3х2 + 5х + 10 = 0.<br> How many solutions does it have

The area of the following equilateral triangle is 62.4 square feet that is he height

Vikentia [17]

The height of this triangle would be 10.4

In order to find this, you first must find the length of the sides. Using a manipulated formula for area of an equilateral triangle, we can determine the lengths of the side. Below if the formula.

S = $\frac{2}{3}3^{\frac{3}{4}} \sqrt{A}$

In this, S is the length of the side and A is the area. So we plug in and get:

S = $\frac{2}{3}3^{\frac{3}{4}} \sqrt{62.4}$

S = $\frac{2}{3}3^{\frac{3}{4}} 7.89$

S = 12

Now that we have the side as 12, we can use the Pythagorean Theorem to find the height. If you split a equilateral triangle down the middle, you are left with two right triangles. Using this right triangle, the hypotenuse would be 12, the first leg would be 6 (half of the base) and the height would be the other leg. So we plug in and solve.

$a^{2} + b^{2} = c^{2}$

$6^{2} + h^{2} = 12^{2}$

$36 + h^{2} = 144$

$h^{2} = 108$

h = 10.4

5 0

3 years ago

The U.S.A. Olympic Synchronized Swimming Team is designing a routine for their upcoming competition. From the center of the pool

Mama L [17]

Answer:

The equation of the circle is;

(x - 2)² + (y - 4)² = 5²

Step-by-step explanation:

We note that the general equation of a circle is given as follows;

(x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The radius of the circle

The given parameters are;

The location of the center of the pool to the center of their formation = 2 feet to the right and 4 feet up from the center of the pool

The point through which the circle which they form goes through = A point 3 feet to the left and 4 feet up from the center of their formation

Taking the center of the pool as the origin of the coordinate plane system, we have;

The coordinate of the center of the circle = The coordinate of their motion from the center of the circle

∴ The coordinate of the center of the circle = (2, 4)

∴ (h, k) = (2, 4)

h = 2, k = 4

The coordinate of the point through which the circle passes = (2 - 3, 4 + 4) = (-1, 8)

∴ The length of the radius, 'r', can be found as, r = √((-3)² + 4²) = 5 or r = √((-1 - 2)² + (8 - 4)²) = 5

r = 5

The equation of the circle is therefore presented by substituting the values of 'h', 'k', and 'r', as follows;

(x - 2)² + (y - 4)² = 5².

4 0

3 years ago

Only answer this if you have an explanation and if you know what the answer is.

Klio2033 [76]

Answer:

G

Step-by-step explanation:

Since there are 50 students being asked, to find a percentage, put the output (the number of students that chose each genre) and the input (the number of students asked all together) in ratio form as a fraction. You will get the fractions 10/50, 16/50, 20/50, and 4/50. Multiply each denominator by two to get the percentage. You will get 20/100, 32,/100, 40/100, and 8/100. If you look at the four answers provided, you can cross out J immediately because it shows that "Other" was the greatest percentage, when it is in fact the smallest. H can be crossed out as well, since the percentage for "Mystery" is over 20% when it should be exactly at 20%. F can be crossed out as well because it shows that "Other" takes up 10%, when it is actually a bit less, 8%. G is the best choice because the percentage that "Other" takes up is a bit less than 10%, so it's safe to say that it shows 8%.

8 0

3 years ago

What is the equation of the line that passes through the point 4, -6 and has a slope of -3

zheka24 [161]

Y = mx + b. Use this equation for most linear functions. Enter the information that is given to you.
$- 6 = - 3(4) + b$
Multiply the -3 and 4 to get 12.
$-6 = - 12 + b$
Now divide the -12 from both sides.
$\frac{ - 6}{ - 12} = \frac{ - 12}{ - 12} + b$
-12 cancels out on the right side and your left with
$- \frac {1}{2} = b$
Now re-enter the info back into the formula.
$y = - 3x - \frac{1}{2}$
Then you've got your formula

4 0

3 years ago

dr.hong prescribed 0.019 liter more mdicine than dr.T dr.E prescibed0.02 less than dr> hong who prescribed them most who pres

Aleks [24]

DrH = DrT + 0.019
DrE = DrH - 0.020
DrH is the most and DrE is the least

6 0

3 years ago

3х2 + 5х + 10 = 0. How many solutions does it have