Triangle JKL is similar to triangle MNO. Find the measure of side MN. Round your answer to the nearest tenth if necessary.

The equation of the ellipse and the equation of the hyperbola can be

derived from the given information and the general form of the equations.

[tex]Part \, A: The \ equation \ of \ the \ ellipse \ is; \displaystyle \frac{x^2}{3^2} + \frac{y^2}{4^2} = 1[/tex]

[tex]Part \, B: The \ equation \ of \ the \ hyperbola \ is; \displaystyle \frac{x^2}{(-4)^2} - \frac{y^2}{(-7)^2} = 1[/tex]

Part C: The domain of the ellipse is; [-3, 3]

The domain of the hyperbola is; (-∞, -4]

Reasons:

Part A: The center of the ellipse = At the origin;

The vertical major axis = 8 units

The minor axis = 6 units

The general equation for an ellipse is presented as follows;

[tex]\displaystyle \frac{x^2}{b^2} + \frac{y^2}{a^2} = 1[/tex]

Where;

[tex]\displaystyle a = The \ \mathbf{ semi \ major \ axis} = \frac{8}{2} = 4[/tex]

[tex]\displaystyle b = The \ semi \ \mathbf{ minor} \ axis = \frac{6}{2} = 3[/tex]

The equation of the ellipse is therefore;

Part B: center of the hyperbola = The origin

The transverse axis = Horizontal

The vertex of the hyperbola = (-4, 0)

[tex]\displaystyle The \ asymptote \ are; \ y = \mathbf{ \pm\frac{7}{4} \cdot x}[/tex]

The general equation of an hyperbola is presented as follows;

[tex]\displaystyle \mathbf{\frac{x^2}{a^2} - \frac{y^2}{b^2}} = 1[/tex]

[tex]\displaystyle The \ asymptote \ are; \ y = \mathbf{\pm\frac{b}{a} \cdot x}[/tex]

The vertices = (a, 0), (-a, 0)

Therefore, by comparison, we have;

a = -4

b = -7

Which gives the equation of the hyperbola as follows;

The above equation can be written as follows;

[tex]\displaystyle \frac{x^2}{(4)^2} - \frac{y^2}{(7)^2} = 1[/tex]

Part C: Given that both equations are equal, we have;

The covertices of the ellipse are; (-3, 0) and (3, 0)

The domain of the ellipse = [-3, 3]

The domain of the hyperbola = x < The negative vertex

∴ The domain of the hyperbola = x < -4 = (-∞, -4]

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Answer:

the frist one

Step-by-step explanation:

hope it helps

Answer:

P= -88

Step-by-step explanation:

Since P=xy (Or x times y)

We can solve it since we know that x and y is: 8 and -11

So 8 times -11

Which is -88

Thus P= -88

Hope this helps!

Answer:

c

Step-by-step explanation:

80 × percent = 48

percent = 48/80

= 0.6

= 60%

Answer:

0.325

Step-by-step explanation:

$63 divide by 24 you'll get 2.625

then $2.95 minus 2.625 you'll get 0.325

Answer:

3.7 meters

Step-by-step explanation:

First, convert the fractions into decimals.

5 1/5 = 5.2

1 1/2 = 1.5

Then subtract them

5.2-1.5=3.7 meters!

Answer:

letter c is the answer

Step-by-step explanation:

hope it helps you

Answer:

The answer is Option C.) 3x+5 = 0

Step-by-step explanation:

Option A, can't be the answer. It doesn't show a linear graph. Therefore it's incorrect.

Option B, can't be the answer. It doesn't show a linear graph either. This one is also incorrect.

Option C, on the other hand, is correct because it's not a linear equation.

Option D, can't be the answer. It shows a graph, but with a squiggly line. Therefore, this one is also incorrect.

Hope this helps!

Have a nice day/night/afternoon.

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Answer:

z = 1

Step-by-step explanation:

-z+7 = 6

so

7-6 = z

1 = z

good luck

Answer:

[tex]\huge\boxed{\sf z = 1}[/tex]

Step-by-step explanation:

-z + 7 = 6

Subtract 7 to both sides

-z = 6 - 7

-z = -1

Divide both sides by -1

z = 1

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

10.41

Step-by-step explanation:

hehe

Answer:

11

Step-by-step explanation:

Total number of pencils needed = 125 × 2 = 250

Total number of boxes = [tex]\frac{250}{24}[/tex] = 10.416

the teacher need to buy 11 boxes

Answer:

Line 3

Step-by-step explanation:

Line three should be

2*3*sqrt(5)-3sqrt(5)

Answer:

check online for more information

Answer:

Step-by-step explanation:

Answer:

  "2" is the exponent

Step-by-step explanation:

There is no exponent in your expression.

__

When the expression is typeset, the superscript text is considered to be an exponent:

  [tex]15(x+3){\boxed{^2}}[/tex]

When the expression is written in plain text, the exponent is indicated by a caret (^):

  [tex]\textsf{15(x+3)\^\ \!\!\boxed{\textsf{2}}}[/tex]

Answer:

[tex] {15x}^{2} + 90x + 135 \\ [/tex]

Step-by-step explanation:

[tex]15 {(x + 3)}^{2} \\ 15(x + 3)(x + 3) \\ 15 |(x(x + 3) + 3(x + 3)| \\ 15( {x}^{2} + 3x + 3x + 9) \\ 15( {x}^{2} + 6x + 9) \\ {15x}^{2} + 90x + 135 \\ [/tex]

Answer:

Step-by-step explanation:

20x+10x-8=0

first of all, you will +8 on both sides so there are no negative numbers onany side

20x+10x=8

now gather everything up

30x=8

divide everything by 30 now to get the value of 1x

30x/30=x

8/30=0.2666666666

Answer:

p(-1)= -5

p(2)= 19

Answer:

-5

Step-by-step explanation:

p(x)=3x+1

p(-2)=3(-2)+1

p(-2)=-6+1

p(-2)=-5

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Answer:

a = jd

Step-by-step explanation:

We want to solve for a given that a/d = j

To do so we want to isolate a (get a by itself )

We can do this by using inverse operations.

We would want to get rid of the d

A is being divided by d.

The inverse of division is multiplication so to get rid of the d we multiply a/d by d but whatever we do to one side we must do to the other so we multiply both sides by d

a/d * d = a

j * d = jd

we are then left with a = jd

And we are done!

Answer:

a = jd

Step-by-step explanation:

We have to solve the equation for a - in other words, we have to find a in terms of d and j. Another way to think about this is that we need a by itself on one side, equal to the other two values in some sort of relationship.

So, how can we accomplish this? Well, currently a is being divided by d, so we should probably multiply both sides by d to get that d away from a. The process is shown below:

[tex]\frac{a}{d} =j[/tex]

[tex]\frac{a}{d} *\frac{d}{1} =j*d[/tex]

[tex]\frac{ad}{d} =jd[/tex]

[tex]a=jd[/tex]

And look at that! We've solved for a in terms of the other two values. If you need any more help or everything I just did was confusing or overwhelming, let me know so I can clarify. :)

Answer: Friday, 1.25 more per hour

Step-by-step explanation: if we take the inches it snowed and divide it by the hours, we get the rate of snowfall for one hour. 15/6=2.5 and 30/8=3.75

To get how much more we take the bigger snowfall per hour minus the smaller snowfall per hour 3.75-2.5=1.25

Answer:

111

Step-by-step explanation:

multiply 33 by 6 because 6 is being subtracted every time and then subtract 198 from 309

Answer:

117

Step-by-step explanation:

Hope this helps!

Answer:

x=13/15

Step-by-step explanation:

2/3=x-1/5

find LCD=15

10/15=x-3/15

add 3/15 to both sides

13/15=x

Answer:

hi there the answer is 72

Step-by-step explanation:

sorry but my work is on a piece of paper in front of me

To map the regular pentagon onto itself, rotate it at angles of 72, 144, 216, and 288 degrees.

A polygon is a geometric form with a limited number of sides that exists in two dimensions. On the sides or edges of polygons, single-direction segments are joined end to end to form a closed shape. Vertices or corners are the points at which two line segments converge to form an angle.

It is given that:

There are five sides to the pentagon.

We are known that the typical pentagon has five vertices and interior angles of 72 degrees each. Rotational symmetry is also present in a regular pentagon.

Angles are 72°,144°,216°, and 288°

Thus, to map the regular pentagon onto itself, rotate it at angles of 72, 144, 216, and 288 degrees.

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Answer:

.91% he wa off by .91% because .91 of 300 is 25 and 300- 25 is 275

Step-by-step explanation:

Answer:  y = -(1/2)x + 3

Step-by-step explanation:

y = 2x - 1

This is in the format of y=mx + b, where m is the slope and b is the y-intercept (the value of y when x=0).

Perpendicular lines have a slope that is the negative inverse of the reference line.  The slope of this reference line is 2, so the slope of a perpendicular kline will be -(1/2).

This yields the equation y = -(1/2)x + b

To find the value of b, we can use the given point, (0,3) and use these values of x and y to solve for b:

y = -(1/2)x + b

3 = -(1/2)(0) + b

b = 3

The equation of a line perpendicular to y = 2x - 1 and goes through point (0,3) is:

y = -(1/2)x + 3

Answer:

1. Whole number

Step-by-step explanation:

It's a negative number, but it is not a decimal, therefore it is a whole number.

Answer:

0.6

Step-by-step explanation:

Trust me

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Hello there today we will solve your problem, we will need to factorize btw...

[tex]{\huge{\boxed{\mathfrak{Equation}}}[/tex]

[tex]{\big{\boxed{\frac{x^2-5x+4}{x^2-4x}}}}[/tex]

First we will factor [tex]x^2-5x+4[/tex], which gives us [tex]\left(x-1\right)\left(x-4\right)[/tex]

[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\left(x-1\right)\left(x-4\right)}{x^2-4x}\\[/tex]

factorize [tex]x^2-4x[/tex] giving us [tex]x\left(x-4\right)[/tex]

[tex]\frac{\left(x-1\right)\left(x-4\right)}{x\left(x-4\right)}[/tex]

cancel the common factor [tex]x-4[/tex]

and we get [tex]\frac{x-1}{x}[/tex]

The amount of money Neela needs to deposit to raise her balance to 0 is; $163

Since Neela's online banking showed she's been charged a monthly fee of $8 on checking accounts and an overdraft protection fee of $35.

Subsequently, she wrote a check of $375 in which case; Three days later a charge of $273 that she had forgot about appeared on the same day that the check cleared.

Since the account showed she had a balance of $530.

Her new account balance is; $530 - $693 = -$163

Therefore, Neela needs to deposit $163 to raise her balance to 0.

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