The population of a town increased by 15% in 2016, and decreased by 5% in 2017. If the population of the town was 60,000 in the beginning of 2016, then what was it at the end of 2017?

Answer:

c) 82

Step-by-step explanation:

<ABE and <BEC are supplementary because they form a line.

<ABE + <BEC = 180

116+ x = 180

Subtract 116 from each side.

116-116+x = 180 -116

x = 64

The angles in triangle ECB add to 180 because it is a triangle

<BEC + <ECB + <CBE = 180

x + 34+y = 180

64 + 34+ y = 180

98 + y = 180

Subtract 98 from each side.

98-98+y = 180-98

y = 82

Answer:

The correct answer is C. f(x) = x - 7

Step-by-step explanation:

In order to find this, you simply need to know that vertical shifts can be added on to the end of parent equations as constants. Since this is a downward shift, we use a negative number.

Brenda will earn $18.75 in interest after 18 months.

To calculate the interest Brenda will earn after 18 months, we can use the simple interest formula:

Principal x Rate x Time = Interest

According to the question, Brenda deposited $500 in a savings account with a simple interest rate of 2.5% per year. Since the time period given is 18 months, we need to convert it to years. 18 months is equivalent to 1.5 years.

Therefore, the interest Brenda will earn after 18 months can be calculated as:

$500 x 0.025 x 1.5 = $18.75

Brenda will earn $18.75 in interest.

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Answer:

168 Km

Step-by-step explanation:

divide 132 Km by 11 to find distance travelled with 1 litre and then multiply this by 14 for distance travelled with 14 litres

= [tex]\frac{132}{11}[/tex] × 14 = 168 Km

Answer:

Correct choice is C

Step-by-step explanation:

Points A and B have coordinates (1,-2) and (4,3), respectively.

1. Rotation counterclockwise of 90° about the origin has a rule:

(x,y)→(-y,x).

Then the image of point A is point A'(2,1) and the image of point B is point B'(-3,4).

2. Refection about the x-axis has a rule:

(x,y)→(x,-y).

Then the image of point A' is point A''(2,-1) and the image of point B' is point B''(-3,-4).

3. Rotation counterclockwise of 270° about the origin has a rule:

(x,y)→(y,-x).

Then the image of point A'' is point A'''(-1,-2) and the image of point B'' is point B'''(-4,3).

4.  Refection about the y-axis has a rule:

(x,y)→(-x,y).

Then the image of point A''' is point A(1,-2) and the image of point B''' is point B(4,3).

The required number of dinosaurs that each of them gets is 39 dinosaurs.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let the number of dinosaurs be x that is distributed among Yolanda and her 3 brothers,
Total persons = 1 + 3 = 4
Total dinosaurs = 156
Each of them gets,
x = 156/4
x = 39 dinosaurs.

Thus, the required number of dinosaurs that each of them gets is 39  dinosaurs.

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Answer:

[tex]6\frac{2}{3}[/tex] ounces of mixed nuts will be in each bag.

Step-by-step explanation:

unit rate is defined as the rates are expressed as a quantity of 1, such as 3 feet per second or 6 miles per hour, they are called unit rates.

Given the statement: Candy buys 20 ounces of mixed nuts. She puts an equal amount of ounces in each of 3 bags.

Total number of mixed nuts Candy buys = 20 ounces.

As she puts an equal amount of ounces in each of  the 3 bags.

Unit rate per bag = [tex]\frac{20}{3} = 6\frac{2}{3}[/tex] ounces.

therefore, [tex]6\frac{2}{3}[/tex] ounces of mixed nuts will be in each bag.

Answer:

[tex]m\angle N=m\angle R=30^{\circ}[/tex]

Step-by-step explanation:

We are given that

[tex]\triangle RST=\triangle NPQ[/tex]

[tex]m\angle R=-7x+9,m\angle N=-10x[/tex]

We have to find the measure of angle R and measure of angle N.

When two triangles are equal then their angles are equal

Therefore, [tex]m\angle R=m\angle N[/tex]

[tex]-7x+9=-10x[/tex]

[tex]-7x+10x=-9[/tex]

By subtraction property of equality

[tex]3x=-9[/tex]

By combine like terms

[tex]x=\frac{-9}{3}=-3[/tex]

By division property of equality

Substitute x=-3 then we get

[tex]m\angle R=-7(-3)+9=21+9=30^{\circ}[/tex]

[tex]m\angle N=m\angle R=30^{\circ}[/tex]

Answer:

30

Step-by-step explanation:

Answer:

Step-by-step explanation:

The point is somewhere on the road. From that point, two poles can be seen at different angles of elevation. One is 30 degrees, and another is 60 degrees.

Call the height of the poles y and the point on the road as x meters away from the base of 60 degree angle to the base pole

(100 - x) * tan(30) = x*tan(60)

The distance to the other pole = 100 - 25 = 75

[tex]\( -3 d^8(-4 d^{-14}) \)[/tex] simplifies to [tex]\(12 d^{-6}\)[/tex].

To simplify the expression [tex]\( -3 d^8(-4 d^{-14}) \)[/tex], you can follow these steps:

1. Distribute the factor [tex]\(-3\)[/tex] to both terms inside the parentheses.

2. Combine the exponents with the same base [tex](\(d\))[/tex].

Let's work through it step by step:

[tex]\[ -3 d^8(-4 d^{-14}) \][/tex]

1. Distribute [tex]\(-3\)[/tex] to both terms inside the parentheses:

[tex]\[ (-3) \cdot d^8 \cdot (-4) \cdot d^{-14} \][/tex]

[tex]\[ = 12 d^8 d^{-14} \][/tex]

2. Combine the exponents with the same base [tex](\(d\))[/tex] by applying the rule [tex]\(a^m \cdot a^n = a^{m+n}\)[/tex]:

[tex]\[ = 12 d^{8 + (-14)} \][/tex]

[tex]\[ = 12 d^{-6} \][/tex]

Therefore, [tex]\( -3 d^8(-4 d^{-14}) \)[/tex] simplifies to [tex]\(12 d^{-6}\)[/tex].

The complete question is given below:

Simplify [tex]\( -3 d^8(-4 d^{-14}) \)[/tex]. Assume that  [tex]d \neq 0[/tex].

the answer is 12/d^6 , D

Answer: 25.13 (choice B)

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

The formula we'll use is

s = r*theta

with

s = unknown arc length

r = radius = diameter/2 = 12/2 = 6 feet

theta = 4pi/3 radians <--- this angle must be in radian mode for the formula to work

Plug those values into the formula and simplify

s = r*theta

s = 6*(4pi/3)

s = 24pi/3

s = 8*pi

s = 8*3.1416

s = 25.1328

s = 25.13

which is approximate and rounded to the nearest hundredth.

Answer:

Option 4 is correct.

The equation [tex]4x^2 -24x + 4y^2 + 72y = 76[/tex] is equivalent to [tex]4(x-3)^2 + 4(y+9)^2 =436[/tex]

Step-by-step explanation:'

Given equation: [tex]4x^2 -24x + 4y^2 + 72y = 76[/tex]

First group the terms with x and those with y;

[tex](4x^2-24x)+(4y^2+72y) = 76[/tex]

Next, we complete the squares.

We can do this by adding a third term such that the x terms and the y terms are perfect squares.

For this we must either add the same value on the other side of the equation or subtract the same value on the same side so that the equality is maintained.

⇒[tex]4(x^2-6x) +4(y+18y) = 76[/tex]

or

[tex]4(x^2 -6x +3^2 -3^2) + 4(y^2 +18y +9^2 -9^2) = 76[/tex]

[tex]4(x^2-6x + 3^2) - 36 + 4(y^2+18y +9^2) - 324 = 76[/tex]

[tex]4(x-3)^2 + 4(y+9)^2 - 360 =76[/tex]

Add 360 on both sides we get;

[tex]4(x-3)^2 + 4(y+9)^2 =360 +76[/tex]

Simplify:

[tex]4(x-3)^2 + 4(y+9)^2 =436[/tex]

Therefore, the given equation is equivalent to [tex]4(x-3)^2 + 4(y+9)^2 =436[/tex]

Answer:

4.8 points per minute

Step-by-step explanation:

Uncle Drew scored 28 points in [tex]5 \frac{5}{6}[/tex] minutes. We have to convert the mixed fraction first:

[tex]t = 5 \frac{5}{6}=\frac{5\cdot 6+5}{6}=\frac{35}{6}[/tex]

So, the time is 35/6 minutes.

In order to find the number of points he scored in a minute, we have to divide the total number of points by the number of minutes, so:

[tex]mean = \frac{28}{35/6}=28 \cdot \frac{6}{35}=4.8[/tex]

So, he scored 4.8 points per minute.

Answer:

4.8

Step-by-step explanation:

The account with the greater principal is Account B with a simple interest of $ 18

What is Simple Interest?

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the first account be = A

Let the second account be = B

Now ,

The simple interest of A = $ 4.50

The simple interest of B = $ 18

The time period t = 18 months = 1.5 years

The rate of interest r for A = 2 %

The rate of interest r for B = 4 %

Now , the equation will be

Simple Interest of A = ( Principal of A x Rate of interest of A x Time ) / 100

Substituting the values in the equation , we get

4.50 = ( P x 2 x 1.5 ) / 100

Multiply by 100 on both sides of the equation , we get

450 = 3P

Divide by 3 on both sides of the equation , we get

Principal of A = $ 150

And ,

Simple Interest of B = ( Principal of B x Rate of interest of B x Time ) / 100

Substituting the values in the equation , we get

18.00 = ( P x 4 x 1.5 ) / 100

Multiply by 100 on both sides of the equation , we get

1800 = 6P

Divide by 6 on both sides of the equation , we get

Principal of B = $ 300

Therefore , the principal of B > principal of A

Hence , the simple interest of B with $ 18 has larger principal

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Answer: A. y=5/6x-3

Step-by-step explanation:

y=mx+b

m=slope

b=y-intercept

I'm almost 100% sure this is right.

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have

[tex]m=\dfrac{5}{6},\ b=-3[/tex]

Substitute:

[tex]\boxed{y=\dfrac{5}{6}x-3}[/tex]

Answer: 24.6 inches

Step-by-step explanation: Since it's a rectangle, and not a rectangular prism, that means it's 2D. Length is the long sides on the top and bottom, and width is the shorter sides on it's left and right. So since there's two of each, just do 8.1 + 8.1 + 4.2 + 4.2 and you have your answer!

This problem is solved by using the concept of percentage as a part of a whole. We find out that 30% of the total distance equals 6 miles. So by setting up the proportion 30/100 = 6/x, we calculate the total distance is 20 miles.

This question is an application of percentage problems in real-life situations, specifically hiking distance. When you use a percentage to describe a part of a whole thing, the thing is always considered to be '100%'. In this case, Michelle's hiking trip is the 'whole thing' or '100%'.

We are told that 6 miles is 30% of the total distance. To find the total distance, we can set up a proportion to solve for it. The proportion would be 30/100 = 6/x.

Let x represent the total distance. So we can write the proportion as:

6 / x = 30 / 100

To solve for x, we can cross multiply and then divide:

100 * 6 = 30 * x

600 = 30x

x = 20

Therefore, the total number of miles Michelle will walk is 20 miles.. So, the total distance that Michelle will walk is 20 miles.

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Answer:

The perpendicular line would be y = 6

Step-by-step explanation:

In order to get this, we must first recognize that the equation given is a vertical line. If our new line is to be perpendicular to it, it must be a horizontal line. All horizontal lines are written as y = (a number). Since we have a point it goes through, we can get that value in the ordered pair. The ordered pair has a y value of 6, which means the equation would be y = 6

Answer:

f(n) = 10 * 5^(n-1)

an = 15-2.5n

Step-by-step explanation:

{(1, 10), (2, 50), (3, 250), (4, 1250)}

The formula for a geometric sequence is

an = a1 * r ^(n-1)

where a1 is the first term and r is the rate in which it increase

a1 =10

r = 5,  each term goes up by a factor of 5

50/10 = 5

250/50 = 5

etc

f(n) = 10 * 5^(n-1)

What is the explicit rule for the sequence?

13, 10.5, 8, 5.5, 3, 0.5, ...

For an arithmetic sequence the formula is

an = a1 + d(n-1)

where a1 is the first term and d is the common difference

a1= 13 and d = -2.5

10.5 -13 = -2.5

8. - 10 = -2.5

etc

an = 13 - 2.5 ( n-1)

Simplifying

an = 13 -2.5n + 2.5

an = 15-2.5n

Answer:

decrease

Step-by-step explanation:

75 is a higher than 25% come man its ez

The number of times of the soft drink that refills will be 7.

Inequality is defined as an equation that does not contain an equal sign.

Soft drinks cost $1.89 and refills cost $0.25 each.

With $3.80 to spend on the soft drink and refills.

Then the maximum number of refills will be given as

Let x be the number of refills.

1.89 + 0.25x ≤ 3.80

         0.25x ≤ 1.91

                 x ≤ 7.64

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Answer:

The correct answer option is 192.

Step-by-step explanation:

We know that f(x) varies directly with [tex]x^{2}[/tex] so we can write it as:

[tex]f(x)[/tex] ∝ [tex]x^{2}[/tex]

Changing it to an equality by the addition of a constant [tex]k[/tex]:

[tex]f(x) = k.x^{2}[/tex]

If f(x) = 75 when x = 5, then we can find the value of k:

[tex]75=k(5)^2[/tex]

[tex]k=\frac{75}{25} =3[/tex]

If k = 3, we can find the value of f(8):

[tex]f(8)=3(8)^2[/tex]

[tex]f(8)=3*64[/tex]

[tex]f(8)=[/tex]192

Answer: (A) 19.3%

Step-by-step explanation:

[tex]\text{Vodka: }2.5\text{ oz }\times\dfrac{\$35}{1\text{ liter }}\times\dfrac{1\text{ liter }}{33.814\text{ oz }}=\$2.59\\\\\text{Vermouth: }0.5\text{ oz }\times\dfrac{\$7.99}{1\text{ liter }}\times\dfrac{1\text{ liter }}{33.814\text{ oz }}=\$0.12\\\\\text{Olive: }\$0.15[/tex]

Vodka + Vermouth + Olive = Total Cost

$2.59  +   $0.12      + $0.15 = $2.86

[tex]\dfrac{\text{cost to make}}{\text{selling price}} = \dfrac{\$2.86}{\$15} = 0.19 = 19\%[/tex]

Answer: Choice A

S9 = (9/2)*(2+26)

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

The formula is

Sn = (n/2)*(a1+an)

where

Sn = sum of the first n terms (nth partial sum)

n = number of terms

a1 = first term

an = nth term

In this case,

n = 9

a1 = 2 (plug in n = 1 into the formula an = 3n-1 and simplify)

an = a9 = 26 (plug n = 9 into the formula an = 3n-1 and simplify)

So,

Sn = (n/2)*(a1+an)

S9 = (9/2)*(2+26)

will help us find the sum of the first 9 terms of this arithmetic sequence

Answer:

A. S9 = (9/2)*(2+26)

Answer:

B  2,3,-3

Step-by-step explanation:

If we use the zero product property, we can set each term =0 to find the roots.

0=(x-2)(x-3)(x+3)

x-2 =0   x-3 =0   x+3=0

x=2   x=3          x=-3

The roots are -3,2,3

Option: B is the correct answer.

The range of the function is:

        B.      5 < y < ∞

Range of a function--

The range of a function is the set of all the values that is attained by the function.

By looking at the graph of the function we see that the function tends to 5 when x→ -∞ and the function tends to infinity when x →∞

Also, the function is a strictly increasing function.

This means that the function takes every real value between 5 and ∞ .

i.e. The range of the function is: (5,∞)

          Hence, the answer is:

                Option: B

Answer:

length = 100 squared  Width = 80 squared

Step-by-step explanation:

You add the to ratio number ( 4+5 ). You take that number (9) and divide with 180. You receive the answer 20.  Then you multiply 20 by 5 to get the length and multiply 20 by 4 to width. Then you just add back the square operation.

Final answer:

The length and width of the rectangle are found by setting up equations using the given ratio and area. By solving the equations, the length is determined to be 15 inches and the width 12 inches.

Explanation:

To find the length and width of the rectangle with an area of 180 square inches and a ratio of length to width of 5:4, we can set up equations using the ratio and area information. Since the area of a rectangle is equal to the length times the width, we can express the length (L) and width (W) in terms of the ratio:

L = 5x

W = 4x

We know that the area (A) is 180 square inches, so:

A = L × W

180 = (5x) × (4x)

180 = 20x₂

Therefore:

x₂ = 180 / 20

x₂ = 9

x = 3

Now we can find L and W by substituting x back into L = 5x and W = 4x:

L = 5 × 3 = 15 inches

W = 4 × 3 = 12 inches

Hence, the length of the rectangle is 15 inches, and the width is 12 inches.

The value of y and x is 11 and 6.  

The m<BED = 40 degrees

The m<BEA = 40 degrees.

From the given diagram, the following statements are true:

AB = BC

3y = 5y - 22

3y - 5y = -22

-2y = -22

y = 11

Similarly, m<DBE = 50 degrees

m<BED = 90 - m<DBE

m<BED = 90 - 50

m<BED = 40 degrees

Since BE = BC = 3y

BE = BC = 3(11) = 33

Also, 7x  - 2 = 40

7x = 40 + 2

7x = 42

x = 6

Get the measure of m<BEA

m<BEA = 7x - 2

m<BEA = 7(6) - 2

m<BEA = 40 degrees

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Question

Describe how to find all the points on a baseball field that are equidistant from second base and third base.

In the figure, m∠DBE=50. Find each of the following.

m∠BEDm angle b e d

m∠BEAm angle b e eh

x

y

BE

BC