this is confusing me please helpppp

Answer:

36 in.

Step-by-step explanation:

find the area of the rectangle and triangle first

area of rectangle = length x height

aR = (6 + 6) x 5

aR = 12 x 5

aR = 60

area of triangle = base x height x 1/2

aT = (6 + 6) x 4 x 1/2

aT = 12 x 4 x 1/2

aT = 24

now, to find the area of the shaded area subtract the triangle from the rectangle

area = rectangle - triangle

a = 60 - 24

a = 36

Answer:

a. 25 seniors are randomly selected; 14 plan to go to a 4 year college

b. 420 students

Step-by-step explanation:

a. the less they have in common, the better

b. 14/25 is only between 25 students. make the denominator the same (750) and multiply the same to the numerator

750/25 = 30

14/25 x 30 = 420/750

Answer:

[tex]\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}[/tex]

Step-by-step explanation:

NOTE :

[tex]x^2+ax=\left( x+\frac{a}{2} \right)^{2} -\left( \frac{a}{2} \right)^{2}[/tex]

………………………………………

f(x) = x² + x +1

     [tex]=x^{2}+2\times \frac{x}{2} +1[/tex]

     [tex]=\left( x+\frac{1}{2} \right)^{2} -\left( \frac{1}{2} \right)^{2} +1[/tex]

     [tex]=\left( x+\frac{1}{2} \right)^{2} - \frac{1}{4}+1[/tex]

     [tex]=\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}[/tex]

Based on the given variation, y does not vary directly with x and the constant of variation are 8, 3.2 and 1.25 respectively.

y = k × x

where,

k = constant of proportionality

y = -40

x = -5

y = k × x

-40 = k × -5

-40 = -5k

k = -40/-5

k = 8

when,

y = 8 and x = 2.5

y = k × x

8 = k × 2.5

8 = 2.5k

k = 8/2.5

k = 3.2

when,

y = 5 and x = 4

y = k × x

5 = k × 4

5 = 4k

k = 5/4

k = 1.25

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Answer:

  $70,300

Step-by-step explanation:

The amount Kaydence saved is the value of an arithmetic series with first term 100 and common difference 100. The number of terms in the sum is 37. The formula for the sum can be used.

The formula for the sum of n terms of an arithmetic series is ...

  Sn = (2a1 +d(n -1))(n/2) . . . . . . first term a1, common difference d

The number of terms being added is ...

  2050 -2014 +1 = 37 . . . . . . years Kaydence made deposits

The formula with a1=100, d=100, and n=37 is ...

  [tex]S_{37}=(2\cdot100+100(37-1))\dfrac{37}{2}=\dfrac{(200+3600)\cdot37}{2}\\\\S_{37}=70,\!300[/tex]

Kaydence would have saved $70,300 by the end of Jan 1, 2050.

Answer:

Original equation:

y = a sin(b(θ -c)) + d

a = vertical dilation (stretch) of the amplitude

b = horizontal compression (shrink) of the period

c = horizontal shift (left/right)

d = vertical shift (up/down)

Your function is:

y = 3 sin(3θ + π) - 2

First, put it into the general from by factoring out the three in the argument of the sine:

y = 3 sin(3(θ + π/3)) - 2

a = vertical (amplitude) dilation = 3

b = horizontal (period) compression = 2π/period = 3

c = horizontal shift = π/3 to the left

d = vertical shift = -2

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation a.}[/tex]

[tex]\rm{2x^2 - 162 = 0}[/tex]

[tex]\huge\textbf{Solving for:}[/tex]

[tex]\rm{2x^2 - 162 = 0}[/tex]

[tex]\huge\textbf{Add \boxed{\bf 162} to both sides:}[/tex]

[tex]\rm{2x^2 - 162 + 162 = 0 + 162}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{2x^2 = 0 + 162}[/tex]

[tex]\rm{2x^2 = 162}[/tex]

[tex]\huge\textbf{Divide \boxed{\bf 2} to both sides:}[/tex]

[tex]\rm{\dfrac{2x^2}{2} = \dfrac{162}{2}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{x^2 = \dfrac{182}{2}}[/tex]

[tex]\rm{x^2 = 81}[/tex]

[tex]\huge\textbf{Take the square root of \boxed{\bf 81}}[/tex]

[tex]\rm{x = \pm \sqrt{81}}[/tex]

[tex]\rm{x = 9\ or\ x = -9}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\textsf{x = } \frak{9\ or } \ \textsf{x = }\frak{-9}}\huge\checkmark[/tex]

[tex]\huge\textbf{Equation b.}[/tex]

[tex]\rm{-\dfrac{1}{2}(x - 3)^2 = -2}[/tex]

[tex]\huge\textbf{Solving for:}[/tex]

[tex]\rm{-\dfrac{1}{2}(x - 3)^2 = -2}[/tex]

[tex]\huge\textbf{Simplify both sides of your equation:}[/tex]

[tex]\rm{-\dfrac{1}{2}x^2 + 3x - \dfrac{9}{2} = -2}[/tex]

[tex]\huge\textbf{Subtract \boxed{\bf -2} to both sides:}[/tex]

[tex]\rm{-\dfrac{1}{2}x^2 + 3x - \dfrac{9}{2} - (-2) = -2 - (-2)}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{- \dfrac{1}{2}x^2 + 3x - \dfrac{5}{2} = 0}[/tex]

[tex]\huge\textbf{Now, we can convert the equation to:}[/tex]

[tex]\rm{-0.5x^2 + 3x - 2.5 = 0}[/tex]

[tex]\large\text{When we changed the equation entirely, we made it easier to solve}\uparrow[/tex]

[tex]\huge\textbf{Use the quadratic formula to solve.}[/tex]

[tex]\large\textsf{The quadratic formula:}[/tex]

[tex]\mathsf{x= \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]

[tex]\huge\textbf{Here are your labels:}[/tex]

[tex]\text{a = }\rm{-0.5}\\\\\text{b = }\rm{ 3}\\\\\rm{c = }\rm{\ -2.5}[/tex]

[tex]\huge\textbf{Your new equation:}[/tex]

[tex]\rm{x = \dfrac{-(3) \pm \sqrt{3^2 - 4(-0.5)(-2.5)}}{2(-0.5)}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{x = \dfrac{-3 \pm \sqrt{4}}{-1}}[/tex]

[tex]\rm{x = 1\ or \ x = 5}[/tex]

[tex]\huge\textbf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\textsf{x = }\frak{1}\ \textsf{or x = }\frak{5}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

[tex]a)\ x_1=-9,\ x_2=9\\\\b)\ x_1=1,\ x_2=5[/tex]

Given equations:

[tex]a)\ 2x^2 - 162 = 0\\\\b) -\dfrac{1}{2}(x-3)^2=-2[/tex]

A) 2x² - 162 = 0

Step 1: Divide both sides by 2.

Step 2: Take the square root of both sides (using both the positive and negative roots).

[tex]\\\implies \sqrt{x^2}=\sqrt{81}\\\\\implies x=\pm\ 9[/tex]

Step 3: Separate into two cases.

[tex]\implies x_1 = -9,\ x_2 =-9[/tex]

----------------------------------------------------------------------------------------------------------------

B) -1/2(x - 3)² = -2

Step 1: Multiply both sides by -2.

[tex]\\\implies -2\left(-\dfrac{1}{2}(x-3)^2\right)=-2(-2)\\\\\implies (x-3)^2=4[/tex]

Step 2: Take the square root of both sides (using both the positive and negative roots).

[tex]\\\implies\sqrt{(x-3)^2}=\sqrt{4}\\\\\implies x-3=\pm\ 2[/tex]

Step 3: Separate into two cases and solve each one.[tex]1)\ x-3=-2\implies x=-2+3\implies \boxed{x=1}\\\\2)\ x-3=2\implies x=2+3\implies \boxed{x=5}[/tex]

There are two methods of solving systems of equations:

Substitution is where we substitute one equation into the other by isolating a certain variable, or a group of terms.

Elimination is where we subtract the two equations. Before doing this, we may have to multiply one equation by a certain number to make sure one variable cancels out.

We're given the following equations:

Because they are organized in the same manner (i.e. x [operation] y [equals] number), it is easier for us to use elimination.

First, multiply the first equation by 2:

[tex]x + 3y = 7\\2(x + 3y) = 2(7)\\2x + 6y = 14[/tex]

Now, subtract the second equation from the one we just created:

[tex]\hspace{10}2x + 6y = 14\\-2x + 4y = 11\\\rule{67}{0.3}\\2y=3[/tex]

Solve for y:

[tex]y=\dfrac{3}{2}[/tex]

To solve for x, we can use substitution in the first equation:

[tex]x + 3y = 7\\\\x + 3(\dfrac{3}{2}) = 7\\\\x + \dfrac{9}{2} = 7\\\\x = 7- \dfrac{9}{2}\\\\x = 7- 4.5\\\\x = 2.5\\\\x=\dfrac{5}{2}[/tex]

[tex]x=\dfrac{5}{2}[/tex]

[tex]y=\dfrac{3}{2}[/tex]

Using the unit circle, the correct answer regarding the comparison of angles w and t is given by:

a. t > w.

For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].

From this, we get that the sine is represented by the vertical axis. As we advance into the second quadrant, as the angle increases, sine decreases. Hence, since sin w > sin t, we have that t > w and option a is correct.

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Answer:

  D.  completing the square

Step-by-step explanation:

The process shown rearranges the standard-form quadratic equation to vertex form. It involves factoring out the leading coefficient and distributing the constant so that the variable terms can be written as a perfect square.

A perfect square trinomial is the square of a binomial. It has the form ...

  (x +b)² = x² +2bx +b²

Given two variable terms, x² and 2bx, the perfect square trinomial can be formed by adding b², which is the square of half the x-term coefficient.

When b² is added to the sum (x² +2bx), the square is complete. The sum (x² +2bx +b²) can be written as the square (x +b)².

This process of adding b² to the sum (x² +2bx) will change the polynomial unless a similar quantity is subtracted. That is why the 3rd line of the problem statement show 4 being added and subtracted inside parentheses:

  y = 5(x² +4x +4 -4) -17

When we're applying this transformation, we do not want to change the equation. We simply want to rearrange it.

In the next step, the subtracted term is brought outside the parentheses. This lets us write the quantity in parentheses as a perfect square.

  y = 5(x² +4x +4) +5(-4) -17

  y = 5(x² +4x +4) -20 -17

This process of adding and subtracting a suitable quantity and rearranging the equation so the variable terms make a perfect square is called ...

  "completing the square."

__

Additional comment

The equation in this form is said to be in "vertex form."

  y = a(x -h)² +k

In this form, the constant 'a' is a vertical scale factor; the ordered pair (h, k) identifies the vertex of the quadratic on a graph.

Subsets with bit strings:

To find the subsets with bit strings:

We need to express a) b) and c) into bit strings.

Firstly, a number of elements in the universal set represent the number of bits in the bit string.

Secondly, 1 = yes element is present in both universal sets as well as in subset.

0 = No, the element is not present in the subset but present in the universal set.

Hence, we have:

a) Subset {3,4,5} = 0011100000  (As there are 3 1's which means only 3,4,5 are present in both universal set and subset.

Similarly,

b) Subset {1, 3, 6, 10} = 1010010001

c) Subset {2, 3, 4, 7, 8, 9} = 0111001110

Therefore, Subsets with bit strings:

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Complete question:

Suppose that the universal set is U={1,2,3,4,5,6,7,8,9,10}. Express each of the following subsets with bit strings (of length 10) where the ith bit (from left to right) is 1 if i is in the subset and zero otherwise.

a) {3, 4, 5}

b) {1, 3, 6, 10}

c) {2, 3, 4, 7, 8, 9}.

OPTION A is the correct answer

Answer:

t = -35/8

Step-by-step explanation:

Divide both sides by 2/5.

Answer:

Step-by-step explanation:

Elasticity Demand

(Q1 - Q2)/(Q1 + Q2)

(P1 - P2)/(P1 + P2)

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We use the chi-square distribution when making inferences about a single population variance.

Short Description of Chi-Square Distribution

The continuous probability distribution known as the chi-square distribution. The number of degrees of freedom (k) a chi-square distribution has determines its shape. This type of sampling distribution has a variance of 2k and a mean equal to its number of degrees of freedom (k). The range is of a chi-square distribution is from 0 to ∞.

Variance plays a key role in the analysis of risk and uncertainty. The sample variance, an unbiased estimator of population variance, is expressed by the following formula of core statistic for a sample size 'n' and Y' as the sample mean:

S² = ∑(Yₓ - Y') / (n-1)

The formula, (n-1)S² / σ² has the central chi-square distribution as χ²ₙ₋₁. Here (n-1) represents the degrees of freedom.

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The values which could be the slope of the line are numbers > 0.

According to the task content, it follows that the given line originates from the lower left quadrant and continues through the upper right quadrant.

It therefore follows that the line is ascending from left to right in which case, the slope of the line is positive.

Hence, the possible values of the slope include the set of numbers greater than 0.

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Answer: C and D

Step-by-step explanation: Trust me bro

The time taken for Jenny to run the same distance at 10% faster is 13.05 seconds

Time taken by Jenny = 14.5 - (10% × 14.5)

= 14.5 - (0.1 × 14.5)

= 14.5 - (1.45)

= 13.05 seconds

Therefore, the time taken for Jenny to run the same distance is 13.05 seconds

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Answer:

y = -3x + 9

Step-by-step explanation:

The slope is

[tex] \frac{6 - 0}{1 - 3} = - 3[/tex]

Substituting into point-slope form, we get

y = -3(x-3)

y = -3x + 9

Answer:

(4)(2)(1)=

4+2+1=

explanation:

Answer:

the third : x + x + x + 2 = 10

Step-by-step explanation:

x = the length of the first 2 pieces.

the third piece will be x+2 ft long.

so, the total length of the original board is the sum of all 3 pieces and must be all in all 10 ft.

10 = x + x + (x + 2) = x + x + x + 2

so, it is the third answer option.

Answer:

48

Step-by-step explanation:

So I attached an image explaining how I solved the problem, but essentially you use the Pythagorean Theorem to define the two other sides, which I named "a" and "b", and then defined them in terms of x, using the Pythagorean Theorem. I finally defined the hypotenuse of the entire triangle which is 36+64 in terms of these two equations. Once that entire thing was set up it was a matter of solving for x, to get 48

Considerando la expresión de una ecuación lineal, la ecuación de la recta que pasa por el punto (5, –8) con pendiente 5 es y= 5x - 33.

Una ecuación lineal o línea se puede expresar en la forma y = mx + b

donde

La ecuación lineal se puede expresar también mediante la ecuación punto-pendiente de la recta, que se plantea si se conoce la pendiente de la recta y cualquiera de sus puntos. Con ello queda determinada la recta, conociendo la pendiente  “m” y un punto  (x1, y1) dado:

y - y1= m(x -x1)

En este caso, la recta que pasa por el punto (5, –8) con pendiente 5.

Reemplazando en la ecuación punto-pendiente de la recta:

y - (-8)= 5(x -5)

Resolviendo:

y + 8= 5(x -5)

Aplicando propiedad distributiva:

y + 8= 5x - 5×5

y + 8= 5x - 25

Aislando la variable "y":

y= 5x - 25 - 8

y= 5x - 33

Finalmente, la ecuación de la recta que pasa por el punto (5, –8) con pendiente 5 es y= 5x - 33.

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The volume of the oblique cylinder is 6867.18 cubic units

The given parameters are:

Height = 27

Radius = 9

The volume is calculated as:

[tex]V = \pi r^2 h[/tex]

So, we have:

[tex]V = 3.14 * 9^2 * 27[/tex]

Evaluate

V = 6867.18

Hence, the volume of the oblique cylinder is 6867.18 cubic units

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The simplified form of R(x) is [tex]R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}[/tex]

From the question, we are to simplify the expression

From the given information,

[tex]f(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30}[/tex]

and

[tex]g(x) =\frac{x^{2}-9x+20 }{x^{2}-12x+36}[/tex]

Also,

[tex]R(x) = f(x) \div g(x)[/tex]

∴ [tex]R(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30} \div \frac{x^{2}-9x+20 }{x^{2}-12x+36}[/tex]

[tex]R(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30} \times \frac{x^{2}-12x+36 }{x^{2}-9x+20}[/tex]

Factoring each of the quadratics

[tex]R(x) =\frac{x^{2}-7x-4x+28 }{x^{2}-6x-5x+30} \times \frac{x^{2}-6x-6x+36 }{x^{2}-4x-5x+20}[/tex]

[tex]R(x) =\frac{x(x-7)-4(x-7) }{x(x-6)-5(x-6)} \times \frac{x(x-6)-6(x-6) }{x(x-4)-5(x-4)}[/tex]

[tex]R(x) =\frac{(x-4)(x-7)}{(x-5)(x-6)} \times \frac{(x-6)(x-6)}{(x-5)(x-4)}[/tex]

Simplifying

[tex]R(x) =\frac{(x-7)}{(x-5)} \times \frac{(x-6)}{(x-5)}[/tex]

[tex]R(x) =\frac{(x-7)(x-6)}{(x-5)(x-5)}[/tex]

[tex]R(x) =\frac{x^{2} -6x-7x+42}{x^{2} -5x-5x+25}[/tex]

[tex]R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}[/tex]

Hence, the simplified form of R(x) is [tex]R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}[/tex]

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Answer:

The maximum amount of people that can go to the amusement park is 15.

Step-by-step explanation:

First you create an equation to represent the question

8.75+25.75x≤420

You put the less than or equal to sign because 420 is the maximum amount of money.

Now you just solve the equation.

25.75x≤420-8.75

25.75x≤411.25

x≤411.25/25.75

x≤15.9708738

Then you have to round down because you cant have .9 of a person.

So x≤15

Then, Check your solution

8.75+(25.75 x 15)≤420

8.75+386.25≤420

395≤420

That is true. But to make sure that is the maximum add another 25.75

395+25.75≤420

420.75≤420

This is equation is false so, our answer is correct.

The maximum amount of people that can go to the amusement park is 15.

The average change in the temperature of the city is 0.87°C.

The average quantity is the sum of all quantities divided by the number of quantities.

In the question, we are informed that a newspaper reports the changes in the temperature of the city over 4 days to be 3.24°C, - 3/8 °C, - 0.15 °C, and 7/9 °C.

We are asked to write an expression to show the daily average change in the temperature of the city.

As we know, the average quantity is the sum of all quantities divided by the number of quantities.

Thus, average = {(3.24 - 3/8 -0.15 +7/9)/4} °C,

or, average = {{324/100 - 3/8 - 15/100 + 7/9}/4} °C,

or, average = [{(23328 - 2700 - 1080 + 5600)/7200}/4] °C,

or, average = 25148/28800 °C,

or, average = 6287/7200 °C = 0.8732 °C ≈ 0.87 °C.

Thus, the average change in the temperature of the city is 0.87°C.

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One landscaper's hourly rate is $15 lower than the other landscaper's. Casey is deciding which of two landscapers to hire. Each landscaper charges an hourly rate plus a fee for each job.

What is system of linear equations?

A set of two linear equations with two variables is a system of linear equations. Casey is deciding between hiring one of two landscapers. Each landscaper bills a fee for each job in addition to an hourly rate. A set of linear equations was appropriately written and solved by Casey using substitution. He solved for the other variable and substituted an expression for one in his work. The intersection of the lines that represent the linear equations is where a system of linear equations finds its solution. Each landscaper bills a fee for each job in addition to an hourly cost. Casey produced a system of linear equations that was correctly written and solved. The hourly rates for both landscapers are the same, however their rates for individual jobs vary.

Casey is deciding between hiring one of two landscapers. Each landscaper bills a fee for each job in addition to an hourly cost. By using substitution, Casey created and properly figured out a set of linear equations. He solved for the other variable and replaced an expression for one in his work, producing the equation 5 = 20.

equation 5=20

20-5 = 15

Therefore, One landscaper's hourly rate is $15 lower than the other landscaper's.

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Answer:

I think that this answer is 22

The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters

Let l,b,h be the dimensions of small gift box V1 = Volume = l*b*h

= 24cm^3

Dimension of Large box are 2.1l , 2.1b,2.1h

Volume of large box = 2.1 l*2.1b*2.1h

= (2.1)^3*lbh

= (2.1)^3*24

V2 =222.264

Volume filled with tissue paper is V2-V1

222.264 - 24

= 198.264cm^3

Hence The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters

The complete question is shown below

Zoe is packaging a gift to send in the mail. A smaller gift box is placed inside a similar yet larger packaging box. The empty space inside the packaging box is filled with tissue paper to keep the gift box from moving. The dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box. The volume of the smaller box is 24 cubic centimeters.What is the volume of the tissue paper in the packaging box?

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