10. Find the value of a²-b if a = 3 and b = -5.

The value of x that makes m parallel to n is 90 degrees.

The value of x that makes m and n parallel is 15.

How to find the angles in parallel lines?

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.

The value of x that makes the line ma and n parallel can be calculated as follows:

180 - x  = x (alternate exterior angle)

180  = 2x

x = 180 / 2

x = 90 degrees

2.

3x - 15 + 150 = 180(supplementary angles)

3x = 180 - 150 + 15

3x = 45

x = 45 / 3

x = 15

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Answer:

4y + 5 = 2

Step-by-step explanation:

4y + 5 = 2  Subtract 5 from both sides

4y = -3  Divide both sides by 4

y = [tex]\frac{-3}{4}[/tex]

Answer:

4y+5=2

Step-by-step explanation:

First, replace "a number" with "y"
The sentence becomes: "The sum of 4 times y and 5 is 2"
Replace "is" with the equals sign, "="
The sentence becomes: "The sum of 4 times y and 5 = 2"
Replace "times" with the multiply symbol, " * "
The sentence becomes: "The sum of 4 * y and 5 = 2"
Replace "the sum of ___ and ___" with " ___ + ___"

The sentence becomes: "4*y + 5 = 2".
the " * " isn't needed since 4y implies multiplication already, so you can optionally remove the *

Answer:

The answer to your question is: B

Explanation:
based on the statistics given, this answer best fits the Queston.

The approximate probability that a randomly selected 10-year-old child will be more than 51.75 inches tall is 0.6915.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. From the information, the heights of 10-year-old children have a normal probability distribution with a mean of 54.6 inches and standard deviation of 5.7 inches.

Based on this, the probability that a randomly selected 10-year old child will be more than 51.75 inches tall will be:

P(X > 51.75)

= P(Z > [(number - mean) / standard deviation)]

= P(Z > [(51.75 - 54.6) / 5.7)]

= P(Z > -0.5)

= 1 - P(Z = -0.5)

This will be looked at in the z table.

= 1 - 0.3805

= 0.6915

Therefore, the probability is 0.6915.

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To find the volume of the prism we just multiply all the measures

The volume is 24 cm³

If the sugar cubes have 1 cm³ of volume, to find how much sugar cubes fit in the box we must divide the volume of the box by the volume of the sugar cubes

Therefore we can fit 24 sugar cubes

Explanation:

In this case we must compare 2 to 4 and 11 to 11/2

1. The first ratio given is 2 to 4

So, the first ratio is 1/2

2. The second ratio given is 11 to 11/2

Finally, since r1 ≠ r2 they are not proportional

ANSWER:

they are not proportional

Based on the given parameters, the amount of the investment after 2 years is $3123

The given parameters about the compound interest are

Principal Amount, P = $3000

Interest Rate, R = 2%

Time, t = 2

Number of times, n = 4 i.e quarterly

Compound interests are different from simple interest, and they are calculated using the following compound interest formula

CI = P(1 + R/n)^nt - P

To calculate the amount, we have:

A = P + CI

So, the equation becomes

A = P + P(1 + R/n)^nt - P

Evaluate the like terms

A = P(1 + R/n)^nt

Substitute the known values in the above equation

A = 3000 * (1 + 2%/4)^(2 * 4)

Express 2% as decimal

A = 3000 * (1 + 0.02/4)^(2 * 4)

Evaluate the sum

A = 3000 * (1.005)^8

Evaluate the exponent

A = 3000 * 1.041

Evaluate the product

A = 3123

Hence, the value of the investment is $3123

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Answer:

600

Step-by-step explanation:

[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]

The parent functions are defined with all coefficients with value 1.

They can be linear, quadratic, cubic, absolute, reciprocal, exponential, logarithmic, square root, sine, cosine, tangent...

Then we can pick a function and transform it in order to include the point (-1,5) in the function definition.

We will use the quadratic parent function:

We will adjust the coefficient a of the quadratic function in order to include (-1,5)

Then, our transformed function is:

The diameter of the outer circle = 12.907 ft

The thickness of the circular pipe = 2.983 ft

The diameter of the inner circle = q = The diameter of the outer circle - The thickness of the circular pipe

⇒ The diameter of the inner circle = 12.907 - 2.983 ft

⇒ The diameter of the inner circle = q = 9.924 ft

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The distance from city C to city D is 5435 miles

The area of mathematics known as algebra aids in the representation of issues or circumstances into mathematical statements. To create a meaningful mathematical expression, it requires variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in all areas of mathematics, including coordinate geometry, calculus, and trigonometry. 2x + 4 = 8 is a basic algebraic expression.When operations like addition, subtraction, multiplication, division, etc. are performed on variables and constants, we obtain algebraic expressions as the mathematical statement.

The distance from city A to city B is 3001 miles Let distance from city A to city B x and distance from city C to city D y

The distance from city A to city B is 3001 miles

x= y - 3001....(i)

x+ y = 7869....(ii)

y- 3001 +y = 7869

2y = 10870

y=5435

The distance from city C to city D is 5435

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length of a cylinder of volume 2 litres and radius 10 cm is 0.0064cm and  the radius of a cylinder of volume 45 cm³ and length 4 cm is 1.8928cm.

PART A

Volume of Cylinder = 2 Litres

Radius of cylinder = r = 10 cm

We need to find the length of a cylinder .

We know , Volume of Cylinder = π[tex]r^{2} h\\[/tex]

On substituting the values of Volume of Cylinder and r , we get

2 = π( [tex]10^{2}[/tex])h

h = 2 / 100π = 0.0064 cm

Here h = length of a cylinder

The length of a cylinder is  0.0064cm .

PART B

radius of a cylinder = r

volume of cylinder = 45 cm³

length of cylinder = h = 4 cm

Volume of Cylinder = π[tex]r^{2} h\\[/tex]

45 = 3.14 [tex]r^{2}[/tex] (4)

[tex]r^{2}[/tex] = 3.5828

r = 1.8928

Radius of a cylinder is 1.8928cm.

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Using mathematical operations we can conclude that the cost per quart of yogurt is $1.29.

So, the cost per quart:

Cost per quart:

Therefore, using mathematical operations we can conclude that the cost per quart of yogurt is $1.29.

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The value of a that makes the solution of the equation is 1/2.

Given,

The equation: 3(2x - 4) = 4(ax - 2)

Solve,

3(2x - 4) = 4(ax - 2),

Open the bracket and multiply:

6x - 12 = 4ax - 8

Add 12 to both sides

6x -12 + 12 = 4ax + 12 - 8

We get,

6x = 4ax + 4

Add - 4ax to both sides:

6x - 4ax = 4ax - 4ax + 4

We get,

6x - 4ax = 4

Take x = 1

Then,

6 × 1 - 4a × 1 = 4

6 - 4a = 4

Now,

Add - 6 to both sides

6 - 6 - 4a = 4 - 6

We get,

-4a = -2

That is,

4a = 2

a = 2/4 = 1/2

That is,

The value of a that makes the solution of the equation is 1/2.

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The largest five-digit multiple of 15 whose digits are all distinct and nonzero is 12345.

Suppose that the number is abcd.efg and belongs to the decimal numerical system. Remember one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more. Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more. We will call d as ones digit, c as tens digit (it get multiplied by 10), b as hundreds digit etc.

WE need to find the five-digit multiple of 15 whose digits are all distinct and nonzero.

Thus, we can see that the largest five-digit multiple of 15 could be ;

12345

Since it must be all distinct and nonzero. so the correct digit is 12345.

Hence, the largest five-digit multiple of 15 whose digits are all distinct and nonzero is 12345.

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We are given the following two numbers to compare

Let us simplify them

So, we can compare them as

The quantity on the left side is greater than the quantity on the right side.

Answer: 100

Step-by-step explanation:

First, we need to know how many workers must be hired to pave one mile.
Which is 5 workers per 1 mile ( 150 / 30 )

Then you can either do
(5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5)
OR
5 x 20 = 100

( if I'm wrong it's like 3 am so I'm a bit slow but I hope I helped )

The correct answer is Option B.

To know how much each message sent costs, knowing that 75 messages cost $6.75, we only have to divide the cost of the total of 75 text messages by the total number of the cost of the message,

So that:

We say, that the cost of each text message is $0.09.

The probability of four coworkers  having different birth months is 0.572 or 55/96

Given there are four coworkers and the condition is they should have different birth months.

As we know probability is the ratio of favorable out comes to the total number of outputs

Favorable outcomes are

For first person 12 months

For second person 11 months

For third person 10 months

For Fourth person 9 months

Total outcomes

For each and every person total outcomes are 12 months which add up to 12 x 12 x 12 x 12 =  [tex]12^{4}[/tex]

Now probability will be

Probability = [tex]\frac{(12)(11)(10)(9)}{12^{4} }[/tex]

Probability = 55/96

Hence the probability of four coworkers having different birth months is 55/96

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Answer:

Iiiieie I just got off your phone with weee

Step-by-step explanation: why did I get a hold for him or

oh yeah that’s fine I’ll let lol I was thinking of going out to the house for the next few weeks so I’m not good enough for that lol I think it’s so so to do that all day and you can get a hold on you for sure and I can help with your stuff and help me help help you get it

the shape of the curved surface is the sphere

So, as a part of the shape is flat

The block may represents a semi sphere

To be able to get the expected value of Z, we will be using the following formula:

We get,

Therefore, the expected value of Z is -12.29.

Answer:

[tex]x = - 8[/tex]

Step-by-step explanation:

[tex]8x = 4x - 32 \\ 8x - 4x = - 32 \\ 4x = - 32 \\ x = - 8[/tex]

Answer:

6, because anything inside | | are positive so -3 will now be 3.

3 minus -3 = 6

Step-by-step explanation:

Hope it helps! =D

The slope of the line that passes through points (10,4) and (7, 3) is 1/3

Here we are dealing with a slope of a line where a slope of a line is the change in the y coordinate with regard to the change in the x coordinate. If P(x1,y1) and Q(x2,y2) are the two points on a straight line, at that point the slope formula is given by:

m = Change in y-coordinates/Change in x-coordinates

m = (y₂– y₁)/(x₂ – x₁)

Since we are given two points (10,4) and (7, 3),  where x₁ and x₂ are 10, 7 whereas y₁ and y₂ are 4, 3

From  the formula we get,

m = (y₂-y₁)/(x₂-x₁)

 = ( 3-4)/(7 - 10)

 = -1/-3

 =1/3

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After evaluating the limit we have came to find that the limit of  [tex]\lim_{x\rightarrow -\infty }\frac{x^2}{x^2\ +4}[/tex] as x approaches ∞- is 1

The value that a function, sequence, or index approaches as an input, or an index, approaches a particular value is known as a limit in mathematics. Limits, which are essential to calculus and mathematical analysis, are required by the definitions of continuity, derivatives, and integrals.

In addition to being closely related to the concepts of limit and direct limit in category theory, the idea of a limit of a sequence is further generalised to encompass the idea of a limit of a topological network.

A limit of a function is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]

To find the limit we will use L'Hôpital's Rule

Find the derivative

⇒ [tex]\lim_{x\rightarrow -\infty }\frac{x^2}{x^2\ +4}[/tex]

⇒ [tex]\lim_{x\rightarrow -\infty }\frac{2x}{2x +0}[/tex]

⇒ [tex]\lim_{x\rightarrow -\infty }\frac{2x}{2x }[/tex]

Evalue -∞ as x

⇒ [tex]\frac{2(-\infty)}{2(-\infty)} }[/tex]

⇒ 1

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Answer:  −8x − 12y − 18q − 42p

Step-by-step explanation:

i did the exam xD