Please help! Using the Pythagorean theory with rectangles!

#10. In order to find a ratio, all we need to do is set up a simple equation and then cross-multiply!

I'll show you !

In this case, we'll take the already established ration (14 : 8 ) and find the equivalent ratio where 7 is in place of 14 (7: x)

x will be the other table value we are looking for!

Now let's set up the equation and cross-multiply!

\(\frac{14}{8} = \frac{7}{x}\)

cross multiply 14 and x, then 8 and 7

We get:  14x = 56

solve to find x!

x = 56/14

x = 4 blankets

Now let's use the ratio 7: 4 to find what goes with 16 in the table!

\(\frac{7}{4} = \frac{x}{16}\)

4x = 112

x = 112/4

x = 28 towels

_________________________________________________-

#11. : Using the same method, I'll fill in the values of the table on #11

16 forks, 10 spoons

8 forks, 5 spoons,

48 forks, 30 spoons

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#12. If the neighbor pays you $17 for every 2 hours of work, we need to find how many times 2 hours goes in 8 hours of work

We do this by dividing

8/2 = 4 times

2 hours of work goes into 8, 4 times!

Now we multiply 4 by $17 to find how much your neighbor owes you!

$17 × 4 = $68

Your neighbor owes you $68 !!!

Answer:

272

Step-by-step explanation:

a. The given table is

Notice, the value of x increases at equal intervals of 1

Also, the value of y increases at an equal interval of 3

This means for the y values the difference between consecutive terms is 3

Also, for the x values, the difference between consecutive terms is 1

Hence, the table represents a linear function

The general form of a linear function is

Where m is the slope

From the interval increase

Hence, m = 3

The equation becomes

To get c, consider the values

x = 0 and y = 2

Thi implies

Hence, the equation of the linear function is

b. The given table is

Following the same procedure as in (a), it can be seen that there is no constant increase in the values of y

Hence, the function is not linear

This implies that the function is exponential

The general form of an exponential function is given as

Consider the values

x =0, y = 3

Substitute x = 0, y = 3 into the equation

This gives

The equation become

Consider the values

x =1, y = 6

Substitute x = 1, y = 6 into the equation

This gives

Therefore the equation of the exponential function is

c. The given table is

As with (b) above,

The function is exponential

Using

When

x = 0, y = 10

This implies

The equation becomes

Also, when

x = 1, y =5

The equation becomes

Therefore, the equation of the exponential function is

The smallest to the largest side is SQ, RS, QR, the correct option is B.

A triangle is a polygon with three sides, angles, and vertices.

The triangle is classified into various types on the basis of the angle and on the basis of the equality of the length of the sides, as obtuse, acute and right-angled triangle and scalene, isosceles and equilateral triangle.

The measure of angle of the triangle is 56°, 83°, and 41°.

From the property of the triangle, the side opposite the bigger measure angle is the largest.

The measure of angle QRS is 41°, angle RQS is 56°, and angle QSR is 83°.

The smallest side will be the side opposite to QRS, i.e. SQ,

The largest side will be the side opposite to QSR, i.e. QR

The side in order from the smallest to the largest, SQ, RS, QR.

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Using implicit differentiation, it is found that the water level is rising a rate of 0.001 ft/sec.

The volume of a pool of length l, width w and height h is given by:

\(V = lwh\)

Applying implicit differentiation, the rate of change of the volume is given by:

\(\frac{dV}{dt} = wh\frac{dl}{dt} + lh\frac{dw}{dt} + lw\frac{dh}{dt}\)

Neither the width nor the length changes, hence \(\frac{dl}{dt} = \frac{dw}{dt} = 0\), and:

\(\frac{dV}{dt} = lw\frac{dh}{dt}\)

We are given that:

\(\frac{dV}{dt} = 0.3, l = 20, w = 40\), hence:

\(\frac{dV}{dt} = lw\frac{dh}{dt}\)

\(0.8 = 20(40)\frac{dh}{dt}\)

\(\frac{dh}{dt} = \frac{0.8}{800}\)

\(\frac{dh}{dt} = 0.001 \)

Water level is rising at rate of 0.001 ft/sec.

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Answer:

2) Midline: \(\displaystyle y = 1\)

Amplitude: \(\displaystyle 2\)

Period: \(\displaystyle 2\pi\)

Horisontal Shift: \(\displaystyle \pi\)

1) Midline: \(\displaystyle y = -2\)

Amplitude: \(\displaystyle 1\)

Period: \(\displaystyle \pi\)

Horisontal Shift: \(\displaystyle 0\)

Step-by-step explanation:

2) \(\displaystyle \boxed{y = 2cos\:(\theta - 1\frac{1}{2}\pi) + 1} \\ y = Acos\:(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{1\frac{1}{2}\pi} \hookrightarrow \frac{1\frac{1}{2}\pi}{1} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} = \frac{2}{1}\pi \\ Amplitude \hookrightarrow 2\)

OR

\(\displaystyle y = Asin\:(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\pi} \hookrightarrow \frac{\pi}{1} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi}\hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 2\)

1) \(\displaystyle \boxed{y = sin\:(2\theta + \frac{\pi}{2}) - 2} \\ y = Asin\:(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} = \frac{2}{2}\pi \\ Amplitude \hookrightarrow 1\)

OR

\(\displaystyle y = Acos\:(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi}\hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 1\)

With the information above, you now should have an ideya of how to interpret trigonometric equations and graphs like these.

I am delighted to assist you at any time.

Answer:

20

Step-by-step explanation:

percentage error = predictions - actual ÷actual × 100

error

\( \frac{82 - 52 \\ }{52} \times 100\)

=

20

Answer:

The domain is \(D_C = [0,\infty)\)

The range is: \(R_C = [20,\infty)\)

Step-by-step explanation:

Domain and range of a function:

The domain of a function are the values that the input assumes, while the range are the values that the output assumes.

In this question:

\(C(m) = 0.05m + 20\)

m is the input, which is the number of phone calls, which can be any number between 0 and infinite. So

The domain is \(D_C = [0,\infty)\)

When the input is m = 0, the value of C(0) = 20. As m increases, so does C(m). This means that:

The range is: \(R_C = [20,\infty)\)

Answer:

Option 1  because

domain: m is Greater than or equal to zero

range: C is greater than or equal to twenty

Step-by-step explanation:

The (C) cost of the bill is always going to start at twenty and be higher depending on how many (m) minutes were used.

Edg2021

Answer:

7 sheets of paper

Step-by-step explanation:

$40-$19=$21

$21/$3=7 sheets of paper.

In words:

I did 40 minus 19 to get 21, and the divided 21 by 3 to get 7 sheets of paper.

Well, this is one possible answer:

-2.07 = -(1/0.7) , where / is the fraction line.

Answer:

Step-by-step explanation:

An equation can be set up and solved based on the relation between the two speeds and the relation between time, speed, and distance.

  time = distance/speed

Let x represent the (slower) speed on the way home. Then the total time for the round trip was ...

  time going + time coming home = total time

  270/(x +11) +270/x = 9

  30x +30(x +11) = x(x +11) . . . . . . multiply by x(x+11)/9

  x^2 -49x -330 = 0 . . . . . . . .  rewrite in standard form

  (x -55)(x +6) = 0 . . . . . . . . factor

x = 55 or x = -6 . . . . . . . solutions to this equation; x < 0 is extraneous

Justin's rate on the way there was 66 mph; on the way home, it was 55 mph.

The possible values for a third quiz score that would give her an average between 85 and 90, inclusive is: 97 ≤ x ≤ 112.

In Mathematics, the average of these quiz scores can be calculated by using the following formula:

Average = Sum of quiz score/Number of quiz scores

Note: Let the variable q represent the student's score on the third (3rd) quiz.

Substituting the given parameters into the formula, we have the following;

Average = (75 + 83 + q)/3

Average = (158 + q)/3

This ultimately implies that, an average between 85 and 90, inclusive is given by this compound inequality:

85 ≤ (158 + q)/3 ≤ 90

Multiplying all through by 3, we have the following:

255 ≤ (158 + q) ≤ 270

Subtracting 158 from both sides of the inequality, we have the following:

97 ≤ x ≤ 112

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The length of the real life plane is 8000 centimetres.

The scale model as a ratio is  1:2000.

A model of a plane has a length of  4 cm. The real life plane has a model of 80 m.

The length of the real life plane in centimetres is as follows:

1 metre = 100 centimetres

80 metres = ?

cross multiply

length of the real life plane in cm = 80 × 100

length of the real life plane in cm = 8000 centimetres

The scale model can be calculated as follows;

scale model = 4 / 8000

scale model = 1 / 2000 = 1:2000

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Answer:

35.6

Step-by-step explanation:

By the Pythagorean Theorem:

\( {x}^{2} + {91.3}^{2} = {98}^{2} \)

\(x = \sqrt{ {98}^{2} - {91.3}^{2} } = 35.6\)

This function written in vertex form include the following: A. f(x) = (x –1)² – 7.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = x² – 2x – 6, we have:

a = 1, b = -2, and c = -6

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-2)/2(1)

Axis of symmetry, Xmax = 2/2

Axis of symmetry, Xmax = 1.

Next, we would determine vertex as follows;

f(x) = x² – 2x – 6

f(x) = 1² – 2(1) – 6

f(x) = -7.

Now, we can write quadratic function in vertex form;

f(x) = a(x - h)² + k

f(x) = (x - 1)² - 7

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Complete Question:

The image shows a geometric representation of the function f(x) = x² – 2x – 6 written in standard form.

What is this function written in vertex form?

f(x) = (x –1)² – 7

f(x) = (x +1)² – 7

f(x) = (x –1)² – 5

f(x) = (x +1)² – 5

Answer:

Step-by-step explanation:

P=4/28=1/7

Answer:

14.3% or 1/7

Step-by-step explanation:

4 / 28

4 students who play a sport and instrument divided by 28 total students

Given:

\((x+9)^2\)

To find:

The given expression as a trinomial in standard form.

Solution:

We have,

\((x+9)^2\)

Using the formula, \((a+b)^2=a^2+2ab+b^2\), we get

\((x+9)^2=x^2+2(x)(9)+(9)^2\)

\((x+9)^2=x^2+18x+81\)

Standard form a trinomial is \(ax^2+bx+c\).

\(x^2+18x+81\) is in the standard form.

Therefore, the required expression is \(x^2+18x+81\).

The angle of rotation about the origin, (0, 0) that maps WXYZ TO W’ X’ Y’Z are

180 degrees

540 degrees

900 degrees

The transformation rule for an angle of 180 degrees is simply a reflection or a flip. This means that any object or figure that undergoes this transformation will be flipped over a line or axis.

The rule is (x, y) will become (-x, -y)

Where 540 degrees = 360 + 180

where 900 degrees = 360 + 360 + 180

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Answer:

  both functions have the same graph

Step-by-step explanation:

The first function is described in terms of its slope and y-intercept, so can be written in slope-intercept form as ...

  y = mx + b . . . . m = slope (-7/9); b = y-intercept (3)

  y = -7/9x +3

__

The second function is written in point-slope form:

  y -k = m(x -h) . . . . m = slope (-7/9), point = (h, k) = (18, -11)

  y +11 = -7/9(x -18)

If we rearrange the second equation to the form of the first, we get ...

  y = -7/9x +14 -11 . . . . eliminate parentheses, subtract 11

  y = -7/9x +3 . . . . . . . matches the equation of the first function

__

Both functions describe the same relation.

Answer:

10

Step-by-step explanation:

This triangle is isosceles, same as the little triangle.

If one side of the little triangle is 3x, then the little side with the tick (let's name it a) is also 3x.

That means the longer side, 2a, is 6x

This triangle is isosceles, so 6x = 4x + 20

Now, if we solve that, x = 10

The answer is 10

Hope this helps :)

Have a good day!

Answer:

2^3 = 8

Step-by-step explanation:

I'm not sure what you mean, but I'll try.

2^3 is the same as \( 2^3 \),

and it means a multiplication of 3 factors of the base, 2.

That means \(2^3 = 2 \times 2 \times 2 = 4 \times 2 = 8\)

Answer:

11

Step-by-step explanation:

using PEMDAS, u have to do parentheses first, x is equal to 6, so thats 7. then u multiply 7 times 2 and thats 14. then u subtract 14 minus 3 and thats 11. Hope this helps

Answer:

A

Step-by-step explanation:

2(x+1)-3

2×(6+1)-3

2×(7)-3

14-3

11

The specified scale factor of the dilation from S to M is 3/2 therefore, the scale factor of the dilation transformation from M to S is 2/3

A dilation is a transformation in which the lengths of the sides of the image are increased or decreased in the proportion, specified by a scale factor to the dimensions of the pre-image.

The specified scale factor from triangle S to triangle M = 3/2

3/2 = 1.5

Therefore, the length of the sides of triangle M are 1.5 times the lengths of the sides of triangle S

Let L represent the length of a side of triangle S, we get;

The length of the corresponding side on triangle M = 1.5 × L

The scale factor from triangle M to triangle S is found by taking the ratio of the corresponding sides of triangle S and M as follows;

Scale factor, SF, from M to S  = Length of a side on triangle S ÷ Length of the corresponding side on triangle

Therefore;

\(SF = \dfrac{L}{1.5\cdot L} = \dfrac{1}{1.5}\)

1.5 = 3/2, therefore;

\(SF = \dfrac{1}{1.5} = \dfrac{1}{\frac{3}{2} } =\dfrac{2}{3}\)

Therefore, the scale factor from M to S is 2/3

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Answer: C

Step-by-step explanation:

Answer:

1.97497

Step-by-step explanation:

Using my calculator, I just put in log(94.4).

Answer: 6/(6+2x) ; (-infinity, -3) U (-3, infinity)

Step-by-step explanation:

(a) This can be read as f(x) composed of g(x). Plug in the expression given for g(x) for every x value in f(x):

(6/x)/(6/x+2)

I gave the terms in the denominator the same denominator to combine the bottom two terms into one term. 6/x + 2 is equal to 6/x + 2x/x -->

(6 +2x)/x

Do the classic keep, change, flip. \(\frac{6}{x} * \frac{x}{6+2x}\)

This simplifies to: \(\frac{6}{6+2x}\)

(b) Domain is all real numbers except for what makes the denominator equal to 0.     6 + 2x = 0 when x = -3. Therefore it is all real numbers except -3.

Answer:

A die usually has 6 sides.

Answer - B (1/2)

Answer:

It would be C

Step-by-step explanation:

I have done this before!

Answer: 44

Step-by-step explanation:

The interior and exterior in these type of problems equal 180. 180 – 136 = 44

Answer:

x=0 or x=3

Step-by-step explanation:

Since it is a geometric sequence, that means term divided by previous term is the same number. Let's call that number, r.

That means we have:

(3x+1)/(2x-1)=r

(7x-1)/(3x+1)=r

Since both of the ratios are the same, then we have

(3x+1)/(2x-1)=(7x-1)/(3x+1)

Cross multiply:

(3x+1)(3x+1)=(2x-1)(7x-1)

Distribute:

9x^2+3x+3x+1=14x^2-2x-7x+1

Combine like terms:

9x^2+6x+1=14x^2-9x+1

Subtract 1 on both sides:

9x^2+6x=14x^2-9x

Subtract 14x^2 on both sides

Add 9x on both sides

-5x^2+15x=0

Factor -5x:

-5x(x-3)=0

-5x=0 when x=0 since -5(0)=0

x-3=0 when x=3 since 3-3=0