 strawberry milkshakes Number of teaspoons of syrup would it take to make just one strawberry milkshake = xEquate the ratio of teaspoons of strawberry syrup to strawberry milkshakes
Teaspoons of strawberry : make strawberry milkshake
3 1/5 : 1 3/4 = x : 1
16/5 ÷ 7/4 = x/1
cross product
16/5 × 1 = 7/4 × x
16/5 = 7/4x
divide both sides by 7/4x = 16/5 ÷ 7/4
x = 16/5 × 4/7
= (16 × 4) / (5 × 7)
= 64 / 35
= 1 29/35 teaspoons
The teaspoons of syrup would it take to make just one strawberry milkshake is 1 29/35 teaspoons
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Hello I need to find the answer on how to find (-8)(-7)(3)
Answers
Answer:
168
Step-by-step explanation:
Hello I need to find the answer on how to find (-8)(-7)(3):
This is asking to find: -8 × -7 × 3 = ?
Because a negative times a negative = positive we have:
56 × 3 = 168
A pyramid is shown.
The pyramid has a base length of 5 centimeters, an altitude of 8 centimeters, and a lateral edge length of 9 centimeters.
What is the volume of the pyramid?
Answers
A music store is having its "Black Friday" sale. The store will give
$5 off for the second item a customer purchases. Emma wants
buy a pair of headphones for $25 and a CD for $18.50. How
much does she need to pay in total?
Answers
Based on the given task content; the amount of money the customer needs to pay if given a discount of $5 off the second item bought is $38.50
The amount paid by the customer after deducting discountItem 1:
Headphones = $25
Item 2:
CD = $18.50
Discount on the second item = $5Amount paid on the second item = original cost - discount
= $18.50 - $5
= $13.50
Total amount the customer needs to pay = cost of item 1 + Amount paid on the second item
= $25 + $13.50
= $38.50
In conclusion, the total amount the customer needs to pay for headphones and CD is $38.50
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Consider a game in which a player rolls one die. If an even number comes up, the player wins the number of dollars showing on the die. If an odd number comes up, the player loses the number of dollars showing on the die. Calculate the expected value for this game. Is the game fair? (Assume that there is no cost to play the game.)
Answers
Answer:
Yes
Step-by-step explanation:
Winning numbers: 2, 4, 6
Losing numbers: 1, 3, 5
The even numbers are greater.
The average even (winning) number is 4.
The average odd (losing) number is 3.
You can win half a dollar on average.
Equation: (1/6)(-1)+(1/6)(2)+(1/6)(-3)+(1/6)(4)+(1/6)(-5)+1/6(6) = 0.5
Select the correct answer. What is the solution to the equation? √3x+3-1=x A. -1 and 2 B. -2 and 1 C. 2 D. 1
Answers
Answer:
A
Step-by-step explanation:
[tex]\sqrt{3x+3}=x+1 \\ \\ 3x+3=x^2+2x+1 \\ \\ x^2-x-2=0 \\ \\ (x-2)(x+1)=0 \\ \\ x=-1, 2[/tex]
Upon substituting both of the values back into the original equation, we see they both work.
I need help with statements 2,4,5, and 7
Answers
We know that:
[tex]\begin{gathered} YW\cong YZ,XY\cong VY \\ XZ=XY+YZ \\ XZ\cong VY+YW=VW \\ XZ\cong VW \end{gathered}[/tex]Above, we use the transitive property
1/8=?/4 how does this get solved?
Answers
Answer: ? = 1/2
Step-by-step explanation:
Your question is a bad example, so let me come up with one.
2/8 = 1/4
This is done by dividing both the numerator and denominator by the same value: 2/8 / 2/2
or
2/2 = 1, 8/2 = 4
We now have 1/4
or 9/36
What can we divide 36 by, 9 by? We need to divide by both for it to work.
9/3 = 3
36/3 = 12
3/12 But we can divide this again
3/3 = 1
12/3 = 4
1/4, we could also have divided 9/36 by 6/6 to get 1/4
For 1/8 to get ?/4, we do
8/? = 4
? = 1/2
, so the answer is 1/2/4 = 1/2*4 = 1/8
HELP ASP ILL GIVE BRAINLIEST AND 50 points
Answers
Answer:
1. 12 days
2. more than 200 miles
3. 11 lawns
4. at least 9 hours (about 9.92 hours)
Step-by-step explanation:
1. 20x < 254, so x < 12.7. We need an integer here, so x = 12 days.
2.
[tex]70 + .15x < 50 + .25x[/tex]
[tex]20 < .10x[/tex]
[tex]200 < x[/tex]
[tex]x > 200[/tex]
3. 65x > 699, so x > 10.8. Since fractions of lawns are not accepted here, Mark must mow at least 11 lawns.
4. Assuming that the speed stays constant, 65x = 645, so x = 9.92 hours. The trip will take at least 9 hours, actually close to 10 hours.
Types of Posts Cost of Each Post Base Price Posts with Words Only S5 $5 Posts with Pictures Only $10 $25 Posts with Words and Pictures $10 $35 Samuel ordered 2 posts with words only and 2 posts with pictures only. After placing his order, Samuel realized he could have saved money if he, instead, ordered 2 posts with words and pictures. Let y represent Samuel's savings, in dollars, and let x represent the number of posts. Which equation could be used to determine the amount of money Samuel could have saved if he ordered 2 posts with words and pictures, instead of his original order? A y = 5x – 5B. y = 5.r + 65C y = -5r + 25D y = 2
Answers
x = Number of posts
y = samuel's savings
If he order 2 posts with words and pictures:
y = 2(10) + 35 = 55
If he order 2 posts with words only and 2 posts with pictures only.
y = 2(5) + 2(10) + 5 + 25 = 10 + 20 + 5 + 25 = 60
Therefore, he could have save 5 dollars
Therefore the equation is:
y = 5x - 5
Answer the following questions:
pahelp pls
Answers
1. Solution of the rational equation [tex]\frac{x}{3} -6=\frac{9}{3}[/tex] is x = 27
How is the equation solved?
[tex]\frac{x}{3} -6=\frac{9}{3}\\\\\frac{x- 18}{3} =\frac{9}{3}\\\\x= 18+9\\\\x= 27[/tex]
2.The two numbers = 2, 6
How to find the two numbers?
Let the two whole numbers = x, y
Given:
x+ y =8 --- (1)
1/x+1/y = 2/3 ---(2)
Considering (2),
[tex]\frac{1}{x} +\frac{1}{y} =\frac{2}{3}\\\\\frac{x+ y}{x y} =\frac{2}{3}\\\\\text{Applying } (1),\\\\\frac{8}{x(8-x)} =\frac{2}{3}\\\\(8x-x^{2} )2 =24\\\\(8x-x^{2} ) =12\\\\x^{2} -8x+12 =0\\\\(x-6) (x-2)= 0\\\\x= 2, 6[/tex]
Substituting x in (1)
We have,
When x = 2 ; y= 6
When x = 6 ; y = 2
So, the two numbers = 2, 6
3. The two numbers = 3, 9
How to find the two numbers?
Let the two whole numbers = x, y
Given:
x- y =6 --- (1)
1/y -1/x = 2/9 ---(2)
Considering (2),
[tex]\frac{x-y}{xy} =\frac{2}{9} \\\\\text{Applying } (1)\\\\\frac{6}{x y} =\frac{2}{9} \\\\x y = 27\\\\(6+y)y = 27\\\\y^{2} +6y-27=0\\\\(y+9) (y-3) = 0\\\\y= 3, -9[/tex]
Since x and y are whole numbers we will have y = 3
When y = 3 ; x=9 (substituting in (1))
So, the two numbers = 9,3
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I am having trouble can u help me please
Answers
From the given histogram, it is found that Class 4 contains the largest number of exam scores.
What is an histogram?An histogram of a data-set is a graph that shows the number of times each element of x was observed, or elements in each range of x were observed.
From the histogram in the problem, we have that:
Class 1 contains 5 scores.Class 2 contains 3 scores.Class 3 contains 7 scores.Class 4 contains 19 scores.Class 5 contains 15 scores.Class 6 contains 18 scores.All these number of scores are given at the center of the bars on the graph.
The largest number among these number of scores is of 19 in Class 4, hence Class 4 contains the largest number of exam scores.
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The number of cars sold weekly by a new automobile dealership grows according to a linear growth
model. The first week the dealership sold six-cars (Po= 6). The second week the dealership sold
nine cars (P₁ = 9).
Write the recursive formula for the number of cars sold, Pn, in the (n + 1)th week.
P₁ = Pn-1 +
Write the explicit formula for the number of cars sold, Pn, in the (n + 1)th week.
Pn=
If this trend continues, how many cars will be sold in the fourth week?
_____cars
Answers
The recursive formula of the function is P(n + 1) = 3 + Pn while the explicit formula is P(n) = 6 + 3(n -1)
The recursive formula of the functionThe given parameters are
Po = 6
P1 = 9
From the question, we understand that the number of cars follows a linear model
This means that the common difference is
d = P1 - Po
So, we have
d = 9 - 6
Evaluate
d = 3
The recursive formula is
P(n + 1) = d + Pn
So, we have
P(n + 1) = 3 + Pn
The explicit formula of the functionFrom the question, we understand that the number of cars follows a linear model
This means that the common difference is
d = 9 - 6
Evaluate
d = 3
The explicit formula is
P(n) = Po + (n -1) * d
So, we have
P(n) = 6 + (n -1) * 3
Evaluate
P(n) = 6 + 3(n -1)
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6. How many 18k stamps can be bought with #2.00?
Answers
By using the method of division, they can buy 11 stamps.
What is division?The procedure or act of dividing the condition of division one of the pieces or groupings into which a whole is divided or is divisible. Distribution can be an act, a process, or an instance of distribution among a number. something that separates, divides, or marks off the act of dividing into portions or the process of being divided. one of the chunks or groups into which a whole can be split up or divided. the action, procedure, or occurrence of distributing among a group. Division is the act or process of splitting something that is already divided.
Given that,
18k stamps can be bought with #2.00
2.00 ÷ 0.18= 11.11
Hence, they can buy 11 stamps.
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Quadrilateral IJKL with vertices I( 5,2 ), J( 9,5), K( 5,-2 ), and L( 2,-3 ) : Reflect in the line x=1. What are the coordinates of J’?
Answers
The Solution:
Given that the vertices of a quadrilateral are:
[tex]I(5,2),J(9,5),K(5,-2)\text{ and L(2,-3)}[/tex]We are required to find the coordinate of J' when J(9,5) is reflected in the line x=1.
The new x-coordinate will become:
[tex]x=1-9=-8[/tex]So, the required coordinate of J' is:
[tex](-8,5)[/tex]Therefore, the correct answer is J'(-8,5)
The weekly repair cost Y for a machine has a probability density function given by f(y)=3(1−y)^2, 0
Answers
Using integrals, the 90th percentile of the given probability distribution is of $53.58.
What is the 90th percentile of the distribution?The amount exceeded only 10% of the time is the 90th percentile of the distribution, which is the value of p for which:
[tex]\int_0^p f(y) dy = 0.9[/tex]
The integral represents the cumulative density function of the distribution, which is the reason why we use it to find the 90th percentile of the distribution.
The function is given by:
f(y) = 3(1 - y)²
Hence the integral is calculated as follows:
[tex]\int_0^p 3(1 - y)^2 dy[/tex]
Applying the integral of the power of y rule, along with the substitution, it is found that:
[tex]\int 3(1 - y)^2 dy = -(1 - y)^3[/tex]
Hence:
[tex]\int_0^p 3(1 - y)^2 dy = -(1 - y)^3|_{y = 0}^{y = p}[/tex]
Applying the Fundamental Theorem of Calculus, considering the value of the definite integral, it is found that:
-(1 - p)³ + 1 = 0.9
-(1 - p)³ = -0.1
(1 - p)³ = 0.1
Applying the cube root to both sides:
1 - p = 0.4642.
p = 1 - 0.4642
p = 0.5358.
This amount is in hundredths of dollars, hence the 90th percentile of the given probability distribution is of $53.58, as 0.5358 x 100 = $53.58.
What is the missing information?The problem is missing, and is given by the image at the end of the answer.
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help me please!!!!!!!!
Answers
Answer:
First option is correct.
Step-by-step explanation:
Normally, Pete's dad deposits $25 into his bank account every week.
Now, he wants to deposit x extra dollars for 8 weeks. So, the total deposits for these 8 weeks will be:
8*(25 + x)
He wants to keep the total deposits above 500. So
8*(25 + x) > 500
Now we solve the inequality similarly to how we would solve an equality.
8*(25 + x) > 500
200 + 8x > 500
8x > 500 - 200
8x > 300
x > 300/8
x > $37.50
So the first option is correct.