The area of a trapezoid is 144cm2. The height is 16cm and the length of one of the parallel sides is 6cm. Find the length of the second parallel side. Express your answer as a simplified fraction or a decimal rounded to two places.

The correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3)

For the first question:

The table shows a proportional relationship between x and y. To describe what the graph of this proportional relationship would look like, we can examine the given data points.

The data points are (12, 3), (8, 26), and (24, ?). We can observe that as x increases, y also increases. This indicates a positive correlation between the variables. Additionally, we can see that the ratio of y to x remains constant for each data point.

Now, let's analyze the answer options:

A. A line passes through the point (0, 0) and continues through the point (3, 12).

This answer option does not align with the given data because there is no data point with an x-value of 3 and a corresponding y-value of 12.

B. A line passes through the point (0, 0) and continues through the point (2, 8).

This answer option aligns with the given data because (2, 8) is a valid data point from the table, and the line passes through the origin (0, 0).

C. A line passes through the point (0, 0) and continues through the point (6, 24).

This answer option does not align with the given data because there is no data point with an x-value of 6 and a corresponding y-value of 24.

D. A line passes through the point (0, 0) and continues through the point (12, 3).

This answer option aligns with the given data because (12, 3) is a valid data point from the table, and the line passes through the origin (0, 0).

Based on the analysis, the correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3). This accurately represents the graph of the proportional relationship given in the table.

For the second question, I'm sorry, but you didn't provide the multiple-choice options or the complete question. Could you please provide the question and options so that I can assist you further?

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Answer:

1 in 10

Step-by-step explanation:

Answer:

15. 4x¹⁰

16. 30m³

Step-by-step explanation:

15. Area of Rectangle is given by A=LW

    since W=x⁵ and L is 4 times W, L=4x⁵

    therefore, A = x⁵(4x⁵) = 4x¹⁰

16. Volume of Rectangular Prism is V=LWH

    W=6L=6m  and  H=5L=5m  and  L=m

   so V = m(6m)(5m) = 30m³

Answer:

In order to round 25.691 to the greatest place or the nearest whole number, first start at the last digit behind the decimal, in the case, being the 1. When it comes to things like this, if the digit is 4&under meaning its the number 4,3,2,1 or 0. If it is 5&up, that means it could be 5-9, making the digit go up (but if its 2, then the digit just goes away, you wont have to worry about that one specific number).

Next step is to round the 9 which makes the 6 go up one digit (meaning it turns into a 7). Now, when you round the seven, it will make the whole number go up one digit, but if you want to round that as well, to start, it's first rounding equaled up to 26. If you're rounding it to a whole tens number, it would be 30. I hope that this helps you understand this subject or topic much better! :3

Step-by-step explanation:

Answer:

2.67 hours

Step-by-step explanation:

Diana: 15 cookies per hour

Jamie: 7.5 cookies per hour

15 + 7.5 = 22.5

22.5 cookies per hour

\(\frac{60}{22.5} =\frac{y}{1}\)

22.5 · y = 60 · 1

22.5y = 60

22.5y ÷ 22.5 = 60 ÷ 22.5

\(y=2\frac{2}{3}\)

\(2\frac{2}{3}\)  rounded to the nearest hundredth is 2.67

The values of x for which f(x) = 7 are x = 61 and x = 21.

To find the values of x for which f(x) = 7, we can set up the equation and solve for x.

The given function is f(x) = 0.5|x - 41| - 3.

Setting f(x) equal to 7, we have:

0.5|x - 41| - 3 = 7.

First, let's isolate the absolute value term:

0.5|x - 41| = 7 + 3.

0.5|x - 41| = 10.

To remove the absolute value, we can consider two cases:

Case: (x - 41) is positive or zero:

0.5(x - 41) = 10.

Multiplying both sides by 2 to get rid of the fraction:

x - 41 = 20.

Adding 41 to both sides:

x = 61.

So x = 61 is a solution for this case.

Case: (x - 41) is negative:

0.5(-x + 41) = 10.

Multiplying both sides by 2:

-x + 41 = 20.

Subtracting 41 from both sides:

-x = -21.

Multiplying both sides by -1 to solve for x:

x = 21.

So x = 21 is a solution for this case.

Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.

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Answer:

a triangle with side measurements of 5, 5, and 5 inches​

Step-by-step explanation:

I took the test.

Construction of triangle with side measurement 2 inch, 3 inch, 5 inch is not possible.

This theorem simply states that the sum of two sides of a triangle must be greater than the third side. If this is true for all three combinations, then you will have a valid triangle.

If triangle has the sides, a ,  b and c then

a + b > c

b + c > a

a + c > b

Given length of the sides,

a)  Triangle made with sides having length 3 inch, 4 inch, 6 inch.

3 + 4 > 6 ; 4 + 6 > 3 ; 3 + 6 > 4

= 7 > 6 ; 10 > 3 ; 9 > 4

Triangle inequality theorem is satisfied, hence triangle construction is possible

b)  Triangle made with sides having length 2 inch, 3 inch, 5 inch.

2 + 3 > 5 ; 3 + 5 > 2 ; 2 + 5 > 3

= 5 = 5 ; 8 > 3 ; 7 > 3

Triangle inequality theorem is not satisfied, hence triangle construction is not possible

a)  Triangle made with sides having length 3 inch, 3 inch, 4 inch.

3 + 3 > 4 ; 3 + 4 > 3 ; 3 + 4 > 3

= 6 > 4 ; 7 > 3 ; 7 > 3

Triangle inequality theorem is satisfied, hence triangle construction is possible

a)  Triangle made with sides having length 5 inch, 5 inch, 5 inch.

5 + 5 > 5 ; 5 + 5 > 5  ; 5 + 5 > 5

= 10 > 5 ; 10 > 5 ; 10 > 5

Triangle inequality theorem is satisfied, hence triangle construction is possible.

Hence, Triangle with side measurements of 2 inch , 3 inch , and 5 inch is not possible to construct.

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First, express the mixed number as a simple fraction:

Back with the equation:

Subtract 3/8 from both sides of the equation:

Answer:

A

Step-by-step explanation:

you can see graph of f(x) changed one unit to the left, since it goes to the left, you should +1 in terms of x. so sqr x+1 is the solution. one way to think about that is you plus one for every x value, that means you get to a point previously for one unit. and turns out it looks like you moves to the left.

Hope that helps

To get the number of different ways for the students to line up, we are going to find the factorial of the number of students as seen below:

Hence, the 5 students can be lined up in 120 different ways.

The horns are frequently used as a signal to indicate the end of a segment or a specific task. Hence, a horn blows is the noise that sounds at the end of a segment.

The noise that sounds at the end of a segment is A horn blows.

In geometry, a segment is a part of a line that connects two points.

For example, line segment AB, which is denoted by AB, connects point A and point B and can be visualized as a portion of a line.

In general, line segments are denoted by their endpoints.

A horn is a cone-shaped instrument that is often used as a warning signal or a musical instrument.

However, it is important to note that noise can occur at the end of a segment in certain contexts and situations.

For example, in the context of audio or video editing, you can apply fade-out effects or specific sound effects to signal the end of a segment.

However, these sounds are not universally applicable and depend on the specific creative choices and technical aspects of the project.

In the transportation sector, horns are commonly used to alert pedestrians and other drivers of an oncoming vehicle's presence.

The sound of a horn is usually a sharp and loud noise that is difficult to ignore.

As a result, horns are frequently used as a signal to indicate the end of a segment or a specific task. Hence, a horn blows is the noise that sounds at the end of a segment.

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Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].

To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).

The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.

In other words, the range of f(x) is (-∞, 5].

So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.

Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.

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Answer:

16 cups a day

Step-by-step explanation:

The rectangular shaped array with 3 rows and 4 columns is drawn

X X X X

X X X X

X X X X

Given data ,

Let the number of rows for the rectangle be r = 3

Let the number of columns for the rectangle be c = 4

So , when r = 3 and c = 4

X X X X

X X X X

X X X X

Hence , the rectangle shaped array is solved

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Equations are statements that have equal values, when compared

The true statement about \(x^2 + 10x = 11\) are x = 1 and x = -11

The equation is given as:

\(x^2 + 10x = 11\)

Rewrite as:

\(x^2 + 10x - 11 = 0\)

Expand

\(x^2 + 11x - x - 11 = 0\)

Factorize

\(x(x + 11) -1( x + 11) = 0\)

Factor out x + 11

\((x -1)(x + 11) = 0\)

Solve for x

x = 1 or x = -11

Hence, the true statement about \(x^2 + 10x = 11\) are x = 1 and x = -11

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Answer:

.aabc=amn0#1211

Step-by-step explanation:

nosascoOsasco n=12.8

The answers for the given questions is mentioned below.

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. It can be solved using methods such as factoring, completing the square, or using the quadratic formula.

a. To find the amount of time since dropping the wrapper when it is 450 feet in the air, we need to solve the equation f(x) = 450, where f(x) is given by f(x) = -16x² - 2x + 600. So we have:

-16x² - 2x + 600 = 450

b. To solve this equation using the quadratic formula, we first need to put it in standard form:

-16x² - 2x + 150 = 0

Now we can apply the quadratic formula, which states that the solutions to the equation ax² + bx + c = 0 are given by:

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = -16, b = -2, and c = 150, so we have:

x = (-(-2) ± √((-2)² - 4(-16)(150))) / 2(-16)

x = (2 ± √(4 + 9600)) / (-32)

x = (2 ± √(9604)) / (-32)

Simplifying:

x = (2 ± 98) / (-32)

So the two solutions are:

x = -3/4 or x = -75/4

c. The solution that makes the most sense in the context of the situation is x = -3/4. This is because the time since dropping the wrapper cannot be negative, and it also cannot be 75/4 seconds, since the wrapper would have hit the ground before then. Therefore, the only sensible solution is x = -3/4, which means that the wrapper was 450 feet in the air 3/4 of a second after it was dropped.

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a). The amount of time since dropping the wrapper is -16x² - 2x + 600 = 450.

b). The two solutions are:

x = -3/4 or

x = -75/4

c). After being lowered, the wrapper was 450 feet in the air for about 3/4 of a second.

A second-degree polynomial equation of the form ax² + bx + c = 0 is a quadratic equation, in which x is the variable and a, b, and c are constants. It can be resolved by applying strategies like factoring, square-rooting, or the quadratic formula.

a). We need to solve the equation to determine the duration since dropping the wrapper at 450 feet in the air.

f(x) = 450,

Where f(x) is given by f(x) = -16x² - 2x + 600. So we have:

-16x² - 2x + 600 = 450

b). We must first convert this equation into standard form before we can answer it using the quadratic formula:

-16x² - 2x + 150 = 0

The quadratic formula, which asserts that the answers to an equation are ax² + bx + c = 0 are given by:

x = (-b ± √(b² - 4ac)) / 2a

In this case,

a = -16,

b = -2, and

c = 150,

so we have:

x = (-(-2) ± √((-2)² - 4(-16)(150))) / 2(-16)

x = (2 ± √(4 + 9600)) / (-32)

x = (2 ± √(9604)) / (-32)

Simplifying:

x = (2 ± 98) / (-32)

So the two solutions are:

x = -3/4 or x = -75/4

c). In light of the circumstance, the answer that makes the most sense is x = -3/4. This is due to the fact that the amount of time passed since dropping the wrapper cannot be negative, nor can it be 75/4 seconds because the wrapper would have already struck the ground by then. The wrapper was 450 feet in the air 3/4 of a second after it was thrown, so the only logical answer is x = -3/4.

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Answer:

B

Step-by-step explanation:

millimeter means one-thousandth of a meter meaning the number of millimeters will be larger by a factor of 1000.

Answer:

B

Step-by-step explanation:

Millimetres is A LOT smaller than meters, meaning the individual number of millimetres is larger than the individual number of meters.

The solution of the inequality 3x < 13 is x < 4.33.

None of the given option is correct.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An inequality,

3x < 13.

Simplifying,

x < 4.33

The graph is given in the attached image.

Therefore, the solution is x < 4.33.

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Answer:

Step-by-step explanation:

View the attached graph for what your image should look like.

I hope this helps or gives you a picture of what it should look like, because it's quite a long process.

Hope this helps!

Answer:

  (a) P(t) = 50·17.5^(t/1.5)   or   P(t) = 50·e^(1.9081t)

  (b) P(5) ≈ 695,713

  (c) P'(5) ≈ 1,327,514

  (d) 4.5 hours

Step-by-step explanation:

You want the exponential function that describes bacterial growth from 50 cells to 875 cells in 1.5 hours, the population after 5 hours, and its rate of growth at that time. You also want to know the time at which the population reaches 250,000.

The function that models exponential growth can be written as ...

  population = (initial population)×(growth factor)^(t/period)

where (growth factor) is the population multiplier over the period.

Here, we are given an initial population of 50, and a growth factor of 875/50 = 17.5 in a period of 1.5 hours. This means we can write the function as ...

  P(t) = 50(17.5^(t/1.5))

Note that the exact problem statement values are used, so no rounding is required.

If this is expressed using an exponent with a base of 'e', then we have ...

  P(t) = 50e^(kt)

Comparing this to the above expression, we see ...

  e^(kt) = 17.5^(t/1.5)

  k = ln(17.5)/1.5 ≈ 1.9081 . . . . take natural logs and divide by t

So, ...

  P(t) ≈ 50(e^(1.9081t))

The cell count after 5 hours is modeled as ...

  P(5) = 50·e^(1.9081·5)

  P(5) ≈ 695,713

Differentiating the population function, we have ...

  P'(t) = 50·(1.9081)(e^(1.9081t) ≈ 95.4067e^1.9081t

Then the rate of change of the population at t=5 is ...

  P'(5) = 1.9081·P(5)

  P'(5) ≈ 1,327,514

The time required for the population to reach 250,000 can be found from ...

  250,000 = 50·e^(1.9081t)

  5,000 = e^(1.9081t) . . . . . . . divide by 50

  ln(5,000) = 1.9081t . . . . . . . take natural logs

  t = ln(5,000)/1.9081 . . . . . .divide by the coefficient of t

  t ≈ 4.5

It will take about 4.5 hours for the population to reach 250,000.

Answer:

Step-by-step explanation:

The BAC (Blood Alcohol Concentration) of a person depends on several factors, such as the amount of alcohol consumed, the time over which the alcohol was consumed, and the weight and gender of the person. For this problem, we will assume that the woman has a normal metabolism and that the alcohol is completely absorbed into her bloodstream.

To calculate the BAC at 8 pm, we need to know the amount of alcohol that the woman consumed and the time over which she consumed it. We are given that she had 2 mixed drinks between 7-8 pm, which contained a total of 2 ounces of liquor. We are also given that she had a glass of wine at 10 pm, but we don't need to consider this for the BAC at 8 pm.

Using the Widmark formula, we can calculate the BAC at 8 pm:

BAC = (Alcohol consumed / (Body weight x r)) - (0.015 x Hours since first drink)

where r is the gender constant (0.55 for females) and 0.015 is the rate at which the liver metabolizes alcohol.

Plugging in the values we know, we get:

BAC = (2 oz / (130 lbs x 0.55)) - (0.015 x 1 hour)

BAC = 0.0208 - 0.015

BAC = 0.0058

Therefore, the woman's BAC at 8 pm was approximately 0.0058, which is below the legal limit for driving in most states in the US.

Answer:

1.The  equation of best fit is ŷ = 2.69152X + 3.45818.

Step-by-step explanation:

This technique allows mathematical sense since it concentrates effort on repaying the loans with the highest interest rates.

You can use the available credit on a credit card to buy things, debt exchanges, and/or cash withdrawals, but you eventually have to pay back the loan's principal.

The fastest way to receive a credit card is to submit an application and then, after being accepted, ask for expedited delivery. When you apply online, you have a chance of getting a quick response. In some circumstances, you might even get your card number immediately away so you can start making purchases.

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Here using the correct order of operations that is PEMDAS, we get the value to be 13.

PEDMAS can be summed up as a mathematical acronym that lists the various arithmetic operations in order of greatest to least practical use.

The letters stand for:

P stands for parentheses.

Exponents are shown as E.

D stands for division.

The letter M stands for multiplication.

A stand for addition.

S stands for subtraction.

Now in the given question,

15 - (4-3)2

First the parentheses

15 - (1)2

Next is exponents.

15 - 2

At last, after subtracting, we get:

13

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Step-by-step explanation:

well that seems like a you problem lol

Answer:

(5 × 10^3) + (3 × 10^2) + (2 × 10^1) + (5 × 10^0) = 5,325

Step-by-step explanation:

Answer:

Step-by-step explanation:

5*10^2 + 6*10 + 3*1 + 8*10^(-1) + 4*10^(-2)

Note how the powers of 10 decline steadily:

10^2, 10, 1, 10^(-1), 10^(-2)

A point on the scatter plot is defined as (19, 3), which means that an input of 19 is mapped to an output of 3.

The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:

(Input, Output).

One point on the scatter plot for this problem has the coordinates given as follows:

(19, 3).

Hence the meaning is that an input of 19 is mapped to an output of 3.

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The internet service provider charges $20 per month plus an initial set-up fee.

Let "x" represent the number of months that are charged, then the monthly fee can be expressed as 20x

Let "y" represent the cost of the internet service after x months.

If the customer paid y=$92 after x=2 months of service, this information represents a point of the relationship that can be expressed as (2,92)

The point-slope form has the following formula:

Where

m is the slope

(x₁,y₁) are the coordinates of one point of the line.

The slope of the line corresponds to the monthly fee for the internet service, so m=$20

The coordinates of the point you have to use is (2,92)

So the equation in point-slope form is

To write the equation in slope-intercept form, the first step is to distribute the multiplication on the parentheses term:

Then pass "-92" to the right side of the equation by adding it to both sides of the equal sign:

The equation in point-slope form is y-92=20(x-2)

The equation in slope-intercept form is y=20x+52

$20 is the slope of the equation and represents the monthly fee for internet service.

$52 is the y-intercept of the equation, it represents the initial set-up fee for the internet service.