Solve the Linear Quadratic system of equations

y=x^(2)+2x-9
y=-2x+3

Answer:

x = 7.5.

The two lines on the side of the triangle in the screenshot show us that the two lines made are the same length. So the difference between the first two values, i.e. 22.3 and 14.9 is the same difference between 14.9 and x.

Step-by-step explanation:

hope this helps. . .<3

good luck!    uωu

Answer:

Step-by-step explanation:

14.9 is the middle value of x and 22.3. So your formula looks like this.

(x + 22.3) / 2 = 14.9          Multiply both sides by 2

2(x + 22.3) / 2 = 14.9*2    Remove the brackets.

x + 22.3   = 29.8              Subtract 22.3 from both sides

x = 29.8 - 22.3                

x = 7.5

Answer:

[tex]\large\sf{average\:rate\:of\:change= \frac{6}{5}\:=\:1.2}[/tex]

Step-by-step explanation:

Given the American customer satisfaction index scores that increased from 61 in 2002, to 71 in 2014:

In order to solve for the average rate of change, we could simply use the average rate of change formula:

Average rate of change = Change in output/Change in input

[tex]\huge\sf{Average\:rate\:of\:change\:=\:\frac{\triangle{y}}{\triangle{x}}\:=\:\frac{(y_2\: -\: y_1) }{(x_2\: -\: x_1)}}[/tex]

Let (x₁, y₁) = (61, 2002)

    (x₂, y₂) = (71, 2014)

Substitute these values into the average rate of change formula:

[tex]\BIGG\sf{Average\:rate\:of\:change\:=\:\frac{\triangle{y}}{\triangle{x}}\:=\:\frac{(y_2\: -\: y_1) }{(x_2\: -\: x_1)}\:=\frac{2014\:-\:2002}{71\:-\:61}\:=\:\frac{12}{10}\:=\:\frac{6}{5}}[/tex]

[tex]\large\bf\sf{Therefore,\:the\:average\:rate\:of\:change= \frac{6}{5}\:=\:1.2}[/tex].

[tex]n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_7=\stackrel{7^{th}\ term}{192}\\ 7=\textit{term position}\\ a_1=\textit{first term}\\ r=\stackrel{\textit{common ratio}}{2} \end{cases} \qquad \qquad a_7=a_1\cdot 2^{7-1} \\\\\\ 192=a_1\cdot 2^6 \implies 192=64a_1\implies \cfrac{192}{64}=a_1\implies \boxed{3=a_1}[/tex]

Answer:

x = 3

Step-by-step explanation:

In a parallelogram the diagonals bisect each other , then

6x + 11 = 5x + 14 ( subtract 5x from both sides )

x + 11 = 14 ( subtract 11 from both sides )

x = 3

Answer:

4

Step-by-step explanation:

Answer:

16383

Step-by-step explanation:

El primer término de la progresión geométrica es 3 y lo llamaremos [tex]a[/tex].

Se tiene que una progresión geométrica es de la forma:

[tex]a, ar, ar^2, ar^3, ar^4, \cdot \cdot \cdot[/tex]

Donde [tex]r \neq 0[/tex] y es la proporción es común. Por lo tanto si el séptimo número de la sucesión es 12.288 este se puede re-escribir como:

[tex]ar^6 = 12.288[/tex]

Si se resuelve la ecuación para hallar [tex]r[/tex] se tiene

[tex]r = \sqrt[6]{\frac{12.288}{a} } = \sqrt[6]{\frac{12.288}{3} } = \sqrt[6]{ 4096} = 4[/tex]

Ahora se halla cada número de la progresión geométrica entre 1 y 7 para finalmente sumarlos

[tex]ar^0+ar^1+ar^2+ar^3+ar^4+ar^5+ar^6[/tex]

[tex]3+12+48+192+768+3072+12288[/tex] = 16383

Por lo tanto la sumatoria de los primeros [tex]7[/tex] términos de la sucesión son 16383

30% × 390 = 117

= 390 - 117

= 507 kw/h

Answer:

a: [tex]f(t)=(t+2)^2-18[/tex]

b: vertex: (-2, -18)

   minimum

c: x = -2

Step-by-step explanation:

Completing the square is difficult to explain in words. but I'll try my best. Let me know if you need any more information.

Part A ===============

Start with the given function in this form:

[tex]f(x)=ax^2+bx+c\\t^2+4t-14[/tex]

We need an additional number, d, and we'll calculate it like this:

[tex]d=(\frac{b}{2a})^2 \\\\d=(\frac{4}{2(1)} )^2\\d=2^2\\d=4[/tex]

d needs to be added and subtracted at the same time. That way we do not change the value of the expression:

[tex]ax^2+bx+d-d+c\\\\t^2+4t+4-4-14[/tex]

And you can separate them like this to make it easier to read:

[tex](t^2+4t+4) + (-4-14)\\(t^2+4t+4)-18[/tex]

Finally, we need to factor the trinomial in the parenthesis. Because we've completed the square, it's now a perfect square trinomial.  The factored form is just:

[tex](x+e)^2[/tex]

where e is half of b, or the square root of c. That looks like this in our case, and you can also expand it to make sure.

[tex](t+2)^2\\\\(t+2)(t+2)\\t^2+2t+2t+4\\t^2+4t+4[/tex]

Put that all together and you get the answer:

[tex]f(t)=(t+2)^2-18[/tex]

Part B ===============

Vertex form is this:

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

where (h, k) is the vertex and a is the scale factor.

In part A, we converted the given function into vertex form. Looking at that, you can see the vertex is at (-2, -18), and the scale factor is 1. When the scale factor is positive, the parabola faces upwards. When it's negative, the parabola faces downwards.

The scale factor is a positive 1 in this case, and if you picture that in your mind, the vertex is at the very lowest point, or the minimum, of the parabola.

Part C ==============

The axis of symmetry is always on the vertex, and that is because the vertex is the exact point where the parabola changes direction from positive to negative, or negative to positive.

The vertex of this parabola is (-2, -18), so the axis of symmetry is at x = -2.

Sorry if that got too long and hard to follow, I can clarify any part of it if needed.

Answer:

3,5,6

Step-by-step explanation:

because 300 divided by 2 is 150

50 divided by 2 is 25

and 6 divided by 2 is 3

Therefore the percentage increase is 72

Answer:

Step-by-step explanation:

Answer:

Yes there is a proportional relationship

Step-by-step explanation:

If we look at earth and the sun, the diameter of the sun is 108 times that of the diameter of earth, and the average distance between the earth and sun is 108 times the suns diameter.

Answer:

Easy

Step-by-step explanation:

Answer: 36,000 divided by 90 is 400

Answer:

400

Step-by-step explanation:

Answer:

24.75 is answer

Step-by-step explanation:

Answer:

That was a good start, but we need the rest of the question.

Step-by-step explanation:

you have the ratio of natural:synthetic so;

3:4

3+4=7

357/7=51

3*51:4°51

153:204

therefore, it'd be 204 litres of synthetic oil!!

i hope this helps you!!

Answer:

1) (4x)² - (5)²

2) (4x + 5) (4x -5)

3) Zeros of b are [tex]\frac{5}{4}[/tex] and [tex]\frac{-5}{4}[/tex] (can also be 1.25 and -1.25)

Answer:

$ 30,000

Step-by-step explanation:

0.15(50,000 - x) - 0.1x = 2,500

7,500 - 0.15x - 0.1x = 2,500

7,500 - 2,500 = 0.15x + 0.1x

5,000 = 0.25x

5,000/0.25 = x

x =20,000

50,000 - 20,000 = 30,000

0.15 * 30,000 = $4,500

0.1 * 20,000 = $2,000

$4,500 - $2,000 = $2,500

The Venn Diagram B, C and D, all represents two sets with common elements.

In B, the circle F is inside the circle G, so F share all of its elements with G. It is like a baby inside the belly of her mother :)

In C, F and G circles intersect and the intersection is their common space, and

the D is like the B.

But A reprents two sets F and G with no common elements. So the answer is A.

Good Luck

Answer:Measure length of each wall including doors and windows. Find the total square feet of the wall(s) by multiplying ceiling height by total wall length.

Step-by-step explanation:

The required area that is to be painted is given as   150 square feet.

Given that,
A wall that is 12 feet high and 15 feet wide is to be painted, but the wall has two rectangular windows (which should not be painted). each window is 3 feet by 5 feet,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Area of the wall = 12 × 15 = 180 square feet
Area of the two windows, = 2 × 3 × 5 = 30 square feet
Area to be painteded = 180 - 30 = 150 square feet,

Thus, the required area that is to be painted is given as   150 square feet.

Learn more about simplification here:

https://brainly.com/question/12501526

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Answer:

1/5(2ln|x|+3*5^1/3)+c

Step-by-step explanation:

Answer:

i agree I can't really explain why though sorry

Heather's mom's estimation is wrong, as they will only save $96.

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

Given that, The special price for the amusement park ticket costs $56. This is 70% of the regular price, Heather's mom says that they would save more than $100 if they bought tickets for their family on opening weekend.

Let the original price of the ticket be x,

70% of x = 56

x = 56x100/70

x = 80

That means, the regular price is $80

On a regular day, ticket will cost = 80x4 = $320

On the special ticket price cost = 56x4 = $224

The saved priced = 320-224 = $96

Hence, Heather's mom's estimation is wrong, as they will only save $96.

For more references on percentage, click;

https://brainly.com/question/29306119

#SPJ1

Answer:

4 Meters

Step-by-step explanation:

Formula

divide the length value by 10

Answer:

Heigh <= 63

Width <= 56

Length <= 61

Step-by-step explanation:

Height: x+7

Width: x

Length: x + 5

(x + 7) + (x) + (x + 5) <= 180 cm^3

3x + 12<= 180

3x <= 180-12

x <= 168/3

x <= 56

Answer:

The answer is D.

Step-by-step explanation:

Radius is half of diameter. So the radius of the circle is 6 in.

The formula for getting the area of circle is:

A = π[tex]r^{2}[/tex]                                π = 3.1416

A = (3.1416)(6)[tex]^{2}[/tex]

A = (3.1416)(36)

A = 113.09 square inches

Answer:

which question can I help you