1 and 2 are vertical angles and 1 euals 5x+12 and 2 equals 6x-11 what does 1 equal

(a) The amount for total expenditures in 2010 was about $160.3 billion.

(b) The first full year in which expenditures exceeded $108 billion was 2010.

In Mathematics and Geometry, an exponential function can be represented by using this mathematical equation:

f(x) = a(b)^x

Where:

Based on the information provided above, the total expenditures on benefits (in billions of dollars) can be modeled by the following exponential function;

[tex]h(x) = 23.4(1.08)^x[/tex]

Part a.

x = 5 + (2015 - 1995)

x = 25 years.

Therefore, the amount for total expenditures in 2015 is given by:

[tex]h(25) = 23.4(1.08)^{25}[/tex]

h(25) = 160.3 billion.

Part b.

For the first full year in which the total expenditures exceeded $110 billion, we have:

[tex]110= 23.4(1.08)^x\\\\\frac{110}{23.4} =1.08^x[/tex]

By taking the natural log (ln) of both sides of the equation, we have:

x = ln(4.7008547008547008547008547008547)/ln(1.08)

x = 1.5477443434287605/0.0769610411361284

x = 20.12 ≈ 20 years

First full year = (20 - 5) + 1995

First full year = 2010.

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Complete Question:

The total expenditures on benefits (in billions of dollars) can be approximated by the function [tex]h(x) = 23.4(1.08)^x[/tex], where x = 5 corresponds to the year 1995

(a) What was the amount for total expenditures in 2015?

(b) What was the first full year in which expenditures exceeded $110 billion?

The correct length of side k in triangle JKL is approximately 35.15 units.

The correct answer is option E.

The length of side k in triangle JKL using the correct values for sin(52°) and sin(97°).

Given:

m∠J = 97 degrees

m∠L = 31 degrees

J = 44

According to the Law of Sines, we have:

sin(∠J) / J = sin(∠K) / k

Substituting the given values:

sin(97°) / 44 = sin(∠K) / k

Now, let's solve for k:

k = (44 * sin(∠K)) / sin(97°)

Using a calculator:

k = (44 * sin(52°)) / sin(97°)

k ≈ (44 * 0.79) / 0.99

k ≈ 35.1

Therefore, the correct length of side k in triangle JKL is approximately 35.15 units making option E the correct answer.

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The question probable may be:

Triangle JKL has the following measures :m∠J=97degree, m∠L=31degree, and j=44. What is the length of side k?

A. 46.3

B. 52.0

C. 22.8

D. 34.9

E. 35.1

The sentence that contains correct punctuation is "Tammy is a good worker; she gets everything done on time."

Option A contains correct punctuation. It has a semicolon which separates two independent clauses and also makes a connection between them. This is the correct use of punctuation. It is also known as a semicolon conjunction.

Option B is incorrect as there is no semicolon between "colors" and "red." There should be a semicolon instead of a comma to create a connection between the two clauses.
Option C is incorrect as there is no need for a semicolon after "going home" because there is no second independent clause following it.
Option D is incorrect as there should be a semicolon between "everything" and "including" since there are two distinct groups of items being listed.
In conclusion, option A is the correct answer because it follows the rules of proper punctuation by using a semicolon correctly to join two independent clauses.

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Answer: 147.57

Step-by-step explanation:

x - .26x = 109.20

0.26 = 26%

subtract 26% from 100% = 74%

109.20 / 0.74 = 147.57

Check work: 147.57 × .26 = 38.37

Then 147.57 - 38.37 = 109.20

Answer: 150cm1  I think

Answer:

y = - 5x - 1 and y = [tex]\frac{1}{3}[/tex] x + 8

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

14

y = - 5x + 4 ← is in slope- intercept form

with slope m = - 5

• Parallel lines have equal slopes , then

y = - 5x + c ← is the partial equation

to find c substitute P (- 1, 4 ) into the partial equation

4 = - 5(- 1) + c = 5 + c ( subtract 5 from both sides )

- 1 = c

y = - 5x - 1 ← equation of parallel line

15

y + 3x = 13 ( subtract 3x from both sides )

y = - 3x + 13 ← in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] , then

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute P (6, 10 ) into the partial equation

10 = [tex]\frac{1}{3}[/tex] (6) + c = 2 + c ( subtract 2 from both sides )

8 = c

y = [tex]\frac{1}{3}[/tex] x + 8 ← equation of perpendicular line

Answer:

The expression simplified can be written as:

16m +  8

Here we want to simplify the following expression:

(8m + 4) + (8m + 4)

To simplify, we start by removing the parenthesis:

8m + 4 + 8m + 4

Now we can change the order of the terms so we get:

8m + 8m + 4 + 4

Now we can group the like terms to get:

(8m + 8m) + (4 + 4)

And simplify this to get:

16m +  8

That is the simplified expression.

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Step-by-step explanation:

Plug in 8 for x, and -7 for y in both systems.

[tex]8a- 7b = 10[/tex]

[tex]8b - 7a = - 5[/tex]

Now, we use the elimination method to isolate a or b.

Let multiply the top equation by 8 and the bottom one by 7.

[tex]64a - 56b= 80[/tex]

[tex]56b - 49a = - 35[/tex]

Eliminate the b variable by adding the two systems.

[tex]15 a= 45[/tex]

[tex]a = 3[/tex]

Now, plug 3 for a into either the systems to find b.

[tex]24 - 7b = 10[/tex]

[tex] - 7b = - 14[/tex]

[tex]b = 2[/tex]

Answer:

12 apples

Step-by-step explanation:

Apples eaten by friend = 5

Apples eaten by me = 7

Toral number of apples eaten together

= 5 + 7

= 12

________

hope this helps!

Answer:

12 apples

Step-by-step explanation:

If 1 person eats 5 apples, and another person eats 7, we should add the amount of apples together to get the total.

5+7

=12

So, 12 apples were ate altogether.

Hope this helps! :)

[tex]f(x)=x[/tex] for [tex]x\leq0[/tex], therfore [tex]f(0)=0[/tex].

the first domain is true for f(0) so we substitute value of x in the first function

[tex]f(x) = x \\ f(0) = 0[/tex]

The Ratio of 1.24 to 0.08 can be expressed as 15.5, 31:2, or 31/2.

To find the ratio of 1.24 to 0.08, we divide 1.24 by 0.08.

1.24 ÷ 0.08 = 15.5

Therefore, the ratio of 1.24 to 0.08 is 15.5.

We can also express this ratio as a fraction. To do this, we write 15.5 as a fraction over 1:

15.5/1

To simplify the fraction, we can multiply both the numerator and the denominator by 10 to get rid of the decimal:

(15.5 × 10)/(1 × 10) = 155/10

Further simplifying the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 5:

(155 ÷ 5)/(10 ÷ 5) = 31/2

So, another way to express the ratio 1.24:0.08 is 31:2.

In conclusion, the ratio of 1.24 to 0.08 can be expressed as 15.5, 31:2, or 31/2.

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The value of the sum of 5 and the square of a number varies depending on the value of n. When n = 1, the result of the expression is 6, when n = 2, the result is 9, and when n = 3, the result is 14. The same applies when n is negative.

The sum of 5 and the square of a number is an expression that can be represented as (n² + 5), where n represents the number whose square is added to 5. The result of the expression varies depending on the value of n. In this answer, we will examine how to find the sum of 5 and the square of a number using various values of n.
If n = 1, then the square of n is equal to 1, and the sum of 5 and the square of n is equal to 6. Therefore, if n = 1, the result of the expression is 6.
If n = 2, then the square of n is equal to 4, and the sum of 5 and the square of n is equal to 9. Therefore, if n = 2, the result of the expression is 9.
If n = 3, then the square of n is equal to 9, and the sum of 5 and the square of n is equal to 14. Therefore, if n = 3, the result of the expression is 14.
If n = -1, then the square of n is equal to 1, and the sum of 5 and the square of n is equal to 6. Therefore, if n = -1, the result of the expression is 6.
If n = -2, then the square of n is equal to 4, and the sum of 5 and the square of n is equal to 9. Therefore, if n = -2, the result of the expression is 9.
If n = -3, then the square of n is equal to 9, and the sum of 5 and the square of n is equal to 14. Therefore, if n = -3, the result of the expression is 14.
In conclusion, the value of the sum of 5 and the square of a number varies depending on the value of n. When n = 1, the result of the expression is 6, when n = 2, the result is 9, and when n = 3, the result is 14. The same applies when n is negative.

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The percentage of boys in the combined group is 60% and the percentage of girls in the combined group is 40%.

Given the number of boys and girls in two groups of students travelling together, we have to determine the percentage of boys and girls in the combined group. Let's solve this problem step by step. Solution:Step 1: Let the number of boys in the combined group be B and the number of girls in the combined group be G.B = 40 + 50 = 90 (Adding the number of boys from both groups)G = 25 + 35 = 60 (Adding the number of girls from both groups)Step 2: Find the total number of students in the combined group.Total students in the combined group = B + G = 90 + 60 = 150 studentsStep 3: Calculate the percentage of boys and girls in the combined group.Percentage of boys = (Number of boys in the combined group/Total number of students in the combined group) × 100= (90/150) × 100 = 60%Percentage of girls = (Number of girls in the combined group/Total number of students in the combined group) × 100= (60/150) × 100 = 40%

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The fraction of the area of the tray occupied by the blondies is 1/9.

To find the fraction of the area of the tray occupied by blondies, we need to determine the area occupied by the blondies and compare it to the total area of the tray.

Let's calculate the area of each individual blondie:

The blondies are squares with 3-inch sides, so the area of each blondie is 3 inches × 3 inches = 9 square inches.

Now, let's calculate the area occupied by the blondies in each row:

Since there are 4 rows of blondies and each row contains 4 blondies, the total number of blondies is 4 rows × 4 blondies per row = 16 blondies.

So, the total area occupied by the blondies is 16 blondies × 9 square inches per blondie = 144 square inches.

Next, let's determine the area occupied by the brownies:

The brownies are squares with 6-inch sides, so the area of each brownie is 6 inches × 6 inches = 36 square inches.

Since there are also 4 rows of brownies and each row contains 4 brownies, the total number of brownies is 4 rows × 4 brownies per row = 16 brownies.

Therefore, the total area occupied by the brownies is 16 brownies × 36 square inches per brownie = 576 square inches.

Now, let's calculate the total area of the tray:

Given that the tray is completely full and has an area of 648 square inches, we can subtract the area occupied by the brownies from the total area to find the remaining area occupied by the blondies:

Total area of the tray - Area occupied by the brownies = Area occupied by the blondies

648 square inches - 576 square inches = 72 square inches.

So, the fraction of the area of the tray occupied by the blondies is:

Area occupied by the blondies / Total area of the tray = 72 square inches / 648 square inches.

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 72 in this case:

72 square inches / 648 square inches = 1/9.

Therefore, the blondies' percentage of the tray's surface area is 1/9.

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The price at the point of equilibrium is d. 80

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

The supply/demand graph

The price at the point of equilibrium is the point where the demand and the supply lines meet

From the attached graph, we can see that they intersect at P = 80

This means that the price at the point of equilibrium is d. 80

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The equation that represents the given sentence "Don's score decreased by 23 is 43" is d - 23 = 43, where d represents Don's score.

To translate the given sentence into an equation, let's break it down:

"Don's score" can be represented by the variable d.

"Decreased by 23" indicates a subtraction operation. So we subtract 23 from Don's score.

"Is" signifies the equal sign in the equation.

"43" is the result or value that Don's score decreased by 23 should be equal to.

Combining all the information, we can write the equation:

d - 23 = 43

This equation states that when we subtract 23 from Don's score (represented by d), the result should be equal to 43. This equation accurately represents the given sentence.

To find the value of Don's score (d), we can solve the equation by isolating the variable:

d - 23 = 43

Adding 23 to both sides of the equation:

d - 23 + 23 = 43 + 23

Simplifying:

d = 66

Therefore, Don's score, represented by the variable d, is equal to 66 based on the given equation.

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None of the answer choices provided (O (-5, -1), O (-1, 5), O (-1, -5), O (-5, 1)) are correct, as the concept of a center does not apply to Linear functions.

To determine the center of the function f(x), we need more information about the function. The expression given, 2x-1, represents a linear function, which is in the form y = mx + b, where m is the slope and b is the y-intercept.

The center of a function is typically associated with quadratic or circular functions and is not applicable to linear functions. Therefore, we cannot determine the center of the function f(x) = 2x - 1 based on the given information.

Thus, none of the answer choices provided (O (-5, -1), O (-1, 5), O (-1, -5), O (-5, 1)) are correct, as the concept of a center does not apply to linear functions.

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Spanning trees assignments are a type of network problem that requires finding the minimum path or tree that spans all nodes or vertices in the network.

This is useful for optimizing the design and efficiency of networks, such as computer networks, transportation systems, and power grids.
A spanning tree is a subset of a graph that connects all vertices without any cycles, making it a tree.

Finding the minimum spanning tree involves selecting the minimum weight edge to add to the tree, while ensuring that there are no cycles.

This can be done using algorithms such as Kruskal's algorithm or Prim's algorithm.

Spanning trees assignments are important in network design and optimization and have applications in various fields such as computer science, electrical engineering, and transportation planning.

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The two points are the tips of the vertical dotted line which represents the measure of the rectangles width and the base of the triangle. To obtain the area of the composite figure, calculate and add the area of each shape.

The figure given is a composite figure which consists of a rectangle and triangle. The polygon could be broken into two pieces by drawing a vertical line from the endpoint of the 28cm line segment of the rectangle.

2.)

To obtain the area of the composite figure, we need to calculate the area of the rectangle and triangle separately and then add them together.

Hence, adding the area of each shape gives the area of the composite figure.

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Answer: correct answer is B

Step-by-step explanation:

I did the assignment

The evaluation of the sinusoidal sine function y = 2·sin(x) + 1 indicates;

Maximum value: 3 at x = π/2

Minimum value: -1 at x = 3·π/2

A sinusoidal function is a periodic function based on either the sine or cosine functions, which oscillates, smoothly, between high and low values.

The specified function is; y = 2·sin(x) + 1

The domain of the input value x is; 0 ≤ x < 2·π

The function is a sinusoidal function which has the form; y = a·sin(b·(x - h)) + k

Therefore, we get;

The amplitude, a = 2

The frequency factor, b = 1

The horizontal shift, h = 0

The vertical shift, k = 1

The points in the interval 0 ≤ x < 2·π, where the sine of the angle is a maximum is; x = π/2, such that we get; sin(π/2) = 1

The points in the interval 0 ≤ x < 2·π, where the sine of the angle is a minimum is; x = 3·π/2, such that we get; sin(3·π/2) = -1

Therefore; Maximum value is;2 × sin(π/2) + 1 = 3 at the point x = π/2

Minimum value is; 2 × sin(3·π/2) + 1 = -1, at the point x = 3·π/2

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Answer: If the area of the square is 144 sq. meter, then the side is 12 meters long. 

Step-by-step explanation:

:P

Emily won the race by reaching the finish line at the same time as John or possibly even earlier.

To determine who won the race and by how many seconds, we can analyze the data provided in John's run.

From the table, we can see that John's time intervals are 4 seconds, 6 seconds, 8 seconds, and 10 seconds. The corresponding distances covered by John at these time intervals are 35 meters, 47.5 meters, 60 meters, and 72.5 meters, respectively.

Now, let's consider Emily's run, taking into account that she gave John a 10-meter head start. This means that Emily's distance covered at each time interval will be 10 meters less than John's distance.

Comparing their distances, we have:

At 4 seconds, John's distance is 35 meters. Therefore, Emily's distance is 35 - 10 = 25 meters.

At 6 seconds, John's distance is 47.5 meters. Therefore, Emily's distance is 47.5 - 10 = 37.5 meters.

At 8 seconds, John's distance is 60 meters. Therefore, Emily's distance is 60 - 10 = 50 meters.

At 10 seconds, John's distance is 72.5 meters. Therefore, Emily's distance is 72.5 - 10 = 62.5 meters.

Now, let's compare their times. Emily's time intervals are the same as John's since they both ran the same race:

At 4 seconds, John covered 35 meters while Emily covered 25 meters.

At 6 seconds, John covered 47.5 meters while Emily covered 37.5 meters.

At 8 seconds, John covered 60 meters while Emily covered 50 meters.

At 10 seconds, John covered 72.5 meters while Emily covered 62.5 meters.

By analyzing their distances and times, we can conclude that Emily won the race. To determine the time difference, we can subtract Emily's time from John's time at each interval:

At 4 seconds, John's time is 4 seconds and Emily's time is also 4 seconds. The time difference is 4 - 4 = 0 seconds.

At 6 seconds, John's time is 6 seconds and Emily's time is 6 seconds. The time difference is 6 - 6 = 0 seconds.

At 8 seconds, John's time is 8 seconds and Emily's time is 8 seconds. The time difference is 8 - 8 = 0 seconds.

At 10 seconds, John's time is 10 seconds and Emily's time is 10 seconds. The time difference is 10 - 10 = 0 seconds.

Therefore, Emily won the race by reaching the finish line at the same time as John or possibly even earlier.

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Question

Emily and John each ran at a constant speed for a 100-meter race. Emily gave John a 10-meter head start. Use the given data below to determine who won the race and by how many seconds

John’s Run

A 2-column table with 4 rows. Column 1 is labeled Time (seconds) with entries 4, 6, 8, 10. Column 2 is labeled Distance (meters) with entries 35, 47.5, 60, 72.5.

Step-by-step explanation:

Area of equalaterial triangle is 1/2bh

Here the base is 7.

The height is 4.2

[tex] \frac{1}{2} (7)(4.2) = 14.7[/tex]

Answer:

a) sum

b) shorter

c) longest

Step-by-step explanation:

a) sum

b) shorter

c) longest

a) The graph of the function represents an exponential decay.

b) The numeric values are given as follows:

An exponential function has the definition presented according to the equation as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The function for this problem is given as follows:

[tex]f(x) = 0.3^x[/tex]

The parameters for this problem are given as follows:

a = 1, b = 0.3.

The numeric values are given as follows:

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The experimental probability of members of Chris's class ending up with heads is about 3/5 or 0.6 (60%).

The experimental probability is one that can be calculated by:

dividing the number of favorable outcomes (the number of heads) by the total number of outcomes (the total number of students).

So, the number of heads recorded was 18, and the total number of students was 30.

Experimental probability = Number of heads / Total number of students

= 18 / 30

So one can simplify the fraction by:

Experimental probability = 3 / 5

Therefore, the experimental probability of members of Chris's class ending up with heads is 3/5 .

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The expression "the product of 4 and g score is 72" in algebraic notation is 4g = 72

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

The product of 4 and g score is 72

Represent the number with g

So the statement can be rewritten as follows:

the product of 4 and g is 72

So, we have the following

4g is 72

"is" means =

So, we have

4g = 72

Hence, the expression "the product of 4 and g score is 72" in algebraic notation is 4g = 72

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This statement follows from the fact that m∠4 + m∠6 = 180°. The statement that completes the proof is C. ∠4 and ∠7 are supplementary.

To complete the proof, let's analyze the given statements and reasons:

m ∥ n (Given) - This statement establishes that lines m and n are parallel.

m∠6 = m∠7 (Vertical angles theorem) - When two lines intersect, the vertical angles formed are congruent.

? (Same-side interior angles theorem) - This step is missing in the given proof. To prove that ∠4 and ∠6 are supplementary, we need to use the same-side interior angles theorem.

The same-side interior angles theorem states that when two parallel lines are intersected by a transversal, the interior angles on the same side of the transversal are supplementary. In this case, lines m and n are parallel, and the transversal is the line that intersects them.

To complete the proof, we can include the missing statement:

∠4 and ∠6 are interior angles on the same side of the transversal (Same-side interior angles theorem).

Now, we can continue with the remaining steps of the proof:

m∠4 + m∠7 = 180° (Definition of supplementary angles) - Supplementary angles add up to 180 degrees.

m∠4 + m∠6 = 180° (Substitution property of equality) - We substitute ∠7 with ∠6 since they are congruent.

∠4 and ∠6 are supplementary (Definition of supplementary angles) - This statement follows from the fact that m∠4 + m∠6 = 180°.

Therefore, the statement that completes the proof is:

C. ∠4 and ∠7 are supplementary.

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