Find the sum.
(y+5) + (3y-9)

Answer:

A) 65

B) 60

Step-by-step explanation:

64.9963 rounds to 65

To the nearest 10 it would round down as the second intiger the 4 is below 5 meaning as a result it rounds down

After rounding  the given number 64.9963:

(a) Near 2 decimal places is: 64.70

(b) And the nearest 10 is: 60

When you round a number to a certain digit, you have to check the value of the digit before the place you want to round off to.

1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

The given number is:

64.9963

To round off the nearest 2 decimal places:

Since the third digit after the decimal is 6 which is greater than 5.

Add 1 to their previous digit.

Therefore,

After rounding near to 2 decimal places the number becomes:

64.70

To round off the nearest 10:

Since the tense digit is 4 and it is less than 5

Therefore,

The number after rounding off the nearest 10 is:

60.

Hence, after rounding the number:

Near 2 decimal places is: 64.70

And the nearest 10 is: 60

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Answer:

50%

Step-by-step explanation:

In rhe beginning, there were 24 + 20 = 44 students trying out in total. After a week, there are 44 - 6 - 2 = 36 students remaining. Of those 36 students, 18 of them are trying out for the basketball team. The percentage of students trying out for the basketball team would be 18/36 = 0.5 = 50%

The simplified expression of [tex]\frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex] is [tex]\frac{8a}{a^8 - 1}[/tex]

The expression is given as:

[tex]\frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]

Add the first two terms

[tex]\frac{a - 1 + a + 1}{(a + 1)(a - 1)} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]

Evaluate

[tex]\frac{2a}{a^2 - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]

Evaluate the first two terms

[tex]\frac{2a^3 + 2a - 2a^3 + 2a}{(a^2 - 1)(a^2 + 1)} - \frac{4a}{a^4 + 1}[/tex]

Evaluate

[tex]\frac{4a }{a^4 - 1} - \frac{4a}{a^4 + 1}[/tex]

Take the LCM

[tex]\frac{4a^5 + 4a - 4a^5 + 4a }{(a^4 - 1)(a^4 + 1)}[/tex]

Evaluate the like terms

[tex]\frac{8a}{a^8 - 1}[/tex]

Hence, the simplified expression is [tex]\frac{8a}{a^8 - 1}[/tex]

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The equation for total pay is y = 10/8x.

Division is the mathematical operation that is used to determine the quotient of a number. In order to determine the total pay for hours from 0 to 8, the pay per hour has to be determined. To determine this value, divide $10 by 8.

Pay per hour = $10 / 8

y = 10/8x.

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The graph of the inequality can be seen in the image at the end.

Here we have the inequality:

y ≥ 4x - 3

To graph this we need to graph the line:

y = 4x - 3

With a solid line (because the points on the line are solutions) and then shade the region above that line.

The graph of the inequality can be seen below.

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Answer:

0.026

Step-by-step explanation:

Twenty-Six = 26 ( But for simplicity in the Next Step write it as 26.)

Then Twenty-Six Thousandths = 0.026

The value of x in the given expression is; x = wz/y

We are given the expression;

w/x = y/z

Now, we want to find the value of x which means we want to make x the subject of the formula. Thus;

Multiply both sides of the given expression by x to get;

(w/x)*x = (y/z)*x

⇒ w = xy/z

Now, multiply both sides by z/y to get;

w(z/y) = (xy/z) * (z/y)

wz/y = x

Thus, the value of x in the given expression is;

x = wz/y

The correct question is;

If w/x = y/z, then what is the value of x

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Step-by-step explanation:

to be a tangent, it would have to have a 90° angle with the radius (12).

and that would make the triangle ABCenter of the circle a right-angled triangle.

and then Pythagoras must apply :

c² = a² + b²

with c being the Hypotenuse (the baseline opposite of the 90° angle). in our case the 20-line.

so,

20² = 12² + 16²

400 = 144 + 256 = 400

yes, it is confirmed, because the Pythagoras principle applies, it is a right-angled triangle, and therefore AB is indeed a tangent.

Answer:

the line AB is tangent to the circle

Step-by-step explanation:

we have :

16² + 12² = 256 +144 = 400

On the other hand:

20² = 400

Then

16² + 12² = 20²

Then

According to the Pythagorean theorem:

The line AB is perpendicular to the radius of the circle

Which means the line AB is tangent to the circle.

Answer:   [tex]\boldsymbol{(x + 4)^2 + (y + 6)^2 = 49}\\\\[/tex]

Work Shown:

[tex](h,k) = (-4,-6) = \text{center}\\\\r = 7 = \text{radius}\\\\(x - h)^2 + (y - k)^2 = r^2\\\\(x - (-4))^2 + (y - (-6))^2 = 7^2\\\\\boldsymbol{(x + 4)^2 + (y + 6)^2 = 49}\\\\[/tex]

To check the answer, you can use a graphing calculator like GeoGebra or Desmos or similar.

The cost of 45 packets of instant noodles given the direct variation is $52.335

let

n = k × p

k = constant of proportionality

34.88 = k × 30

34.88 = 30k

k = 34.88/30

k = 1.16266666666666

Approximately,

k = 1.163

Find n when p = 45

n = k × p

= 1.163 × 45

n = $52.335

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Answer: None

Step-by-step explanation:

There is no triangle with an angle measure of 0 degrees.

Answer:

1/100

Step-by-step explanation:

The answer is 1/100 because we don't know how many people are in the group but do know that only 1 person has been taken from the group and the probability will be 1 out of how many people are in the group so we just put 100 there as we don't know how many people are in the group.

Ps: Sorry if this is wrong, this is just a guess.

Answer: B

Step-by-step explanation:

The area of entire rectangle is (9)(4)=36.

The area of the square inside is [tex]x(x)=x^2[/tex]

Subtracting the areas, we get [tex]36-x^2[/tex]

Answer:

Step-by-step explanation:

eq of line perpendicular to 3x+5y=10 is

5x-3y=a

where a is constant.

it passes through (3,2)

5(3)-3(2)=a

a=15-6=9

reqd. eq. is 5x-3y=9

or

3y=5x-9

y=5/3 x-3

gradient=5/3

y-intercept=-3

or

5y=-3x-10

y=-3/5 x-2

slope=-3/5

slope of reqd. line=-1/(-3/5)=5/3

eq. of line through (3,2) is

y-2=5/3(x-3)

3y-6=5x-15

3y=5x-15+6

3y=5x-9

y=5/3 x-3

Step-by-step explanation:

Answer

a - 8

------------+

2

Using it's concept, the desired probability is:

P(Female|Junior) = 75%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 8 Junior Students, out of which 6 are Female, hence the probability is:

P(Female|Junior) = 6/8 = 0.75 = 75%.

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The expression is equivalent to 2 , option C is the right answer.

An expression in maths is a statement that contains , constants , variables and mathematical operators.

The expression given in the question is

[tex]\rm \dfrac { 4^{\frac{5}{4}} * 4^{\frac{1}{4}}} {4^{\frac{1}{2}}}[/tex]

Applying exponent rule

[tex]\rm a^m * a^n = a^{m+n}[/tex]

[tex]\rm \dfrac { 4^{\frac{5}{4} +\frac{1}{4}}} {4^{\frac{1}{2}}}[/tex]

Applying exponent rule

[tex]\rm \dfrac{a^m}{a^n} = a^{m-n}[/tex]

[tex]\rm { 4^{\frac{5}{4} +\frac{1}{4} -{\frac{1}{2}}}[/tex]

On solving the exponents

=(6/4) -(1/2)

=4/4

=1

=[tex]\rm 4^{\frac{1}{2}}[/tex]

= 2

Therefore the expression is equivalent to 2 , option C is the right answer.

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Answer:

AABC and AXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the third side of each triangle

Answer:

5

Step-by-step explanation:

2 × 2 = 4

3× 3 = 9

4 × 4 =16

5 × 5 =25

16 is the only number and closest number to 21 to subtract from

the price that they should charge on the 2 year extended warranty is in order to break even is $10.

the price at which the company would breakeven is:

= percentage of product that will fail x replacement cost

solving gives:

= 4% x 250

= $10

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Answer:

C. 29

Step-by-step explanation:

[tex]f(x) = -3x^3 + 2x^2 +24[/tex]

• To calculate [tex]f(-1)[/tex] , we have to replace x with -1 in the definition of [tex]f(x)[/tex] , and calculate the value:

[tex]f(-1) = -3(-1)^3 + 2(-1)^2 + 24[/tex]

         ⇒ [tex]-3(-1) +2(1) + 24[/tex]

         ⇒ [tex]3 + 2 + 24[/tex]

         ⇒ [tex]29[/tex]

[tex]\huge\boxed{\textsf{C.}\ 29}[/tex]

We have this equation:

[tex]f(x)=-3x^3+2x^2+24[/tex]

Substitute [tex]x=-1[/tex]:

[tex]f(-1)=-3(-1)^3+2(-1)^2+24[/tex]

Simplify to find the final answer:

[tex]\begin{aligned}f(-1)&=-3(-1)+2(1)+24\\&=3+2+24\\&=5+24\\&=\boxed{29}\end{aligned}[/tex]

James must mix 60 millilitres of 10% solution and 40 millilitres of 50% solution.

Given that, James needs to mix a 10% acid solution with a 50% acid solution to create 100 millilitres of a 26% solution.

Let the acid solution needs to mix with 10% be x ml and the acid solution needs to mix with 50% will be 100 - x ml.

Now,

10% x + 50% ( 100 - x ) = 26% ×100

⇒[tex]\frac{10x}{100} +\frac{50(100-x)}{100}=\frac{2600}{100}[/tex]

⇒10x + 50( 100 - x ) = 2600

⇒10 x + 5000 - 50x = 2600

⇒10 x - 50 x = 2600-5000

⇒-40 x = -2400

⇒x=60

Therefore, James must mix 60 millilitres of 10% solution and 40 millilitres of 50% solution.

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Answer:

Step-by-step explanation:

The best way to answer a question like this one is to use a graphing program on the internet. This graph was done with desmos

It looks to me that the equation is g(x)  = 10(x - 5)^2 - 37

I checked to see that this is correct, and thank goodness it is.

The graph is shown below.

Answer:

any # where -2<=x<7

Step-by-step explanation:

(x-7) would be negative and (x+3) positive, resulting in f(x) being negative.

Answer: $36.68 or $35.97. Read below.

Step-by-step explanation: You need to multiply the 12 foot by 12 foot and you would get 144 sq feet. Then divide 47 into 144. You will be left with 3.06, and if you need to round, you can round that to 3. Then you need to multiply 3 by $11.99 and you will be left with the cost for the paint, which is $35.97 if you do round to a three, and $36.68 if you do not round the three. So your answer is either $36.68 or $35.97 depending on whether you round or not.

Hello,

    9k - 2  88

⇔ 9k - 2 + 2 ≥ 88 + 2

⇔ 9k ≥ 90

⇔ 9k/9 ≥ 90/9

⇔ k ≥ 10

S = [10 ; + ∞ [

Answer:

k ≥ 10

Step-by-step explanation:

9k - 2 ≥ 88

Step 1 : Add 2 on both sides.

9k - 2 + 2 ≥ 88 + 2

9k + 0 ≥ 90

9k ≥ 90

Step 2 : Divide 9 on both sides.

9k/9 ≥ 90/9

k ≥ 10

The composite function of the paintings Jenny completes in a year is

[tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]

A composite function is a function made of other functions, where the output of one function is the input to the other function.

An example of the composite functions 2x+3 and [tex]x^{2}[/tex] together make the composite function [tex](2x+3)^{2}[/tex]

We have [tex]P(w)=\frac{1}{2}w+1[/tex]

Here, P(w) represents the number of paintings Jenny completes in some w weeks. and

J(y)  represents the number of weeks per year.

As J(y) is the number of weeks spent per year in painting, we can calculate the paintings completed in a year by substituting

w as J(y) in the equation we have

Then the equation becomes:[tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]

Hence this is the composite function that would represent the number of paintings Jenny completes in a year.

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