1. What is the y intercept of the equation
2y - 5x = 16?
A -2.5
B 2
C -5
D 8.

The measure of the central angle θ in degrees and then multiply by 1/(2π). Then that result by πr²

We will use the following points to find the area of the sector;

First of all, the angle that is formed in a full rotation is 2π.

The area of a circle is given by the formula; A = πr²

The central angle is given by the angle symbol θ. Thus, we have to multiply the area of the circle by a factor θ/2π

Thus, the area of a sector is given by the formula;

A = (θ/2π) * πr²

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The word that best describes line segment ID in the image given showing a circle is: a chord.

A chord can simply be described as a line segment in a circle that connects two points on the circumference of a circle to each other.

The largest chord in a circle is a the diameter. A circle can have as many chords as possible.

Considering the image given above, ID is a line segment which connects points I and D which are on the circumference of the circle together. Therefore, ID can best be described as a chord.

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To work to pay for the refurbished computer exists 89 hours.

Tax compliance refers to policy actions and individual behavior aimed at ensuring that taxpayers are paying the right amount of tax at the right time and securing the correct tax allowances and tax reliefs.

Tax is defined as a mandatory financial charge or some other type of levy imposed on a taxpayer (an individual or legal entity) by a governmental organization in order to fund government spending and various public expenditures (regional, local, or national).

First estimate all the deduction

FICA = $10 per hour × 0.0765 = $0.77 per hr

Fed tax = $10 per hr × 0.12 = $1.2 per hr

State tax = $10 per hr × 0.08 = $0.8 per hr

Remaining pay = 10 – 0.77 – 1.2 – 0.8 = $7.23 per hour

Time required = $640 / $7.23 per hr

Time required = 89 hours

Therefore, the correct answer is option c) 89 hours.

The complete question is:

You are debating about whether to buy a new computer for $800.00 or a refurbished computer with the same equipment for $640.00. If you are paid $10.00/hour and your deductions are FICA (7.65%), federal tax withholding (12%), and state tax withholding (8%), how many hours do you have to work to pay for the refurbished computer?

a) 111 hours

b) 98 hours

c) 89 hours

d) 87 hours

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Step-by-step explanation:

\(\huge{ \mathfrak{ \purple{Answer}}}\)

Equation is

x+ 45 = 90°

And,

x = 90 - 45 = 45°

\( \sf{\red{x = 45}}\)

To show that the angle bisector of an equilateral triangle is perpendicular to the base​, we can assume an equilateral triangle with sides ABC. Next, we can get an angle bisector in the middle represented by BD which becomes perpendicular to the base BC.  

After getting the angle bisector, we would see that the line segment BD, divides angle BAC into two equal angles, each measuring 30 degrees. Now, we can draw a perpendicular line from point D to the base BC.

We could also draw a line E, which is the perpendicular line that intersects the base BC. We want to show that BD is perpendicular to BC, which means we need to show that angle BDE is a right angle.

Since the sum of angles BDA and ADE is 90 degrees (they form a right angle), and the sum of angles BAD, ABD, and BDA is 180 degrees, it follows that angle BDE must be a right angle.

Therefore, we have shown that the angle bisector of an equilateral triangle is perpendicular to the base.

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Answer:

B

Step-by-step explanation:

a prime polynomial is one which does not factor into 2 binomials.

its only factors are 1 and itself

attempt to factorise the given polynomials

3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )

= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(3x² - 2) ← in factored form

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

3x³ - 2x² + 3x - 4 ( factor the first/second terms

= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored

thus this polynomial is prime

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

4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )

= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term

= (2x + 1)(2x² + 3) ← in factored form

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

4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )

= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(4x² - 3) ← in factored form

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

the only polynomial which does not factorise is

3x³ - 2x² + 3x - 4

Answer:

\( - n - 6n + 4 = 53 \\ \\ - n - 6n = 7n \\ \\ 7n = 53 - 4 \\ \\ \ \\ 7div 7n = 49 \div 7 \\ \\ n = 7\)

The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1)(x - 2)

We have to given that;

Expression is,

⇒ [x /(x² - x - 2)]  + [ (x - 1) / (x - 2) ]

We can simplify as;

⇒ [x / (x² - x - 2)]  + [(x - 1) / (x - 2)]

⇒ [x / (x² - 2x + x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / [ x (x - 2) + 1(x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / (x - 1) (x - 2)] + [(x - 1) / (x - 2)]

⇒ [1/(x - 2)] [ x/(x - 1) + (x - 1) ]

⇒ [1 / (x - 2)]  × [ x + (x - 1)²] / (x - 1)

⇒ [x + (x - 1)² ] / [(x - 1) (x - 2)]

⇒ (x + x² - 2x + 1) / (x - 1) (x - 2)

⇒ (x² - x + 1) / (x - 1) (x - 2)

Hence, The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1) (x - 2)

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Answer:

a. Using the empirical rule, approximately 68% of healthy adults have body temperatures within 1 standard deviation of the mean, or between 97.52°F and 98.70°F.

b. Using the empirical rule, approximately 99.7% of healthy adults have body temperatures between 96.34°F and 99.88°F, which is within 3 standard deviations of the mean.

Step-by-step explanation:

If there's a number that has for example 6/5 the / means dividing

Answer:

Substitution

Substitution

Elimination

Elimination

Substitution

Elimination

Explanations are given below

Step-by-step explanation:

Hello!

This is because you already have a solution for a variable, y, and you can simply plug in the value of y for the second equation

The same thing as above, you already have the value of y, and you can simply plug it into the second equation.

You should use elimination because you can simply eliminate the variable y by adding the two equations, as they have the same coefficient of 3.

Same as above, simply add the two equations to eliminate x, because they have the same coefficients of 7.

You have the value for y, so simply plug it into the other equation to solve for x.

You have -2x in both equations, and subtracting the equations will eliminate the variable x, and you can then solve for y.

Answer:

3/8 because they ate 5 and there were 8

Answer:

$75

Step-by-step explanation:

he makes $44 and then you add the dollar per 31 books making $75

Earning an A in algebra this semester is an example of (A) a long term goal.

One of the many branches of mathematics is algebra, which means "reunion of shattered pieces, setting of bones" in Arabic. Algebra, which is a common thread throughout practically all of mathematics, is essentially the study of mathematical symbols and the rules for using them in formulas.

Since there are a wide variety of application for Algebra in our day-to-day lives and in the modern sciences, so a good score in Algebra will not only get a good score for the results but also help learn valuable information for the future. Hence it is a long-term goal.

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Answer:

Answer will be A 200( 12+3)

Answer:

See below!

Step-by-step explanation:

Let the two numbers be x and y

x + y = 66 ----------------(1)

2x = y + 15

2x - y = 15 ---------------(2)

Add both equations

x + y + 2x - y = 66 + 15

x + 2x = 66 + 15

3x = 81

Divide both sides by 3

Put x = 27 in Eq. 1

27 + y = 66

Subtract 27 to both sides

y = 66 - 27

\(\rule[225]{225}{2}\)

Answer:

Step-by-step explanation:

half the base times the height

expand and simplify (2x + 1)(x + 3)

answer : \(2x^2+7x+3\)

-

explanation : expand the polynomial using the FOIL method.

-

FOIL : a technique for distributing two binomials. the letters FOIL stand for first, outer, inner, last. first means multiply the terms which occur first in each binomial, outer means multiply the outermost terms in the product, inner means multiply the innermost terms, and last means multiply the terms which occur last in each binomial.

-

step 1 : multiply each term in the first parentheses by each term in the second parentheses (FOIL)

ex : \(2x * x+2x * 3+x+3\)

step 2 : calculate the product

ex: \(2x^2+2x * 3+x+3\)

step 3 : calculate the product

ex: \(2x^2+6x+x+3\)

step 4 : collect like terms

ex: \(2x^2+7x+3\)

-

solution : \(2x^2+7x+3\)

hope this helps !

- audrey ♡

Answer:

There are 7 tenths

Step-by-step explanation:

The tenths spot is the first spot over to the right of the decimal place, so there are 7 tenths

As we know that 10 tenths are there in 1 so, there are total 27 tenths are there in the 2.7

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

10 tenths make up one, hence there are,

2.7 × 10 = 27 tenths in 2.7

There is one more way to check this,

2.7 ÷ (1/10)

= 2.7 × 10

= 27

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The requried, correct statment is shown below,

B) The report accurately states the results because a mean score of 3.2 is greater than the predicted average of 3 on the statement regarding prioritizing free time.

C) The report does not accurately interpret the result of the statement regarding prioritizing free time.

D) The report of the study should state that there is a strong correlation between participation in sports and the ability to prioritize free time rather than make a broad conclusion.

Statement A is not true as it suggests a specific sampling method is necessary for accuracy, which is not necessarily the case. The study can still be accurate if the sample is randomly selected and sufficiently large.

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Answer:

2a+2a-3b-3b+3c

hope this helps

have a good day :)

Step-by-step explanation:

Vector v can be written as the sum of two vector components, \(v_x = -5i\)  and \(v_y = 6j\)

To write vector v as the sum of two vector components, we need to decompose it into two vectors along different directions.

v = -5i + 6j

w = 3i + 4j

We can decompose vector v into two components, one along the x-axis and the other along the y-axis.

Let's denote the component along the x-axis as \(v_x\) and the component along the y-axis as \(v_y.\)

The x-component, \(v_x,\) represents the projection of vector v onto the x-axis and can be found using the dot product of v and the unit vector i:

\(v_x = v . i = (-5i + 6j) . i = -5i . i + 6j . i = -5\)

Similarly, the y-component, \(v_y,\) represents the projection of vector v onto the y-axis and can be found using the dot product of v and the unit vector j:

\(v_y = v . j = (-5i + 6j) . j = -5i . j + 6j . j = 6\)

Now, we can write vector v as the sum of its components:

\(v = v_x + v_y = -5i + 6j\)

So, vector v can be written as the sum of two vector components: -5i along the x-axis and 6j along the y-axis.

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The following ordered pairs are the solutions to this system of inequalities;

B. (-4, -10)

C. (2, -5)

E. (10, -10)

F. (0, 5)

2x - 3y ≥ 10

3x + 4y ≤ 5

Check all that applies:

A. (-1, 6)

Substitute into the first inequality

2x - 3y ≥ 10

2(-1) - 3(6) ≥ 10

-2 - 18 ≥ 10

-20 ≥ 10

False

3x + 4y ≤ 5

B. (-4, -10)

2x - 3y ≥ 10

2(-4) - 3(-10) ≥ 10

-8 + 30 ≥ 10

22 ≥ 10

True

C. (2, -5)

2x - 3y ≥ 10

2(2) - 3(-5) ≥ 10

4 + 15 ≥ 10

19 ≥ 10

True

D. (-6, 5)

2x - 3y ≥ 10

2(-6) - 3(5) ≥ 10

-12 - 15 ≥ 10

- 27 ≥ 10

False

E. (10, -10)

2x - 3y ≥ 10

2(10) - 3(-10) ≥ 10

20 + 30 ≥ 10

40 ≥ 10

True

F. (0, 5)

2x - 3y ≥ 10

2(0) - 3(5) ≥ 10

0 - 15 ≥ 10

-15 ≥ 10

False

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There are 67 emus and 201 sheep

An equation is a mathematical statement that shows that two expressions are equal. An equation is written by placing an equal sign (=) between two expressions, with one expression on each side of the equal sign. There are different types of equations, including linear equations, quadratic equations, polynomial equations, and systems of equations.

Let the number of the emus be x

The total number of animals is 266

We have that;

266 = 3x + x

266 = 4x

x = 266/4

x = 67 emus

Number of sheep = 3(67) = 201 sheep

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Answer:

B. (b x d) - c

Step-by-step explanation:

i. -(a x d) + b

= -(6 x \(\frac{1}{2}\)) + 8

= -3 + 8

= 5

ii. (b x d) - c

(8 x \(\frac{1}{2}\)) - 4

= 4 - 4

= 0

iii. 2(b x f) + a

= 2(8 x \(\frac{1}{4}\)) + 6

= 4 + 6

= 10

iv. (a x e) - c

= (6 x \(\frac{1}{3}\)) - 4

= 2 - 4

= -2

Thus, the expression which is equivalent to 0 is that of option B.

Answer:

10.5

Step-by-step explanation:

Just one tenth off!

C. The volume of  26% soil he should add to the 16% to create a mixture that is 23% sand is 23.3 m³

For a  landscaper wants to use a mixture of soil and sand to ensure proper water drainage.

The volume of  26% soil he should add to the 16% to create a mixture that is 23% sand is calculated as follows;

Let the volume of the  26% soil = x

To determine the value of "x", we form the equation below, using the rules of equilibrium of a mixture or solution;

[0.16(10) + 0.26(x)]/(x + 10) = 0.23

multiply both side of the equation with "(x + 10)"

0.16(10) + 0.26(x) = 0.23(x + 10)

1.6 + 0.26x = 0.23x + 2.3

0.26x - 0.23x = 2.3 - 1.6

0.03x = 0.7

x = 0.7/0.03

x = 23.3 m³

Thus, the volume of  26% soil he should add to the 16% to create a mixture that is 23% sand is 23.3 m³.

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