write the expression x^2+8x-5 and x^2-4x-2 in the form (x+a)^2 +b

Answer:

The dimensions are 45 feet by 40 feet.

Step-by-step explanation:

Recall that the area of a rectangle is given by:

[tex]\displaystyle A=w\ell[/tex]

Where w is the width and l is the length.

The length is five feet longer than the width. Thus, we can write that:

[tex]\ell = w+5[/tex]

The total area is 1800 square feet. Substitute:

[tex]1800=w(w+5)[/tex]

Solve for w. Distribute:

[tex]w^2+5w=1800[/tex]

Subtract 1800 from both sides:

[tex]w^2+5w-1800=0[/tex]

Factor. We can use 45 and -40. Hence:

[tex]\displaystyle (w+45)(w-40)=0[/tex]

Zero Product Property:

[tex]w+45=0\text{ or } w-40=0[/tex]

Solve for each case:

[tex]\displaystyle w=-45\text{ or } w=40[/tex]

Since the width cannot be negative, we can ignore the first solution.

So, the width is 40 feet. Since the length is five feet longer, the length is 45 feet.

The dimensions are 45 feet by 40 feet.

Answer:

What function?

Step-by-step explanation:

Answer:

Jon Applebe withdrew 37.15% of the amount he initially deposited.

Step-by-step explanation:

Given that Jon Applebee deposited $ 619 in his savings account, and I have later withdrew $ 230, to determine the integer that represents the amount Jon Applebee deposited the following calculation must be performed:

619 = 100

230 = X

230 x 100/619 = X

23,000 / 619 = X

37.15 = X

Therefore, Jon Applebe withdrew 37.15% of the amount he initially deposited.

Answer:

$1.50

Step-by-step explanation:

so its

4.5 ÷ 3

which

1.5

Answer:

Step-by-step explanation:

It’s G

Answer:

[tex] { - 3}^{2} + (4 + 7)(2) \\ = - 9 + 22 \\ = 13[/tex]

Answer:

(in the image)

Step-by-step explanation:

I'm not sure I understood your question completely but I hope this helps.

Answer:

sin(x)

Step-by-step explanation:

sec x tanx(1 - sin^2 x)

1 - sin^2 x = cos^2 x

sec(x)tan(x)cos^2(x)

[tex]\frac{1}{cos(x)}[/tex] * [tex]\frac{sin(x)}{cos(x)}[/tex] * cos^2(x)

[tex]\frac{sin(x)cos^2(x)}{cos^2(x)}[/tex]

sin(x)

Answer:

D. 4x² + 3x/2 - 7

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = x/2 - 3

g(x) = 4x² + x - 4

(f + g)(x) is f(x) + g(x)

Step 2: Find

Answer:

The answer is C.

Step-by-step explanation:

(f+g)(x)= f(x)+g(x).

So that would be x/2-3 + 4x^2+x-4.

If you combine like terms that would be:

4x^2+x/2+x-4-3=

4x^2+3/2x-7

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Explanation:

The phrasing "2/3 of 4/5 of his 2nd exam on his 3rd test" is a bit clunky in my opinion. It seems more complicated than it has to be.

The student got 80 on the second exam. 4/5 of this is (4/5)*80 = 0.8*80 = 64. Then we take 2/3 of this to get (2/3)*64 = 42.667 approximately. If we assume only whole number scores are given, then this would round to 43.

Let x be the score on the fourth exam. Since 5 points of extra credit are given, the student actually got x+5 points on this exam.

So we have these scores

Adding up these scores and dividing by 4 will get us the average

(sum of scores)/(number of scores) = average

(70+80+43+x+5)/4 = 80

(x+198)/4 = 80

x+198 = 4*80

x+198 = 320

x = 320 - 198

x = 122

So the student got a score of x+5 = 122+5 = 127 on the fourth exam.

Answer: [tex]\$1.45[/tex]; [tex]\$3.6[/tex]

Step-by-step explanation:

Given

A dozen roses in a gift box costs $21

Similarly, 20 roses in a gift box costs $32.6

Suppose the price of single rose and gift box is [tex]x[/tex] and [tex]y[/tex]

[tex]\therefore 12x+y=21\quad \ldots(i)\\\Rightarrow 20x+y=32.6\quad \ldots(ii)[/tex]

Solving (i) and (ii) ,  we get

[tex]x=\$1.45;y=\$3.6[/tex]

Thus, the price of the one rose is [tex]\$1.45[/tex] and the price of gift box is [tex]\$3.6[/tex]

Answer:

1.45 and 3.5

Step-by-step explanation:

Answer: 36in2

Step-by-step explanation:

A= base *height

=12*3

=36

The Area of the figure is 36 in².

The area of a parallelogram refers to the total number of unit squares that can fit into it and it is measured in square units (like cm2, m2, in2, etc). It is the region enclosed or encompassed by a parallelogram in two-dimensional space.

The area of a parallelogram can be calculated by multiplying its base with the altitude. The base and altitude of a parallelogram are perpendicular to each other. The formula to calculate the area of a parallelogram can thus be given as,

Area of parallelogram = b × h square units

where,

b is the length of the base

h is the height or altitude

Given:

base= 12 in

height= 3 in

Area of parallelogram,

= base * height

=12* 3

= 36 in²

Learn more about Area of parallelogram here:

https://brainly.com/question/16052466

#SPJ2

Answer:

like about $500 and because of the ca!erlsn

Options :

A.The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded below the line

B.The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded above the line.

C. The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded below the line.

D.The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line

Answer:

D.The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line

Step-by-step explanation:

The equation y > 3x – 8

Interpreting as a linear relation :

y > ax + b

Where, a = slope ; b = intercept

a = 3 ; that is a slope value of 3

b = -8 ; that is an intercept value of - 8

Since the inequality is >, a dashed line is used (dashed like is used for > and <) ; since we a have a greater than sign, the graph will be shaded above the dashed line.

Answer: The answer is D on edu 2021

Step-by-step explanation:

D.The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line

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Explanation:

We have these two functions

which represent the amounts for his friend and William in that order. Strangely your teacher mentions William first, but then swaps the order when listing the exponential function as the first. This might be slightly confusing.

The table of values is shown below. We have t represent the number of years and t starts at 0.5. It increments by 0.1

The f(t) and g(t) columns represent the outputs for those mentioned values of t. For example, if t = 0.5 years (aka 6 months) then f(t) = 12.48 and that indicates his friend has 12,480 dollars in the account.

I've added a fourth column labeled |f - g| which represents the absolute value of the difference of the f and g columns. If f = g, then f-g = 0. The goal is to see if we get 0 in this column or try to get as close as possible. This occurs when we get 0.09 when t = 1.0

So we don't exactly get f(t) and g(t) perfectly equal, but they get very close when t = 1.0

It turns out that the more accurate solution is roughly t = 0.9925 which is close enough. I used a graphing calculator to find this approximate solution.

It takes about a year for the two accounts to have the same approximate amount of money.

Answer:

B

Step-by-step explanation:

Answer:

x is down and up and y is up then down

Step-by-step explanation:

I think

Answer:

Slope is undefined. Line parallel to y-axis.

Step-by-step explanation:

By Analytic Geometry, we can determine the slope of a line by knowing two distinct lines and using the definition of secant line:

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] (1)

Where:

[tex](x_{1}, y_{1})[/tex] - Coordinates of the initial point.

[tex](x_{2}, y_{2})[/tex] - Coordinates of the final point.

[tex]m[/tex] - Slope.

If we know that [tex](x_{1}, y_{1}) = (17, -13)[/tex] and [tex](x_{2}, y_{2}) = (17, 8)[/tex], then the slope of the line is:

[tex]m = \frac{8-(-13)}{17-17}[/tex]

[tex]m = \frac{21}{0}[/tex]

The slope is undefined, which means that line is parallel to y-axis.

Answer:

ΔEFG ~ ΔRPQ - Angle Angle Angle Theorem

ΔEFG ~ ΔRFQ - Side Side Side Proportional Theorem

Step-by-step explanation:

First set : using triangle sum theory to find missing angle. Letters should match congruent angles when creating statement.

Second set :

[tex]\frac{EG}{RQ}[/tex] = [tex]\frac{10}{12}[/tex] =  [tex]\frac{5}{6}[/tex]

[tex]\frac{EF}{RF}[/tex] =  [tex]\frac{15}{18}[/tex] =  [tex]\frac{5}{6}[/tex]

[tex]\frac{FG}{FQ}[/tex] =  [tex]\frac{20}{24}[/tex] =  [tex]\frac{5}{6}[/tex]

Recall that variation of parameters is used to solve second-order ODEs of the form

y''(t) + p(t) y'(t) + q(t) y(t) = f(t)

so the first thing you need to do is divide both sides of your equation by t :

y'' + (2t - 1)/t y' - 2/t y = 7t

You're looking for a solution of the form

[tex]y=y_1u_1+y_2u_2[/tex]

where

[tex]u_1(t)=\displaystyle-\int\frac{y_2(t)f(t)}{W(y_1,y_2)}\,\mathrm dt[/tex]

[tex]u_2(t)=\displaystyle\int\frac{y_1(t)f(t)}{W(y_1,y_2)}\,\mathrm dt[/tex]

and W denotes the Wronskian determinant.

Compute the Wronskian:

[tex]W(y_1,y_2) = W\left(2t-1,e^{-2t}\right) = \begin{vmatrix}2t-1&e^{-2t}\\2&-2e^{-2t}\end{vmatrix} = -4te^{-2t}[/tex]

Then

[tex]u_1=\displaystyle-\int\frac{7te^{-2t}}{-4te^{-2t}}\,\mathrm dt=\frac74\int\mathrm dt = \frac74t[/tex]

[tex]u_2=\displaystyle\int\frac{7t(2t-1)}{-4te^{-2t}}\,\mathrm dt=-\frac74\int(2t-1)e^{2t}\,\mathrm dt=-\frac74(t-1)e^{2t}[/tex]

The general solution to the ODE is

[tex]y = C_1(2t-1) + C_2e^{-2t} + \dfrac74t(2t-1) - \dfrac74(t-1)e^{2t}e^{-2t}[/tex]

which simplifies somewhat to

[tex]\boxed{y = C_1(2t-1) + C_2e^{-2t} + \dfrac74(2t^2-2t+1)}[/tex]

Answer:

0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean life of 82 months with a standard deviation of 7 months.

This means that [tex]\mu = 82, \sigma = 7[/tex]

Sample of 71

This means that [tex]n = 71, s = \frac{7}{\sqrt{71}}[/tex]

What is the probability that the mean monitor life would be greater than 83.8 months?

1 subtracted by the p-value of Z when X = 83.8. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{83.8 - 82}{\frac{7}{\sqrt{71}}}[/tex]

[tex]Z = 2.17[/tex]

[tex]Z = 2.17[/tex] has a p-value of 0.985.

1 - 0.985 = 0.015

0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors

Answer:

the result gaven by dividing one number by another

Answer: hello your question was poorly written but i was able to the get missing parts online which enabled me resolve your question

answer:

a) a = 0.1096

b) 1.89 watts

Step-by-step explanation:

Std of output voltage = 0.25 volt

H0 : μ = 5 volts

Ha : μ ≠ 5 volts

n = 16

a) Acceptance region = 4.9 ≤ X ≤ 5.1  

Determine the value of a

value of a = 0.0548 + 0.0548

                 = 0.1096

attached below is the reaming solution

note : a is a type 1 error

b) power of test

True mean output voltage = 5.1 volts

P = - 1.89 watts

power cant be negative hence the power of the test  = 1.89 watts

Answer:

A

Step-by-step explanation:

Number of suitcases on a plane is discrete because you can only have an integer amount. You can't have a fraction of a suitcase on a plane.

Answer:

36 introverts

Step-by-step explanation:

Total number of adults in the survey = 120

Ratio of introverts to extroverts = 3:7

Number of introverts = ratio number of introverts / ratio total × 120

Ratio number of introverts = 3

Ratio total = 3 + 7 = 10

Number of introverts = 3/10 × 120

= 36

The answer is (a)..........

Answer:

See explanation

Step-by-step explanation:

Given

[tex]M \to[/tex] randomly selecting a male

[tex]B \to[/tex] randomly selecting someone with blue eyes

Solving (a): Interpret P(M|B)

The above implies conditional probability

The interpretation is: the probability of selecting a male provided that a person with blue eyes has been selected

Solving (b): is (a) the same as P(B|M)

No, they are not the same.

The interpretation of P(B|M) is: the probability of selecting a person with blue eyes provided that a male has been selected

Answer:

Slope = [tex]\frac{4}{3}[/tex]

Equation of the line → [tex]y=\frac{4}{3}x[/tex]

Step-by-step explanation:

Let the equation of diagonal OA is,

y = mx + b

Here, m = Slope of the line OA

b = y-intercept

Slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Therefore, slope of the line passing through O(0, 0) and A(3, 4) will be,

m = [tex]\frac{4-0}{3-0}[/tex]

m = [tex]\frac{4}{3}[/tex]

Since, line OA is passing through the origin, y-intercept will be 0.

Therefore, equation of OA will be,

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