Using diagonals from a common vertex, how many triangles could be formed from a
16-gon?

Answer:

6x^2 + 23x + 21

Step-by-step explanation:

3x+7 x 2x+3

= 3x(2x) + 3x(3) + 7(2x) + 7(3)

= 6x^2 + 9x + 14x + 21

= 6x^2 + 23x + 21

Answer: $227,226.51

Step-by-step explanation:

First, we need to convert the period to weeks.

9 1/2 years = 9.5 years

1 year = 52 weeks

9.5 years = 494 weeks

Next, we can use the formula for the future value of an annuity:

FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)

where:

PMT = payment amount per period

r = annual interest rate

n = number of compounding periods per year

t = number of years

Plugging in the given values:

PMT = $300

r = 0.055 (5.5% expressed as a decimal)

n = 52 (compounded weekly)

t = 9.5 years = 494 weeks

FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)

FV = $227,226.51

Therefore, the future value of the annuity is approximately $227,226.51.

a. Constant speed, C =  0. 19 miles/minutes

b. The fraction representing her constant speed is  1/x miles/minutes

c. The time it takes her to drive exactly 1 mile is 5. 38 minutes

The formula for calculating constant speed is expressed as;

Constant speed = total distance covered/ total time taken

From the information given, we have that;

Now, substitute the values into the formula

Constant speed = 1. 3 / 7

Divide the values

Constant speed = 0. 19 miles/minutes

When distance 1 mile, time taken = x minutes

Constant speed = 1/x miles/minutes

If 1. 3 miles = 7 minutes

Then, 1 mile = x

cross multiply

x = 7/1. 3

x = 5. 38 minutes

Hence, the constant speed is 0. 19 miles/minutes

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Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Using proportions, it is found that due to the smaller division of the exchange rate by the cost, the souvenir would be less expensive in Egypt.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The souvenir would be less expensive in the country in which the division of the exchange rate by the cost is smaller.

In Britain, the cost is of 17, with an exchange rate of 0.83, hence the cost in US dollars is:

c = 17/0.83 = $20.48.

In Egypt, the cost is of 288, with an exchange rate of 18, hence the cost in US dollars is:

c = 288/18 = $16.

16 < 20.48, hence the souvenir would be less expensive in Egypt.

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Pairs of congruent angles are angle IRF and angle MRN and angle QRT and angle QRU. Option A and option B are correct.

What is the congruency of triangles?

Angles and the corresponding sides of another triangle are equal, then both triangles are said to be congruent.

In Δ PQR and ΔABC, as shown below, we can identify that;

PQ = AB, PR = AC, and QR = BC, and ∠P = ∠A, ∠Q = ∠B, and ∠R = ∠C. Then we can say that Δ PQR ≅ ΔABC.

Conditions of congruence in Triangles:

If two triangles are the same size and shape, they are said to be congruent. It is not necessary to locate all six corresponding elements of both triangles to determine that they are congruent. According to research and experiments, there are five prerequisites for two triangles to be congruent. SSS, SAS, ASA, AAS, and RHS congruence characteristics are among them.

We are given the following:

As per the diagram, those angles that split equally are congruent

Also, the angles in the square in the middle are 45 degrees each and the triangles are cut into equal parts which are congruent.

Thus, the pairs of congruent angles are angle IRF and angle MRN and angle QRT and angle QRU. Option A and option B are correct.

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A 1.5 standard deviations above the mean IQ score is 122.5.

An expression that depicts the relationship between two or more numbers and variables is called an equation.

A dependent variable is one that depends on another variable, whereas an independent variable does not depend on any other variable for its value.

Giving the z score are:

z is calculated as (raw score - mean) / standard deviation.

with a standard deviation of 15 and a mean of 100. The z-score of 1.5 is equal to the IQ score that is 1.5 standard deviations above the mean, so:

1.5 = (x - 100)/15

x = 122.5

A 1.5 standard deviations above the mean IQ score is 122.5.

The Complete Question is IQ score.

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Answer:

  x = 1

Step-by-step explanation:

You want to know the value of x in the trapezoid with adjacent angles (43x+2)° and 135°.

The two marked angles can be considered "consecutive interior angles" where a transversal crosses parallel lines. As such, they are supplementary.

  (43x +2)° +135° = 180°

  43x = 43 . . . . . . . . . . . . . . divide by °, subtract 137

  x = 1 . . . . . . . . . . . . . . . divide by 43

The value of x is 1.

__

Additional comment

Given that the figure is a trapezoid, we have to assume that the top and bottom horizontal lines are the parallel bases.

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Answer:

Step-by-step explanation:

6/10 or 3/5

The sketch for slope is attached below.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Point               Slopes

(1, 1)                     (a) 3

_                        (b) -3

_                        (c) -5/2

_                         (d) Undefined

a) Now, using slope intercept form

y - 1= 3 (x-1)

y- 1= 3x- 3

y= 3x - 2

(b) Equation of a line has a slope -3 is given by

y - 1= (-3) (x-1)

y-1 = 3- 3x

y = -3x + 4

(c) Equation of a line has a slope -5/2 is given by

y - 1= (-5/2) (x-1)

y-1 = -5/2x + 5/2

y= -5/2x + 7/2

(d) The line parallel to y axis and passes through given point : x=1

"undefined" means the line is vertical.

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Answer:

x= ( 0,1 )

Step-by-step explanation:

your graph it

\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the concept of Lines.

We know that perpendicular lines have a inverse negative slope, such that

m1*m2 = -1

hence, m1 = -1/m2

so the perpendicular line is,

==> y-(5) = 3/2(x-(-6))

==> y+5 = 3/2(x+6)

==> y+5 = 3/2*(x) +9

=> y = 3/2(x) +9-5

==> y = 3/2*(x) + 4

hence the correct option is D.)

The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

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

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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Answer:

the first

Step-by-step explanation:

becasue you have -4 and it drops by 5 each hour so your timing it by 5 so 5h then sinv=ce it drops its -5h.

Answer:

The answer should be B

Step-by-step explanation:

Answer:

Item price now= 3.95

Step-by-step explanation:

To find out the price now, we will subtract 79 (original price) by 95% of 75. That will equal the discounted price. Finding the percentage of anything, we can use the formula, Total amount•percentage/100. The total amount is 79, and the percentage is 95. 79•95=7505, 7505/100=75.05. Now, 95% of 79 is 75.05, 79-75.05=3.95. $3.95 is the price now of the item. Though, I am unsure what a ALEKS calculator is. Have a nuce time, and joyful day

Answer:

Step-by-step explanation:

Let the first integer be x and the second integer be y. If the first integer is 7 more than 2 times another, then x = 7+2y

The two integers will be y and 7+2y. If the product of both integers is 60, then;

y(7+2y) = 60

7y + 2y² = 60

2y² + 7y -60 = 0

2y²-8y+15y-60 = 0

2y(y-4)+15(y-4) = 0

(2y+15)(y-4) = 0

2y+15= 0 and y-4 = 0

2y = -15 and y = 4

y = -15/2 and 4

Taking the positive integer, y = 4

To get the other integer, we will substitute y = 4 into the equation x = 7+2y;

x = 7+2(4)

x = 7+8

x = 15

Hence the two integrs are 15 and 4

Answer:

f^-1(x) = log2(f^-1(x) – 1 + 3).

Step-by-step explanation:

The inverse of a function "f" is denoted as "f^-1", and it reverses the effect of the original function. In other words, if "f(x)" is a function that maps some input "x" to an output "y", then the inverse function "f^-1(x)" would map the output "y" back to the original input "x".

In this case, to find the inverse of the function f(x) = 2^x + 1 – 3, we can follow these steps:

Swap the roles of x and y in the original equation to obtain y = 2^x + 1 – 3.

Solve for x in terms of y to obtain x = log2(y – 1 + 3).

Replace y with the inverse function notation f^-1 to obtain f^-1(x) = log2(f^-1(x) – 1 + 3).

Therefore, the inverse of the given function f(x) = 2^x + 1 – 3 is f^-1(x) = log2(f^-1(x) – 1 + 3).

Answer:

8

Step-by-step explanation:

Let's take the first number as X.

Then,

X+2X+(2X-3)=37

5X=37+3

5X=40

X=40/5

X=8

First number=8

Answer:

Step-by-step explanation:

Based on the information provided, the residual plot makes sense based on the scatter plot.

In the given scatter plot, the points are plotted with horsepower on the x-axis and observed MPG (miles per gallon) on the y-axis. The scatter plot shows the relationship between horsepower and MPG for the motorcycles.

The residual plot, on the other hand, shows the differences between the observed MPG values and the predicted MPG values based on the regression line or model. Residuals represent the vertical distances between the observed data points and the regression line.

Looking at the residual plot, we can see that the residuals are scattered randomly around the zero line. Some residuals are positive, while others are negative, indicating that the observed MPG values deviate both above and below the predicted MPG values.

Given this information, option A is the correct answer: "The random residual plot makes sense because the scatter plot appears to have a linear relationship." The scatter plot does not necessarily suggest a positive or negative relationship between horsepower and MPG. It simply shows the general trend or pattern. The random distribution of residuals in the residual plot indicates that the regression model is capturing the relationship adequately, and the variations or deviations from the regression line are random, which is expected in a good regression model.

The residual plot created by Jorge does make sense as it reflects the negative relationship between horsepower and miles per gallon present in the original scatter plot. As the horsepower increases, the miles per gallon decreases which is depicted accurately in the residual plot made.

The best answer for this is B. The random residual plot makes sense because the scatter plot appears to have a negative relationship. A residual plot is a graph that is used to examine the goodness of fit in regression and ANOVA analysis. It is the differences between the observed and predicted values of data. The points in a residual plot are randomly dispersed around a horizontal axis if the corresponding regression model is appropriate for the data.

In this case, the scatter plot demonstrates a negative relationship between the horsepower of motorcycles and miles per gallon. As the horsepower increases, the miles per gallon decrease. This negative relationship is reflected in the pattern of residuals, which fluctuates around the zero line on the y-axis of the residual plot. Consequently, the random distribution of residuals on Jorge's plot does make sense given the scatter plot data.

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Answer:

B) c=25 +10p +5h

id expect 25 per night with the n variable next to it but i guessed not

, but one night would cost 25 but with the addition of 10 per person and 5 for every hour of a late checkout

Answer:

A

Step-by-step explanation:

C=25

25= How much she was Paid

p=People

1person is 10$

10$Was given in

10+

Late fee 5$

Then by there she gets Her 25

C=25-10p-5h

Each of the five friends needs to pay £14.40 to cover the cost of the birthday person's meal.

To calculate how much each of the five friends needs to pay, we can use the concept of averages or mean.

The total cost of the meal for 6 people is £12 per person. This means that the total cost of the meal is 6 * £12 = £72.

Since the other five friends have decided to pay for the birthday person's meal, they will evenly divide the total cost of £72 among themselves.

To find the average amount each friend needs to pay, we divide the total cost by the number of friends paying, which is 5:

£72 / 5 = £14.40

Using the concept of averaging or finding the mean allows us to distribute the cost equally among the friends, ensuring fairness in sharing the expenses.

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Adrian run in one hour is 5.698 km.

How to calculate speed, Distance and Time ?

Given,

Adrian ran in 1.5 hours = 8.547 km

We know, in 1.5 hours there is 90 minutes

so, in 1 min adrian ran = 8.547 / 90

                                    =  0.09496 km

We need to find the km in one hour means in 60 minutes

So, Adrian ran in 60 min = 60 * 0.09496

                                         =  5.6979 km or 5.698 km per hour

Hence, Adrian run in one hour is 5.698 km.

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the answer would be 0.56

Answer:

a: 0.0016

Step-by-step explanation:

Got it right on the test.

Hope this helps :)

Answer:

B

Step-by-step explanation:

given scale is 1 inch represents 7.5 feet

then we require to calculate how many 7.5 feet there are in each dimension.

to obtain this divide each dimension by 7.5, that is

13 ÷ 7.5 ≈ 1.73 ( to 2 decimal places )

26 ÷ 7.5 ≈ 3.47 ( to 2 decimal places )

then dimensions are approximately 1.73 inches by 3.47 inches

Answer:

Because all elements in set B can be found in set A

Answer:

"The slope and y-intercept values indicate characteristics of the relationship between the two variables x and y. The slope indicates the rate of change in y per unit change in x. The y-intercept indicates the y-value when the x-value is 0."

https://education.ti.com/html/t3_free_courses/calculus84_online/mod02/mod02_lesson3.html#:~:text=The%20slope%20and%20y%2Dintercept%20values%20indicate%20characteristics%20of%20the,the%20x%2Dvalue%20is%200.

Step-by-step explanation:

Answer:

\(\frac{28 + 6a}{a}\)

Step-by-step explanation: