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The product and the sum of the functions will be 3x² - 6x - 24 and 4x + 2. The value of the function (f - g) at x = 4 is negative 18.

In mathematics, functions are everywhere and are necessary for constructing physical connections. A function is a statement, rule, or law that establishes the connection between two variables.

The functions are given below.

f(x) = x - 4

g(x) = 3x + 6

Then the product of the functions will be

(f × g)(x) = (x - 4)(3x + 6)

(f × g)(x) = 3x² -12x + 6x - 24

(f × g)(x) = 3x² - 6x - 24

Then the sum of the functions will be

(f + g)(x) = x - 4 + 3x + 6

(f + g)(x) = 4x + 2

Then the difference in the functions at x = 4 will be

(f - g)(4) = (x - 4) - (3x + 6)

(f - g)(4) = x - 4 - 3x - 6

(f - g)(4) = -2x - 10

(f - g)(4) = -2 (4) - 10

(f - g)(4) = -8 -10

(f - g)(4) = -18

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Answer:

The answer is choice c. This is because texts present the same facts in fiction or nonfiction life.

Answer: (a) 8 : 15 (b) 8 : 7

Step-by-step explanation: all marbles is 8+7 = 15

ratio of blue marbles to ALL marbles

8 : 15

ratio of blue marbles to red

8 : 7

Two polygonal regions are similar with scale factor 7, if the area of the smaller region is 490 cm² then the area of the larger region would be 3430 cm²

An equation is an expression that shows the relationship between two or more numbers and variables.

Dilation is the increase or decrease in the size of a figure by a scale factor.

Two polygonal regions are similar with scale factor 7. The area of the smaller region is 490 cm², hence:

Area of larger region = 7 * 490 cm² = 3430 cm²

Two polygonal regions are similar with scale factor 7, if the area of the smaller region is 490 cm² then the area of the larger region would be 3430 cm²

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[tex]y=f(x)= \dfrac x 3 \\\\\text{Replace x with y and then solve for y,}\\\\~~~~x = \dfrac y 3\\\\\implies y = 3x \\\\\implies f^{-1}(x) =3x[/tex]

Answer:

56.31 degrees

Step-by-step explanation:

6 = opposite and 4 = adjacent

Tan = opposite over adjacent

Tan(theta)=6/4

=56.30993247

Answer:

Ok hello my name is Christopher and I have already done this and the answer is (6,-7)

Step-by-step explanation:

Answer:

Because -4 is 4 units away from 0.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

30 grames.

Step-by-step explanation:

5 x 6 = 30.

Step-by-step explanation:

remember, a probability is always desired cases over possible cases.

and the combination of the probabilities of two (or more) events means to multiply these probabilities.

the probability to get a specific number on the spinner is 1/4 (1 desired number over 4 possible numbers).

so, to get first a number less than 3 ... - that means, the only desired outcome is the number 2.

so,

1/4

to get 5 on the second spin ?

again,

1/4

the combination of both events into one delivers the probability of

1/4 × 1/4 = 1/16

Answer:

Step-by-step explanation:

x + 3 = -x - 1

2x + 3 = -1

2x = -4

x = -2

y = -2 + 3

y = 1

(-2, 1)

answer is A

Answer:

y=x-7

Step-by-step explanation:

Rise over run

-6-(-7)

---------- = 0

-4-(-4)

Point Slope form

y+7=0(x+4)

Y=MX + B

y=x-7

The equation of the line passing through the points (−4,−7) and (−4,−6) in the form of a will be a + 4 = 0.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

The equation of the line passing through the points (−4,−7) and (−4,−6) will be

y + 6 = [(−6 + 7) / (−4 + 4)] (x + 4)

y + 6 = (1/0)(x + 4)

x + 4 = 0

Put x = a, then the equation will be

x + 4 = 0

a + 4 = 0

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Answer:

Geary street :D

they intersect here

click on the photo. it's not a link it's a screenshot of where they intersect

The area of the training field to the nearest whole number is 8719 msq. meter

The given field is made up of a rectangle and 2 semi circles. The formula for calculating the area of the field is:

Area of the field = area of circle + area of rectangle

Area of field = 3.14(32)² + (86)(64)
Area of field = 3215.36 + 5504

Area of the field = 8719 msq. meter

Hence the area of the training field to the nearest whole number is 8719 msq. meter

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Answer:

y = x/5280  

Step-by-step explanation:

y  miles =  x feet / 5280

Answer:

-2

Step-by-step explanation:

Slope of a line, given two points : formatslope=y2−y1x2−x1=4−2−2−(−1)=2−1=−2

Answer :

Explaination :

Here we are given with two equations,

So in order to calculate the number of hours (h). We would simply substitute the value of f in first equation. (i.e., keeping them equal)

>> 7h + 20 = 10h + 5

>> 10h - 7h = 20 - 5

>> 3h = 15

>> h = 15 / 3

>> h = 5

Answer: -17/4

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

x^2 + y^2 - 8x + 12y + 40 = 0

x^2 - 8x + y^2 + 12y = -40

Complete the square on the x and y terms:-

(x - 4)^2 - 16 + ( y + 6)^2 - 36 = -40

(x - 4)^2 + (y + 6)^2 = -40 + 16 + 36

(x - 4)^2 + (y + 6)^2 = 12

So the centre is at (4, -6) and the radius is √12.

Answer:

The circle is centered at (4,-6) and has a radius of √12.

Step-by-step explanation:

The standard form for the circle equation is:

[tex](x-a)^2+(y-b)^2=r^2[/tex]

You have:

[tex]x^2+y^2-8x+12y+40=0[/tex]

First complete the square for the 'x' terms:

[tex](x^2-8x+40)+y^2+12y=0[/tex]

[tex](x^2-8x+16-16+40)+y^2+12y=0[/tex]

[tex](x^2-8x+16)+y^2+12y+24=0[/tex]

[tex](x-4)^2+y^2+12y+24=0[/tex]

The 'x' terms are now in standard form. Work on the 'y' terms by completing the square once again:

[tex](x-4)^2+(y^2+12y+36-36+24)=0[/tex]

[tex](x-4)^2+(y^2+12y+36)-12=0[/tex]

[tex](x-4)^2+(y+6)^2-12=0[/tex]

Add the 12 to the other side:

[tex](x-4)^2+(y+6)^2=12[/tex]

The circle is centered at x = 4, y = -6, and has a radius of √12.

Answer:

C

Step-by-step explanation:

the circumference (C) of a circle is calculated as

C = 2πr = πd ( d is the diameter and d = 2r ) , then

C = πd = 3.14 × 26 = 81.64 in

Answer:

4 weeks

Step-by-step explanation:

Given information:

Given equation:

[tex]\sf b = 85 + w(10 + 8)[/tex]

(where b is the balance and w is the number of weeks)

To find the number of it will take to have a balance of $150, substitute b = $150 into the given equation and solve for w:

[tex]\implies \sf 85+w(10+8)=150[/tex]

[tex]\implies \sf 85+18w=150[/tex]

[tex]\implies \sf 85+18w-85=150-85[/tex]

[tex]\implies \sf 18w=65[/tex]

[tex]\implies \sf \dfrac{18w}{18}=\dfrac{65}{8}[/tex]

[tex]\implies \sf w=3.6111...[/tex]

[tex]\implies \sf w=4\:weeks[/tex]

Therefore, there will be $150 in the bank account 4 weeks from now.

Answer: 2/sqrt6

Step-by-step explanation:

tan theta=perpendicular/base so

cot theta =base /perependicular=sqrt2/2

while sin theta=perpendicular/hypotenous=2/x

here x is unkown to find it we will use pythagoras theorem

(hypoteneous)^2=(Base)^2+(perependicular)^2

                            =(sqrt 2)^2+(2)^2

                            =2+4

  (hypoteneous)^2=6

  hypotenous   =sqrt6

so

sin theta=2/sqrt6

Answer:

12/13

Step-by-step explanation:

36/39

Divide by 3

12/13

2000cm³.

The volume of any 3d shape is the length x height x width.

This case it is 25 x 10 x 8.

Answer:

( 4u + a ) + ( y + 6 )

Step-by-step explanation:

4u(y+6) + a(y+6) ...

The answer is ( 4u + a ) + ( y + 6 )

Answer:

x = 4.55

Step-by-step explanation:

Tan(75) = 17/x

3.73 = 17/x

x3.73 =17

x = 4.55