The length of a rectangle is 8 inches more than the width. the perimeter is 44 inches. find the length and width of the rectangle

Answer: x = [tex]\sqrt{y^2 -1}[/tex]

Step-by-step explanation:

The coefficients for the polynomial with degree 3, roots: x = 2, x =

-1, and x = 3, and with a leading coefficient of 1 is given as -4 and 6. Hence, the polynomial turns out as x³ + (-4)x² + x + 6.

It is given that the polynomial is of degree 3 and its roots are,

x = 2

x = -1

x = 3

Thus, the factors of the polynomial would be,

(x - 2), (x + 1), and (x - 3)

The polynomial an be written in terms of its factors, with a leading coefficient of 1, as follows,

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

= (x² -2x + x -2)(x - 3)

= (x² -x -2)(x - 3)

= x³ - 3x² - x² + 3x - 2x + 6

= x³ - 4x² + x + 6

= x³ + (-4)x² + x + 6

Hence, the required coefficients of the polynomial are, (-4) and 6.

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If one travels 175 miles in 2hour 30 mins then his speed is 70 mph .

Distance travels= 175 miles

time is taken to cover 175 miles = 2.5 hours

We have to find out the speed in mph.

We know that,

Distance = speed x time

⇒speed = distance / time

Putting the value of distance and time, we get:

speed = 175 / 2.5 = 70 mph

Hence the final answer is 70 mph.

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The number of observation given in the following data set 14. This is also called the size of the population.

It is important to note that the above data possess the minimum value of 12 and the maximum value of 25. As indicated in the attached image, the data set is normally distributed.

The measures of central tendency are given as follows;

Q1 --> 15

Q2 --> 18.5

Q3 --> 22
IQR  = 7

Mean Absolute Deviation (MAD) = 3.5

Min = 12

Max = 25.

It is to be noted that the above indictors are called Descriptive Statistics.

The features of a sample or data set, such as a variable's mean, standard deviation, or frequency, are described or referred to as descriptive statistics.

We can better grasp a data sample's constituent parts by using inferential statistics.

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Answer: S=6√6 m².

Step-by-step explanation:

                                   Heron's formula

                            [tex]\displaystyle\\\boxed {S=\sqrt{p*(p-a)(p-b)(p-c)} }[/tex],

a, b, c - sides of a triangle,

[tex]\displaystyle\\p=\frac{a+b+c}{2}[/tex]

S - triangle area.

a=7 m,  b=5 m,  c=6 m.

[tex]p=\frac{7+5+6}{2} \\p=\frac{18}{2} \\p=9 (m).[/tex]

Hence,

[tex]S=\sqrt{9*(9-7)*(9-5)*(9-6)}\\S=3*\sqrt{2*4*3}\\S=3*2*\sqrt{2*3} \\S=6\sqrt{6} \ (m^2).[/tex]

There are 2 people are stepping onto the roller coaster per minute at peak time

According to statement

Given Flow time = 10 minutes.

Given Inventory = 20.

We use the formula then

I = R × T,

Therefore R = I / T.

Substitute the values in formula then

Flow rate = 20 / 10 = 2 people per minute.

So, There are 2 people are stepping onto the roller coaster per minute at peak time

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The tax due for the single taxpayer whose income is as described is; $14,459.5.

It follows from the task content that the tax due for a single taxpayer whose taxable income is; $65,725 is to be determined.

Since, the taxable income falls between the range; $40,526 to $86,375, 22% of the income is the tax due and hence, the tax due can be evaluated as follows;

= (22/100) × $65,725

= 14,459.5

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The length of a taut belt around the two pulleys is 79.3 cm.

The length of a taut belt around the two pulleys is calculated as follows;

Shapes formed within the two circles of the pulley.

From top to bottom, a rectangle, a right triangle and a trapezium.

The height of the right triangle is equal to length of the rectangle

base of the right triangle = radius of big circle - radius of small circle

base of the right triangle = (0.5 x 12 cm) - (0.5 x 6 cm) = 3 cm

tan α = height/base

tan (72.54)  = h/3

h = 3 tan(72.54)

h = 9.54 cm

The length of the trapezium at bottom is equal to length of rectangle at top, L = h = 9.54 cm

Portion of belt in contact with circumference of small circle is subtended by an angle = 2 × 72.54 = 145.08°

Length of belt in contact with circumference of smaller circle

= 2πr (θ/360)

= (2 x 6 cm)π x (145.08/360)

= 15.19 cm

Portion of belt in contact with circumference of big circle is subtended by an angle = 360 - 145.08° = 214.92⁰

Length of belt in contact with circumference of smaller circle

= 2πr (θ/360)

= (2 x 12 cm)π x (214.92 / 360)

= 45.01 cm

= 9.54 cm + 9.54 cm + 15.19 cm + 45.01 cm

= 79.28 cm

= 79.3 cm

Thus, the length of a taut belt around the two pulleys is 79.3 cm.

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Answer:

Step-by-step explanation:

43

I dont exactly know if this is correct sorry if its wrong

Answer:

D

Step-by-step explanation:

When a function is being shifted to the left, all x values will be added by y units shifted. (The constant that comes with x is excluded, eg. 3x shifted by 2 units left, becomes 3(x+2) and not 3x+2.)

Likewise, when a function is being shifted to the right, all x values will be subtracted by y units shifted. (Constant rules applies as well.)

Given f(x) is shifted 3 units right,

the new function, g(x) becomes:

[tex] g(x) = {(x - 3)}^{2} + 5(x - 3) - 1[/tex]

Therefore the answer is D in this case.

Answer:

Step-by-step explanation:

hello :

P(E and F)=0.7×0.6 =0.42

The true statement about the plane include:

It should be noted that a vertical plane simply passes through a vertical line.

In this case, Point H is not on plane R and the e line containing points F and G is on plane R.

The correct options are 1,2,4, and 5.

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Answer:

a,b,d,e

Step-by-step explanation:

The solution to the given expression [98/(82 + 283)] * (69 - 29) is; 784/73

We want to solve the expression;

[98/(82 + 283)] * (69 - 29)

Let us first simplify the first part which is;

98/(82 + 283) = 98/365

Then let us simplify the second part which is;

69 - 29 = 40

Thus, we have the expression;

(98/365) * 40

This can be simplified further to get;

(98/73) * 8 = 784/73

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The required value is 70. Using the permutations formula the required value is calculated. I.e.,  P(76, x) = P(76, 70).

The formula for permutations is

nPr = P(n, r) = n!/(n - r)!

Where P -number of permutations,

n - number of objects in the given set

r - number of choosing objects

The given series is

76 × 75 × 74 × ... × 6 = P(76, x)

We know that,

76!  = 76 × 75 × 74 × ... × 1 ...(i)

But to get the required series,

Divide the equation (i) by 6! = (76 - 70)!

Then,

76!/(76 - 70)! = 76 × 75 × 74 × 73 ... × 6

So, x = 70.

That is,

n!/(n - r)! = P(n, r)

⇒ 76!/(76 - 70)! = P(76, 70) = 2.618743E+108

Hence the required x value is 70.

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Answer:

x - 11

Step-by-step explanation:

Answer:

Option A.

Step-by-step explanation:

Demonstration

[tex]y=\frac{7}{4} x+7[/tex]

for x = -4

[tex]y=\frac{7}{4} (-4)+7=-\frac{28}{4} +7=-7+7=0[/tex]

for x= 0

[tex]y=\frac{7}{4}(0) +7=0+7=7[/tex]

for x= 4

[tex]y=\frac{7}{4} (4)+7=\frac{28}{4} +7=7+7=14[/tex]

Hope this helps

The number of blue balls that are needed to balance four green, two yellow and two white balls is 16 blue balls.

Green(g)

Blue (b)

Yellow (y)

White (w)

First step is to formula an equation

3g=6b

g=2b

2y=5b

y=5/2b

4w=6b

w=3/2b

Second step is to substitute

4g+2y+2w

=4(2b)+2(5/2b)+2(3/2b)

=8b+5b+3b

=16b

Therefore 16 blue balls are needed.

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The steps in Mia's method were smaller than in Jenna's, which was an advantage.

The same result will be obtained by adding the products of multiplying the sum of two or more addends by a number as opposed to multiplying each addend separately by the number.

The direct algorithm process suggested in this paper is known as the direct calculation method (DCM), and it can deal with using confinement loss as an incremental step to simulate the effect of moving tunnel face excavation, calculating the stresses and displacements in each step, and drawing the results.

Jenna's technique:

[tex]\begin{aligned}&5(30+4) \\&=(5)(30)+(5)(4) \\&=150+20 \\&=170\end{aligned}[/tex]

Mia's technique:

[tex]\begin{aligned}&5(30+4) \\&=(5)(34) \\&=170\end{aligned}[/tex]

Both used the right approach, albeit in different ways.

One uses the distributive property, whereas the other uses direct calculation.

Consequently, Jenna and Mia came to the same conclusion.

However, Mia's approach has one advantage over Jenna's: it requires fewer steps.

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The algebraic expression for the difference between the squares of the two numbers, supposing the two numbers to be a and b, is

a² - b² = (a + b)(a - b).

An algebraic expression is a combination of terms, where the terms are separated using mathematical operators like plus (+), minus (-), multiply (*), and divide (/).

The terms are combinations of numerals and variables.

Variables are represented alphanumerically, which can hold any value as per the expression they are used in.

In the question, we are asked to write the algebraic expression for the difference between the squares of two numbers.

We assume the two numbers to be a and b respectively.

Thus, we are asked to write an expression for the difference between the square of a and square of b, that is, we are asked to write an expression for a² - b².

We know that a² - b² is an identity, which can be shown as (a + b)(a - b).

Thus, the algebraic expression for the difference between the squares of the two numbers, supposing the two numbers to be a and b, is a² - b² = (a + b)(a - b).

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See below for the organized result in a two-way frequency table

The given parameters are:

Candies = 18

Chocolate and Caramel = 10

None = 3

Chocolate = 12

Using the above parameters, we have the following rows and columns:

                                           Chocolate

                                           Present            Absent     Total

Caramel     Present                  

                   Absent

                   Total

Next, we populate the table as follows:

                                           Chocolate

                                           Present            Absent     Total

Caramel     Present                  10                  3

                   Absent

                   Total                       12

The total number of candies is 18.

So, we have:

                                    Chocolate

                                           Present            Absent     Total

Caramel     Present                  10                  3             13

                   Absent

                   Total                       12                 6               18

Subtract the cells from the column total

                                    Chocolate

                                           Present            Absent     Total

Caramel     Present                  10                  3             13

                   Absent                    2                   3             5

                   Total                       12                   6              18

The above represents the organized result

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The perimeter of a rectangle is the sum of its side lengths.

A rectangle is special in that sides opposite one another have equal length. So if [tex]x[/tex] is the length of the horizontal sides, the total perimeter of the rectangle is

[tex]4\,\mathrm{cm} + 4\,\mathrm{cm} + x\,\mathrm{cm} + x\,\mathrm{cm} = (8+2x)\,\mathrm{cm}[/tex]

We're given the perimeter is actually 18 cm, so

[tex]8+2x = 18[/tex]

Solve for [tex]x[/tex].

[tex](8 + 2x) - 8 = 18 - 8[/tex]

[tex]2x = 10[/tex]

[tex]\dfrac12 \cdot 2x = \dfrac12 \cdot 10[/tex]

[tex]\boxed{x = 5}[/tex]

Answer:

144=12², so 144^3/2=(12²)^(3/2)=12³=1728.

this answer is not from the internet

go check yourselves

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Calculate the total amount invested by summing up all the values of the investment.

Total = 50,000

Calculate the weight of each investment. For WOOPS, weight = 5000 / 50000 = 10% and so on.

Now, Expected Return = sum of weight x Returns = 10% x 0.14 + 20% x 0.16 + ... + 18%x 0.18 = 16.01%

b) Similarly,

Beta of the portfolio = sum of weight x beta = 10% x 0.6 + 20% x 0.8 + ... + 18% x 0.18 = 0.7605

c) Portfolio has less systematic risk as the beta for the average market is 1, which is above the portfolio

d) Using CAPM, Return = Rf + beta x (Rm - Rf) = 4% + 0.7605 x (14% - 4%) = 11.605%

To calculate the expected return of a portfolio, the investor needs to know the expected return of each security in the portfolio and the total weight of each security in the portfolio. This means that investors need to sum the weighted averages of the expected returns (RoRs) of each security.

Investors are based on estimates of the expected rate of return on securities, assuming that what has proven to be true in the past will be true in the future. Investors do not use the structural view of the market to calculate the expected return. Instead, it determines the weight of each security in the portfolio by dividing the value of each security by the total value of the security.

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Answer:

nearest what?

Step-by-step explanation:

nearest tens's=340

nearest hundred's=300

The circle E, circle F and circle G are the circles which are congruent (similar) to the circle A has a radius of 6.

Let us discuss about the structure of each circles.

The circle D has the secant with the length 12. The secant means the straight line joining two points on the circle. So, we can't conclude that the secant will always be the diameter. Hence, it has different shape compared to circle A.

The circle E has the radius with length 6. The radius is same as the radius of the circle A. So, it is similar to the circle A.

The circle D has the secant with the length 6. Similar to the condition of circle D, it is not congruent to circle A.

The circle F has the diameter with length 12. Which means, the radius of this circle is with length 6. Hence, it is similar to the circle A.

The circle G has the diameter with length 12. Which means, the radius of this circle is with length 6. Hence, it is similar to the circle A.

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Answer:

Circles E and F are congruent to circle A

Step-by-step explanation:

12 = 2 × 2 × 3

18 = 2 × 3 × 3

56 = 2 ×2 × 2 × 7

Now

Common factor = 2

Remaining factor = 2 × 3 × 2 × 3 × 7

LCM = RF × CF

= 504

hence the lCM of 12 , 18 and 56 is 504...

[tex]...[/tex]

Answer:

200

Step-by-step explanation:

Let's call the number x :
12.5% of x = 25

Changing 12.5% into decimal would be 0.125

Now we have the equation :

0.125x = 25

Divide both sides by 0.125 to make x the subject :

x = 25 ÷ 0.125

x = 200

To check we can substitute this value into the question :

12.5% of 200 = 25

Hope this helped and have a good day

Answer:

[tex]h(x)=-0.11(3)^{-x}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=0.11(3)^x[/tex]

Reflection in the x-axis:

When reflecting a function in the x-axis, make the whole function negative:

[tex]\implies g(x)=-f(x)[/tex]

[tex]\implies g(x)=-0.11(3)^x[/tex]

Reflection in the y-axis:

When reflecting a function in the y-axis, make the x variable negative:

[tex]\implies h(x)=g(-x)[/tex]

[tex]\implies h(x)=-0.11(3)^{-x}[/tex]

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Answer:

the answer to this question is d

Step-by-step explanation:

h(x)=-0.11(3)^-x