point M(6.8) was rotated counterclockwise to M'(-8,6). Describe the degrees of the rotation and write an algebraic rule to represent the rotation

If 14 inches of wire cost 42 cents, with 21 cents can be bought  7 inch of wire

Information about the problem:

Calculating how much 1 inch cost, we have:

1 inch cost= Inches bought cost  / Inches bought

1 inch cost= 42 cents / 14 inches

1 inch cost= 3 cent/inch

Calculating how much can be bought with 21 cents:

Inches of wire= Amount / 1 inch cost

Inches of wire= 21 cent / 3 cent/inch

Inches of wire= 7 inch

Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.

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Answer: XYW = 32, WYZ = 85

Step-by-step explanation:

We are looking for what x is, which we can find with the formula:

117 = (6x+44) + (-10x+65)

117 = -4x + 109

8 = -4x

x = -2

We can verify this is correct by plugging it in and seeing if they add up to 117.

6x + 44 (XYW)

= 6(-2) + 44

= -12 + 44

= 32

-10x + 65 (WYZ)

= -10(-2) + 65

= 20 + 65

= 85

32 + 85 = 117

Answer:

59. a₁ = 4

60. a₁ = 10

Step-by-step explanation:

The general equation for the sum of the first n terms Sₙ of a geometric sequence with common ratio r and first term a₁ is

[tex]S_n = a_1 \dfrac{1-r^n}{1-r}[/tex]    

Problem 59

Here we are given
[tex]S_n = \dfrac{31}{4}\\\\r = \dfrac{1}{2}[/tex]

So we can plug these values into the above equation and get [tex]a_1[/tex]

Let's first compute [tex]1 - r^n[/tex]
[tex]1 - r^n = 1 - \left(\dfrac{1}{2}\right)^5\\\\\left(\dfrac{1}{2}\right)^5 = \dfrac{1}{32}\\\\1 - r^n = 1 - \left(\dfrac{1}{2}\right)^5 = 1-\dfrac{1}{32} = \dfrac{32}{32}-\dfrac{1}{32} = \dfrac{31}{32}[/tex]

[tex]1- r = 1 - \dfrac{1}{2} = \dfrac{1}{2}[/tex]

So
[tex]\dfrac{1-r^n}{1-r} = \dfrac{31}{32} \div \dfrac{1}{2} = \dfrac{31}{32} \times \dfrac{2}{1} = \dfrac{31}{16}[/tex]

Substituting this value into [tex]S_n = a_1 \dfrac{1-r^n}{1-r}[/tex]  we get

[tex]\dfrac{31}{4} = a_1\dfrac{31}{16}[/tex]

Multiplying both sides by [tex]\dfrac{16}{31}[/tex]
[tex]\dfrac{31}{4} \times\dfrac{16}{31} = a_1\dfrac{31}{16} \times\dfrac{16}{31}\\\\4 = a_1 \textrm{or alternatively }\\ \\\boxed{a_1 = 4}[/tex]

Problem 60

Use the same technique as above

[tex]S_8 = 2550, r = 2\\\\S_8 = a_1 \times \dfrac{1-r^8}{1-r}\\\\\\2550 = a_1 \times \dfrac{1-2^8}{1-2}\\\\2550 = a_1 \times \dfrac{1 - 256}{1-2}\\\\2550 = a_1 \times \dfrac{-255}{-1}\\\\2550 = a_1 \times255\\\\== > a_1 = \dfrac{2550}{255}\\\\\boxed{a_1=10}[/tex]

Answer:

  37/50

Step-by-step explanation:

You want the fraction of integers in the range [1, 100] that are divisible by 2, 3, or 5.

Attached is a Venn diagram showing how the divisibility of numbers from 1 to 100 stacks up. Circle A includes all 50 numbers divisible by 2; Circle B counts all 33 numbers divisible by 3; and Circle C counts the 20 numbers divisible by 5.

Where the circles overlap, there are counts of the numbers divisible by the relevant combination of factors. For example, there are 3 numbers divisible by 2, 3, and 5. (They are 30, 60, 90.)

In all, there are 74 numbers in the range 1–100 that are divisible by 2, 3, or 5.

The probability that a card chosen at random will have a number divisible by 2, 3, or 5 is 74/100 = 37/50.

  P( 2, 3, or 5 divides N) = 37/50.

__

Additional comment

Roughly, the number of numbers in range [A, B] divisible by n is (B -A)/n. This is how we arrived at the counts shown in the attachment. For example, There are 100/(2·5) = 10 numbers divisible by both 2 and 5. Of those, there are 10/3 = 3 divisible also by 3. So, the number 3 is found in the area ABC, and the number 10-3=7 is found in the area AB'C.

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The quotient of the given expression 2 3/4 and 7/8 is 22/7

Quotient refers to a number resulting from the division of one number by another. 12 ÷ 2 = 6 the quotient is 6

Dividend is number or expression that is to be divided by another. 12 ÷ 2 = 6 the dividend is 12

Divisor is the number or expression that is to be divided by another. 12 ÷ 2 = 6 the divisor is 2

Quotient of 2 3/4 and 7/8?

= 2 3/4 ÷ 7/8

= 11/4 ÷ 7/8

= 11/4 × 8/7

= (11 × 8) / (4 × 7)

= 88/28

= 22/7

Therefore, the quotient of the given expression 2 3/4 and 7/8 is 22/7

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By unitary method, we get that the total cost of mixture per pound = 50 cents.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Given:

Cost of 1 pound sunflower seeds = 32 cents.

Cost of 1 pound cracked corn = 18 cents.

Available sunflower seeds = 10lb = 10 pounds

Available cracked corn = 16lb = 16 pounds

To find: Cost of the mixture per pound

Finding:

By unitary method, Cost of 1 pound sunflower seeds = 32 cents.

Cost of 10 pounds sunflower seeds = 32(10) = 320 cents.

Again, by unitary method,

Cost of 1 pound cracked corn = 18 cents.

Cost of 16 pound cracked corn

= 18(16) cents

= 288 cents.

Therefore, total cost of mixture per pound

= 32 + 18 = 50 cents.

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Vertical angles or contrary angles are the statement that Terra's proof is still absent. The angles formed opposite to each other when two lines cross each other are equal.

Terra describes the parallelogram nature of the diagram. Because they are vertical or opposite angles, these angles are equal.

The angles formed opposite to each other when two lines cross each other are equal. As a result, we have discovered that either vertical angles or opposite angles make up Terra's proof.

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The image of the points after they are reflected across the x-axis are J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)

From the question, we have the following parameters that can be used in our computation:

J(1, 9), K(7, 4), L(8, 13), M(-2, 1)

Also from the question we have the transformation to be

Transformation: reflection across the x-axis

The rule of the reflection across the x-axis is represented as

(x, y) = (x, -y)

Substitute the known values J(1, 9), K(7, 4), L(8, 13), M(-2, 1) in the above equation, so, we have the following representation

J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)

Hence, the image of the points are J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)

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If the main courses at a restaurant all contain rice or onion and of the 23 choices, 17 contain onion and 14 contain rice, then the number of dishes containing both rice and onion will be equal to 8.

The number of dishes that contain both rice and onion at the restaurant can be calculated by using an algebraic expression.

An algebraic expression can be defined as an equation in which both numerals and letters are present.

An algebraic expression for this problem can be given as,

(14 - x) + x + (17 - x) = 23

Here x is equal to the number of dishes containing both rice and onion.

14 + 17 - x + x - x = 23

31 - x = 23

x = 31 - 23

x = 8

Hence, the number of dishes that contain both rice and onion is calculated to be 8.

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The numbers from least to greatest are arranged as -

-3.2, -0.32, 3/2, 2

Given is the sequence of numbers as -

-0.32, - 3.2, 2, 3/2​

The given sequence of numbers is -

-0.32, -3.2, 2, 3/2​

The numbers from least to greatest are -

-3.2, -0.32, 3/2, 2

Therefore, the numbers from least to greatest are arranged as -

-3.2, -0.32, 3/2, 2.

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The probability that a randomly chosen fitness club member signs up for a free running session is 0.4.

Let total s members sign up for the weightlifting session.

So, the total members for the running session is 2x.

And the total members for the swimming session be 2x.

Also here it is given that, thirty of the fitness center members sign up for a free session.

⇒ x + 2x + 2x = 30

⇒ 5x = 30

⇒ x = 30/5

⇒ x = 6

Thereofre, the probability that a randomly chosen fitness club member signs up for a free running session

= total number of members in running session/ number of members sign up for a free session

= 12/30

= 0.4

Hence, the probability that a randomly chosen fitness club member signs up for a free running session is 0.4.

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The relation that is represented in the table is a function. YES.

For every relation that represents a function, the each of the x-value (domain element/input) corresponds to exactly one y-value (range element/output).

In the table given showing a relation, every single x-value (input) has exactly only one possible y-value (output) that it is assigned to. The x-values, 1, -1, 3, and 5, each have a specific y-value they each correspond to.

Thus, based on the definition of a function, the relation that is represented in the table is a function. YES.

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Answer:

[tex]\boxed {y = \dfrac{1}{3}x - \dfrac{7}{3}}[/tex]

Step-by-step explanation:

If we have a line y = mx + b where m is the slope and be is the y-intercept then a line perpendicular to this line will have slope -(1/m)

So the slope of the line perpendicular to y = -3x + 5 will be [tex]-\dfrac{1}{3}[/tex] = + 1/3 = 1/3

So the perpendicular line equation is

y = (1/3)x + b where b is the y intercept of this line

Since it passes through the point x = 4, y = -1 we plug in these values for x and y and solve for b

We get
[tex]-1=\dfrac{1}{3}\cdot \:4+b[/tex]

Switch sides
[tex]\dfrac{1}{3}\cdot \:4+b=-1[/tex]

[tex]\dfrac{4}{3}+b=-1[/tex]

Subtract  [tex]\dfrac{4}{3}[/tex]  from both sides

[tex]b = -1 - \dfrac{4}{3} = -\dfrac{3}{3} -\dfrac{4}{3} = -\dfrac{7}{3}[/tex]

So the equation of the perpendicular line is
[tex]\boxed {y = \dfrac{1}{3}x - \dfrac{7}{3}}[/tex]

The vector is -2i+7j and the two parallel vectors with length 4 is u=-8/√53i+28/√53j and u=8/√53i-28/√53j respectively

The points are p(-4,-2) and q(3,-4)

The vector qp = vector p -vector q

qp= <-4+2,3+4>

qp=-2i+7j

|QP|=√(-2)^2+(7)^2

|QP|=√4+49

|QP|=√53

The unit vector in direction of QP is 1/√53(-2i+7j)

To get a unit vector parallel in direction of QP, multiply by 4

u=-8/√53i+28/√53j

Multiplying by -4 to get another parallel vector of length 4, we get

u=8/√53i-28/√53j

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Answer:

6,720

Step-by-step explanation:

Answer:

31 square miles

Step-by-step explanation:

We basically have three shapes here.  

The top rectangle:

A= l x w = 7 x 2 = 14

The middle rectangle:

A= l x w = 4 x 2 = 8

The triangle

A = 1/2 x b x h = (3 x 6)/2 = 18/2 = 9

Add the area of all three: 14 + 8 +9 = 31

The equation of the linear function represented by the table below in slope-intercept form is y = 7x + 4

The equation of a line in point-slope form is expressed as y = mx + b

where

m is the slope

b is the intercept

Using the coordinate points (0,4) and (1, 11)

Slope = 11-4/1-0

slope = 7

The y-intercept is at the point (0,4)

Determine the equation

y = mx + b

y = 7x + 4

Hence the equation of the linear function represented by the table below in slope-intercept form is y = 7x + 4

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5p/6  an expression for the gradient of the line perpendicular to the line segment joining (3p, 6) to (-2p, 10).

Use the slope formula to find the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or the change in the y values over the change in the x values. The coordinates of the first point represent x1 and y1

gradient of the line segment joining (3p, 6) to (-2p, 10)

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

m =( 10 -4)/ ( -2p - 3p)

m= 6/ (-5p)

m= -6/5p

we know that

Gradient of a line perpendicular to a line with a gradient of m = -1/m

Gradient of a line perpendicular to a line with a gradient of -6/5p = 5p/6

Hence 5p/6  an expression for the gradient of the line perpendicular to the line segment joining (3p, 6) to (-2p, 10).

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The slope of the line passes through the points (6,10) and (6,−2) is undefined.

Here,

The points are (6,10) and (6,−2).

We have to find the slope of the line passes through the points (6,10) and (6,−2).

What is slope of line?

The slope of the line passes through the points (x₁, y₁) and (x₂, y₂) is;

[tex]m = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

Now,

The points are (6,10) and (6,−2).

Hence, The slope of the line passes through the points (6,10) and (6,−2) is;

[tex]m = \frac{-2 -10 }{6-6 }= \frac{-12}{0}[/tex]

Which in undefined.

Therefore, The slope of the line passes through the points (6,10) and (6,−2) is undefined.

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the slope of the line that passes through the points (6,10) and (6,−2) is undefined.

Step-by-step explanation:

False, parallel lines have not the same slope whereas perpendicular lines have because of this. Perpendicular lines have equal slopes.

The steepness and direction of a line, read from left to right, is referred to as its slope. Finding the ratio of will allow you to determine the slope or gradient. Between two places on the line, either by using the rise (vertical change) to the run (horizontal change). a slope-intercept version of a linear equation (y = mx + b).

based on the facts provided;

Two parallel lines' slopes are always their negative reciprocal of one another. The other has a slope of -3/2 if one has a slope of 2/3.

Therefore, perpendicular lines do not have equal slopes.

The sentence is

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Answer:

x = 3

Step-by-step explanation:

Use the distributive property to multiply 4 by 5x+3. Subtract 14x from both sides. Combine 20x and −14x to get 6x. Subtract 12 from both sides. Subtract 12 from 30 to get 18. Divide both sides by 6. Divide 18 by 6 to get 3.

Answer:

20x+12=14x+30

6x=18

x=3

Step-by-step explanation:

First, apply the distributive property:

4(5x+3) = 4 · 5x + 4 · 3 = 20x+12

Now, we have this equation

20x+12=14x+30

We need to group the elements now.

So, to bring all the elements with an "x," we subtract 14x from both sides.

20x-14x+12=14x+30-14x

We have this now

6x+12=30

Now, let's subtract 12 on both sides

6x+12-12=30-12

6x=18

Divide both sides by 6

x=3

2) BA and CD are parallel (segments that are collinear with parallel segments are parallel)

3) CDAB is a parallelogram (a quadrilateral with two pairs of parallel sides is a parallelogram)

4) ∠B is congruent to ∠D (opposite angles of a parallelogram are congruent)

5) m∠B = m∠D (congruent angles)

6) m∠D=115° (transitive property)

7) m∠EDA=65° (linear pair)

8) m∠EAD=65° (base angle of an isosceles triangle)

9) m∠E = 50° (sum of angles in a triangle)

Answer:

15, 1

Step-by-step explanation:

I'm assuming the answer should be limited to only positive integers. Either way, looking at 16 and 14, they are 2 apart and their average is 15. Since 15 is one from 16 and 14 both, the answer is 15 and 1.

15-1 = 14

15+1 = 16

Answer:

6.0

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.00

Based on the prices of the homes in the neighborhood, the median home price is A) 166

What is the median home price?

L is for a home below $110 and H is for a home above $190. The distribution of home prices can therefore be shown as:
190, 120, 166, 173, 190, 190, 190, 123, 127, 110

In an ordered list, this becomes:

= 110, 120, 123, 127, 166, 173, 190, 190, 190

The median is the price in the middle and we can see this price is $166

In conclusion, the median home price is $166.

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Answer:

1.5 or 1 ½ pages per min

Step-by-step explanation:

7.5/5=1.5

She reads 1 ½ pages per min

Answer: 1.5 pages per minute

Step-by-step explanation:

Divide the total number of pages she read by 5, the amount of time it took her. So it should look like this: 7.5/5

The answer is 1.5 pages per minute.

Answer 1120.5

Step-by-step explanation:

Step-by-step explanation:

linear

8+2x=18

2x=10

x=5

Answer:

What's the wildflowers trails current length so I can help

The probability of getting a number 6 as the first card and a queen as the second card is 4/663.

Probability is mathematically defined as the ratio of the number of outcomes of a particular event or occurrence to the total number of outcomes.

For a standard deck, there are 52 total outcomes since there are 52 cards. A standard deck is divided into four suits - hearts, clubs, spades, and diamonds - with 13 cards each. Each suit has nine numbered cards from 2 to 10, three face cards (king, queen, and jack), and an ace.

The probability of having a numbered 6 card is 4/52. The probability is the same for getting a queen. Although, the probability of getting 6 as the first card and the queen as the second is different. This kind of probability requires the multiplication rule.

First card probability = 4/52

Second card probability = 4/51

The total number of outcomes for the second card is reduced since the first card is not replaced.

Probability (6 then queen) = (4/52)(4/51)

Probability (6 then queen) = 4/663

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