Write a real-life word problem that can be solved using the system of equations below. Include a definition of the variables. x + y = 325 y = x + 27

Answer:

Set y = 0, evaluate the quadratic at h=−b2a and solve for k.

k=9 I think..... I'm not completely sure but I think that's how it is

Answer:

[tex]\displaystyle \text{Vertex} = \left(k, 3-k^2\right)[/tex]

Step-by-step explanation:

We are given the quadratic equation:

[tex]y=x^2-2kx+3[/tex]

Where k is a non-zero constant.

And we want to determine the vertex of the parabola in terms of k.

The vertex of a parabola is given by the formulas:

[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = 1, b = -2k, and c = 3.

Find the x-coorinate of the vertex:

[tex]\displaystyle x=-\frac{(-2k)}{2(1)}=\frac{2k}{2}=k[/tex]

To find the y-coordinate, we substitute the value we acquired back into the equation. So:

[tex]\displaystyle \begin{aligned} y(k)&=(k)^2-2k(k)+3\\&=k^2-2k^2+3\\&=3-k^2\end{aligned}[/tex]

Therefore, our vertex in terms of k is:

[tex]\displaystyle \text{Vertex} = \left(k,3-k^2\right)[/tex]

Answer:

[tex]\text{A. }1\leq x \leq6[/tex]

Step-by-step explanation:

A constant intervals occurs when the function is neither increasing or decreasing. In the graph, we see this occurs from [tex]x=1[/tex] to [tex]x=6[/tex]. Therefore, the interval in which the graph is constant is [tex]\boxed{\text{A. }1\leq x \leq6}[/tex]

Answer: 56, 8

Step-by-step explanation:

Given

The ratio of goldfish to gallons of water is 7:2

If there is 16 gallons of water. For x goldfish, We can write

[tex]\Rightarrow \dfrac{7}{2}=\dfrac{x}{16}\\\\\Rightarrow x=7\times8\\\Rightarrow x=56[/tex]

If there are 28 fish, for y gallons of water we can write

[tex]\Rightarrow \dfrac{7}{2}=\dfrac{28}{y}\\\\\Rightarrow y=2\times 4\\\Rightarrow y=8\ \text{gallons}[/tex]

Answer:

-2x-11=0

1) Add 11 to both sides

Dividde both sides by - 2

X= _11/2

Drcimal form: - 5.5

Answer:

C

Step-by-step explanation:

12b + 30f = 240

7b + 10f = 125

Multiply the second equation by -3

12b + 30f = 240

-21b -30f = -375

Add up the two equations

-9b = -135

b = $15

Substitute this value in one of the two equations

12 * 15 + 30f = 240

180 + 30f = 240

30 f = 60

f = $2

Answer:

Option (2)

Step-by-step explanation:

To get the transformation applied in triangle ABC to map triangle DEF we will apply the following rules.

If a point A of triangle ABC maps the point D of triangle DEF,

Coordinates of point A → (-4, -5)

Coordinates of point D → (2, 6)

First point A is shifted to quadrant (4) from quadrant (3),

Rule for the translation,

A(x, y) → A'(x + 6, y - 1)

A(-4, -5) → A'(2, -6)

Followed by reflection across x-axis (y = 0)

A'(x, y) → D(x, -y)

A'(2, -6) → D(2, 6)

Therefore, Option (2) will be the answer.

Answer:

[tex]a = 2 \\ b = 11[/tex]

Step-by-step explanation:

[tex] {x}^{2} + 4x + 4 - 4 - 7 = {(x + 2)}^{2} - 11[/tex]

Step-by-step explanation:

It doesn't matter what order they are drawn in, so youi have a combination problem

26C5

My calculator gives the answer directly,

It is 65780

Answer:

The answer is A, that's the correct one

Answer:

[tex]P(Cheese) = 0.30[/tex]

Step-by-step explanation:

Given

[tex]Cheese = 36[/tex]

[tex]Pepperoni = 64[/tex]

[tex]Veggie = 20[/tex]

Required

[tex]P(Cheese)[/tex]

This is calculated as:

[tex]P(Cheese) = \frac{Cheese}{Total}[/tex]

[tex]P(Cheese) = \frac{36}{36+64+20}[/tex]

[tex]P(Cheese) = \frac{36}{120}\\[/tex]

[tex]P(Cheese) = 0.30[/tex]

Answer:

y = (x + 3)² - 6

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

f(x) = x² + 6x + 3

Using the method of completing the square

add/subtract ( half the coefficient of the x- term)² to x² + 6x

f(x) = x² + 2(3)x + 9 - 9 + 3

     = (x + 3)² - 6 ← in vertex form

Answer:

Have you got it now?

Step-by-step explanation:

Answer: The remainder is 0.

Step-by-step explanation:

We are given:

Dividend polynomial = [tex]6x^5+4x^4-27x^3-7x^2+27x+\frac{3}{2}[/tex]

Divisor polynomial = [tex]2x^2-3[/tex]

We divide the dividend by the divisor using the long division method.

In this method, the final answer written in the bottom is considered as remainder and the uppermost polynomial is considered as the quotient.

The long division of the two polynomials is attached in the image below.

From the image, we can say that the remainder of the two is 0

Answer: 99/130

Payment made by any method except credit card is 95+4=99 and altogether there is three payment method including a credit card which sums up to 130.

So the probability is 99/130.

Answer:

the answer to A,B,C

Step-by-step explanation:

all the points are on the graph

all answers

b) slope -1

intercept 1

c)(x+3)(x-1)

intercepts (-3,0),(1,0)

vertex (-1,-4)

Answer:

[tex]X= \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \left[\begin{array}{ccc}21\\20\\\end{array}\right] \\[/tex]

Step-by-step explanation:

Given the simultaneous equation

x+y=21

5x+4y=20

To write in matrix form, it must be in the form AX= b

X = A⁻¹b

A⁻¹ is the inverse of matrix A

A is a 2by2 matrix

X is the variables

b is a column matrix

The expression will therefore be written as;

[tex]A=\left[\begin{array}{ccc}1&1\\5&4\\\end{array}\right] \\\\|A| = 1(4)- 5(1)\\|A| = 4-5\\|A| = -1\\A^{-1} = -\left[\begin{array}{ccc}4&-1\\-5&1\\\end{array}\right] \\\\A^{-1} = \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \\[/tex]

Hence the required product matrix that represent X is;

[tex]X= \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \left[\begin{array}{ccc}21\\20\\\end{array}\right] \\[/tex]

The lower the frequency the least common the average.

There are two frequencies that are 1, which would be the least common.

The answer is C. 0.320-0.329 and 0.360 -0.369

Answer:

option C

Step-by-step explanation:

option c is contains the two batting averages which have a frequency of 1, this means that they both only occurred once which is the least amount of times any of the batting averages has occurred.

Step-by-step explanation:

my answer is in the image above

Answer:

I've attached the Answer here

Answer:

guessing that the area of the inner rectangle is 10m²

and the other rectangle is 16m*10m= 160m²

we can say that

(16-x) * (10-x) = 10

for the area of the inner rectangle

let's calculate the lefthand side of the equation

160 - 16x -10x + x² = 10

160 -26x +x² = 10

subtract 10 on both sides

150 -26x +x² = 0

rearrange

x² -26x + 150 = 0

looks like something we can throw the pq formula on to solve for x

with p = -26 and q = 150

[tex]x = - \frac{ - 26}{2} \frac{ + }{ - } \sqrt{( \frac{ - 26}{2})^{2} - 150 } [/tex]

[tex]x = 13 \frac{ + }{ - } \sqrt{169 - 150 } [/tex]

[tex]x = 13 \frac{ + }{ - } \sqrt{19 } [/tex]

[tex]x1 = 8.64[/tex]

[tex]x2 =17.36 [/tex]

we need to interpret this solutions

but to be sure on this, I need the unreadable text of the photographed problem

Answer:

C

Step-by-step explanation:

y=-7x-11

Step-by-step explanation:

How to Calculate the Semi Interquartile Range / Quartile Deviation. As the SIR is half of the Interquartile Range, all you need to do is find the IQR and then divide your answer by 2. Note: You might see the formula QD = 1/2(Q3 – Q1). Algebraically they are the same.

Answer:

Determine AC with the pythagorean theorem, then you can find CD by subtracting AD.

with DC and BC, you can find BD. again, with the pythagorean theorem

Answer:

20

Step-by-step explanation:

Find AC

[tex]\sqrt{65^{2} -16^{2} } = 63[/tex]

Substract

63 - AD = 12

Find "?"

[tex]\sqrt{12^{2} +16^{2} } = 20[/tex]

Question 23

Recall that a kite in geometry is any four sided figure where we have two different pairs of adjacent sides that are the same length.

We're told that PS = 4.5 and RS = 6. So this isn't an adjacent pair of congruent sides. But we can say that PS and PQ are one pair of adjacent congruent sides. That makes PQ to be 4.5 cm long.

Similarly, RS = RQ = 6 is the other pair of adjacent congruent sides. Notice that triangle PQR reflects over line PR to get triangle PSR.

See the diagram below.

Answer:

39.24 sec

How long will it take a 1500 W motor to lift a 300 kg piano to a sixth-story window 20 m above? All tutors are evaluated by Course Hero as an expert in their subject area. Answer is t = 39.24 sec

Step-by-step explanation:

It will take the motor 39.2 seconds to lift the piano to the sixth-story window.

Given the following data;

We know that acceleration due to gravity is equal to 9.8 m/s².

To find how long it will take to lift the piano to the sixth-story window;

First of all, we would have to determine the gravitational potential energy required to lift the piano up.

Mathematically, gravitational potential energy is given by the formula;

[tex]G.P.E = mgh[/tex]

where:

Substituting into the formula, we have;

[tex]G.P.E = 300*9.8*20[/tex]

G.P.E = 58,800 Joules

Next, we would determine the time using the following formula;

[tex]Time = \frac{Energy}{Power}[/tex]

Substituting the values into the formula, we have;

[tex]Time = \frac{58800}{1500}[/tex]

Time = 39.2 seconds.

Therefore, it will take the motor 39.2 seconds to lift the piano to the sixth-story window.

Find more on power, time and energy here: https://brainly.com/question/20488953

Answer:

c

Step-by-step explanation:

all real values of x where 1 < x < 4

Answer:

c

Step-by-step explanation:

trust me

Answer: 87.

Step-by-step explanation:

Let x be the tens digit, then (x - 1) - unit digit.

x + x - 1 = 15

2x - 1 = 15

2x = 15 + 1

2x = 16

x = 16 ÷ 2

x = 8 - the tens digit.

8 - 1 = 7 - the units digit.

87 - the number.