Given below is an equation of a parabola. What are the coordinates of the vertex?
y = (x + 2)^2

a (–2, 0)
b (2, –2)
c (–2, 2)
d (2, 0)

Answer:

y = 1/3x - 19/3

Step-by-step explanation:

3y = x -3

y = 1/3x -3

Slope = 1/3

Point= (1,-6)

y-intercept = -6 - (1/3)(1) = -6 - 1/3 = -19/3

[tex]\large\underline{\sf{Solution-}}[/tex]

Given function is

[tex]\rm \longmapsto\:f(x) = \dfrac{1}{ \sqrt{ |cosx| + cosx} } [/tex]

Now,

[tex]\rm \longmapsto\:f(x) \: is \: defined \: if \: |cosx| + cosx > 0[/tex]

We know,

[tex]\begin{gathered}\begin{gathered}\bf\: \rm \longmapsto\: |x| = \begin{cases} &\sf{ - x \: \: when \: x < 0} \\ \\ &\sf{ \: \: x \: \: when \: x \geqslant 0} \end{cases}\end{gathered}\end{gathered}[/tex]

So,

[tex]\begin{gathered}\begin{gathered}\bf\: \rm \longmapsto\: |cosx| + cosx = \begin{cases} &\sf{ \: \: 0 \: \: when \: cosx \leqslant 0} \\ \\ &\sf{ \: \: 2 \: cosx \: \: when \: cosx > 0} \end{cases}\end{gathered}\end{gathered}[/tex]

So,

[tex]\rm\implies \:f(x) \: is \: defined \: when \: cosx > 0[/tex]

So, from graph we concluded that cosx > 0 in the following intervals.

[tex]\begin{gathered}\boxed{\begin{array}{c|c} \bf cosx & \bf \: x \: \in \: \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf + ve & \sf \bigg( - \dfrac{\pi}{2} ,\dfrac{\pi}{2} \bigg) \\ \\ \sf + ve & \sf \bigg(\dfrac{3\pi}{2} ,\dfrac{5\pi}{2} \bigg) \\ \\ \sf + ve & \sf \bigg(\dfrac{7\pi}{2} ,\dfrac{9\pi}{2} \bigg) \end{array}} \\ \end{gathered}[/tex]

So, if we generalized this we get

[tex]\rm\implies \:cosx > 0 \: when \: x \: \in \: \bigg(\dfrac{(4n - 1)\pi}{2} ,\dfrac{(4n + 1)\pi}{2} \bigg) \: \forall \: n \in \: Z[/tex]

Hence,

Domain of the function is

[tex]\red{\rm\implies \boxed{\tt{ \: x \in \: \bigg(\dfrac{(4n - 1)\pi}{2} ,\dfrac{(4n + 1)\pi}{2} \bigg) \: \forall \: n \in \: Z}}}[/tex]

[tex]\textsf{More to know :-} \\[/tex]

[tex]\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c} \bf T-eq & \bf Solution \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf sinx = 0 & \sf x = n\pi \: \forall \: n \in \: Z\\ \\ \sf cosx = 0 & \sf x = (2n + 1)\dfrac{\pi}{2}\: \forall \: n \in \: Z\\ \\ \sf tanx = 0 & \sf x = n\pi\: \forall \: n \in \: Z\\ \\ \sf sinx = siny & \sf x = n\pi + {( - 1)}^{n}y \: \forall \: n \in \: Z\\ \\ \sf cosx = cosy & \sf x = 2n\pi \pm \: y\: \forall \: n \in \: Z\\ \\ \sf tanx = tany & \sf x = n\pi + y \: \forall \: n \in \: Z\end{array}} \\ \end{gathered}\end{gathered}[/tex]

Answer:

Hello there! I think the answer to your question

C

Because a "A positive voltage is a  voltage that pushes electrons out of a battery."

The midpoint is the middle of the line. Thus for a line segment, it is finding the halfway point between the x and y values.

Midpoint = ( [¹/₂ (x₁ + x₂)] , [¹/₂(y₁ + y₂)])

∴ for a line segments with endpoints (4,-7) and (12, -1),

 Midpoint = ( [¹/₂ (12 + 4)] , [¹/₂(-7 - 1)])

                = ( [¹/₂ (16)] , [¹/₂(-8)])

                = (8, -4)  (OPTION A)

Applying the points given, it is found that the growth rate of the exponential function is:

c. 50%

An exponential function has the following format:

[tex]y = a(1 + r)^x[/tex]

In which:

In this problem:

[tex]y = a(1 + r)^x[/tex]

[tex]75 = 15(1 + r)^4[/tex]

[tex](1 + r)^4 = 5[/tex]

[tex]\sqrt[4]{(1 + r)^4} = \sqrt[4]{5}[/tex]

[tex]1 + r = 1.4953[/tex]

[tex]r = 1.4953 - 1[/tex]

[tex]r = 0.4953[/tex]

Thus, approximately 50%, option c.

A similar problem is given at https://brainly.com/question/23416643

Answer:

50% is the correct answer

Step-by-step explanation:

I took the test.

Answer:

Simply substract 0.39 from 0.54 = 0.15

Therefore the carpenter is left with 0.5 metre of wood.

The temperature in Fahrenheit after preheating for 2 minutes is 103⁰F

The question looks incomplete but we can as well find the temperature in Fahrenheit after preheating for 2 minutes

Give the function t = 19m + 65 that represents the temperature t (in degrees Fahrenheit) of an oven after preheating for m minutes.

If t = 2,

t = 19(2) + 65

t = 38 + 65

t = 103⁰F

Hence the temperature in Fahrenheit after preheating for 2 minutes is 103⁰F

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The total number of ways in which the 3 people line up for the 3 cashiers is 36 ways.

First, we consider the number of ways in which we can arrange the 3 cashiers. Since order matters, we use permutation. So, we have ³P₃ ways of arranging the 3 cashiers. ³P₃ = 3 × 2 × 1 = 6 ways.

Also, the number of ways we can arrange the 3 people to line up since order matters is ³P₃ =  3 × 2 × 1 = 6 ways.

So, the total number of ways in which we can arrange both the 3 cashiers and the 3 people in a line is ³P₃ × ³P₃ = 6 × 6 = 36 ways.

The total number of ways in which the 3 people line up for the 3 cashiers is 36 ways.

Learn more about permutations here:

https://brainly.com/question/12974932

Answer:

60 ways

Step-by-step explanation:

So, sadly there is no real algorithm that I could find for this so I just went ahead and listed all the ways that the people can be organized

3,0,0

0,3,0

0,0,3

2,1,0

2,0,1

1,2,0

1,0,2

0,2,1

0,1,2

1,1,1

So, we have 10 ways to organize them. But we need to remember that there are also 6 ways to randomly organize 3 people. So, 10x6 is 60

Answer:

3x-15

Step-by-step explanation:

(x-5)(8-5)

(x-5)(3)

re-order

(x-5)×3

3(x-5)

Distribute

3(x-5)

3x-15

Answer:

if the teacher buys 4 packa of markers and 3 packs of pens she would have the same amount

Answer:

y = 1/2x -4

Step-by-step explanation:

Slope intercept form is y = mx+b where m is the slope and b is the y intercept

2x-4y = 16

Subtract 2x from each side

2x-4y-2x = -2x+16

-4y =-2x+16

Divide each side by -4

-4y/-4 = -2x/-4 +16/-4

y = 1/2x -4

The slope is 1/2 and the y intercept is -4

Answer:

y = -2

Step-by-step explanation:

Answer:

x= 17.5

y= 35

Step-by-step explanation:

Steps are in attachment.

Answer:

• For x (Acute angle property)

[tex]{ \rm{(2x + 10) \degree + 30 \degree + 6x=180 \degree}} \\ \\ { \rm{8x + 40=180}} \\ \\ { \rm{8x = 140}} \\ \\ { \boxed{ \underline{ \rm{ \: \: x =17.5 \: \: }}}}[/tex]

• For y ( Interior angle sum of triangles )

[tex]{ \rm{(y + 10) \degree + 6x \degree + 30 \degree = 180 \degree}} \\ \\ { \rm{y + 10 + 30 + (6 \times 17.5) = 180}} \\ \\ { \rm{y +145 = 180 }} \\ \\ { \boxed{ \underline{ \rm{ \: \: y = 35 \: \: }}}}[/tex]

9514 1404 393

Answer:

  1400 in 2020

Step-by-step explanation:

The number of students is increasing by 100 each year, so in 3 more years, the number will be 1100 +3×100 = 1400 students in 2020.

The answer is x = 88

Answer:

x = -4

Explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

x = -4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

Step 2: Subtract 5 from both sides.

Step 3: Divide both sides by -7.

Step 4: Check if solution is correct.

Therefore, x = -4.

Answer:

5

Step-by-step explanation:

if the triangles are congruent then the side lengths must be equal:

JL=PM

PN=LK

NM=JK and

4y + 12 = 32 subtract 12 from both sides

4y = 20 divide both sides by 4

y = 5

Answer: y = -4

Step-by-step explanation:

If x = 1

1 = 2y + 9

1 - 9 = 2y

-8 = 2y

y = -8/2

y = -4

please give me a brainliest answer

Answer:

[tex]y = ( - 4)[/tex]

Step-by-step explanation:

Given that,

[tex]x = 1[/tex]

Question :

[tex]x = 2y + 9[/tex]

You have to find the value of y. So, make the y as the Subject

[tex]x = 2y + 9 \\ x - 9 = 2y \\ \frac{x - 9}{2} = \frac{2y}{2} \\ \frac{x - 9}{2} = y[/tex]

Now replace 1 instead of x

[tex]y = \frac{x - 9}{2} \\ y = \frac{1 - 9}{2} \\ y = \frac{ - 8}{2} \\ y = - 4[/tex]

Hope this helps you.

Let me know if you have any other questions :-)

1. C because 3×3=9

9×3=27

27×3=81.....

2. Answer is C explaination in picture number 2

3. D explaination in picture number 1

Step-by-step explanation:

Here is the answer to the question

Answer:

-2/1

Step-by-step explanation:

Rewrite equation in point-slope form

y=-2x+3

in y=mx+b, m= the slope

The slope of the line is -2/1

Any lines parallel to this line will have the same slope

Answer:

6x(x+2xy+y^2)

Step-by-step explanation:

Answer:

x = 12.2 mi

Step-by-step explanation:

Given the two sides of the right triangle:

a = 6.1 mi

b = 10.6 mi

c = x

Use the Pythagorean Theorem to solve for the value of the hypotenuse, x:

c² = a² + b²

c² = (6.1)² + (10.6)²

[tex]\sqrt{(c^{2})} = \sqrt{37.21 + 112.36}[/tex]

c = 12.2 mi

Therefore, the value of the hypotenuse is:  x = 12.2 mi

___________

[tex] \: [/tex]

[tex]\boxed{ \rm{answer \: by \: { \boxed{ \rm{☆HayabusaBrainly}}}}}[/tex]

x² = (10,6)² + (6,1)²

x² = 112,36 + 37,21

x² = 149,57

x = 12,22mi✔

Malcom Davis earnings is an illustration of equations and proportions.

Let the profit be P, and the gross income be G.

So, we have:

[tex]\mathbf{P= G - 100000}[/tex]

(a) The equations

For plan A, we have:

[tex]\mathbf{A = \frac{1}{90}G}[/tex] ----1/90 of the company's gross income

For plan B, we have:

[tex]\mathbf{B = \frac{1}{60}P}[/tex]  ----1/90 of the company's profit

When both are the same, we have:

[tex]\mathbf{A= B}[/tex]

This gives

[tex]\mathbf{\frac{1}{90}G= \frac{1}{60}P}[/tex]

Substitute [tex]\mathbf{P= G - 100000}[/tex]

[tex]\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}[/tex]

Hence, the equation is: [tex]\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}[/tex]

(b) Solve the equation in (a), and intepret

[tex]\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}[/tex]

Cross multiply

[tex]\mathbf{60G = 90G - 9000 000}[/tex]

Collect like terms

[tex]\mathbf{90G - 60G = 9000 000}[/tex]

[tex]\mathbf{30G = 9000 000}[/tex]

Divide both sides by 30

[tex]\mathbf{G = 3000 00}[/tex]

The gross income must be $300000, for Dave to earn the same amount with either plan.

(c) His earnings based on (c)

We have:

[tex]\mathbf{A = \frac{1}{90}G}[/tex]

Substitute [tex]\mathbf{G = 3000 00}[/tex]

[tex]\mathbf{A = \frac{1}{90} \times 300000}[/tex]

[tex]\mathbf{A = 3333.33}[/tex]

His earning is $3333.33 when the plans are the same

(d) If the gross income in less than (b)

If the gross income is less than $300,000, then plan A would better for Malcom Davis, because his earnings in plan A would be greater than plan B

Read more about equations at:

https://brainly.com/question/20893366

An advantage of debt consolidation is: B. You will have one monthly payment to manage.

Debt consolidation can be defined as the way in which a person borrow  or collect a loan so as to payoff their old debt or liabilities.

One of the advantage of debt consolidation loan is that you will have one monthly payment to manage or one bill to pay  per  month instead of several bill.

Therefore the correct option is B.

Learn more about debt consolidation here:https://brainly.com/question/11199005

#SPJ1

Answer:

3, -6, 12, -24, 48, -96, 192, -384, 768, -1536, 3072, -6144...

×-2

Geometric sequence

Answer:

5

Step-by-step explanation:

Hope it helps. :D

Answer:

144 I think have a good day

Answer:

y = -3x - 2

Step-by-step explanation:

M: -3

B: -2

Hello macelynn190!

[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]

[tex] \huge \tt \frac{5 - 2(a + 3b)}{2} [/tex]

[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]

To solve this question we need to substitute the given values of 'a' & 'b' in the equation & then simplify it.

Given,

Now, substitute this in the place of 'a' & 'b'..

[tex]\large \tt \frac{5 - 2(a + 3b)}{2} \\ = \large \underline{\underline{\tt \: \frac{5 - 2((4) + 3(1))}{2} }}[/tex]

Lastly, simplify it...

[tex]\large \tt \: \frac{5 - 2((4) + 3(1))}{2} \\ = \large \tt\frac{5 - 2(4 + 3)}{2} \\ = \large \tt \: \frac{5 - 2(7)}{2} \\ = \large \tt \: \frac{5 - 14}{2} \\ = \large \tt\frac{-9}{2} \\ = \large \boxed{\boxed{ \bf \: -\frac{9}{2}=-4.5}}[/tex]

__________________

Hope it'll help you!

ℓu¢αzz ッ

Given info:-

Simplify: 5-2(a+3b)/2. When a=4 and b=1.

[5-2(a+3b)]/2

Now, put a=4 and b=1 (Because this is given in question only)

so,

⇛[5-2{4+3(1)}]/2

⇛[5-2{4+3}]/2

⇛[5-2{7}]/2

⇛[5-2×7]/2

⇛[5-14]/2

⇛-9/2 Ans.

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