What is the area of the trapezoid shown below?

Answer:

y = 2x + 1

Step-by-step explanation:

From the table attached,

x          y            Difference [tex][d=(y_2-y_1)][/tex]

-1         -1                   -

0          1              1 - (-1) = 2

1           3             3 - 1 = 2    

2          5             5 - 3 = 2

Since,there is a common difference 'd' = 2

Therefore, this table represents a linear equation.

Let the equation is,

y = mx + b

where 'm' is the slope and 'b' is the y-intercept.

Two points lying on the linear equation are (-1, -1) and (0, 1)

Slope 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{1+1}{0+1}[/tex]

m = 2

And y-intercept 'b' = 1 unit

Therefore, equation of the line will be,

y = 2x + 1

Answer:

Step-by-step explanation:

It is not perfectly linear because the difference between the y values is not constant. However, when you use the regression function on your calculator and enter the L1 values as your x's and the L2 values as your y's and use the LinReg equation, you get an r-squared value of .999900 and an r value of .999950. So it linear, with your answer being "linear, because the r value for the linear model is closest to 1".

In this question, we have two columns, you giving the time and the other the distance. We have to identify it the relationship is linear or exponential.

First, I am going to explain when we have a linear relation and when we have an exponential relation, then we observe the data and solve this question, getting the following correct answer:

linear, because the r value for the linear model is closest to 1

Linear and exponential data:

If the absolute value of the change assume close values, it is linear.

If the rates are, it is exponential.

Data:

t = 1 -> d = 530

t = 2 -> d = 1050

t = 3 -> d = 1600

t = 4 -> d = 2110

t = 5 -> d = 2650

Subtractions:

2650 - 2110 = 540

2110 - 1600 = 510

1600 - 1050 = 550

1050 - 530 = 520

Divisions(rates):

2650/2110 = 1.25

2110/1600 = 1.32

1600/1050 = 1.52

1050/530 = 1.98

The rates change considerably more than the subtractions, so it is linear relationship, and the correct option is:

linear, because the r value for the linear model is closest to 1.

For more on linear/exponential growths, you can check https://brainly.com/question/24282972

Answer:

[tex]b = \frac{(d-c)}{a}[/tex]

Step-by-step explanation:

ab + c = d

Subtract c from both sides

ab + c - c = d -c

         ab = d - c

Divide both sides by 'a'

[tex]\frac{ab}{a}=\frac{d-c}{a}\\\\b = \frac{(d-c)}{a}[/tex]

Answer:

b = (d - c)/a

Step-by-step explanation:

just took this test

Answer:

9.1 hours

Step-by-step explanation:

Given

Sally

Speed = 66mph

Keith

Speed = 75mph

Time = 8 hours

Required

Determine how long Sally has traveled

To solve this, we make use of Speed formula.

Speed = Distance/Time

Make Distance the subject of formula

Distance = Speed * Time

For Sally:[Substitute 66mph for speed]

Distance = 66 * Time ------ Equation 1

For Keith [Substitute 75mph for speed and 8 hours for Time]

Distance = 75 * 8

Distance = 600m----- Equation 2

From the question, we understand that Keith caught up; this implies that they've both traveled the same distance.

Hence;

Equation 1 = Equation 2

66 * Time = 600

Time = 600/66

Time = 9.1 hours

Hence, Sally has traveled 9.1 hours

you are correct. all angles (except central) are not equal (iff TU and CB are not parallel)

the triangles are not similar

Answer:

it's A

They don't give you enough information to determine if they are similar or not

Answer:

mean is adding up all the numbers.

range means the difference between the Lowest and highest value.

Step-by-step explanation:

when we add the answer is 240.6.

divide it to 12..do the final answer is 20.05

range is 25.4_16.3

9.1

Answer:

Mean: 20.05

Range: 9.1

Step-by-step explanation:

To find the mean in this problem, first you add all the following numbers together then subtract by the quantity.

20.1 + 19.6 + 18.0 + 17.8 + 25.2 + 18.7 + 21.9 + 16.3 + 25.4 + 20.5 +17.8 + 19.3

= 240.6

Now, divide by the quantity which is 12 since there's 12 numbers.

240.6 divided by 12 = 20.05.

The mean is 20.05.

To find the range in the problem, you must subtract the smallest value from the largest value.

In this case, 16.3 is the smallest value and 25.4 is the largest.

25.4 - 16.3 = 9.1

9.1 is the range.

Hope this helps you!

Answer:

54.528

Step-by-step explanation:

Answer:

4.10526315789

Step-by-step explanation:

Answer: 4.10526315789

Step-by-step explanation:

Answer: $10

Step-by-step explanation:

let x = the price of green fabric, then x+2 = blue fabric price

8x+5(x+2)=62

8x+5x+10=62

    13x+10=62

          13x=52

              x=4

price of green fabric=$4

price of blue fabric=$6

4+6=$10

Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

You don't get a free answer. I am, after all, a high school math teacher, so there has to be a lesson in with this.

The discriminant is part of the quadratic formula. It is:

[tex]b^2-4ac[/tex]. If this value is found to be > 0 and a perfect square, there are 2 real roots; if this value is found to >0 and not a perfect square, there are 2 complex roots; if this value is found to be = 0, then there is 1 real root with a multiplicity of 2; and finally, if this value is found to be < 0, then there are 2 imaginary roots. Also, it would help to know that, because we are dealing with the discriminant, which comes from the quadratic formula, and quadratics, by definition, have 2 solutions, you must have 2 solutions listed as the possible roots for the equation. Our equation is:

[tex]-4x^2=-8-10x[/tex] but in order to determine the a, b, and c for the discriminant, that equation has to be in standard form, set equal to 0:

[tex]-4x^2+10x+8=0[/tex]

From this we can see that a = -4, b = 10, and c = 8. Filling in the discriminant:

[tex]10^2-4(-4)(8)[/tex] which gives us a value of

100 - [4(-4)(8)] (don't forget orders of operation here!)

100 - (-128) = 100 + 128 = 228

This value is greater than 0 but is not a perfect square, so there are 2 complex roots. That means that there will be radicals in the solutions.

Answer:

Step-by-step explanation:

You gave very clear instructions on how to draw this graph, so that's what I did. What you need to remember in particular with limits is that you do not care in the least what happens AT the x value of 2, only what happens as it is being approached. Because we are asked the limit as x is approaching from the left and the right, this is a one-sided limit question. In order for the limit to exist as x approaches 2 (NOT from the left or the right), the limit would have to agree from the left and the right, and this one doesn't. Having said that there is "a horizontal line crossing the y-axis at 5 that ends at the open point (2, 5)..." is a limit approaching x from the left. Therefore,

[tex]\lim_{x \to 2^-} f(x)=5[/tex]

Having also said there is "...another horizontal line starting at the open point (2, -3) and continues to the right..." is a limit approaching x from the right. Therefore,

[tex]\lim_{x \to 2^+} f(x)= -3[/tex]

The closed point at (2, 1) is where x IS, and remember that we don't care about what happens AT x. So disregard this point in limits.

Answer:

Row 10 and in column F

Step-by-step explanation:

rows 1 and 3 are decreasing and we are looking for an increase so we can cross those out immediately.

However we do see a pattern in rows 2 to 4 (add 8) so if we add 8 for 3 more rows than we get 37 but add 8 more and we get 45.

from 37 to 43 is 6 more than 37 so we have 4 columns but if we add 3 more we get the 6 columns also column f.

Hope this helps!

Answer:

D: 4x² - 4x + 1

Step-by-step explanation:

(2x - 1) ( 2x - 1)

4x² - 2x - 2x + 1

4x² - 4x + 1

The correct answer is d) 4x2 - 4x + 1.

The area of a square is found by squaring the side length:

(2x-1)? = (2x-1)(2x-1) = 2x*2x - 2x*1 - 2x*1 - = 1(-1) = 4 x 2 - 2x - 2x + 1 = 4x2-4x+1

Answer:

see below

Step-by-step explanation:

3, 12, 48, 192

We are multiplying by 4 each time  (12/3 =4)

The 5th term

192 *4 =768

The 6th term

768 *4 =3072

The th term

3072 *4 =12288

To find the common ratio, take the second term and divide by the first

2/4 = 1/2

The common ratio is 1/2

Problem 1

---------------------------

Explanation:

The first term is a = 3 and the common ratio or multiplier is r = 4. We start with 3 and multiply each term by 4 to get the next one. The nth term of this geometric sequence is

a(n) = a*(r)^(n-1)

a(n) = 3*(4)^(n-1)

Plug in n = 7 to get the seventh term

a(7) = 3*(4)^(7-1)

a(7) = 3*(4)^6

a(7) = 3*4096

a(7) = 12288

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

Problem 2

----------------------

Explanation:

To find the common ratio, we pick any term but the first one and divide it over its previous term

r = common ratio

r = (second term)/(first term) = 2/4 = 1/2 = 0.5

r = (third term)/(second term) = 1/2 = 0.5

r = (fourth term)/(third term) = 0.5/1 = 0.5

Each term is cut in half to get the next one.

Answer:

Perimeter = 32 meters

Step-by-step explanation:

1 meter = 1m = 100 cm = 100 centimeters

400cm = 400/100 = 4 meters

Rectangle Perimeter = 2(legth + width)

                                   = 2(12 + 4)

                                   = 2*16

                                    = 32 meters

Answer:

Problem 1)  frequency:  160 heartbeats per minute, period= 0.00625 minutes (or 0.375 seconds)

Problem 2) Runner B has the smallest period

Problem 3) The sound propagates faster via a solid than via air, then the sound of the train will arrive faster via the rails.

Step-by-step explanation:

The frequency of the football player is 160 heartbeats per minute.

The period is (using the equation you showed above):

[tex]Period = \frac{1}{frequency} = \frac{1}{160} \,minutes= 0.00625\,\,minutes = 0.375\,\,seconds[/tex]

second problem:

Runner A does 200 loops in 60 minutes so his frequency is:

[tex]\frac{200}{60} = \frac{10}{3} \approx 3.33[/tex]   loops per minute

then the period is: 0.3 minutes (does one loop in 0.3 minutes)

the other runner does 200 loops in 65 minutes, so his frequency is:

[tex]\frac{200}{65} = \frac{40}{13} \approx 3.08[/tex]   loops per minute

then the period is:

[tex]\frac{13}{40} =0.325\,\,\,minutes[/tex]

Therefore runner B has the smaller period

Answer:

C. C only

Step-by-step explanation:

Well to determine if the given graphs are functions we need to do the vertical line test to all the graphs,

A. This fails the vertical line test because the vertical line could pass through 2 points on the lines.

B. this also fails because a vertical line could pass through 2 points.

C. This passes because the vertical line doesn’t touch 2 points.

Answer:

$60

Step-by-step explanation:

Answer:

60$

Step-by-step explanation:

3 gallons per hr

multiply by 4

12gl  per 4hrs

5 dl per gl

multiply by 12

60 dl per 12 gl

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

   ✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                  PEACE!

Answer:

1.) P = 8g + 50

2.) Find the attached file for the graph.

Step-by-step explanation:

Let the profit = P

And g = good sold.

Given that each yo-yo sells for $8.00

The rate or the slope of the equation will be 8

Also, it is given that they must pay a clerk $50.00 a day to sell them. A flat rate of 50 dollars is an intercept of the equation.

Using the general linear equation of

Y = mX + C

The equation for the profit the store will make in a day will be.

P = 8g + 50

Please find the attached file for the graph

Answer:

5x^2 +24x +1

Step-by-step explanation:

First you'll want to find the area of the larger rectangle, and then you'll subtract the area of the smaller rectangle (which is not shaded) to get your answer.

Larger Rectangle:

A = length * width

A = (2x + 3)(4x - 5) = (8x^2 - 10x + 12x - 15) = 8x^2 + 2x - 15

Smaller Rectangle:

A = length * width

A = (x - 8)(3x + 2) = (3x^2 + 2x - 24x - 16) = 3x^2 - 22x - 16

Larger Rectangle minus Smaller Rectangle:

(8x^2 + 2x - 15) - (3x^2 - 22x - 16)

5x^2 +24x +1

Answer:

Its usual speed is 25 kilometre/hour

Step-by-step explanation:

Let the usual  time duration for a journey of 300 km. = t

Let the usual speed = v

The parameters given are;

The time duration for the 300 km. journey at increased speed = t - 2

The increased speed of the passenger train = v + 5

Distance, d = Speed, v × Time, t

Therefore, we have;

v × t = 300

∴ t = 300/v

Also (v + 5)×(t - 2) = 300

Substituting the value of t = 300/v, we have;

(v + 5)×(300/v - 2) = 300

[tex]- \dfrac{2 \cdot v^2 - 290 \cdot v - 1500}{v} = 300[/tex]

Which gives;

2·v² + 10·v - 1500 = 0

Which is equivalent to v² + 5·v - 750 = 0

Therefore we have;

(v + 30)·(v - 25) = 0  whereby v = -35 or 25 km/h

v = Natural number = 25 km/hour

Therefore its usual speed is 25 kilometre/hour.

THIS IS THE COMPLETE QUESTION BELOW;

Rosemary walks each week for exercise. Let d represent the distance walked and h represent the number of hours spent walking.

Last week: walked 18 miles in 6 hours

This week: d = 2.5h

Which statement must be true?

A.This week, she walked a greater distance.

B. Last week, she walked a greater distance

C. This week, she walked at a faster pace.

D. Last week, she walked at a faster pace

Answer

OPTION B is correct

B)Last week, she walked a greater distance

Step-by-step explanation:

We were told Rosemary walks each week for exercise.

From the question,

✓d represented the distance walked

✓h represent the number of hours spent walking.

A)Last week: she walked 18 miles in 6 hours

Then, if she walks 18 miles in 6 hours, we can be expressed as (18miles/6hour)

= 3 miles per hour

B)This week: d = 2.5h

This implies that she she walked 2.5 miles per hour this week since the distance is expressed in miles and time in hours.

So we can conclude that last week she walked 3 miles per hour which is more greater than 2.5 miles per hour which she walks this week.

Therefore, OPTION B is correct, (Last week, she walked a greater distance)

Answer:

It's b

Step-by-step explanation:

Answer:

The graph will shift 9 units to the right

Sorry about my hand writing

Answer: It moves 9 units to the right

Step-by-step explanation:

It moves 9 units to the right is because if it's inside parentheses it moves right/left instead of up/down. I also talked to my Algebra Teacher about it and got it right in the final test.

Answer:

E) 45

Step-by-step explanation:

Since b is 90 degrees, and lines CB and BA are equal (as seeen with the 2 lines across them) we can assume that this angle is 45 degrees, half or 90 degrees.

Angle C is also equal to angle A

Answer:

E

Step-by-step explanation:

Using the fact that the sum of angles in a triangle is 180 degrees, we can write the following equation to solve for 3x:

3x + 3x + 90 = 180

3x + 3x = 90

2 * 3x = 90

3x = 45°

Answer:

a is 15, b is 15, c is -15, and d is -15 also

Step-by-step explanation:

The 2 parallel lines that surround the number are called "absolute value signs" everything inside them has an outcome of a positive number and in this case the number is 15. Like I said the number(s) inside the absolute value signs have to have a outcome of a positive number, notice in c and d there is a negative sign outside the absolute value signs. Therefore you multiply the negative seperately so, 15(-1) is -15.

Answer:

a) 148.52

Step-by-step explanation:

If sum of two angles is 180, then they are supplementary

Ratio = 10 : 47

Smaller angle = 10x

Larger angle = 47x

10x + 47x = 180

57x = 180

Divide  both sides by 57

x = 180/57

x = 3.16

Larger angle = 47x = 47 * 3.16 = 148.52

Step-by-step explanation:

theanswer is 64 degrees

Answer:

Step-by-step explanation:

The shape could be divided into a rectangle and a trapezoid ( bottom part )

Let's find the area of the given shape:

Area of the given shape = [tex] \mathsf{ (l \times b) + \frac{1}{2} (b1 + b2)h}[/tex]

plug the values

[tex] \mathsf{ = (3.5 \times 9) + \frac{1}{2} (9 +9 - (5 + 2) \times 2}[/tex]

[tex] \mathsf{ = (3.5 \times 9) + \frac{1}{2} (9 + 2)(2)}[/tex]

[tex] \mathsf{ = 31.5 + \frac{1}{2} \times 11 \times 2}[/tex]

[tex] \mathsf{ = 31.5 + 11}[/tex]

[tex] \mathsf{ = 42.5 \: {units}^{2} }[/tex]

Hope I helped!

Best regards!

Answer:

Yes

Step-by-step explanation:

Answer:

y < -4

Step-by-step explanation:

-5y+6>26

subtract 6 from each side

-5y+6-6>26-6

-5y > 20

Divide each side by -5. remembering to flip the inequality

-5y/-5 < 20/-5

y < -4