Simplify the expression.
Write your answer without negative exponents. NEED AN ANSWER ASAP​

Answer:

The standard equation of the parabola is:

[tex]y=-\frac{3}{2}x^2+12x-18[/tex]

Step-by-step explanation:

An x intercept of 2 means that the point (2, 0) is in the graph of the parabola.

We can also write the general expression for the parabola in vertex form, since we can use the information on the coordinates of the vertex: (4, 6) - recall that the axis of symmetry of the parabola goes through the parabola's vertex, so the x-value of the vertex must be x=4.

[tex]y-y_{vertex}=a\,(x-x_{vertex})^2\\y-6=a\,(x-4)^2[/tex]

Now we can find the value of the parameter "a" by using the extra information about the point (2, 0) at which the parabola intercepts the x-axis:

[tex]y-6=a\,(x-4)^2\\0-6=a\,(2-4)^2\\-6=a\,4\\a=-\frac{6}{4} =-\frac{3}{2}[/tex]

Then the equation of the parabola becomes:

[tex]y-6=-\frac{3}{2} \,(x-4)^2\\y-6=-\frac{3}{2} (x^2-8x+16)\\y-6=-\frac{3}{2}x^2+12x-24\\y=-\frac{3}{2}x^2+12x-18[/tex]

Answer:

X=20

Step-by-step explanation:

The answer is C

Answer:

[tex]x \geq -91/2[/tex]

Step-by-step explanation:

[tex]6(x+8) \geq -43 + 4x[/tex]

Resolving Parenthesis

[tex]6x+48 \geq -43 + 4x[/tex]

Collecting like terms

[tex]6x - 4 x \geq -43-48[/tex]

[tex]2x \geq -91[/tex]

Dividing both sides by 2

[tex]x \geq -91/2[/tex]

Answer:

x ≥ - 91 / 2

Step-by-step explanation:

In this sample problem, the first thing we want to do is expand the part in parenthesis through the distributive property. This will make the simplification process easier. Another approach would be to divide either side by x + 8, but let's try the first.

Approach 1 : [tex]6(x+8) = 6x + 6 8 = 6x + 48[/tex]

[tex]6x + 48 \geq - 43+4x[/tex] - so we have this simplified expression. We now want to isolate x, so let's combine common terms here. Start by subtracting 6x from either side,

[tex]48 \geq - 43-2x[/tex] - now add 43 to either side,

[tex]91\geq -2x[/tex] - remember that dividing or multiplying a negative value changed the inequality sign. Dividing - 2 on either side, the sign changes to greater than or equal to, with respect to x,

[tex]- 91 / 2 \leq x[/tex], or in other words [tex]x \geq - 91 / 2[/tex]. This is our solution.

Step-by-step explanation:

Let the original price be x

After increasing by 20% the price is 3000

Thus,

x + ( x × 20%) = 3000

x + 20x/100 = 3000

x + x/5 = 3000

(5x + x)/5 = 3000

6x/5 = 3000

x = 3000 * 5/6

x = 2500

Hope it helps :)

Answer:

26

Step-by-step explanation:

Given that:

At time, t=0, Billy puts 625 into an account paying 6% simple interest

At the end of year 2, George puts 400 into an account paying interest at a force of interest, 1/(6+t), for all t ≥ 2.

If both accounts continue to earn interest indefinitely at the levels given above, the amounts in both accounts will be equal at the end of year n. Calculate n.

In order to calculate n;

Let K constant to be the value of time for both accounts

At  time, t=0, the value of time K when Billy puts 625 into an account paying 6% simple interest is:

[tex]K = 625 \times (1+ 0.06 K)[/tex]

[tex]K = 625 +37.5 K[/tex]

At year end 2; George  amount of 400 will grow at a force interest, then the value of  [tex]K = 400 \times e^{\int\limits^2_k {\dfrac{1}{6+t}} \, dx }[/tex]

[tex]K =400 \times \dfrac{6+K}{6+2}[/tex]

[tex]K =400 \times \dfrac{6+K}{8}[/tex]

[tex]K =50 \times ({6+K})[/tex]

[tex]K =300+50K[/tex]

Therefore:

If K = K

Then:

625 + 37.5 = 300 +50 K

625-300 = 50 K - 37.5 K

325 = 12.5K

K = 325/12.5

K = 26

the amounts in both accounts  at the end of year n = K = 26

The answer is Diagram 4 or D

Explanation:

A Venn diagram is a type of model that represents sets, and their relationships. Additionally, each set is usually named with a letter and symbols such as ∪ or ∩ are used to represent specific zones of the diagram. In the case of the symbol ∩, this is used to represent the intersection between two sets. This means X ∩ Z represents the intersection between X and Z. Therefore, the correct representation is the fourth diagram, which shows in red only the intersection between these two sets.

Answer:

See below.

Step-by-step explanation:

None of the choices represent the intersection of sets X and Z, so there is some mistake with this problem. The question is not correct for these choices.

Answer:

x= 155°

straight line equals 180°

since you have a side that equals to 25°

you subtract

180°-25° = 155°

Answer:

D. x^2 - 6x + 7.

Step-by-step explanation:

The roots are 3 plus or minus sqrt(2). That means the equation is...

(x - [3 + sqrt(2)]) * (x - [3 - sqrt(2)])

= [x - 3 - sqrt(2)] * [x - 3 + sqrt(2)]

= x^2 - 3x - xsqrt(2) - 3x + 9 + 3sqrt(2) + xsqrt(2) - 3sqrt(2) - (sqrt(2))^2

= x^2 - 3x - 3x + 9 - 2 - xsqrt(2) + xsqrt(2) + 3sqrt(2) - 3sqrt(2)

= x^2 - 6x + 7.

Hope this helps!

Answer:

(x+y)/xy or  (1/x + 1/y) portion of the leaves

Step-by-step explanation:

Let the total work done to rake the leaves be a for representation.

Thus,

given Maya takes x minutes to rake the leaves

thus,

work done by may in x minutes = a

dividing both side by x

work done by maya in x/x = 1 minutes = a/x

similarly

given Calra takes y minutes to rake the leaves

thus,

work done by may in y minutes = a

dividing both side by y

work done by maya in y/y = 1 minutes = a/y

__________________________________

Total work done by both in 1 minutes = a/x + a/y = a(1/x+1/y) = a(x+y)/xy

Thus, if a is the total work , then they do (x+y)/xy of a work in one minute.

Thus, (x+y)/xy portion of leaves do they rake in one minute if they work together.

Answer: old machine 150, new machine 280

Step-by-step explanation:

given data:

Old machine = 25t

New machine = 35t

where t = hrs

we dont know the time for old machine so we assume it to be ( t ),

while that of the new machine is ( 14-t ) hours for new machine, and sum of 430 components.

therefore;

25t +490 - 35t = 430

-10t = -60

divide both sides by -10

t = 6 hours for the first machine.

6hrs * 25 components /hr

= 150 component parts For old machine.

for new machine

= 14 - t ........... eq1.

where ( t = 6 ), substitute t into the equation

= 14 - 6

= 8 hours for the second machine

= 8 * 35

= 280 components parts

Step-by-step explanation:

Hello there!!

no need to be panic we will help you, alright.

look solution in picture ok...

sorry for cutting in middle.

Hope it helps...

Answer:

Short answer A,B,D

Step-by-step explanation:

The ideas from the excerpt would be most appropriate to include in a summary are;

Summary is known to be a form of quick or short review of what has happened in a specific passage.

The summary  is regarded as a statement that present the main points of a passage as seen above.

Learn more about novels from

https://brainly.com/question/19599489

Answer:

26^7=8 031 810 176

Step-by-step explanation:

The word has 7 letters. So the word have 7 places where any of 26 letters can be placed.

Any of 26 letters can stay at 1st place

Any of 26 letters can stay at 2-nd place (because letters can be repeated)

Any of 26 letters can stay at 3rd place  

Any of 26 letters can stay at 4th place

Any of 26 letters can stay at 5th place

Any of 26 letters can stay at 6th place

Any of 26 letters can stay at 7th place  

So N= 26*26*26*26*26*26*26=26^7=8 031 810 176

Answer:

  1

Step-by-step explanation:

David Joyner might be the first name, so you may only have to check 1 name.

Answer:

46/100.

Step-by-step explanation:

46 / 100 = 0.46

46 / 1,000 = 0.046

0.046 < 0.46

So, 46/100 is greater than 46/1,000.

Hope this helps!

46/100 is greater because it equals 0.46 while 46/1000 would equal 0.046.

the slope of the line is 3

Step-by-step explanation:

F (x)=x³-2x²+x+1,

Then F (-x)= - x³ - 2x² - x + 1

Tell me if I'm right.

Hope this helps.

Have a great day!

Answer:

work is shown and pictured

Correct Answer would be

D: (2,3)

Answer:

area = 1800 m²

Step-by-step explanation:

area of one triangle = 900 m²

if a parallelogram has the same height and base as the triangle, then that means the area or the two triangle and shaped as a parallelogram

is twice the area given.

area = 900 * 2

area = 1800 m²

Answer:

Well Plan D

Step-by-step explanation:

Answer:

plan D.

Step-by-step explanation:

2021 edge

Answer:

See below.

Step-by-step explanation:

So, we have:

[tex]\sec(\theta)=-2/\sqrt{3}[/tex]

Recall that secant is simply the reciprocal of cosine. So we can:

[tex]\cos(\theta)=(\sec(\theta))^{-1}=(-2/\sqrt{3})^{-1}\\\cos(\theta)=-\sqrt{3}/2[/tex]

Now, recall the unit circle. Since cosine is negative, it must be in Quadrants II and/or III. The numerator is the square root of 3. The denominator is 2. The whole thing is negative. Therefore, this means that 150 or 5π/6 is a candidate. Therefore, due to reference angles, 180+30=210 or 7π/6 is also a candidate.

Therefore, the possible values for theta is

5π/6 +2nπ

and

7π/6 + 2nπ

Answer:

C) tan(39°) = 11/15

Step-by-step explanation:

SohCahToa

tangent = opposite / adjacent

The given angle is 39°. The angle directly opposite of 39° is 11 and the angle adjacent to 39° is 15.

Answer:

tan(39°) = 11∕15

Step-by-step explanation:

Answer:

Henry had the best record for the number of shots made

Step-by-step explanation:

From the given information.

Four friends are on a basketball team.

Henry

Allison

Arthur

Trevor

We are being told that Henry made 0.45  of his shots out of all his attempts

Allison made Arthur made of her shots  of his shots.

i,e Arthur did the work for Allison , so out of Arthur's shot , we have to  figured out Allison shots,

Trevor missed 58% of his shots.

i.e Trevor failed 0.58 of his shot, If he failed 0.58 shot

Then the attempts Trevor made is :

= 1 - 0.58

= 0.42

SO , Trevor made 0.42 shots out of all his attempt

N:B We are not given any information about Arthur's shots , so we can't determine Allison shot as well.

Therefore; we will focus on only Henry and Trevor shots

So ;

Henry made 0.45  of his shots

Trevor made 0.42 out of his shots

We can thereby conclude that :

Henry had the best record for the number of shots made

Answer:

He stitched 1 shirt in 6 hours.

He can stitch 1/6 of a shirt in one hour

Step-by-step explanation:

Given Mike can stitch 7 shirts in 42 hours

No. of shirt stitch in one hour = total no of shirt stitch/total time taken

No. of shirt stitch in one hour = 7/42 = 1/6

Thus, he can stitch 1/6 of a shirt in one hour

Time taken to stitch 1 shirt = total time taken by him to stitch 7 shirts/ total no. of shirt stitch(i.e 7)  = 42/6 = 6 hours.

Thus, he stitched 1 shirt in 6 hours.

Answer:

He can stitch 1/6 of a shirt in one hour

Step-by-step explanation:

Because he stitched  7 shirts in 42 hours

42/7 = 6

so 6 hours per shirt

In one hour:

1/6

Answer:

It means the left side of the equation equals the right side of the equation regardless of the value of the variables. The solution is all real numbers for each variable

Step-by-step explanation:

Answer:

ln(2000) = 7.601

Step-by-step explanation:

For this we need to know the rules of logarithms, specifically the product rule and the power rule.  The product rule is simply ln(a*b) = ln(a) + ln(b).  The power rule is simply ln(a^b) = b ln(a).

With these rules, let's begin to simplify the expression:

4 ln(2) + 3 ln(5)

= ln(2^4) + ln(5^3)

= ln(16) + ln(125)

= ln(16 * 125)

= ln(2000)

= 7.601

Hope this helps.  Cheers.

A logarithm is a power to which a number must be raised in order to get some other number.

The value of the expression 4 log 2 + 3 log 5 as a single number is 3.30102.

A logarithm is a power to which a number must be raised in order to get some other number.

Example:

log 10 = 1

log 100 = log 10² = 2 log 10 = 2 x 1 = 2
log 1000 = log 10³ = 3 log 10 = 3 x 1 = 3

log 0 = undefined

log 1 = 0

We have,

Some formulas for log:

log[tex]x^{n}[/tex] = n log x

log mn = log m + log n

Given,

4 log 2 + 3 log 5

= log [tex]2^{4}[/tex] + log [tex]5^{3}[/tex]

= log 16 + log 125

= log (16 x 125)

= log 2000

= 3.30102

Thus the value of the expression 4 log 2 + 3 log 5 as a single number is

3.30102.

Learn more about log here:

https://brainly.com/question/14407082

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Answer:

[tex](-\infty, \infty)[/tex]

Step-by-step explanation:

Every number, when you raised to the second power is positive, therefore that inequality would be all real numbers.

[tex](-\infty, \infty)[/tex]

Step-by-step explanation:

x² + 11x + 121/4 = 125/4

x² + 11x + 121/4 - 125/4 = 0

x² + 11x - 1 = 0

after that apply quadratic formula

x = ( -b + or - √b² - 4ac ) ÷ 2a

x = (-11 + or - √11² - 4×1×-1 ) ÷ 2×1

+ = 0.090169....

- = -11.090168.....

x = 0.090 or x = -11.09

Answer:  b.  24(x + 2) = (y + 3)²

Step-by-step explanation:

Vertex: (-2, -3)

Focus:  (4, -3)

                  ↓

                same y-value so equation will be y²

Equation: a(x - h) = (y - k)²

Given: h = -2,  k = -3,   a = 4[4 - (-2)] --> a = 24

Input those values into the equation:  24(x + 2) = (y + 3)²