MATHEMATICS HIGH SCHOOL

Find an equation in standard form for the hyperbola with vertices at (0, ±10) and asymptotes at y=+- 5/4x.

Answers

Answer 1
Answer:

Answer:

Step-by-step explanation:

Given that vertex of the hyperbola is

(0,10) and(0,-10)

Hence the hyperbola will have equation of the form

(y^2)/(a^2) -(x^2)/(b^2) =1

Since vertex has y coordinate as 10, we have a =10

So equation would be(y^2)/(10^2) -(x^2)/(b^2) =1

Since asymptotes are y =±5x/4

we have equation of both asymptotes is

y^2-(25x^2)/(16) =0\ny^2/25-x^2/16 =0\ny^2/100-x^2/64 =0

Since hyperbola will have equations same as asymptotes except with difference of constant terms as 1 instead of 0, we have

equation as

(y^2)/(100) -(x^2)/(64) =1
Answer 2
Answer: The equation of this hyperbola in standard form:
y² / a² + x² / b² = 1.
y = +/- a/b x
a / b = 5 / 4
a = 10
10 / b = 5 / 4
b = (10 · 4) : 5
b = 8
Answer:
The equation of the hyperbola is:
y² / 100 - x²/ 64 = 1

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Partition the model to prove that the following number sentence is true 2/5 + 4/10

Answers

Final answer:

In order to prove the sentence 2/5 + 4/10, a partitioned model could be used. Here, 2/5 equates to 4 out of 10 parts and 4/10 equates to 4 out of 10 parts. Adding these provides a total of 8 out of 10 parts, thereby proving the sentence is true.

Explanation:

To prove the number sentence 2/5 + 4/10 is true using a partitioned model, you need to start by understanding that fraction addition involves just combining the fractions. If you partitioned a model into 10 equal parts representing 1 whole, 2/5 would be 4 parts and 4/10 would be 4 parts. Adding these together 4parts (being 2/5) + 4parts (being 4/10) makes 8 parts. Since 1 whole is made up of 10 parts, 8 parts equate to 8/10 or 0.8. Therefore, 2/5 + 4/10 = 0.8 or 8/10 validating the sentence as true.

Learn more about Fraction Addition here:

brainly.com/question/34291287

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Use the given information to write the equation of the line.
slope 2, y-intercept - 4

Answers

Answer : y = 2x - 4

Hope this helps (:

Find value of X in the given right triangle.

Answers

Answer:

44.4

Step-by-step explanation:

it is a right angled triangle so

with reference angle x

perpendicular (p) = 7

hypotenuse (h) = 10

so Now

sin x = p/h

sin x = 7 / 10

x = sin^-1( 7/ 10)

x = 44.42°

Rounding to nearest tenth

= 44.4°

Answer:

7.1

Step-by-step explanation:

you use the Pythagorean theorem to solve this problem. a^2+b^2=c^2.

you are finding value of b plug the variables in = 7^2+b^2=10^2

=49+b^2=100

subtract 49 from both sides

b^2=51

Square root of 51 =7.141 round to nearest tenth =7.1

If f(x) = x2 − 2x + 9 and g(x) = 8 − x, what is (f o g)(−4)?

Answers

I hope this helps you

Write a equation of the line that passes through (-2,-3) and has a slope of 5

Answers

To get the Slope-Intercept form of a line, you first need to put it into Point-Slope form, which is y - y_1 = m (x - x_1) where x_1 and y_1 are the given coordinates and m is the given slope. So, plug your given information into the equation.

y + 3 = 5 (x + 2)   Use the Distributive Property
y + 3 = 5x + 10   Subtract 3 from both sides
      y = 5x + 7

How to simplify -64^(1/3)

Answers

-64^{(1)/(3)}=\sqrt[3]{-64}= \sqrt[3]{(-4)^3} =-4
You need to find a number that you can multiply by itself 3 times and wind up with -64 .

Like [ N x N x N = -64 ] .

Try some small numbers:

1 x 1 x 1 = 1
2 x 2 x 2 = 8
3 x 3 x 3 = 27
4 x 4 x 4 = 64 . . . There it is ... almost !  The right number, but the wrong sign.

Now try (-4).
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