Mathematics High School

Help me with this question

Answers

Answer 1

Answer:

D choice

Step-by-step explanation:

From:

$ \displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{9}{6} \cdot \frac{ {a}^{4} }{ {a}^{7} }}$

9/6 can be simplified as 3/2.

$ \displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{3}{2} \cdot \frac{ {a}^{4} }{ {a}^{7} }}$

Law of Exponent

$ \displaystyle \large{ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }$

Therefore:

$ \displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{3}{2} \cdot {a}^{4 - 7} } \\ \displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{3}{2} \cdot {a}^{ - 3} } \\ $

Law of Exponent II

$ \displaystyle \large{ {a}^{ - n} = \frac{1}{ {a}^{n} } }$

Therefore:

$ \displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{3}{2} \cdot \frac{1}{ {a}^{3} }}$

Now, multiply.

$ \displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{3}{2 {a}^{3} } }$

Related Questions

7. Determine the values that would make the fraction undefined:
$ \frac{ {x}^{2} + 2x - 8 }{ {x}^{2} - 3x - 10 } $

Answers

Hello there!! Here is ur answer!!

Question: Determine the values that would make the fraction undefined:

$ \frac{ {x}^{2} + 2x - 8 }{ {x}^{2} - 3x - 10 } $

Solution:To make a fraction undefined , you have to make the fraction's denominator equal to zero...

let the denominator x² - 3x - 10 is f(x),

• Setting this factor equal to 0,

→ x² - 3x - 10 = 0

• By using Middle term splitting method,

→ x² - 5x + 2x - 10 = 0

→ (x² - 5x) + (2x - 10) = 0

• Taking common,

→ x( x - 5 ) + 2( x - 5 ) = 0

→ ( x - 5 ) ( x + 2 ) = 0

• Again, setting these factors equal to 0,

we get,

( x - 5 ) = 0 and ( x + 2 ) = 0

→ x = 5 → x = -2

Hence, the values that would make the fraction undefined is x = 5,-2...

Hope this helps you!!Have a bless day!!Best of luck!! :)

The values x = 5 and x = -2 would make the fraction undefined since they would result in a zero denominator.

To find the values that would make the fraction undefined, we need to identify any values of x that would make the denominator equal to zero.

The denominator of the fraction is ($x^2 - 3x - 10$). We need to solve the equation:

$x^2 - 3x - 10 = 0$

To factorize the quadratic equation, we look for two numbers that multiply to -10 and add up to -3. These numbers are -5 and 2:

(x - 5)(x + 2) = 0

Now, we can set each factor equal to zero and solve for x:

x - 5 = 0 => x = 5

x + 2 = 0 => x = -2

Therefore, the values x = 5 and x = -2 would make the fraction undefined since they would result in a zero denominator.

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hat is the variance of the number of fixed elements, that is, elements left in the same position, of a randomly selected permutation of n elements? [hint: let x denote the number of fixed points of a random permutation. write x

Answers

Let X be the number of fixed points of a random permutation of n elements. A fixed point is an element that remains in the same position after the permutation. Thus, the probability that an element is fixed is 1/n, and the probability that it is not fixed is (n-1)/n.

Using the linearity of the expected value, we can calculate the expected value of X as:

E(X) = E(X1 + X2 + ... + Xn) = E(X1) + E(X2) + ... + E(Xn)

where Xi is the indicator random variable that is equal to 1 if the i-th element is fixed and 0 otherwise. Since the probability of an element being fixed is 1/n, we have E(Xi) = 1/n. Therefore,

E(X) = n * (1/n) = 1

To find the variance of X, we need to compute E(X^2) - E(X)^2. We can use the fact that X^2 = X1 + X2 + ... + Xn, where Xi is the indicator random variable that is equal to 1 if the i-th and j-th elements are both fixed and 0 otherwise. Then,

E(X^2) = E(X1 + X2 + ... + Xn)^2 = E(X1^2 + X2^2 + ... + Xn^2) + 2 E(X1X2 + X1X3 + ... + X(n-1)n)

Since there is only one way to fix two elements out of n, we have E(XiXj) = 1/(n(n-1)). Therefore,

E(X^2) = n * (1/n) + n(n-1) * (1/(n(n-1))) = 1 + 1/n

Finally, the variance of X is

Var(X) = E(X^2) - E(X)^2 = 1 + 1/n - 1^2 = 1/n

Therefore, the variance of the number of fixed elements of a randomly selected permutation of n elements is 1/n.

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System analysts define an object's attributes during the systems design process. true or false?

Answers

The statement "System analysts define an object's attributes during the systems design process" is true because defining object attributes is an essential part of the systems design process to ensure that the system meets the desired functional requirements.

In systems design, objects are used to represent real-world entities that are relevant to the system being developed. These objects have attributes that describe their characteristics or properties, which are used to identify and manipulate them within the system. System analysts define these attributes during the systems design process to ensure that the system meets the desired functional requirements.

For example, in a library system, a book object may have attributes such as title, author, publisher, and ISBN. Defining these attributes helps ensure that the system can properly manage and retrieve books as needed. Object-oriented design is a popular approach to systems design that relies heavily on defining objects and their attributes.

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How many angles are created when two parallel
lines are cut by a transversal? How many different
angle measures are there?

Answers

Answer:

eight angles

Step-by-step explanation:

A bricklayer lays 4 bricks the first day of the job. On each day thereafter, he lays three times the number of bricks he laid on the previous day. If he continues this pattern, how many bricks in total will he have laid at the end of the fifth day? Responses 10 bricks 10 bricks 24 bricks 24 bricks 324 bricks 324 bricks 484 bricks

Answers

At the end of the fifth day, a bricklayer has laid 324 bricks on the job.

What is multiplication?

Multiplication is a mathematical arithmetic operation.

It is also a process of adding the same types of expression to some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given, a bricklayer lays 4 bricks on the first day on the job.

On each day thereafter, he lays three times the number of bricks he laid on the previous day.

And he continued his pattern.

Let x be the number of bricks he laid in the previous day.

Then according to the question,

The number of bricks in total is = 3x

For the second day, x =4

Number of the bricks he laid on the second day = 12

Now the x =12 for the third day.

Number of the bricks he laid on the third day = 36

Now x = 36 for the fourth day.

Number of the bricks he laid on the fourth day = 108

Now the x = 108 for the fifth day.

Number of the bricks he laid on the fifth day = 324

Therefore, 324 bricks he has laid at the end of the fifth day.

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tyreek invested $8,000 into an account that pays 12% simple interest annually. what will the balance of his account be after ten years?

Answers

Answer:

I belive it would be $17,600

Step-by-step explanation:

The way I did it might be confusing but.

12% of 8,000 is 960

960 * 10 is 9,600

9,600 + 8,000 = 17,600

PLEASE ANSWER AS SOON AS YOU SEE THIS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Which expression is equivalent to 5 (2 + 7)? 2 (5 + 7) 2 + 7 (5) 5 (2) + 7 5 (2) + 5 (7)

Answers

Answer:

D. 5 (2) + 5 (7)

Step-by-step explanation:

Given expression:

5(2 + 7)

Distribute this to get:

a(b + c) = ab + ac5(2 + 7) = 5(2) + 5(7)

Correct choice is D

Answer:

D. 5 (2) + 5 (7)

Step-by-step explanation:

Given expression:

• 5(2 + 7)

Distribute this to get:

• a(b + c) = ab + ac

• 5(2 + 7) = 5(2) + 5(7)

correct choice is D

If the original quantity is 5 and the new quantity is 4, what is the percent decrease?
The percent decrease is
%.

Answers

Answer:

The percent decrease is 20%

Step-by-step explanation:

$5 \times \frac{20}{100 } $

$ = 1$

$5 - 1 \\ = 4$

Answer:

the percent decrease is 20%

Step-by-step explanation:

the

Write each function in standard form. Determine the x-intercepts of the function.

Y=-4(x+2)(x+3)

Answers

Answer:

X Intercept (-2,0), (-3,0) and Standard form y = -4x^2 - 20x - 24

Step-by-step explanation:

To write a polynomial in standard form, simplify, and then arrange the terms in descending order.

y = ax^2 + bx + c

y = (−4x−8) (x+3)

Expand (−4x−8) (x+3) using the FOIL Method

y = −4x ⋅ x − 4x ⋅ 3 − 8x−8 ⋅ 3

Simplify and combine like terms.

y = −4x^2 − 20x − 24

Hope this can help

What are the solutions to the equation W 2w 3 4?.

Answers

By using the cross multiplication, we can determine the solutions to the equation w=2 , w=6.

How is cross multiplication defined?

By multiplying the numerator of one side by the denominator of other side and equating the resulting two products, cross multiplying can be used to solve a fractional equation when each side has a fraction with a single denominator.

Given the expression $\frac{w}{2w-4} = \frac{4}{w}$

By using cross multiplication, we have

$w^{2} = 4(2w-3)\\ w^{2} = 8w-12\\w^{2}-8w+12=0\\(w-2)(w-6)=0\\w=2 and w=6$

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is 0.70 a rational or irrational?

Answers

Answer:

Rational

Step-by-step explanation:

As 0.70 can be represented as 70/100 or 7/10

the multiplicative inverse of -87

Answers

Multiplicative Inverse of 87 is defined as what you can multiply with 87 to get 1.

If the Multiplicative Inverse of 87 is x, the problem can be written as a function as follows:

87(x) = 1

Thus, to get the answer, we divide 1 by 87 like this:

1 / 87 = 0.01149425

Note that the answer is rounded to the nearest 8 decimals if necessary. We can prove that the answer is correct: 0.01149425 multiplied by 87 equals 1.

The Multiplicative Inverse of postive 87 has a positive answer and the Multiplicative Inverse of negative 87 has a negative answer. Therefore, the Multiplicative Inverse of -87 is -0.01149425.

hope this helps

:))

Answer:

-1/87

Step-by-step explanation:

The multiplicative inverse is just a number reversed. A whole number, when being multiplied by a fraction, is written over 1.

Let's say that number is 2. 2 becomes 2/1 and the multiplicative inverse would be 1/2.

A student uses the following steps to prove the sine sum identity. The proof is incorrect.

Answers

Answer:

Step 4 is incorrect ⇒ C

Step-by-step explanation:

Let us check step by step

∵ sin(x + y)

∵ sin(z) = cos($\frac{\pi}{2}$ - z)

→ Replace z by (x + y)

∴ sin(x + y) = cos($\frac{\pi }{2}$ - [x + y])

∴ Step 2 is correct

∵ cos($\frac{\pi }{2}$ - [x + y]) = cos($\frac{\pi }{2}$ - x - y])

∵ take [$\frac{\pi }{2}$ - x] as the 1st angle and y as the 2nd angle

∴ cos($\frac{\pi }{2}$ - x - y]) = cos([$\frac{\pi }{2}$ - x] - y)

∴ Step 3 is correct

∵ cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

→ Replace a by ([$\frac{\pi }{2}$ - x] and b by y

∴ cos([$\frac{\pi }{2}$ - x] - y) = cos($\frac{\pi }{2}$ - x)cos(y) + sin($\frac{\pi }{2}$ - x)sin(y)

∴ Step 4 is incorrect, the second angle is y not (-y)

∵ cos($\frac{\pi }{2}$ - x) = sin(x)

∵ sin($\frac{\pi }{2}$ - x) = cos(x)

∴ cos($\frac{\pi }{2}$ - x)cos(y) + sin($\frac{\pi }{2}$ - x)sin(y) = sin(x)cos(y) + cos(x)sin(y)

∴ Step 5 is correct

Answer:

C. Step 4

Step-by-step explanation:

got it right on edge :)

if g(x)=x-2 and h(x)=x^2-1 , what is ( h+g)(x)

Answers

Answer:

$x^{2} + x -3$

Step-by-step explanation:

1. Write out the equation

$(x-2)+( x^{2} -1)\\$

2. Add like-terms

$x^{2} +x-3$

Step-by-step explanation:

(X^2-1+x-2)

(X^2+x-2x-2)

X(x+1)-2(x+1)

(X-2)(x+1)

an angle drawn in standard position measures 10 radians. in what quadrant does its terminal ray lie? show the reasoning that leads to your answer

Answers

An angle drawn in standard position measuring 10 radians has its terminal ray lying in the third quadrant. The reasoning behind this can be explained by understanding the relationship between the angle measurement and the quadrants in the coordinate plane.

In the standard position, an angle is drawn with its initial side along the positive x-axis and its terminal side determined by the angle measurement. In the coordinate plane, the quadrants are divided into four sections: first quadrant (positive x and y), second quadrant (negative x, positive y), third quadrant (negative x and y), and fourth quadrant (positive x, negative y).

In this case, the angle measures 10 radians, which is greater than π radians (approximately 3.14). Since π radians is half of a circle (180 degrees) and represents the boundary between the second and third quadrants, an angle measuring 10 radians is greater than π and thus falls in the third quadrant.

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What does laissez-faire mean? a. to let be b. to buy c. to control d. to contribute

Answers

The phrase "lassez-faire" comes from the French and means "to allow to do."

It suggests that governments and the law shouldn't meddle with business, finance, or people's working life in terms of economics. It ought to leave them alone and refrain from interfering.

Laissez-faire: what is it?

Laissez faire is an economic theory that advocates letting business and industry owners choose how their employees are paid and treated without interference from the government. This approach is in favor of an unrestricted free market. In English, the term is translated as "let do," which means "let people do what they choose." John Smith

The importance of laissez-faire theory?

Businesses in a free-market economy are less subject to governmental prohibitions that would make doing business more difficult. In such a setting, businesses are more inclined to take chances and invest in the economy.

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1. Vivienne, John, and Nassim ran for 6th grade class president. ● Vivienne got six votes for every three votes that John got. ● Nassim got two votes for every vote that Vivienne got. Overall, 148 6th-grade scholars voted in the class president election. How many votes did each class president candidate receive?

Answers

John get 21 votes, Vivienne got 42 votes, and Nassim got 84 votes using the concept of equations.

Define equations.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It demonstrates the equal relationship between the expressions presented on the left and right sides.

Let t the number of votes John got = x

So, the number of votes Vivienne received = 2x

Also, the number of Votes Nassim received = 2 (2x)

= 4x

The total number of votes is given by

= x + 2x + 4x

= 7x

Given the total number of voters = 148

So, we can write an equation

7x = 148

x = 148/7

x ≈ 21

So, John get 21 votes

Vivienne got 2(21) = 42 votes

Nassim got 4(21) = 84 votes

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What are the missing parts that correctly complete the proof?

Answers

Answer: 2. PX=QX ----------- Definition of bisector.

3. AXP and AXQ ----------- Definition of perpendicular.

4. AXP=AXQ ------------- All right angles are congruent.

6. AXP=AXQ ------------ SAS congruence

7. AP=AQ -------------Corresponding parts of congruent triangles

Step-by-step explanation:

You finally get an allowance! You put $2 away. In January, $4 away. In February, $8 away. In March, $16 away. In April and followed this savings pattern through to December. How much money do you have in 12 months?

Answers

Add all the numbers together to find your answer.

___________________________________________

Remember : In April and followed this savings pattern through to December.

35 flower and 7 vase she want to put the same number in each vase

Answers

Answer:5 in each

Step-by-step explanation:

35/7=5

Answer: 5 flowers in each vase.

Step-by-step explanation: We want to divvy up 35 flowers equally into each vase, so we divide 35 by 7 to get 5 flowers for each vase. (35/7=5)

Hope this helps! :)

solve the equation for y. ax + by = c

Answers

Answer:

y = ( c-ax)/b

Step-by-step explanation:

ax + by = c

Subtract ax from each side

ax-ax + by = c-ax

by = c-ax

Divide each side by b

by/b = ( c-ax)/b

y = ( c-ax)/b

How is solving for speed similar to solving for time?

Answers

Answer:

Rate and speed are similar since they both represent some distance per unit time like miles per hour or kilometers per hour.... To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.

Answer:

In my opinion solving for speed is similar to solving for time because when trying to do both of those you want to have a certain amount of time left for instance solving for speed I could Say "oh I want to solve this math question fast!"

Solving it fast will mean I have time left to do something else same with solving for time

"I want to solve this math question for time!" Meaning I want to solve it fast enough to have time left Hopefully this is what you want in an answer! I'm sorry if this isn't what you want

O skaters are racing toward the finish
race. The first skater has a 40 meter
d and is traveling at a rate of 12 meters
second. The second skater is travelin
ate of 14 meters
per
second. How long
it take for the second skater to pass
st skater?

Answers

The first skater has a 40 meter d and is traveling at a rate of 12 meters second, second skater is traveling rate of 14 meters per second. it will take 20 seconds for second skater to pass the first skater.

What is the definition of time?

Time is continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in conscious experience. Time is often referred to as fourth dimension, along with three spatial dimensions.

Time has long been an important subject of study in religion, philosophy, and science, but defining it in manner applicable to all fields without circularity has consistently eluded scholars. Nevertheless, diverse fields such as business, industry, sports, the sciences, and performing arts all incorporate some notion of time into their respective measuring systems.

12x+40=14x

40=2x

x=20

it will take 20 seconds for second skater to pass the first skater.

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A parking garage allows users to park the first hour free and then charges $2. 50 for each additional hour or fraction of an hour. Which equation represents this situation?.

Answers

Answer:

4hours + 1hour = $2.50

Step-by-step explanation:

four hours free= 0 charge

1 hour = $2.50

therefore 4 + 1 = $2.50

C
f
33 mi
44 mi
What is the length of the hypotenuse?
C =
miles

Answers

Answer:

The hypotenuse is 55 miles

Step-by-step explanation:

Given the sides of a right angle triangle as 33 and 44 miles, we want to get the hypotenuse

Mathematically, by Pythagoras’ theorem, the hypotenuse square is the sum of the squares of the other two sides

So we have;

h^2 = 33^2 + 44^2

h^2 = 3025

h = √3025

h =55 miles

Which of these sets of ordered pairs satisfies an exponential equation? (1) {(1, -1), (2, -8), (3, -27), (4, -64)} (2) {(1, -1), (2, -4), (3, -9), (4, -16)} (3) {(1, -2), (3, -8), (5, -32), (7, -128)} (4) {(1, -2), (3, 2), (5, 6), (7, 10)}