The function a(b) relates the area of a trapezoid with a given height of 12 and
one base length of 9 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid.
2.b19
a(b)-12..
Which equation below represents the inverse function b(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
A. b(a)-2-9
B. b(a)-+9
OC. b(a)- +6
OD. b(a)-9-6

Answer:

Suppose that x is the length and y the width of the rectangle. Then we have 2x+2y=80 and x=y+4. Therefore, 2(y+4)+2y=80 or 4y+8=80 or 4y=72 or y=18 and x=22

Step-by-step explanation:

The volume of the cylinder is 275m³.

We have given that,

Lateral surface of cylinder = 220m²

Height (h) = 14m

Let radius of cylinder = r

Then 2πrh = 220m²

⇒ × 22/7 × r × 14 =  220m²

[tex]$ \Rightarrow \text r = \frac{220 \times 7}{2 \times 22\times 14}[/tex]

[tex]$ \Rightarrow \text r = \frac{220 \times 7}{2 \times 22\times 14}[/tex]

[tex]$ \Rightarrow \text r = \frac{5}{2} = 2.5[/tex]

Now we can find the volume,

Volume of cylinder = πr²h

= 22/7 × (2.5)² × 14

=  22 × 6.25 × 2

= 275m³

Thus, the volume of the cylinder is 275m³.

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The volume of the cylinder is 274.75 cubic meter.

All of the sides of the object are the lateral p of an object, except its base and top (when they exist). The lateral surface area is the lateral surface zone. This is to be distinguished from the overall surface area, which, along with the base and top areas, is the lateral surface area.

Given that, the lateral surface area of a cylinder of length 14m is 220 m².

We know that, the lateral surface area of a cylinder is 2πrh.

Here, 2πrh=220

2×3.14×r×14=220

87.92r=220

r=220/87.92

r=2.5 meters

We know that, the volume of a cylinder is πr²h

Here, volume = 3.14×2.5²×14

= 3.14×6.25×14

= 274.75 cubic meter

Therefore, the volume of the cylinder is 274.75 cubic meter.

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The expression "3 to the 3rd exponent" means that the number 3 is multiplied three times and is represented as 3³ and the value of this expression is 27 .

The expression is given as ; "3 to the 3rd exponent" ;

we have to represent it in exponential form and find the value ,

The number 3 to the 3rd exponent means that , the number 3 is multiplied three times , which is denoted as : ⇒ [tex]3\times 3 \times 3[/tex] ;

Since the base of all the numbers is same that is 3 , So , by the Law Of Exponents , the exponents/powers gets added ;

So , the expression becomes ⇒ [tex]3^{1+1+1}[/tex] ;

On adding the exponents ,

we get ;

⇒ [tex]3^{3}[/tex] ;

and the value of this exponential form  is 27 .

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Step-by-step explanation:

Step 1: Create a division problem with the numbers being divided lined up one above the other.

Step 2: Divide the first digit of the dividend (917) by the divisor (7), and write the quotient (130) above the dividend.

Step 3: Multiply the divisor (7) by the quotient (130) and write the product (910) below the dividend (917).

Step 4: Subtract the product (910) from the dividend (917) and write the difference (7) below the product.

Step 5: Bring down the next digit of the dividend (917), making the next number to divide (7).

Step 6: Divide the new number by the divisor, and write the quotient, this case 0 (since 7 doesn't divides into 7) above it, and add the remainder, which is still 7.

Step 7: The remainder is the final result of the division. 917 divided by 7 is 130 with a remainder of 7, so the final answer is 130 remainder 7, this can be represented as 130 R 7.

Note: Even though it is not shown in the explanation above, to check the solution is correct, you could also multiply the quotient (130) by the divisor (7) and add the remainder (7) to get back to the dividend (917)

It's also worth to note that the final remainder could be seen as the number we couldn't divide and the quotient as the result of the division.

Answer: r = -3, t = -4

Step-by-step explanation:

6r-6t=6

3r-6t=15

Using the elimination method, you can get

3r=-9

r=-3

Substitute -3 for r, and you get

-9-6t=15

-6t=24

t=-4

r=-3,t=-4

Answer:

r,t=-3,-4

Step-by-step explanation:

[1]    6r - 6t = 6

  [2]    3r - 6t = 15

The solution set of the given system is (5/7, 12/7).

Now, According to the question:

The given equations are:

5x + 2y = 7 …. (1)

y = x + 1 ….. (2)

Let us solve the system of linear equations using the substitution method.

Substituting equation (2) in (1)

5x + 2(x + 1) = 7

By further calculation

5x + 2x + 2 = 7

So we get

7x = 7 - 2

7x = 5

Divide both sides by 7

x = 5/7

Substitute the value of x in equation (2)

y = 5/7 + 1

Taking LCM

y = (5 + 7)/7

y = 12/7

Therefore, the solution set of the given system is (5/7, 12/7).

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Answer:

67

Step-by-step explanation:

.__. that it

The two most common errors that people make when creating while loops are infinite loops and off-by-one errors.

Error in math is when an incorrect result is obtained from a mathematical calculation. It can be caused by a mistake made in the calculation (such as a wrong formula or an incorrect use of a calculator) or by a misunderstanding of the problem being solved. Error in math can also be caused by a wrong assumption about the data being used. Regardless of the cause, an error in math can have serious consequences, as incorrect results can lead to incorrect decisions and actions.

An infinite loop is when a while loop is created that never ends, as the condition that the loop checks for never becomes false. An off-by-one error is when the loop is written in such a way that the loop will run one iteration too many or too few. This can lead to incorrect results and cause the loop to miss or repeat certain parts of the loop. To prevent these errors, it is important to have a clear understanding of the loop's condition and to always test the loop thoroughly before using it.

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Answer:no

Step-by-step explanation:

1. N

2. O

The factor of 2 is 1 and 2.

What is a factor?

In mathematics, an integer m that can be multiplied by another integer to create n is known as a divisor of an integer n, also known as a factor of n. One can also state that n is a multiple of m in this situation.

Factors are also known as divisors. This means they can divide evenly into the number they're a factor of.

Here,

We have to find the possible factors of 2.

We concluded that the factor of 2 is 1 and itself.

Factors of 2 are all the numbers which on multiplying give the result of 2. Factors of 2 are 1 and 2 only.

Hence, the factor of 2 is 1 and 2.

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2x2 aspect ratio means that the width is twice the height, which is commonly used in computer graphics, video and image processing.

The aspect ratio of an image or a display refers to the ratio of the width to the height of the image or display. A 2x2 aspect ratio means that the width of the image or display is twice the height. This aspect ratio is commonly used in computer graphics, video, and image processing. It is also known as a "square aspect ratio" because the width and height have the same ratio (1:1).

For example, a 2x2 aspect ratio is used in the QR Code standard, which is used for storing small amounts of data in a two-dimensional barcode. In this case, the width of the QR code is twice the height, making it square.

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(c+1) (c-7) = cc - 7c + c - 7 = c^2 - 7c - 7

So the simplified form of (c+1) (c-7) is c^2 - 7c - 7

Answer:

[tex]c^2-6c-7[/tex]

Step-by-step explanation:

[tex](c+1) (c-7)[/tex]

Apply the FOIL mothed.

[tex]cc+c\left(-7\right)+1\cdot \:c+1\cdot \left(-7\right)[/tex]

[tex]c^2-6c-7[/tex]

Answer:

each group will have 7 students in it.

Step-by-step explanation:

Ms. Higgins has 28 students in her gym class and wants to put them in 4 equal groups.

divide the total number of students by the number of groups.

28 students / 4 groups = 7 students per group.

So, each group will have 7 students in it.

Answer:

x=24, y=12. (24, 12).

Step-by-step explanation:

Let x and y be the two numbers that we seek.

Then x+y=36 and x-y=12.

x+y=36

x-y=12

----------

2x=48

x=48/2

x=24

24+y=36

y=36-24=12

Both Aiden's and Natalie's tennis balls can cover the same distance of the catapult length is 40.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

Given:

As, we know the linear intercept form,

y = mx + b

Where m is the rate of change (slope) and b is the initial value of y.

Now, From the graph of both Aiden's and Natalie's data, we can see that the point of intersection is at (-40, 90).

Also, which shows x axis at 40 is the distance.

So, Both of them Aiden's and Natalie's tennis balls can cover the length of 40.

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Answer:

32768

Step-by-step explanation:

8^6 ÷ 8

8^6= 262144

262144 ÷ 8 = 32768

32768

Hope this helps.

The probability of the two cards being A and A, P(A, A), is 1/9.

The correct option is the second option, one ninth.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

A set of 3 cards, spelling the word ADD, are placed face down on the table.

And we have to determine P(A, A) if two cards are randomly selected with replacement.

From the formula for probability, we have that

P(A) = Number of favorable outcomes / Total number of possible outcomes

P(A) = 1/3

Then,

The probability of selecting two cards that have A and A with replacement is,

P(A, A) = P(A) × P(A)

P(A, A) = 1/3 × 1/3

P(A, A) = 1/9

Therefore, the probability is 4/9.

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Answer:

15° & 75°

Step-by-step explanation:

An equilateral triangle is one in which all three sides are congruent. It also has the property that all three interior angles are equal. In other words, all three angles of an equilateral triangle are always 60°.

So ∠ABE = 90+60=150.  

because ABCD is square so AB = BC

because BEC is equilateral triangle, so BC = BE = AB

so we know in ABE triangle the 2 sharp angles are the same

so ∠AEB = (1/2) * (180-150) = 15

so ∠DAE = 90-15 =75

[tex]2v+8v-5v[/tex]

Combine Like Terms:

[tex](2v+8v-5v)[/tex]

[tex]\fbox{5v}[/tex]

Based on the attached boxplot, approximate percentage of the people who entered the amusement park met the height requirement for the attraction is 50%.

A boxplot is a way to present a five number summary in a box chart. The main part of the box shows where the middle portion of the data, the interquartile range. At the ends of the box, we will find the first quartile (Q1 or the 25% mark) and the third quartile (Q3 or the 75% mark). The bottom of the box is the minimum (the smallest number in the set) and the top of the box is the maximum (the largest number in the set). And, the median is represented by a line in the center of the box.

From the boxplot can be seen that:

Minimum = 43

Maximum = 64

Q1 (first quartile) = 46

Q3 (third quartile) = 58

Median = 48

In the passage, given that a person must be at least 48 inches tall to ride the attraction. So, this is the same number as median value, that is 48. Thus, 50% the amusement visitors are eligible for the requirement, and the 50% others are not.

Hence, the percentage of the people who entered the amusement park met the height requirement for the attraction is 50%.

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Answer:

9

Step-by-step explanation:

After driving for 5 hours, Arun's car would have used up 5 gallons of gas (1 gallon per hour for 5 hours). Therefore, the amount of gas left in the tank after driving for 5 hours would be 9 gallons - 5 gallons = 4 gallons.

To find the amount of gas left after t hours, we can use the formula:

Gas left after t hours = 9 - (1 x t)

Where t is the number of hours driven.

So, the amount of gas left after t hours would be 9 - t gallons.

After driving for 5 hours, Arun would have 4 gallons of gas left in his tank. If he drives for t hours, he would have (9 - t) gallons of gas left in his tank. The calculations are based on the fact that Arun's car uses 1 gallon of gas per hour of driving.

To answer this question, we must understand that Arun's car uses 1 gallon of gas for every hour of driving. So, if he drives for 5 hours, his car will use 5 gallons of gas. Arun starts with 9 gallons of gas, so we subtract the 5 gallons of gas used from the 9 gallons of gas he started with. The result is:

9 - 5 = 4 gallons

So, after driving for 5 hours, Arun would have 4 gallons of gas left in his tank.

Similarly, if he drives for t hours, his car will use t gallons of gas. So, to find how much gas would be left after driving for t hours, we subtract t gallons from the 9 gallons he started with:

9 - t = (9 - t) gallons

Thus, after driving for t hours, Arun would have (9 - t) gallons of gas left in his tank.

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The assertions are thought to be established truths since they explain scientific laws rather than speculations or Fourier's hypotheses and do not offer justifications for their veracity.

Scientific rules are those that have been established by experimenters or scientists after years of observations and experiments for scientific purposes. Laws are not established facts. They don't even offer an explanation for why scientific rules hold true.

The five most well-known scientific laws are: Bernoulli's law of fluid dynamics; Dalton's law of partial pressures; Hooke's law of elasticity; and Fourier's law of heat conduction.

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The correct question is -

Which statements describe scientific laws but not theories or hypotheses? Check all that apply.

They are likely to change as new evidence is discovered.

They do not provide explanations for why they are true.

They are considered to be proven facts.

They have not yet been tested.

They are the bases for experiments instead of the results.

A table of equivalent ratios for the number of customers and minutes for customers that entered the store are as follows:

Customers            Hours

1                                4

12                              6

10                              40

In order to have a proportional relationship and equivalent ratios, the number of customers (x) and the number of minutes (y) must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 12/3

Constant of proportionality (k) = 4.

When minutes y = 4, the number of customers (x) is given by:

x = y/k

x = 4/4

x = 1.

When the number of customers (x) = 10, the number of minutes (y) is given by:

y = kx

y = 4(10)

y = 40.

Next, we would use an online graphing calculator to plot the points on a coordinate axes as shown in the image attached below.

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The substitution technique includes simplifying the given equation, solving one of the equations for any unknown value, substituting the step 2 solution in another equation, solving the new equation, and finally solving the equation to find the second variable.

The substitution method is the algebraic method to solve different linear equations. In this technique, the value of one variable from either of the equation is substituted in the other equation.

In this technique the following steps are used to solve an equation by substitution method:

Step 1. Simplify the given equation by removing the parenthesis.

Step 2. Solve one of the equations for any unknown value.

Step 3. Substitute step 2 result in the other equation.

Step 4. Now solve the equation which gets from step 3 obtained using elementary arithmetic operations.

Step 4. Finally, solve the final equation for the second variable.

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The time taken to print the 5 more pages will be 1.25 seconds.

For the stated question-

The printer at Jack's prints 36 pages in 2 minutes and 24 seconds.

This can be written as;

2*60 + 24  seconds ---> 36 pages

120 + 24  seconds ---> 36 pages

144 seconds ---> 36 pages

Time taken to print 1 page.

1 page ---> 36 / 144 seconds.

Thus, to print 5 more pages.

5 page ---> 36 / 144 * 5 seconds.

5 page ---> 1.25 seconds.

Thus, the time taken to print the 5 more pages will be 1.25 seconds.

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The solutions of the inequality [tex]2x^{2} + x - 6 = 0[/tex] are 3/2, -2. This can be found by using the Quadratic Formula, which states that for any quadratic equation of the form [tex]ax^{2} +bx + c = 0[/tex], the solutions are [tex]x = -b +/-\sqrt{b^{2} -4ac} /2a[/tex].

Discriminant: b² - 4 a c = 1 - 4(2)(-6) = 1 + 48 = 49

Solution 1: x = [tex]-b + \sqrt{b^{2} -4ac} /2a[/tex] = (-1 + √49)/(2×2) = (-1 +7)/4 = 6/4 = 3/2

Solution 2: x = [tex]-b-\sqrt{b^{2} -4ac} /2a[/tex]= (-1 - √49)/(2×2) = -8/4 = -2

So, the two solutions are 3/2 and -2.

The equation can also be written as,

[tex]2x^{2} +4x -3x-6=0[/tex]

[tex]2x(x+2) -3(x+2) = 0[/tex]

[tex](2x-3)(x+2) = 0[/tex]

x = 3/2, -2

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Equivalents are things that are equal or have the same value. in mathematics, for example, the fraction 3/4 and the decimal 0.75 are the same value

Any 2 terms in mathematics are said to be equivalent if the are identical in terms of values. They do not necessarily have to be "equal"

For example, 8 can be said to be equal to 8 but 8 is "equivalent" to

4 + 4

1 + 7

10 - 2 etc.

This can also be considered for conversion systems.

For example- 1 kg is equvalent to 1000 grams.

Just like in all the examples we considered before, equivalency can be drawn when fractional forms are converted into decimal forms.

1/2 is equivalent to 0.5

Hence for 3/4, we need to write a decimal value for the same

3/4 = 75/100 = 0.75

Hence 3/4 will be equivalent to 0.75

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Answer:

£145

Step-by-step explanation:

£101.5 divided by 7 gives you £14.5 per each dress then times the £14.5 by 10 and that will give you in total £145 for 10 dresses