Determine which integer in the solution set will make the equation true. t − 42 = −14 S: {−56, −28, 3, 28}

Answer:

y = 10 , ∠ C = 40° , ∠ D = 76°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ DEF is an exterior angle of the triangle , then

∠ C + ∠ D = ∠ DEF , that is

4y + 7y + 6 = 116

11y + 6 = 116 ( subtract 6 from both sides )

11y = 110 ( divide both sides by 11 )

y = 10

Then

∠ C = 4y = 4(10) = 40°

∠ D = 7y + 6 = 7(10) + 6 = 70 + 6 = 76°

Answer:

y = 10

∡C = 40°

∡D = 76°

Step-by-step explanation:

Supplementary angles sum 180°

116° and ∡E are supplementary angles:

116 + E = 180°

E = 180 - 116

E = 64°

∡E = 64°

Internal angles of a triangle sum 180°

∡D   + ∡C + ∡E = 180°

7y+6 + 4y + 64 = 180

7y + 4y + 6 + 64 = 180

11y + 70 = 180

11y = 180 - 70

11y = 110

y = 110/11

y = 10

Then:

∡C = 4y = 4*10 = 40°

∡D = 7y + 6 = 7*10 + 6 = 70 + 6 = 76°

Answer: Postulate

Step-by-step explanation:

Side-Side-Side (SSS) Postulate

If three sides of one triangle are congruent to three sides of another triangle, then the two are congruent.

The values of sin2x, cos2x and tan2x is -3/5, -4/5 and 3/4 respectively.

What is sine function?

The ratio of the opposite side's length to the hypotenuse of a right-angled triangle is known as the sine function in trigonometry. A right triangle's unknown sides or angles can be determined using the sine function. The ratio of the side opposite the angle (also known as the perpendicular) and the hypotenuse is known as the sine of an angle in a right-angled triangle.

The ratio of the perpendicular of a right-angled triangle to the hypotenuse is known as the sine of the angle. The following is the sin formula: sin = Perpendicular / Hypotenuse.

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The percentage is calculated by dividing the required value by the total value and multiplying by 100.

The amount earned by 217% more from last year to this year.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Amount earned last year = 1,459,632,852

Amount earned this year = 4,632,859,678

The best estimate of the amount earned this year than last year.

= [ (4,632,859,678 - 1,459,632,852 ) / 1,459,632,852 ] x 100

= ( 3173226826 /1,459,632,852 ) x 100

= 217 %

Thus,

The amount earned by 217% more from last year to this year.

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Single bookcase units with two sides, top and bottom should be no wider than 36 inches without a center support.

Each shelf can hold 33 books

There are 1221 mystery books

Therefore the number of shelves he will need to build can be calculated as follows

= 1221/33

= 37

Hence Landon will need to build 37 shelves,

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The ratio of the radii of smaller circle to that of larger circle is 1/√2.

Let the Radius of smaller circle is "r".

So the area of the smaller circle will be π(radius)²=πr²

Let the Radius of the larger circle is "R".

So the area of the larger circle will be π(radius)²=πR².

In question it is given that, the area of the smaller circle is half of the area of larger circle.

That means,

area of smaller circle=1/2 area of larger circle

area of smaller circle=1/2 area of larger circleπr²=1/2 πR²

area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²

area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²r²/R²=1/2

area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²r²/R²=1/2r/R=√1/2

area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²r²/R²=1/2r/R=√1/2r/R=1/√2

Ratio of smaller circle to that of larger circle is 1/√2 .

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The likelihood that every girl is on the same team is 1/252.

A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Since the team's student lineup is not crucial, a mixture will be employed.

C(10,5) = 252 is the number of possible methods to choose 5 students from a class of 10.

Rest Team B will consist of 5 students. Consequently, there are 252 items in the sample space.

Let two women join team A. then the number of methods for choosing the final three members from the eight remaining members C(8,3) = 56

Likewise if two girls are in team B then possible number of different groups is 56.

Therefore total number of different groups such that two girls  are in one team is 56+56 = 112.

The required probability is

P(two girls  are in one team) = 112 / 252

Number of ways of selecting all girls in one team and boys in another team is 1. So required probability is

P( girls in one team) = 1/ 252

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For the above system of equations, 4x-4y=12 and 16x-6y=-12, the values of x and y are 4.5 and -10 respectively.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here,

4x-4y=12

16x-6y=-12

multiply equation 1 by 4,

16x-16y=48

-16x+6y=12

-10y=60

y=-10

-16x-60=12

-16x=72

x=72/16

x=4.5

The value of x is 4.5 and y is -10 for the given system of equation as 4x-4y=12 and 16x-6y=-12.

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Answer:

125 in^2

Step-by-step explanation:

Assuming that s is the length of a side in the base.

Answer: 6.3x + 2.885

Step-by-step explanation:

Since there is only one factor of x, we cannot simplify x.

We can simplify the constants though.

6.3x + (-7.015 + 9.9)

= 6.3x + 2.885

Answer:

6 sqrt(2)

Step-by-step explanation:

sqrt(50) + sqrt(2)

Rewrite sqrt(50) as sqrt(25*2)  = sqrt(25) * sqrt(2) = 5 sqrt(2)

5 sqrt(2) + sqrt(2)

6 sqrt(2)

The value of the variable 'y' will be 3. Then the correct option is A.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of the linear equation is given below.

2x - 5y = 1                ...1

-3x + 2y = - 18         ...2

Multiply equation 1 by 2 and equation 2 by 5, then we have

4x - 10y = 2

-15x + 10y = - 90

Add both equations, then we have

4x - 15x = 2 - 90

11x = 88

x = 8

Then the value of the variable 'y' is calculated as,

-3 (8) + 2y = - 18

- 24 + 2y = - 18

2y = 24 - 18

2y = 6

y = 3

The worth of the variable 'y' will be 3. Then the right choice is A.

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Answer: The value of x is 0.625

Step-by-step explanation:

x=5/0.8

since figure A is scaled to 5 by 0.8, we divide 5 by 0.8 to find x.

x=0.625

The value of x that will make L || M is x/2

As a parallel line part of the qualities include that the slopes of the lines  are equal  

The equation of line is L = 2x + 5 and M = x - 5

The slope intercept form of the form as

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

to make line L parallel to line M

2x ⇔ x

hence x in line L will be equal to x/2

L = 2x + 5

L = 2(x/2) + 5

L = x + 5

L = x + 5 is parallel with M = x - 5

L = 2x + 5 is parallel with M = 2x - 5

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The required slopes of the line are as follows,
(a) y = 12, the slope is m = 0,
(b) x = -13, the slope is not defined.
(c) -6y = -2x + 30, the slope is positive, m = 1 / 3.
(d) 3x + 5y =15, the slope is negative, m=  -3/5.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

here,
(a)
y = 12

Comparing the above expression with the standard equation of line y = mx + c,
From comparison,
mx = 0
m = 0

(b)
x = -13,
x + 13 = 0
Comparing the above expression with the standard equation of line y = mx + c,
From comparison,
mx = 1 / 0     (because the equation does not contain the term y)
m =  not defined.

Similarly,
(c) -6y = -2x + 30, the slope is positive, m = 1 / 3.
(d) 3x + 5y =15, the slope is negative, m=  -3/5.

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Answer:

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain. For all values of a and b, f = (a,b)|

If every element in set A has exactly one and only one image in set B, then the relation is said to be a function.

A function is a relation from a non-empty set B such that its domain is A and it never has the same first member in two different ordered pairs.

In arithmetic, a function can be represented as:

a set of ordered pairs

an arrow diagram

a table form

a graphical form

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Answer:

10 and 8

Step-by-step explanation:

must be in the ratio 5:4, 5 x 4 =20, so if you multiply by 2 the ratio is 10:8 (same thing). The least common multiple of 10 and 8 is 40 because you can do 10 x 4 = 40 and 8 x 5 = 40.

answer:the answer for digital index of 23475 is 3

answer: 3

explanation: the digital index is 3 because 23475 is divisible by 3

Answer:

Radius is equal to 2.86 cm

Step-by-step explanation:

C = Perimeter = 18 cm

Perimeter of a circle = 2*PI*r

C = 2*pi*r

18 = (2)*(3.14)*r

18 = 6.28*r

r = 18/6.28

r = 2.86 cm

The equation which represent the following problem is s = 200/5

Average speed of an object refers to the rate of total distance traveled by the total time taken.

Average speed, s = Total distance traveled, d / Total time taken, t

Average speed = Total distance traveled / Total time taken

= 200 miles / 5 hours

= 40 miles per hour

In conclusion, the situation can be represented by the equation s = 200/5

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Answer:

$51.75

Step-by-step explanation:

Use a tip calculator.

The equation of the required line is given as y = -23x - 92.

A straight line can be written in the form of equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

The given problem can be solved as follows,

The equation of the line is  y = −23x + 32.

Then, its slope is given by -23.

Since the parallel lines have the same slope, the slope of the line parallel to  y = −23x + 32 is -23.

Now, the equation of the line passing through (4, -7) and parallel to the given line can be written as,

(y + 7)/(x - 4) = -23

=> y + 7 = -23x - 92

=> y = -23x + -99

=> y = -23x - 92

Hence, the equation of the line passing through (4, -7) and parallel to y = −23x + 32 is  y = -23x - 92.

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The kind of sequence is a prime number if Norma cuts 3, 5, 8, 13 roses from the four bushes.

A prime number is a natural number higher than 1 that is not the sum of two lesser natural numbers. A composite number is any natural number that is more than 1 but not a prime. As an illustration, the number 5 is prime since there are no other ways to write it either a product than as 1 5 or 5 1. The basic arithmetic theorem states that every natural number greater than 1 is either a prime itself or can be factored as a product of primes that is unique up to their order, making primes a prominent concept in number theory.

Given,

The number of roses cut by Norma from the first rose bush are 3 roses.

And from the second rose bush are 5 roses and from the third rose bush are 8 roses.

And from the fourth rose bush are 13 roses.

1     2     3     4

3     5     8      13

Here, the roses are 3, 5, 8, 13

Therefore, the kind of sequence is a prime number.

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a) The taxes to be paid for someone with a taxable income of $39,000 are of: $4,680.

b) The piece-wise function is defined as follows:

c) The tax rates are used as the slope for each linear definition of the piece-wise functions, while the bounds of the intervals are used to calculate the intercept.

The amount of taxes owed is obtained applying the proportion of the tax rate relative to the annual salary.

The tax rate for a taxable income of $39,000 is of 12%, hence the amount is given as follows:

0.12 x 39000 = $4,680.

The piece-wise functions for this problem are all derived considering the intervals with the tax brackets,

For the first tax bracket, the proportion is merely applied, as follows:

0.1x, 0 ≤ x ≤ 10275;

For each bracket, starting on the second, the maximum tax rate of the previous rate is calculated, and added to the excess of the income relative to the maximum of the previous tax bracket multiplied by the proportion.

For the first tax bracket, the maximum income is of:

$10,275.

The maximum tax of the first tax bracket is of:

0.1 x 10275 = 1027.5. -> the maximum value of the nth bracket is the starting value of the nth+1 bracket.

Then the function for the second bracket rate is obtained as follows:

f(x) = 1027.5 + 0.12(x - 10275), 10276 ≤ x ≤ 41175.

The same procedure is applied to any of the remaining brackets, taking the previous bracket to obtain the function.

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The size of the subculture or group under studied determines the sampling size in ethnography. In this regard, it might not be possible to predetermine the participant count. The complete subculture or group being studied serves as the study sample size in anthropological research.

The non-random sample that best resembles stratified random sampling is quota sampling.

Using the non-probability sampling technique of quota sampling, researchers select a sample of people who are typical of the population. These people are chosen by researchers based on specific traits or qualities. In order to use market research samples for data collecting, they decide on and set sample quotas. These samples accurately reflect the entire population. The interviewer's or researcher's knowledge of the population will be the only factor used to select the final subgroup.

Probability sampling means that every member of the population has a chance of being selected.

There are four main types of probability sample.

Simple random sampling.

Systematic sampling.

Stratified sampling.

Cluster sampling.

For instance, a tobacco company would want to know which age group in a given city loves which brand of smokes. The age groups of 21–30, 31–40, 41–50, and 51+ are subject to survey quotas. Based on these findings, the researcher makes an estimation of the smoking trend in the city's inhabitants.

Therefore,

The size of the subculture or group under studied determines the sampling size in ethnography. In this regard, it might not be possible to predetermine the participant count. The complete subculture or group being studied serves as the study sample size in anthropological research.

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Answer:

Step-by-step explanation:

Answer:   -4608

========================================================

Explanation:

a = 9 = first term

r = -2 = common ratio

We multiply each term by -2 to generate the next term

The nth term for this geometric sequence is a*(r)^(n-1) which becomes 9(-2)^(n-1)

If you tried plugging in say n = 2, you should find that,

9(-2)^(n-1)

9(-2)^(2-1)

9(-2)^1

9(-2)

-18

So that confirms the second term. I'll let you try the other values of n to confirm it further.

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

From here, you plug in n = 10 to find the tenth term

9(-2)^(n-1)

9(-2)^(10-1)

9(-2)^9

9(-512)

-4608

Answer:

Q14    x = 3

Q15    No unique solution

Step-by-step explanation:

Q14

The value of x where the line crosses the x axis is the solution for x

Here we see the line crosses the x axis at x = 3 so solution is x =3

Mathematically,

2x - 3 = 3

2x = 3 + 3  adding 3 to both sides

2x = 6

x = 6/2 = 3

Q15

This is a horizontal line which crosses the y-axis at y = 1

Since this does not cross the x axis but is parallel to it, there is no unique solution for x

Mathematically,
-4x + 2 = -4x + 1

Adding 4x to both sides we get the absurdity that 2 = 1 and that indicates no unique solution for x. Alternatively we can say that x has an infinite number of solutions