What is the area of a triangle with vertices at (−4, 1) , (−7, 5) , and (0, 1) ?

Solve x^2 +14x=15 by completing the square

ivanzaharov [21]

Answer:

x = -15 and x = 1

Step-by-step explanation:

Since we have to use the complete the square method, we first need to rewrite the equation in the form $x^{2}+2ax+a^{2}=(x+a)^{2}$ .

This results in $x^{2} + 14x + 7^{2} = 15 + 7^{2}$ .

Next, we simplify the equation to get $x^{2} +14x+7^{2} = 64$ .

Factoring the left side gives us $(x+7)^{2} = 64$ .

Finally we solve the equations: $x+7=\sqrt{64}$ and $x+7=-\sqrt{64}$ .

This gives us x=1, and x=-15

6 0

2 years ago

Read 2 more answers

How do I use the intermediate value theorem to prove every polynomial of odd degree has at least one real root?

Anon25 [30]

Answer:

Step-by-step explanation:

3 0

1 year ago

Check-Ins 2 NC Math 1

fomenos

The maximum amount of profit the carnival makes based on the number of tickets sold is 6.5 thousand of dollars,

<h3>How to determine the difference?</h3>

The function is given as:

f(x) = -0.5x^2 + 5x - 6

Differentiate the function

f'(x) = -x + 5

Set to 0

-x + 5 = 0

Make x the subject

x = 5

Substitute x = 5 in f(x)

f(5) = -0.5 * 5^2 + 5 * 5 - 6

f(5) = 6.5

The table is not given.

Hence, the maximum amount of profit the carnival makes based on the number of tickets sold is 6.5 thousand of dollars,

Read more about quadratic functions at:

brainly.com/question/18797214

5 0

1 year ago

the dog needs a 1/3 of a cup of dog food each day. the bag holds 5 cups of dog food how many days will it last ?

sleet_krkn [62]

Answer:

15 days

Step-by-step explanation:

You have 5 cups of food, and you give him 1/3 a day.

So, 5 divided by 1/3, which would get you 15 days. Or you could cross-multiply, meaning you multiply across, but in this case I just made them line up so you can see how to do it. $(food)/(cupsperday) = 5/\frac{1}{3} \\OR\\\frac{(food)}{1}*(cupsperday) = \frac{5}{1} *\frac{3}{1}$

7 0

2 years ago

EMERGENCY HELP! A steady stream of water flows into a partially-filled rectangular tank. After 6 minutes, there are 87 gallons o

german

Answer:

$y=9x+33$

33 gallons of water to begin with.

Step-by-step explanation:

So we essentially are given two coordinates: (6,87) and (21,222). To find an equation, we simply need to find the slope and y-intercept. We know it's a linear equation because it's a steady stream, meaning a constant slope.

The slope is:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{222-87}{21-6}=135/15=9$

So, the rate at which the stream flows is 9 gallons per minute.

Now, let's find the initial amount of water. To do this, we can use point-slope form. Pick either of the two points. I'm going to use (6,87).

$y-y_1=m(x-x_1)\\y-87=9(x-6)\\y-87=19-54\\y=9x+33$

So, there were 33 gallons of water in the tank to begin with.

3 0

2 years ago

What is the area of a triangle with vertices at (−4, 1) , ​ (−7, 5) ​ , and ​ (0, 1) ​?

What is the area of a triangle with vertices at (−4, 1) , (−7, 5) , and (0, 1) ?