What is the standard form of an ellipse with foci at (0, ±2), and vertices at (0, ±4)?

In the equation 2.5x + 2y = 225, the term 2.5x represents the cost of dried fruit, with 2.5 being the cost per pound.

In the provided equation 2.5x + 2y = 225, where x stands for the pounds of dried fruit and y represents the pounds of nuts, the term 2.5x signifies the cost associated with the dried fruit in making the trail mix.

The coefficient 2.5 represents the cost per pound of dried fruit, which is $2.50. Therefore, multiplying the pounds of dried fruit (x) by the cost per pound (2.5) gives the total cost of the dried fruit in the trail mix. In essence, 2.5x calculates the financial contribution of the dried fruit to the overall cost of producing the trail mix.

For example, if there are 10 pounds of dried fruit (x = 10), then 2.5 times 10 equals 25, representing the cost, in dollars, of the dried fruit in the trail mix. This interpretation extends to any quantity of dried fruit used in the trail mix.

In summary, the term 2.5x in the equation 2.5x + 2y = 225 specifically denotes the cost associated with the pounds of dried fruit (x) used in producing the trail mix.

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The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b).

We have the points (4, -5) and (0, -2) → y-intercept → b = -2.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute:

[tex]m=\dfrac{-2-(-5)}{0-4}=\dfrac{-2+5}{-4}=\dfrac{3}{-4}=-\dfrac{3}{4}[/tex]

Therefore we have the equation of a line

[tex]y=-\dfrac{3}{4}x-2[/tex]

Convert to the standard form: [tex]Ax+By=C[/tex]

[tex]y=-\dfrac{3}{4}x-2\qquad\text{multiply both sides by 4}\\\\4y=-3x-8\qquad\text{add 3x to both sides}\\\\\boxed{3x+4y=-8}[/tex]

So for this, I will be putting the equation into slope-intercept form then rearranging it into standard form. Firstly, we need to solve for the slope. To do this, take the 2 coordinates given to us and solve as such:

[tex]\frac{-5-(-2)}{4-0}=-\frac{3}{4}[/tex]

Now, one of the coordinates given to us is (0,-2), which is the y-intercept. With all this info, our slope-intercept equation is [tex]y=-\frac{3}{4}x-2[/tex] . From here we can solve for the standard form.

Firstly, add 3/4x onto both sides of the equation:

[tex]\frac{3}{4}x+y=-2[/tex]

Now, it may appear that we are finished. However, 3/4 is not an integer (Integers are whole numbers). To make it an integer, we need to multiply both sides by 4:

[tex]3x+4y=-8[/tex]

In short, the standard form of this equation is 3x + 4y = -8.

162

... (total paving stones) / bricks = 5 / 2

Multiplying by bricks gives ...

... (total paving stones) = (5/2)·bricks = 5/2·120 = 300

Then the number of gray paving stones is ...

... (gray stones) = (total paving stones) - (tan stones) . . . . tan + gray = total

... = (total paving stones) - 46% · (total paving stones) . . . . tan is 46% of total

... = (100% - 46%)·(total paving stones) = 54% · (total paving stones)

... = 54/100 · 300 . . . . put in the total number of paving stones

... (gray stones) = 162

Answer: 162

Step-by-step explanation:

Answer: 140 Hot dogs and 83 sodas.

Step-by-step explanation:

Alright, so we will say that h = hot dogs and s = sodas.

h + s = 223

I have used the guess and test strategy to get:

h = 140

140 - 57 = 83

s = 83

Check: 83 + 140 = 223

Answer:

(-10, 0) , (-4, 0)

Step-by-step explanation:

[tex]\text{We know that the parabola is given by the quadratic equation.}\\\text{let the general equation of the parabola is}\\\\y=a(x-h)^2+k, \text{ where (h, k) is the vertex of the parabola.}\\\\\text{here we have given that vertex, }(h,k)=(-7,45), \text{ so above equation gives}\\\\y=a(x-(-7))^2+(45)\\\\y=a(x+7)^2+45\\\\\text{now this parabola has y-intercept at }(0,-200), \text{ so with this point}\\\text{above equation gives}[/tex]

[tex]-200=a(0+7)^2+45\\\\\Rightarrow -200=49a+45\\\\\Rightarrow 49a=-245\\\\\Rightarrow a=-\frac{245}{49}=-5\\\\\text{so the equation of the parabola is}\\\\y=-5(x+7)^2+45[/tex]

[tex]\\\text{Now to find the x-intercepts, we set }y=0, \text{ so we get}\\\\-5(x+7)^2+45=0\\\\\Rightarrow -5(x+7)^2=-45\\\\\Rightarrow (x+7)^2=\frac{-45}{-5}\\\\\Rightarrow (x+7)^2=9\\\\\Rightarrow (x+7)=\pm \sqrt{9}\\\\\Rightarrow x+7=\pm 3\\\\\Rightarrow x=-7\pm 3\\\\\Rightarrow x=-7-3, \text{ and } x=-7+3\\\\\Rightarrow x=-10, \text{ and } x=-4\\\\\text{so x-intercepts of parabola occur at: }(-10,0), \text{ and }(-4,0)[/tex]

Answer:

11 feet wood will tenly use to make the frame.

Step-by-step explanation:

As given

Tey is making a square frame for her painting.

She is using 4 pieces of wood that are each 2.75 feet long.

Tenly uses wood to make the frame = Number of pieces of wood × Length of each pieces

Here

Number of pieces of wood = 4

Length of each pieces = 2.75 feet

Put in the above

Tenly uses wood to make the frame = 4 × 2.75

                                                             = 11 feet

Therefore 11 feet wood will tenly use to make the frame.

Answer:

The answer is C

Step-by-step explanation:

I just answered it on edg

The second step is

2.5 (42 ÷ 3.2 – 2 + 3) - 5.2

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Step 1:

2.5 (42 ÷ 3.2 – 10(0.2) + 3) - 5.2

Step 2:

2.5 (42 ÷ 3.2 – 2 + 3) - 5.2

Step 3:

2.5 (13.125 + 1) - 5.2

Step 4:

2.5 (14.125) - 5.2

Step 5:

35.3125 - 5.2

Step 6:

30.1125

Thus,

The value of the expression is 30.1125.

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Answer:

The answer is: undefined or infinite

Hope this helps.

We can use the points (-1, 3) and (-1, 1) to solve.

Slope formula: y2-y1/x2-x1

= 1-3/-1-(-1)

= -2/0

= 0

This line is straight so it's undefined.

Hope This Helped! Good Luck!

Answer:

y = 0x + 9

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

here m = 0 and c = 9, hence

y = 0x + 9

The equation of a horizontal line is normally written as y = 9

with the x- term omitted

The equation of a line with a slope of 0 and a y-intercept of 9 is y = 9, which represents a horizontal line on the graph.

The student is asking about the equation of a line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Given that the slope (m) is 0, and the y-intercept (b) is 9, the equation of the line is simply y = 0x + 9. Since any number multiplied by zero is zero, this simplifies to y = 9.

Therefore, the equation of the line with a slope of 0 and a y-intercept of 9 in slope-intercept form is y = 9. This represents a horizontal line that crosses the y-axis at 9.

Answer:

B) cos 55

Step-by-step explanation:

Consider a right angle triangle with 35 angle, the other angle = 180 - 90 - 35 = 55

sin 35 = opposite side of 35 angle / hypothesis

Opposite side of 35 angle is the same as the adjacent side of 55 angle

sin 35 = adjacent side of 65 angle / hypothesis = cos 55

The answer is B.

Answer:

2/9

Step-by-step explanation:

Answer:

1 foot = 0.305 meters.

Convert 1 meter to feet:

1 meter = 1/0.305 = 3.28 feet

Find the weight in pounds per meter:

5 pounds x 3.28 feet = 16.4 pounds per meter.

Convert pounds per meter to kilograms per meter:

16.4 pounds x 0.454 kilograms per pound = 7.44 kg/m

y-y1 = m(x-x1) ..... point slope form

y-2 = -4(x-1) ... plug in the given info; solve for y

y-2 = -4x+4

y = -4x+4+2

y = -4x+6

Answer is choice C

Answer:

C.   y = -4x + 6

Step-by-step explanation:

First write it in point-slope form ( because that is what you are given):-

y - y1 = m(x - x1):-

y - 2 = -4(x - 1)

y - 2 = -4x + 4

y = -4x + 6 (answer)

The equation of the line parallel to the graph of 14x - 7y = 1 that passes through the point at (-2, 4) is y = 2x + 8. The correct option is C.

To find the equation of the line parallel to the graph of 14x - 7y = 1 that passes through the point at (-2, 4), we first need to determine the slope of the given line. We can write the given equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Starting with 14x - 7y = 1, we solve for y:

The slope of the original line is 2, so a line parallel to it will also have a slope of 2. Using the point-slope form of a line equation, y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex]), and the point (-2, 4), we get:

Therefore, the equation of the line parallel to 14x - 7y = 1 and passing through (-2, 4) is y = 2x + 8.

Complete Question:

Find the equation of the line parallel to the graph of 14x-7y=1 that passes through the point at (-2,4).

Select the correct response:

[tex]\begin{aligned}A) \:& y=2 x+3 \\B)\: & y=\frac{1}{2} x+3 \\C) \:& y=2 x+8 \\D) \:& y=-\frac{1}{2} x-3\end{aligned}[/tex]

Answer: 15

from what i believe

Step-by-step explanation: i did the math that i thought it was and i did 240 divided by 16 and i got 15 hope this helps.

Answer:

1

Step-by-step explanation:

(x +3) appears only once as a factor, hence the multiplicity of the root x=-3 is 1.

Answer:

19

Step-by-step explanation:

The ratio of green beans (g) to pumpkin (p) is ...

... g : p = 1 : 5

Then the ratio of green beans to the total is ...

... g : (g+p) = 1 : (1+5) = 1 : 6

Since you have

... g/total = (1/6)

... g = total · 1/6

you can substitute 114 for the total to find ...

... g = 114 · 1/6 = 19

Answer: $1.25 decrease

Step-by-step explanation:

I am not positive but I think this is how you calculate it:

 (.25)($10) + (.75)(-$5)

= $2.50      +    -$3.75

= -$1.25

Answer:

The hyperbolas which open horizontally are:

(x+2)^2/3^2-(2y-10)^2/8^2=1

(x-1)^2/6^2-(2y+6)^2/5^2=1

Step-by-step explanation:

A hyperbola with equation of the form:

(x-h)^2/a^2-(y-k)^2/b^2)=1 opens horizontally

Then, the hyperbolas which open horizontally are:

(x+2)^2/3^2-(2y-10)^2/8^2=1

(x-1)^2/6^2-(2y+6)^2/5^2=1

Answer:

[tex]\frac{(x-2)^2}{3^2}-\frac{(2y-10)^2}{8^2}=1[/tex]

and

[tex]\frac{(x-1)^2}{6^2}-\frac{(2y+6)^2}{5^2}=1[/tex]

Step-by-step explanation:

There are 2 types of hyperbolas:

Horizontal:

[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]

Vertical:

[tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex]

If the x term is positive then parabola is horizontal.

If the y term is positive then parabola is vertical.

so, only first two equations are in which x term is positive.

hence, equations are

[tex]\frac{(x-2)^2}{3^2}-\frac{(2y-10)^2}{8^2}=1[/tex]

and

[tex]\frac{(x-1)^2}{6^2}-\frac{(2y+6)^2}{5^2}=1[/tex]

If you mean the y coordinate of that line, then it would be negative because it goes through -4 on the y axis.

Answer:

We are given that there are total 170 toy robots

Number of defective robots out of total 170 toy robots [tex]=20[/tex]

We have to find the percentage of toy robots that are disaffected.

The percentage of toy robots that are disaffected is given below:

[tex]\frac{20}{170} \times 100[/tex]

[tex]0.1176 \times 100[/tex]

[tex]11.76[/tex]

Therefore, the percent of toy robots that are disaffected is [tex]\bold{11.76\%}[/tex]

Answer:

591

Step-by-step explanation:

the closest number to 600 out of every combo

195

159

951

915

519

591

Answer: 591

Step-by-step explanation:

From the digit 1, 9 and 5. The following numbers can be gotten if we use the 3 numbers.

159

195

519

591

915

951

Of all the numbers, the closest to 600 are 519 and 591.

To the nearest 100, 519 gives 500 while 591 gives 600. Therefore, the answer is 591.

Answer:

42

Step-by-step explanation:

The median is 29 . The third quartile is the middle number of the last 5 numbers.

This is 42

Answer:

42

Step-by-step explanation:

We are given that a data set

20,21,24,25,28,29,35,37,42,43,44

We have to find the value of third quartile of the given data set.

To find the third quartile we will use the given below formula

[tex]Q_3=\frac{3}{4}\times (n+1)^{th} term[/tex]

Where n=Total number of term

We have n=11

By using the formula

[tex]Q_3=\frac{3}{4}\times (11+1)^{th}[/tex] term

[tex]Q_3=9^{th}[/tex] term

[tex]9^{th}[/tex] term=42

Hence, third quartile=42

The formula of a volume of a rectangle prism:

[tex]V=lwh[/tex]

l - length

w - width

h - height

We have

[tex]l=n^2+2;\ w = 10,\ h=n+5[/tex]

Substitute:

[tex]V=(n^2+2)(10)(n+5)=(10n^2+20)(n+5)\\\\=(10n^2)(n)+(10n^2)(5)+(20)(n)+(20)(5)\\\\=10n^3+50n^2+20n+100[/tex]

The volume of the aquarium in terms of n is calculated by multiplying its length (n2 +2 inches), width (10 inches), and height (n + 5 inches) giving the formula V = (n2 + 2)  imes (n + 5)  imes 10, which expands to V = 10n3 + 60n2 + 20n + 100 cubic inches.

We use the formula V = length  times width  times height, where the volume V is the space inside the aquarium. The question provides the dimensions of the aquarium in terms of n: the length (n2 +2 inches), height (n + 5 inches), and width (10 inches).

To calculate the volume, simply multiply the dimensions together:

Volume, V = (n2 + 2)  imes (n + 5)  imes 10

Expanding the expression gives us the volume V in cubic inches as a function of n:

V = 10n3 + 60n2 + 20n + 100 cubic inches

Answer:

the length is 5 times the width of the prism

Step-by-step explanation:

the volume of this rectangular prism is [tex]5x^3[/tex]

volume of the prism = length * width * height

Length of the prism = 5x

Width = x

height =x

Length of the prism = 5x = 5* width of the prism

So, the length is 5 times the width of the prism

The largest interior diameter of the new pipe that would still fit inside the old one is 0.38 inches, after taking into account the thickness of the plumbing tape and additional space requirement.

The plumber is attempting to fit a new pipe into an old pipe with an interior diameter of 0.63 inches. We need to take into account the thickness of the plumbing tape that will add an extra 0.15 inches to the diameter, as well as the requirement that the new pipe must be 0.1 inches smaller to fit inside the old pipe.

To calculate the largest interior diameter the new pipe can have, we should do the following:

So, the largest interior diameter of the new pipe that will fit in the old one is 0.38 inches.

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3. Answer: y = 4

Step-by-step explanation:

Need to find the slope (m):

  [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

  [tex]\dfrac{4 - 4}{-3-1}[/tex]

= [tex]\dfrac{0}{-4}[/tex]

= 0

Now input ONE of the points (1, 4) and the slope (m = 0) into the Point-Slope formula:

y - y₁ = m(x - x₁)

y - 4 = 0(x - 1)

y - 4 = 0

y      = 4

********************************************************************

4. Answer: [tex]\bold{y = \dfrac{2}{3}x + 3}[/tex]

Step-by-step explanation:

 [tex]y - y_1 = m(x - x_1)[/tex]

 [tex]y - 1 = \dfrac{2}{3}(x - (-3))[/tex]

 [tex]y - 1 = \dfrac{2}{3}(x + 3)[/tex]

 [tex]y - 1 = \dfrac{2}{3}x + 2[/tex]

 [tex]y = \dfrac{2}{3}x + 3[/tex]

Answer:

B

Step-by-step explanation:

The expected value of profit margin is the sum of the product of profit margin and probability.

Wrench A:

... 10×.05 +20×.6 +30×.2 +40×.15 = 0.5 +12 +6 +6 = 24.5

Wrench B:

... (20+40)×.3 +(30+50)×.2 = 18 +16 = 34

Wrench C:

... 15×.4 +30×.5 +(45+60)×.05 = 6 +15 +5.25 = 26.25

Wrench D:

... 5×.2 +10×.4 +15×.15 +20×.25 = 1 +4 +2.25 +5 = 12.25

___

Clearly, Wrench B has the greatest expected profit margin. That would be the one Jose should order if he's trying to maximize his profit.

The formula:

[tex]\theta=\dfrac{\theta\pi}{180}[/tex]

We have

[tex]\theta=453[/tex]

Substitute:

[tex]453^o=\dfrac{453\pi}{180}=\dfrac{453\pi:3}{180:3}=\dfrac{151\pi}{60}\to\boxed{B)}[/tex]

The conversion of 453° into radians is 151π/60.

The angle made by taking the radius and wrapping it round the circle.

Given that, 453°

To convert any degree into radians, we multiply by π/180

453*π/180 = 151π/60

Hence, The conversion of 453° into radians is 151π/60.

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Answer:

It should be A, $12.75

Step-by-step explanation: Add 10.5+10.5+10.5+4.5+4.5+6.75= $47.25, subtract 60-47.25= $12.75