SECTION (A) (Answer ALL questions) a) Iff:R → R is defined by f(x) = x2 +3, find the function g such that (fog)(x) =9x2 – 12x+7.​

Answer:

(a) [tex]\sf y=\dfrac{11}{20}x+7[/tex]

(b) $16.90

Step-by-step explanation:

Part (a)

Add a line of best fit (see attached).

Find two points on the line:  (7, 0) and (20, 18)

Use these points to find the slope of the line:

[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{18-7}{20-0}=\dfrac{11}{20}[/tex]

Use the found slope and one of the points in the point-slope form of the linear equation to find an equation for the line of best fit:

[tex]\sf\implies y-y_1=m(x-x_1)[/tex]

[tex]\sf\implies y-7=\dfrac{11}{20}(x-0)[/tex]

[tex]\sf\implies y=\dfrac{11}{20}x+7[/tex]

Part (b)

Substitute x = 18 into the equation and solve for y:

[tex]\sf\implies y=\dfrac{11}{20}(18)+7=\$16.90[/tex]

[tex] \mathsf\red{♧ANSWER♧}[/tex]

[tex] \mathsf \blue{5 \frac{2}{5} - 3 \frac{7}{10} }[/tex]

[tex] \blue \implies \mathsf \green{ \frac{27}{5} - \frac{37}{10} }[/tex]

[tex] \blue \implies \mathsf \green{2( \frac{27}{5} ) - \frac{37}{10} }[/tex]

[tex] \blue \implies \mathsf \green{ \frac{54}{10} - \frac{37}{10} }[/tex]

[tex] \blue \implies \mathsf \green{ \frac{17}{10} = 1 \frac{7}{10} = 1.7}[/tex]

[tex]~~~\dfrac{d}{dx} f(x) \\ \\=\dfrac{d}{dx} \left(x^3 \cdot \log_6 x \right)\\\\=x^3\dfrac{d}{dx} \left(\log_6 x\right) + \log_6 (x)\dfrac d{dx} x^3 \\\\=x^3 \cdot \dfrac 1{x \ln 6} + \log _6 (x) \cdot 3x^2\\\\=\dfrac{x^2}{\ln 6} + \log_6(x) \cdot 3x^2\\\\\\=x^2 \left(\dfrac 1{\ln 6} + 3\log_6 x \right)[/tex]

[tex]\text{The derivative is now in a form of}~ x^A (B + C \log_D (x))[/tex]

Answer:

Step-by-step explanation:

3. Use Cosine law to find the  length of the unknown side (PR)

q² = p² +  r² - 2prCos Q

q is the opposite side of ∠Q;  

p is the opposite side of ∠P; p = 33

r is the opposite sides of ∠R ; r = 67

q² = 33² + 67² -  2* 33*67 Cos 19°

    = 1089 + 4489 - 4422 * 0.95

     = 1089 + 4489 - 4200.9

    = 1377.1

q = √1377.1

q = 37.1

PR = 37.1

To find the angle use law of sin

[tex]\sf \dfrac{q}{Sin \ Q} =\dfrac{p}{Sin \ P}\\\\\\\dfrac{37.1}{Sin \ 19}=\dfrac{33}{Sin \ P} \\\\\\\dfrac{37.1}{0.33}=\dfrac{33}{Sin \ P}\\\\\\37.1* Sin \ P = 33 *0.33\\\\Sin \ P =\dfrac{33*0.33}{37.1}[/tex]

Sin P = 0.3

[tex]P = Sin^{-1} 0.3\\[/tex]

P = 17.5°

∠R = 180 - (19 + 17.5)

    = 143.5°

The question is not clear.

Answer:

wheres the question

Step-by-step explanation:

??????

Answer:

Step-by-step explanation:

c

Answer as a fraction = 7/9 which is exact

Answer in decimal form = 0.778 which is approximate

=========================================================

Explanation:

The time gap from 8 to 15 is 15-8 = 7 minutes.

The time gap from 7 to 16 is 16-7 = 9 minutes.

Divide those differences: 7/9 = 0.778 approximately

The 7's go on forever, but rounding at some point will bump the last 7 to an 8.

Answer:

t = 55

Step-by-step explanation:

The figure is a  straight line and the sum of angles that make a straight line is 180 degrees

90 + t+ 35 = 180

125+t = 180

Subtract 125 from each side

125 +t-125 = 180-125

t = 180-125

t = 55

Answer:

530.66 in²

area of circle: πr²

Answer:

pretty sure its 530.66 in.²

Step-by-step explanation:

Answer:

1. x² + 12x + 27

2. x² + 11x + 18

3. x² + -14x + 48

Step-by-step explanation:

When you multiply polynomials, you use FOIL.

First

Outer

Inner

Last

For example, to solve the first polynomial (x + 3)(x + 9), you would multiply the first term in each parenthesis to each other. In this case, it would be x · x, which would be equal to x². The next step would be to multiply the first term in the first parenthesis to the last term in the second parenthesis, which are the outer terms. You get 9x when you multiply x by 9. Then, you multiply the inner terms of the polynomial, which is the last term of the first parenthesis and the first term of the second parenthesis. You get 3x. The last part of FOIL is to multiply the last term in each parenthesis to each other. You would multiply 9 and 3 and get 27. Your answer would be x² + 9x + 3x + 27. Simplify the equation to get x² + 12x + 27. That is your final answer. Do the same thing to the other equations to find the answer. (MAKE SURE TO CHECK THE SIGN OF THE TERMS YOU ARE MULTIPLYING FIRST. )

I hope this helped and please mark me as brainliest!

Answer:

What do you mean?

Step-by-step explanation:

Answer:

44 mm

Step-by-step explanation:

radius = 22 mm

diameter = 2 * radius = 44 mm

Answer:

Step-by-step explanation:

The given properties of one pair of parallel sides in the four sided

quadrilateral, indicates that the shape is a trapezium.

Response:

The area of the shape is 35 square unit

Area of trapezoid

The Schwarzschild radius of the black hole depends on its mass

The Schwarzschild radius of this supermassive black holeis 0.091 AU

The Schwarzschild radius (r) is calculated using:

[tex]r_s = \frac{2GM}{c^2}[/tex]

Where:

G =  Gravitational constant = 6.67408 × 10-11 m3 kg-1 s-2

M = Mass of the object = 4.6 x 10^6 solar masses

c = Speed of light = 299792458 m / s

Express the mass in Kg

M = 4.6 x 10^6 * 9.2 * 10^18 = 9.15 * 10^36 kg

Substitute the above values in the equation

[tex]r_s = \frac{2 * 6.67408 * 10^{-11} * 9.15 * 10^36}{299792458 ^2}[/tex]

Evaluate the expression

[tex]r_s = 13589425339.6[/tex] m

Express as km

[tex]r_s = 13589425.3396[/tex] km

Expressas AU

[tex]r_s = \frac{13589425.3396}{1.5 * 10^8}[/tex]

Evaluate the quotient

[tex]r_s = 0.09059616893[/tex]

Approximate

[tex]r_s = 0.091\ AU[/tex]

Hence, the Schwarzschild radius of this supermassive black holeis 0.091 AU

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Answer:

B

Step-by-step explanation:

ED

The number of regular tickets are 70, the number of student tickets are 110 and the number of children tickets are 30.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, you are studying last year’s event and know that 210 people attended last year’s school carnival.

The number of regular tickets sold was 10 more than twice the number of children’s tickets sold.

Let the number of children tickets be x.

Then, number of regular tickets be 2x+10

Let the number of student tickets be y.

You are studying last year’s event and know that 210 people attended last year’s school carnival.

x+2x+10+y=210

3x+y=200 --------(I)

The total amount of money collected for tickets was $710.

Now, 5(2x+10)+3y+x=710

10x+50+3y+x=710

11x+3y=660 --------(II)

Substitute y=200-3x in equation (II), we get

11x+3(200-3x)=660

11x+600-9x=660

2x=60

x=30

Substitute x=30 in equation (I), we get

3(30)+y=200

y=110

Number of regular tickets =2x+10

= 70

Therefore, the number of regular tickets are 70, the number of student tickets are 110 and the number of children tickets are 30.

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Answer:

8/9

Step-by-step explanation:

Answer:

405g of flour, 3 teaspoons baking powder, 6 tablespoons sugar, 390ml of milk and 3 eggs and 6 tablespoons of oil

Step-by-step explanation:

She wants to triple the recipe, so she must multiply each amount of each ingredient by three:

135 × 3 = 405

1 × 3 = 3

2 × 3 = 6

130 × 3 = 390

1 × 3 = 3

2 × 3 = 6

Answer:

1.5625

Step-by-step explanation:

rround to 2

[tex]\\ \rm\rightarrowtail y=(x-3)(x+3)=x^2-9[/tex]

Zeros are x intercepts

#2

#3

Axis of symmetry=x=0

#4

Answer:

Given quadratic equation:  y = (x - 3)(x + 3)

Zeros (x-intercepts)

The zeros of a quadratic equation are the points where the graph of the quadratic equation crosses the x-axis.  So the x-intercepts (zeros) are when y = 0

⇒ (x - 3)(x + 3) = 0

⇒ (x - 3) = 0  so  x = 3

⇒ (x + 3) = 0  so  x = -3

Therefore, the x-intercepts are at (3, 0) and (-3, 0).

y-intercept

The y-intercept is the point where the graph crosses the y-axis.  So the y-intercept is when x = 0

⇒ (0 - 3)(0 + 3) = -9

Therefore, the y-intercept is at (0, -9)

Vertex

Expand the equation so that it is in standard form y = ax² + bx + c:  

⇒ y = x² - 9

x-value of vertex is -b / 2a ⇒ -0 / 2 = 0

substitute the found value of x into the equation to find y:

⇒ y = (0)² - 9 = -9

Therefore, the vertex is (0, -9)

Axis of symmetry

Axis symmetry of a quadratic equation is x = a where a is the x-value of the vertex.

Therefore, the axis of symmetry is x = 0

Point G is on line segment FH. Given FG = 7 and GH = 2, the length of line segment FH is 9 units.

The length of line segment FH can be determined by adding the lengths of its two parts, FG and GH.

This is based on the property that the whole length of a line segment is equal to the sum of its parts.

Given that FG = 7 and GH = 2,

we can find the length of FH as follows:

FH = FG + GH

FH = 7 + 2

FH = 9

So, the length of line segment FH is 9 units.

This is a basic principle in geometry where the total length of a segment can be calculated by adding the lengths of its individual parts.

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Answer:

mention the blanks please...if u mention iam ready to answer

Answer:

19.400

Step-by-step explanation:

19.400 equals out to 42769.67886386625

Answer:

(Choice B)

Step-by-step explanation:

(7, 0)

7 - 7 = 0

Here, we can see that when 7 is subtracted from x, we get 0 (our y)

Hope this helps!