The problem solving plan identifies steps to organize your information. Which of the following answer choices are included in the steps to organize your information?
A. Organize the problem and find the question.
B. Solve the problem and change your strategy if necessary.
C. Write the facts, organize your thoughts and define your strategy.
D. Organize the steps and underline the question.

Area = length x width

Area = 21 square cm

Width = x

Length = 3x + 2

21 = 3x+ 2 * x

21 = 3x ^2 + 2x

Subtract 21 from both sides:

3x^2 + 2x -21 = 0

Use the quadratic formula to solve for x:

-2 +/- sqrt(2^2-4*3(-21))/(2*3)

X = 7/3 and -3

A dimension can’t be a negative value so x needs to be 7/3

Width = x = 7/3 = 2 1/3 cm

Length = 3(7/3) + 2 = 9 cm

Check: 9 x 2 1/3 = 21

Dimensions: width 2 1/3 cm length 9 cm

Answer:

The dimensions of the rectangle are 7 by 3 centimeters.

Step-by-step explanation:

We are given that the length of a rectangle is two centimeters less than three times its width. In other words:

[tex]\displaystyle \ell = 3w-2[/tex]

Given that the area of the rectangle is 21 square centimeters, we want to determine the dimensions of the rectangle.

Recall that the area of a rectangle is given by:

[tex]A= w\ell[/tex]

Substitute:

[tex](21)=w(3w-2)[/tex]

Solve foro the width. Distribute:

[tex]3w^2-2w=21[/tex]

Isolate the equation:

[tex]3w^2-2w-21=0[/tex]

Factor. Find two numbers that multiply to 3(-21) = -63 and add to -2.

-9 and 7 suffice. Hence:

[tex]3w^2-9w+7w-21=0 \\ \\ 3w(w-3)+7(w-3) = 0 \\ \\ (3w+7)(w-3)=0[/tex]

Zero Product Property:

[tex]3w+7=0\text{ or } w-3=0[/tex]

Solve for each case. Hence:

[tex]\displaystyle w = -\frac{7}{3}\text{ or } w=3[/tex]

Since width cannot be negative, we can ignore the first solution.

Therefore, our width is three centimeters.

And since the length is two less than three times the width, the length is:

[tex]\ell = 3(3) - 2 = 7[/tex]

The dimensions of the rectangle are 7 by 3 centimeters.

Answer:

[tex]2x {}^{3} + {8x}^{2} - 6x - 31 + \frac{ - 128}{x - 4} [/tex]

Place the coefficients in the right place.

Answered by GAUTHMATH

Answer:

Sự khác biệt giữa nhiệt độ - 7 độ C và - 12 độ C trên biểu đồ phân tán là gì

Step-by-step explanation:

By definition of conditional probability,

P(X ≤ 0.5 | X ≤ 1) = P((X ≤ 0.5) and (X ≤ 1)) / P(X ≤ 1)

but if X ≤ 0.5, then it's automatic that X ≤ 1, so

P(X ≤ 0.5 | X ≤ 1) = P(X ≤ 0.5) / P(X ≤ 1)

Given the PDF of X,

[tex]f_X(x) = \begin{cases}2e^{-2x}&\text{if }x\ge0\\0&\text{otherwise}\end{cases}[/tex]

the CDF would be

[tex]P(X\le x) = F_X(x) = \displaystyle\int_{-\infty}^x f_X(t)\,\mathrm dt[/tex]

[tex]F_X(x) = \begin{cases}0&\text{if }x<0\\1-e^{-2x}&\text{if }x\ge0\end{cases}[/tex]

So we have

P(X ≤ 0.5 | X ≤ 1) = (1 - exp(-2 × 0.5)) / (1 - exp(-2 × 1))

… = (1 - exp(-1)) / (1 - exp(-2))

… = (1 - 1/e) / (1 - 1/e ²)

… = (e ² - e) / (e ² - 1)

… = e / (e + 1) ≈ 0.7312

Answer:

True

Step-by-step explanation:

Considering the above definition of Pooled Variance, the correct answer is TRUE.

This is because Pooled variance is used to determine the reasonable estimates of variance, where several repeated tests are expected at each value.

This helps to provide greater precision estimates of variance.

Answer:

Option B

Step-by-step explanation:

Answered by Gauthmath

lmk if you don't understand my handwriting

Answer:

2.5

Step-by-step explanation:

You can change the equation from multiplication to division to get rate or time. We need the rate, so the equation should look like this now:

[tex]Distance/Time=Rate[/tex]

Now, we need to plug in the numbers we have...

[tex](5)/(2)=Rate[/tex]

...and solve for Rate:

[tex]Rate=2.5[/tex]

Answer:

The value of [tex]x[/tex] is 10.

Step-by-step explanation:

Both angles ABC and CBD are complementary, that is, the sum of the measures of both angles equals 90°, that is:

[tex]\angle ABC + \angle CBD = 90^{\circ}[/tex] (1)

If we know that [tex]\angle ABC = 5\cdot x[/tex] and [tex]\angle CBD = 4\cdot x[/tex], then the value of [tex]x[/tex] is:

[tex]5\cdot x + 4\cdot x = 90^{\circ}[/tex]

[tex]9\cdot x = 90^{\circ}[/tex]

[tex]x = 10[/tex]

The value of [tex]x[/tex] is 10.

Step-by-step explanation:

I cannot draw a diagram here.

but I can explain what to do in general.

the shortest distance from a point to a line is always via a connecting line that is perpendicular to the given line and his through the given point.

and then the distance from the given point to the intersection point is calculated.

every line is defined in the form like

y = ax + b

where a is the slope of the line, and b is the intersection point on the y-axis (the offset from point 0).

the slope of a line is the ratio y/x defining how many units y changes when x changes a certain amount of units.

in our example,

y = 5x - 10

5 (or rather 5/1) is the slope of the line.

it means that y grows by 5 units every time x grows by 1 unit.

a perpendicular line (cuts the original line with a 90 degree angle) has a related slope : it reverts x and y and flips the sign :

5/1 turns into -1/5

that means at the perpendicular line whenever x grows by 5 units, y goes down by 1 unit.

so, the first approach for the perpendicular line is

y = -1/5 x + b

to get b we use the given point (6, 5) that has to be in the perpendicular line.

5 = -1/5 × 6 + b

25/5 = -6/5 + b

31/5 = b

=> y = -1/5 x + 31/5

the intersecting point is now where both lines are equal

5x - 10 = -1/5 x + 31/5

25x - 50 = -x + 31

26x = 81

x = 81/26

y = 5×(81/26) - 10 = 405/26 - 260/26 = 145/26

the distance of the given point (6, 5) to the line intersection point (81/26, 145/26) is the calculated as

distance² = (6 - 81/26)² + (5 - 145/26)²

distance = sqrt((6-81/26)² + (5-145/26)²)

since the result was not requested here, I save us the calculation.

Answer:

11 /36 of a pound

Step-by-step explanation:

Take the pounds and divide by the number of people

2 3/4 ÷ 9

Change the mixed number to an improper fraction

(4*2+3)/4 ÷9

11/4 ÷9

Copy dot flip

11/4 * 1/9

11/36

Answer:

I think the area is 60 but i couldn't figure out the perimeter, sorry.

Step-by-step explanation:

Answer:

perimeter = 36 m

area = 60 m²

Step-by-step explanation:

there is some missing information. for example about the types of the shapes. e.g. if the triangle on the top is an isosceles triangle (2 equal sides). or if the rectangle at the bottom is actually a square with 6 m on all sides. in order to make the sloped side of the top triangle a round, whole number, i assume that the bottom part is a square.

so, the area of this combined shape is the area of the bottom square plus the area of the top triangle.

area square As = 6×6 = 36 m²

so, one side of the triangle is also 6 m, the other is 14-6 = 8 m.

the area of such a right-angled triangle is half of the full rectangle of 6×8.

area triangle At = 6×8/2 = 48/2 = 24 m²

total area = As + At = 36 + 24 = 60 m²

the perimeter of the total shape is the sum of all sides.

so, 14, 6, 6 and ... the baseline/ Hypotenuse of the top triangle.

for that r need the mentioned Pythagoras :

c² = a² + b²

where a and b are the sides, and c is the Hypotenuse (the side opposite of the 90 degree angle).

so, in our case of an isosceles triangle with a 90 degree angle :

c² = 8² + 6² = 64 + 36 = 100

c = 10 m

so, the perimeter is

14+6+6+10 = 36 m

Answer:

33

Step-by-step explanation:

6x4+9= 33

Answer:

The 98% confidence interval for the population mean is between 21 and 23.8 years.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.327\frac{4.2}{\sqrt{49}} = 1.4[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 22.4 - 1.4 = 21 years.

The upper end of the interval is the sample mean added to M. So it is 22.4 + 1.4 = 23.8 years.

The 98% confidence interval for the population mean is between 21 and 23.8 years.

9514 1404 393

Answer:

  D.  y = -0.32x² -1.26x +15.81

Step-by-step explanation:

This is one of those multiple-choice questions where you only need a vague idea of what the answer is supposed to look like.

In this case the answer must be a quadratic equation with a negative leading coefficient. (The parabola opens downward.)

The only answer choice that is a 2nd degree polynomial with a negative leading coefficient is choice D.

__

A: linear equation

B: exponential equation

C: quadratic that opens upward (positive leading coefficient)

D: quadratic that opens downward -- the answer you're looking for

Answer:

2240

Step-by-step explanation:

4(5)(7)(7+9)

=2240

Answer:

x = 2240

Step-by-step explanation:

x= 4ab(b+9)

x= 4(5)(7)(7+9)

x= 4(35)(16)

x= 4(560)

x= 2240

Answer:

26 miles per gallon

Step-by-step explanation:

Take the miles and divide by the gallons

455 miles / 17.5 gallons

26 miles per gallon

9514 1404 393

Answer:

  11.6 cm

Step-by-step explanation:

As the page title tells you, the Pythagorean theorem must be applied more than once. As you know, it tells you the square of the hypotenuse is the sum of the squares of the two sides.

  AD² = ED² +EA²

  EA² = AD²-ED² = 7² -6² = 13

  EA = √13 ≈ 3.606

__

  CD² = ED² +EC²

  EC² = CD² -ED² = 10² -6² = 64

  EC = √64 = 8

__

The length of the horizontal diagonal is ...

  AC = EA +EC = 3.6 +8 = 11.6 . . . cm

Answer:

x=10

Step-by-step explanation:

[tex]\frac{3}{3}[/tex]=[tex]\frac{x+3}{13}[/tex]

Solve by cross multiplying

13×3=39

3(x+3)=3x+9

3x+9=39

3x=30

x=10

Answer:

x=10

Step-by-step explanation:

Assuming that the triangles are similar to each other, you can set up ratios

[tex]\frac{3}{3}=\frac{13}{x+3}[/tex]

since 3/3 is 1 and we know that anything other than 0 over itself is 1, we can deduce that x=10

Answer:

96

Step-by-step explanation:

Mode is the number that appears most often

96 appears twice and is the only numbers that appears more than once

96 is the mode

Answer: TRUE

Step-by-step explanation:

An arithmetic sequence is a sequence in which the difference between each term (number) is a constant.

Given the sequence is {3, -6, -15, -24}

3 - (-6) = 9

-6 - (-15) = 9

-15 - (-24) = 9

As we can see from above, the difference between the given terms is all 9. Therefore, it is indeed an arithmetic sequence.

Hope this helps!! :)

Please let me know if you have any questions

Answer:

true

Step-by-step explanation:

Answer:

Not a function

Step-by-step explanation:

There are two points in the set that have the same x-value or "input": (6,4) and (6,-4). This fails the vertical line test which means that one input will give two potential outputs. This cannot make a function.

9514 1404 393

Answer:

  (6,2)

Step-by-step explanation:

As is often the case with multiple-choice problems, you don't actually need to know the detailed working. You just need to know what the answer looks like.

When point X is dilated by a factor of 2 with point Z as the center of dilation, it will move to a location twice as far from Z. You can tell by looking at the graph that X' will be in the first quadrant, above and to the right of the location of X. The only sensible answer choice is ...

  X' = (6, 2)

_____

Additional comment

X is a distance of X-Z = (4, 0) -(2, -2) = (2, 2) from Z Doubling that will put the image point a distance of 2(2, 2) = (4, 4) from Z. When this is added to Z, we find ...

  X' = Z + (4, 4) = (2+4, -2+4) = (6, 2)

Answer:

the answer to this question is 1

Step-by-step explanation:

the reason to that is because when the line goes over 2 and -2.

Answer:

first part is decreasing and increasing

second part is 3 and 5

Step-by-step explanation:

edg 2021

Answer:

bdFd574)466&!'!9+/"(&$4+√®=™]

Answer:

Step-by-step explanation:

y+5=0

y=-5

it is a line down 5 units parallel to x-axis.

you can take infinie points say (1,-5),(5,-5) ,(7,-5) etc.

Answer:

y = - 5

Step-by-step explanation:

In two dimensions, this is a line parallel to the x - axis. You can also think of it as a locus, the infinite set of points fulfilling  (,− 5)  — any real value of x, but y has to be -5.

Extending it to three dimensions, it is a plane parallel to the x-axis and also to the z-axis, or the locus  (,− 5, ).

Answer:

he worked 8 hours

Step-by-step explanation:

104= 8 x 6 + 7x

104= 48 + 7x

56= 7x

x=8

104 - 48= 56

56/7

Answer:

Equation - 7h + 8t = $104

Hours Worked = 8

Step-by-step explanation:

First, let's create an equation!

7h + 8t = $104 (Our variables are h = # of hours, and t = # of tables)

Now, we have to input what we know! We know that Allen worked 6 tables.

7h + 8(6) = $104

and finally we can solve this equation!

7h + 48 = $104

     -48     -48

7h = 56

÷7    ÷7

h = 8

In conclusion, Allen worked 8 hours!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO