marcy drew a scale drawing of a petting zoo. the goat pen, which is 9 meters wide in real life, is 15 centimeters wide in the drawing. what is the scale of the drawing?

By using algebra properties and given that the linear equation 4 · x + 2 · y = 20, the value of (8 · x + 4 · y) / 5 is equal to 8.

Herein we find a linear equation equal to a given number and we are asked to find a number associated with a modified form of the formula, this can be done by using algebra properties. The complete procedure is shown below:

4 · x + 2 · y = 20                               Given

2 · (4 · x + 2 · y) = 20 · 2                  Compatibility with multiplication

8 · x + 4 · y = 40                               Associative and distributive properties

(1 / 5) · (8 · x + 4 · y) = (1 / 5) · 40      Compatibility with multiplication

(8 · x + 4 · y) / 5 = 8                          Multiplication of fractions / Result

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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:21/2

Step-by-step explanation:

Answer:

-7/6

Step-by-step explanation:

If the temperature changes by -7/18 degrees, that shows us that it will continue to decrease, so we can assume the answer will be negative, which means we can get rid of the answers 21/6 and 7/6. If you add and multiply -7 by 3, you'll get -21, which would be -21/18. Then you would simply the answer, giving you -7/6.

Hope this helps!!! :)

Answer:

your question is did you mean why 2n is 2n 2 serve that this queston with not involved

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 2021st term of the sequence is (- n - 2017).

Given,

A sequence is constructed by listing all the possible numbers that contain no digit greater than 3 in ascending order.

We need to find out what is the 2021st term of this sequence.

An arithmetic sequence is a sequence where the difference between the consecutive terms is the same.

Example: 2, 4, 6, 8, 10

4 - 2 = 2

6 - 4 = 2

8 - 6 = 2

The nth term of an arithmetic sequence is given by:

= a + ( n - 1 ) d

Where a = the first term

d = common difference

Let the sequence that contains no digit less than 3 in ascending order be:

3 - n, 3 - (n + 1), 3 - (n+2), 3 - (n+3), 3 - (n+4),......

Where n = any real number from 1.

We see that the common difference is -1.

3 - (n+1) - (3 - n)

= 3 - n - 1 - 3 + n

= -1

3 - (n+2) - [3-(n+1)]

= 3 - n - 2 - 3 + n + 1

= -1

Find the 2021st term.

We have,

a = 3 - n

d = -1

n = 2021

= a + ( n - 1 ) d

= (3 - n) + ( 2021 - 1 ) (-1)

= 3 - n - 2020

= - n - 2017

Thus the 2021st term of the sequence is - n - 2017.

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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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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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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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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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Answer:

Step-by-step explanation:

I hope this answer help you

Answer:

h = 16.0 cm

Step-by-step explanation:

Note: I am assuming that the surface area of 258 is the total surface area which includes the Lateral Area (L) and Base Area(B)

Total Surface Area of a right cone

= Lateral Area(L) + Base Area(B)

All numbers in intermediate calculations are rounded to tenth of centimeter i.e. 1 decimal point

Base Area is the area of the circle with radius 4 = [tex]\displaystyle \pi \cdot16 = 50.3[/tex] cm²
Total Area = 258 cm²

So Lateral Area = 258 - 50.3 = 207.7 cm²

Lateral Area is given by the formula
[tex]\displaystyle L = \pi r s \textrm{ where s is the slant height }[/tex]

So we get

[tex]\displaystyle \rm pi \cdot 4 \cdot s = 207.7\\\\\textrm {This gives } s = \dfrac{207.7}{4\pi} = 16.5\\\\[/tex] cm

Slant height is given by the formula:
[tex]s = \sqrt{r^2 + h^2} \textrm{ where r is the radius and h the height}[/tex]
Plugging in values we get
[tex]16.5 = \sqrt{4^2 + h^2} = \sqrt{16 + h^2}[/tex]

Square both sides
[tex]16.5^2 = 16 + h^2[/tex]

==> [tex]h^2 = 16.5^2 - 16 = 256.25\\\\h = \sqrt{256.25} = 16.003 = 16.0[/tex]  rounded to 1 decimal place

So final answers is h = 16 cm

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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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 value of x is 6° and value of z is 67°

We know that when two lines intersect then the vertically opposite angles are equal.

So according to the given figure

      (11x + 47)° = (6x + 77)°

Solving the above equation for x we get

        11x° + 47° = 6x° + 77°

         5x° = 30°

          x = 6°

Thus the value of x is 6°

Also note that the linear pair of angles make 180°. That is sum of the two angle is 180°. As we can see from the figure ∠z  and (6x + 77)° make linear pair of angles, therefore there sum will be equal to 180°.

Thus,   ∠z  + (6x + 77)° = 180°

             ∠z + (6*6 + 77)° = 180°

            ∠z + 113° = 180°

             ∠z = 67°

Hence the value of z is 67°

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Answer:

8

Step-by-step explanation:

the perimeter is the sum of the 3 sides of the triangle.

Given perimeter = 26 , then

2a - 3 + 2a + 3a + 1 = 26 , that is

7a - 2 = 26 ( add 2 to both sides )

7a = 28 ( divide both sides by 7 )

a = 4

then

shortest side = 2a - 3 = 2(4) - 3 = 8 - 3 = 5

longest side = 3a + 1 = 3(4) + 1 = 12 + 1 = 13

the difference between the 2 sides is 13 - 5 = 8

the longer side is 8 units bigger than the shortest side

Answer:

6.0

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.00

Answer:

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

Side length of Rhombus ABCD is  8+2√2 unit

EFGH is a rectangle :

We know that ,

E, F , G , H are midpoints of AB, BC, CD , DA respectively

Since ABCD is a rhombus

AB = BC = CD = DA

AB ll CD  and BC ll DA

since,  E, F , G , H are midpoints of AB, BC, CD , DA respectively

from the figure below we can say that ,

1) AB ll CD ll FH and AB= CD = FH

2) BC ll DA ll GE and BC = DA = GE

Using mid point theorem we can say that ,

GH = EF = 1/2 AC and FG= EH = 1/2 BD

Since for the figure EFGH opposite sides are equal and and parallel , and the diagonals are equal in length we can say that EFGH is a rectangle.

Perimeter of a rectangle = 2(a+b) = 2( GH + EH ) = 2 (EF + GF) = 2 ( 1/2 AC + 1/2 BD )

= 2 x 1/2 ( AC + BD ) = 16

⇒ AC + BD = 16  (1)

now area of a rectangle is given by

A = ab = GH x EH = EF x GF = 1/2 AC x 1/2 BD = 1/4 (AC x BD) = 14

⇒AC x BD = 14 x 4 = 56

from equation (1)

AC ( 16 - AC) = 56

= 16 AC - AC ^2 = 56

⇒ AC^2 - 16 AC + 56 = 0

AC = 8 +/- 2√2

BD = ( 16 - AC) = 8 +/- 2 √2  = side length of rhombus ABCD

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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

The area of the third square is 24 units square.

The squares forms a right angle triangle.

The side length of a square are equal.

Therefore, the side length of each square contribute to the three sides of the right triangle formed. The unknown length of the right triangle is the hypotenuse side of the triangle. That unknown length is the side length of the square.

area of a square = l²

where

area of the first square = l²

√8 = l

l = 2√2 units

area of the second square = l²

√16 = l

l = 4 units

The length of the squares are the legs and hypotenuse of the right triangle formed.

using Pythagoras theorem,

Therefore,

(2√2)² + 4² = c²

16 + 8 = c²

c = √24

c = 2√6 units

area of the third square = (2√6)² = 24 unit²

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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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Step-by-step explanation:

linear

8+2x=18

2x=10

x=5

Answer 1120.5

Step-by-step explanation:

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.

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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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:

The hours travelled on the highway is 1.3 hours.

The first step is to determine the distance Sam travelled on the city road. The formula that would be used is the average speed formula. The average speed is the ratio of total distance travelled and the total time travelled.

Average speed = distance /time

average speed x time = distance

Distance = 35 x 1.5 = 52.50 miles

The second step is to determine the distance travelled on the highway.

Distance travelled on the high way = 140 - 52.50 = 87.50 miles

Now, determine the total hours travelled:

Hours travelled = distance / average speed

87.50 / 65 = 1.3 hours

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Answer: Sam traveled 1.3 hours.

Step-by-step explanation:

Answer:

1870

Step-by-step explanation:

Answer:

c) 1,870

Step-by-step explanation:

374 multiplied 5 times, or 374 in a group of 5, equals 1,870.

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