p and q are both prime numbers with p < q.
They are each less than 18
Give an example where p + q is odd but not prime.

Answer:  49   &  82

Step-by-step explanation:

*the total degrees for each triangle is 180 degrees

9)  Start with the triangle furthest left- subtract 71 and 57 both from 180.  That leaves you with 52 degrees for that third angle.  The angles that all make a straight line or straight angle add up to 180 degrees as well.  Now, subtract the 52 and 65 from 180, which leaves you with 63 degrees for the first angle in the second triangle.  Now subtract the 63 and 68 from 180, which leaves you with 49 degrees for that answer.

10)  For this one, you will start with the triangle further right, since it already has two angles shown.  Subtract the 85 and 35 from 180, which gives you 60 degrees for that third angle.  Then, you can use the vertical angles to fill in its opposite angle in the first triangle (vertical angles are equal).  This means that the first triangle has angles of 38 and 60 degrees, so subtract those both from 180, giving you 82 degrees for that answer.

The components are Nx= Ncosθ  and Ny= -Nsinθ

We know that the vector quantities are those quantities that have magnitude as well as direction.

Each vector quantity can be divided into two parts a horizontal and vertical component, the vertical component is known as the sine component while the horizontal component is known as the cosine component.

A vector component is the product of its length and the component angle.

Generally, F sinθ is the vertical component and F cosθ is the horizontal component,

Now, from the diagram the horizontal component of vector 'r' is

Nx= Ncosθ

and, the vertical component will be

Ny= -Nsinθ

this is in the opposite direction

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The factor of its area less than the initial area is 1/4

The given parameters can be represented as:

Second sheet = 1/2 * The first sheet

Assume the sheet is rectangular, the area of the sheet is calculated as:

Area = Length * Width

So, the area of the second sheet is

Second sheet = 1/2Length * 1/2Width

This gives

Second sheet = 1/4(Length * Width)

So, we have:

Second sheet = 1/4 * First sheet

Hence, the factor of its area less than the initial area is 1/4

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Check the picture below.

The set of inequalities that represents the constraints of the situation is y ≤ 2x, x + y ≥ 30 and a point (x, y) that is the feasible region is (10, 20)

The given parameters are:

Number of hours = at least 30 hours a week

This means that

x + y ≥ 30

Also, we have:

The number of hours Daniel works as a tutor (y) is at most twice the number he works as a teacher (x).

This means that

y ≤ 2x

Substitute y ≤ 2x in x + y ≥ 30

x + 2x ≥ 30

This gives

3x ≥ 30

Divide

x ≥ 10

Substitute x ≥ 10 in y ≤ 2x

y ≤ 2 x 10

Evaluate

y ≤ 20

Hence, the set of inequalities that represents the constraints of the situation is y ≤ 2x, x + y ≥ 30 and a point (x, y) that is the feasible region is (10, 20)

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Answer:

p) zero

q) 10,559.5

r) from $37,001 to $87,000

Step-by-step explanation:

p) zero

q) Tax = 3,572 + (58,500 - 37,000)(0.325)

= 3,572 + 6,987.5

= 10,559.5

r) from $37,001 to $87,000

Answer:

1. true

2. false

3. false

4. true

Step-by-step explanation:

Value of the given function f(x) = 5x +2 , g(x) = 8 -3x for the following condition:

a. g(f(-2)) =32

b. f(g(x)) =42 -15x

As given in the question,

Given function:

f(x) = 5x + 2

g(x) = 8 - 3x

Value of the function for the following condition:

a. g(f(-2))

f(x) = 5x + 2

⇒f(-2) = 5(-2) + 2

⇒f(-2) = -8

g(f(-2))= g(-8)

         = 8 - 3(-8)

         = 32

b. f(g(x)) = f(8-3x)

             = 5(8 -3x) + 2

             =42 -15x

Therefore, value of the given function f(x) = 5x +2 , g(x) = 8 -3x for the following condition:

a. g(f(-2)) =32

b. f(g(x)) =42 -15x

The complete question is :

Given function  f(x) = 5x + 2 and g(x) = 8 - 3x, find the following value.

a. Find g[f(-2)].

b. Find f(g(x)).

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The distance between two points [tex](x_{1}, y_{1} )[/tex] and [tex](x_{2} ,y_{2})[/tex] is given by

[tex]d = \sqrt{ (x_{2} -x_{1})^{2} +(y_{2} -y_{1})^{2} }[/tex]                   …(1)

Given points are:

C = (7,-4) = [tex](x_{1}, y_{1} )[/tex]

D = (-8,-5) = [tex](x_{2} ,y_{2})[/tex]

Substituting the values in equation (1), we get

[tex]CD = \sqrt{ (-8-7)^{2} +(-5-(-4))^{2} }[/tex]    

[tex]CD = \sqrt{ (-15)^{2} +(-1)^{2} }[/tex]

[tex]CD = \sqrt{{ 225} +1 }[/tex]

[tex]CD = \sqrt{{ 226 }[/tex]

[tex]CD = 15.03}[/tex]

After Rounding it to nearest tenth, we get

CD = 15 units

Hence, the distance between the points (7,-4) and (-8,-5) is 15 units.

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The measurements can be explained as low accuracy and high precision.

Accuracy is how close or far off a given set of measurements are to their true value.

Precision is how close or dispersed the measurements are to each other.

Given,

His height = 5 feet 3 inches

Friend measures you three times and gets these results =5 ft 10 in, 5 ft 9.5 in and 5 ft 10.5 in

Here, the measurements are closely dispersed but the measurements are far from actual measurement.

Hence, the measurements can be explained as low accuracy and high precision.

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The value of m and b of the linear equation are 4 and 19 respectively

The linear equation is represented as y = mx + b, contains the point (-4, 3) and is perpendicular to the line 5x + 20y = 9

Linear equation can be represented as follows:

In slope intercept form,

y = mx + b

where

Therefore, the linear equation y = mx + b contains the point (-4, 3) and is perpendicular to the line 5x + 20y = 9.

Perpendicular lines follows the following rules:

m₁ m₂ = -1

Therefore, let's find the slope of the second equation and use it to find the slope of the linear equation that passes through (-4, 3).

5x + 20y = 9

20y = -5x + 9

y = -1 / 4 x + 9 / 20

Hence,

- 1 / 4 m₂ = - 1

m₂ = 4

Therefore, let's find the equation since we have gotten the slope.

y = 4x + b

It's passing through (-4, 3)

3 = 4(-4) + b

3 = -16 + b

b = 3 + 16

b = 19

Therefore, the value of m and b of the linear equation are 4 and 19 respectively

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Answer:

Shapes S and D are congruent because they are both parallel to the line. Shapes M and S have the same area since they both cover 6 triangles.

Step-by-step explanation:

Answer:6.5m

Step-by-step explanation:

Answer:

(-13, -10)

Step-by-step explanation:

Your original point is (-17, -13)  The instruct tell you to move the point 4 units to the right and down 7 units.

-17 + 4 = -13

-3 - 7 = -10

Answer is 7/3

Step-by-step explanation:

Answer:

[tex]\frac{23}{6}[/tex] or 3.833333...

Hope this helps

Step-by-step explanation:

[tex]4+(-\frac{1}{2} *\frac{1}{3} )\\\\4+ (-\frac{1}{6} )\\\\4-\frac{1}{6} \\\\\frac{24}{6} -\frac{1}{6} \\\\\frac{23}{6}[/tex]

In the given triangle , ∠n = 50° and ∠m = 35°

In the geometry, angle is defined as the geometry formed by the multiple rays. Or we can also say that the angle is a figure formed by two rays with having same initial point. The rays are also known as the sides of the angle. A angle can have two rays.

Some common terms related to angles :

In the given question mark the triangle as ABC and the mid line as point D.

that means,

∠A = ∠n

∠B = ∠m

and, in ΔABC

∠C = 60 + 35 =95

now, as ΔCDB is isosceles triangle therefore,

∠m = ∠C = 35°

Also, as sum of all angle of triangle is 180

Therefore, ∠A + ∠B + ∠C = 180

=> ∠n + ∠m + 95 = 180

=> ∠n + 35 + 95 = 180

=> ∠n = 180- 130

=>∠n = 50

Hence in the triangle given , ∠n = 50 and ∠m = 35

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The three arithmetic means between 12 and 44 are -

20, 26, 36.

We have two numbers 12 and 44.

We have to determine the three arithmetic mean between these numbers.

Assume that x, y and z are in AP, then -

y - x = z - y

2y = x + z

y = (x + z)/2

Here -  y is called the arithmetic mean of x and z.

According to the question -

Assume that the three arithmetic means between the two numbers are -

12, a, b, c, 44

Then -

12 , 12 + d, 12 + 2d, 12 + 3d, 44

will be an AP with common difference 'd'.

Now, we have -

a[5] = 44

Using the formula for nth term of an AP, we get -

a + (n - 1)d = 44

12 + 4d = 44

4d = 32

d = 8

Therefore, the three arithmetic means are -

12 + 8 = 20

12 + 2 x 8 = 26

12 + 3 x 8 = 36

Hence, the three arithmetic means between 12 and 44 are -

20, 26, 36

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The required cost of the punch is $4 per gallon.

Given that,
Anika spent $38 on 9.5 gallons of fruit punch.
To determine what is the cost per gallon.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Total volume purchased = 9.5 gallons
Total cost = $38
Now,
The ratio of the total cost of punch to the volume of fruit punch purchases the total cost will give as the cost per gallon. So,
cost per gallon = 38 / 9.5
                      = $4 per gallon

Thus, the required cost of the punch is $4 per gallon.

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Answer:

3.8439141e+15

Answer:33.1

Step-by-step explanation: 3.61 × 10-3 =33.1

Step-by-step explanation:

429 × 10⁷

hopefully it will help you

When the signs of the integers are the same, 1) add the integers and copy the 2) same sign. When the signs are 3) different, subtract them and use the sign of the number with the greater 4) absolute value. If we add two same numbers with different signs, then the answer is equal to 5) zero . The sum of any two negative integers is always a 6. )negative integer. The sum of any two positive integers is a 7) positive integer.

Integers are a subset of real numbers that contains all rational numbers except decimals or fractions

When the signs are the same, add the integers and copy the same sign.

Examples: (+2) + (+8) = +10

                   -1 + (-4 )= -5

When the signs are different, we subtract and use the sign of the number with the bigger absolute value.

Examples; +12 + (-4) = +8

                  -12 + (+4) = -8

If we add two same numbers with different sign then the answer is equal to zero.

Examples: +5+ (-5) = 0

                 -1 + +1 = 0

The sum of any two negative integers is a always a negative integer.

Examples: -3 + (-5) = -8

                 -16 + (-10) = -26

The sum of any two positive integers is a always a positive integer.

Examples: +12 + +56 = +68

               +35 + + 15= +50

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The cost of 11 cans of dog food will be equal to $10.12.

What is unitary method ?

The unitary method is a method in which , you first determine the value of a single unit before determining the value of the required quantity of units.

It is given that the cost of 20 cans of dog food at store B is $18.40.

We need to find cost of 1 can of dog food and that can be calculated by dividing the cost of cans of dog food by total no. of cans.

i.e.,

Cost of 1 can of dog food = $ 18.40 ÷ 20

So ,

The cost of 1 can of dog food will be :

= $0.92

Now , the cost of 11 cans of dog of food will be calculated by multiplying cost of 1 can of food to 11 cans of dog food which will be :

= 11 × $ 0.92

= $10.12

Therefore , the cost of 11 cans of dog food will be equal to $10.12 .

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Answer:  is #b

Step-by-step explanation:

Answer:

Did you mean 138/8?

If so, 17.25 is correct.

Answer:

hope it helps you

Step-by-step explanation:

thankss :) if its wrong let me know

The measure of angle JKN is 108 degrees

From the figure, we have the following parameters

Angle 1 equals Angle 2

Where

Angle 1 = Angle JKP = 3r + 12

Angle 2 = Angle PKN = 4r - 2

Recall that

Angle 1 equals Angle 2

So, we have

3r + 12 = 4r - 2

Evaluate the like terms

r = 14

Substitute r = 14 in Angle 1 = Angle JKP = 3r + 12 and Angle 2 = Angle PKN = 4r - 2

Angle 1 = Angle JKP = 3 * 14 + 12 = 54

Angle 2 = Angle PKN = 4 * 14 - 2 = 54

The measure of angle JKN is calculated as

Angle JKN = Angle 1 + Angle 2

So, we have

Angle JKN = 54 + 54

Evaluate

Angle JKN = 108

Hence, the measure of angle JKN is 108 degrees

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Answer:

d=1

Step-by-step explanation:

First let's simplify the first equation, 0.5(7d+4) by applying the distributive property

0.5(7d+4)

(0.5 x 7d) + (0.5 x 4)

3.5d+2

Now let's move all terms containing d to the left side of the equation
So add 1.5d to the left

3.5d+2 = 7-1.5d

3.5d+2+1.5d=7

5d+2=7

Move all terms not containing d to the right side of the equation

5d+2=7

5d=7 -2

5d=5

Finally, divide each term by 5 to simplify

5d/5 = 5/5

d=1

If the length of a rectangle is 3 more than twice the width and the perimeter is 36 inches, then the area of the rectangle is equal to 65 in².

The length and width of the rectangle can be determined by using the formula for the perimeter of the rectangle,

P = ( L + W ) × 2

P = 2L + 2W

Here L is equal to the length of the rectangle and W is the width of the rectangle.

As the length is 3 more than twice the width, we can write the length of the rectangle as,

L = 3 + 2W

Putting L = 3 + 2W in the equation of perimeter,

P = 2L + 2W

As P = 36

36 = 2( 3 + 2W) + 2W

36 = 6 + 4W + 2W

6W = 30

W = 30 ÷ 6

W = 5

The length of the rectangle can be found by putting W = 5 in the equation,

L = 3 + 2W

L = 3 + 2(5)

L= 3 + 10

L = 13

Therefore, the length and width of the rectangle are equal to 13 and 5 respectively

As, area = width × length

area = 5 × 13

area = 65

Hence, the area of the rectangle is equal to 65 square inches.

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Answer:

n= 26.5

Step-by-step explanation:

Comment

You need some sort of formula for this question. But you more or less have to invent it.

Formula

Temperature midnight = noon - temperature drop

Givens

temperature drop = 28.4

temperature midnight = -1.9

Temperature noon = x

Solution

-1.9 = x - 28.4                       Add 28.4 to both sides

-1.9 + 28.4 = x-28.4+28.4    Combine

Answer

26.5 = x