Write the equation of the line in point-slope form that passes through the points
(
−
8
,
2
)
and
(
6
,
8
)
.

Answer:

Step-by-step explanation:

The domain is the set of x values and the range is the set of y values.

For the relation to the function, each value of x must map onto no more than one value of y.

Answer:

The Domain is -2 [is less than or equal to] x < 0

The Range is 0 [is less than or equal to]  y < 2

This is NOT a function

Step-by-step explanation:

sry if this is a bit confusing:

[is less than or equal to] is just the sign that means what is said; this is bc you cant use that sign on keyboard

Based on the triangle similarity theorem, the length of AK is: A. 9.

Based on the triangle similarity theorem, the ratios of the corresponding side lengths of two triangles that are similar to each other are equal and their lengths are proportional to each other.

Given that triangle FIM and triangle LAK are similar triangles, therefore, the ratio is true:

FM/LK = IM/AK

Length of FM = 8 units

Length of LK = 12 units

Length of IM = 6 units

Length of AK = ?

Substitute

8/12 = 6/AK

8(AK) = (6)(12)

8(AK) = 72

Divide both sides by 8

8(AK)/8 = 72/8

AK = 9

AK = LA = 9

LA = 9 units

Therefore, based on the triangle similarity theorem, the length of AK is: A. 9.

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For the two similar triangles, the length of side DA = 4 units.

For the two triangles;

ΔABC ≡ ΔADE

The ratios of their side will be equal

Thus,

CB/ED = AB/DA

Put the values of the sides from given diagram.

2/4 = 2/DA

Cancel the common 2 and cross multiplying.

DA = 4 units.

Thus, the length for the side DA is 4 units.

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Using Venn sets, it is found that 30 athletes own none of the items.

The missing information is the question, which asks how many athletes own none of the items.

For this problem, we consider the following sets:

10 owned all three items, hence:

(A ∩ B ∩ C) = 10.

57 owned a convertible and a TV, hence:

(A ∩ B) + (A ∩ B ∩ C) = 57.

(A ∩ B) = 47.

50 owned a TV and a store, hence:

(B ∩ C) + (A ∩ B ∩ C) = 50

(B ∩ C) = 40.

29 owned a convertible and a store, hence:

(A ∩ C) + (A ∩ B ∩ C) = 29.

(A ∩ C) = 19.

136 owned a sporting goods store, hence:

C + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 136

C + 19 + 40 + 10 = 136

C = 67.

117 of them owned a giant screen TV, hence:

B + (A ∩ B) + (B ∩ C) + (A ∩ B ∩ C) = 117

B + 47 + 40 + 10 = 117

B = 20.

135 of them owned a convertible, hence:

A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 135

A + 47 + 19 + 10 = 135

A = 59.

There were 292 athletes on the survey, hence the number who owned none is given as follows:

None + A + B + C + (A ∩ B) + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 292

None + 59 + 20 + 67 + 47 + 19 + 40 + 10 = 292

None + 262 = 292

None = 30.

30 athletes own none of the items.

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The value of y is 9.

Perimeter is the total length of the boundary of any closed shape. It is basically the sum of all the sides of a given figure.

Perimeter of a rectangle is given by [ 2( l + b ) ] or (2 l + 2 b ) or

( l + l + b + b), here l and b represent the length and breadth of the given rectangle.

Perimeter of the given rectangle = 166 units               ( given )

Length of the given rectangle = 5y                                ( given )

Breadth of the given rectangle = (4y + 2)                     ( given )

By putting values in the formula, we get

perimeter = 2 ( l + b )

166 = 2 [ (5y) + (4y + 2) ]

166 = 2 [ 5y + 4y + 2 ]

166 = 2 [ 9y + 2 ]

166 = 2*9y + 2*2

166 = 18y + 4

166-4 = 18y  ( moving 4 to other side thus changing the sign to negative )

162 = 18y

162/18 = y  ( moving 18 to other side for further solution )

y = 9

Therefore, the value of y for which the perimeter of the given rectangle is 166 units is 9.

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The value of y is 9.

The whole length of any closed shape's boundary is known as its perimeter. In essence, it is the total of a given figure's sides.

A rectangle's perimeter can be calculated using [2(l + b)] or (2 l + 2 b) or

(l + l + b + b), where l and b stand for the provided rectangle's length and width

The rectangle's perimeter is 166 units ( given )

The rectangle's length is 5y ( given )

Given rectangle's width equals (4y + 2) ( given )

When we enter values into the formula, we obtain

perimeter = 2 ( l + b )

166 = 2 [ (5y) + (4y + 2) ]

166 = 2 [ 5y + 4y + 2 ]

166 = 2 [ 9y + 2 ]

166 = 2*9y + 2*2

166 = 18y + 4

166-4 = 18y  ( moving 4 to other side thus changing the sign to negative )

162 = 18y

162/18 = y  ( moving 18 to other side for further solution )

y = 9

Therefore, the value of y for which the perimeter of the given rectangle is 166 units is 9.

The balance of current assets of the firm is 54 million dollars.

The total of all current assets is the current asset balance. These include cash, cash equivalents, pre-paid expenses, inventories, and any other assets that are anticipated to be turned into cash throughout the course of the following year.

Any debts owed by your business to others, including bank loans, mortgages, unpaid bills, IOUs, and other sums of money, are referred to as liabilities.

We know that to calculate the balance of current assets we use the formula.

Current assets=working capital +current liabilities

Working capital=net income÷(profit margin × sales to working capital)

Now given the working capital=$20 million

Profit margin=5%

Working capital=20÷(8×5%)

or, working capital = 50

Now current assets=Working capital+liabilities

Hence balance of current assets= 50+4 million dollars

=54 million dollars

Therefore the firm's balance of current assets is 54 million dollars.

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The equation that represents the cost of jake's cell phone bill is -

y = 2x + 40 . Option - B is the correct alternative.

We have a graph representing jake's cell phone bill.

We have to write a equation that represents the cost of jake's cell phone bill.

The general equation of a straight line is given by -

y = mx + c

where -

m → slope of line.

c → y - intercept of line.

According to the question -

The y - intercept of the line is at the coordinates (0, 40). Now, we have to find the slope of this line. Consider the two coordinates -

A(0, 40) and B(10, 60)

Slope of a straight line is given by -

m = y₂ -y₁ / x₂ - x₁

m = 60 - 40 / 10 - 0

m = 20 / 10

m = 2

Now, substituting the values in the general equation of line, we get -

y = 2x + 40

Hence, Option B → y = 2x + 40 is the correct alternative.

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If [tex]\hat\gamma-c\hat\alpha-d\hat\beta[/tex] is perpendicular to both [tex]\hat\alpha[/tex] and [tex]\hat\beta[/tex], then their dot products are zero.

Recall that for any vector [tex]\hat x[/tex], [tex]\hat x\cdot \hat x = \|\hat x\|^2[/tex].

Now, we have

[tex](\hat\gamma - c\hat\alpha - d\hat\beta) \cdot \hat\alpha = (\hat\gamma\cdot\hat\alpha) - c\|\hat\alpha\|^2 - d (\hat\beta\cdot\hat\alpha) = 0[/tex]

[tex]\hat\gamma\cdot\hat\alpha = 5 + 0 - 16 = -11[/tex]

[tex]\|\hat\alpha\|^2 = 1^2 + 1^2 + (-2)^2 = 6[/tex]

[tex]\hat\beta\cdot\hat\alpha = -1 + 2 - 6 = -5[/tex]

[tex]\implies 6c - 5d = -11[/tex]

and

[tex](\hat\gamma - c\hat\alpha - d\hat\beta) \cdot \hat\beta = (\hat\gamma\cdot\hat\beta) - c(\hat\alpha\cdot\hat\beta) - d \|\hat\beta\|^2 = 0[/tex]

[tex]\hat\gamma\cdot\hat\beta = -5 + 0 + 24 = 19[/tex]

[tex]\|\hat\beta\|^2 = (-1)^2 + 2^2 + 3^2 = 14[/tex]

[tex]\implies 5c - 14d = -19[/tex]

Solve for [tex]c[/tex] and [tex]d[/tex]. By elimination,

[tex]5(6c - 5d) - 6(5c - 14d) = 5(-11) - 6(-19)[/tex]

[tex]-25d + 84d = -55 + 104[/tex]

[tex]59d = 59[/tex]

[tex]\boxed{d=1}[/tex]

[tex]6c-5 = -11[/tex]

[tex]6c=-6[/tex]

[tex]\boxed{c=-1}[/tex]

Answer:

2 of the sides are 15 inches and the other 2 sides are 68 inches

Step-by-step explanation:

2(8+4L)+2L=166

16+8L+2L=166

16+10L=166

10L=150

L=15

15(4)+8=68

Answer:

177.464x−1

Step-by-step explanation:

How many times larger is (1.064x⋅101)+(7x⋅10−1)

Remove parentheses.

1.064x⋅101+7x⋅10−1

Simplify each term.

Multiply 101 by 1.064.

107.464x+7x⋅10−1

Multiply 10 by 7.

107.464x+70x−1

Add 107.464x and 70x.

177.464x−1

Answer:

6, 4 and 12 are factors

Step-by-step explanation:

Divide 96 by each value. If the result is an integer then it is a factor

96 ÷ 18 = 6.333 ← not a factor

96 ÷ 6 = 16 ← factor

96 ÷ 4 = 24 ← factor

96 ÷ 12 = 8 ← factor

96 ÷ 14 = 6.857.. ← not a factor

Answer:

D neither

Step-by-step explanation:

Because they both don't have big numbers so the are unequal

Answer:

952.32

Step-by-step explanation:

The algebraic solution for the variable x is as follows:

The equation is represented as follows;

2 / 5 (2 - x) = - 1 / 3 x + 1 / 2

open the bracket on the left side

2 / 5 (2 - x) = - 1 / 3 x + 1 / 2

4 / 5  - 2x / 5 = - 1 / 3 x + 1 / 2

Add 1  /3 x to both sides

4 / 5  - 2x / 5 = - 1 / 3 x + 1 / 2

4 / 5  - 2x / 5 + 1 / 3 x  = - 1 / 3 x + 1 / 3 x  + 1 / 2

4 / 5 + 1 / 3 x - 2 / 5 x = 1 / 2

4 / 5 + 5x - 6x / 15 = 1 / 2

4  / 5  - x / 15 = 1 / 2

subtract 4 / 5 from both sides

4  / 5 - 4 / 5  - x / 15 = 1 / 2 - 4 / 5

- x / 15 = 5 - 8 / 10

- x / 15 = - 3 / 10

cross multiply

- x / 15 = - 3 / 10

-10x = - 45

divide both sides by -10

x = 45  /10

x = 9 / 2

Therefore, the algebraic solution for the variable x is 9 / 2.

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Answer:

D. -9.7

Step-by-step explanation:

the square root of 40 is 6.32

-16 + 6.32 = -9.68

-9.68 rounded the nearest tenth is -9.7

The probability that a prisoner selected at random from this prison is female and at least 25 years old is 1/64

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

GIven that 2/3 of the inmates are under 25 years of age also, that 3/5 of the inmates are male and that 5/8 of the inmates are female or 25 years of age or older.

The number of mother inmates = 75% (100) = 75

The number of inmates, who are not mothers = 100 - 75 = 25

Selecting an inmate who is not a mother =  1/4

Selecting 3 female who are not mothers = 1/64

Therefore, the probability that a prisoner selected at random from this prison is female and at least 25 years old is 1/64

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The angled relationship is the Same-side interior angle where x is 6 and ∠EFG is 102°

For the parallel lines ED and FG, where EF is the transversal,

The angle DEF and the angle EFG are same-side interior angles.

By the same-side interior angle theorem, we can say that the interior angles on the same side of the transversal are supplementary (the sum of the angles is 180°).

∠DEF = 13x°

∠EFG = 17x°

∠DEF + ∠EFG = 180°

13x + 17x = 180

30x = 180

x = 6

∠DEF = 13x = 13*6 = 78°

∠EFG = 17x = 17*6 = 102°

Therefore, the angles follow the same-side interior angles relationship, x = 6 and ∠EFG = 102°

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According to the question, the given parameters has relationship between the length and the width of the rectangle.

The perimeter of the rectangle is 18 inches.

Now, using standard perimeter as well as area formulas of a rectangle. Therefore, the equation can become:

Let us assume, the width of the rectangle be 'w' inches

The length of a rectangle be (9w - 11)

As we know, perimeter of a rectangle is 2(l + w)

Substitute the calculated parameters in the perimeter formula:

18 = 2(9w - 11 + w)

⇒ 9 + 11 =10w

⇒ w = 2 inches and l = 7 inches

Then, the calculated width is 2 inches and length is 7 inches.

What is rectangle?

Rectangle is two-dimensional shape. It has four sides, four corners and four angles. In this opposite sides are equal to each other. And the opposite sides are equal and parallel to each other.

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The difference in scores between Player A and Player B will be 17.

From the information, Player A finished first in a tournament at a golf club with a score of 8, or eight strokes under par. Player B, had a score of +9, or 9 strokes over par.

Therefore, the difference in scores between Player A and Player B will be:

= 9 - (-8)

= 9 + 8

= 17

Therefore, the difference in scores between Player A and Player B will be 17.

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The interquartile range of the concert tickets sold is 72. (the second option).

A box plot is a graph that is used to study the distribution and level of a set of scores. The box plot consists of two whiskers and a box. The first whisker represents the minimum number and the end of the second whisker represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

The interquartile range is the difference between the third quartile and the first quartile.

Interquartile range =  third quartile - first quartile

369 - 297 = 72

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The number of ways that they can share these fruits if each person must have at least 1 fruit will be 12 ways.

From the information, 6 apples and 5 oranges are shared among 3 people and the apples are indistinguiable, oranges are also indistinguiable.

Therefore, the number of ways that they can share these fruits if each person must have at least 1 fruit will be:

= (6 - 3)! × (5 - 3)!

= 3! × 2!

= 3 × 2 × 2

= 12

Therefore, the number of ways that they can share these fruits if each person must have at least 1 fruit will be 12 ways.

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The monthly payment when Jack takes the loan will be B. $319.44

From the information, the interest will be:

= Principal × Rate × Time / 100

= ($10000 × 5 × 3)/100

= $1500

The total amount to be repaid will be:

= $10000 + $1500

= $11500

Therefore, the monthly payment will be:

= $11500 / 36

= $319.44

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Answer:

6

Step-by-step explanation:

Due to the segment addition postulate, XY + YZ = XZ.

By substituting the values in, we get that [tex](3k-2)+(7k+4)=4k+38[/tex]

Simplifying gives us that [tex]10k+2=4k+38[/tex]

[tex]6k=36[/tex]

[tex]k=6[/tex]

The bread that has the greatest ratio of Calories to slices is the Wheat bread

The table of values is given as

Wheat bread

Slice - Calories

2 - 160

4 - 320

6 - 480

The missing graph that represents the graph of rye bread is added as an  attachment

On the graph, we have the following table of values

Rye bread

Slice - Calories

2 - 130

4 - 260

6 - 390

We start by calculating the rates of each table using

Rate = Calories/Slice

So, we have

Wheat bread = 160/2

Wheat bread = 80

Rye bread = 130/2

Rye bread = 65

80 is greater than 65

Hence, the bread that has the greatest ratio of Calories to slices is the Wheat bread

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The Area of the figure ≈ 19 units²

Area of a semicircle = 1/2(πr²), where r is the radius.

Area of a triangle = 1/2(b)(h), where b is the base and h is the height of the triangle.

The figure can be decomposed into a semicircle and a triangle.

Area of the figure = 1/2(πr²) + 1/2(b)(h)

r = 1/2(7) = 3.5 units

π = 3.14

b = 7 units

h = 3 units

Substitute

Area of the figure = 1/2(3.14)(3.5²) + 1/2(7)(3)

Area of the figure ≈ 19 units²

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According to the GEMDAS rule the value of the 26-6+ (0+3)*26-6 ÷26- I:

= [tex]96\frac{10}{13}[/tex]

The GEMDAS rule can be used to summarize or evaluate difficult numerical equations containing several binary operations. Important Information: 1. In a specific simplification, if you have simultaneous multiplication and division, perform the operations sequentially from left to right.

If you mess up the order of parenthesis, exponents, multiplications, including addition and subtraction, the PEMDAS rule prevents you from getting the wrong result.

Applying the GEMDAS rule:

26-6+ (0+3)*26-6 ÷26- I

= 26-6+ (0+3)*26-6 ÷26- I

= 26-6+ 78 -6÷ 26-1

= 26-6+78- [tex]\frac{6}{26}[/tex] -1

= 1258/13

= [tex]96\frac{10}{13}[/tex]

According to the GEMDAS rule the value of the 26-6+ (0+3)*26-6 ÷26- I:

= [tex]96\frac{10}{13}[/tex]

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Answer: answer is 3

Step-by-step explanation:

Answer:

Point W.

Step-by-step explanation:

Line [tex]n[/tex] is on plane [tex]A[/tex]. Line [tex]m[/tex], however, is not on any plane shown, but intersects plane [tex]A[/tex] and line [tex]n[/tex].

The number of plans that cost between 41.46 and 63.42 is 504 to the nearest whole number

We have the following data to solve this problem with

n = 738 home owners

standard deviation sd = 10.98

The number of plans is between 41.46 and 63.42

Such that we will have

p(41.46 < x< 63.42)

Then we would have

P(41.46 - 52.44 / 10.98) < z< (63.42 - 52.44 / 10.98)

= P (-1 < z < 1)

We have p(z < 1) = 0.8413

therefore p(z > 1) = 1 - 0.8413

= 0.1587

0.8413 - 0.1587 = 0.6826

This is the same as 68.26%

68.26% x 738 = 503.76

~ 504

Therefore we would have the conclusion that the number of plans that cost between 41.46 and 63.42 is 504 to the nearest whole number.

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