Find the center, vertices, and foci of the ellipse with equation 2x2 + 8y2 = 16.

A) Center: (0, 0); Vertices: the point zero comma negative two square root two and the point zero comma 2 square root two ; Foci: Ordered pair 0 comma negative square root 6 and ordered pair 0 comma square root 6

B) Center: (0, 0); Vertices: (-8, 0), (8, 0); Foci: Ordered pair negative 2 square root 15 comma 0 and ordered pair 2 square root 15 comma 0

C) Center: (0, 0); Vertices: (0, -8), (0, 8); Foci: Ordered pair 0 comma negative 2 square root 15 and ordered pair 0 comma 2 square root 15

D) Center: (0, 0); Vertices: the point negative square root six comma zero and the point square root six comma zero ; Foci: Ordered pair negative square root 6 comma 0 and ordered pair square root 6 comma 0

Answer:

Step-by-step explanation:

12/24 reduces to 1/2, whereas 3/4 does not reduce.  This pair of ratios does not form a proportion.

If both ratios reduced to the same common value, that would represent a proportion.  

Answer:

Step-by-step explanation:

12/24 reduces to 1/2, whereas 3/4 does not reduce. This pair of ratios does not form a proportion.

If both ratios reduced to the same common value, that would represent a proportion.

Answer:

The distance between the two is:

d=1600km

Hope this helps! :)

Step-by-step explanation:

so, we know A and B left at the same time, one from city A and the other from city B, they're both moving towards each other, and they met in 5hrs.

now, by the time they met, car A has been running for 5hrs already,

and car B has also been running for 5hrs, so the time for both is the same, when they met, each had been running for 5hrs

if B has a speed rate of "r", then A's speed rate is " r - 10"

now, the next to last paragraph

"If the first automobile had left city A 4 1/2 hours earlier than the other automobile left city B, then the two would have met 150 km away from B."

IF, a big if, but they didn't, they left at the same exact time, so that's just an IF

if A had left 4 1/2 hrs earlier, they'd had met 150km from B

so... by the time A had been running already for 4.5 hrs, car B starts off, goes off and they meet 5hrs later, when they meet, car A would have been running for 5hrs, 4.5 + .5 hrs, but car B would had been running for only half an hour when they met

that means car B met car A half an hour later from when it started, and met A 150kms away from its starting point

that means car B can cover 150km in just half an hour

that gives us a speed rate of 150/.5  

which is 300kmh

now, if car B is 300kmh, car A has r-10, or 300-10, or 290kmh

so, car A's rate is really just 290

now, let's say the total distance is AB

so, by the time car A had been running for 5hrs, it had covered a distance of "d"

by the time car B had been running for 5hrs, it had then covered the slack, or " AB - d "

I am pretty sure it is x^2 - 37x

but i am not completely sure

Answer:

1/4

Step-by-step explanation:

So, we can create this representation of a in relation with b, since we know a is smaller than b by 1/5 of b, we can say that a is equal to 4/5 of b, right?

[tex]a = \frac{4}{5} b[/tex]

To invert the ratio, we need to isolate B, so we multiply both sides of the equation by 5/4

[tex]a * \frac{5}{4} = * \frac{5}{4} * \frac{4}{5} b = b\\ \\ b = \frac{5}{4} a[/tex]

So, we have b being 1/4 bigger than a.

Answer:

113

Step-by-step explanation:

area of a trapezoid: 1/2 (A+B)h

A is base 1 and B is base 2; h is height

so we have two trapezoids; we just need to add them together

trapezoid 1: ((7+14) x 6)/2

21 x 6 = 126/2 = 63

trapezoid 2: ((10+10) x 5)/2

20 x 5 = 100/2 = 50

50 + 63 = 113

The original area of the garden is 1,000 square feet. When the garden is reduced to 2/5 of its original size, the new area becomes 400 square feet. Therefore, the scale of the new drawing is 2:5.

The original area of the rectangular garden is 100 feet by 10 feet which equals 1,000 square feet. Next season, the garden is decreased to 2/5 of its size. To find the new area of the garden, you multiply the original area by 2/5.

1,000 square feet * 2/5 = 400 square feet.

Therefore, the size of the garden is reduced to 400 square feet which reflects a scale of 2:5 (2 represents the new size, 5 represents the original size) in the new drawing.

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The scale of the new drawing after the garden is decreased to 2/5 of its original size is 2/5.

In this problem, we are given the dimensions of a rectangular garden: 100 feet by 10 feet. We need to find the scale of the new drawing after the garden is decreased to 2/5 of its original size.

To find the scale, we can use the proportionality of the areas to the squares of the distances. The original area of the garden is 100 feet * 10 feet = 1000 square feet.

When the garden is decreased to 2/5 of its original size, the new area becomes 1000 square feet * 2/5 = 400 square feet.

In terms of the scale, the new area is 400 square feet, which is 2/5 of the original area. Therefore, the scale is 2/5.

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Answer:

8

Step-by-step explanation:

2+6+8+12+12 is 40 divide that by 5 and it gives you 8

Answer:

c

Step-by-step explanation:

Since it's a rectangle, then the X will be -1 and 1, and the area is 10 square units, as now there are 6 already from 0 to AB, so to add 4 more, so the answer would be C

Answer: Bentley got $20 for her allowance.

Step-by-step explanation: linear increase would be something added to an equation.

 she started with 40,

she spent 10 on flip flops and also spent 15 of sunglasses those are decreases

she added 20 for allowance which is an increase and we can assume she gets the same amount of allowance every week

 so that would be the linear increase

The linear increasing interval in Bentley's financial scenario is when she receives her $20 allowance, which adds to her total amount of money

The part of the scenario that is best represented by a linear increasing interval is when Bentley got $20 for her allowance. A linear increasing interval on a graph shows quantities that are increasing over time. In Bentley's case, her total amount of money increases from whatever she had left after buying the flip-flops, by $20, when she receives her allowance. This is the only instance in the described activities where her total monetary amount increases

Answer:

Yes, because these widths result in a positive value for area.

Step-by-step explanation:

in imagine math it is c or the bottom left one for me

The question involves using a quadratic function to model the area of a rectangle with a given perimeter. The function is not applicable to a width of 100 feet since it exceeds the logical constraints of the rectangle's perimeter.

The student is asking about determining the dimensions of a rectangular area given a fixed perimeter and using a function to find the area for a given width, w. The function provided, A(w)=24w−w^2, is a quadratic function that models the area of a rectangle with a fixed perimeter of 144 feet. When the width is defined as w=100 feet, we cannot use this particular function to find the area because it would imply an unrealistic negative length for the remaining side, given the fixed perimeter constraint. Therefore, the function can only model the situation over the interval where 0 < w < 24, as the width must be less than half of the perimeter for a rectangle.

The mean weight of the chocolate candies is 0.918 grams, the median weight is 0.913 grams, and the mode (most frequent weights) are 0.957 grams and 0.911 grams.

First, let's add all these values of the weights of the chocolate candies up and then divide by the number of observations to find the mean. The total sum is 13.957, and there are 24 observations. So, the mean value is 13.957/24 = 0.918 grams.

Next, we arrange the values in ascending order to find the median. The middle two values in this data set are both 0.913, so the median is 0.913 grams.

Finally, to find the mode we look for the value that occurs most frequently in the data set. Here we see that the numbers 0.957 and 0.911 both appear twice, therefore, our data set has two modes: 0.957 and 0.911 grams.

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Answer:

12

Step-by-step explanation:

The correct answer is 12

yes It has at least one set of parallel lines

C is gonna be your answer here

The correct answer is C.

I would like to answer all the questions.

Hope I can help.

2x-10=2. (Answer=6)

2x=12 (you move the -10 to the other side of the equation to make it positive)

Then you divide by 2

2x divided by 2 equals x 12 divided by 2 is 6

So your number is 6. x=6

And you can check this by redoing the equation but putting 6 instead of x

2(6)-10=2

12-10=2

2=2

This equation is true therefore, your unknown number is 6

Final answer:

The problem is solved by setting up an equation where the larger number (2x) is diminished by 10 equals the smaller number (x) plus 2. Solving for x reveals that the smaller number is 12 and the larger number is therefore 24.

Explanation:

Let's denote the smaller number as x and the larger number as 2x since one number is twice another number. The problem states that if the larger number is diminished by 10, the result, which is 2x - 10, is 2 more than the smaller number. Therefore, we can write the equation:

2x - 10 = x + 2.

To solve for x, we first add 10 to both sides of the equation:

2x = x + 12.

Then, we subtract x from both sides:

x = 12.

Now that we know the smaller number is 12, the larger number is twice that, which means the larger number is 24.

In conclusion, the two numbers in question are 12 and 24.

Answer:

The mean shall be 10.67 and the standard deviation shall be 6.09

Step-by-step explanation:

There are calculators online that can help u with problems like these :)

Answer:

True

Step-by-step explanation:

The formula for an area of a circle is a = pi times radius squared

Answer:

True.

Step-by-step explanation:

To calculate the area of a circle you have to use the formula Area = PI times radius squared.

Answer:

The correct answer is D) f(x) = (x^2 - 2)/3

Step-by-step explanation:

To find an inverse function, swap x and f(x) and then solve for the new f(x). That will be the new inverse function.

f(x) = √3x+2

x = √3f(x)+2

x - 2 = √3f(x)

x^2 - 2 = 3f(x)

(x^2 - 2)/3 = f(x)

Answer:

(x - 4)(x - 12)

Step-by-step explanation:

Note that 4(12) = 48 and that 4 + 12 = 16.  Thus, we can surmise that

x² - 16x + 48 = (x - 4)(x - 12).

Answer:

The answer is A

Step-by-step explanation:

for edge

Answer:

C

Step-by-step explanation:

Anything on quadrants II and III have a X value less than 0. This includes points C, D, and J which is answer choice C.

Answer:

C

Step-by-step explanation:

The X-Axis runs horizontally from left to right. The y-axis runs up and down. X coordinates to the left of the y-axis are negative, because the origin, where the two lines intersect, is 0,0.

Answer:

(-4, 4)

Step-by-step explanation:

The solution of f(x) - g(x) = 0 is the same as that of f(x) = g(x).

If f(x) = g(x), that implies that the two graphs cross one another.

The point of intersection is (-4, 4).  This is the solution.

Answer:

D

Step-by-step explanation:

The horizontal asymptote is found by considering the ratio of the coefficients of the highest degree terms on the numerator and denominator, that is

coefficient of 6x² on the numerator ⇒ 6

coefficient of 9x³ on the denominator ⇒ 9

The horizontal asymptote is

y = [tex]\frac{6}{9}[/tex] ⇒ y = [tex]\frac{2}{3}[/tex] → D

The student's question seems to involve solving for x in an equation involving 64 and 42. However, specific details necessary for doing so are missing. Example solutions are provided for x in equations x + 64 = 42 and 42 = 64 - x.

The question seems to be asking you to solve an equation where x is unknown, but there are no other specifics given. It's unclear what the relationship is between x, 64, and 42. However, I'll give an example of how x could be solved in an equation. If you had an equation such as x + 64 = 42, you would rearrange this to find that x = 42 - 64, which means x = -22.

However, in a different equation, x might be found in a different manner. For example, if you have the equation 42 = 64 - x, you rearrange to find x = 64 - 42, so x = 22. This all depends on the equation given, which isn't clear in this case.

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Answer:

(1/2, ∞ ).  This corresponds to Answer B

Step-by-step explanation:

Important:  enclose that negative exponent (-2/3) inside parentheses:

1/3e^(x- 2/3) + 1/2

and also that coefficient, 1/3:

(1/3)e^(x- 2/3) + 1/2

The range of the exponential function y = e^x is (0, ∞ ); that is, y is always positive, never zero or negative.  

The function of that "1/2" is to shift the entire graph 1/2 unit up.

Thus, the range   (0, ∞ )  becomes  (1/2, ∞ ).  This corresponds to Answer B.

Answer:

Answer is B for plato or edmentum

Step-by-step explanation:

she could feed 20 people. To find the answer put 22/8 simplify to get 11/4 then multiply by 5/5

Answer:

22/8 simplify to get 11/4 then multiply by 5/5

Step-by-step explanation:

[tex] \frac{8}{7} = 114\%[/tex]

A faction who's numerator is larger than it's denominator will always produce an equivalent percentage larger than 100%

Answer:

x = 5/2 or 2.5

Step-by-step explanation:

1/4x = 5/8

To find the value of X;

We multiply both sides by 4

1/4 x × 4 = 5/8 × 4

 x = 5/2 or 2.5

To solve the problem we must know about fractions.

A fraction is a way to describe a part of a whole. such as the fraction [tex]\dfrac{1}{4}[/tex] can be described as 0.25

The value of x is [tex]\bold{\dfrac{5}{2}}[/tex] or 2.5.

Given to us,

To remove the denominator from the x side, we multiply both sides of the equation with the denominator of x.

[tex]{\dfrac{1}{4}\times x \times 4\ =\ \dfrac{5}{8} \times 4}[/tex]

Canceling the values we get,

[tex]1 \times x = \dfrac{5}{2}[/tex]

[tex]x = \dfrac{5}{2}[/tex]

Thus, the value of x is  [tex]\bold{\dfrac{5}{2}}[/tex] ,further we can simplify by dividing 5 by 2 and we will get 2.5 as the result.

Hence, the value of x is [tex]\bold{\dfrac{5}{2}}[/tex] or 2.5.

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Answer:  a) 8%

               b) 34%

               c) 12%

Step-by-step explanation:

[tex]a)\quad \dfrac{January\ Clothing}{January\ Payments}=\dfrac{234.75}{2800.00}=0.083\implies \large\boxed{8\%}\\\\\\b)\quad \dfrac{January\ Housing}{January\ Payments}=\dfrac{945.20}{2800.00}=0.337\implies \large\boxed{34\%}\\\\\\c)\quad \dfrac{January\ Transportation}{January\ Payments}=\dfrac{347.46}{2800.00}=0.124\implies \large\boxed{12\%}[/tex]

Answer:

x = -8(y - 5)² + 3

Step-by-step explanation:

When info about focus and directrix is given, we want to use the standard equation of a parabola x - h = 4p(y - k)^2.  

p is the signed distance between focus and vertex (or that between directrix and vertex).  Here the directrix, x = 7, lies to the right of the vertex, (3, 5), which indicates that this horizontal parabola opens to the left.  The total vertex to directrix distance is 7 - 3, or 4; dividing this result by 2 results in 2; thus p = -2 (a signed distance).  

Now we substitute the given and calculated info into the equation

x - h = 4p(y - k)^2:

x - 3 = 4(-2)(y - 5)², or

x - 3 = -8(y - 5)², or x = -8(y - 5)² + 3

Answer:

[tex](y-5)^2=8(x-5)[/tex]

Step-by-step explanation:

We are given that the focus of a parabola is (3, 5) and the directrix is x = 7.

The y-coordinate of the vertex should be same as the focus (k = 5). So the x-coordinate of the vertex would be:

p + (3) =  7 - p

2p = 7 - 3

p = 4/4

p = 2

The x-coordinate of the vertex would be:

h= p + (3)

h = 2 + 3

h = 5

The vertex coordinate would be: (h, k) = (5, 5)

For a vertex (h, k), the formula for equation would be  

[tex](y-k)^2=4 p(x-h)[/tex]

[tex](y-5)^2=4 \times 2(x-5)[/tex]

[tex](y-5)^2=8(x-5)[/tex]

Answer:

140 pigs and 120 cows

Step-by-step explanation:

20+50=70

70x2=140(number of pigs)

140-20=120(number of cows)