Compare. Write <,>, or =. (Example 1)

Ill i need to know is the fraction please

murzikaleks [220]

Answer:

6/10 i think

Step-by-step explanation:

625 divided by 15 is 41.6 so i'd be 40+1+6/10

6 0

2 years ago

Read 2 more answers

A circle has the equation 2x²+12x+2y²−16y−150=0.

KonstantinChe [14]

Answer: B. The coordinates of the center are (-3,4), and the length of the radius is 10 units.

Step-by-step explanation:

The equation of a circle in the center-radius form is:

$(x-h)^{2} +(y-k)^{2}=r^{2}$ (1)

Where $(h,k)$ are the coordinates of the center and $r$ is the radius.

Now, we are given the equation of this circle as follows:

$2x^{2}+12x+2y^{2}-16y-150=0$ (2)

And we have to write it in the format of equation (1). So, let's begin by applying common factor 2 in the left side of the equation:

$2(x^{2}+6x+y^{2}-8y-75)=0$ (3)

Rearranging the equation:

$x^{2}+6x+y^{2}-8y=75$ (4)

$(x^{2}+6x)+(y^{2}-8y)=75$ (5)

Now we have to complete the square in both parenthesis, in order to have a perfect square trinomial in the form of $(a\pm b)^{2}=a^{2}\pm+2ab+b^{2}$ :

For the first parenthesis:

$x^{2}+6x+b^{2}$

We can rewrite this as:

$x^{2}+2(3)x+b^{2}$

Hence in this case $b=3$ and $b^{2}=9$ :

$x^{2}+2(3)x+3^{2}=x^{2}+6x+9=(x+3)^{2}$

For the second parenthesis:

$y^{2}-8y+b^{2}$

We can rewrite this as:

$y^{2}-2(4)y+b^{2}$

Hence in this case $b=-3$ and $b^{2}=9$ :

$y^{2}-2(4)y+4^{2}=y^{2}-8y+16=(y-4)^{2}$

Then, equation (5) is rewritten as follows:

$(x^{2}+6x+9)+(y^{2}-8y+16)=75+9+16$ (6)

Note we are adding 9 and 16 in both sides of the equation in order to keep the equality.

Rearranging:

$(x-3)^{2}+(y-4)^{2}=100$ (7)

At this point we have the circle equation in the center radius form $(x-h)^{2} +(y-k)^{2}=r^{2}$

Hence:

$h=-3$

$k=4$

$r=\sqrt{100}=10$

8 0

2 years ago

Someone please help me. Thanks!

fiasKO [112]

The answer is c because you need to multiply both numbers inside the parentheses by the number on the outside

5 0

1 year ago

Read 2 more answers

A contractor purchases 7 dozen pairs of padded work gloves for $103.32. He incorrectly calculates the unit price at $14.76 per p

kvv77 [185]

Answer:

The correct unit price would be $1.23.

The contractor divided 103.32 by 7, resulting in an error.

Step-by-step explanation:

If we know a dozen equals 12, then 7 dozen looks like:

$7(12)$

Multiply.

$84$

Now we know the contractor purchases 84 pairs of padded work gloves.

Let's find our unit price:

unit price = $\frac{cost}{units}$

Substitute.

unit price = $\frac{103.32}{84}$

Divide.

unit price = $1.23$

__

To find the error of the contractor, let's try substituting in a number (7) provided in the question to see if we get $14.76 per pair:

$\frac{103.32}{7}$

Divide.

$14.76$

7 0

2 years ago

Solve the equation. show all work 18^(r-10)=93

Elina [12.6K]

Recall the logarithm rules :

a^y = x is the same as log_a x = y

In this case,

a = 18
y = r - 10
x = 93

So,

18^ (r-10) = 93

is the same as

log_18 93 = r - 10

Solve for r to get :

10 + log_18 93 = r

3 0

2 years ago