Stephan cuts a 50-yard ribbon. One piece is 7 yards longer than the other. What is the length of each piece?

Answer:

B

Step-by-step explanation:

B is the best answer because it's a lot of students and unbiased

The internal angles of 64.801° (2 in total) and 115.199° (2 in total) lead to a maximum area of 27.88 square units.

Quadrilaterals are figures formed by four line segments and whose sum of internal angles equals 360°. By geometry we know that the area of a trapezoid is the average of the length of the two bases (B, b), in inches, multiplied by the height of the quadrilateral.

A = 0.5 · (B + b) · h   (1)

By trigonometry the measure of the longer base and the height of the isosceles trapezoid are, respectively:

B = b + 2 · l · cos θ   (2)

h = l · sin θ   (3)

Where θ is an internal angle, in degrees.

By (2) and (3) in (1):

A = 0.5 · (2 · b + 2 · l · cos θ) · (l · sin θ)

A = (b + l · cos θ) · (l · sin θ)

A = b · l · sin θ + l² · sin θ · cos θ

A = b · l · sin θ + 0.5 · l² · sin 2θ  (4)

If we know that b = 6 in and l = 4 in, then the area of the isosceles trapezoid is represented by the following function:

A = 24 · sin θ + 8 · sin 2θ   (5)

Now we determine the angle associated to the maximum area by graphic approach.

According to this approach, the internal angles of 64.801° (2 in total) and 115.199° (2 in total) lead to a maximum area of 27.88 square units. [tex]\blacksquare[/tex]

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Answer:

Step-by-step explanation:

Divide the numerator by the denominator.

Write down the whole number part of the quotient.

Take the remainder and write it over the original denominator.

Answer: 7

Step-by-step explanation:

Answer:

472 :)

Step-by-step explanation:

47.2/0.1 = 472

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Answer:

48 + 8x = 9

Step-by-step explanation:

4 + [tex]\frac{2}{3}[/tex] x = [tex]\frac{3}{4}[/tex]

multiply through by 12 ( the LCM of 3 and 4 ) to clear the fractions

48 + 8x = 9

Answer:

this answer is 0.83

Step-by-step explanation:

5/8 is 0.625, 3/4 is 0.75 and 0.625 divided by 0.75 is 0.83

Answer: 5/6

All you have to do is combine the two equations, like so [tex]\frac{5*4}{8*3}[/tex]

Multiply [tex]\frac{20}{24}[/tex]

Then simplify [tex]\frac{5}{6}[/tex]

Answer:

  86.7%

Step-by-step explanation:

For questions regarding values related to a normal distribution, a suitable calculator is required. Numerous calculators, apps, web sites, and spreadsheets are capable of answering this question.

__

One standard deviation above the mean is 327 +27 = 354, so the value is expected to be slightly more than 50% +34% = 84%. It is no surprise, then, that a calculator tells you 86.7% of the data is below 857.

_____

Additional comment

The "empirical rule" tells you 68% of the area is within 1 standard deviation of the mean. The distribution is symmetrical, so half that, 34%, is between the mean and 1 standard deviation above the mean. Of course, 50% of the data is below the mean.

Answer:

- sin (x)

Step-by-step explanation:

Presumably you mean the second derivative of y with respect to x, d²y/dx².

Compute the first derivative. By the chain rule,

[tex]\dfrac{dy}{dx} = \dfrac{dy}{dt} \times \dfrac{dt}{dx} = \dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]

Differentiate the two parametric equations with respect to t :

[tex]x = \sin(t) \implies \dfrac{dx}{dt} = \cos(t)[/tex]

[tex]y = \cos(t) \implies \dfrac{dy}{dt} = -\sin(t)[/tex]

Then the first derivative is

[tex]\dfrac{dy}{dx} = \dfrac{-\sin(t)}{\cos(t)} = -\tan(t)[/tex]

Now, dy/dx is a function of t, so we can denote it by, say, dy/dx = f(t). Then by the chain rule, the second derivative will be

[tex]\dfrac{d^2y}{dx^2} = \dfrac{df}{dx} = \dfrac{df}{dt} \times \dfrac{dt}{dx} = \dfrac{\frac{df}{dt}}{\frac{dx}{dt}}[/tex]

Differentiating f(t) :

[tex]f(t) = -\tan(t) \implies \dfrac{df}{dt} = -\sec^2(t)[/tex]

Then the second derivative is

[tex]\dfrac{d^2y}{dx^2} = \dfrac{-\sec^2(t)}{\cos(t)} = \boxed{-\sec^3(t)}[/tex]

and since y = cos(t), we can go on to say

[tex]\dfrac{d^2y}{dx^2} = -\dfrac1{y^3}[/tex]

Step-by-step explanation:

7.2

5

24

2345

6303

-3

2467.2

5

24

2345

6303

-3

246

The linear function is given by table B and the equation y = ( 1/2 )x + 3.2

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution

On a graph, a linear equation forms a straight line. On a graph, a nonlinear equation produces an S-curve, a bell curve, or another nonlinear shape.

Given data ,

Let the linear function be represented as A

Now , the value of A is

Let the x values be x = { 0 , 2 , 4 , 6 , 8 }

Let the y values be y = { 3.2 , 4.2 , 5.2 , 6.2 , 7.2 }

Now , the equation of line is y - y₁ = m ( x - x₁ )

where m is the slope

m = ( 4.2 - 3.2 ) / ( 2 - 0 )

m = 1/2

On simplifying , we get

y - 3.2 = ( 1/2 ) ( x - 0 )

Adding 3.2 on both sides , we get

y = ( 1/2 )x + 3.2

Hence , the linear function is y = ( 1/2 )x + 3.2

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⠀

Explanation :

⠀

We know,

[tex]{ \longrightarrow{\qquad \pmb {\sf Volume_{(Sphere)} = \dfrac{4}{3} \pi {r}^{3} }}}[/tex]

⠀

Here,

⠀

Substituting the values in the formula :

⠀

[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4}{3} \times3.14 \times {\bigg(7 \bigg)}^{3} }}}[/tex]

⠀

[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4}{3} \times 3.14 \times 343 }}}[/tex]

⠀

[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4 \times 3.14 \times 343}{3} }}}[/tex]

⠀

[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4308.08}{3}}}}[/tex]

⠀

[tex]{ \longrightarrow{\qquad \pmb {\sf Volume_{(Sphere)} = 1436.02 }}}[/tex]

⠀

Therefore,

Answer: 6 outfits

Step-by-step explanation:

$620 should be greater than the price of the new bicycle + 3 * bicycle reflectors + a pair of bike gloves + unknown number of biking outfits

Therefore, the inequality will be:

620 ≥ 261.04 + 3 × 13.07 + 13.57 + 51.03x

620  ≥ 313.82 + 51.03x

[tex]\text{Solving \ for \ x}[/tex]

[tex]620\ge \:313.82+51.03x[/tex]

[tex]\mathrm{Switch\:sides}[/tex]

[tex]313.82+51.03x\le \:620[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}100[/tex]

[tex]313.82\cdot \:100+51.03x\cdot \:100\le \:620\cdot \:100[/tex]

[tex]\mathrm{Refine}[/tex]

[tex]31382+5103x\le \:62000[/tex]

[tex]\mathrm{Subtract\:}31382\mathrm{\:from\:both\:sides}[/tex]

[tex]31382+5103x-31382\le \:62000-31382[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]5103x\le \:30618[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}5103[/tex]

[tex]\frac{5103x}{5103}\le \frac{30618}{5103}[/tex]

[tex]\text{Simplify}[/tex]

[tex]{x\le \:6}[/tex]

Therefore, Brianna can buy 6 or fewer outfits while staying within her budget

Answer:

49ft²

Step-by-step explanation:

A=bh

A=bh=9.8·5=49

Answer:

(5*2) + (1/2)(2+2+2)*4)

Step-by-step explanation:

Area of Triangle = (1/2)(2 + 2 + 2 )* 4)

Area of Rectangle = 5 * 2

Total Area = (5*2) + (1/2)(2+2+2)*4)

Answer:

I believe it would be 9.

Step-by-step explanation:

Finding Dialation: 16/12 = 1.3
Height: 16/1.3 = 12
Width: 12/1.3 = 9

Answer: TThere is no picture

Step-by-step explanation:

Answer:

Hope the picture will help you. Make sure to mark my answer brilliant

Scale factor is 5

So

Answer:

Points of kite JKLM:

J = (1, -2)

K = (2, -1)

L = (1, 2)

M = (0, -1)

To dilate a figure about a point, draw a line from the point to each point of the figure, then extend (or reduce) the line so that it is the length of the original line multiplied by the scale factor.

So to dialate JKLM about the origin by scale factor of 5, draw a line from (0, 0) to each point of the kite.  Extend the lines so that they are each 5 times the original lengths.  These are the dilated points

Points of kite dilated by sf 5 (shown in blue on the attached diagram):

J' = (5, -10)

K' = (10, -5)

L' = (5, 10)

M' = (0, -5)

Answer:

Step-by-step explanation:

The figure has 2 triangular and 3 rectangular faces.

This is a right triangular prism.

Find the area of each face and add up to get the total surface area.

Each triangle has base of 10 and height of:

Total surface area is

Answer:

Step-by-step explanation:

It would be about 3.14 as since it is only 1 inch pi is multiplyed by one and when rounding pi to the hundreths you get 3.14 hope this helps

Answer:

4 < x < 12

Step-by-step explanation:

Given:

[tex]\displaystyle \large{9|x-8| < 36}[/tex]

Divide both sides by 9:

[tex]\displaystyle \large{|x-8| < 4}[/tex]

Theorem:

For [tex]\displaystyle \large{|x-a| < b}[/tex], since absolute is less than a constant, the interval or solution is:

[tex]\displaystyle \large{-b < x-a < b}\\\displaystyle \large{-b+a < x < b+a}[/tex]

Therefore:

[tex]\displaystyle \large{|x-8| < 4 \to -4 < x-8 < 4}\\\displaystyle \large{-4+8 < x < 4+8}\\\displaystyle \large{4 < x < 12}[/tex]

Therefore, the solution is 4 < x < 12

Answer:

4 < x < 12

Step-by-step explanation:

9|x - 8| < 36

Divide both sides by 9:

|x - 8| < 4

Solution 1

(x - 8) < 4

Add 8 to both sides:

x < 12

Solution 2

-(x - 8) < 4

-x + 8 < 4

Subtract 8 from both sides:

-x < -4

Divide both sides by -1 (remembering to change the direction of the sign):

x > 4

Therefore, the solution to the inequality is   4 < x < 12

236 x 0.126

29.736 MB have been downloaded

Answer:

y = -1.4x + 16

Step-by-step explanation:

the slope is -1.4x

Use the slope formula:-

[tex]\displaystyle\frac{y2-y1}{x2-x1}[/tex]

Plug in the values:-

[tex]\displaystyle\frac{9-2}{5-10}[/tex]

Simplify:-

[tex]\displaystyle\frac{7}{-5}= -\frac{7}{5}[/tex]

 [tex].~~~~~~~\uparrow\sf{Slope}[/tex]

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

Answer:1)x =-30

2)x=-30

Step-by-step explanation: 1:  2(3x+5)=5(x-4) ( remove the parenthesis)

then 6x+-5x=-20x-10 (collect the like trems calulate) so (-20 and -20 on each side) the x=-20-10.

 2: 6x+10=5x-20 (move the like trems) so move the variable to the left hand side and change its sign like this 6x+10-5x=-20

6x-5x=-20-10

x=-20-10 which it ='s  x=-30

follow my TT at yvngxmiia

Solving Stepwise:

Additional Explanation

Distributive property:

symmetric property of equality:

subtraction property of equality:

closure property:

division property of equality:

Answer:

(i) [tex]y = 2x(x-5)[/tex]

(ii)  zeros:  x = 0 and x = 5

axis of symmetry:  x = 2.5

(iii)  vertex:  (2.5, -12.5)

(iv) see attached

Step-by-step explanation:

Part (i)

Factor:  [tex]y=2x^2-10x[/tex]

Factor out the common term [tex]2x[/tex]:

[tex]\implies y=2x(x-5)[/tex]

Part (ii)

Zeros occur when [tex]y=0[/tex]

[tex]\implies 2x(x-5)=0[/tex]

Therefore:

[tex]\implies 2x=0 \implies x=0[/tex]

[tex]\implies (x-5)=0 \implies x=5[/tex]

So the zeros are x = 0 and x = 5

The axis of symmetry of a parabola is x = a where a is the midpoint of the zeros.

[tex]\textsf{midpoint of zeros}=\dfrac{0+5}{2}=2.5[/tex]

Therefore, the axis of symmetry is [tex]x=2.5[/tex]

Part (iii)

The axis of symmetry is the x-coordinate of the vertex. To find the y-coordinate of the vertex, substitute this into the given equation.

[tex]\implies 2(2.5)^2-10(2.5)=-12.5[/tex]

So the vertex is (2.5, -12.5)

Part (iv)

Plot the zeros and the vertex.

As the leading coefficient is positive, the parabola will open upwards, so the vertex is the minimum point.

Draw the axis of symmetry, then sketch the parabola, ensuring each side of the axis of symmetry is symmetrical.

*see attached*

The surface area of the given figure is 90 feet².

The area of a three dimensional object on it's outer surface is called the surface area of the object.

The given figure is a rectangular prism.

A rectangular prism consists of 4 rectangular lateral faces and 2 rectangular bases.

Surface area of the rectangular prism is the area of each of the faces.

Combining all these area, area of a rectangular prism can be found by the formula,

Area = 2 (lw + wh + lh)

where l is the length, w is the width and h is the height.

Given, l = 3 feet, w = 3 feet and h = 6 feet

Area = 2 [ (3 × 3) + (3 × 6) + (3 × 6)]

        = 2 (9 + 18 + 18)

        = 90 feet²

Hence the surface area is  90 feet².

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Answer:

  19 -d

Step-by-step explanation:

The number Johnson has left is found by subtracting the number he gave away from the number he started with.

  19 -d . . . . . . . number of ice cream bowls left