consider the parabola with a focus at the point (0,-3) and directrix y=2 . which two equations can be used to correctly relate the distance from the focus and the directrix to any point (x,y) on the parabola ?

Answer:

11.39

Step-by-step explanation:

-3.86+6.82=2.96

abs(2.96)=2.96

----------------------

4.02-12.45=-8.43

abs(-8.43)=8.43

-----------------------

1(2.96)+8.43=2.96+8.43=11.39

Answer:

The kinetic energy of the roller coaster is 1600000 J.

Step-by-step explanation:

Given:

Mass of the roller coaster is 8000 Newton's and speed 20.0 meters/seconds.

Now, we need to find the kinetic energy [tex]E_{k}[/tex] of the roller coaster.

So, Mass of roller coaster (m) = 8000 N.

Velocity of roller coaster (v) = 20.0 m/s.

Now, putting the formula of kinetic energy:

[tex]E_{k} = \frac{1}{2}\times m\times v^{2}[/tex]

[tex]E_{k}=\frac{1}{2} \times 8000\times 20^{2}[/tex]

[tex]E_{k}=\frac{1}{2} \times 8000\times 400[/tex]

[tex]E_{k}=\frac{1}{2} \times 3200000[/tex]

[tex]E_{k}=1600000[/tex]

Therefore, the kinetic energy of the roller coaster is 1600000 J.

Answer:

x = 7,y = 8

Step-by-step explanation:

(20 + x + y )/ 5 = x

4x = 20 + y

x ≥ 6

y ≥ 6

if x = 6, y = 4 No

if x = 7, y = 8 Yes!

Answer:

x = 26    m∠DAB =  80°      m∠ADC = 100°

Step-by-step explanation:

Given,

ABCD is a parallelogram in which AB ║ DC and AD║ BC.

m∠DAB = 4x-24  

m∠ADC = 2x+48

Solution,

Since ABCD is a parallelogram so sum of two consecutive angle is 180°.

[tex]m\angle DAB+m\angle ADC=180\°\\4x-24+2x+48=180\°\\6x+24=180\°\\6x=180-24\\6x=156\\x=\frac{156}{6}=26[/tex]

Now substituting the value of x we get the value of ∠DAB and ∠ADC .

[tex]m\angle DAB=4x-24=4\times26-24=104-24=80\°[/tex]

[tex]m\angle ADC=2x+48=2\times26+48=52+48=100\°[/tex]

Thus the value of x is 26 and m∠DAB is 80° and m∠ADC is 100°

Answer:

C

Step-by-step explanation:

Given the two functions, we need to find

(g ° f)(4)

This means, we need to put the function f(x) INTO the function g(x) and then evaluate that new function at x = 4.

We put the whole expression of f(x) into "x" of g(x). Shown below:

[tex]f(x)=x^2-3\\g(x)=\frac{x+2}{x}\\(gof)(x)=\frac{x^2-3+2}{x^2-3}\\(gof)(x)=\frac{x^2-1}{x^2-3}[/tex]

Now we plug in 4 into x and evaluate:

[tex](gof)(x)=\frac{x^2-1}{x^2-3}\\(gof)(4)=\frac{4^2-1}{4^2-3}\\(gof)(4)=\frac{15}{13}[/tex]

Thus,

correct answer is C

Answer:

q = 8

Step-by-step explanation:

Given the 2 equations

p + q = 36 → (1)

p - q = 20 → (2)

Add the 2 equations term by term

2p = 56 ( divide both sides by 2 )

p = 28

Substitute p = 28 into (1)

28 + q = 36 ( subtract 28 from both sides )

q = 8

If p + q = 36, and p -q = 20, then q = B

The given question is an example of an algebraic equation that involves the use of BODMAS and the substitution method.

Let

From equation (1)

Let p = 36 - q.

Then we can substitute the value of p into equation (2)

p - q = 20

36 - q - q = 20

36 - 2q = 20

collecting the like terms

-2q = 20 - 36

- 2q = - 16

Divide both sides by (-2)

q = -16/-2

q = 8

Therefore, we can conclude that the value of q = 8

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Answer:

B

Step-by-step explanation:

You could plug in the point given with another point but for simplicity, you can count how far away you are from the vertex. (Since the y intercept is at 0,0)

Go up 3 spots from the vertex, and then go one spot to the right. Ay now you're at (1,3)

You went up 3 and right 1, which translates to simply 3

Answer:

x=1/2

Step-by-step explanation:

4x-5(x-2)=12x+4-x

4x-5x+10=12x-x+4

-x+10=11x+4

-x-11x+10=4

-12x+10=4

-12x=4-10

-12x=-6

12x=6

x=6/12

simplify

x=1/2

Answer: x = 1/2

Explanation :

First write the equation as you see it:

4x-5(x-2)=12x+4-x

Next do the math in the parentheses:

4x-5x+10=12x-x+4

Combine the x’s:

-12x+10=4

Switch the 10 and put it on the other side:

-12x=4-10

Change to negative to positive:

12x=6

Divide:

x=6/12

Simplify

x=1/2

Thus, you answer is x = 1/2

Hope this helps! :)

Answer:

A deck=52

Probability of selecting black cards 26/52

26/52*3/52

Step-by-step explanation:

Correct me if I am wrong.

Answer:

$1.95 is 15% of 13 dollars

Answer:

13 - 15% (1.90) = 11.10

Step-by-step explanation:

13 - 15% (1.90) = 11.10

Answer:

$343

Step-by-step explanation:

To get 30% of 490 we divide 30% by 1

30% ÷ 1 = 147

Now, we subtract 490 by 147

490 - 147 = 343

Answer:

ivan will

Step-by-step explanation:

16mph

16/3=5.333

60/3=20minutes

so instead of 5 miles in 20 minutes like pedro ivan did 5.333 repeating

Answer:

[tex]\sqrt{85}[/tex]

Step-by-step explanation:

Calculate the distance d using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (6, - 2)

d = [tex]\sqrt{(6+1)^2+(-2-4)^2}[/tex]

  = [tex]\sqrt{7^2+(-6)^2}[/tex]

  = [tex]\sqrt{49+36}[/tex]

  = [tex]\sqrt{85}[/tex] ← exact distance

Answer:

he other guy is wrong there is no 85

Step-by-step explanation:

Answer:

3/6 or 1/2 or 50:50 there all right

Step-by-step explanation:

I am guessing that by simple dice you mean a 6 sided die and we know that 6 sided dice goes up to 6 and there are 3 prime number up to 6 which are 2 3 5 so if 3 out of 6 numbers are prime it is half of the dice so there is a 50/50 chance you role a prime number

Let the number of rectangles = R

Perimeter is 2(L) + 2(W)

The length remains the same when you add more triangles ( 6).

The width changes by multiplying the width by the number of rectangles.

Since the width of the rectangles are 1, multiply the number of rectangles R by 1 to get R.

Now replace W in the perimeter frmula with R:

Now the perimetr would be: P = 2L + 2R

Answer:

6

Step-by-step explanation:

you take 18 and divide it by 3

Answer:

120 Grams.

Step-by-step explanation:

In the illustration, the dial is on 30 grams as the increments increase by 5 grams per tick mark. Taking this info, we can say that since the eggs have the same mass then 30 × 4 is equal to 120 grams.

Answer:

x=110

Step-by-step explanation:

66*20=6*2*x

1320=12x

x=1320/12

x=110

Answer:

[tex]\frac{72}{q}[/tex] number of cheerleaders, she would expect to forget their bows.

Step-by-step explanation:

Kaley estimates that 2 out of every q cheerleaders will forget to bring their bows for practice.

So, if there are q cheerleaders then 2 of them will forget to bring their bows.

Then if there are 1 cheerleader then [tex]\frac{2}{q}[/tex] of them will forget to bring their bows.

Finally,  if there are 36 cheerleaders then [tex]\frac{2 \times 36}{q} = \frac{72}{q} [/tex] of them will forget to bring their bows.

Therefore, [tex]\frac{72}{q}[/tex] number of cheerleaders, she would expect to forget their bows. (Answer)

Answer:

8 liters of 15% solution and 72 liters of 65% solution

Step-by-step explanation:

If x is the liters of 15% solution, and y is the liters of 65% solution, then:

x + y = 80

0.15x + 0.65y = 0.60(80)

Solve the system of equations with substitution or elimination.  Using substitution:

0.15x + 0.65(80 − x) = 0.60(80)

0.15x + 52 − 0.65x = 48

4 = 0.5x

x = 8

y = 72

You need 8 liters of 15% solution and 72 liters of 65% solution.

8 liters of the 15% solution and 72 liters of the 65% solution are required.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

If x is the liters of 15% solution, and y is the liters of 65% solution, then:

x + y = 80

0.15x + 0.65y = 0.60(80)

Use substitution or elimination to solve the mathematical model. Using a substitute

0.15x + 0.65(80 − x) = 0.60(80)

0.15x + 52 − 0.65x = 48

4 = 0.5x

x = 8

y = 72

8 liters of the 15% solution and 72 liters of the 65% solution are required.

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He is correct.

The further away ( to the left) from 0 a negative number is the smaller it is.

Billy correctly determined that −3/4 is smaller than −1/4 by plotting them on a number line. Numbers further to the left on the number line are smaller, and thus −3/4 is less because its absolute value is greater than that of −1/4 when both are negative.

Billy is correct in determining that −3/4 is smaller than −1/4. On a number line, negative numbers to the left are smaller than those to the right. Since −3/4 is further to the left than −1/4, it is indeed the smaller number. Comparing fractions with negative signs can initially be challenging, but remembering that the further left a number is on the number line, the smaller it is, can help clarify comparisons.

When plotting fractions on a number line, it is helpful to consider the absolute value of those fractions. The absolute value of −3/4 is 3/4, and the absolute value of −1/4 is 1/4. Since 3/4 is greater than 1/4, the negative version, −3/4, will be further to the left than −1/4 and therefore less than −1/4.

Answer:

B

Step-by-step explanation:

A.) If you plug in 5 for t, you'd get -5 squared + 10(5) - 16

Which would equal 25 + 50 - 16 = 59

Answer a says t is less than 5, so for example let's plug in 4. You'd get a lower number, which means its decreasing. A is wrong

B.) Now let's plug in 8 for t.

-8 squared = 64.

64 + 10(8) - 16 = 144 - 16 = 128

Your answer here is positive, and B states is t > 8. Any number above 8 is going to give you a positive number and it is increasing

Answer:

B. t>8

Step-by-step explanation:

Answer: x=-1,-2

Step-by-step explanation:

X^2+3x+2=0

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

x=-1,-2

Answer:

120.

Step-by-step explanation:

If you're asking for LCM the answer is 120.

Answer:

Step-by-step explanation:

3, 5 and 8 are Relatively prime numbers (LCD(3, 5, 8) = 1).

Therefore LCM(3, 5, 8) = 3 · 5 · 8 = 120

Answer:

0.5x + 7.5 / (x + 6)

Step-by-step explanation:

Let x be the number of wooden beads

wooden bead = $0.50 each

glass bead = $1.25 each

since average cost of bead = (cost of wooden bead + cost of glass bead)/ total number of beads

equation is (0.5x + (6*1.25))/(x + 6)

The model equation is therefore 0.5x + 7.5 / (x + 6)

x equals 22

____________________________________________

The Segment Postulate states the following:

Given two end points A and B, a third point C lines on the segment AB if and only if the distances between the points satisfy the equation:

[tex]\overline{AB}=\overline{AC}+\overline{CB}[/tex]

____________________________________________

From the figure:

[tex]\overline{AC}=8+x \\ \\ \overline{CB}=10 \\ \\ \overline{AB}=40[/tex]

Our goal is to find x:

[tex]\overline{AB}=\overline{AC}+\overline{CB} \\ \\ Substituting \ values: \\ \\ 40=(8+x)+10 \\ \\ 18+x=40 \\ \\ Subtracting \ 18 \ from \ both \ sides: \\ \\ 18-18+x=40-18 \\ \\ \boxed{x=22}[/tex]

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If Jerri decides to make four small cakes out of a large cake recipe, she should divide the quantity of the required ingredient (in this case, cinnamon) by 4. Hence, for each small cake, she should use 1/12 of a tablespoon of cinnamon.

The recipe Jerri is working with requires one-third of a tablespoon of cinnamon for a large cake. If she decides to use the same recipe to make four small cakes, she should divide the quantity of the cinnamon by 4, as the four smaller cakes together will make up the same quantity/volume as the one large cake.

The calculation can be done as follows: (1/3) tablespoon of cinnamon divided by 4 equals 1/12 tablespoon. Therefore, for each smaller cake, Jerri should use 1/12 of a tablespoon of cinnamon.

The correct answer is (A) 1/12 of a tablespoon.

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Step-by-step explanation: In algebra, we use the word slope to describe how steep a line is. Slope can be found using the ratio [tex]\frac{rise}{run}[/tex] between any two points that are on that line.

To get from one point on the graph to another point, we would rise 2 units which means go up to units and run -1 unit or go across 1 unit to the left.

The variable that is used to represent slope is m. So for this line we would say that m = -2

The base b represents the y-intercept of the line. The of the base as how far we are going up or down on the y-axis. Since we go up 5 units on the y-axis, we have a base of 5 so b = 5.

Remember, slope = rise/run.

We can use the points (-1, 7) and (3, -1) to solve.

_______

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

= -1-7/3-(-1)

= -8/4

= -2

_______

The y-intercept is given in the line but let's solve just to check.

y = mx + b

7 = -2(-1) + b

7 = 2 + b

7 - 2 = 2 + b - 2

5 = b

Now, we can see that y-intercept is 5.

_______

After solving for both the slope and y-intercept we can put this into slope-intercept form.

y = mx + b

y = -2x + 5

_______

m = -2

b = 5

_______

Best Regards,

Wolfyy :)

The equation for Louis's purchase is: [tex]x+y=8[/tex]

The equation for Kate's purchase is: [tex]y+z=9[/tex]

The equation for Biff's purchase is: [tex]x+y+z=13.50[/tex]

Step-by-step explanation:

First of all we have to define variables for each item involved in the purchase

Let x represent burger

y represent soda

z be the slice of pizza

Then

"Louis bought a burger and soda for $8"

[tex]x+y=8[/tex]

"Kate purchased a slice of pizza and soda for $9"

[tex]y+z=9[/tex]

"Biff purchased a burger, a slice of pizza and a soda for $13.50"

[tex]x+y+z=13.50[/tex]

The equation for Louis's purchase is: [tex]x+y=8[/tex]

The equation for Kate's purchase is: [tex]y+z=9[/tex]

The equation for Biff's purchase is: [tex]x+y+z=13.50[/tex]

Keywords: Linear Equations, Variables

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The completed table shows that the product of wavelength and frequency (k) is approximately constant for X-rays, radio waves, green light, and UV rays. Here are the final values for a, b, c, and d: [tex]a = \frac{1}{3} \times 10^{8} \, \text{m/s} , \ b = \frac{1}{3} \times 10^{8} \, \text{m/s} , \ c = \frac{1}{3} \times 10^{8} \, \text{m/s} , \ d = \frac{2}{15} \times 10^{-8} \, \text{m/s}.[/tex]

To determine if wavelength varies inversely with frequency, we can use the formula [tex]\(k = \text{wavelength} \times \text{frequency}\).[/tex]. Rearranging this formula to solve for k, we get [tex]\(k = \frac{1}{\text{frequency}} \times \text{wavelength}\)[/tex].

Now, we can calculate the values of k for each type of radiation:

[tex]\[a = \frac{1}{3 \times 10^{18}} \times (1 \times 10^{-10}) = \frac{1}{3} \times 10^{-28} \, \text{m/s}.\]\[b = \frac{1}{3 \times 10^9} \times (1 \times 10^{-1}) = \frac{1}{3} \times 10^{-10} \, \text{m/s}.\]\[c = \frac{1}{5 \times 10^{11}} \times (600 \times 10^{-6}) = \frac{1}{3} \times 10^{-8} \, \text{m/s}.\]\[d = \frac{1}{7.5 \times 10^{14}} \times (4 \times 10^{-7}) = \frac{4}{30} \times 10^{-21} \, \text{m/s}.\][/tex]

Now we express the values in terms of [tex]\(10^8\)[/tex]:

[tex]\[a = \frac{1}{3} \times 10^{-20} \, \text{m/s} = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[b = \frac{1}{3} \times 10^{-2} \, \text{m/s} = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[c = \frac{1}{3} \times 10^{0} \, \text{m/s} = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[d = \frac{4}{30} \times 10^{-13} \, \text{m/s} = \frac{2}{15} \times 10^{-8} \, \text{m/s}.\][/tex]

So, the completed table is as follows:

[tex]\[a = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[b = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[c = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[d = \frac{2}{15} \times 10^{-8} \, \text{m/s}.\][/tex]