Write the quadratic equation in standard form: 2x^2+3x+7=x

A girl asks her father how many ties he has and he answers with a riddle: "Seven-eighths of my ties plus five." How many ties do

KonstantinChe [14]

So 5= $\frac{1}{8}$ , or 12,5% of his ties
x=100%; x=5*8=40 ties her father has.

4 0

2 years ago

The product of 4, and a number increased by 8, is -48

german

Answer:

4n + 8 = -48

n = -14

Step-by-step explanation:

Using key words from the problem, you can set up an equation with the proper operations to solve for the variable. Product = multiplication, so the 'product of 4 and a number' = 4n. Increased = addition, so increased by 8 = 4n + 8. The word 'is' means equal to, so:

4n + 8 = -48

In order to solve for 'n', you use inverse (opposite) operations and whatever you do to one side of the equation, you do to the other:

Subtract 8: 4n + 8 - 8 = -48 - 8 or 4n = -56

Divide 4: 4n/4 = -56/4

Solve for 'n': n = -14

8 0

3 years ago

What transformations are needed to change the parent cosine function to y=3cos(10(x-pi))?

juin [17]

Answer:

The graph of $y=cos(x)$ is:

*Stretched vertically by a factor of 3

*Compressed horizontally by a factor $\frac{1}{10}$

*Moves horizontally $\pi$ units to the rigth

The transformation is:

$y=3f(10(x-\pi))$

Step-by-step explanation:

If the function $y=cf(h(x+b))$ represents the transformations made to the graph of $y= f(x)$ then, by definition:

If $0$ then the graph is compressed vertically by a factor c.

If $|c| > 1$ then the graph is stretched vertically by a factor c

If $c$ then the graph is reflected on the x axis.

If $b> 0$ The graph moves horizontally b units to the left

If $b$ The graph moves horizontally b units to the rigth

If $0$ the graph is stretched horizontally by a factor $\frac{1}{h}$

If $h> 1$ the graph is compressed horizontally by a factor $\frac{1}{h}$

In this problem we have the function $y=3cos(10(x-pi))$ and our parent function is $y = cos(x)$

The transformation is:

$y=3f(10(x-\pi))$

Then $c =3>1$ and $b =-\pi < 0$ and $h=10 > 1$

Therefore the graph of $y=cos(x)$ is:

Stretched vertically by a factor of 3.

Also as $h=10$ the graph is compressed horizontally by a factor $\frac{1}{10}$ .

Also, as $b =-\pi < 0$ The graph moves horizontally $\pi$ units to the rigth

6 0

2 years ago

Find the midpoint of the line segment joining the points P1 and P2. P1 = (x, 8); P2 = (0, 9)

ipn [44]

Answer:

(x/2 , 17/2)

Step-by-step explanation:

To find a midpoint, you average the x's and average the y's. Average them by adding the x-coordinates and divide by 2. Same with the y's.

The x's are x for P1 and 0 for P2.

x+0 / 2

=x/2

This will be the x-coordinate of the midpoint. Then for the y, use 8 and 9, the y's.

8+9 / 2

= 17/2

This will be the y-coordinate of the midpoint.

The midpoint is:

(x/2 , 17/2)

You could also divide 17/2 and get 8.5 then the midpoint would be:

(x/2 , 8.5)

5 0

1 year ago

In ΔMNO, the measure of ∠O=90°, the measure of ∠N=40°, and NO = 8.1 feet. Find the length of OM to the nearest tenth of a foot.

kolbaska11 [484]

Answer: 6.8 feet

Step-by-step explanation:

8 0

2 years ago