How many times does the quadratic function below intersect the x-axis? y = x+3x+15

The sum of two books and a pencil is $6.00. The difference of cost between 3 books and 2 pencils is $ 2.00. Find the cost of a b

Gala2k [10]

Answer:

The book costs $2 and the pencil also costs $2.

Step-by-step explanation:

It is easy to get the value of the book and the pencil if we use algebraic expressions.

Let x be the cost of the book and let y be the cost of the pencil.

The sum of 2 books and a pencil is $6.00

2x + y = $6.00

The difference of cost between 3 books and 2 pencils is $2.00.

3x - 2y = $2.00

Step 1: Let's get the value of y first.

2x + y = 6

y = 6 - 2x

Step 2: Let's substitute the value of y and look for the value of x.

3x - 2y = $2.00

3x - 2(6-2x) = 2

3x - 12 + 4x = 2

7x = 12 + 2

7x = 14

x = $\frac{14}{7}$

x = $2 (this is the cost of the book)

Step 3: Let's substitute the value of x and look for the value of y.

2x + y = 6

2 (2) + y = 6

4 + y = 6

y = 6 - 4

y = $2 (this is the cost of the pencil)

Let's check:

2x + y = $6

2(2) + 2 = 6

4 + 2 = 6

6 = 6 (CORRECT)

8 0

3 years ago

Plz solve for the area, questions 10,11,and 12 plz

marishachu [46]

Answer:

10-52.85ft squared 11-144.84centimeters squared 12-304meters squared

Step-by-step explanation:

A-bh/2 10-7*15.1=105.7/2=52.85ft squared

A-bh 11-10.2*14.2=144.84cenitmeters squared

A-bh 20*15.2=304meters squared

4 0

3 years ago

A rectangular patio has an area of 91 fl. The length is 6 feet

puteri [66]

Answer:

Total area equation = tex]w(w+6)=91[/tex]

b/2 = 3

Dimensions of the patio: width = 7 feet, length = 13 feet

Step-by-step explanation:

The area of a rectangle is given the formula:

$A=wl$

where

$w$ is the width

$l$ is the length

We know from our problem that the area of the patio is 91 square feet, so $A=91$ . We also know that the length is 6 feet longer then the width, so $l=w+6$ .

Replacing values in our area equation

$A=wl$

$91=w(w+6)$

$w(w+6)=91$

Expanding the left side:

$w*w+6w=91$

$w^2+6w=91$

Remember that to complete the square we need to add half the coefficient of the linear term squared. The lineal term is $w$ , so its coefficient is 6. Now, half its coefficient or $\frac{b}{2} =\frac{6}{2} =3$ . Finally, $3^2=9$ .

To complete the square we need to add 9 to both sides of the equation:

$w^2+6w+9=91+9$

$w^2+6w+9=100$

Notice that the left side is a perfect square trinomial (both $w^2$ and 9 are perfect squares), so we can express it as:

$(w+3)^2=100$

Now that we completed the square, we can solve our equation

- Take square root to both sides

$\sqrt{(w+3)^2} =\pm\sqrt{100}$

$w+3=\pm10$

- Subtract 3 from both results

$w=10-3,w=-10-3$

$w=7,w=13$

Since length cannot be negative, $w=7$ is the solution of our equation.

We now know that the width of our rectangular patio is 7 feet, so we can find its length:

$l=w+6$

$l=7+6$

$l=13$

We can conclude that half the coefficient of the width is $\frac{b}{2}=3$ , the width of the patio is 7 feet, and its length is 13 feet.

7 0

3 years ago

Which of the following could represent the graph of f(x)=x^4+x^3-8x^2-12x

Ad libitum [116K]

Answer:

Plot f(x)=x^4+x^3-8x^2-12x

Step-by-step explanation:

7 0

3 years ago

What is the arc measure of an arc with length 4.189 cm and radius equal to 3 cm.'?

Mazyrski [523]

Given that the arc length is 4.189 cm and the radius is 3 cm, the size of the arc will found as follows;
C=theta/360 πd
suppose:
size of arc=theta=x
d=3*2=6 cm
hence;
4.189=x/360*π*6
4.189=0.0524x
x=4.189/0.0524
x=80.004°
The size of the arc length is 80.004°

6 0

3 years ago