What is the product of all values of b that satisfy (b-2)(b-8) +4= 0 ?
A) 10
B) 12
C) 16
D) 20

9514 1404 393

Answer:

  x > -1 and x ≠ 3

Step-by-step explanation:

The function value will be positive when there are an even number of negative factors. The factors change sign at x = -1, are zero at x = 3. The expression is positive for ...

  x > -1 and x ≠ 3

Ernie will owe an interest of $268

Answer:

Step-by-step explanation:

Given the log function [tex](y-1)log_{10}(4) = log_{10} 16\\ \\[/tex] to get the value of y, the following steps must be carried out;

[tex](y-1)log_{10}(4) = log_{10} 16\\\\(y-1)log_{10}(2^2) = log_{10} 2^4\\\\ (y-1)2log_{10}(2) = 4log_{10} 2\\ \\DIvide\ both\ sides\ by \ log_{10}2\\\\\frac{2(y-1)log_{10}2 }{log_{10}2} = \frac{4log_{10}2}{log_{10}2} \\\\2(y-1) = 4\\\\[/tex]

Open the bracket

[tex]2y-2(1) = 4\\\\2y -2 = 4\\\\add \ 2 \ to \ both \ sides\\\\2y-2+2 = 4+2\\\\2y = 6\\\\Divide \ both \ sides\ by \ 2\\\\2y/2 = 6/2\\\\y = 3[/tex]

Hence the value of y is 3

Answer: The slope of the line that passes through (2, 12) and (4, 20) is 4.

The value of the y-intercept is 9.

Step-by-step explanation:

Slope of line passing through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]

Then, the slope of the line that passes through (2, 12) and (4, 20) = [tex]\dfrac{20-12}{4-2}[/tex]

[tex]=\dfrac{8}{2}=4[/tex]

So, the slope of the line that passes through (2, 12) and (4, 20) is 4.

To find the y-intercept of 3x + 2y = 18, first write in slope intercept form y=mx+c ( where c= y-intercept ).

[tex]2y=-3x+18\\\\\Rightarrow\ y=-\dfrac{3}{2}x+9[/tex]

By comparison,  c= 9

Hence, the value of the y-intercept is 9.

Answer:

Simplify:

[tex]-4^2-5(1^3)[/tex]

So you get:

[tex]-21\\[/tex]

Answer:

[tex]\huge\boxed{-21}[/tex]

Step-by-step explanation:

-x²-5y³

Given that x = 4, y = 1

[tex]-(4)^2-5(1)^3[/tex]

[tex]-16-5(1)\\-16-5\\-21[/tex]

Answer:

5 lawns

Step-by-step explanation:

Firstly, the equation is 25x + 10 = 135

Ezri makes $25 for every lawn she mows (25x) and has an automatic $10 per day (10). In order to make $135 we take what she makes each day and set it equal to 135.

To solve, we subtract 10 from both sides to create 25x = 125. We then divide 25 from both sides to get x=5. This means that Ezri needs to mow 5 lawns in order to make $135.

I hope this is helpful to you!

**To anyone out there seeing this - let me know if you think I made a mistake and I will fix it.**

Answer:

Coefficient of Correlation

Step-by-step explanation:

Coefficient of Correlation is a value that ranges between -1 to 1, which is used to denote the closeness or linear relationship between two variables.

The closer the value of the coefficient is to -1 or 1, the stringer the relationship that exists between two variables.

A negative value suggests a negative relationship. Which means, as one variable decreases, the other variable increases.

A positive coefficient of correlation shows a positive relationship between two variables. Which means, as one variable increases, the other also increases.

If the Correlation coefficient is 0, it means there's no relationship between the variables.

Answer:

The area of larger triangle is 48 ft².

Step-by-step explanation:

Assuming that the area of triangle formula is A = 1/2 × base × height. Then, you have to substitute the following values :

[tex]area = \frac{1}{2} \times b \times h[/tex]

[tex]let \: b = 12,h = 8[/tex]

[tex]area = \frac{1}{2} \times 12 \times 8[/tex]

[tex]area = \frac{1}{2} \times 96[/tex]

[tex]area = 48 \: {feet}^{2} [/tex]

Given that;

A∞bh

A=kbh. where k is a constant

For smaller triangle

A=kbh

16=8(4)k

16=32k

k=½

For bigger triangle

A=kbh

Where k=½ , b= 12 and h=8

A=½(12)8

A=48 square feet

Answer:

6:10 pm

Step-by-step explanation:

she skate for 2 h and 14 min so,

8:24- 2:14

=6:10 pm

Answer:

Attachment 1 : Option C

Attachment 2 : Option A

Step-by-step explanation:

( 1 ) Expressing the product of z1 and z2 would be as follows,

[tex]14\left[\cos \left(\frac{\pi \:}{5}\right)+i\sin \left(\frac{\pi \:\:}{5}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{3\pi \:}{2}\right)+i\sin \left(\frac{3\pi \:\:}{2}\right)\right][/tex]

Now to solve such problems, you will need to know what cos(π / 5) is, sin(π / 5) etc. If you don't know their exact value, I would recommend you use a calculator,

cos(π / 5) = [tex]\frac{\sqrt{5}+1}{4}[/tex],

sin(π / 5) = [tex]\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}[/tex]

cos(3π / 2) = 0,

sin(3π / 2) = - 1

Let's substitute those values in our expression,

[tex]14\left[\frac{\sqrt{5}+1}{4}+i\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}\right]\cdot \:2\sqrt{2}\left[0-i\right][/tex]

And now simplify the expression,

[tex]14\sqrt{5-\sqrt{5}}+i\left(-7\sqrt{10}-7\sqrt{2}\right)[/tex]

The exact value of [tex]14\sqrt{5-\sqrt{5}}[/tex] = [tex]23.27510\dots[/tex] and [tex](-7\sqrt{10}-7\sqrt{2}\right))[/tex] = [tex]-32.03543\dots[/tex] Therefore we have the expression [tex]23.27510 - 32.03543i[/tex], which is close to option c. As you can see they approximated the solution.

( 2 ) Here we will apply the following trivial identities,

cos(π / 3) = [tex]\frac{1}{2}[/tex],

sin(π / 3) = [tex]\frac{\sqrt{3}}{2}[/tex],

cos(- π / 6) = [tex]\frac{\sqrt{3}}{2}[/tex],

sin(- π / 6) = [tex]-\frac{1}{2}[/tex]

Substitute into the following expression, representing the quotient of the given values of z1 and z2,

[tex]15\left[cos\left(\frac{\pi \:}{3}\right)+isin\left(\frac{\pi \:\:}{3}\right)\right] \div \:3\sqrt{2}\left[cos\left(\frac{-\pi \:}{6}\right)+isin\left(\frac{-\pi \:\:}{6}\right)\right][/tex] ⇒

[tex]15\left[\frac{1}{2}+\frac{\sqrt{3}}{2}\right]\div \:3\sqrt{2}\left[\frac{\sqrt{3}}{2}+-\frac{1}{2}\right][/tex]

The simplified expression will be the following,

[tex]i\frac{5\sqrt{2}}{2}[/tex] or in other words [tex]\frac{5\sqrt{2}}{2}i[/tex] or [tex]\frac{5i\sqrt{2}}{2}[/tex]

The solution will be option a, as you can see.

Answer:

240

Step-by-step explanation:

! means factorial or to multiply by the previous number down to one so 5!=5*4*3*2*1=120 120*2=240.

Answer:

40% depreciation over the 4 years

10% depreciation per year

Step-by-step explanation:

The number of years between buying and selling is:

2020 - 2016 = 4

4 years

The amount of depreciation in the 4 years is:

AED 1,500 - AED 900 = AED 600

The percent depreciation for the 4 years is:

(1500 - 900)/1500 * 100% = 40%

The percent depreciation per year is:

40%/4 = 10%

Answer:

62,500 pi

Step-by-step explanation:

diameter = radius + radius

d = 2r

r = d/2

A = 4pi r^2

= 4 pi (d/2)^2

= 4pi d^2/4

= 4pi* 250^2/4

= 4pi * 62,500/4

= 4pi * 15625

= 62,500 pi

Answer:

The same mean  ⇒  the same symmetry axis

Bigger standard deviation major spread

Step-by-step explanation: See Annex

The annex shows two different normal curves:

1.-  N (μ₀ ; σ₁ )

2.- N (μ₀ ; σ₂ )

Where   σ₁  > σ₂

They both have the same symmetry  axis ( they have the same mean and both curves have to be symmetrically related to the mean )

Normal distribution curves spread symmetrically at both sides of the mean, but the wider curve is the one that has the bigger standard deviation.  Standard deviation is a measure of the spread of the curve.

Whenever deviation is high, the data is more dispersed than when deviation is low.

Let the mean be 2.

Let the standard deviation be 0.3 for first graph. The data is more clustered around mean.

Let the standard deviation be 0.6 for second graph. The data is less clustered more dispersed from mean.

For more information, refer this link:

https://brainly.com/question/12421652

Answer:

A. 5(1 + 2x) + 1 + 2x

D. 7(1 + 2x) - 2x - 1

E. 3(2 + 4x)

9514 1404 393

Answer:

  (-2.5, 1)

Step-by-step explanation:

The desired point is the weighted average of the end points, where the weight of each point is the fraction of distance from the opposite end.

  P = 5/8(-1, 7) +3/8(-5, -9) = (-5-15, 35-27)/8 = (-2.5, 1)

The desired point is (-2.5, 1).

Answer:

y = 4x + 21

Step-by-step explanation:

Hello!

Point-slope form is y - y1 = m(x - x1)

y1 is the y point

x1 is the x point

m is the slope

Put in what you know

y - -3 = 4(x - -6)

Subtracting a negative is the same as adding

y + 3 = 4(x + 6)

Distribute the 4

y + 3 = 4x + 24

Subtract 3 from both sides

y = 4x + 21

The answer is y = 4x + 21

Hope this helps!

Answer:

32cm

Step-by-step explanation:

The area of sqaure is a^2

Side will be

underroot of 64 =8

Premeter of sqaure is 4a = 4×8 = 32cm

first we need to find length.

here.

Area= 64cm^2

or, 64= l^2

using formula area = length × length

therefore solving we get ,

length = 8 cm.

now,

perimeter = 4l

= 4 × 8 cm.

= 32 cm..........

Answer:

79/120

Step-by-step explanation:

5/24+9/20

to add the fractions the denominator (bottom part) has to be the same. ex you can add one third and one third to make two thirds. but you wont know what 1/2 + 1/3 is.

convert to same denominator. to do this, the fractions themselves need to stay the same value but the bottom number needs to change. ex 1/2=2/4 and 1/3= 2/6. when you multiply and divide the top and bottom part of the fraction by the same number, the value of the fraction stays the same. ex 3/6 divide both parts by 3 you get 1/3. so 3/6=1/3

to get the common denominator we have to find the least common multiple, or LCM (since 5 and 9 dont share any common factors.)

24 and 20 LCM

=120

convert both 5/24+9/20 to x/120 and y/120

5/24 multiply by 5 on top and bottom

=25/120

9/20 multiply by 6 on top and bottom

=54/120

25/120+54/120

=(25+54)/120

=79/120

Answer:

6 pies

Step-by-step explanation:

For 60 - 89 cherries there are 10 pies

For 90 -119 cherries there are 4 pies

10 -4 = 6

There are 6 more pies in the 60 -89 cherries category than in the 90-119 category

Answer:

Step-by-step explanation:

Given  1 caplet = 325 mg of medication, to calculate the number of caplet 975mg of medication will contain, we will follow the steps below;

Let  1 caplet = 325 mg of medication

x caplet = 975 mg of medication

Cross multiply

325 * x = 1 * 975

325x = 975

Divide both sides by 325

325x/325 = 975/325

x = 3

Hence 3 caplets contains 975 mg of medication.

Answer:

[tex]\Large \boxed{\sf \bf \ \ 2(x-4)^3(x+2)^2 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

Construct a polynomial function with the following properties...

... fifth degree

It means that the polynomial can be written as below.

[tex]a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0 \ \text{ with }a_5\text{ different from 0}\\\\\text{ or } k(x-x_1)(x-x_2)(x-x_3)(x-x_4)(x-x_5) \\\\ \text{ with k different from 0 and } (x_i)_{1\leqi\leq 5 } \text { are the roots.}[/tex]

... 4 is a zero of multiplicity 3

We can write the polynomial as below.

[tex]k(x-4)(x-4)(x-4)(x-x_4)(x-x_5)=k(x-4)^3(x-x_4)(x-x_5)[/tex]

... −2 is the only other zero

Because this is the only other zero, we can deduce that -2 is a zero of multiplicity 2.

[tex]k(x-4)(x-4)(x-4)(x-x_4)(x-x_5)\\\\=k(x-4)^3(x-(-2))(x-(-2))\\\\=k(x-4)^3(x+2)^2[/tex]

... leading coefficient is 2.

Finally, it means that k = 2 and then the polynomial function is:

[tex]\large \boxed{2(x-4)^3(x+2)^2}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

f(x) = 7

Step-by-step explanation:

f(x) = f(-x) it is even

-f(x)=f(-x) it is odd

f(x) = (x – 1)^2 neither even nor odd

f(x) = 8x   this is a line  odd functions

f(x) = x^2 – x  neither even nor odd

f(x) = 7  constant  this is an even function

Answer:

answer is f(x)= 7

Step-by-step explanation:

just took edge2020 test

Answer:

(3,-1)

Step-by-step explanation:

Graph boths functions (picture below)

Answer:

The probability is  [tex]P( \= X \ge 70 ) = 0.07311[/tex]

Step-by-step explanation:

From the question we are told that

    The  population mean is  [tex]\mu = 68[/tex]

      The standard deviation is  [tex]\sigma = \sqrt{36} = 6[/tex]

      The  sample size is  [tex]n = 19[/tex]

Generally the standard error of the mean is mathematically represented as  

            [tex]\sigma_{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]

=>         [tex]\sigma_{\= x } = \frac{6 }{\sqrt{19} }[/tex]

=>         [tex]\sigma_{\= x } = 1.3765[/tex]

Generally the probability that their average score will be at least 70 is mathematically represented as

            [tex]P( \= X \ge 70 ) = 1 - P( \= X < 70 ) = 1 - P(\frac{ \= X - \mu }{\sigma_{\= x}} < \frac{70 - 68}{ 1.3765} )[/tex]

Generally [tex]\frac{ \= X - \mu }{\sigma_{\= x}} = z(The \ z-score \ of \ \= X )[/tex]

So

          [tex]P( \= X \ge 70 ) = 1 - P( \= X < 70 ) = 1 - P(Z <1.453 )[/tex]

From the z-table

            [tex]P(Z <1.453 ) = 0.92689[/tex]

=>          [tex]P( \= X \ge 70 ) = 1 - P( \= X < 70 ) = 1 - 0.92689[/tex]

=>         [tex]P( \= X \ge 70 ) = 1 - P( \= X < 70 ) = 0.07311[/tex]

=>          [tex]P( \= X \ge 70 ) = 0.07311[/tex]

If y = y(x), then the derivative with respect to x is dy/dx. Differentiating both sides of the given equation gives

d/dx [4x ² + y ²] = d/dx [36]

8x + 2y dy/dx = 0

2y dy/dx = -8x

dy/dx = -4x/y

The turning points of the curve, taken as a function of x, are those points where the derivative vanishes.

-4x/y = 0   ===>   x = 0

This value of x corresponds to two points on the curve,

4×0² + y ² = 36   ===>   y ² = 36   ===>   y = ±6

So there are two turning points, (0, -6) and (0, 6).

Answer:

  -3 (removable), +5

Step-by-step explanation:

Maybe you have ...

  [tex]f(x)=\dfrac{x+3}{x^2-2x-15}=\dfrac{x+3}{(x+3)(x-5)}=\dfrac{1}{x-5}\quad x\ne-3[/tex]

This will have discontinuities (points where the function is undefined) at ...

The discontinuity as x = -3 is removable by defining f(-3) = -1/8.

Answer:

4

Step-by-step explanation:

There are 4 reflectional symmetry

Answer:

It's option a. 36 + 6x^2 = 28x

Step-by-step explanation: