Simplify each expression by writing the expression without absolute value bars

Answer:

[tex]\frac{x2}{a} - \frac{y2}{b2} = 1[/tex]

Step-by-step explanation:

A hyperbola is the locus of a point such that its distance from a point to two points (known as foci) is a positive constant.

The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:

[tex]\frac{X2}{16} - \frac{b}{4} = 1[/tex]

The coordinates of the foci is at (±c, 0), where c² = a² + b²

Given that  a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:

I don't feel like explaining so...

a. = 4

The foci c is at +/-2√5, using c² = a² + b²:

B = 2

Substituting the value of a and b to get the equation of the hyperbola:

[tex]\frac{x2}{a2} - \frac{y2}{b2} = 1[/tex]  

[tex]\frac{x2}{16} - \frac{b2}{4} = 1[/tex]

Answer:

I think is 15 dollars.

Step-by-step explanation:

each pound cost 1.5 multiply it by 10

Answer:

$15

Step-by-step explanation:

4 pounds are $6

10pounds are $?

1 pound would be $1.5, because 6/4 = 3/2= 1.5

If one pound is 1.5 dollars, 10 pounds would be 10*1.5=$15

Answer: 65 kmh

Step-by-step explanation:

70 kmh for 2 hours = 140 km.

63 kmh for 5 hours = 315 km

140 + 315 = 455/7 total hours = 65 kmh

Answer:

35

All angles of a triangle = 180 degrees subtract 40 from 180 and you get 140

180-40=140 because the other angles are equal with the same equation to get them divide 140 by 2 140/2=70  then you have to get h alone so you divide by the other 2 in the equation 70/2=35  h=35

Answer:

55

Step-by-step explanation:

In triangle ABC (LET'S SAY TRIANGLE IS ABC)

Angle A=40

Angle B = Angle C = x (since 2h is beside B and C both)

40+x+x=180 (Angle sum property)

40+2x=180

2x=140

x=70

2h+70=180 (Angle in a straight line=180)

2h=110

h=55

9514 1404 393

Answer:

Step-by-step explanation:

The rhombus has several relevant properties.

The last of these relations can be used to find x:

  7x° = 35°

  x = 35°/7° = 5

The second of the relations can be used to find y:

  3y° = 90°

  y = 90°/3° = 30

The first of the relations can be used to find z:

  10z -8 = 5z +32

  5z = 40 . . . . . . . . . add 8-5z

  z = 40/5 = 8

I = $ 1,200,000.00

Equation:

I = Prt

Calculation:

First, converting R percent to r a decimal

r = R/100 = 3%/100 = 0.03 per year,

then, solving our equation

I = 1000000 × 0.03 × 40 = 1200000

I = $ 1,200,000.00

The simple interest accumulated

on a principal of $ 1,000,000.00

at a rate of 3% per year

for 40 years is $ 1,200,000.00.

Answer:

It has 5 Faces.

The 4 Side Faces are Triangles.

The Base is a Square.

It has 5 Vertices (corner points)

It has 8 Edges.

Step-by-step explanation:

btw you can choose 3

Answer:

4.

Step-by-step explanation:

The orientation of the shape is the same  4 times during 360 degree turn.

Answer:

4

Step-by-step explanation:

Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation.

Answer:

slope = -5 equation= y=-5x+100

Step-by-step explanation:

pick the x and y intercepts as your points to find the gradient that is

(20,0) and (0,100)

slope =∆y/∆x

=100/-20

= -5

take point(20,0) and (x,y) to find equation using the slope

equation becomes y= -5x+100

Answer:

32

Step-by-step explanation:

The perimeter is equal to sum of side lengths

4x + z + 3 + 5z - 3 = 80 add like terms

10z = 80 divide both sides by 10

z = 8 PR is 4z so 8*4 = 32

[tex] \frac{x {}^{0}y {}^{ - 3} }{x {}^{2}y {}^{ - 1} } \\ = \frac{1y {}^{ - 3} }{ {x}^{2}y {}^{ - 1} } \\ = \frac{1 \times 1}{ {x}^{2} y {}^{2} } \\ \\ = \frac{1}{ {x}^{2}y {}^{2} } [/tex]

Step by Step Explanation:

#CarryOnLearning

Answer:

Step-by-step explanation:

8 .) Probability of students has no pets in senior = No. of outcomes favourable / Total no.of outcome

= 15 / 24

9.) Probability of students has pets in junior = No.of outcomes favourable / Total no. of outcomes

= 37/52

Answer:

1 9 3

Step-by-step explanation:

i think only this much

Answer:

1,3 and 9

As Nine is divisible by 1,3 and 9

If central angle is 360° then Arc length is circumference.

An angle with the circle's center as its vertex is referred to as a central angle. The radius refers to each side of the angle that extends outward from the center to a particular point on the circle.

A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole. A circle's circumference is calculated by multiplying its diameter by the constant. This measurement of a circle's diameter is necessary for someone crossing a circular park or for enclosing a circle. The units for the circumference, which is a linear variable, are the same as those for length.

Since, when considering the circle's central angle we consider 360° which is the central angle of the whole circle.

So, when considering the arc length of a sector, we consider the arc length of the whole circle which is the circumference.

Learn more about circles here-

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Answer:

5 =x

Step-by-step explanation:

The top and the bottom are the same length

17 = 3x+2

Subtract 2 from each side

17-2 = 3x+2-2

15 =3x

Divide by 3

15/3 = 3x/3

5 =x

Answer:

x = 5

Step-by-step explanation:

3x + 2 = 17

3x + 2 - 2 = 17 - 2

3x = 15

3x ÷ 3 = 15 ÷ 3

x = 5

Answer:

832.6lbs

Step-by-step explanation:

Answer:

B =53.15010235

Step-by-step explanation:

Since this is a right triangle, we can use  trig functions

tan theta = opp / adj

tan B =  20 /15

Take the inverse tan of each side

tan ^ -1 ( tan B) = tan ^-1( 20/15)

B =53.15010235

Answer:

56%

Step-by-step explanation:

because of the 56% it had to be true to be in the question at all.

Step-by-step explanation:

a)

[tex] \frac{1 + \sin y}{ \cos y} + \frac{ \cos y}{1 + \sin y} = \frac{1 + 2 \sin y + \sin^{2} y + \cos ^{2} y}{ \cos y(1 + \sin y)} [/tex]

[tex] = \frac{2 + 2 \sin y}{ \cos y (1+ \sin y)} = \frac{2}{ \cos y} = 2 \sec y[/tex]

b)

[tex] \frac{ \cot x}{ \tan x + \cot x} = \frac{ \cos x}{ \sin x( \frac{ \sin x}{ \cos x} + \frac{ \cos x}{ \sin x} )} [/tex]

[tex] = \frac{ \cos x}{ \frac{ \sin^{2} }{ \cos x} + \cos x } = \frac{ \cos x}{ \frac{ \sin ^{2} x + \cos^{2} x}{ \cos x} } [/tex]

[tex] = \cos ^{2} x[/tex]

c) Note that cscx = 1/sinx so

[tex] \csc^{2} \theta \tan^{2} \theta - 1= \frac{1}{ \cos^{2} \theta } - 1[/tex]

[tex] = \frac{1 - \cos^{2} \theta }{ \cos \theta} = \frac{ \sin^{2} \theta}{ \cos ^{2} \theta } = \tan^{2} \theta[/tex]

Answer:  6x - 7y = 21

Step-by-step explanation:

sorry if its wrong

If s=side, then each side is 12m.

It got cut off but

12mx12m=144m^2 because mxm=m^2.

heart if helpful

From the graph,

g(2) = 4 ( from the coordinate (2,4))

[ The green line represent the function g(x)]

f(2)= 0

[ The red line represent the function f(x)]

(g + ƒ)(2) = g(2)+f(2) = 4+0 = 4

OPTION A is the correct answer

The answer is 48 notepads.

Answer:

x=25

Step-by-step explanation:

43=2x-7 (since the midpoint separate a line into two equal halves)

43+7=2x

50/2=x

25=x

Answer:

x=25

Step-by-step explanation:

Since M is the midpoint, you can set your formula up as

43 = 2x-7

43+7=2x

50/2=x

25=x

Answer: 4145.43

Have a great day! ;)

Answer:

d.156.

x+24=180 ( being staright angle)

Answer:

# of rows: 34

# of seats in each row: 46

Step-by-step explanation:

r - # of rows

s - # of seats in each row

r * s = 1564

s = r + 12

(34) * (46) = 1564

(46) = (34) + 12

Hope this helps!

Answer:

I think its

im not sure

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

the answer is 13

the answer is 13

the answer is 13

the answer is 13

the answer is 13

The quotient obtained by dividing 4x²+3x+2 will be 4x + 15 hence option (A) will be correct.

An equation can be defined in numerous ways. Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.

A formula known as an equation uses the same sign to denote the equality of two expressions.

In another word, the equation must be constrained with some constraint.

Given that

dividend  =  4x²+3x+2

divider = x -3

⇒ (x - 3) / 4x²+3x+2

⇒ (x - 3) / 4x²+3x+2

→ First it will goes for 4x time so 4x × (x - 3) = 4x² - 12x

Quotient = 4x

so (4x²+3x+2) - (  4x² - 12x ) = 15x + 2

(x - 3) / 4x²+3x+2

→ Second time it goes for 15 so 15 × (x - 3) = 15x -45

Quotient = 15

so  (15x + 2 ) - (  15x -45 ) = 47

Hence, 47 will be the remainder and the quotient will be (4x + 15).

For more about the equation, here:

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