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Answer:

x²/4 + y²/16 = 1

Step-by-step explanation:

Foci on the y axis: major axis parallel to y axis

x²/b² + y²/a² = 1

x²/4 + y²/16 = 1

The required equation of an ellipse is given by x²/4 + y²/16 = 1

Given that,
Length of the major axis: 4 Length of the minor axis: 2 Foci are on the y-axis with center (0,0)​, the equation of the ellipse is to be determined.0

Ellipse is defined as the cross-section of the cone when cutting it with a plane parallel to its base.

Here,
Standard equation of the ellipse with origin as the center,
x²/a² + y²/b² = 1
where a and b are the minor and major axis of the ellipse.
From the given, we have a = 2 and b = 4
So the equation of the ellipse,
x²/4 + y²/16 = 1

Thus, the required equation of an ellipse is given by x²/4 + y²/16 = 1.

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Answer:

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As QR is parallel to ST Rs is parallel TU QS is congruent to SU the measure of their included angle is also same ∠QRS ≅ ∠STU.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

Given, Line segment QR is parallel to line segment ST.

Line segment RS is parallel to line segment TU, And line segment QS is similar to line segment SU.

So, The included angle of two pairs of parallel lines will also be the same as

line segment QS is similar to line segment SU.

∴ ∠QRS is similar to ∠STU.

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Answer:

21

Step-by-step explanation:

set up proportion and solve

18/12=x/14 (cross multiply)

252=12x

21=x

Answer:

4:1

Step-by-step explanation:

hope this helps

Answer:

The ratio is 1 hour to 1.5 laptops

Step-by-step explanation:

If you divide the time by amount done, there you have the answer.

Answer:

90

Step-by-step explanation:

Answer:

90 cupcakes

Step-by-step explanation:

So, to solve this question all we have to do is add the number of cupcakes that Dan brought and the number of cupcakes that his friend bought.

So the expression would look like this:

36 + 49 + 5 = 90

So, in conclusion, the bake sale had 90 cupcakes to sell

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Answer:

15

Step-by-step explanation:

If I am not mistaken, since n is 6 you would replace n with 6 so it would be 6+3+6= 15.

I hope this helps :)

[tex]{\underline{\underline{\bf{Given:}}}}[/tex]

[tex]{\underline{\underline{\bf{Need\:to\:find:}}}}[/tex]

[tex]{\underline{\underline{\bf{Formula\:to\:be\:used:}}}}[/tex]

Pythagorean Theorem:

[tex]\underline{\boxed{\sf{{Base}^{2}+{Perpendicular}^{2}={Hypotenuse}^{2}}}}[/tex]

[tex]{\underline{\underline{\bf{Solution:}}}}[/tex]

According to the given data, we know the measures of Perpendicular and Hypotenuse. Hence, the measure of the base (Side FE) can be found by substituting the given measures in Pythagorean Theorem.

[tex]\implies{\sf{{Base}^{2}+{Perpendicular}^{2}={Hypotenuse}^{2}}}[/tex]

[tex]\implies{\sf{{EF}^{2}+{DF}^{2}={DE}^{2}}}[/tex]

[tex]\implies{\sf{{EF}^{2}+{(13.6)}^{2}={(16.2)}^{2}}}[/tex]

[tex]\implies{\sf{ EF = \sqrt{ {(16.2)}^{2} - {(13.6)}^{2} } }}[/tex]

[tex]\implies{\sf{ EF = \sqrt{ 262.44 - 184.96 } }}[/tex]

[tex]\implies{\sf{ EF = \sqrt{77.48 } }}[/tex]

[tex]\implies{\sf{EF=\red{\underline{\underline{8.802\:m}}}}}[/tex]

[tex]{\underline{\underline{\bf{Required\:answer:}}}}[/tex]

Answer:

0.4

Step-by-step explanation:

Answer:

160 pounds

Step-by-step explanation:

If she has 3 boxes and there's 40 more pounds than if she had one, that means each box is 20 pounds so multiply 20 by 8 and you get 160 pounds

Answer:

Step-by-step explanation:

2.50

The percentage is calculated by dividing the required value by the total value and multiplying it by 100.

If Nancy has to buy an item that cost $30 with a 5% off and Ninda has to buy an item that cost $25 with a 10% off.

The difference between individual pay is $6.

The percentage is calculated by dividing the required value by the total value and multiplying it by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

Nancy:

Coupon = 5% off

Cost of the purchase = $30

Amount to pay:

= 30 - (5/100) x 30

= 30 - 30/20

= 30 - 1.5

= $28.5

Linda:

Coupon = 10% off

Cost of the purchase = $25

Amount to pay:

= 25 - (10/100) x 25

= 25 - 2.5

= $22.5

The difference between individual pay:

= 28.5 - 22.5

= $6

Thus

The difference between individual pay is $6.

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Answer:

1 and 2 are not polyhedrons, as a circle has infinite sides

1. cone, 1 vertex

2. sphere, nothing

3. pentagonal prism?

wait but can't every face be a base???

anyway 7 faces, 10 vertices

4. triangular prism

5 faces, 6 vertices

Step-by-step explanation:

We have given the figure

We have to determine whether each solid is a polyhedron.

Then identify the solid.

If it is a polyhedron, name the bases, and faces.

edges, and vertices.

A vertex is a point of where the first derivative of curvature is zero. This is typically a local maximum or minimum of curvature, and some authors define a vertex to be more specifically a local extremum of curvature.

1 and 2 are not polyhedrons, as a circle has infinite sides

1. cone, 1 vertex

2. sphere, nothing

3. pentagonal prism

anyway 7 faces, 10 vertices

4. triangular prism

5. faces, 6 vertices

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Answer:

89.14

Step-by-step explanation:

Given:

Figure of a triangle.

To find:

The values of x.

Solution:

In the figure, we have an angle bisector.

According to the angle bisector theorem, an angle bisector of a triangle always divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Using angle bisector theorem, we get

[tex]\dfrac{x}{7}=\dfrac{15}{14}[/tex]

Multiply both sides by 7.

[tex]x=\dfrac{15}{14}\times 7[/tex]

[tex]x=\dfrac{15}{2}[/tex]

[tex]x=7.5[/tex]

Therefore, the value of x is 7.5 units.

The equation –2 = –2 is always true, so no value of x will make the equation true. The correct solution of the equation is that there is no solution.

In mathematics, an equation is a statement that shows the equality between two expressions. It contains an equals sign (=) that separates the two expressions. The expressions on both sides of the equals sign can be numbers, variables, or functions. The equation represents a relationship between the expressions that must hold true for all values of the variables involved. Solving an equation means finding the values of the variables that satisfy the equation. Equations are used in various fields, such as physics, engineering, economics, and many others, to model and solve real-world problems.

Here,

The error made by the student is assuming that -2 is the solution to the equation without actually solving it. The equation -2 = -2 is always true, which means that the equation is an identity and has no solution. So, the correct solution of the equation is that there is no solution.

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Answer:

Factoring the trinomial: [tex]x^2+13x+12[/tex] we get the factors [tex]\mathbf{(x+1)(x+12)}[/tex]

Step-by-step explanation:

We need to factor the trinomial: [tex]x^2+13x+12[/tex]

We can factor the trinomial by breaking the middle term i.e 13x

Such that adding or subtracting gets the both terms we get 13x and multiplying both terms we get 12x^2

We can break 13x as: 12x and x

Adding them we get 13x and multiplying them we get 12x^2

So,

[tex]x^2+13x+12\\=x^2+12x+x+12\\=x(x+12)+1(x+12)\\=(x+1)(x+12)[/tex]

So, Factoring the trinomial: [tex]x^2+13x+12[/tex] we get the factors [tex]\mathbf{(x+1)(x+12)}[/tex]

Answer:

Yes

Step-by-step explanation:

Sure. For example 5.1+13.9>12.7 or 5.1+12.7>13.9 or 13.9-5.1<12.7

Answer:

Yes

Step-by-step explanation:

Answer:

5 x 3/4 < 5

2 x 4/3 > 2

6 x 5/5 = 6

4/7 x 1/8 < 4/7

2/5 x 7/7 = 2/5

1/3 x 6/4 > 1/3

Answer: B. 77

Sub x =6 into the given expression

4x^2 - 12x + 5

= 4(6)^2 - 12(6) + 5

= 144 - 72 + 5

= 77

[tex]\\ \sf\longmapsto 4x^2-12x+5[/tex]

[tex]\\ \sf\longmapsto 4(6)^2-12(6)+5[/tex]

[tex]\\ \sf\longmapsto 4(36)-72+5[/tex]

[tex]\\ \sf\longmapsto 144-67[/tex]

[tex]\\ \sf\longmapsto 77[/tex]

Answer:

f(x-7) =  x -12

Step-by-step explanation:

horizontal translation 7 units right: f(x-7)

f(x) = x - 5

f(x-7) = x-7 -5 = x -12

Answer:500(1.2)^x

Plato :)

Answer:

3

Step-by-step explanation:

PLATO

Answer:

15 fifths

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

3/2 is equal to 1.5 and 3 1.5s can fit in 5 equaling 4.5

Answer:

Step-by-step explanation:

Move

2x-3

x2+4x+3

to the left side of the equation by subtracting it from both sides.

x+2

x2-9

+

x-3

x2-2x-3

-

2x-3

x2+4x+3

=0

Simplify

x+2

x2-9

+

x-3

x2-2x-3

-

2x-3

x2+4x+3

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Answer: the sum is 5

Step-by-step explanation:

Answer:

8000

Step-by-step explanation: