1.
Rule/Equation: y = slope (x) +/- y-intercept
OR y = m(x) +/- b
X
2
6
10
14
18
y
12
8
4
0
TABLES TO EQUATIONS #2
-4
Slope (growth rate):
y-intercept (starting value):
2
Equation:

In order to find 5a-3b, lets find 5a. This is given by

Similarly, -3b is given by

Then, by substituting our results into the expression 5a-3b, we get

This can can be done by adding entry by entry, that is

Therefore, the answer is

The angle in the fourth quadrant associated with trigonometric function is 314.415°. The exact values of the six trigonometric functions are listed below:

In this problem we find the exact form of a trigonometric function and the related quadrant on a Cartesian plane. By definition of the sine function and the features of the sine, the exact value has the following form and conditions:

y / √(x² + y²) = - 5 / 7, x > 0, y < 0

Then,

y = - 5, √(x² + y²) = 7

√[x² + (- 5)²] = 7

x² + 25 = 49

x² = 24

x = √24

x = 2√6

Then, the angle associated to the trigonometric function is:

θ = tan⁻¹ (y / x)

θ = tan⁻¹ (- 5 / 2√6)

θ ≈ 314.415°

And the five other trigonometric functions are:

cos θ = 2√6 / 7

tan θ = - 5 / 2√6

cot θ = - 2√6 / 5

sec θ = 7 / 2√6

csc θ = - 7 / 5

The angle associated with trigonometric function is 314.415°.

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Step-by-step explanation:

I assume the ? is the left leg of the left triangle.

the middle line (right leg of the smaller left triangle, and the left leg of the larger right triangle) bisects the top angle of the main large triangle (because the top angles left and right from the middle line are equal).

that means per the angle bisector theorem

5 / 4 = 10 / ?

5 = 10×4/? = 40/?

?×5 = 40

? = 40/5 = 8

we have

see the attached figure to better understand the problem

please wait a moment (to fill the table)

Answer:

102 / 105 = 0.971428571

Step-by-step explanation:

i used a calculator c:

Answer:

x = 42

see below for the angle measures.

Step-by-step explanation:

The angle marked 2x - 9 is sort of outside the triangle. It is called an exterior angle. The other two angles are called remote interior angles. "Remote" means that they are away from the exterior angle. When you have this set up, the two remote angles added together EQUAL the exterior one.

x+5 + 28 = 2x - 9

x + 33 = 2x - 9

Subtract x.

33 = x - 9

Add 9.

42 = x

So x = 42° which if you put that back into the expressions you can find the measures of the one remote interior angle (the other we know is 28°) and the exterior angle.

remote int angle:

x+5

= 42 + 5

= 47°

Exterior angle:

2x - 9

= 2(42) - 9

= 84 - 9

= 75°

(You can also then find the completely unmarked angle which is 180°- 75° which is 105°)

Answer:

78.5 square meters

Explanation:

• Given:, A circle with a radius of 5 meters.

• To find:, Area of the circle

The area of a circle is calculated using the formula:

Substitute 5 for r and 3.14 for π:

The area of the circle is approximately 78.5 square meters.

Answer:

See the picture below

Step-by-step explanation:

The events are independent because there is no evidence of dependece between the events, the box can contain one or two prices or be any size.

The possible number of ways of selection by using combination formula is 3060.

What is combination?

A grouping of items where the order in which they were chosen is irrelevant is known as combination.

Given that the number of people in the group is 18. Only 4 people will be member of the council.

The formula of combination is [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex] , where r number of objects are selected from n objects.

In the given question the value of n is 18 and the value of r is 2.

Substitute the value of n and r in [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex].

[tex]^{18}C_{4}=\frac{18!}{4!(18-4)!}[/tex]

Solve the above expression:

18^C_4 = 18x17x16x15x14/4x14

18^C_4 = 18x17x16x15/4x3x2x1

3060 18^C_4 = 3060

The number of ways such selection is 3060.

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We want to know what's the probability of spinning a number greater than two

There are 2 spinnings greater than two, of a total of 8. therefore, the probability I will be

The probability is 1/4

The number of miles to drive for 30 gallons is 960 miles

From the question, the function definition is given as

d(g) = 32g

Where g represents the number of gallons and d represents the distance

The function value to calculate is given as

d(30)

This means that we calculate the number of miles to drive for 30 gallons

So, we have

d(30) = 32(30)

This gives

d(30) = 32 x 30

Evaluate the product

d(30) = 960

Hence, the function value is d(30) = 960

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Answer:15216.31 Fluid Ounces

Step-by-step explanation:

Using percentages we can conclude that 95% of votes that is 2,314 votes (B) cannot be guaranteed which is 1,023 votes more than the projected 53% winning votes (1,291 votes).

So, candidate A has a projection of winning 53% votes.

A sample of 2436 voters is pulled, then:

Can candidate A be guaranteed 95% votes which are:

Difference: 2,314 - 1,291 = 1,023

Therefore, using percentages we can conclude that 95% of votes that is 2,314 votes (B) cannot be guaranteed which is 1,023 votes more than the projected 53% winning votes (1,291 votes).

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The phrase of the expression x - 6 is 6 less than a number.

Expression:

The expression refer the sentence with a minimum of two  numbers/variables and at least one math operation in it.

Given,

Here we have the expression x -6.

And we need to convert this expression in order to get the phrase form.

In order to get the phrase form, we have to translate the given expression into word.

While we looking into the given expression we have identified the following three terms.

They are, x , (-) and 6.

Here x represents the unknown number.

(-) represents that we have to less the unknown number by the given number.

And 6 is the given number.

So, the phrase for this situation is 6 less than a number.

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The relation that represents a function is given as follows:

B. The second graph.

A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.

For a point in the standard format (x,y), we have that:

In a graph, the equivalent to this is that there can be no vertically aligned points.

Then, for the options in this problem, we have that:

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Answer:

1.5 m/s

Step-by-step explanation:

Distance = 6.8×1609.344 = 10943.5392

time=2×60×60 = 7200

velocity= distance/time = 10943.5392/7200= 1.51 m/s

As the y-values of a function are the values that the function takes, the largest y-value of a function is called the maximum value of the function

ANSWER

EXPLANATION

When a line segment is divided by ratio m:n, the coordinates of the point of division are given as:

where (x₁, y₁) and (x₂, y₂) are the coordinates of the ends of the line.

Therefore, we have that:

Therefore, the coordinates of point C are:

Those are the coordinates of C.

Answer:

SAS Congruence Rule

A triangle is said to be congruent to each other if two sides and the included angle of one triangle is equal to the sides and included angle of the other triangle.

Answer: SAS (side side angle postulate.)

Step-by-step explanation:

can be used to prove triangles congruent.

sides and the corresponding angle of the other, then the triangles are congruent.

The perimeter of a rectangle is given by:

Where:

P = perimeter = 252 ft

w = width = 5 ft

l = lenght

Then, substitute the values:

And solve for l:

Answer: length = 73 ft

The ratio House blend/Organic Free Trade blend is the same and must remain the same.

So, the proportion is:

Where x is the unknown amount of the Organic Free Trade blend.

So, from the proportion, we have:

Answer: 156 pounds of Organic Free Trade blend

Answer:

a. 0.8 = 0.5 + 0.3

b. 30.9 = 2.7 + 28.2

c. 15.4 = 3.1 + 2.4 + 9.9

d. 17.4 = 15.2 + 1.4 + 0.8

e. 42.5 = 39.2 + 2.5 + 0.8

f. 8 = 4 + 4

g. 35 = 23 + 8 + 4

h. 84 = 53 + 3 + 28

i. 121 = 11 + 17 + 93

j. 35 = 24 + 8 + 3

Answer: see the attachment

Step-by-step explanation:

h = # of hours worked

{10h and {15(h-40)+400 are both functions i.e. simplified equations

simply fit the # of hours worked in each equation to get the values. you can also double check your work or to understand better

to do so, take (h) # of hours worked and multiply by the pay rate. This gives the total pay over the work week. then take the extra hours beyond the 40. ie 7.  if $10 is the pay rate per hour and OT is 1.5xnormal pay then 10x1.5=15. Multiply 15x7 and you get 105 then add to 400 and you get $505. 400 comes from 10(40).

part b and c is just setting the functions.

so instead of 40 hrs per week your full-time rate is now 38 and anything beyond would be counted as overtime. so a normal work week of 38 hrs x the $10/hr would equate to $380 for the week.

part c, if the hours per week were kept normal at 40hrs/week but the pay rate is increased this then changes 10 = h to 12 = h. if 12=h and you work 40hrs/week, then 12(40)=$480 for the normal work week. also this changes your OT pay from 10(1.5)=15 to 12(1.5)=$18

Answer:

6

Step-by-step explanation:

We can round $4.98 up to $5.

Then do $30 / $5 = 6

Go back and check if 6 works:

$4.98 × 6 = $29.88 which is less than $30.

So the answer is 6

. Write the equation for the line: (Hint: there are two points given to you!)

________________________

y= mx + b

the slope is m

or

(y - y1) = m (x - x1)

___________________

points (x,y)

point 1 (4, 4) x1 = 4; y1 = 4

point 2 (3 , -1) x2= 3; y2 = -1

The slope m = (y2- y1) / (x2 -x1)

m=(-1 - 4 )/( 3 - 4)

m= -5/-1 = 5

(In this case, you choose which point you want to put as point one and point two, you will always get the same answer)

____________________

(y - 4) = 5 (x - 4)

y= 5x -20 +4

y= 5x - 16

The equation for the line is y= 5x - 16

__________________

Do you have any questions regarding the solution?

The expression when factorized is (5x + 1)(x + 1)(x - 3)

From the question, the expression is given as

5x³ - 9x² - 17x - 3

Express 9x² as 5x² - 15x²  + x²

So, we have

5x³ - 9x² - 17x - 3 = 5x³ + 5x² - 15x²  + x² - 17x - 3

Express -17x as x - 3x - 15x

So, we have

5x³ - 9x² - 17x - 3 = 5x³ + 5x² - 15x²  + x² + x - 3x - 15x  - 3

Rearrange the terms

5x³ - 9x² - 17x - 3 = 5x³ + 5x² - 15x²  - 15x  + x² + x - 3x - 15x - 3

Group the terms in 4's

5x³ - 9x² - 17x - 3 = (5x³ + 5x² - 15x²  - 15x)  + (x² + x - 3x - 15x - 3)

Factorize each group

5x³ - 9x² - 17x - 3 = 5x(x² + x - 3x - 3) + 1(x² + x - 3x - 3)

So, we have

5x³ - 9x² - 17x - 3 = (5x + 1)(x² + x - 3x - 3)

Factorize x² + x - 3x - 3

5x³ - 9x² - 17x - 3 = (5x + 1)(x(x - 3) + 1(x - 3))

So, we have

5x³ - 9x² - 17x - 3 = (5x + 1)(x + 1)(x - 3)

Hence, the factorized expression is (5x + 1)(x + 1)(x - 3)

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The equation using the distributive property is 8 (5 + 2) = (8 × 5) + (8 × 2)

Given,

The equation: 8 ( 5 + 2) = (__×___) + (___×__)

Distributive property:

The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

Here,

8 (5 + 2)

Using distributive property open the brackets:

8 (5 + 2) = (8 × 5) + (8 × 2)

Now,

8 (5 + 2) = 40 + 16

That is,

8 (5 + 2) = 56

So,

The equation using the distributive property is 8 (5 + 2) = (8 × 5) + (8 × 2)

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