match the system of equations with the solution set.hint: solve algebraically using substitution method.A. no solutionB. infinite solutionsC. (-8/3, 5)D. (2, 1)

Two radical expressions are called like terms if they have the same degree and the same radicand.

So, like radical terms, best describes terms that have the same degree and the same radicand.

Like radicals are those, that have the same root number and radicand.

So, the correct answer is option C.

Solution

Box 1 : Apply Quotient Identities

The answer for the first box is

Box 2: Write as one expression

The answer for the second box is

Before the box 3, please note the identity

Note: Trigonometry I dentities

Box 3: Apply Double - Number Identities

Substitute 14 for n and 20 for E in the equation to determine the value of proportionality constant.

Substitute 280 for h and 7 for n in the equation to obtain the value of E.

So value of E is 40.

The point with a coordinate of (2,5) will be translated into y=-x line.

The transformation for y=-x would be:

1. x'= -y

2. y'= -x

For x=2 and y=5 would be:

x'= -y

x'= -5

y'= -x

y'= -2

The translated coordinate would be: (-5, -2)

We can find the volume of a cone using the formula

Where

h = height

r = radius

Remember that

Therefore, let's find out the radius first, the problem says that the diameter is 6cm, then

The radius is 3cm and the height is 10cm, let's use it in our formula:

The problem also say to use = 3.14, then the volume is

Therefore, the volume is

We need to convert 8640 in³ into ft³.

1 in³ is equal to 0.0005787037 cubic feet.

Hence, we can convert it using the rule of three:

Then:

1 in³----------- 0.0005787037ft³

8640 in³ ----------- x

where x= (8640in³*0.0005787037 ft³)1 in³

x = 5ft³

Hence, you have 5ft³ of fabric.

Given:

a.) H = 37 hours

b.) R = $6

Let's find the gross pay, G:

Therefore, the gross pay is $222.

Definitions in Algebra

A variable is a letter or symbol that represent numbers in a general way.

A coefficient is a number that multiplies a variable

A term is a combination of numbers and variables, all of them multiplied.

An exponent represents multiple products, like 2*2*2= 2^3

The answer is shown in the image below:

Given the points (-8,5) and (6,5), we can find the equation of the line first by finding the slope with the following formula:

in this case, we have the following:

since the slope is m = 0, we have that the line is a horizontal line that goes through the points (-8,5) and (6,6), then, the equation of the line is:

in slope-intercept form the equation would be:

Data:

Dolphin 1: 200ft

Dolphin2:

30% farther: 200ft+60ft=260ft

-Find the 30% of 200

Ascende 25 1/2 feet and then descended 40 1/2 feet:

Substract to the initial 260ft the 25 1/2 ft and add 40 1/2:

To sum or substract mixed numbers write it as fractions:

Then You have:

You can also write the 260 as a fraction with the same denominator (2):

Notice that:

Therefore 3 is a root of the given polynomial.

Now, we can use this root to factor the polynomial:

Using the synthetic division algorithm we get that:

The roots of the above polynomial are:

Therefore:

Answer:

APY means Annual Percentage Yield

The APY is given by the formula:

where r is the rate (in decimals)

n is the number of times the interest was compounded

A) For the money invested at 14% compounded semiannually

r = 14% = 14/100

r = 0.14

n = 2

Substitute n = 2, r = 0.14

B) For the money invested at 13% compounded continuously

The hypotenuse is 20 V 3

Given that longer leg = 30

Hypotenuse is given as:

EXPLANATION

The probability that Event A happening is the following:

The probability of Event A not happening is the following:

Therefore, we have:

Plugging in the terms into the expression:

1.8 + P(Not malfunctioning) = 100%

Subtracting -1.8 to both sides:

Subtracting numbers:

In conclusion, the probability of not malfunctioning is 0.982

Given the equation:

We will solve the equation to find y

Multiply the equation by 4 to eliminate the denominators

Combine the like terms

Subtract (17) to both sides

Divide both sides by (-15)

So, the answer will be y = 3

slope intercept form:

y= mx+b

Where:

m= slope

b= y-intercept

total pounds: y

number of weeks: x

the total number of pounds must be equal to the pounds already collected (100) plus the product of the number of weeks (x) and the number of pounds collected per week (25)

y= 100+25x

To collect 400 pounds, replace y by 400 and solve for x ( weeks)

400 = 100+25x

400-100= 25x

300=25x

300/25 = x

12 = x

12 weeks to collect 400 pounds

Given

Find

The value of x.

Explanation

length of AB = 22 - 3 = 19

using the trignometric ratios , we have

Final Answer

Therefore , the length of x is 8.548

The first method simlpy executes the distributive property of multiplication over addition, and the definition of the imaginary number, i.

The second method factored out 4i first then perform the operation on the terms left inside the parenthesis , then executes the distributive property of multiplication over addition and the definition of the imaginary number, i.

I prefer the first method . It's simple and straight forward,

Given:

We're given the steps a student took to solve the simple interest formula.

To find:

The algebraic error in student's work.

Step-by-step solution:

Let us first solve the equation and then we will spot the error in the solution:

A = P(1 + rt)

A = p + prt

A - p = prt

A - p / pt = r

Upon comparing both solutions, we can clearly see that the student made a mistake in the second step in the multiplication process.

The student should write A = p + prt in the second step in place of

A = p + rt, because p is multiplied with the whole bracket.

We have to calculate the zeros of the function with the quadratic formula.

The roots are x1=7.742 and x2=0.258, both reals., both

From the triangles ∠ABC ≅ ∠MNP.

Given we have two triangles ABC and PNM

Both triangles have same shape but different angles.

we need to find ∠ABC ≅ ?

we can notice that :

∠A ≅ ∠M

∠B ≅ ∠N

∠C ≅ ∠P

hence these angles are similar to each other.

So,  ∠ABC ≅ ∠MNP.

Hence we get the answer as ∠ABC ≅ ∠MNP.

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Given:

Adding equation(1) and equation(2)

The system has infinitely many solution .

They must satisfy the equation:

Height of lift = x + x = 2x

We can find x using triangle ABC by the cosine rule

Height of lift = 2 X 3.831m = 7.662m

This will be converted to cm by multiplying by 100

Height of lift = 7.662 X 100 cm

= 766.2 cm

= 766cm ( nearest cm )

Hence the answer is 766cm

Solution

For this case we can do the following:

and we can find the answer with this:

Given the Division:

You can identify that have to divide 420 by 10. This means that you need to move the Decimal Point 1 place to the left. Notice that, if you do this, you get:

Notice that now the digit that was placed in the Ones Place, is in the Tenths Place. Therefore, each original digit was shifted one place to the right.

Hence, the answer is:

Given

Find

Graph the parabola of the given function

Explanation

solve the equation

vertex can be found by using the formula,

x = 2 , substitute this in equation to get y value,

y = -1

if x = 0 then y =3 and if y= 0 then x = 1, 3

Final Answer

The value of the equation that we have here is given as 16r² + 24

The equation that we are to simplify here is given as -2r(-13r+5r-12).

In order to open the brackets we would have to multiply -2r with all of the values that are in the bracket.

The mathematical signs that are used in the question have to be well thought of as well before the calculation is done

We would have 26r² - 10r² + 24

26r² - 10r² + 24

because they have the same powers they would be able to subtract

16r² + 24

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Linear Expressions MC)

Simplify -2r(-13r+5r-12).

O-162-24r

162+24

162+24r

O-162 + 24r

Given:

Find: differentiation

Explanation: on differentitaion with respect to x

put the value of

we get,