16 and -10 are the solutions to which one of the fol-
lowing equations?
A. |x-2|= 14
B. |x-2|= 8
C. |x+2|= 12
D. |x-3|= 13
E. |x+3|=13

If we express  [tex]3x^2-6x-2[/tex] in the form  [tex]a(x-h)^2+k[/tex], then a + h + k = -1

The given quadratic expression is:

[tex]3x^2-6x-2[/tex]

To express [tex]3x^2-6x-2[/tex] in the form [tex]a(x-h)^2+k[/tex], follow the steps below

Rewrite [tex]3x^2-6x-2[/tex] as  [tex]3x^2-6x+3-5[/tex]

Factorize common terms

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

This can be further simplified as:

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

Therefore, the vertex form of the equation  [tex]3x^2-6x-2[/tex] is [tex]3(x-1)^2-5[/tex]

Compare [tex]3(x-1)^2-5[/tex] with  [tex]a(x-h)^2+k[/tex]

a = 3, h = 1, k = -5

a  +  h  +  k  =  3  +  1 - 5

a  +  h  +  k  =  -1

Therefore if we express  [tex]3x^2-6x-2[/tex] in the form  [tex]a(x-h)^2+k[/tex], then a + h + k = -1

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Answer:

b)

Step-by-step explanation:

2x + 2y = 6 ---> y=-1x+3

4x – 6y = 12 ---> y= 4/6x -2

Answer:

I think it is a

Step-by-step explanation:

You have to solve those systems first. In the first option, x would be equal to 3 and y would be 0. Therefore, the intersection is (3; 0)

The number of workers needed to assemble 68 computers in 16.40 hours is 17 workers

let

number of hours = h

number of computers = c

number of workers = w

h = k × c / w

where,

k = constant of proportionality

h = 10.25

w = 16

c = 40

h = k × c / w

10.25 = k × 40 / 16

cross product

10.25 × 16 = k × 40

164 = 40k

k = 164/40

k = 4.1

If

c = 68

h = 16.40

h = k × c / w

16.40 = 4.1 × 68 / w

cross product

16.40w = 4.1 × 68

16.40w = 278.8

w = 278.8 / 16.40

w = 17 workers

Therefore, the number of workers needed to assemble 68 computers in 16.40 hours is 17 workers

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Answer:

20

Step-by-step explanation:

first term + second term = 4

tenth term = 19

fifth term + sixth term = ?

Since this is an arithmetic sequence:

first term = a

second term = a+d

tenth term = a+9d

Then we have

[tex]2a+d=4 \\ a+9d=19[/tex]

Upon solving the system of equation we have:

[tex]a=1 \\ d=2[/tex]

Since:

fifth term = a+4d

sixth term = a+5d

The final answer is:

fifth term + sixth term = [tex]2a+9d=2+18=20[/tex]

Answer:

where does the normal line to the ellipse x2−xy y2=3 at the point (−1,1) intersect the ellipse for the second time?

Step-by-step explanation:

they Juan Carlos y los sigo pliss yyi de bvz

Answer:

Exact Form: 309/25

Mixed Form: 12 and 9/25

Step-by-step explanation:

The value of y as x tends to 2 is infinity since the curve progresses to infinity at this point that is [tex]\lim_{x \to 2} f(x) = \infty[/tex]

Find the graph attached. From the graph, we can see that the range of the function is the values along the y-axis and is from the minimum point on the curve (y = -2) to infinity

From the graph, we can deduce that the value of y as x tends to 2 is infinity since the curve progresses to infinity at this point.

Therefore we can conclude that [tex]\lim_{x \to 2} f(x) = \infty[/tex]

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Answer:10r-54

Step-by-step explanation: you need to distribute following pemdas

Answer:

17$

Step-by-step explanation:

Answer:

$17

Step-by-step explanation:

Since the discount is 15%, and 100% would be the full price, 100 - 15 = 85. You are paying 85% of the price. 20 * .85 = 17.

The correct option is (B).24 miles.

Z-score is basically another term for the specific number of standard deviations. I suppose we can assume normality here, even though it isn't given, so I'd make a rough sketch.

Otherwise, just use the basic formula:

[tex]z_{score} =\dfrac{x-\mu}{\sigma}[/tex]

 Given that,

[tex]\bar{x}=29[/tex] (statistic for a mean) and [tex]s=3.6[/tex] (statistic for a standard deviation).

Since z-score must be Less than 1.5, So

[tex]1.5> \dfrac{x-29}{3.6}\\[/tex]

[tex]1.5 \times3.6 > x-29\\5.4+29> x\\34.4> x[/tex]

I just used normal cdf and got [tex]23.6<x<34.4[/tex].

Hence the correct option is (B).24 miles.

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Answer:

B

Step-by-step explanation:

Correcct on edge22

Step-by-step explanation:

similar triangles mean that all angles are the same, and the side lengths of one triangle correlate to the corresponding sides of the other triangle by the same factor.

that means that the sides 2 (ED) and x (CB) have the same relation as the 6+4 (AD) and the 6 (AB) sides.

so,

x/2 = 6/(6+4) = 6/10 = 3/5

x = 2 × 3/5 = 6/5 = 1.2

Answer: If it was the other way around I would have helped you  

Step-by-step explanation:

e.g.    

Answer:

3x^3

Step-by-step explanation:

First: you multiply the exponents inside the parenthesis with the one outside.

12*1/3=  4

3*1/3=1

you get 81x^(4)/3x

divide everything by 3:  27x^(4)/x

now subtract exponents (when dividing), you get: 27x^3

Now 1/3 is the same thing as cube root, so cube root of 27 is, thus the answer is: 3x^3

Answer:

Last one

Step-by-step explanation:

17 times 3 is 51

Answer:

is it the first one

Step-by-step explanation:

cause

51 divide by 3 is 17

Answer:

150˚

Step-by-step explanation:

To find the supplement of a 30˚ angle, we need to know what an supplement in geometry is.

A supplement is when two angles add up that results in 180

So what value adds to 30˚ will get 180?

To find out that we just subtract 180 with 30

Which is 150

Thus the Supplement of a 30˚ angle is 150˚

Hope this helps!

Answer:

The answer is t^-1 (r)=120r/120-r

i hope this is right sry if im wrong have a good day :)

The inverse of Janine's equation is [tex]r = \frac{120t}{120-t}[/tex] .

Resistance is a measure of the opposition to current flow in an electrical circuit. Resistance is measured in ohms, symbolized by the Greek letter omega (Ω).

According to the question

Janine is building a circuit that contains two lightbulbs in parallel.

One of the lightbulbs has a resistance of 120 ohms.

R = 120ohms

r = resistance of the second lightbulb

t = total resistance in the circuit  

[tex]t = \frac{120r}{r+120}[/tex]

Now,

The inverse of Janine's equation in which we will make r independent

[tex]t = \frac{120r}{r+120}[/tex]

[tex]t(r+120) = 120r[/tex]

[tex]tr + 120t = 120r[/tex]

[tex]120t = 120r - tr[/tex]

[tex]120t = r(120-t)[/tex]

[tex]r = \frac{120t}{120-t}[/tex]

Hence, the inverse of Janine's equation is [tex]r = \frac{120t}{120-t}[/tex] .

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#SPJ2

The quadratic equation is given by y = -2x² + 4x + 1

The standard form of a quadratic equation is given by:

y = ax² + bx + c

At point (1, 3):

3 = a(1)² + b(1) + c

a + b + c = 3      (1)

At point (2, 1):

1 = a(2)² + b(2) + c

4a + 2b + c = 1      (2)

At point (-2, -15):

-15 = a(-2)² + b(-2) + c

4a - 2b + c = -15      (3)

Solving equations 1, 2 and 3 simultaneously gives:

a = -2, b = 4, c = 1

The quadratic equation is given by y = -2x² + 4x + 1

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Answer:

Step-by-step explanation:

Binomial Probability

P(x) =  n!/(n-x)!x! * p^x q^(n-x)

P(x) = probability there will be x required outcomes (here x is 3)

n = number of trials (here it is 10)

p = probability of 1 required outcome (getting a 4) on a single roll ( = 1/6).

q = probability of required outcome not occurring on a single roll.

p = 1/6

q = 1 -1/6 = 5/6

n = 10

x = 3

So the required probability

= 10!/ 7!3! (1/6)^3 (5/6)^7

= 0.155.

Answer:

MOREEE

Step-by-step explanation:

8a + b

a=3

b=1

(8×3)+1

=24+1

=25

the answer is d)25

Answer: The answer is X equals 10 2/3.

Explanation: This is a proportion. We see that the right rectangle when turned to the right is proportional to the left rectangle. On the left rectangle, the smaller side is 6 ft, and the larger side is 16 ft. On the right rectangle, the smaller side is 4 ft. 6 ÷ 1.5 = 4, therefore 16 ÷ 1.5 = 10 2/3.

Answer:

Answer in the image

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

g(x) = 2x + 2

g(3) = 2*3 + 2             Substitute 3 for x.

g(3) = 6 + 2                 Multiply.

g(3) = 8                       Add.

Answer:

g(3) = 11

Step-by-step explanation:

Substitute x = 3 into g(x) , that is

g(3) = 3² + 2 = 9 + 2 = 11

Answer:

x (Fancy Gold fish) = 3

y (Common goldfish) = 29

Step-by-step explanation:

Fancy goldfish x cost $3 each

common goldfish y cost $1 each

Graph: y  = 20 +  3x (I'm hoping this is the correct line equation, please do leave a comment below if it's not)

Thus, we graph it by subtitude either the x or y values. (Or you can use just X = 1,2,3).

Now, to find how many of each type of goldfish Tasha can buy. We subtitude the line equation by either using x = 3 or y = 1

Using either values to solve the equation, we get:

x = 3

y = 29

Hope this helps!

Answer:

Subtract 2x from each side, Subtraction Property

Step-by-step explanation:

Answer:

Price of rice per gram =  $ 0.006  per gram or 0.6 cents per gram .

Step-by-step explanation:

Given: David wants to make 10 servings, where each serving has 75 grams of rice.

Total quantity of rice required = 10 x 75 = 750 grams

Overall, David spends 4.50 dollars on rice.

i.e. cost of 750 grams of rice = 4.50 dollars

Price of rice per gram =(cost of 750 grams of rice ) ÷ 750

= (4.50 dollars )  ÷ 750

=  $  0.006  per gram.

Price of rice per gram =  $ 0.006  per gram.

Answer:

0.006

Step-by-step explanation:

Step-by-step explanation:

They needed a lingua franca to be able to communicate.

Answer:

[tex]-\frac{10t}{3}+6[/tex]

Step-by-step explanation:

[tex]7 \frac{1}{3}t-(10 \frac{2}{3} t-6)[/tex]

Convert [tex]7\frac{1}{3}[/tex] to a mixed number

[tex]7\frac{1}{3}=\frac{7\cdot 3+1}{3}[/tex]

[tex]=\frac{22}{3}[/tex]

[tex]\bold{\frac{22}{3}t-\left(10\frac{2}{3}t-6\right)}[/tex]

Convert [tex]10\frac{2}{3}[/tex] into a mixed number

[tex]10\frac{2}{3}=\frac{10\cdot 3+2}{3}[/tex]

[tex]=\frac{32}{3}[/tex]

[tex]\bold{\frac{22}{3}t-\left(\frac{32}{3}t-6\right)}[/tex]

[tex]=\frac{22t}{3}-\frac{32t}{3}+6[/tex]

[tex]\bold{=\frac{-10t}{3}+6}[/tex]

Terms

Follow the PEMDAS order of operation:

You do these steps in the order for which the equation comes. For example, start with the exponents if there are not any parentheses.