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3 years ago

Write this equation in standard form 9x^2-4y^2-24y-72=0

1 answer:

4 0

$9x^2-4y^2-24y-72=0\\
\\
9x^2-4y^2-24y=72\\
\\
9x^2-(4y^2+24y+36)=72-36\\
\\
9x^2-4(y+3)^2=36\\
\\
\frac{9x^2}{36}-\frac{4(y+3)^2}{36}=\frac{36}{36}\\
\\
\boxed{\frac{x^2}{4}-\frac{(y+3)^2}{9}=1}$

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In a mathematics class, half of the students scored 79 on an achievement test. With the exception of a few students

Yakvenalex [24]

In this situation, you have:
The mode is 79 (that’s the most common number).
The median is 78.5 (the middle value or the average of the two middle values, since there is an even number of test scores).
The mean is less than both of those, as it was brought down by the few scores of 49.

The means the mean will be less than median.

Answer: C

3 0

3 years ago

Triangle DEF has vertices D(0,0), E(7,0), and F(3,7).

Leni [432]

Answer:

(3, 1.7)

Step-by-step explanation:

The point at which the vertices of a triangle meet is known as the orthocenter of the triangle. The orthocenter passes through the vertex of the triangle and is perpendicular to the opposite sides.

Two lines are perpendicular if the product of their slopes is -1.

The slope of the line joining D(0,0), F(3,7) is:

$m_1=\frac{7-0}{3-0}=\frac{7}{3}$

The slope of the line perpendicular to the line joining D and F is -3/7. The orthocenter is perpendicular to the line joining D and F and passes through vertex E(7, 0). The equation is hence:

$y-y_1=m(x-x_1)\\\\y-0=-\frac{3}{7} (x-7)\\\\y=-\frac{3}{7}x+3 \ .\ .\ .\ (1)$

The slope of the line joining E(7,0), and F(3,7). is:

$m_1=\frac{7-0}{3-7}=-\frac{7}{4}$

The slope of the line perpendicular to the line joining E and F is 4/7. The orthocenter is perpendicular to the line joining E and F and passes through vertex D(0, 0). The equation is hence:

$y-y_1=m(x-x_1)\\\\y-0=\frac{4}{7} (x-0)\\\\y=\frac{4}{7} x\ .\ .\ .\ (2)$

The point of intersection of equation 1 and equation 2 is the orthocenter. Solving equation 1 and 2 simultaneously gives:

x = 3, y = 1.7

4 0

2 years ago

Find 2x2 − 2z4 + y2 − x2 + z4 if x = −4, y = 3, and z = 2.<br><br> Is -3 the correct answer?

Ket [755]

We're given the algebraic expression 2x^2 - 2z^4 + y^2 - x^2 + z^4

By hypothesis, x = -4, y = 3 and z = 2

Let's replace each letter by its given value:

2x^2 - 2z^4 + y^2 - x^2 + z^4
2(-4)^2 - 2(2)^4 + (3)^2 - (-4)^2 + (2)^4
(2*16) - 2*16 + 9 - 16 + 16
32 - 32 + 9 - 16 + 16
9

So wrong. The correct answer is not -3, but 9.

Hope this helps! :D

6 0

3 years ago

Which of the following does NOT describe a rational number? A- Non-repeating decimal B- Perfect square (ex: square root of 4) C-

alexandr1967 [171]

Answer:

Non-repeating decimal

Step-by-step explanation:

As a example, 32.93729, would be a never ending number. Which means it's not a rational number, it is a irrational number.

6 0

3 years ago

Read 2 more answers

Solve the equation: 1/6d+2/3=1/4(d-2)

nlexa [21]

d/6+2/3=1/4(d-2)

d/6+2/3=d-2/4

2d+8=3(d-2)

2d+8=3d-6

8=3d-6-2d

8=d-6

8+6=d

14=d

d=14

8 0

3 years ago