How do I write this expression:The quantity seven plus Z, squared

Answer:

The perimeter of one of the trapezoids is equal to [tex](16+8\sqrt{2})\ in[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The perimeter of a square is

[tex]P=4b[/tex]

where

b is the length side of the square

step 1

Find the length side of the smaller square

[tex]16=4b[/tex]

[tex]b=16/4=4\ in[/tex]

step 2

Find the length side of the large square

[tex]48=4b[/tex]

[tex]b=48/4=12\ in[/tex]

step 3

Find the height of one trapezoid

The height is equal to

[tex]h=(12-4)/2=4\ in[/tex]

step 4

Remember that in this problem, one trapezoid is equal to one square plus two isosceles right triangles.

Find the hypotenuse of one isosceles right triangle

Applying Pythagoras Theorem

[tex]c^{2}=4^{2} +4^{2} \\ \\c=4\sqrt{2}\ in[/tex]

step 5

Find the perimeter of one of the trapezoid

The perimeter is equal to

[tex]P=(4\sqrt{2} +4+4\sqrt{2}+12)\\ \\P=(16+8\sqrt{2})\ in[/tex]

Answer:

27.3 Inches

Step-by-step explanation:

Answer:

  (3)  y = 12

Step-by-step explanation:

The circle is centered at (x, y) = (-5, 2) and has a radius of 10. Hence the most positive y-value is y = 12.

___

Complete the squares of x-terms and of y-terms.

  (x^2 +10x) + (y^2 -4x) = 71

  (x^2 +10x +25) + (y^2 -4x +4) = 71 + 25 + 4

  (x +5)^2 +(y -2)^2 = 10^2 . . . . . . . a circle centered at (-5, 2) with radius 10.

Answer:

[tex]4\frac{17}{24}[/tex] feet

Step-by-step explanation:

Total length of the board = [tex]7\frac{1}{3}=\frac{22}{3}[/tex] feet

Length of board that is removed from the larger board = [tex]2\frac{5}{8}=\frac{21}{8}[/tex]

When a smaller board is removed, the length of the remaining board can be calculated using subtraction as:

Remaining Length of board = Total Length - Length of smaller board

= [tex]\frac{22}{3}-\frac{21}{8}\\\\\text{Taking LCM, which is 24}\\\\ =\frac{8(22)-3(21)}{24}\\\\ =\frac{113}{24}\\\\ =4\frac{17}{24}[/tex]

This means [tex]4\frac{17}{24}[/tex] feet of board remains after removing the smaller board from it.

Answer:

f(x) ^-1 = 1/5 x

Step-by-step explanation:

f(x) = 5x

y =5x

To find the inverse, exchange x and y and solve for y

x =5y

Divide each side by 5

1/5x = 5y/5

1/5 x = y

1/5 x = f(x) ^-1

f(x) ^-1 = 1/5 x

Answer:

  Bagel

                                       plain                          

Tuna Eggs Chicken salad Cream cheese butter

                                      Poppy

Tuna Eggs Chicken salad Cream cheese butter

                                      Wheat

Tuna Eggs Chicken salad Cream cheese butter

3b

There are 15 combinations because tuna, eggs, chicken salad, cream cheese, and butter = 5

there are 3 different types of bagels plain poppy and wheat. with this information you can tell that the 5 combinations x 3 bagel types equal 15 total

Answer:

$95.48 was his commission

Step-by-step explanation:

First we need to find what the retail cost of the chest is.  If it's marked up 150%, we use 763.84 + 1.5(763.84) which gives us a retail price of $1909.60.  If Ben makes 5% on the sale as his commission, then we take 5% of 1909.60 which, in algebraic terms, looks like this:  .05(1909.60) which is $95.48

Answer:

1/4 ft

Step-by-step explanation:

The area is given by the product of length and width. Since the width of the rectangle was not changed, the new length L satisfies the equation ...

(1/6 ft)·L = 11/72 ft²

Multiplying by 6/ft tells us the new length:

L = (6/ft)·11/72 ft² = 11/12 ft

The original length is 2/3 ft shorter so is ...

L -2/3 ft = 11/12 ft -8/12 ft = 3/12 ft

L = 1/4 ft

Answer:

Each element is either included or not in a subset.

--> 2^6 = 64

Hope this helps you out!

64. 2 to the 6th power

Answer:

  0.5 cm

Step-by-step explanation:

You are given angles B and C and side b, so you can put those values into the given equation:

  sin(105°)/(2 cm) = sin(15°)/c

Multiply this equation by c·(2 cm)/sin(105°) and you get ...

  c = (2 cm)·sin(15°)/sin(105°) ≈ 0.535898 cm

  c ≈ 0.5 cm

_____

Comment on the given equation

When using the Law of Sines to find side lengths, I prefer to write the proportion in a form with the side length of interest in the numerator:

  b/sin(B) = c/sin(C)

or

  c/b = sin(C)/sin(B)

Using either of these forms, it is one step to find the value of c: Multiply the equation by the inverse of the coefficient of c.

  c = b·sin(C)/sin(B)

It’s A the region one

Answer:

A). when the region is divided into a greater number of rectangles.

Step-by-step explanation:

This forms the basics of integration.

Integration can be use to calculate areas under the curve. To find the area under the curve we try to approximate the area under the curve by using rectangles. When we increased the number of rectangles of equal width of the rectangles, a better approximation of the area is obtained. We then find the area of each infinitesimally small rectangle and then integrate by taking two limits, the upper limit and the lower limit.

Answer:

C) 5000(0.987783)^t

Step-by-step explanation:

The monthly interest rate is the APR divided by 12, so is 22%/12 ≈ 0.018333.

Each month, the previous balance (B) has interest charges added to it, so the new balance is ...

balance with interest charges = B + (22%)/12×B = 1.018333×B

The minimum payment is 3% of this amount, so the new balance for the next month is ...

balance after payment = (1.018333B)(1 - 0.03) = 0.987783B

Since the balance is multiplied by 0.987783 each month, after t payments, the balance starting with 5000 will be ...

5000×0.987783^t . . . . . . . . . matches choice C

Answer:

5.13 feet

Step-by-step explanation:

So, we have the full dimensions of flag #1, and we have the partial dimensions of flag #2, which should follow the same ratio as flag #1, since not indicated otherwise.

When you need to compare dimensions like that, the easiest way to proceed is to do a cross-multiplication. Let's say x is the length of flag #2 we're looking for.  It's ratio over the width of flag #2 will be the same as the ratio of the length of flag #1 over its width, so:

[tex]\frac{x}{2.7} = \frac{1.9}{1}[/tex]

If we isolate x, we have x = (2.7 * 1.9) / 1 = 5.13 feet

Which makes sense since we know the result should be a bit less than 2.7 times 2.

3x+2+x+8=180; 4x+10=180; 4x=170; x= 170/4= 42.5

Angle on top is x+8=42.5+8=50.8

Angle on the bottom is 3x+2=3•42.5+2= 129.5

The value of x is 42.5.

The fundamental characteristics listed below make it simple to recognise parallel lines.

Straight lines that are always the same distance apart from one another are called parallel lines.

No matter how far apart they are in any direction, parallel lines will never intersect.

Given:

From figure (x+8) and(3x+ 2) are angles on same side of transversal.

So, (x+ 8) + (3x+ 2)= 180

4x+ 10 = 180

4x = 180- 10

4x= 170

x= 170/4

x= 42.5

Hence, the value of x is 42.5.

Learn more about parallel line here:

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Answer:

60

Step-by-step explanation:

<H + <T = 180

2x+ 60 + x + 30 = 180

3x + 90 = 180

3x = 90

 x = 30

<T = x + 30 = 30 + 30 = 60

Answer

<T = 60

Answer: 50 degrees.

Step-by-step explanation:

The sum of the interior angles of a triangle is 180 degrees. Then, you can find the missing angle "x" of the larger triangle (Observe the figure attached):

[tex]53\°+45\°+x=180\°\\x=180\°-53\°-45\°\\x=82\°[/tex]

We know that:

[tex]x+y+68\°=180\°[/tex]

Then, "y" you need to substitute values and solve for "y":

[tex]y=180\°-68\°-82\°=30\°[/tex]

Then the angle ? is:

[tex]?=180\°-30\°-100\°\\?=50\°[/tex]

ANSWER

?=50°

EXPLANATION

From the diagram,

x+45+53=180

x+98=180

x=180-98

x=82°

Using angles on a straight line property,

x+68+y=180

82+68+y=180

150+y=180

y=180-150

y=30°

Using the sum of interior angles of the triangle,

?+y+100=180

?+30+100=180

?+130=180

?=180-130

?=50°

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point

We have the equation:

[tex]y-5=-\dfrac{2}{3}(x+9)\\\\y-5=-\dfrac{2}{3}(x-(-9))[/tex]

Therefore we have

the slope m = -2/3

and the point (-9, 5)

A slope

[tex]m=\dfrac{rise}{run}[/tex]

rise = -2

run = 3

From the point (-9, 5) ⇒ 2 units down and 3 units to the right.

Answer:

x = ± 2i

Step-by-step explanation:

The equation has no real roots, gut has complex roots

Given

x² = - 4 ( take the square root of both sides )

x = ± [tex]\sqrt{-4}[/tex]

  = ± [tex]\sqrt{4(-1)}[/tex]

[ Note that [tex]\sqrt{-1}[/tex] = i ]

  = ± [tex]\sqrt{4}[/tex] × [tex]\sqrt{-1}[/tex] = ± 2i

Answer:

[tex]f(x)=\left\{ \begin{array}{rcl}\dfrac{8}{3}x+4&\text{for}&x\le3\\\\-3(x-3)^2+12&\text{for}&x>3\end{array} \right.[/tex]

Step-by-step explanation:

The line to the left of x=3 goes up from 4 to 12 as x goes from 0 to 3. Thus, the slope of it is ...

slope = (12 -4)/(3 -0) = 8/3

It intersects the y-axis at y=4, so its equation is ...

y = (8/3)x +4

__

For x > 3, we observe that the curve falls 3 units (from 12 to 9) as x goes from 3 to 4, then falls 9 units (from 9 to 0) as x goes from 4 to 5. The slope of the curved portion at x=3 looks like it might be zero, suggesting a polynomial function instead of an exponential function.

We note that the change in the value of y=x^2 as x goes from 0 to 1 is 1, then as x goes from 1 to 2, it is 4-1 = 3 — 3 times the change in the first interval. This suggests a quadratic function that has been scaled by a vertical factor of -3, and had its vertex moved to (3, 12). Such a function is described by ...

y = -3(x -3)² +12

Then the graph is modeled by a piecewise function, defined as a line for x < 3, and as a quadratic curve for x > 3. Since the function is continuous at x=3, we can put "or equal to" signs on either or both of these boundaries. We choose to write it as ...

f(x) = (8/3)x +4, x ≤ 3; -3(x -3)² +12, x > 3.

____

The graph of our function is attached. It substantially matches the given graph.

ANSWER

B. [tex](x,y)\to (0.5x,0.5y)[/tex]

EXPLANATION

From the diagram, MN=6 units.

and M'N'=3 units.

The quadrilateral KLMN was dilated to obtain K'L'M'N'

We can observe that,

[tex] |M'N'| = 0.5|MN| [/tex]

This means that the scale factor of the dilation is 0.5.

The mapping for the dilation is :

[tex](x,y)\to (0.5x,0.5y)[/tex]

The correct answer is B.

Answer:

Step-by-step explanation:

The easiest way for me to answer your question is just to do it. If we agree, all well and good. If we don't, then you have the way I did it.

A = (4.75*x + 125)/10000

A = (4.75*10000 + 125) / 10000

A = (47500 + 125) / 10000

A = 47625/10000

A = 4.76

So it looks like we both think it is A.

The question is deceptive because the 125 is really quite small compared to 47500.

Answer:

A. $4.76

Step-by-step explanation:

This case is fairly typical of average cost problems. There is some fixed cost that is amortized over the number of T-shirts produced, and there is some variable cost associated with each item.

Here, if you divide out the equation, you get ...

A = 4.75 + 125/x

Then for x=10,000, the value of A is ...

A = 4.75 +125/10,000 = 4.75 +0.0125 ≈ 4.76

_____

Once you see that the fixed cost of $125 is divided by 10,000, you can look for an answer choice that is very slightly higher than $4.75.

Answer:

Step-by-step explanation:

Pick any point that is clearly on the line. (g, c) = (12, 40) is the end point, so will do nicely. The value of r (the constant of proportionality) is the slope of the line, which is the ratio of the y-value of the point to the x-value (or c to g, in this case).

  r = c/g = 40/12 = 10/3  . . . . . . the exact value of the constant r

Then your equation is ...

  c = 10/3g . . . . . . put the value of r where r is in the equation you are given

Answer:

y=2x-9 or D

Step-by-step explanation:

To get the slope of the perpendicular line, you find the negative reciprocal.  The negative reciprocal of -1/2 is 2.

Then, you need to find the y-intercept.  Considering the line has to pass through the point (2,-5), you can use the slope to find that the y-intercept is -9.  

Answer:

~24.4%

Step-by-step explanation:

A circle is 360 degrees, we all know this.

The angle representing Techno is 28° While Country has a 60°. Combine this and we get 88° of people total chose country or techno. 88° divided by 360° gives us 0.2444444... With percentages, we move the decimal two places to the right, giving us:

~24.4%

Answer:

  12 cm

Step-by-step explanation:

The square of the length of the tangent segment is equal to the product of near and far distances to the circle from the point of intersection of the secant and tangent:

  (8 cm)^2 = (4 cm)(4 cm +x)

  16 cm = 4 cm +x . . . . . . divide by 4 cm

  12 cm = x . . . . . . . . . . . . subtract 4 cm

Ashley ran on the track for 4 miles. Option C is correct.

Solving word problems.

In the track event (joggling), the distance of the track is 1 mile (i.e. it represents a single mile).

It was noted that Ashley jogged for 4 times. Now, the length of the joggling time multiplied by the numbers of time Ashley jogged on this track will be how far Ashley ran on the track.

How far Ashley ran on the track = 1  × 4

How far Ashley ran on the track = 4 miles.

Thus, Ashley ran on the track for 4 miles.

The complete question.

The jogging track is of a mile long. If Ashley jogged around it 4 times, how far did she run? A.2 miles  B. 1/2 miles  C. 4 miles D. 5 miles.

Answer:

  $311.74

Step-by-step explanation:

A financial calculator computes the payment amount to be $311.74.

___

Your graphing calculator may have the capability to do this. Certainly, such calculators are available in spreadsheet programs and on the web.

___

The appropriate formula is the one for the sum of terms of a geometric series.

  Sn = a1·((1+r)^n -1)/(r) . . . . . where r is the monthly interest rate (0.005) and n is the number of payments (480). Filling in the given numbers, you have ...

  $620827.46 = a1·(1.005^480 -1)/.005 = 1991.4907·a1

Then ...

  $620827.46/1991.4907 = a1 ≈ $311.74

To achieve a retirement income of $4000 per month with a 6% APR compounded monthly, a nest egg of $620,827.46, and a retirement plan spanning 40 years, one should deposit about $288.69 into the account each month.

This question pertains to the concept of future value and annuities in finance. The purpose is to determine the monthly deposits required to achieve a specified future value, which in this case is the desired retirement income. Here, we use the future value of a series formula: FV = P * [((1 + r)^nt - 1) / r], where P is the monthly payment, r is the monthly interest rate, n is the number of times interest is compounded per year, and t is the time in years. Given that the future value FV is $620,827.46, the interest rate r is 0.06/12 (since it's compounded monthly), n is 12 (compounded twelve times a year), and t is 40 years. The aim is to solve for P, the monthly payment: P = FV / [((1 + r)^nt - 1) / r]. Plugging in the given values, the result is approximately $288.69. Thus, to receive a retirement income of $4000 per month, you should deposit about $288.69 into the account each month.

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Answer:

0.184

Step-by-step explanation:

There are 38 seniors, of which 7 prefer evening classes.

7/38 ≈ 0.184

The question involves mathematical sampling techniques to generate categorical data from a high school population, which is shown in a pie chart and involves creating a stratified sample by selecting students from each year.

The question pertains to a mathematical concept used in the selection of a sample from a population, which in this scenario, is a group of high school students. This involves using a random number generator to select two class years (freshman, sophomore, junior, or senior) and then including all students from those two years in the sample. The sampling process will result in categorical data, which can be represented in a pie chart as shown in Solution 1.10.

Moreover, organizing the students' names by classification and selecting 25 students from each (a, d) ensures a stratified sample of high school students across different academic stages.

In the context of the presented educational tasks, students might explore how their learning experiences have intersected with personal and global changes, engaging in an analysis of polymorphism, continuous variation, and clinal distribution based on surveyed traits among their peers (Conclusion).

Answer:

C. n + n + 1 = 37; n = 18; n + 1 = 19

Step-by-step explanation:

If we let n represent the smaller integer, then the larger one is n+1. Their sum is 37, so you have ...

n + (n+1) = 37

When you subtract 1 and collect terms, you have ...

2n = 36

Dividing by 2 gives you ...

n = 18

Then the larger integer is ...

n+1 = 19

The matching choice is C.

The parallel line of RU would need to be the mid point S and midpoint M

Segment SM would be the parallel line.

Answer:

Though I'm not quite sure (as this is a bit of a trick Question) the only Parallel to Line/segment to RU would MS. Given the question they are asking MS are the only two points that run adjacent/parallel to RU. Hope this helps

Step-by-step explanation:

The answer is:

The area of the rectangle is equal to [tex]12units^{2}[/tex]

To find the area of the rectangle shown on the coordinate plan, first, we need to calculate the distance between the points that conforms two of the sides of the rectable (base and height).

We can use any of the four vertex points shown on the coordinate plane, so, we will use the points:

1 - (-4,1)

2 - (-1,-2)

3 - (-3,-4)

Then, calculating the length of the sides, we have:

Base:

[tex]Base=distance(FirstPoint,SecondPoint)=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}[/tex]

[tex]Base=\sqrt{(-1-(-4))^{2}+(-2-1)^{2}}\\\\Base=\sqrt{(3)^{2}+(-3)^{2}}\\\\Base=\sqrt{(9+9)}=\sqrt{18}units[/tex]

Height:

[tex]Height=distance(SecondPoint,ThirdPoint)=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}[/tex]

[tex]Height=\sqrt{(-3-(-1))^{2}+(-4-(-2))^{2}[/tex]

[tex]Height=\sqrt{(-2)^{2}+(-2)^{2}[/tex]

[tex]Height=\sqrt{4+4}[/tex]

[tex]Height=\sqrt{8}units[/tex]

Therefore, calculating the are of the rectangle, we have:

[tex]Area=base*height\\\\Area=\sqrt{18unis}*\sqrt{units}=\sqrt{144}=12units^{2}[/tex]

Hence, the area of the rectangle is equal to [tex]12units^{2}[/tex]

Have a nice day!

Aswer:

The area of the rectangle is 12 sq. units

step-by-step explanation:

From the question :

we first find the length and width of the rectangle using the distance formula.

For the length we use the points

(-1,-2) and (-4,1)

[tex]l = \sqrt{( {x - x_1)}^{2} + ( {y - y_1)}^{2} } [/tex]

[tex]l = \sqrt{( { - 1 - ( - 4))}^{2} +{(-2 - 1)}^{2} } [/tex]

[tex]l = \sqrt{{3}^{2} +{( - 3)}^{2}}[/tex]

[tex]l = \sqrt{9 + 9} [/tex]

[tex]l = \sqrt{18} = 3\sqrt{2} \: units[/tex]

For the width, let us take the points (-6,-1) and (-4,1)

[tex]w = \sqrt{ {( - 6 - ( - 4))}^{2} + {(-1 - 1) }^{2} }[/tex]

[tex]w = \sqrt{ {2}^{2} + {( - 2)}^{2} }[/tex]

[tex]w = \sqrt{4+4}[/tex]

[tex]w = \sqrt{8 } = 2 \sqrt{2} \: units[/tex]

The area of the rectangle

[tex] = l \times w[/tex]

[tex]A = 3 \sqrt{2} \times 2\sqrt{2} [/tex]

[tex]A = 3 \times 2 \times 2[/tex]

[tex]A =12 \: sq.units[/tex]