Choose the correct sum of the polynomials (6x3 − 8x − 5) + (3x3 + 6x + 2). 9x3 − 2x − 3 3x3 + 2x + 3 3x3 − 2x − 3 9x3 + 14x + 3

Answer:

D) 36x²-4

Step-by-step explanation:

36x²+12x-12x-4

36x²-4

[tex](6x - 2)(6x + 2) \\ = {(6x)}^{2} - {(2)}^{2} \\ = {36x}^{2} - 4[/tex]

Answer:

D.

[tex] {36x}^{2} - 4[/tex]

Hope you could understand.

If you have any query, feel free to ask.

Answer:

Step-by-step explanation:

That's an awful lot of points. You don't have to give that many. 10 or 15 points would be more than enough.

The graph touches the x axis at 1 point. That means its basic formula is y = (x - a)^2

Since it  upside down, the formula is y = -(x - a)^2. A couple of other things are true.

a = 1 because that's where the graph touches the x axis. y = - x^2 has shifted 1 unit to the right.

Finally the y intercept is -4 which means that the final equation is y = -4(x-1)^2

That's all preliminary. The actual question is, what does the discriminate look like?

y = -4(x^2 - 2x + 1)

y = -4x^2 + 8x - 4

a = - 4

b = 8

c = - 4

sqrt(b^2 - 4ac)

sqrt(8^2 - 4(-4)(-4) )

sqrt(64 - 64) = 0

The answer is the third one. The answer will always be 0 when the graph touches the x axis and does not go through it.

Answer:

D

Step-by-step explanation:

vertical is basically the x axis, so the y axis has to be 0. using elimination, (0,8) and (0,7) are the only ones left.

Answer:

The vertex form is f(x) = (x + 5)² + 12

The minimum value of f(x) is point (-5, 12)

Step-by-step explanation:

1) The vertex form of a quadratic equation f(x) = x² + 10·x + 37,  which is the form f(x) = a·(x - h)² + k is found as follows;

For the general form of the quadratic equation, f(x) = a·x² + b·x + c

h = -b/(2·a) and k = f(h)

Therefore, for f(x) = x² + 10·x + 37,

a = 1, b = 10

∴ h = -10/2 = -5

k = f(-5) = (-5)² + 10×(-5) + 37 = 12

The vertex form is f(x) = a·(x - h)² + k gives;

f(x) = 1·(x - (-5))² + 12 = (x + 5)² + 12

The vertex form is f(x) = (x + 5)² + 12

2) The minimum value of x is found when d(f(x))/dx = 0

d(f(x))/dx = d(x² + 10·x + 37)/dx = 2·x + 10

d(f(x))/dx = 0 = 2·x + 10

x = -10/2 = -5

We check that it is the minimum by f''(x) being positive;

f''(x) = d(2·x + 10)/dx = 2 which is positive and x = -5 is the x-coordinate of the minimum value of f(x)

The x-coordinate of the minimum value of f(x) minimum value is f(-5) = (-5)² + 10×(-5) + 37 = 12

Therefore, we have;

The minimum value of f(x) = (-5, 12)

Answer:

The vertex is (-5,f(-5)=12), The minimum value of f(x) is 12.

Answer:

135 units²

Step-by-step explanation:

The area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

To calculate h use Pythagoras' identity on the right triangle on the left

h² + 8² = 17²

h² + 64 = 289 ( subtract 64 from both sides )

h² = 225 ( take the square root of both sides )

h = [tex]\sqrt{225}[/tex] = 15 , thus

A = 9 × 15 = 135 units²

Answer:

x=-7/2, x=4/3

Step-by-step explanation:

[tex]6x^2+13x-28=0[/tex]

Multiply 6 and -28 to get -168

Find 2 numbers that multiply to 168 but add to 13

They are 21 & -8

Rewrite the equation into:

[tex]6x^2+21x-8x-28=0[/tex]

Factor

[tex]3x(2x+7)-4(2x+7)=0[/tex]

(3x-4)(2x+7)=0

3x=4

x=4/3

2x=-7

x=-7/2

Answer:

I think its C because if I remember correctly zero of the function is just the x intercept

answer:

-1

here's the explanation below :))

Answer:

Step-by-step explanation:

If A laptop battery has 81% power after 1 hour of use

It looses 19 % of its energy in one hour.

The difference between 81% and 24% is 57%

The slope of the line of rate of decrease of battery percentage is 19% per hour.

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is

y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is it's graph or the rate of change is large.

We know slope(m) of a line = (y₂ - y₁)/(x₂ - x₁).

The problem can be constructed as having two points (1, 81) and (4, 24).

∴ Slope(m) = (24 - 81)/(4 - 1).

Slope(m) = - 57/3.

Slope(m) = - 19.

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A Gallup poll asked 1200 randomly chosen adults what they think the ideal number of children for a family is. Of this sample, 53% stated that they thought 2 children is the ideal number. Construct and interpret a 95% confidence interval for the proportion of all US adults that think 2 children is the ideal number.

Answer:

at 95% Confidence interval level: 0.501776   < p < 0.558224

Step-by-step explanation:

sample size n = 1200

population proportion [tex]\hat p[/tex]= 53% - 0.53

At 95% confidence interval level;

level of significance ∝ = 1 - 0.95

level of significance ∝ = 0.05

The critical value for [tex]z_{\alpha/2} = z _{0.05/2}[/tex]

the critical value [tex]z _{0.025}= 1.96[/tex] from the standard normal z tables

The standard error S.E for the population proportion can be computed as follows:

[tex]S,E = \sqrt{\dfrac{\hat p \times (1-\hat p)}{n}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.53 \times (1-0.53)}{1200}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.53 \times (0.47)}{1200}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.2491}{1200}}[/tex]

[tex]S,E = 0.0144[/tex]

Margin of Error E= [tex]z_{\alpha/2} \times S.E[/tex]

Margin of Error E= 1.96 × 0.0144

Margin of Error E= 0.028224

Given that the confidence interval for the proportion  is  95%

The lower and the upper limit for this study is as follows:

Lower limit: [tex]\hat p - E[/tex]

Lower limit: 0.53 - 0.028224

Lower limit: 0.501776

Upper limit: [tex]\hat p + E[/tex]

Upper limit: 0.53 + 0.028224

Upper limit: 0.558224

Therefore at 95% Confidence interval level: 0.501776   < p < 0.558224

Answer:

10

Step-by-step explanation:

it is Pythagoras theorem

6*6=36

8*8=64

64+36=100

square root of 100 is 10

Answer:

Step-by-step explanation:

y = -5x + 3 ........... Equation 1

y = 1 ................ Equation 2

To solve the equation substitute equation 2 into equation 1

That's

Substitute y = 1 into y = - 5x + 3

So we have

1 = - 5x + 3

Group like terms

- 5x = 1 - 3

- 5x = - 2

Divide both sides by - 5

x = 2/5

Substitute x = 0.4 into equation 1

That's

y = - 5( 0.4 ) + 3

y = - 2 + 3

The solution for the system of equations is

Hope this helps you

Answer:

A. (0.4, 1)

Step-by-step explanation:

just took the edg. 2020 unit test

Answer:

[tex]\displaystyle A = 15x^2 + 11x + 2\text{ cm}^2[/tex]

Step-by-step explanation:

We are given that the length and width of a rectangle is given by:

[tex]\ell = (5x + 2)\text{ cm} \text{ and } w = (3x+1)\text{ cm}[/tex]

And we want to find the area of the rectangle.

Recall that the area of a rectangle is given by:

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

Substitute:

[tex]A = (3x+1)(5x+2)[/tex]

Expand and simplify:

[tex]\displaystyle \begin{aligned}A &= 5x(3x+1) + 2(3x+1) \\ &= (15x^2+5x)+(6x+2) \\ &= (15x^2)+(5x+6x)+(2) \\ &= 15x^2 + 11x +2 \end{aligned}[/tex]

Hence, the area of the rectangle is:

[tex]\displaystyle A = 15x^2 + 11x + 2\text{ cm}^2[/tex]

Answer:

(a) 1:12

(b) 12:1

(c) 1:100

(d) 100:1

Answer:

A) both functions are linear

B) f(x) = 7446.4x + 178713.6 and f(x) = 11000x + 179000

C) House 2 will value $106894.4 more than house 1.

Step-by-step explanation:

A) Value Increase from year 1 to year 2:

House 1: 193,606.40 - 186,160 = 7446.4

House 2: 201,000 - 190,000 = 11000

Value Increase from year 2 to year 3:

House 1: 201,350.66 - 193,606.40 = 7744.26

House 2: 212,000 - 201,000 = 11000

This means that a constant increament in x variable gives a constant increament in both houses vales. Then, both functions are linear.

B) The slope is the same as the value increment from one year to the next one.

slope (m) of House 1: 7446.4

slope (m) of House 2: 11000

General formula of a line:

f(x) = mx+b

Replacing with a known point:

House 1

186,160 = 7446.4(1) + b

b = 186,160 - 7446.4 = 178713.6

equation: f(x) = 7446.4x + 178713.6

House 2

190,000 = 11000(1) + b

b = 190,000 - 11000 = 179000

equation: f(x) = 11000x + 179000

C) Replacing x = 30 into each equaiton:

Value of House 1 after 30 years

f(x) = 7446.4(30) + 178713.6 = 402105.6

Value of House 2 after 30 years

f(30) = 11000(30) + 179000 = 509000

Then, house 2 will value 509000 - 402105.6 = $106894.4 more than house 1.

Answer:

2x+1

Step-by-step explanation:

f(x) = x + 1

g(x) = 2x

f(g(x)) = Replace x in the function f(x) with the function g(x)

f(g(x)) = g(x) +1

         = 2x+1

Answer:

f(g(x)) = 2x + 1

Step-by-step explanation:

Substitute x = g(x) into f(x) , that is

f(g(x))

= f(2x)

= 2x + 1

Answer:

Step-by-step explanation:

√324=18

√576=24

√704=26.532....

===============================================

Work Shown:

d = common difference

p = first term = 24

q = second term = a+d = 24+d

r = third term = q+d = 24+d+d = 24+2d = 6

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

Solve for d

24+2d = 6

2d = 6-24

2d = -18

d = -18/2

d = -9

We add -9 to each term to get the next term. This is the same as subtracting 9 from each term to get the next term.

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

First term = 24

Second term = 24-9 = 15

Third term = 15-9 = 6

We get the sequence 24, 15, 6

Answer:

D. Terms that have identical variable parts

Step-by-step explanation:

Like terms refers to terms that have identical variable parts.

For example:

Given the expression

2xy + z + x + 3y - 5z + 4y - xy + 3x

The like terms in the expression are:

2xy - xy= xy

z - 5z= -4z

x + 3x= 4x

3y + 4y=7y

The new expression will be

xy - 4z + 4x + 7y

Answer:

20 hours

Step-by-step explanation:

Computer download=5 hours

Computer + Extra processor=4 hours

Computer's rate =1/5 per hour

Computer + extra processor rate=1/4 per hour

Extras processor rate=1/x

Where,

x=how long it takes extra processor to get the job done on its own.

To find x, we have to solve the equation

1/5 + 1/x = 1/4

Subtract 1/5 from both sides

1/5 + 1/x -1/5 = 1/4-1/5

1/x=1/4-1/5

1/x = 5-4/20

1/x = 1/20

Cross product

1(20)=x(1)

20=x

x=20 hours

It would have taken the new extra processor alone 20 hours to download the movie

Answer:

  B.  8x + 9y = 6

Step-by-step explanation:

You can eliminate answer choices A and C because their leading coefficient is negative. In standard form, the leading coefficient is positive.

For the remaining two equations, you can check to see if the given points are on the line

B: for point (-6, 6), we want 8(-6) +9(6) = 6 . . . true

  for point (3, -2), we want 8(3) +9(-2) = 6 . . . . true

The appropriate equation is 8x +9y = 6.

D: (we don't need to check to know it won't work after the above)

__

The equation in standard form, can be written from ...

  (Δy)(x -a) = (Δx)(y -b) . . . . . for some point (a, b)

The values of Δx and Δy are the differences between corresponding coordinates.

  Δy = 6 -(-2) = 8

  Δx = -6 -3 = -9

For point (-6, 6), the above equation becomes ...

  8(x +6) = -9(y -6)

  8x +48 = -9y +54 . . . . eliminate parentheses

  8x +9y = 6 . . . . . . . . . . add 9y-48

[tex](2n+1)^2=4n^2+4n+1[/tex] therefore, the first blank is 1.

[tex]4n^2+4n+1=2(2n^2+2n)+1[/tex] therefore, the two other blanks are both 2.

The number in the proof ''The square of the sum of two consecutive integers is odd'' is 2 and 2.

To prove that, The square of the sum of two consecutive integers is odd.

The expression to prove is,

Let us assume that two consecutive integers are n and (n + 1).

Hence, the expression is written as,

[n + (n + 1)]² = (2n + 1)²

= (2n)² + 2 × 2n × 1 + 1²

= 4n² + 4n + 1

= 2 (2n² + 2n) + 1

= odd

Therefore, the number in the blanks are 2 and 2.

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Answer:

28 4/9

Step-by-step explanation:

5 1/3 times 5 1/3

Triangle HIJ is similar to triangle MNO  by the angle-angle similarity theorem if ∠O ≅ ∠J.

An equation is an expression that shows the relationship between two or more numbers and variables.

Two triangle are said to be similar if the ratio of their corresponding sides are in the same proportion and corresponding angles are congruent.

Triangle HIJ is similar to triangle MNO  by the angle-angle similarity theorem if ∠O ≅ ∠J.

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Answer:

vertex(-3,27)

Step-by-step explanation:

f(x)= x^2+ 6x + 36 ( a=1,b=6,c=36)

V(h,k)

h=-b/2a=-6/2=-3

k=f(-3)=3²+6(-3)+36

f(-3)=9-18+36=27

vertex(-3,27)

Step-by-step explanation:

Hi there!

From above question;

A cuboid has a length of 25cm, a width of 5cm and height of (x-2)cm.

Length (l) = 25cm

width (b) = 5cm

height (h) = (x-2)cm.

a).

Volume= l*b*h

V = 25*5*(x-2)

V = 125(x-2)

V = 125x - 250 → Answer

b).

(i)

V = 750cm³

V = 125x - 250

750 = 125x - 250..........(i)

(ii)

The equation (i) is: 750 = 125x - 250

or, 125x = 750+250

or, 125x = 1000

or, X = 1000/125

Therefore, X= 8cm.

(iii)

Height (h) = x-2

= 8-2

= 6

Therefore, height is 6cm.

Hope it helps!

Answer:

around 17 mistakes

Step-by-step explanation:

We can write a ratio to solve

54 words             300 words

------------------ = -------------------

3 mistakes             x mistakes

Using cross products

54x = 3*300

54x = 900

Divide by 54

54x/54 = 900/54

x =50/3

x = 16.66666666(repeating)

around 17 mistakes

X = mistakes in 300 words

54/3 = 300/X

54X = 3 x 300

X = 900/ 54

X = about 17 words, since 16 and 2/3 rounded to the nearest tenth is 17

Answer:

Does the answer help you?

Answer:

c. the subtraction property if equality

Step-by-step explanation:

i just did this and got it right

The justification for step 3 in the solution process is the division property of equality option (A) the division property of equality is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The equation is:

0.8a - 0.1 a =  a - 2.5

The above equation represents the linear equation in one variable.

Step 1: 0.7a = a - 2.5  (adding like terms)

Step 2: -0.3a = -2.5  ( subtraction property of equality)

Step 3: a =  8.3 (the division property of equality)

Thus, the justification for step 3 in the solution process is the division property of equality option (A) the division property of equality is correct.

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