Mathematics High School

Which expression is equivalent to (r^5/4

Answers

Answer 1

Answer:

Step-by-step explanation:

• Multiplying two numbers with same bases is the same as adding their powers:

∴ [tex](\frac{4^{\frac{5}{4} } \cdot 4^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]

⇒ [tex](\frac{4^{\frac{5}{4} } ^ + ^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]

⇒ [tex](\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]

• Dividing two numbers with same bases is the same as subtracting their powers:

∴ [tex](\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]

⇒ [tex](4^{{\frac{6}{4} - \frac{1}{2} }})^{\frac{1}{2} }[/tex]

⇒ [tex](4^{1})^{\frac{1}{2} }[/tex]

⇒ [tex]4^{\frac{1}{2}[/tex]

• Raising anything to the power of [tex]\frac{1}{2}[/tex] is the same as square-rooting it:

∴ [tex]4^{\frac{1}{2}[/tex]

⇒ [tex]\sqrt{4}[/tex]

⇒ 2

Related Questions

One leg of a right triangle has a length of 5m. The other sides have lengths that are consecutive integers. Find these lengths.

Answers

The lengths of the other two sides of the right triangle are 12 and 13

Pythagorean theorem

From the question, we are to determine the lengths of the other sides of the triangle

From the given information,

The other sides have lengths that are consecutive integers

Thus,

If the length of the other side is x

Then,

The hypotenuse will be x + 1

By the Pythagorean theorem, we can write that

(x+1)² = x² + 5²

(x+1)(x+1) = x² + 25

x² + x + x + 1 = x² + 25

x² - x² + x + x = 25 - 1

2x = 24

x = 24/2

x = 12

∴ The other leg of the right triangle is 12

Hypotenuse = x + 1 = 12 + 1 = 13

Hence, the lengths of the other two sides are 12 and 13

Learn more on Pythagorean theorem here: https://brainly.com/question/4584452

#SPJ1

Each score in a set of data is multiplied by 3, and then 4 is subtracted from the result. If the original mean is 10 and the original standard deviation is 5, what are the new mean and new standard deviation

Answers

The new mean and standard deviation is 26 and 15, when each score in data set is multiplied by 5 and then 7 is added.

According to the question,

Original mean is 10 and original standard deviation is 5 . In order to find to new mean and standard deviation when each score in data set is multiplied by 5 and then 7 is added.

First "change of scale" when every score in a data set is multiplied by a constant, its mean and standard deviation is multiplied by a same constant.

Mean: 10*3 = 30

Standard deviation: 5*3 = 15

Secondly "change of origin" when every score in a data set by a constant, its mean get added or subtracted by the same constant and standard deviation remains constant.

Applying change of origin in the above mean and standard deviation

Mean: 30 - 4 = 26

Standard deviation: Remains same = 15

Hence, the new mean and standard deviation is 26 and 15, when each score in data set is multiplied by 5 and then 7 is added.

Learn more about Mean and standard deviation here

https://brainly.com/question/26841432

#SPJ4

p(x)= x2-x-12 and q(x)=x+3 find p(x) ÷ q(x) The question of O-MATH

Answers

Hello,

[tex] \frac{p(x)}{q(x)} = \frac{ {x}^{2} - x - 12}{x + 3} = \frac{(x - 4)(x + 3)}{x + 3} = x - 4[/tex]

Answer:

Step-by-step explanation:

Last week salazar played 13 more tennis games than perry. if they played a combined total of 53 games. How many games did salazar play?

Answers

If last week Salazar played 13 more tennis games than Perry and they played a combined total of 53 games, then Salazar played a total of 33 games.

Let the total number of games played by Perry be x.

It is given that, Salazar played 13 more tennis games than Perry.

⇒ Total games played by Salazar = x + 13

Also, Salazar and Perry played a combined of 53 games.

Hence, total number of tennis games played by Salazar and Perry = 53

⇒ Games played by Salazar + Games played by Perry = 53

⇒ x + (x + 13) = 53

2x + 13 = 53

2x = 53 - 13

2x = 40

x = 40 / 2

x = 20

Therefore, total number of games played by Salazar = x+13

= 20 + 13

= 33

Thus, Salazar played total 33 games.

Learn more on total here:

https://brainly.com/question/14306809

#SPJ1

I need to find the equation of the line

Answers

Answer:

y = 3x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line

m = [tex]\frac{3-0}{0-(-1)}[/tex] = [tex]\frac{3}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = 3x + 3 ← equation of line

Answer:

y = 3x + 3

Step-by-step explanation:

See attached image.

How do I solve this?

Answers

Answer:

first option

Step-by-step explanation:

to find the zeros equate f(x) to zero , that is

2x² + 8x - 3 = 0 ( add 3 to both sides )

2x² + 8x = 3 ← factor out 2 from each term on the left side

2(x² + 4x) = 3

to complete the square

add/subtract ( half the coefficient of the x- term )² to x² + 4x

2(x² + 2(2)x + 4 - 4) = 3

2(x + 2)² - 8 = 3 ( add 8 to both sides )

2(x + 2)² = 11 ( divide both sides by 2 )

(x + 2)² = [tex]\frac{11}{2}[/tex] ( take square root of both sides )

x + 2 = ± [tex]\sqrt{\frac{11}{2} }[/tex] ( subtract 2 from both sides )

x = - 2 ± [tex]\sqrt{\frac{11}{2} }[/tex]

that is

x = - 2 - [tex]\sqrt{\frac{11}{2} }[/tex] , x = - 2 + [tex]\sqrt{\frac{11}{2} }[/tex]

Answer:

x = -2 - √11/2 and - 2 + √11/2.

Step-by-step explanation:

2x^2 + 8x - 3 = 0

Divide first 2 terms by 2:

2(x^2 + 4x) - 3 = 0

2(x^2 + 4x) = 3

Complete the square:

2 [ (x + 2)^2 - 2^2) = 3

2(x + 2)^2 - 8 = 3

2(x + 2)^2 = 11

(x + 2)*2 = 11/2

x + 2 = ± 11/2

x = -2 ± √11/2

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?

y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2

Answers

The inequality represented by the graph is; B: y > 3x + 2

How to Interpret Inequality Graphs?

We are told that the line goes through the coordinates;

(-3, -7) and (0, 2)

Now, formula to find the slope is;

m = (y2 - y1)/(x2 - x1)

m = (2 - (-7))/(0 - (-3))

m = 9/3

m = 3

Since it's a dashed straight line and everything to the left is shaded, then it means that the inequality represented by the graph is;

y > 3x + 2

Read more about Inequality Graphs at; https://brainly.com/question/11234618

#SPJ1

Answer:

Step-by-step explanation:

edge 23

Ilean works as a welder and web designer. As a welder, she earns $18 per hour. Last week she worked 푥 hours as a welder and her friend paid her $75 to design a web page. Write an expression to represent the total amount Ilean earned last week.

Answers

The expression that represent the total amount Ilean earned last week is 27(18) + 75

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Let y represent the total amount Ilean earned last week for working x hours.

Since she worked for 27 hours and earned $75 to design a web page. Hence:

y = 27(18) + 75

The expression that represent the total amount Ilean earned last week is 27(18) + 75

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Find the value of x in each figure

Answers

Answer here is
X = 124

A manufacturer of window frames knows from long experience that 5 percent of the production will have some type of minor defect that will require an adjustment. What is the probability that in a sample of 20 window frames: a. None will need adjustment

Answers

0.385 is the probability under given conditions.

Lets simplify the above problem,

Given n=20, p=0.05, q=0.95

Probability that in a sample of 20 window frames:

None will need adjustments.

P(x=0)= 0.95^20 = 0.3585

At least one will need adjustment?

P(x>=1) = 1 - P(x=0)

= 1 - 0.3585

= 0.6415

More than two will need adjustment?

P(x>2) = 1 - P(x=0) -P(x=1) -P(x=2)

= 1 - 0.3585 - 20C1(0.05)^1*(0.95)^19 - 20C2(0.05)^2*(0.95)^18

= 0.6415 - 20*0.05*0.3774 - 190*0.0025*0.3972

= 0.2641-0.18868

= 0.0755

Hence 0.385 is the solution of the given problem.

Learn more about Probability on:

https://brainly.com/question/13604758

#SPJ4

[tex]20-x-x^{2}[/tex]

solve this equation by class 9 course

Answers

The factored expression of the polynomial is (4 - x)(5 + x)

How to solve the polynomial?

The polynomial expression is given as;

20 - x - x^2

Expand the expression

20 - 5x + 4x - x^2

Factorize the expression

5(4 - x) + x(4 - x)

Factor out 4 - x

(4 - x)(5 + x)

Hence, the factored expression of the polynomial is (4 - x)(5 + x)

Answers

Answer:

18 posters

Step-by-step explanation:

Posters posted last week: 81/3 = 27 posters

Remaining posters: 81-27 = 54 posters

Posters posted this week: 54/3 = 18*2 = 36 posters

Posters remaining: 54-36 = 18 posters

can someone please help me

Answers

Based on the knowledge of trigonometric expressions and properties of trigonometric functions, the value of the sine function is equal to - √731 / 30.

How to find the value of a trigonometric function

Herein we must make use of trigonometric expressions and properties of trigonometric functions to find the right value. According to trigonometry, both cosine and sine are negative in the third quadrant. Thus, by using the fundamental trigonometric expression (sin² α + cos² α = 1) and substituting all known terms we find that:

[tex]\sin \theta = -\sqrt{1 - \cos^{2}\theta}[/tex]

[tex]\sin \theta = - \sqrt{1 - \left(-\frac{13}{30} \right)^{2}}[/tex]

sin θ ≈ - √731 / 30

Based on the knowledge of trigonometric expressions and properties of trigonometric functions, the value of the sine function is equal to - √731 / 30.

To learn more on trigonometric functions: https://brainly.com/question/6904750

#SPJ1

Which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

Answers

The rule which states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities is "Multiplicative rule".

What is Multiplicative rule?

The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.

If A and B are dependent events, then the probability of both events occurring simultaneously is given by:

[tex]P(A \cap B)=P(B) \cdot P(A \mid B)[/tex]

The likelihood of both events occurring simultaneously in an experiment where A and B are two independent events is given by:

[tex]P(A \cap B)=P(A) \cdot P(B)[/tex]

Multiplication Theorem of Probability:

The multiplication guidelines that we use in probability have already been taught to us, including;

[tex]\begin{aligned}&P(A \cap B)=P(A) \times P(B \mid A) \text {; if } P(A) \neq 0 \\&P(A \cap B)=P(B) \times P(A \mid B) \text {; if } P(B) \neq 0\end{aligned}[/tex]

Therefore, the relationship between two events is explained by the probability multiplication rule.

Set AB represents the events in which both events A and B have occurred for two events A and B related to a sample space S.

Consequently, (AB) indicates that occurrences A and B happened at the same time. You can write the event AB as AB.

Using the characteristics of conditional probability, the likelihood of event AB is calculated.

To know more about rule of multiplication, here

https://brainly.com/question/15050512

#SPJ4

The length of a rectangle plus its width is 24 cm. The area is 135 cm. What are the length and width of the rectangle

Answers

Answer:

[tex]l = 5.63 \\ [/tex]

hope this helps

Please help!!!!!!!!!!

Answers

Answer: 18.7

Step-by-step explanation:

Find the lengths of AB, BC, and CA

AB = [tex]\sqrt{(4-(-1))^{2} + (-1-4)^{2} }[/tex] = 5[tex]\sqrt{2}[/tex] ≈ 7.1

BC = [tex]\sqrt{(0-(-1))^{2} + (-3-4)^{2} }[/tex] = 5[tex]\sqrt{2}[/tex] ≈ 7.1

CA = [tex]\sqrt{(0-4)^{2} + (-3-(-1))^{2} }[/tex] = 2[tex]\sqrt{5}[/tex] ≈ 4.5

7.1 + 7.1 + 4.5 = 18.7

Drag each description to the correct location to complete the flow chart proof. Given: . D is the midpoint of . . Prove: is an isosceles triangle.

Answers

The isosceles triangle is proved below.

How to illustrate the triangle?

The complete information wasn't found. The proofing of the triangle will be illustrated. It should be noted that the angles opposite to the equal sides of an isosceles triangle are also equal.

Proof: Consider an isosceles triangle ABC where AC = BC.

We need to prove that the angles opposite to the sides AC and BC are equal, that is, ∠CAB = ∠CBA.

We first draw a bisector of ∠ACB and name it as CD.

Now in ∆ACD and ∆BCD we have,

AC = BC (Given)

∠ACD = ∠BCD (By construction)

CD = CD (Common to both)

Thus, ∆ACD ≅∆BCD (By SAS congruence criterion)

So, ∠CAB = ∠CBA (By CPCT)

Learn more about triangles on:

https://brainly.com/question/1058720

#SPJ1

How many distinct triangles can be formed for which m∠E = 64°, g = 9, and e = 10?
triangle(s)

How many distinct triangles can be formed for which m∠J = 129°, k = 8, and j = 3?
triangle(s)

Answers

Answer:

Step-by-step explanation:

For two side measures and one angle measure to form one distinct triangle, the given angle must be between the given sides, or opposite the longest side.

When the given measures are ...

E = 64°g = 9e = 10

The given angle is opposite the longest side, so one distinct triangle can be formed.

No triangle can be formed if the given angle is opposite the shorter given side, and either of ...

the angle is right or obtusethe ratio of shorter to longer sides is less than the sine of the given angle.

Additional comment

As we can see from the above, the only ambiguous cases arise when the given angle is opposite the shorter given side. When that happens, the ratio of the shorter to longer given side relative to the sine of the given angle determines the nature of the solution:

two distinct triangles if the ratio is greater than the sineone right triangle if the ratio is equal to the sine.

Answer:

Step-by-step explanation:

Find the five-number summary for the data.
{236, 202, 218, 208, 225, 229, 211, 237, 223, 206, 217, 216, 232, 225, 208}

Answers

Minimum: 202

Quartile (Q1): 208

Median: 218

Quartile Q3: 229

Maximum: 237

What is the Five-Number Summary?

The max and min value, the lower and upper quartiles, and the median of a data comprise the five-number summary.

Given the data: 236, 202, 218, 208, 225, 229, 211, 237, 223, 206, 217, 216, 232, 225, 208, we would have the following:

Minimum: 202 (least value)

Quartile (Q1): 208 (center of the first half of the data)

Median: 218 (center of the data when ordered)

Quartile Q3: 229 (center of the second half of the data)

Maximum: 237 (highest value).

Learn more about the five-number summary on:

https://brainly.com/question/24809873

#SPJ1

Question is DOWN↓ PLS ANSWER I WILL MARK BRAINLIEST.....

Answers

Answer: Anita's

Step-by-step explanation:

Anita's shape would have the longest sides because she only has 4 total sides, while the others have 5, 6, and 10

This means that if the total perimeter for each of the shapes was 10 units,

Anita's shape would have side lengths of about 2.5 units while the others would have side lengths of 2, 1.6, and 1 units.

This means Anita's shape has the longest sides

Office procedure note this 39-year-old patient returns to the office today because of a defect on the nail of his left big toe. he was seen three times in the last four months for this problem. this defect is very suspicious, and i felt it best to biopsy a portion of the nail plate and bed. the sample was sent to pathology. i told the patient that he will be called with the results, and then i will decide how to proceed. cpt code(s):

Answers

The CPT code that is used here is CPT code 11755.

What is the CPT code 11755?

This is the code that is used as the biopsy of the nail bed. The CPT code is used to report this procedure.

Then it would be determined if it is a case of melanoma or lesion that is causing the issues with the individuals nails.

Answers

At 0 hour, the amount of water in this pond is 2,660 liters.At 1 hour, the amount of water in this pond is 3,225 liters.No, the amounts given in parts (b) and (c) are not equal because because the line doesn't pass through the origin (0, 0) of the graph.

How to determine the amount of water?

By critically observing the graph above, the amount of water in this pond at 0 hour is equal to 2,660 liters.

Similarly, the amount of water in this pond at 1 hour is equal to 3,225 liters.

Next, we would determine the rate of increase:

Rate = Δy/Δx

Rate = (3225 - 2660)/(1 - 0)

Rate = 665.

The amounts given in parts (b) and (c) are not equal because because the line doesn't pass through the origin (0, 0) of the graph.

Read more about rate at: https://brainly.com/question/26388020

#SPJ1

Part E:
Write the equation of the graphed function f(x), where a is the leading coefficient. Use the factors found in part D. Express the function as the product of its leading coefficient and the expanded form of the equation in standard form.

Answers

The equation for the graphed function is (x+20)(x+5)(x-15).

How to illustrate the equation?

It should be noted that a graph shows the relationship between variables.

From the graph, the equation is x³+10x²-275x-1500.

In this case, this can be as - (x + 20)(x + 5)(x - 15)

The graph crosses the x axis. The coefficient is negative because the graph rises to the left.

Learn more about equations on:

brainly.com/question/11948360

#SPJ1

According to the weather report, there is a 25% chance of snow in the mountains tomorrow. how likely is it to snow tomorrow in the mountains?

Answers

It is likely is it to snow tomorrow in the mountains is 1/4

A chance is the occurrence of events without apparent purpose or cause. It is simply the possibility that something will happen. When chance is defined in mathematics, it is called probability. Probability is the extent to which an event is likely to occur, measured by the ratio of favorable cases to the total number of possible cases. Mathematically, the probability that an event occurs is equal to the ratio of the number of cases favorable to a particular event to the number of all possible cases. The theoretical probability of an event is referred to as P(E). P(E) = number of outcomes more favorable to E/Nnumber of all possible outcomes of the experiment

We need to find that what is the chance that it will snow tomorrow in the mountains

According to the weather report, there is a 25% chance of snow in the mountains tomorrow.

Therefore the possible chance that it will snow tomorrow is 25/100 = 1/4

Learn more about possible chances here:

https://brainly.com/question/28052733

#SPJ4

Write an expression using fractions to show how to determine the amount that each person will pay. Then calculate each person's contributions showing all steps in long division.

Me: $14.89
Friend 1: $7.27
Friend 2: $25.67
Friend 3: $11.59

Answers

The fraction based on the information given illustrated for each person.

How to illustrate the information?

Me: $14.89

Friend 1: $7.27

Friend 2: $25.67

Friend 3: $11.59

Total = $59.42

The fraction for each person will be:

Me: $14.89 = 14.89/59.42 = 0.25

Friend 1: $7.27 = 7.27/59.42 = 0.12

Friend 2: $25.67 = 25.67/59.42 = 0.32

Friend 3: $11.59 = 11.59/59.42 = 0.195

Learn more about fractions on:

brainly.com/question/78672

#SPJ1

What are the factors of 3x2 23x − 8? (3x − 4)(x 2) (3x − 2)(x 4) (3x − 8)(x 1) (3x − 1)(x 8)

Answers

Answer:

(3x − 1)(x 8)

Step-by-step explanation:

Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Answers

Answer:

The radius of the circle is 3 units. TRUE

The center of the circle lies on the x-axis. TRUE

The center of the circle lies on the y-axis. FALSE

The standard form of the equation is (x – 1)² + y² = 3. FALSE

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. TRUE

Step-by-step explanation:

x² + y² - 2x - 8 = 0

x² - 2x + y² = 8

Complete the square in x.

x² - 2x + 1 + y² = 9

(x - 1)² + y² = 3²

Center: (1, 0); radius: 3

The radius of the circle is 3 units. TRUE

The center of the circle lies on the x-axis. TRUE

The center of the circle lies on the y-axis. FALSE

The standard form of the equation is (x – 1)² + y² = 3. FALSE

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. TRUE

PLEASE HELP IM STUCK

Answers

Answer:

-2

Step-by-step explanation:

The slope of a line is rise/run

So, just see how much the line rises/how much the line runs

In this case, the line rises 2 units for every -1 unit it runs

So, the slope is -2

Which function could be a stretch of the exponential decay function shown on the graph?

f(x) = 2(6)x
f(x) = One-half(6)x
f(x) = 2(one-sixth) Superscript x
f(x) = One-half (one-sixth) Superscript x

Answers

We find that the function that could be a stretch of the exponential decay is [tex]f(x) = 2\cdot \left(\frac{1}{6} \right)^{x}[/tex]. (Correct choice: C)

What function represents a stretch of a exponential decay function?

Exponential functions are trascedent functions whose form is described below:

[tex]y = a\cdot r^{x}[/tex] (1)

Where:

a - Stretch factorr - Growth rate

There are two conditions for a stretch factor and exponential decay: (i) a > 1, (ii) 0 < r < 1. Thus, we find that the function that could be a stretch of the exponential decay is [tex]f(x) = 2\cdot \left(\frac{1}{6} \right)^{x}[/tex]. (Correct choice: C)

Remark

The picture is missing and it cannot be found, but statement is still solvable as there is only one choice that responds the question.

To learn more on exponential functions: https://brainly.com/question/11487261

#SPJ1

The graph of a relation is shown.

A coordinate plane with a straight line. The line starts in the lower left quadrant and continues up through the uppercase right quadrant. The line passes through the y-axis slightly below the origin, and then passes through the x-axis slightly to the right of the origin.
Which of these values could be the slope of the line? Select two options.

–2

0

Answers

The values which could be the slope of the line are numbers > 0.

Which values could be the slope of the line?

According to the task content, it follows that the given line originates from the lower left quadrant and continues through the upper right quadrant.

It therefore follows that the line is ascending from left to right in which case, the slope of the line is positive.

Hence, the possible values of the slope include the set of numbers greater than 0.