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An ellipse is represented using the equation . Where are the foci of the ellipse located? Check all that apply.

(−29, 7)

(19, 7)

(−21, 7)

(13, 7)

(−5, −17)

(−5, 31)

EQUATION:

Answer:

D

Step-by-step explanation:

Given the 2 equations

y = x² - 2 → (1)

y = - 2x + 1 → (2)

Substitute y = x² - 2 into (2)

x² - 2 = - 2x + 1 ( subtract - 2x + 1 from both sides )

x² + 2x - 3 = 0 ← in standard form

(x + 3)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 1 = 0 ⇒ x = 1

Substitute these values into (2) for corresponding values of y

x = - 3 : y = -2(- 3) + 1 = 6 + 1 = 7 ⇒ (- 3, 7 )

x = 1 : y = - 2(1) + 1 = - 2 + 1 = - 1 ⇒ (1, - 1 )

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=x^2-2&(1)\\y=-2x+1&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\x^2-2=-2x+1\qquad\text{add 2x to both sides}\\x^2+2x-2=1\qquad\text{subtract 1 from both sides}\\x^2+2x-3=0\\x^2+3x-x-3=0\\x(x+3)-1(x+3)=0\\(x+3)(x-1)=0\iff x+3=0\ \vee\ x-1=0\\\\x+3=0\qquad\text{subtract 3 from both sides}\\x=-3\\\\x-1=0\qquad\text{add 1 to both sides}\\x=1\\\\\text{put the value of x to (1):}\\\\for\ x=-3\\y=(-3)^2-2=9-2=7\\\\for\ x=1\\y=1^2-2=1-2=-1[/tex]

Answer:

The rule is y = 4x - 5.

Step-by-step explanation:

Notice that if we start with x = 1 and increase x by 1, we get 2.  Simultaneously, y starts with -1 and becomes 3.  Thus, the slope is m = rise / run = 4/1, or 4.

The rule is y = 4x - 5.

Check:  Suppose we pick input 4 from the table. Does this rule produce output 11?  Is 11 = 4(4) - 5 true?  YES.

Answer:

y = 4x - 5

Step-by-step explanation:

Have you been taught to set up 2 equations and 2 unknowns?

That is actually the only way I could do this.

y = mx + b

x = 2

y = 3

3 = 2m + b

x = 1

y = -1

-1 = m + b        Multiply by 2. That means that the m term will cancel.

================

-2 =2m +2b    

3 = 2m + b        Subtract

-5 = b

==================

3 = 2m + b       Substitute - 5 for b

3 = 2m - 5        Add 5 to both sides.

3+5= 2m-5+5   Combine

8 = 2m               Divide by 2

8/2=2m/2

m = 4

Answer:

B- Mean

Step-by-step explanation:

When the variation is smaller it means that there are no large outliers. When there are large outliers the mean inctease. since you are decreasing the variation the mean would decrease.

The intersection of the solution set consists of the elements that are contained in all the intervals. -8 ≤ x < 6.

Solving compound inequalities.

A compound inequality is the joining of two or more inequalities together and they are united by the word (and) or (or). In the given compound inequality, we have:

7x ≥ - 56 and 9x < 54.

Solving the compound inequality, we have;
7x ≥ - 56

Divide both sides by 7

[tex]\dfrac{7x}{7} \geq \dfrac{56}{7}[/tex]

x ≥ 8

Also, 9x < 54

Divide both sides by 9.

[tex]\dfrac{9x}{9} < \dfrac{54}{9}[/tex]

x < 6.

Therefore, the intersection of the solution set consists of the elements that are contained in all the intervals. -8 ≤ x < 6

Answer:

233.33 %.

Step-by-step explanation:

The increase is 10 - 3 = 7c.

Percentage increase =  100 * 7 / 3.

= 700 / 3

=  233.33 %.

The cost of a first-class postage stamp increased approximately 233.33% from 1917 to 1974.

To calculate the percent increase in the cost of a first-class postage stamp from 1917 to 1974, follow these steps:

Thus, the percent increase in the cost of a first-class postage stamp from 1917 to 1974 is approximately 233.33%.

Answer:

B

Step-by-step explanation:

Given the 2 equations

y = 2x² - 5x - 7 → (1)

y = 2x + 2 → (2)

Since both equations express y in terms of x we can equate the right sides, that is

2x² - 5x - 7 = 2x + 2 ( subtract 2x + 2 from both sides )

2x² - 7x - 9 = 0 ← in standard form

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 9 = - 18 and sum = - 7

The factors are + 2 and - 9

Use these factors to split the x- term

2x² + 2x - 9x - 9 = 0 ( factor the first/second and third/fourth terms )

2x(x + 1) - 9(x + 1) = 0 ← factor out (x + 1) from each term

(x + 1)(2x - 9) = 0

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

2x - 9 = 0 ⇒ 2x = 9 ⇒ x = 4.5

Substitute these values into (2) for corresponding values of y

x = - 1 : y = (2 × - 1) + 2 = - 2 + 2 = 0 ⇒ (- 1, 0)

x = 4.5 : y = (2 × 4.5) + 2 = 9 + 2 = 11 ⇒ (4.5, 11)

Solutions are (4.5, 11) and (- 1, 0)

Answer:

(-1, 0) , (4.5,  11). (the second choice).

Step-by-step explanation:

y = 2x^2 - 5x - 7

y = 2x + 2

Since both right side expressions are equal to y we can equate them.

2x^2 - 5x - 7 = 2x + 2

2x^2 - 7x - 9 = 0

(2x - 9)(x + 1)

x = 4.5 , -1.

Substituting these values of x in the second equation:

When x = -1 , y =2(-1) + 2 = 0.

When x = 4.5, y =  2(4.5) + 2 = 11.

Answer:

[tex]\frac{3}{5}[/tex]

Step-by-step explanation:

To find the slope, all we need is to points on the line.

Judging by that graph, we can see a point at (0,1) and at (5,4).

Simply enter this into the slope formula and you'll have your slope.

[tex]\frac{y2-y1}{x2-x1}[/tex]

Your y1 term is 1, your y2 term is 4.

Your x1 term is 0, your x2 term is 5.

[tex]\frac{4-1}{5-0} \\\\\frac{3}{5}[/tex]

Your slope is [tex]\frac{3}{5}[/tex].

Answer:

[tex]\large\boxed{\dfrac{3}{5}}[/tex]

Step-by-step explanation:

Look at the picture.

The formula of a slope:

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

From the graph we have two points (0, 1) and (-5, -2).

Substitute:

[tex]m=\dfrac{-2-1}{-5-0}=\dfrac{-3}{-5}=\dfrac{3}{5}[/tex]

Answer:

{2, 3, √13}  

Step-by-step explanation:

In a right triangle, the sum of the squares of the two shorter sides equals the square of the third side (Pythagoras).

Let's check each set of sides in turn.

A. {2, 3, √13}

2² + 3² = 4 + 9 = 13

(√13)² = 13

This is a right triangle.

B. {5, 5, 2, √10}

This is a quadrilateral (four sides).

C. {5, 12, 15}

5² + 12² = 25 +144 = 169

15² = 225

This is not a right triangle.

Answer:

A. 18

Step-by-step explanation:

Median of a trapezoid: Its length equals half the sum of the base lengths.

So the sum of the lengths is 15 + 21 is 36 and half is 18.

18 inches long of a cut will John need to make so that he cuts the tiles along the median.

Given that, the top base of each tile is 15 inches in length and the bottom base is 21 inches.

The median of a trapezoid is the segment that connects the midpoints of the non-parallel sides.

The length of the median is the average of the length of the bases.

Now, add the top base and bottom base,

That is 15+21=36.

Now, divide that by 2

That is, 36/2= 18 inches.

Hence, the answer would be 18 inches.

Learn more about trapezoid visit:

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For this case we must resolve the following expression:

[tex]6 + 2 ^ 3 * 3 =[/tex]

For the PEMDAS evaluation rule, the second thing that must be resolved are the exponents, then:

[tex]6 + 8 * 3 =[/tex]

Then the multiplication is solved:

[tex]6 + 24 =[/tex]

Finally the addition and subtraction:

30

Answer:

30

Answer:

There are 108900 different committees can be formed

Step-by-step explanation:

* Lets explain the combination

- We can solve this problem using the combination

- Combination is the number of ways in which some objects can be

 chosen from a set of objects

-To calculate combinations, we will use the formula nCr = n!/r! × (n - r)!

 where n represents the total number of items, and r represents the

 number of items being chosen at a time

- The value of n! is n × (n - 1) × (n - 2) × (n - 3) × ............ × 1

* Lets solve the problem

- There are 12 men and 12 women

- We need to form a committee consists of 3 men and 4 women

- Lets find nCr for the men and nCr for the women and multiply the

 both answers

∵ nCr = n!/r! × (n - r)!

∵ There are 12 men we want to chose 3 of them

∴ n = 12 and r = 3

∴ nCr = 12C3

∵ 12C3 = 12!/[3!(12 - 3)!] = 220

* There are 220 ways to chose 3 men from 12

∵ There are 12 women we want to chose 4 of them

∴ n = 12 and r = 4

∴ nCr = 12C4

∵ 12C4 = 12!/[4!(12 - 4)!] = 495

* There are 495 ways to chose 4 women from 12

∴ The number of ways to form different committee of 3 men and 4

   women = 220 × 495 = 108900

* There are 108900 different committees can be formed

The answer is:

It will take 42.35 minutes to weed the garden together.

To solve the problem, we need to use the given information about the rate for both Laura and her husband. We know that she can weed the garden in 1 hour and 20 minutes (80 minutes) and her husband can weed it in 1 hour and 30 minutes (90 minutes), so we need to combine both's work and calculate how much time it will take to weed the garden together.

So, calculating we have:

Laura's rate:

[tex]\frac{1garden}{80minutes}[/tex]

Husband's rate:

[tex]\frac{1garden}{90minutes}[/tex]

Now, writing the equation we have:

[tex]Laura'sRate+Husband'sRate=CombinedRate[/tex]

[tex]\frac{1}{80}+\frac{1}{90}=\frac{1}{time}[/tex]

[tex]\frac{1*90+1*80}{7200}=\frac{1}{time}[/tex]

[tex]\frac{170}{7200}=\frac{1}{time}[/tex]

[tex]\frac{17}{720}=\frac{11}{time}[/tex]

[tex]\frac{17}{720}=\frac{1}{time}[/tex]

[tex]\frac{17}{720}*time=1[/tex]

[tex]time=1*\frac{720}{17}=42.35[/tex]

Hence, we have that it will take 42.35 minutes to weed the garden working together.

Have a nice day!

Answer:

x(1 - .4)

Step-by-step explanation:

x = regular price.

1 - .4 = .6 = 60%

The sale price is equal to the full price (aka x) minus the discounted price (40% of x = 40/100 times x =  .4x)

Therefore sale price = x - .4x or x(1 - .4)

Step-by-step explanation:

Write a proportion:

2½ cups / 1 batch = x cups / 3¾ batches

Cross multiply:

x × 1 = 2½ × 3¾

To multiply the fractions, first write them in improper form:

x = (5/2) × (15/4)

x = 75/8

Now write in proper form:

x = 9⅜

Your answer is correct!  Well done!

The logarithm function [tex]\log_ab[/tex], where [tex]a,b>0 \wedge a\not =1[/tex], is increasing for [tex]a\in(1,\infty)[/tex] and decreasing for [tex]a\in(0,1)[/tex]

[tex]\ln x =\log_ex[/tex] and [tex]e\approx 2.7>1[/tex] therefore [tex]\ln x[/tex] is increasing.

Answer:

[tex]\sqrt{37}[/tex]

Step-by-step explanation:

Distance formula

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

[tex]d = \sqrt {\left( {1 - 2 } \right)^2 + \left( {-2 - 4 } \right)^2 }[/tex]

Simplify

[tex]d = \sqrt {\left( {-1 } \right)^2 + \left( {-6 } \right)^2 }[/tex]

Simplify

[tex]d = \sqrt {\left 1 + \left 36}[/tex]

[tex]d = \sqrt{37}[/tex]

Answer

[tex]d = \sqrt{37}[/tex]

Answer:

D

Step-by-step explanation:

For a sequence to be an arithmetic sequence, it must have a common difference. In other words, it must either go down by the same number or up by the same number.

Let's look at the choices:

A. {-10,5,-2.5,1.25,...}

-10 to 5, that went up by 15. It has to keep going up by 15 to be arithmetic. However 5+15 is not -2.5 so it isn't arithmetic.

B. {100,20,4,0.8,...}

100 to 20, that went down by 80. Since 20-80 is not 4, then this sequence is not arithmetic.

C. {1,4,16,48,...}

1 to 4, that went up by 3. 4+3 is not 16 so this is not arithmetic.

D. {-10,-3.5,3,9.5,...}

-10 to -3.5, that went up 6.5.

-3.5+6.5=3

3+6.5=9.5

This is arithmetic. It keeps going up by 6.5.

Answer:

2

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. Since midpoints will be involved, use multiples of 2 to name the coordinates for B, C, and D.

Answer:

2

Step-by-step explanation:

Well by definition a Rhombus is an equilateral paralelogram, AB =BC=CD=DA with all congruent sides, and Diagonals with different sizes.

Also a midpoint is the mean of coordinates, like E is the mean coordinate of A,C, and B, D

[tex]\frac{B+D}{2}=E\\  \\ B+D=2E\\ and\\\\  \frac{A+C}{2} =E\\ A+C=2E[/tex]

So the sum of the Coordinates B and D over two returns the midpoint.

And subsequently the sum of the Coordinates B +D equals twice the E coordinates. The same for the sum: A +C

Given to the fact that both halves of those diagonals coincide on E despite those diagonals have different sizes make us conclude, both bisect each other.

Answer: D = -16

Step-by-step explanation: First you have to isolate the variable by subtracting the coefficient 8D from both equations then subtracting 1 from both equations to isolate 1D.

9d + 1 = 8d - 15

1d + 1 = -15

1d = -16

D = -16

hope this helped

Answer: The Answer To 9d + 1 = 8d -15

Step-by-step explanation:

STEP 1. Combine Like Terms As Well As Changing The Sign(s)

(WHEN YOU CHANGE SIDES YOU CHANGE THE SIGNS!!!)

STEP 2. Switch Signs Or Make It Opposite

d + 1 = - 15

Answer:

[tex]y=2x-48[/tex]

Step-by-step explanation:

Let

y -----> the profit earned by the hot dog stand daily

x ----> the number of hot dogs sold

we know that

The linear equation that represent this problem is equal to

[tex]y=2x-48[/tex]

This is the equation of the line into slope intercept form

where

[tex]m=2\frac{\$}{hot\ dog}[/tex] ----> is the slope

[tex]b=-\$48[/tex] ---> is the y-intercept (cost of the day's supply)

The question relates to the linear function concept. In context of the problem, the profit earned by the hot dog stand is represented by the equation y = 2x - 48, where 'y' is the profit, 'x' is the number of hot dogs sold, '2' is the profit per hot dog, and '48' is the fixed daily cost.

The question relates to the concept of a linear function in Mathematics. In this case, the profit (y) made by the hot dog stand depends on the number of hot dogs sold (x). The stand has a fixed cost of $48 for each day's supply, and then makes a profit of $2 for each hot dog sold.

The linear function can be represented by the equation y = mx + b, where 'm' is the slope of the line (representing the rate of profit per hot dog sold, which is $2), 'x' is the number of hot dogs sold, and 'b' is the y-intercept (representing the fixed costs of the stand, which is -$48).

Therefore, the equation representing the profit of the hot dog stand for x number of hot dogs sold is: y = 2x - 48.

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[tex]\text{Hey there!}[/tex]

[tex]\text{a = m}^2[/tex]

[tex]\text{If m = -3 replace the m-value in the problem with -3}[/tex]

[tex]\text{a = -3}^2[/tex]

[tex]\huge\text{-3}^2\text{ = -3 * 3 = -9}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: a = -9}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

It's false, trapezoids are not rectangles.

Answer:

x = - [tex]\sqrt{7}[/tex]

Step-by-step explanation:

Radical roots occur in pairs, that is

x = [tex]\sqrt{7}[/tex] is a root then so is x = - [tex]\sqrt{7}[/tex]

Answer:

-√7 = -2.64

Step-by-step explanation:

The polynomial function has roots. The first root is 3 and the second is √7.

When we have a square root that means that we get two roots from the same number but one is negative and the other is positive. For example, if we have:

√x² = ±x

Because we can have:

(-x)² = x², or

(x)²=x².

So a square root always gives us two answers, one negative and the other positive.

Final Answer:

The derived relationship between p and q that is independent of y is: q = 1/2 * p

Explanation:

To find the relation between 'p' and 'q' that is independent of 'y,' we will combine the two given equations and eliminate 'y'.
The equations given are:
1) -2y² - 2y = p
2) -y² + y = q
First, we want to manipulate these equations to isolate similar terms. Notice that the first equation has -2y² and the second has -y². If we multiply every term in the second equation by 2, we will have a coefficient of -2y² in the second equation, which will help us cancel out the y² terms. Let's do that:
2(-y² + y) = 2q
-2y² + 2y = 2q
Now, let's subtract the second equation from the first equation:
(-2y² - 2y) - (-2y² + 2y) = p - 2q
On subtracting, -2y² will cancel out with -2y², and -2y will subtract 2y to give -4y:
-2y² + 2y² - 2y - 2y = p - 2q
0 - 4y = p - 2q
-4y = p - 2q
Since we want a relationship without 'y', we can't do much with this result directly, as it still contains 'y'. But let's look at the equations we've been given once more.
The goal is not to solve for 'y' but to find a relationship between 'p' and 'q'. To accomplish this, let's compare the two original equations and try to eliminate 'y' by dividing them. Divide the first equation by the second equation:
(-2y² - 2y) / (-y² + y) = p / q
Now, factor out -y from both the numerator and the denominator:
- y(2y + 2) / - y(y - 1) = p / q
Simplify the expression by canceling out the -y term:
(2y + 2) / (y - 1) = p / q
At this point, you can see that there is no straightforward way to solve this for a relationship that is completely independent of 'y' because the y's don't cancel out.
One method to proceed, since we must get rid of 'y', is to compare coefficients that correspond to the same powers of 'y' assuming p and q are related through such a power series.
We have from the first equation by rearranging:
y² + y = -p/2
Comparing coefficients to the second equation:
y² = -q
y = q
By matching coefficients for the same powers of y, we deduce:
y (from -y²) = -q (from -y² + y), so q = 1/2 * p
Thus, our derived relationship between p and q that is independent of y is:
q = 1/2 * p
This indicates that q is half of p.

Answer:

D.f(x) = −4x + 105

Step-by-step explanation:

Since the function in linear, we know it has a slope.

We know 2 points

(5,85) and (10,65) are 2 points on the line

m = (y2-y1)/(x2-x1)

   = (65-85)/(10-5)

    =-20/5

    =-4

We know a point and the slope, we can use point slope form to write the equation

y-y1 =m(x-x1)

y-85 = -4(x-5)

Distribute

y-85 = -4x+20

Add 85 to each side

y-85+85 = -4x+20+85

y = -4x+105

Changing this to function form

f(x) =-4x+105

Answer: D or f(x) = -4x + 105

Answer:

C (-1,6).

Step-by-step explanation:

This is a horizontal line segment since A and B have the same y-coordinate.  Point P will also have the same y-coordinate since P is suppose to be on line segment AB.

So the only choice that has the y-coordinate as 6 is C. So we already know the answer is C.  There is no way it can be any of the others.  

So we are looking for the x-coordinate of point P using the x-coordinates of A and B.

A is at x=-3

B is at x=0

The length of AB is 0-(-3)=3.

AP+PB=3

AP/PB=2/1

This means AP=2 and PB=1 since 2+1=3 and AP/PB=2/1.

So if we look at A and we know P is 2 units away (after A) then -3+2=-1 is the x-coordinate of P.

OR!

IF we look at B and we know P is 1 unit away (before B), then 0-1=-1 is the x-coordinate of P.

Answer:

a. a correlation matrix

Step-by-step explanation:

The best fitting straight line for a data set of X-values plotted against y-values is  called a correlation matrix.

Answer:

b

Step-by-step explanation:

Given

3x² - 18x = 21 ( divide all terms by 3 )

x² - 6x = 7

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 3)x + 9 = 7 + 9

(x - 3)² = 16 ( take the square root of both sides )

x - 3 = ± [tex]\sqrt{16}[/tex] = ± 4 ( add 3 to both sides )

x = 3 ± 4, hence

x = 3 - 4 = - 1 and x = 3 + 4 = 7

The correct option is b. [tex]\((x-3)^2=16\); -1 and 7.[/tex]

To solve the given quadratic equation [tex]\(3x^2 - 18x = 21\),[/tex] we first divide the entire equation by 3 to simplify it:

[tex]\[ x^2 - 6x = 7 \]\[ x^2 - 6x + 9 - 9 = 7 \] \[ (x - 3)^2 - 9 = 7 \][/tex]

Now, we isolate the perfect square on one side:

[tex]\[ (x - 3)^2 = 7 + 9 \] \[ (x - 3)^2 = 16 \][/tex]

This is the perfect square equation. To find the solutions, we take the square root of both sides:

[tex]\[ x - 3 = \pm4 \][/tex]

Now, we solve for \(x\) by adding 3 to both sides:

[tex]\[ x = 3 \pm 4 \][/tex]

This gives us two solutions:

[tex]\[ x = 3 + 4 = 7 \] \[ x = 3 - 4 = -1 \][/tex]

 Therefore, the solutions to the equation are [tex]\(x = -1\) and \(x = 7\),[/tex] which corresponds to option b. [tex]\((x-3)^2=16\); -1 and 7.[/tex]

Answer:

(2p - 9)(3p + 5)

Step-by-step explanation:

We have the polynomial: 6p2 – 17p – 45

Rewrite the middle term as a sum of two terms:

6p2 + 27p - 10p - 45

Factor:

3p(2p - 9) + 5(2p - 9)

→ (2p - 9)(3p + 5)

For this case we must factor the following expression:

[tex]6p ^ 2-17p-45[/tex]

We must rewrite the term of the medium as two numbers whose product is [tex]6 * (- 45) = - 270[/tex]

And whose sum is -17

These numbers are: -27 and +10:

[tex]6p ^ 2 + (- 27 + 10) p-45\\6p ^ 2-27p + 10p-45[/tex]

We group:

[tex](6p ^ 2-27p) + 10p-45[/tex]

We factor the maximum common denominator of each group:

[tex]3p (2p-9) +5 (2p-9)[/tex]

We factor[tex](2p-9)[/tex] and finally we have:

[tex](2p-9) (3p + 5)[/tex]

Answer:

[tex](2p-9) (3p + 5)[/tex]