The question asks, "Find the equation of the ellipse with the following properties.

The ellipse with x-intercepts (5, 0) and (-5, 0); y-intercepts (0, 3) and (0, -3)."
I know that the equation for an ellipse is x^2/a^2+ y^2/b^2=1 but I have no idea how to create the equation given x-intercepts and y-intercepts. Please help! Thank you.

Answer:

x ≤-18

Step-by-step explanation:

3-x/2≥12

Subtract 3 from each side

3-3-x/2≥12-3

-x/2≥9

Multiply each side by -2 to clear the fraction.  Remember to flip the inequality since we are multiplying by a negative

-3 * -x/2 ≤ -2 *9

x ≤-18

Answer:

x ≤ - 18

Step-by-step explanation:

Given

3 - [tex]\frac{x}{2}[/tex] ≥ 12

Multiply all terms by 2

6 - x ≥ 24 ( subtract 6 from both sides )

- x ≥ 18

Multiply both sides by - 1, remembering to reverse the sign as a consequence of multiply by a negative quantity.

x ≤ - 18

Answer:

[tex]3ab^2\sqrt[3]{b}[/tex]

if the problem was [tex]\sqrt[3]{27a^3b^7}[/tex].

Step-by-step explanation:

Correct me if I'm wrong by I think you are writing [tex]\sqrt[3]{27a^3b^7}[/tex].

[tex]\sqrt[3]{27a^3b^7}[/tex]

I'm first going to look at this as 3 separate problems and then put it altogether in the end.

Problem 1: [tex]\sqrt[3]{27}=(3)[/tex] since  [tex](3)^3=27[/tex].

Problem 2:[tex]\sqrt[3]{a^3}=(a)[/tex] since [tex](a)^3=a^3[/tex]

Problem 3: [tex]\sqrt[3]{b^7}[/tex].  This problem is a little harder because [tex]b^7[/tex]is not a perfect cubes like the others were. But [tex]b^7[/tex] does contain a factor that is a perfect cube. That perfect cube is [tex]b^6[/tex] so rewrite [tex]b^7[/tex] as [tex]b^6 \cdot b^1[/tex] or [tex]b^6 \cdot b[/tex].

So problem 3 becomes [tex]\sqrt[3]{b^6 \cdot b}=\sqrt[3]{b^6}\cdot \sqrt[3]{b}=b^2 \cdot \sqrt[3]{b}[/tex].  The [tex]b^2[/tex] came from this [tex](b^2)^3=b^6[/tex].

Anyways let's put it altogether:

[tex]3ab^2\sqrt[3]{b}[/tex]

Answer:

The last picture or

The picture with 3 lines on EF and TR, 1 line one EG, 1 line on SR, 2 lines on ST and 2 lines on GF

Step-by-step explanation:

Since EF and RT have 3 lines and FG and TS have 2 lines, they are similar

Answer:

Step-by-step explanation:

If [tex]\triangle EFG \cong \triangle RTS[/tex], it can be deducted the following:

[tex]\angle E \cong \angle R\\\angle F \cong \angle T\\\angle G \cong \angle S[/tex]

Also,

[tex]EF \cong RT\\FG \cong TS\\EG \cong RS[/tex]

Notice that the last imag shows the correct congruence, because it shows the congruence between sides as we said before.

Answer:

C

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ← r is the radius

Consider

[tex]\frac{x^2}{2^2}[/tex] + [tex]\frac{y^2}{2^2}[/tex] = 1, that is

[tex]\frac{x^2}{4}[/tex] + [tex]\frac{y^2}{4}[/tex] = 1

Multiply through by 4

x² + y² = 4 ← equation of circle

This is the equation of a circle centred at the origin with radius 2

Answer:

(3×20%+2×70%)/3+2=40%

Step-by-step explanation:

Assuming the potions are the same type or do mix then probably the concentration of the potion depends on the type of reaction they have to each other.

Yet we can average the percentage of the active ingredient by the principle mentioned above

Answer:

The final concentration is 40%.

Step-by-step explanation:

Let x the concentration of final solution.

3 liters of solution (1) with 20% concentration is mixed with 2 liters of 70% solution producing (3 + 2) = 5 liters of x% mixture.

Now 3 × (20%) + 2 × (70% = 5 (x%)

3 × 0.2 + 2 × 0.7 = 5 (0.1x)

0.6 + 1.4 = 0.05x

2 = 0.5x

x = 2/0.05

= 40%

The final concentration is 40%.

The answer is B) Link below

Answer:

B

Step-by-step explanation:

I just did it

Answer:

Step-by-step explanation:

The given expression is:

-3(6f - 12) = 36 - 18f

To prove that L.H.S=R.H.S:

Multiply -3 (6f-12)

-3(6f)-3(-12)

=-18f+36

=36-18f

Hence it is proved that L.H.S = R.H.S....

The equation y = -10 (x) (x - 5) models the height.

Option A is the correct answer.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

66x = 8 is an equation.

We have,

From the table,

We can make ordered pairs in the form of (x, y).

(0, 0), (1, 40), (2, 60), (3, 60), (4, 40), (5, 0).

So,

We will choose the equation that satisfies the ordered pairs.

y = -10 (x) (x – 5)

This can be used as the equation.

For (0, 0), (1, 40), (2, 60), (3, 60), (4, 40), (5, 0)

i.e x = 0, 1, 2, 3, 4, 5

y = -10 x 0 = 0

y = -10 x 1 x -4 = 40

y = -10 x 2 x -3 = 60

y = -10 x 3 x -2 = 60

y = -10 x 4 x -1 = 40

y = - 10 x 5 x 0 = 0

y = 10 (x) (x - 5)

This can not be used since the y value is a negative value.

y = -10 (x – 5)

This is not possible.

y = 10 (x – 5)

This is not possible.

Thus,

The equation y = -10 (x) (x - 5) satisfy the given table values.

Learn more about equations here:

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To find which equation models the height of a projectile \( y \) seconds after being fired based on the given data, we can substitute the given x-values (time in seconds) into each equation and check whether the result matches the corresponding y-values (height in meters).
Let's go through each of the given equations and the provided points one by one:
1. Equation \( y = -10(x)(x – 5) \)
When \( x = 0 \), the height \( y \) should be 0.
Substituting the value into the equation, \( y = -10(0)(0 – 5) = 0 \), which matches the given point (0, 0).
When \( x = 1 \), the height \( y \) should be 40.
Substituting the value into the equation, \( y = -10(1)(1 – 5) = -10(-4) = 40 \), which matches the given point (1, 40).
When \( x = 2 \), the height \( y \) should be 60.
Substituting the value into the equation, \( y = -10(2)(2 – 5) = -10(-1) = 60 \), which matches the given point (2, 60).
When \( x = 3 \), the height \( y \) should be 60.
Substituting the value into the equation, \( y = -10(3)(3 – 5) = -10(-2) = 60 \), which matches the given point (3, 60).
When \( x = 4 \), the height \( y \) should be 40.
Substituting the value into the equation, \( y = -10(4)(4 – 5) = -10(-1) = 40 \), which matches the given point (4, 40).
When \( x = 5 \), the height \( y \) should be 0.
Substituting the value into the equation, \( y = -10(5)(5 – 5) = -10(0) = 0 \), which matches the given point (5, 0).
Since all the points match perfectly with the results from Equation 1, we confirm that Equation 1 models the height of the projectile accurately. Therefore, the correct equation is:
\( y = -10(x)(x – 5) \)
This quadratic equation represents a parabolic trajectory, which is typical for the motion of a projectile under gravity, with no air resistance, and assuming that the projectile lands at the same level from which it was fired.

Answer:

x=-1.282

Step-by-step explanation:

To solve the equation [tex]-4x-1=5^x+4[/tex] by graphing, you have to plot graphs of two functions:

[tex]y=-4x-1\\ \\y=5^x+4[/tex]

The x-coordinate of the point of intersection is the solution of the equation.

The graph of the function [tex]y=-4x-1[/tex] is shown in attached diagram with red line and the graph of the function [tex]y=5^x+4[/tex] is shown with blue curve.

The point of intersection has approximate coordinates (-1.282, 4.127), so the solution (correct to three decimal places) of the equation is x=-1.282

Answer:

[tex]y+1=3(x+1)[/tex]

Step-by-step explanation:

Ok so we are looking for line parallel to the line containing points (0,-3) and (2,3).

Parallel lines have the same slope.

So let's find the slope of the line containing the points (0,-3) and (2,3).

You can use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].

However, I just like to line up the points vertically and subtract them vertically, then put 2nd difference over 1st difference. Like this:

(0 , -3)

-(2 ,  3)

-----------

-2     -6

So the slope is -6/-2 or just 3.

So the slope of the line we are looking for has slope 3 (or m=3) and your line should contain the point (-1,-1).

The point slope form of a line is:

[tex]y-y_1=m(x-x_1)[/tex] where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point you know on the line.

So we just plug into that equation now.  That gives us:

[tex]y-(-1)=3(x-(-1))[/tex]

Simplify a bit:

[tex]y+1=3(x+1)[/tex]

Answer:

The answer is: y+1=(3x+1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The vetex form of an equation of a parabola y = ax² + bx + c:

y = a(x - h)² + k

(h, k) - coordinates of a vertex

We have the equation y = 3x² + 3.

y = 3(x - 0)² + 3 → h = 0, k = 3

A is the correct answer.

break down the word problem.

You also have to recognize key words which figure into mathematical symbols.

ex. sum of a number and 20 is x+20

square of the number and 9 is (x+9)^2

please vote my answer brainliest! thanks.

Answer:

[tex]\large\boxed{y=\dfrac{4}{3}x}[/tex]

Step-by-step explanation:

The line passes through the origin has an equation y = mx

m - slope

The formula of a slope of a line passes through the origin

and a point (x, y):

[tex]m=\dfrac{y}{x}[/tex]

We have the point (6, 8). Substitute:

[tex]m=\dfrac{8}{6}=\dfrac{8:2}{6:2}=\dfrac{4}{3}[/tex]

Finally:

[tex]y=\dfrac{4}{3}x[/tex]

Answer:

Step-by-step explanation:

18 - r = 12         subtract 18 from both sides

18 - 18 - r = 12 - 18

-r = -6            change the signs

r = 6

Check

18 - 6 = 12         CORRECT

Answer:

Expressing the distance from the shore by the time needed to reach that distance at an invariable speed of 4.2f/s then f=4.2 p

Answer:

f=4.2p

Step-by-step explanation:

Answer:

There are 35 different sets of 3 books Joe could choose

Step-by-step explanation:

* Lets explain how to solve the problem

- Combination is a collection of the objects where the order doesn't

 matter

- The formula for the number of possible combinations of r objects from

 a set of n objects is nCr = n!/r!(n-r)!

- n! = n(n - 1)(n - 2)................. × 1

Lets solve the problem

- Joe has one book each for algebra, geometry, history, psychology,

 Spanish, English and Physics in his locker

∴ He has seven books in the locker

- He wants to chose three of them

∵ The order is not important when he chose the books

∴ We will use the combination nCr to find how many different sets

  of three books he can choose

- The total number of books is 7

∴ n = 7

∵ He chooses 3 of them

∴ r = 3

∵ 7C3 = 7!/3!(7 - 3)! = 7!/3!(4!)

∴ [tex]7C3=\frac{(7)(6)(5)(4)(3)(2)(1)}{[(3)(2)(1)][(4)(3)(2)(1)]}=35[/tex]

∴ 7C3 = 35

* There are 35 different sets of 3 books Joe could choose

Answer:

[tex]((\frac{2}{3})^0)^{-3}=1[/tex]

Step-by-step explanation:

We need to find the value of [tex]((\frac{2}{3})^0)^{-3}[/tex]

Solving:

We know, [tex](a^b)^n = a^{b*n}[/tex]

[tex]((\frac{2}{3})^{0*-3})[/tex]

[tex](\frac{2}{3})^0[/tex]

a^0 = 1

so,

[tex](\frac{2}{3})^0=1[/tex]

So, the value of [tex]((\frac{2}{3})^0)^{-3}=1[/tex]

Answer:

5⁄18 < x

Step-by-step explanation:

Start by adding like-terms [⅓ and 2⁄9] with 9 being the Least Common Denominator [LCD]. Since 2⁄9 already has a 9 in the denominator, it does not get touched, so in order to make ⅓ a denominator of 9, we simply multiply both terms by 3, to get 3⁄9. So, adding that to 2⁄9 gives you 5⁄9, also giving you 5⁄9 + x > ⅚. Now, we have to find the LCD again because we have two unlike fractions. Now, our Least Common Denominator is 18, so multiply both terms in ⅚ by 3 [15⁄18] and multiply both terms in 5⁄9 by 2 [10⁄18]. Now you have two like fractions to work with, and you can clearly see that your answer is x > 5⁄18. Although the answer is written in reverse, it is still the same concept.

I am joyous to assist you anytime.

Answer:

D. G(x) = 7x2

Step-by-step explanation:

Given a function f(x), the function kf(x) is stretched by a factor of k. In this case, if we stretch the function f(x) = x^2 by a factor of 7, the new function is going to be:

g(x) = 7x^2. Therefore, the correct option is option D.

Answer:

The system has no solution

Step-by-step explanation:

we have

y=5x+10 -----> equation C

The slope of the equation C is m=5 and the y-intercept is b=10

y=5x+2 -----> equation D

The slope of the equation C is m=5 and the y-intercept is b=2

Remember that

If two lines are parallel, then their slopes are the same

Equation C and equation D are parallel lines with different y-intercept

therefore

The system has no solution (the lines do not intersect)

Answer:

2.94cm^2

Step-by-step explanation:

If you're referring to the mathswatch question, this gets you 2/3 :)

Answer:

330

Step-by-step explanation:

Evaluate the sum of 14 terms and subtract the sum of the first 3 terms

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ], so

[tex]S_{14}[/tex] = 7 [ (2 × 6) + (13 × 3)]

                         = 7(12 + 39) = 7 × 51 = 357

[tex]S_{3}[/tex] = 6 + 9 + 12 = 27

Sum of terms from 4 th to 14 th = 357 - 27 = 330

Answer:

Step-by-step explanation:

If it's any help, these numbers, rearranged in ascending order, are

-5/2, 0, 3/4, 3.

Place a bold dot at -5/2 on your number line.  This is halfway between -2 and -3.  Next, place such a dot at 0.  Next, place a dot at 3/4, which is between 0 and 1 but closer to 1.  Last, place a dot at 3.

Answer:

0.19

Step-by-step explanation:

A correlation coefficient is a measure of how well the line of best fit fits the data.  The higher the correlation coefficient, up to 1.0 or -1.0, the better the fit. A positive correlation coefficient means an increasing data set, while a negative correlation coefficient means a decreasing data set.

We can see that this line of best fit is increasing, so our correlation coefficient will be positive.

However we can also see that the points are fairly scattered; this means this is not a very good fit.  This means that 0.19 is the better fit.

Answer:

Good question! The correct answer is a) increases and b) increases.

While the pair of answers a) decreases and b) decreases or the pair a) stays the same and b) stays the same would be technically correct answers, this is the best way of describing the trend of the scatter plot; typically, trends are described by how the dependent or y-variable responds to the independent or x-variable increasing.

Answer:

a) increases and b) increases.

Step-by-step explanation:

Answer:

Required probability = 2/3

Step-by-step explanation:

When rolling a 6 sided die, the out comes are

1, 2, 3, 4, 5 and 6

Total number of outcomes = 6

To find the probability

The required outcome is a number greater than 2, therefore possible outcomes are,

3, 4, 5, and 6

Number of possible outcomes = 4

Required probability = 4/6 = 2/3

Answer:

Determine the theoretical probability of rolling a number larger than 2 on a standard 6-sided cube.

2/3

Step-by-step explanation:

Answer:

Both obtuse angles - 124°

Both acute angles - 56°

Step-by-step explanation:

The two given obtuse angles are equal. Therefore you get an equation

[tex]9y+7 = 2y+98\\7y=91\\y=13[/tex]

So the obtuse sizes of the two given angles are [tex]13*9+7=2*13+98=124[/tex]°

And the sizes of the acute angles are [tex]180-124=56[/tex]°

Without a clear relationship between the expression (9y+7) and the angle measurement (2y+98)°, we cannot find a unique value for y. However, the measure of the angle would vary with y according to the formula (2y+98)°.

The given expression is (9y+7) and the measure of the angle is (2y+98)°. We aren't given a specific equation that links the expression to the measure of the angle, so we cannot find a unique value for y. However, if a particular relationship between the expression and the measure of the angle is provided, such as them being equal, we can use algebraic methods to solve for y.

As for measures of angles, in general, if we know the value of y, we can substitute that into the (2y+98)° to find the specific angle. Without knowing the value of y or a particular relationship between (9y+7) and (2y+98)°, we can say that the measure of the angle varies with y according to the formula (2y+98)°.

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Answer:

7.5 = 2x + 2.1

Step-by-step explanation:

The perimeter of a triangle is the sum of the sides.  In an isosceles triangle, two sides are the same length.  If x is the length of the two sides and y is the length of the third side, then:

P = 2x + y

Given that P = 7.5 and y = 2.1:

7.5 = 2x + 2.1

Answer: The equation that can be used to find the value of x is

2x + 2.1 = 7.5

Step-by-step explanation: An isosceles triangle is a type of triangle which has two of its sides equal to each other. It also has two it's angles (the base angles) equal to each other.

From the question, the given triangle has the shortest side, y to be 2.1 m. This means side y is shorter than the other two sides. Hence, the other two sides must be the sides that are equal to each other. These other two sides are denoted by x ( see the attachment for an illustrative diagram).

The perimeter of a triangle is the sum of all its sides. Therefore, the perimeter (P) of the given triangle is

P = x + x + y

P = 2x + y

From the question, P = 7.5 m

and y = 2.1 m

Hence,

7.5 m = 2x + 2.1 m

2x + 2.1 m = 7.5 m

This equation can be used to find the value of x. The equation can also be written as:

2x = 7.5 m - 2.1m OR

x = (7.5 m - 2.1m) / 2

Answer:

Q1: D

Q2: D

Step-by-step explanation:

Question No 1:

The given sequence is:

-2, 0, 3, 7, ...

We can easily determine that this is not an arithmetic sequence because the common difference between terms is not same.

i.e.

0-(-2) = 0+2 = 2

3-0 = 3

7-3 = 4

As the common difference is not same so the sequqnce is not an arithmetic sequence.

Question no 2:

Given sequence is:

28, 18, 8, -2, ..

We can see that the common difference is -10 i.e 18-28 = -10

And it is same for all numbers.

The standard formula for arithmetic sequence is:

[tex]a_n=a+(n-1)d\\Here\\a = 28\\d=-10\\So,\\a_n=28+(-10)(n-1)\\a_n=28-10n+10\\a_n=38-10n[/tex]

Now for the 52nd term:

[tex]a_{52} = 38-10(52)\\= 38-520\\=-482[/tex] ..

Answer:

I think the answer is A

Step-by-step explanation:

Answer:

C.

Step-by-step explanation: The other answer was not right on edge* but i belive that it is C.