Answer the questions below. Be sure to mark all answers that apply

\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

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Answer:

1.1574 heart beats per second

Step-by-step explanation:

In order to solve this problem, you need to keep converting the units of time from day to hour to minutes to seconds. If a heart beats a 100,000x per day , the ratio of heart beats a day is 100,000 beats / 1 day .Use the equation below.

\(\frac{100,000 beats}{1 day} * \frac{1 day}{24 hours} * \frac{1 hour}{60 minutes} * \frac{1 minute}{60 seconds}\)

100,000/24/60/60 = 1.1574 beats a second

Answer:

\( y = mx +b\)

With m the slope and b the intercept

For this case the intercept can be identified as b =3 since is the intersection value at the y axis (x=0).

The slope can be founded using any two points. For instance we can select (0,3) and (-2,0) and we have the following formula:

\( m=\frac{y_2 -y_1}{x_2 -x_1}\)

And replacing we got:

\( m =\frac{0-3}{-2-0}= \frac{3}{2}\)

And then our equation would be given by:

\( y = \frac{3}{2}x +3\)

Step-by-step explanation:

We need to find a equation in the form:

\( y = mx +b\)

With m the slope and b the intercept

For this case the intercept can be identified as b =3 since is the intersection value at the y axis (x=0).

The slope can be founded using any two points. For instance we can select (0,3) and (-2,0) and we have the following formula:

\( m=\frac{y_2 -y_1}{x_2 -x_1}\)

And replacing we got:

\( m =\frac{0-3}{-2-0}= \frac{3}{2}\)

And then our equation would be given by:

\( y = \frac{3}{2}x +3\)

Answer:

what

Step-by-step explanation:

Answer:

2 1/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

let present age of father=y

present age of son=x

then y=3x

after 15 years age of father=y+15

and age of son=x+15

∴y+15=2(x+15)

y+15=2x+30

y-2x=30-15

y-2x=15

∴3x-2x=15

x=15

y=3x=15×3=45

father's present age=45 years

Answer:

The selling price of the diamond necklace at Shamin Jewelers after 10% discount is:

$442 * 0.9 = $397.80

The selling price of the same necklace at the competitor's store after 34% and 14% discount is:

$527 * 0.66 * 0.86 = $247.08

So, Shamin Jewelers needs to offer an additional discount to meet the competitor's price:

$397.80 - $247.08 = $150.72

To calculate the additional rate of discount, we divide the difference by the original selling price at Shamin Jewelers and multiply by 100:

($150.72 / $442) * 100 = 34.11%

Therefore, Shamin Jewelers must offer an additional 34.11% discount to meet the competitor's price.

Step-by-step explanation:

The best way to solve an equation of the form Ax+by=c could be either substitution, completing the squares or graphical method depending on the type of equation given.

Quadratic equation

The equation in the form Ax+by=c is a quadratic problem which could be approached in different ways depending on the specific equation given and the information provided.

The methods of approach are substitution, completing the squares or graphical method which all have proven to be suitable ways to arrive at the solution.

Hence, either of the three methods are good ways to solve such equation.

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Answer:

by solving the angles of triangles we get A= 35 degree

Answer:

how do i cancel i dont know this

Step-by-step explanation:

Answer:

76 m^2

Step-by-step explanation:

To find the area of the figure, you must divide the figure into multiple shapes. By dividing the figure into a 4 x 9 rectangle and a 5 x 8 rectangle, you can calculate the area of these two figures and add them together. After doing this, your answer should be 76 m^2.

Answer:

See the image for marked congruences.

1. JM ≅ LM                           |      Given

2. △JML is isosceles          |      definition of isosceles

3. ∠MJL ≅ ∠MLJ                  |       isosceles triangle theorem

4. m∠MJL = m∠MLJ             |      definition of ≅

5. JK ≅ LK                            |      Given

6. △JKL is isosceles           |      definition of isosceles

7. m∠KJL = m∠KLJ              |       isosceles triangle theorem

8. m∠MJL + m∠KJM = m∠KJL                         |  adjacent angle theorem

9. m∠MLJ + m∠KMJ = m∠KLJ                         |  adjacent angle theorem

10. m∠MJL + m∠KJM = m∠MLJ + m∠KLM      |   transitive property of =

11. m∠MJL + m∠KJM = m∠MJL + m∠KLM      |   substitution

12. m∠KJM = m∠KMJ          |        subtraction

13. ∠KJM ≅ ∠KLM                |        definition of ≅

14. △KJM ≅ △KLM             |        SAS theorem

15. ∠JKM ≅ ∠LKM                |        CPCTC

16. KM bisects ∠JKL            |        definition of bisector

Area of a square is expressed using the formula;

A = L^2

L is the side length of the square

From the question, we are given;

L = 1 meter

The multiplication equation for the area of the square will be;

A = 1 meter * 1 meter

A = 1m^2

Each silver bead costs $0.50, and each green bead costs $1.

Let's assume the cost of each silver bead is 's' dollars, and the cost of each green bead is 'g' dollars.

According to the given information, the necklace requires 25 silver beads and 15 green beads, and the bracelet requires 10 silver beads and 5 green beads.

The total cost of the necklace beads is $27.50, and the total cost of the bracelet beads is $10.

Using this information, we can set up the following system of equations:

25s + 15g = 27.50 (Equation 1)

10s + 5g = 10 (Equation 2)

We can solve this system of equations using any appropriate method, such as substitution or elimination.

Let's use the elimination method to solve the system:

Multiplying Equation 2 by 3, we get:

30s + 15g = 30 (Equation 3)

Subtracting Equation 3 from Equation 1:

25s + 15g - (30s + 15g) = 27.50 - 30

-5s = -2.50

s = 0.50

Now, substituting the value of s into Equation 2:

10(0.50) + 5g = 10

5 + 5g = 10

5g = 5

g = 1

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The solution is Option A.

The coordinate of the triangle after the translation is given by A' ( 0 , -3 ) with 4 units right and 4 units down

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the coordinate of the triangle be represented as A

Now , the coordinate A = A ( -4 , 1 )

Now , the coordinate of the triangle after translation is A' ( 0 , -3 )

when there is a translation of the coordinate A by 4 units to the right , we get

A to 4 units right = A ( -4 + 4 , 1 )

The new coordinate of A = A ( 0 ,  1 )

Now , A to 4 units down , we get

The coordinate of A' = A' ( 0 , 1 - 4 )

The coordinate of A' = A' ( 0 , -3 )

Hence , the translated coordinate is A' ( 0 , -3 )

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Answer:

There is 12% of last semester's college costs was spent on books. Step-by-step explanation: Since we have given that.

Step-by-step explanation:

The solution to the equation x²+6x+9=20 is x = -2√5 - 3 or x = 2√5 -3 option option (B) and option (D) are correct.

What is a quadratic equation?

Any equation of the form  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

x = [-b± (√b²-4ac )] / 2a

The quadratic equation:

x²+6x+9=20

x²+6x -11 = 0

a = 1, b = 6, c = -11

x₁,₂ = [-6±√6² - 4.1.(-11)]/2(1)

x = -3 + 2√5 , x = -3 - 2√5

Thus, the solution to the equation x²+6x+9=20 is x = -2√5 - 3 or x = 2√5 -3 option option (B) and option (D) are correct.

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The value of the given expression to satisfied the equivalent relation of the expression is \(4x^{2} \sqrt{3x}\)

Define equivalent relation:

An equivalent relation is a relation that satisfies three properties: reflexivity, symmetry, and transitivity. Reflexivity means that every element in the set is related to itself. Symmetry means that if one element is related to another, then the second element is related to the first. Transitivity means that if one element is related to a second element, and the second element is related to a third element, then the first element is related to the third element. An equivalent relation partitions a set into subsets called equivalence classes, where each class contains elements that are related to each other by the relation. Equivalence relations are used in many areas of mathematics, including algebra, topology, and set theory, and are important for understanding properties such as congruence and similarity.

According to the given information:

⇒ \(\sqrt{48x^{5} }\)

⇒ \(\sqrt{24*2 * x^{4}*x }\)

⇒ \(\sqrt{16 * 3 * x^{4} * x}\)

⇒ \(4x^{2} \sqrt{3x}\)

Hence, option 'c' are correct one.

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The transformation from the graph of f(x) = x to the graph of g(x) = (1/9)·x -2, is a rotation and a translation. The correct option is therefore;

The transformation are a rotation and a translation

A translation transformation is a transformation in which there is a displacement of all points on the preimage figure in a specified direction.

The transformation from f(x) = x to f(x) = (1/9)·x - 2, includes a slope reduction by a factor of (1/9), or rotating the graph of f(x) = x in the clockwise direction, and a translation of 2 units downwards, such that the y-intercept changes from 0 in the parent function, f(x) = x to -2 in the specified function f(x) = (1/9)·x - 2, therefore, the translation includes a rotation clockwise and a translation downwards by two units

The correct option is the second option; The transformation are a rotation and a translation

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Given,

The equation of the parabola is (-3, 2).

The length of conjugate axis is 8 units.

The length of transverse axis is 12 units.

The parabola is parallel to the x axis.

The conjugate of the axis is,

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Answer:

83 kids total

Step-by-step explanation:

There are 54 girls on the playground. There are 25 fewer boys than girls on the playground. How many kids are on the playground?

girls = 54

boys = 54 - 25 = 29

54 + 29 = 83 kids total

kids that are on the playground are 83.

Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. The product can meet are the quantities that are included, and the outcome of the operation, or the final response, is referred to as the sum.

The total number of girls that are present is 54

The data given is that there are

25 fewer boys taht are4 present

The total number of boys will be

boys = 54 - 25 = 29

The number of kids that are present will be the total of boys and girls that are present.

Kids = boys + girls

54 + 29 = 83 kids total

The quantity of kids that are present in the playground is 83.

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Answer:

   =(s^2 - t^2)/4

Step-by-step explanation:

a + b = s and a - b = t,

Add the two equations together

a + b = s

a - b = t

----------------

2a = s+t

a = (s+t)/2

Subtract the two equations

a + b = s

- a + b = -t

-------------------

2b =(s-t)

b = (s-t)/2

We want to find ab

ab = (s+t)/2 *  (s-t)/2

FOIL

    =(s^2 - t^2)/4

Answer:

Therefore, the Forest Service will open trials on April 23rd.

Step-by-step explanation:

On January 15th, snow pack = 150 inches.

Snow pack decreases 11 inches per week.

The trials for hiking would be opened when the snow will be gone.

The snow will be gone in the number of weeks it takes to decease.

Number of weeks required = \(\frac{150}{11}\)

                                 = 13.64 weeks

Number of weeks required ≅ 14

Thus, it would take a maximum of 14 weeks for the snow to be gone from January 15th.

Therefore, the Forest Service will open trials on April 23rd.

The checkboxes are denoted by brackets ([]) for checked and 'x' for unchecked states, respectively.

The fertilizing techniques that would be most effective for each example are as follows:

1. Farm with numerous workers and sensitive crops:

a. UDP (Unchecked )

b. Precision management (Checked)

2. A gardener raising produce for a family:

a. UDP (Checked).

b. Precision management (Unchecked )

3. Company that delivers corn to 10 states:

a. UDP (Unchecked)

b. Precision management (Checked)

Please note that the checkboxes are denoted by brackets ([]) for checked and 'x' for unchecked states, respectively.

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Answer:

c. Cluster random sample

Step-by-step explanation:

Missing word "every participant in those meetings. What type of sample is this? a. Simple random sample, b. Stratified random sample, c. Cluster random sample, d. None of the above"

In the cluster sampling, researchers will divide a certain population into smaller groups which is known as clusters, then, they randomly select among these clusters to form a sample. In cluster sample, the clusters to be included are selected at random and all members of the cluster are included.

Answer:

y = -6x + 20

Step-by-step explanation:

Answer:

This is not correct because it shows y+10 minus y but thats not correct!

Step-by-step explanation:

The value of the inverse function f-¹ (3) is (e) 11

From the question, we have the following parameters that can be used in our computation:

f(x) = x - 8

To calculate the inverse value at f-¹ (3)

We set the value to 3

using the above as a guide, we have the following:

x - 8 = 3

Evaluate the like terms

x = 11

Hence, the value of the inverse function is (e) 11

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Complete question

if f(x) = x - 8, what is the value of f-¹ (3)?