All categories

2 years ago

The sum of 3 consecutive odd integers is 39. what are the integers?

1 answer:

4 0

Suppose the first odd integer is x, the next one will be x+2, the third one will be x+4
add up these three integers, you will have 3x+6=39
3x=33
x=11
the three consecutive odd integers are 11,13,15

You might be interested in

− 4 y − 3 + 3 y = 8 − 2 y − 15

Neporo4naja [7]

Answer:

y= -4

Step-by-step explanation:

simplify both sides of the equasion

add 2y to both sides

add three to both sides

and your answer is y= -4

7 0

3 years ago

Let $f(x) = 2x^2 + 3x - 9,$ $g(x) = 5x + 11,$ and $h(x) = -3x^2 + 1.$ Find $f(x) - g(x) + h(x).$

Viefleur [7K]

QUESTION 1

Given that:

$f(x)=2x^2+3x-9$ ,

$g(x)=5x+11$ ,

and

$h(x)=-3x^2+1$

Then;

$f(x)-g(x)+h(x)=2x^2+3x-9-(5x+11)+(-3x^2+1)$

$f(x)-g(x)+h(x)=2x^2+3x-9-5x-11-3x^2+1$

Group similar terms;

$f(x)-g(x)+h(x)=2x^2-3x^2+3x-5x-11-9+1$

Simplify;

$f(x)-g(x)+h(x)=-x^2-2x-19$

QUESTION 2

Given that;

$f(x)=4x-7$ .

$g(x)=(x+1)^2$

and

$s(x)=f(x)+g(x)$

Substitute the functions;

$s(x)=4x-7+(x+1)^2$

Substitute x=3

$s(3)=4(3)-7+(3+1)^2$

$s(3)=12-7+(4)^2$

$s(3)=5+16$

$s(3)=21$

QUESTION 3

Given:

$f(x)=3x+2$

$g(x)=x^2-5x-1$

$f(g(x))=f(x^2-5x-1)$

This implies that;

$f(g(x))=3(x^2-5x-1)+2$

Expand the parenthesis;

$f(g(x))=3x^2-15x-3+2$

$f(g(x))=3x^2-15x-1$

QUESTION 4

The given function is;

$f(x)=3(x-6)^2+1$

Let

$y=3(x-6)^2+1$

$\Rightarrow y-1=3(x-6)^2$

$\Rightarrow \frac{y-1}{3}=(x-6)^2$

$\Rightarrow \sqrt{\frac{y-1}{3}}=x-6$

$\Rightarrow x=6+\sqrt{\frac{y-1}{3}}$

The range is:

$\frac{y-1}{3}\ge0$

$y-1\ge0$

$y\ge1$

The interval notation is;

$[1,+\infty)$

6 0

3 years ago

What is absolute value? can you solve problems using the absolute value?

vesna_86 [32]

An absolute value is positive value of any value. So the abs value of -28 is 28. The abs value of 67 is 67. Makes sense?

If it were |27-3| for example, treat the inside of a abs as parenthesis, so you must complete PEMDAS inside of it to reduce the equation to |24|, unless you wanted it to become |27| - |3|.

For functions, this becomes slightly different and more difficult, especially when adding a variable such as x. Look below for a sample equation.

|2x-3|=1

This equation will actually have (and most others) 2 solutions for x. To find these, you’ll need to multiply the inside of the abs by -1 for one equation, and leave it as it is for the other!

2x-3=1 -(2x-3)=1

Now you have to solve BOTH equations to get your correct x-value answers.

For the first listed equation:

2x=4

x=2

For the second listed equation:

-2x+3=1

-2x=-2

x=-1

So you get the x-values -1 and 2 which both make the parent function true!

3 0

3 years ago

Read 2 more answers

What is the domain of the given function?

Sonja [21]

Answer: Choice A) {-4, -1, 3, 5, 6}

The domain of a relation is the set of possible x inputs. All we do is list the x coordinates of the given points. The order doesn't matter but your book has decided to list the x values from smallest to largest.

Side note: the list of possible output y values is known as the range.

5 0

2 years ago

Read 2 more answers

Sienna has 5 3/4 pounds of grapes. She eats 1/8 pound and gives 2 1/2 pounds to her brother. How many pounds of grapes does Sien

zheka24 [161]

Answer:

Sienna has 5 3/4 pounds of grapes. She eats 1/8 pound and gives 2 1/2 pounds to her brother. How many pounds of grapes does Sienna have left?

Answer

5.0/5

The pounds of grapes left with seinna is 3.125 or pounds

Solution:

Given that Sienna has pounds of grapes

She eats pound and gives pounds to her brother

To find: pounds of grapes left with seinna

We can find the pounds of grapes left with seinna by subtracting the pounds of grapes she ate and pounds of grapes she gave to brother from the total pounds of grapes she had

Pounds of grapes left with seinna = total pounds of grapes - pounds of grapes she ate - pounds of grapes she gave to brother

Substituting the values we get,

Thus the pounds of grapes left with seinna is 3.125 or poundsStep-by-step explanation:

5 0

2 years ago

Read 2 more answers