STEPS
1)
1. Write the coordinates of the 1st and
2nd points.
2. Label the coordinates of the first point
as
(X1,Y1) and the 2nd point as (X2
Y2).
3. Use the formula
m=Y2-Y
X2 - X
1st Point 2nd Point
1st Point:
2nd Point:
m=Y-Y
X2 - X
m=Y-Y
X2 - X

The specified function's vertex form is [tex]g(x) = 4(x+5)^2 - 100[/tex]

If a quadratic equation is written in the form

[tex]y=a(x-h)^2 + k[/tex]

then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

If a polynomial p(x) can be written as:

[tex]p(x) = [f(x)]^2[/tex]

where f(x) is also a polynomial, then p(x) is called as perfect square polynomial

For the considered case, the polynomial specified is;

[tex]g(x) = 40x + 4x^2[/tex]

[tex]g(x) = 40x + 4x^2\\g(x) = 4(x^2 + 10) = 4(x^2 + 10 + 25 -25)\\g(x) = 4(x^2 + 10 + 25) - 100 = 4(x+5)^2 - 100\\[/tex]

Thus, the vertex form of the considered polynomial is [tex]g(x) = 4(x+5)^2 - 100[/tex]

Standard form of a quadratic polynomial is [tex]ax^2 + bx + c[/tex]

Thus, we get: the considered polynomial in standard form as:

[tex]g(x) = 4x^2 +40x[/tex]

[tex]g(x) = 40x + 4x^2 \\g(x) = 4x(10 + x)[/tex]

The considered polynomial has only two terms, therefore, its not a trinomial.

Thus,  the specified function's vertex form is [tex]g(x) = 4(x+5)^2 - 100[/tex]

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Answer:

g(x)=4(x+5)^2-100

Step-by-step explanation:

Have the day you deserve :)

Answer:

87.50

Step-by-step explanation:

75,000 x 28% ÷ 12

She will budget $225 for her emergency savings for the month of March

We have:

Gross = $75,000 per year.

Payroll deductions = 28%

So, the net pay is:

Net = (1 - 28%) * $75,000

Evaluate

Net = $54000

The net income per month is:

Monthly = $54000/12

Evaluate

Monthly = $4500

5% of her net income goes to emergency.

So, we have:

Emergency = 5% * $4500

Evaluate

Emergency = $225

Hence, she will budget $225 for her emergency savings for the month of March

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Answer: The Egyptians, Babylonians, and Archimedes.

Step-by-step explanation: The Egyptians and Babylonians were the first known civilizations to use pi.  At the time, Egyptians devised the approximated value of pi as 3.1605.  Archimedes, however, did the first calculation of pi, with its approximate value of 3.141592 or 3.14 to make it shorter.  

Hopefully, this helps you!

Answer:

12.12

Step-by-step explanation:

4% of 110 = 4.4

4.4 x 3 = 12.12

Answer:

544 miles

Step-by-step explanation:

this problem is a multiplication problem, if one inch is 32 mile, and  San Antonio to El Paso is 17 inches you have to multiply 17 and 32 to get 544 miles

Answer:

544 miles

Step-by-step explanation:

Since 1 inch equals 32 miles, [tex]17inches\cdot 32miles=544miles[/tex]

Answer:

Step-by-step explanation:

Price of cellophone = ₹4500

Gst additionally = 12%

= 12% of ₹4500

= 12/100 * 4500

= ₹12*45

= ₹540

Total = ₹4500 + ₹540

= ₹5040

Answer:

Rs. 5040

Step-by-step explanation:

Price of cellphone=Rs. 4500

Gst additionally=12%

=12% of Rs. 4500

12/100 * 4500

=Rs. 12*45

=Rs.540

=Total=4,500+540

=Rs.5040

Answer: A linear system of two equations with two variables is any system that can be written in the form. ... A solution to a system of equations is a value of x and a value of y that, when substituted into the equations, satisfies both equations at the same time. For the example above x=2 and y=−1 is a solution to the system

Step-by-step explanation:

[tex]\\ \rm\rightarrowtail x^2+3\sqrt{3}x+6[/tex]

[tex]\\ \rm\rightarrowtail x^2+\sqrt{3}x+2\sqrt{3}x+6[/tex]

[tex]\\ \rm\rightarrowtail x(x+\sqrt{3})+2\sqrt{3}(x+\sqrt{3})[/tex]

[tex]\\ \rm\rightarrowtail (x+2)(x+2\sqrt{3})[/tex]

Using the quadratic formula,

[tex]x1 = \frac{ - b - \sqrt{3} }{2a} = \frac{ - 3 \sqrt{3} - \sqrt{3} }{2} = \frac{ - 4 \sqrt[]{3} }{2} [/tex]

[tex]x1 = - 2 \sqrt{3} [/tex]

[tex]x 2 = \frac{ - b + \sqrt{3} }{2a} = \frac{ - 3 \sqrt{3} + \sqrt[]{3} }{2} = \frac{ - 2 \sqrt{3} }{2} [/tex]

[tex]x2 = - \sqrt{3} [/tex]

Your factored equation can be written in the form of:

(x-x¹)(x-x²)

(x+2√3)(x+√3)

The two joggers who are 21 miles apart travel at a speed 8 mph and 6 mph respectively and would meet after one and half hours.

An equation is an expression used to show the relationship between two or more variables and numbers.

Let a represent the speed of the faster jogger and represent the speed of the other jogger. Hence:

a = b + 2 (1)

Also:

In one and half hour (1.5 h):

a = d₁/1.5

d₁ = 1.5a

b = d₂/1.5

d₂ = 1.5b

d₁+ d₂ = 21

1.5a + 1.5b = 21   (2)

From both equation 1 and 2:

a = 8, b = 6

The speed of the joggers is 8 mph and 6 mph respectively.

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Answer: a)  Unimodal and symmetric

b) 0.26

c) 0.038

Step-by-step explanation:

Given: Sample size of investors (n)= 131

True proportion of smartphone users(p)  =26%

a) Since sampling distribution for the sample proportion is approximately normal when n is larger.

Normal distribution is Unimodal and symmetric.

So correct option : Unimodal and symmetric

b)  mean of this sampling​ distribution = p = 0.26

c)  standard deviation of the sampling​distribution = [tex]\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.26\times (1-0.26)}{131}}=\sqrt{0.00146870229008}[/tex]

[tex]=0.0383236518364\approx0.038[/tex]

Answer:

418.75

Step-by-step explanation:

5025/12 (12 months in one year)

418.75 or almost 420 dollars a month

to check the answer:

418.75*12

5025

Answer:

9.75$

Step-by-step explanation:

Answer:

9.75$

Step-by-step explanation:

The original price of the shirt is $15, and it's on sale for 35% off. What is the item's sale price?

First, convert the 35% to a real mathematical number. For percents, this is always done by dividing the 35% by 100%, or 35% / 100% = 0.350.

Second, find out what 35% of $15 is. This is the amount of the sale discount. This is always found by multiplying 0.350 by the item's cost $15, like this:

0.350 x $15 = $ 5.25.

So for this sale, you'll save $ 5.25 on this item.

This means, the cost of the item to you is

$15 - $ 5.25 = $ 9.75.

1,3 is right correct right answer

The coordinate point for A is (1,3) Therefore, option B is the correct answer.

WE know that rhombus can be defined as a special parallelogram as it fulfills the requirements of a parallelogram, i.e. a quadrilateral with two pairs of parallel sides.

Since a rhombus has all four sides equal just like a square.

Given that, Point C (2, 1), Point B (3,4) and Point D (4,2)

The coordinate point for A that would make ABDC a rhombus.

So, the coordinate point for A is (1,3).

Therefore, option B is the correct answer.

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Answer:

The answer is congruent

The height of the rocket after 5 seconds would be 0 feet.

A quadratic equation is in the form:

y = ax² + bx + c

Let y represent the height after x seconds.

At point (0, 0):

0 = a(0)² + b(0) + c

c = 0

At (0.5, 20.5):

20.5 = a(0.5)² + b(0.5) +0

0.25a + 0.5b = 20.5

At point (2, 36.25):

30.41 = a(2)² + b(2) + 0

4a + 2b = 30.41

Hence:

a = -17.2, b = 49.6

Hence:

y = -17.2x² + 49.6x

At 5 seconds:

y = -17.2(5)² + 49.6(5) = -197

The height of the rocket after 5 seconds would be 0 feet.

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Answer:

I think it's 600 I think it might be wrong

Answer:

3.66666. . . = 11/3 = 3  2/3

Step-by-step explanation:

Use distributive property.

3 ⋅ x = 3x

3 ⋅ (-1) = -3

3x - 3 + 4 = 12

Add -3 to 4

1

3x + 1 = 12

Subtract 1 from both sides.

3x = 11

Divide both sides by 3

3.666666. . .

This can also be written as 11/3

11/3 can be simplified to 3  2/3

Hope I helped :)

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Answer:

You divide the smaller number by the bigger, or the received points out of the total, so you would divide 99 by 150 giving you 66%

Answer : 66%

Explanation : 33 ÷ 50  Or 99 ÷ 150

Answer:

h = 5.2 cm

using Pythagoras theorem:

a² + b² = c²

3² + h²  = 6²

h² = 36 - 9

h² = 27

h = 3√3

h = 5.2 cm

Answer:

c)41

Step-by-step explanation:

∠DBE = (∠ABE +∠DBC) -∠ABC

          = (74 + 103)  -136

          = 177 - 136

          = 41

We can transform the mathematical sentence into the equation:

(2/3)*x - (2*y)^2 = 43

Here we have the sentence:

" Two thirds of a number decreased by the product of a number and two, squared, is 43"

First, we can define x as "the number"

Then:

" Two thirds of a number..." is:

(2/3)*x

Now we add the next part:

"... decreased by the product of a number and two, squared, is 43"

Assuming that this is another number, let's call it y, we have:

(2/3)*x - (2*y)^2 = 43

This is our two-variable equation.

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Answer:

The number of solutions is equal to the highest power exponent.

That is a cubic equation, so it has 3 solutions.

Step-by-step explanation:

Sorry, I couldn't figure out the last one, it just takes a lot of trial and error and luck :(

You know that S times A is the digit N. Then, A squared plus whatever the first digit of the2 digit number XN is MA.

A cannot be five because if you were to do 5 times 5 it would be 25. A squared is 25 and the last digit is already A so added on to anything else the equation would be false. So the only considerable value for S would be one, but then A times S would be 5, but N is not A. I hope you get what I mean.

A cannot be 6 for the same reason (just change the 5 to six on my last pragraph).

If A were 7 then you'd have to find something to add to 49 to make it end in 7, which means adding 6. 7 times 9 is 63, so S could be 9. 79 times 7 is 573. That is the answer. A = 7, S = 9, M = 5, N = 3.

As for NINE - FOUR = FIVE, E - R is E so R must be 0.The only one digit number a number can be subtracted by to get itself is 0.

Now, N - U = V, or 1N - U = V

Let's say N is 3 and U is 6. V would be 7.

We've just took one from I. I - 1 - O = I. 1+O must be 10 or 0, but O must be positive, so O = 9. Let's say I is 5.

We just borrowed one form N. N-1 - F = F. N - 1 = 2 times F.

But we know that N is 3. 2 = 2 times F. F is 1.

Let's just make E = 8

My final answer is 3538 - 1960 = 1578

There are MANY other answers though.

N = 3, I = 5, E = 8, O = 9, U = 6, R = 0, V = 7.

Answer:

200*20

÷100 ,=100+56

29+63

Step-by-step explanation:

200×20 =40000

40000÷100 =

100

Answer:

very last one

Step-by-step explanation:

hope it helps

Answer:

3.125 U.S. cups

take how many cups are in one ounce and multiply it.

Answer:

C

Step-by-step explanation:

The correct option is C because lines can extend its length in both side infinitely. It contains arrowheads indicating it can extend.

Pls rate.........

A line is an undefined term because it describes something that does not have width or depth. thus, option C is correct answer.

If the ray lies onto the considered line segment(overlapping), then it can be said belonging to the considered line segment.

(line segment has 2 fixed ends, whereas a ray has one end only, other end is not fixed)

A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).

A lines can extend its length in both side infinitely. It contains arrowheads indicating it can extend.

A line is an undefined term because it describes something that does not have width or depth. thus, option C is correct answer.

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