Based on the illustration, what is the relationship between angle 1 and angle 3?

1. They are complementary.

2. They are congruent angles.

3. They are supplementary.

4. They form a right angle.

The answers are as follow

1. ∠a and ∠b are supplementary angles, ∠b and ∠c are supplementary angles: given

2. m∠a + m∠b = 180, m∠b + m∠c = 180 : definition of supplementary angles

3. m∠a + m∠b = m∠b + m∠c : substitution property of equality

4. m∠a = m∠c: subtraction property of equality

5. ∠a ≅ ∠c: if two angles have the same measure, then they are congruent.

The proof is shown below:

Congruence in two or more triangles depends on the measurements of their sides and angles. The three sides of a triangle determine its size and the three angles of a triangle determine its shape. Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal. They are of the same shape and size.

Two triangles are said to be congruent if they are of the same size and same shape. Necessarily, not all the six corresponding elements of both the triangles must be found to determine that they are congruent. Based on studies and experiments, there are 5 conditions for two triangles to be congruent. They are SSS, SAS, ASA, AAS, and RHS congruence properties.

Given that:

∠A and ∠B are supplementary angles, ∠B and ∠C are supplementary angles

So,  ∠A + ∠B = 180,

∠B + ∠ C= 180 b  (supplementary angles)

∠A + ∠B = ∠B + ∠C

∠A = ∠C

Hence,  ∠A ≅ ∠C (if two angles have the same measure, then they are congruent).

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Answer:

The answer would be 250.

Step-by-step explanation:

Cindy started off with 250 lollipops, gave away 30 (which is 12% of 250) and stayed with 220.

250-30=220

if I say 5/8 in in Magna to take to make a desk magnet

i.e 5/8 magnet require= to make 1 desk magnet

Thus,

We need to find the number of desk magnet can make with the help of 12 1/2 magnet tape

9514 1404 393

Answer:

  2.5 hours

Step-by-step explanation:

The price of stock A is described by ...

  A = 14.63 + 0.09t . . . . . . where t is time in hours after 9 A.M.

And the price of stock B is ...

  B = 15.13 - 0.11t

The two prices will be equal when ...

  A = B

  14.63 +0.09t = 15.13 -0.11t

  0.20t = 0.50 . . . . . . . . . . . . . add 0.11t -14.63 to both sides

  t = 0.50/0.20 = 2.5

The prices of the two stocks will be the same in about 2.5 hours.

The amount to be at $6500, and the time it will take is about 6 years and 4 months.

Compound interest is computed as interest on the principle of an account plus any accrued interest.

Compound interest can be calculated using the following formula:

x = P (1+r/n\()^{nt}\)

,where x = compound interest

P = principal (the initial deposit or loan amount)

r = annual interest rate

n = the number of compounding periods per unit of time

t = the number of time units the money is invested or borrowed for

Given:

Tony deposited 5000 dollars into an account with a 4.2 percent annual interest rate compounded semi-annually.

First, convert R as a percent to r as a decimal

r = R/100

r = 4.2/100

r = 0.042 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(6,500.00/5,000.00) / ( 2 × [ln(1 + 0.042/2)] )

t = ln(6,500.00/5,000.00) / ( 2 × [ln(1 + 0.021)] )

t = 6.312 years

Therefore, t = about 6 years 4 months.

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In summary, the difference between these two regression equations is mainly in the notation used to represent the regression coefficients, with lowercase letters used in simple linear regression models and uppercase letters used in multiple linear regression models.

In mathematics, an equation is a statement that asserts that two mathematical expressions are equal to each other. It usually contains one or more variables, which are placeholders for values that can vary. Equations are used to describe mathematical relationships and to solve problems. They can take many forms, such as linear equations, quadratic equations, polynomial equations, exponential equations, and so on. The specific form of an equation depends on the type of problem being solved and the mathematical relationships involved.

Here,

Both the regression equations ^y = b0 + b1x and Y = B0 + B1x are used to model the relationship between a dependent variable (y or Y) and an independent variable (x). However, the key difference between these two equations lies in the notation used to represent the regression coefficients.

In the first equation ^y = b0 + b1x, the regression coefficients are represented with lowercase letters (b0 and b1). This notation is typically used in simple linear regression models where there is only one independent variable. The hat symbol (^) over the y indicates that this is an estimated value of y based on the model.

In the second equation Y = B0 + B1x, the regression coefficients are represented with uppercase letters (B0 and B1). This notation is typically used in multiple linear regression models where there are two or more independent variables. The capitalization of the letters helps to distinguish them from the coefficients in the simple linear regression model.

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Answer:

5437

Step-by-step explanation:

Subtract the original amount 6,719 and 1282

you get 5,437

Hope this helps!

Have a nice day! :D

Mark brainliest if possible pls :)

Answer:

$13.5

Step-by-step explanation:

l= P×R×T/100

I= 12,500×9×12/100

l= $13,5

The interest earned for his investment after 12 years is $13,500.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Given that, P=$12,500, rate of interest=9% and time period=12 years.

Here, simple interest = (12500×9×12)/100

= 1350000/100

= 13,500

So, the interest is $13,500

Therefore, the interest earned for his investment after 12 years is $13,500.

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Answer:

2x + 12

Step-by-step explanation:

2(x + 6) =

2(x) + 2(6) =

2x + 12

Hope that helps!

Answer:

2x+12 by distributing

2x=-12

x=-6

i think the answer is 9

Step-by-step explanation:

step 1. simplify both sides of the equation

step 2. add 17 to both sides

step 3. multiply both sides by 3

answer a =9

The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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Answer:

Step-by-step explanation:

One sentence on globalization from the text: The process of globalization has brought significant changes to the world economy, including the emergence of new trade patterns and the increasing interconnectedness of markets.

One sentence on how the absence of plantation owners perpetuated cruel treatment of slaves by overseers: In the absence of plantation owners, overseers were left with unchecked power over the enslaved population, often resulting in brutal treatment and violence

here is the answer please mark me bainliest

The expand form will be;

⇒ 28x² - 44x

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 4x (7x - 11)

Now,

Solve the expression as;

⇒ 4x (7x - 11)

⇒ 4x × 7x - 4x × 11

⇒ 28x² - 44x

Thus, The expand form will be;

⇒ 28x² - 44x

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The box plot shows the distribution of the data classified in quartiles.

If we want to know about the mean of the data set, we can only that it will be located within the range of the data set.

It will be closer to the median as the distribution gets less skewed.

By looking at the box plot, we can not confirm that April's mean is higher than October's mean, as the plots are overlapped.

We can not also concluded about the relation between the spread of the data and the relation with the mean.

Then, the most appropiate conclusion from the options is "There is no way of telling what the means are".

Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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Answer: 36/12 = 3

Step-by-step explanation:

Answer:

The expression should be something like: 36/12

The equation we can use to find x is:

\(x^{2}\) + \(86^{2}\) = \(100^{2}\)

We can use the Pythagorean theorem to find x. In the sketch, the ladder, the ground, and the building form a right triangle. The vertical leg of the triangle is the height of the building, which is 86 ft. The horizontal leg is the distance we want to find, which is x ft. The length of the ladder is the hypotenuse of the triangle, which is 100 ft. Therefore, we have:

\(x^{2}\) + \(86^{2}\) = \(100^{2}\)

Simplifying and solving for x, we get:

\(x^{2}\) + 7396 = 10000

\(x^{2}\) = 2604

x ≈ 51

Therefore, the equation we can use to find x is:

\(x^{2}\) + \(86^{2}\) = \(100^{2}\)

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The blank spaces in the statements area. S, R, and Q  are distinct points that are collinear: b. TX and QS are distinct lines that intersect. c. Point Y and line QS are coplanar. d. Another name for plane P is: plane QSY.

Points that lie on the same straight line are collinear points.

If two lines are lie on the same plane, they are referred to as coplanar lines.

(a.) S, R, and Q are on a straight line. Therefore S, R, and Q  are distinct points that are collinear.

b. TX and QS are distinct lines that intersect.

c. Point Y and line QS are on the same plane. Therefore:

Point Y and line QS are coplanar.

d. Another name for plane P is: plane QSY.

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Answer:

6n+2

Step-by-step explanation:

9514 1404 393

Answer:

  (A)  1 only

Step-by-step explanation:

Factor numerator and denominator and see what cancels.

  \(f(x)=\dfrac{2x^2+14x-16}{x^2-9x+8}=\dfrac{2(x-1)(x+8)}{(x-1)(x-8)}=\dfrac{x-1}{x-1}\cdot\dfrac{2(x+8)}{x-8}\\\\f(x)=\dfrac{2x+16}{x-8}\qquad x\ne1\)

The factor of x-1 in the original denominator means the expression is undefined at x=1. The reduced expression is defined there, so the discontinuity at x=1 could be removed by defining f(1) = -18/7.

There is a removable discontinuity at x=1 only. The discontinuity at x=8 is a vertical asymptote where the function changes sign. It cannot be removed by defining a value for the function there.

If an object hits the ground with a velocity of 25.7 meters per second, it was dropped from a height of 33.7 meter .

In the question ,

it is given that

the when the object is dropped from height h then the velocity with which it hits the ground is given by the formula

v = √(19.6×h)

to find the height it was dropped , and it hits the ground with velocity 25.7 meter per second ,

we substitute v = 25.7 in the equation v = √(19.6×h) ,

we get ,

25.7 = √(19.6×h)

squaring both the sides , we get

19.6 × h = 25.7²

19.6 × h = 660.49

h = 660.49/19.6

h = 33.698

h ≈ 33.7

Therefore ,If an object hits the ground with a velocity of 25.7 meters per second, it was dropped from a height of 33.7 meter .

The given question is incomplete , the complete question is

Suppose that an object is dropped from a height of h meters and hits the ground with a velocity of v meters per second. Then v = √(19.6×h) . If an object hits the ground with a velocity of 25.7 meters per second, from what height was it dropped?

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Answer:

Train B travels faster

Step-by-step explanation:

See attachment for complete question

Since both trains are travelling at constant speed, we can pick any non zero equivalents of distance and time to calculate the rate at which they both travel.

For Train A

\(Distance = 12.5m\)

\(Time = 1s\)

\(Rate = Distance/Time\)

\(Rate = 12.5m/1s\)

\(Rate = 12.5m/s\)

For Train B

\(Distance = 100m\)

\(Time = 4s\)

\(Rate = Distance/Time\)

\(Rate = 100m/4s\)

\(Rate = 25m/s\)

By comparison:

\(25m/s > 12.5m/s\)

Hence,

Train B travels faster

The missing statement in the proof specified is given by: Option B: ∠BCA≅∠DCB

What is the reflexive property of congruence?

According to the reflexive feature of congruence, the geometric quantity under consideration—be it an angle, a line segment, a form, etc.—is congruent to itself.

The third step's key concept in this instance is the "Reflexive Property of Congruence."

The fourth phase comes to the conclusion that the ΔABC~ΔBDC criteria for similarity are met.

Since it was established in the second stage that ∠ABC≅∠BDC

Therefore, in order for the fourth step to apply angle-angle similarity, which requires the angles of two considered triangles to be congruent, we must demonstrate another angle pair of triangles ΔABC and ΔBDC being congruent in the third step.

Internal angle C is the common angle in the triangles ABC and BDC.

As a result, it is consistent with itself due to its reflexive characteristic.

We obtain the following notation for internal angle C from triangle ABC:

Angle ACB and BCA(both will work)

Triangle BDC gives us the following notation for internal angle C:

Angle DCB and BCD(Both will function.)

They fit together. The second choice takes angle C into account, so:

∠BCA≅∠DCB (second option) is the missing statement.

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Answer:

(2x+1)^2 or 4x^2+4x+1

Step-by-step explanation:

I'm going to assume you need to find f(g(x)) when f(x)=x^2 and g(x)=2x+1

You first need to find g(x) which is 2x+1

You then take the f(x) function and replace x with 2x+1

This means our new equation is

(2x+1)^2

Your teacher may or may not want you stop here, really only you know the answer to that

But if we expand this we'll find that (2x+1)^2=4x^2+4x+1

The equivalent expression of (f o g) is 4x² + 4x + 1.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Two functions are given.

f(x) = x²

g(x) - 2x + 1

Now,

(f o g)(x) = f(g(x))

g(x) - 2x + 1

So,

f(g(x)) = f(2x + 1)

Now,

f(2x + 1)

= (2x + 1)²

= 4x² + 4x + 1

Thus,

The expression of (f o g) is 4x² + 4x + 1.

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Answer:

22 weeks

Step-by-step explanation:

it is 22 weeks because if you divide 39 by 2 then it is 19.5 and if you divide 429 by 19.5 you will get 22 hope this helps.

The equation can you use to find the rental cost, d, of each day they used the RV is 895=8d+55

What does $895 comprises of?

The $895 paid  for the duration of the trip consists of the payments for the RV for 8 days and additional amount of $55 which is for the outdoors upgrade.

The equation that can be used to determine rental cost per , d , per day considers that the total rental cost is number of days, 8 days  multiply by the rental  cost per day, which is d, and also that the final $55 is specifically for outdoors upgrade

Total cost=d*8+$55

Remember total cost of the trip is $895

$895=8d+$55

Which we can rewrite the expression by ignoring the dollar sign as below:

895=8d+55

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The constant of proportionality is 5/2. The correct options are C and E.

The constant of proportionality, k, can be defined as the ratio of y to x, if x is the independent variable and y is the dependent variable and they are both in a proportional relationship.

This means that:

Constant of proportionality (k) = y/x.

Using the graph given, the value of k can be calculated using a point on the line, (2, 5):

Constant of proportionality (k) = y/x = 5/2 [this is also 2.5]

If a museum charges $2.50 per each student, then it means the constant of proportionality, k = 5/2.

Therefore, the correct options are: C and E.

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The conditional statement has a false converse will be the four-sided polygon may be square. Then the correct option is A.

There have been two main categories of arguments in the studies of logic: conditional statements and polyamorous statements. These assertions, which are referred to as compound statements, are created by combining two other statements.

The converse statement should also be true when its condition is reversed.

Let's check all the options. Then we have

A.  If a figure is a square, then it has four sides. The converse of the statement is false.

B.  If a point has an x-coordinate 0, then it lies on the y-axis. The converse of the statement is true.

C.  If two angles are congruent, then they have the same measure. The converse of the statement is true.

D.  If two planes are parallel, then they have no points in common. The converse of the statement is true.

The conditional statement has a false converse will be the four-sided polygon may be square. Then the correct option is A.

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The true statement about the graphed function is:

F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).

Looking at it's graph, we have that:

Researching this problem on the internet and looking at the graph of the function, the correct statement is given by:

F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).

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