What is the value of f(g(1))?

Answer:

The equation of the polynomial in vertex form is [tex]y +8= (-2)\cdot (x-3)^{2}[/tex], its vertex is [tex](h,k) = (3, -8)[/tex].

The expression of the axis of symmetry is [tex]x = 3[/tex].

The y-intercept of the function is -26.

Step-by-step explanation:

The vertex form of the second order polynomial is defined by the following expression:

[tex]y-k = C\cdot (x-h)^{2}[/tex]  (1)

Where:

[tex]x[/tex] - Independent variable, dimensionless.

[tex]y[/tex] - Dependent variable, dimensionless.

[tex]h,k[/tex] - Coordinates of the vertex, dimensionless.

[tex]C[/tex] - Vertex constant, dimensionless.

Let [tex]y = -2\cdot x^{2}+12\cdot x - 26[/tex], then we proceed to present the produre for the determination of the vertex form:

1) [tex]y = -2\cdot x^{2}+12\cdot x - 26[/tex] Given

2) [tex]y = (-1)\cdot (2\cdot x^{2})+(-1)\cdot (-12\cdot x) + (-1)\cdot (26)[/tex] [tex](-a)\cdot (-b) = a\cdot b[/tex]/[tex](-a)\cdot b = -a\cdot b[/tex]

3) [tex]y = (-1)\cdot (2\cdot x^{2}-12\cdot x +26)[/tex] Distributive property

4) [tex]y = [(-1)\cdot (2)]\cdot (x^{2}-6\cdot x +13)[/tex] Associative and distributive properties

5) [tex]y = (-2)\cdot [(x^{2}-6\cdot x+9)+4][/tex] [tex](-a)\cdot b = -a\cdot b[/tex]

6) [tex]y = (-2) \cdot [(x-3)^{2}+4][/tex] Perfect square trinomial

7) [tex]y = (-2)\cdot (x-3)^{2}+4\cdot (-2)[/tex] Distributive property

8) [tex]y = (-2)\cdot (x-3)^{2}+(-8)[/tex] [tex](-a)\cdot b = -a\cdot b[/tex]

9) [tex]y +8= (-2)\cdot (x-3)^{2}[/tex] Compatibility of addition/Existence of the additive inverse/Modulative property/Result.

The equation of the polynomial in vertex form is [tex]y +8= (-2)\cdot (x-3)^{2}[/tex], its vertex is [tex](h,k) = (3, -8)[/tex].

The axis of symmetry is a line perpendicular to axis in which the square component of the vertex form is set. The expression of the axis of symmetry is [tex]x = 3[/tex].

The y-intercept is the value of the polynomial when [tex]x = 0[/tex], then, the value is:

[tex]y = -2\cdot (0)^{2}+12\cdot (0) -26[/tex]

[tex]y = -26[/tex]

The y-intercept of the function is -26.

Answer:

i think it might be 15m

Step-by-step explanation:

Answer:

the answer above is correct

Answer:

boxes

7

8

58.1

119.7

Step-by-step explanation:

look when u solve this it equals

8.3(7)+7.7(8)=119.7 but it tells u to add 61.6 so u go backwards subtract

119.7-61.6

58.1

just plug in

8.3(7)+7.7(8)=____+61.6

plug in

58.1+61.6

119.7

Answer:

I'm pretty sure it's neither? You need a graph or something for that

Answer:

I think its perpendicular

Step-by-step explanation:

When writing these points on a graph they make a square so when you connect the lines from the coordinates they cross making them perpendicular!

Answer:

5/100

1/20

Step-by-step explanation:

Answer: 5/100

Step-by-step explanation:

Answer: A, B, C, and E

Step-by-step explanation:

If both sides are real numbers, then the product will be a real number.

If in at least one of the sides we have a complex number, then the product will be real if:

The other number is zero.

The other number is the conjugate of the first.

This is when:

Suppose we have a number:

z = a + b*i

The conjugate will be:

w = a - b*i

And the product between them is:

(a + b*i)*(a - b*i) = a^2 + a*b*i - a*b*i + b^2 = a^2 + b^2

Then the options that will have a real answer are:

A. (4+5i)(4-5i) = 4^2 + 5^2 = 16 + 25 = 41

B. (4 + 91)*(41 - 9) = 3040

C. (3 + 2*i)*(3 -2*i) = 3^2 + 2^2 = 9 + 4 = 13

E. (312 + 7i)*(312 - 7i) = 312^2 + 7^2 = 97,393

Answer:

36  x 2 - 49 y 2

Step-by-step explanation:

6  x (6x) +6 x ( - 7 y ) + 7 y (6x) +7 y ( - 7 y)

The grouped frequency distribution for the data with the given intervals is 2, 4, 2 and 2 respectively.

Given that, ten cyclists were each asked the distance in miles they biked last week. The distance travelled by 10 cyclists is 3, 20, 6, 3, 7, 8, 13, 10, 18 and 12.

We need to complete the grouped frequency distribution for the data.

In this type, the data is arranged and separated into groups called class intervals. The frequency of data belonging to each class interval is noted in a frequency distribution table. The grouped frequency table shows the distribution of frequencies in class intervals.

Now, the frequency distribution for the given intervals is as follows:

That is, for intervals 1 to 5 the frequency is 2.

For intervals 5 to 10 the frequency is 4.

For intervals 11 to 15 the frequency is 2.

For intervals 16 to 20 the frequency is 2.

Therefore, the grouped frequency distribution for the data with the given intervals is 2, 4, 2 and 2 respectively.

To learn more about the grouped frequency distribution visit:

brainly.com/question/4679134.

#SPJ2

Answer:

Following are the solution to the question:

Step-by-step explanation:

The objective is to find the orthogonal trajectory of the family curves:

[tex]x^2+2y^2=17k^2[/tex]

The family curves are: [tex]x^2 + 2y^2=17k^2[/tex]  

Differentiate the equation with the respect of x.

[tex]\to x^2+2y^2=17k^2 \\\\\to 2x+4y \frac{dy}{dx} =0\\\\\to \frac{dy}{dx} =- \frac{2x}{4y}\\\\\to \frac{dy}{dx} =- \frac{x}{2y}[/tex]

The negative reciprocal is:

[tex]\to \frac{dy}{dx} =-\frac{1}{-\frac{x}{2y}}\\\\\to \frac{dy}{dx} = \frac{2y}{x}[/tex]

Integration of the above equation:

[tex]\to \frac{dy}{dx} = \frac{2y}{x} \\\\\to \int \frac{dy}{2y} = \int \frac{dx}{x}\\\\\to \frac{1}{2} \log y = \log x + \log C\\\\\to \log y = 2 \log x + 2\log C \\\\\to \log y = \log x^2 +\log C^2 \\\\\to y = Ax^2 \ \ \ \ \ \ \ \ \ (A=C^2)[/tex]

Hence, the orthogonal trajectory of the family of the curves [tex]x^2 + 2y^2 =17k^2 \ \ is \ \ y=Ax^2[/tex]

[tex]f(x)=2x^2+6x-4[/tex]

Find the f(-5) by substituting x = -5 in the equation.

[tex]f(-5)=2(-5)^2+6(-5)-4\\f(-5)=2(25)-30-4\\f(-5)=50-34\\f(-5)=16[/tex]

Therefore, the answer is f(-5) = 16.

Answer:

1080 boys

Step-by-step explanation:

2400 x 0.45 = 1080

Answer: It is B/Spinner 2

Answer:

Slope is -2

y intercept is -3

Equation :y=-2x-3

Step-by-step explanation:

Answer:

3.26 Euro I believe.

Step-by-step explanation:

9514 1404 393

Answer:

  see below

Step-by-step explanation:

When the intercepts are given, plot those and draw a line through them.

_____

Additional comment

The equation shown with the graph is the equation of a line in "intercept form." It is especially useful in a case like this where the intercepts are given.

Answer: 10 yards

Step-by-step explanation: 50% = 1/2

1/2 x 20 = 10

15 yeards mowed by Wednesday

Answer:

y = 8x

Step-by-step explanation:

The slope is 8, the y-intercept is 0. The slope-intercept form is written:

y = mx + b

So this situation would be written y =  8x + 0 or just y = 8x.

Hope it helps!

Answer:

11

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

g(x) = x³ - 4

h(x) = x² + 2

h(-2) is x = -2

g(-1) is x = -1

Step 2: Find h(-2) - g(-1)

Answer:jkcv

ijfklgjk

Step-by-step explanation:

vn vvcxkhvxcl

Answer:

2x - 4

Step-by-step explanation:

f(x) = x - 7

= 2x + 3 - 7

= 2x - 4

Answer:

WARNING! .39 AND .76 IS WRONG.

THE PEOPLE ABOVE ARE INCORRECT.

THE ANSWER IS EITHER .37 OR .62

I believe the correct answer is .62 --> .25 + .37 = .62 . This also makes sense.

(C)

ED2021

The probability that a randomly chosen college student exercises in the morning or afternoon are 0.37.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

From the given Venn diagram, we see that

Probability that the student exercises in the afternoon

P(A) = 0.14 + 0.37 = 0.51

Probability that the student exercises in the morning

P(M) = 0.25 + 0.37 = 0.61

Now, the probability that a randomly chosen college student exercises in the morning or afternoon

P(A ∩ M) = 0.37

Learn more about probability here;

https://brainly.com/question/11234923

Answer:

50xy

Step-by-step explanation:

(2x)(5y)(5y)

~Simplify

(2x)(25y)

~Multiply

50xy

Best of Luck!

Answer: Many people assume that because DNA is so small, we can't see it without powerful microscopes. But in fact, DNA can be easily seen with the naked eye when collected from thousands of cells.