Value: 2
In the year 2000, the population of Ohio was 11.03 million people. By the year 2017 the
population of Ohio was 11.66 million people. Create an equation modeling the
population, p, of Ohio given the year, t. Round to the nearest hundredth if necessary.
O a. p=11.1t+232.14
O b. p=11.1t-11.66
O c. p=0.09t+191.93
O d. p=0.04x-68.97
Check Answer

The measure of angle B is x, while the measure of angle A is 2·x. The 70° measure of angle C and the angle sum property of the interior angles of a triangle indicates that angle B is [tex]36.\overline 6^{\circ}[/tex] and angle A is [tex]73.\overline 3^{\circ}[/tex]

The interior angles of a triangle are the angles formed by the sides sides of the triangle.

The question can be solved by making use of the known properties of a triangle.

The angle sum property of the interior angles in a triangle gives;

The sum of the interior angles of a triangle is 180°

Therefore; x + 2·x + 70 = 180

3·x = 180° - 70° = 110°

[tex]x = \dfrac{110^{\circ}}{3} = 36\frac{2}{3} ^{\circ}[/tex]

The measure of angle A is 2·x

Which gives;

[tex]A = 2 \times 36\frac{2}{3} ^{\circ} = 73\frac{1}{3} ^{\circ} = 73.\overline 3^{\circ}[/tex]

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Reflection across the y-axis is H(-1,-3), Z(-1,2) W(-4,1).

When point M (h,k) is reflected along the y-axis, the image M' with coordinates of forms in the second quadrant (-h, k).

Thus, we get the conclusion that when a point is mirrored along the y-axis, the y-coordinate stays constant but the x-coordinate changes to the negative.

H(1,-3) → H(-1,-3)

Z(1,2) → Z(-1,2)

W(4,1) → W(-4,1)

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Answer:

j=3

Step-by-step explanation:

distribute

-3(j-8)+-6=-9

-3j+24-6=9

-3j+18=9

-3j=-9

j=3

Hopes this helps pleae mark brainliest

Answer:

j = 9

Step-by-step explanation:

Let's solve for the value of j,

→ -3(j − 8) + (-6) = -9

→ -3j + 24 - 6 = -9

→ -3j + 18 = -9

→ -3j = -9 - 18

→ j = (-27)/(-3)

→ j = 27/3

→ [ j = 9 ]

Hence, the value of j is 9.

Answer: [tex]\frac{4\sqrt{x} }{t^2}[/tex]

Step-by-step explanation:

You can start by either applying the exponent to both the numerator and denominator (exponent rule), or make things simpler by dividing first. Doing the latter allows me to show both properties. Since the terms in the fraction are being multiplied, we can divide common terms which will leave us with [tex]\frac{16x}{t^4}[/tex] on the inside. Now that it is simplified, we can apply the exponent. We will end up with 4x^1/2 in the numerator and t^2 in the denominator. If the exponent seems daunting, it is also helpful to know that raising something to the exponent of 1/2 is basically taking the square root of it.

Answer:

68°

Step-by-step explanation:

The angles are equal to each other.  Set them equal and solve for x

5x + 18 = 8x - 12  Subtract 5x from both sides of the equation

18 = 3x - 12  Add 12 to both sides of the equation

30 = 3x  Divide both sides by 3

10 = x

Now that you have found x plug is back into  5x + 18

5(10) + 18

50 + 18 = 68

Answer:

∠ FLJ = 68°

Step-by-step explanation:

∠ EKG and ∠ FLJ are alternate exterior angles and are congruent , then

8x - 12 = 5x + 18 ( subtract 5x from both sides )

3x - 12 = 18 ( add 12 to both sides )

3x = 30 ( divide both sides by 3 )

x = 10

Then

∠ FLJ = 5x + 18 = 5(10) + 18 = 50 + 18 = 68°

The required feet added to both the length and width of the patio is 6 feet.

Given that,
A square patio had the same number of feet added to its length and width. The equation A(x) = x² + 12x + 36 represents the area of the new patio in square feet, where 'x' was the length and width of the original patio, in feet.

Here,

According to the question,
A(x) = x² + 12x + 36
A(x) = x² + 6x + 6x + 36
A(x) = (x + 6)(x + 6)

Length = width = x + 6

Thus, the required feet added to both the length and width of the patio is 6 feet.

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Answer:

  (x -3)² -10

Step-by-step explanation:

You want the vertex form of x² -6x -1, found by completing the square.

The square of a binomial is ...

  (x -a)² = x² -2ax +a²

The constant in this perfect square trinomial is the square of half the coefficient of the linear term: a² = (-2a/2)²

To complete the square for the given quadratic, the perfect square trinomial must have a constant of (-6/2)² = 9. We can add and subtract 9 to rearrange the quadratic to the desired form.

  x² -6x -1

  = (x² -6x +9) -1 -9 . . . . . . . +9 -9 was added

  = (x -3)² -10

The arc length of the segment it 6.28 meters

From the question, we have the following parameters:

Central angle, x = 72 degrees

Diameter, d = 10 centimeters

The radius of the circle can be calculated using

r = d/2

So, we have

r = 10/2

Evaluate

r = 5 cm

The exact arc length using the central angle measure is calculated as:

Arc length = x/360 * 2πr

Substitute the known values in the above equation

Arc length = 72/360 * 2π * 5

Evaluate

Arc length = 6.28

Hence, the exact arc length using the central angle measure is 6.28 meters

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Possible question

The diameter of the circle is 10 centimeters and the measure of is 72º. Find the length of arc

Round your calculations to the nearest tenth. Complete your work in the space provided.

On Wednesday 1/6 of the patio area is left to tile

Let the patio area be x

On Monday, he tiled 1/3 of his patio = 1/3 x

on Tuesday, he tiled 1/2 of the patio area = 1/2 x

The area left to tile on Wednesday

= x - (1/3 x + 1/2 x)

x - 1/3 x - 1/2 x

(6x - 2x - 3x)/6

= 1/6 x

The area left to tile on Wednesday is 1/6 of the patio area

Therefore,  1/6 of the patio area is left to tile on Wednesday

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Answer:

[tex]m=-8/3[/tex], the options are wrong

Step-by-step explanation:

[tex]3m-4-\frac{3}{2}m+8=0 \\ \\ 6m-8-3m+16=0 \\ \\ 3m+8=0 \\ \\ m=-\frac{8}{3}[/tex]

The question is incorrect.

The distance between the two points (3, π/6) and (2, π/3) in polar coordinates is 1.614 units

The points are (3, π/6) and (2, π/3)

The polar coordinate system is the system that represent a point by a distance from a fixed reference point and angles from a reference direction

The distance between the two points

d = [tex]\sqrt{r_1^2+r_2^2-2r_1r_2cos(theta_1-theta_2)}[/tex]

(3, π/6) is the coordinates of first point

(2, π/3) is the coordinates of second point

Substitute the values in the equation

d = [tex]\sqrt{3^2+2^2-2(3)(2)cos(\pi/6 - \pi /3)}[/tex]

d = [tex]\sqrt{9+4-12(\frac{\sqrt{3} }{2} )}[/tex]

d = [tex]\sqrt{13-6\sqrt{3} }[/tex]

d = 1.614 units

Hence, the distance between the two points (3, π/6) and (2, π/3) in polar coordinates is 1.614 units

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The percentage is the indicating hundredth thus the percentage of people speeding on this road who noticed the sign would be 84% - 75% = 9%.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

As per the given,

Percentage of people who notice the speed limit = 84%

The percentage of people who notice the sign and follow the speed limit is 75%.

Therefore, 84% - 75%  = 9% are the percentage speeding and noticed.

Hence "The percentage is the indicating hundredth thus the percentage of people speeding on this road who noticed the sign would be 84% - 75% = 9%".

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If they took 1 hour and 35 minutes to complete the test and finished at 1:20 they started at 11:45.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, The total time of the math test Raven took was 1 hour and 35 minutes.

Now he finishes the test at 1:20.

So, One hour before the time was 12:20.

20 minutes before that was exactly 12:00 and 15 minutes before that was

11:45 so a total of 1 hour and 35 minutes.

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The grams of fat that are contained in one serving of the low-fat yogurt are: 3.7968g.

To obtain the number of grams of fat that is contained in one serving of the low-fat yogurt, we need to first note the percentage content of the low-fat version of yogurt.

100 - 45.75% = 54.25% or 0.5425

Since one serving of the yogurt contains 7g of fat, then the low-fat serving will be equal to:

7g × 0.5425  = 3.7968

So, the total gram of fat for one serving of the low-fat yogurt is equal to:

3.7968g

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Answer:

Store B

Step-by-step explanation:

Store A: $2.50 ÷ 2 = $1.25

Store B: $3.25 ÷ 3 = $1.08 (to nearest cent)

Store B offers the better deal.

The function notation of the following are:

f(1) = 5

f(0) = 1

f(-3) = -11

f(8) = 33

Given:

x is the input.

the function is 4x+1

f(x) is the output.

we are asked to determine the values of the following :

a. f(1)

x = 1

so f(x) = 4x+1

f(1) = 4(1)+1

f(1) = 4+1

f(1)=5

b. f(0)

x = 0

so f(x) = 4x+1

f(0) = 4(0)+1

f(0) = 0+1

f(0)=1

c. f(-3)

x = -3

so f(x) = 4x+1

f(-3) = 4(-3)+1

f(1) = -12+1

f(1)= -11

d. f(8)

x = 8

so f(x) = 4x+1

f(8) = 4(8)+1

f(8) = 32+1

f(1)=33

Hence we get the required values.

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She made sales of =$61,200.00

acc to our  question-

Step-by-step explanation:

1.5% = 0.015 , 4% = 0.04 , 5% = 0.05

16,000 × 0.015 = $240.00

$25,000 × 0.04 = $1,000.00

$2,250.00 - ($240.00 + $1,000.00) = $1,010.00

$1,010.00 ÷ 0.05 = $20,200.00

$20,200.00 + $25,000.00 + $16,000.00 = $61,200.00

hence,She made sales of =$61,200.00

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Answer:

5 with a remainder of 49

Step-by-step explanation:

The inequality to represent the number of tickets Bianca can buy without over drawing on her debit card is 14.50 + 6.50x ≤ 50  .

In the question ,

it is given that

amount of money present in Bianca's Debit card = $50

amount of money spend on lunch = $14.50

cost of 1 movie ticket = $6.50

le the number of ticket = "x"

according to the question ,

the inequality is

14.50 + 6.50x ≤ 50

6.50x ≤ 50 - 14.50

6.50x ≤ 35.5

x ≤ 35.5/6.50

x ≤ 5.46

≈ 5

Therefore , The inequality to represent the situation is 14.50 + 6.50x ≤ 50  

, and the number of tickets she can buy is 5 .

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See attachment, this took me a while so please say thanks and rate <3

For Jeremy the new balance due was $8.9  .

In the question ,

it is given that ,

bill received by Jeremy with balance due =  $35.60  

also given that after an error occurred  ,

the new balance was 1/4 of the original balance due .

So , the new balance due is = (1/4) × (original balance due)

Substituting the value of original balance due ,

we get ,

new balance due = (1/4) × (35.60)

= 35.60/4

On Simplifying further ,

we get ,

= 8.9

Therefore , For Jeremy , the new balance due was $8.9  .

The given question is incomplete , the complete question is

Jeremy received a bill with a balance due of $35.60. After an error was corrected, the new balance was 1/4 of the original balance due. What was the new balance due ?

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The math shows the world is designed, and that design is symmetry and spirals.

How is math found in nature What is the significance of mathematical patterns in nature?

Mathematics is seen in many beautiful patterns in nature, such as symmetry and spirals. Both are aesthetically appealing and proportional. Symmetry can be radial, where the lines of symmetry intersect a central point such as a daisy or a starfish.

Here,

If Hailey used math to describe the design in nature: the number of legs insects and spiders have, the number of petals on flowers, and even the patterns of spots on some animals. The math shows the world is designed, and that design is symmetry and spirals.

Hence, the math shows the world is designed, and that design is symmetry and spirals.

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Answer:

  no, no, yes, yes

Step-by-step explanation:

You want to know which of the ordered pairs are solutions to the given system of equations: 6x -3y = 9, y = 2x -3.

The attached graph shows that the two equations describe the same line. The given points are plotted on the same graph. The ones on the line are solutions.

  (4, -5) . . . not a solution

  (-1, 8) . . . not a solution

  (7, 11) is a solution

  (0, -3) is a solution

The answer is option (a)

Hope this answer helps you

Answer:

192

Step-by-step explanation:

If 20% is the profit, then 80% is the cost.

.8 x 240 = 192

Check the picture below.

Answer:

[tex]\textsf{a.} \quad x = 1 - \sqrt{7},\quad x = 1 + \sqrt{7}[/tex]

b.  y = -6

c.  Minimum point at (1, -7).

d.  Domain:  (-∞, ∞)

e.  Range:  [-7, ∞)

f.  See attachment.

Step-by-step explanation:

Given function:

[tex]\text{f}(x)=x^2-2x-6[/tex]

As per the question, use a graphing calculator to graph the given function.

The x-intercept(s) are the points at which the curve crosses the x-axis.

The y-intercept is the point at which the curve crosses the y-axis.

From inspection of the graph:

The domain of a function is the set of all possible input values (x-values).

The domain of the given function is unrestricted.

The range of a function is the set of all possible output values (y-values).

As the function has a minimum point at y = -7, the range is restricted.

Graph label the axes using a scale of 1 (see attachment).

By performing some simple mathematical operations, the answers to all the subparts are:

So, the answers after multiplication are:

Therefore, by performing some simple mathematical operations, the answers to all the subparts are:

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