All categories

3 years ago

Use the functions a(x) = 3x + 10 and b(x) = 5x − 6 to complete the function operations listed below.

Mathematics

2 answers:

Romashka-Z-Leto [24]3 years ago

8 0

Answer:

(a + b) = 8x +4

(a - b) = -2x +16

(a * b) = $15x^{2}+32x-60$

Step-by-step explanation:

We have been given the functions;

a(x) = 3x + 10 and b(x) = 5x − 6

Part A:

(a + b) = a(x) + b(x) # we simply add the two given functions

(a + b) = 3x + 10 + 5x − 6

(a + b) = 8x + 4

Part B:

(a - b) = a(x) - b(x) # we simply subtract the two given functions

(a - b) = (3x + 10 ) - (5x − 6)

(a - b) = 3x + 10 -5x +6

(a - b) = -2x + 16

Part C:

(a * b) = a(x)*b(x)

# we simply find the product of the two given functions

(a * b) = (3x + 10)*(5x − 6)

(a * b) = $15x^{2}-18x+50x-60=15x^{2}+32x-60$

Masja [62]3 years ago

4 0

Part A

The functions a(x) = 3x + 10 and b(x) = 5x − 6 to complete the function operations listed below.

(a+b)(x)=a(x)+b(x)

(a+b)(x)=(3x+10)+(5x-6)

(a+b)(x)=3x+5x+10-6

(a+b)(x)=8x+4

Part B.

(a-b)(x)=a(x)-b(x)

(a-b)(x)=(3x+10)-(5x-6)

Expand the parenthesis to get:

(a-b)(x)=3x+10-5x+6

(a-b)(x)=3x-5x+10+6

(a-b)(x)=-2x+16

Part C

(a*b)(x)=a(x)*b(x)

(a*b)(x)=(3x+10)*(5x-6)

We expand to get:

$a \times b = 15 {x}^{2} - 18x + 50x - 60$

$a \times b = 15 {x}^{2} + 32x - 60$

You might be interested in

How do I solve tan(62) = 12/x?

notsponge [240]

Answer:

x = 6/31 = 0.194

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

(62)-(12/x)=0

Step by step solution :

Step 1 :

Simplify ——

Equation at the end of step 1 :

62 - —— = 0

Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using x as the denominator :

62 62 • x

62 = —— = ——————

1 x

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

62 • x - (12) 62x - 12

————————————— = ————————

x x

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

62x - 12 = 2 • (31x - 6)

Equation at the end of step 3 :

2 • (31x - 6)

————————————— = 0

Step 4 :

When a fraction equals zero :

4.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

2•(31x-6)

————————— • x = 0 • x

Now, on the left hand side, the x cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

2 • (31x-6) = 0

Equations which are never true :

4.2 Solve : 2 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.3 Solve : 31x-6 = 0

Add 6 to both sides of the equation :

31x = 6

Divide both sides of the equation by 31:

x = 6/31 = 0.194

Answer :

x = 6/31 = 0.194

Rate?

3 0

3 years ago

At practice, Diego does twice as many push-ups as Noah, and also 40 jumping jacks. He does 62 exercises in total.

IRINA_888 [86]

Answer:

Step-by-step explanation:

x = number of pushups he did

4 0

3 years ago

Read 2 more answers

How much is three half’s plus one fifth

Maslowich

Let's make it an expression.

Three half's= 3/2 Plus= + one fifth= 1/5

We need to turn 3/2 and 1/5 so that they have the same denominator. Let's use 10.

3/2→15/10 1/5→2/10

15/10+2/10=17/10=1 7/10

So, three half's plus one fifth is 1 7/10.

7 0

3 years ago

Read 2 more answers

Someone please help.

Alexxandr [17]

Hi there!

$f(x)+f(x+1)=4f(x)$

There are 3 parts to this equation:

f(x)

f(x+1)

4f(x)

We must first determine these three parts separately.

1) f(x)

We're given that $f(x)=3^x$ :

⇒ $f(x)=3^x$ :

2) f(x+1)

Now, we must find f(x+1). To do so, add 1 to x in the original function $f(x)=3^x$ :

⇒ $f(x+1)=3^x^+^1$

3) 4f(x)

To find 4f(x), multiply the original function $f(x)=3^x$ by 4:

$4f(x)=4*3^x$ :

4) Put it all together

Now, plug each of the three parts into the equation $f(x)+f(x+1)=4f(x)$ :

$f(x)+f(x+1)=4f(x)$

$3^x+3^x^+^1=4*3^x\\3^x+3^x*3=4*3^x$

Factor the left side

$3^x*(1+3)=4*3^x$

Divide both sides by 3^x

$1+3=4\\4=4$

Because this equation is true, $f(x)+f(x+1)=4f(x)$ is therefore true.

I hope this helps!

3 0

3 years ago

What's 1/8 as a fraction

Pani-rosa [81]

That means one whole is cut into 8 parts, and one of those eight parts is considered to be one-eighth of a whole
{think about it like a pizza with 8 slices]

8 0

3 years ago