Use the functions a(x) = 7x + 10 and b(x) = 12x - 18 to complete the function operations listed below.
Part A: Find (a + b)(x). Show your work.
Part B: Find (a - b)(x). Show your work.
Part C: Find (a - b)(x). Show your work.
Part D: Find a[b(x)]. Show your work.

Answer:

[tex]y=\frac{1}{4} x-1.[/tex]

Step-by-step explanation:

1) if the lines are perpendicular, then the second slop is 0.25;

2) the equation of the 2d line is y=0.25x+i, where i - unknown intercept;

3) it is possible to calculate the unknown intercept, if to substitute the given coordinates into the equation y=0.25x+i:

-4=-12*0.25+i; ⇔ i=-1.

4) finally, the required equation is:

[tex]y=\frac{1}{4} x-1.[/tex]

Answer:

1% × 77 = n

I used multiplication since "of" counts as multiplication.

Answer:

-1/2 or - 0.5

Step-by-step explanation:

[tex]cos (\frac{2\pi }{3}) = cos 120^{o} = -\frac{1}{2}[/tex]

Answer:

#16 play basketball and football

The equation of the graphed line 2x + 3y = -6 written in standard form is,[tex]\rm y= -\frac{2}{3}x -2[/tex] and for line 2x + 3y = 6 will be,[tex]\rm y = \frac{-2}{3}x+2[/tex]

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

a) 2x + 3y = -6

The line in which the standard form is found as;

Ax + By + C = 0

The typical form of a slope intercept is

y = mx+c

where m denotes the slope and b the line's y-intercept.

[tex]3y= -6-2x\\\\ y=\frac{-6-2x}{3}\\\\ y= -\frac{2}{3}x -2[/tex]

To obtain the slope standard form, we rewrite. The obtained equation is in the form of the slope-intercept.

b) 2x + 3y = 6

The line in which the standard form is found as;

Ax + By + C = 0

The typical form of a slope intercept is

y = mx+c

where m denotes the slope and b the line's y-intercept.

[tex]\rm 3y= 6-2x \\\\ y= \frac{6-2x}{3} \\\\ y = \frac{-2}{3}x+2[/tex]

Hence, The equation of the graphed line 2x + 3y = -6 written in standard form is,[tex]\rm y= -\frac{2}{3}x -2[/tex]

To learn more, about equations, refer;

https://brainly.com/question/10413253

#SPJ1

What is the equation of the graphed line written in standard form?

2x + 3y = -6, 2x + 3y = 6

Summary:

a. The equation of the graphed line 2x + 3y = -6 written in standard form is y= -2/3 x -2.

b. The equation of the graphed line 2x + 3y = 6 written in standard form is y= -2/3 x +2.

Answer:

2 yards ; 6 feet ; 72 inches ;

Step-by-step explanation:

2:6:72

1:3:12

1:3 is the ratio of Yards -> Feet

3:12 is the ratio of Feet -> Inch.

6ft = Pete

2 yards = Reggie

72 inches = Jackson

-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)

The graph of the function looks like V. And the vertex of the function will be at (-3, 0).

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function is given below.

f(x) = |x + 3|

Then the graph of the function looks like V. And the vertex of the function will be at (-3, 0).

The graph of the function is given below.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ1

The volume of the given rectangular pyramid.

[tex]\large\boxed{Formula:V=\frac{1}{3}lbh}[/tex]

First, multiply the length (5), breadth (4) and height (3).

[tex]5×4×3[/tex]

[tex]= 60 \: cm [/tex]

Now, divide 60 by 3.

[tex]\frac{60}{3}[/tex]

[tex]\large\boxed{V= 20 \: {m}^{3}}[/tex]

Therefore, the volume of the given rectangular pyramid is 20 cubic meters.

The only key feature that these functions have in common is that they have the same y-intercept. So the correct option is D.

Here we have the functions:

[tex]f(x) = -x^2 + 2x + 1\\\\g(x) = 2^x[/tex]

f(x) is quadratic, and g(x) is exponential.

Notice that the exponential function has a positive base, so it is increasing. For the quadratic equation we can see a negative leading coefficient, so it opens downwards.  So first and second options are false.

Also, g(x) never intersects the x-axis, so third option is false.

Finally, the y-intercepts of the given functions are:

[tex]f(0) = -0^2 + 2*0 + 1 = 1\\\\g(0) = 2^0 = 1[/tex]

So the y-intercepts are equal, meaning that the correct option is D.

If you want to learn more about y-intercepts:

https://brainly.com/question/24363347

#SPJ1

Answer:

Both f(x) and g(x) have the same y-intercept of (0, 1).

Step-by-step explanation:

I got it right on the test.

The answers are 8 and 2

A function is an equation that establishes a relationship between two or more variables.

Analysis:

r(x) x s(x) = 2[tex]\sqrt{x}[/tex] x [tex]\sqrt{x}[/tex] = 2x

r2(4) = 2 x 4 = 8

r(x)/s(x) = 2[tex]\sqrt{x}[/tex]/ [tex]\sqrt{x}[/tex] = 2

In conclusion, the values of the product and quotient of the functions are 8 and 2 respectively.

Learn more about functions; brainly.com/question/25638609

#SPJ1

Answer:

Egypt.

Step-by-step explanation:

We need to set up our conversion factors for each currency.

British Pounds and Egyptian Pounds:

0.83 £ (Europe) = 1 U.S. Dollar

18 E£ (Egypt) = 1 U.S. Dollar

Cost of a Souvenir in Europe:

The cost of souvenir in Europe is 13£. Using our conversion rate, we get

[tex]13\pounds \cdot \frac{\$1}{0.83 \pounds}=\$15.66[/tex]

Cost of a Souvenir in Egypt:

The cost of a souvenir in Egypt is 342 E£. So we have

[tex]342 \text{ E}\pounds\cdot \frac{\$1}{18 \text{ E}\pounds}=\$19[/tex]

Based on our calculations, it is cheaper to buy a souvenir in Europe than in Egypt.

Answer:

it costs rupee 3000 of 50 such pens

Explanation:

first, you have to multiply 50 x 60 which is 3000

second, two dozens of pens, right? so i add double 25 up which is 50 pens.

hope it helps and stay safe! (brainliest me pls)

The probability that a customer likes cake and pie is 0.16.

Probability is used to determine the odd that a random event would happen. The odds that the event happens usually lie between 0 and 1.

The probability that a customer likes cake and pie = total number of customers who like cake and pie / total number of customers

4/25 = 0.16

To learn more about probability, please check: https://brainly.com/question/13234031

#SPJ1

Answer:

see the attachment photo!

Answer:

0.0001 or 1/10000 or 1 ten thousandths

Step-by-step explanation:

The 1 is 4 places after the decimal point so has a value of :

0.0001 or 1/10000 or 1 ten thousandths

Hope this helped and have a good day

Answer:

2(7x-1)

Step-by-step explanation:

14 & 2 gcf 2 factor and wal lah!

Answer:

6

Step-by-step explanation:

We can think of the 10 black bags as 2 sets of 5-black bags (10 divided into groups of 5; 10 / 5 ; is 2 groups/sets). So, we would also have two sets of 3 (3 x 2 = 6), or 6 bags.

5 : 3 = 10 : 6

(multiply both numbers by 2)

The area of the circle inside the square shape is 200.96 cm²

The length of the square is given as:

L = 16 cm

This represents the diamater (d) of the circle.

The area of the circle is then calculated as:

Area = π(d/2)²

This gives

Area = 3.14 * (16/2)²

Evaluate

Area = 200.96

Hence, the area of the circle is 200.96 cm²

Read more about areas at:

https://brainly.com/question/24487155

#SPJ1

The directrix of the parabola is [tex]y = \frac {-49}{16}[/tex]

The parabola equation is given as:

[tex]\frac 14(y + 3) = (x -2)^2[/tex]

A parabola is represented as:

[tex]4p(y - k) =(x -h)^2[/tex]

By comparing both equations, we have:

4p = 1/4 ==> p = 1/16

-k= 3 ==> k = -3

The directrix is represented as:

y = k - p

So, we have:

[tex]y = -3 - \frac 1{16}[/tex]

Take the LCM

[tex]y = \frac {-16 * 3- 1}{16}[/tex]

Evaluate

[tex]y = \frac {-49}{16}[/tex]

Hence, the directrix of the parabola is [tex]y = \frac {-49}{16}[/tex]

Read more about parabola at:

https://brainly.com/question/1480401

#SPJ1

Answer:

three boys shared D 10,500.00 in the ratio 6:7:8.find the largest share.

Answer:

C. (3x+12) + x = 180

Step-by-step explanation:

the 2 angles create a straight line which is 180 degrees, so (3x+12) + x = 180

An equation is formed of two equal expressions. The value of x for which the equation has a solution is 1.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution for 10x+16=6x+20 is,

10x + 16 = 6x + 20

10x - 6x = 20 - 16

4x = 4

x = 1

Hence, the value of x for which the equation has a solution is 1.

Learn more about Equation:

https://brainly.com/question/2263981

#SPJ1

Answer:

3 cartons of sugar 5 cartons of flour and 4 cartons of rice

Step-by-step explanation:

First find the least common factor being 60 then divide by the number of packets each carton comes with to find how many cartons you need of each

Answer:

COA opposite/ adjacent

16/12

A

Answer:

A.

Step-by-step explanation:

if x≠-4, then the correct answer is

[tex]A. \ F(x)=\frac{1}{x+4}.[/tex]

There are no outliers in the dataset of the heights in feet of 25 trees

The sorted dataset is given as:

25, 27, 33, 34, 34, 34, 35, 37, 37, 38, 39, 39, 39, 40, 41, 45, 46, 47, 49, 50, 50, 53, 53, 54, 54

Outliers are relatively far from other elements of the dataset.

The highest and the least elements are 54 and 25, respectively.

Other elements of the dataset are relatively close to these two elements

Hence, there are no outliers in the dataset of the heights in feet of 25 trees

Read more about outliers at:

https://brainly.com/question/3631910

#SPJ1

Answer:

80,202 = 8.0202 × 10⁴