Which of the following is the equation of a parabola with focus (0,2) and directrix y = -2?

Answer:

D.1.001

Step-by-step explanation:

You cannot have a probability greater than 1.  1 is it will happen  ( 100%)

Answer:

D: 3780 square feet

Step-by-step explanation:

Let the length be L. Let the width be W.

The area of a rectangle is length times width, so

A = LW

The area is 420 square feet, so

LW = 420

Now you multiply the length by 3 and multiply the width by 3.

The length is now 3L, and the width is now 3W.

The area of the new rectangle is the new length times the new width.

new area = 3L * 3W

new area = 3 * 3 * LW

new area = 9 * LW

LW was the original area, and it is 420 square feet, so the new area is 9 times the old area.

new area = 9 * 420 square feet

new area = 3780 square feet

Answer:

The two equal (same length) sides are 10.68 metres each.

Step-by-step explanation:

45.56 - 24.2 = 21.36 m (length of the 2 equal sides)

21.36 ÷ 2 = 10.68 metres

Answer:

10.68 m

Step-by-step explanation:

We are given that a perimeter of 5-sided figure =45.56 m

Two side of same length

Sum of three sides of given figure=24.2 m

We have to find the length of each side of the same length and explain.

Let x be the length of each side of same length

We know that

Perimeter of 5- sided figure=Sum of  length of  five sides

Therefore,

x+x+24.2=45.56

[tex]2x+24.20=45.56[/tex]

[tex]2x=45.56-24.2[/tex]

[tex]x=\frac{21.36}{2}=10.68[/tex]

Hence, length of each side of same length=10.68 m

a= 92(18) =1656

Area= 1656m

p= 2(92+18) =220

Perimeter= 220m

Answer:

[tex]\frac{1}{72}[/tex]

Step-by-step explanation:

We have been given that there are total 9 people who entered the drawing competition. There are 3 prizes to be distributed to the winners. The total number of ways that 3 prizes can be awarded to the 9 people can be determined as 9*8*7 = 504.

The total number of ways in which I win the first prize and my mom wins the second prize would be 1*1*7 = 7.

Therefore, the probability that I win the first prize and my mom wins the second prize would be: [tex]\frac{7}{504}=\frac{1}{72}[/tex]

Answer:

it’s 7

Step-by-step explanation:

Answer:

19.25ft

Step-by-step explanation:

area = length x width so 3.5 x 5.5 = 19.25

Answer:

The area of the frame is 19.25 feet.

Step-by-step explanation:

We can see from the information that the wooden frame is a rectangle since length and breadth are unequal.

breadth = 3.5 ft

length = 5.5 ft

The formula for area of a rectangle is = A = L x b

Area = 3.5 * 5.5

Area = 19.25 feet

The slope-intercept form of the equation, which represents how much allowance Hari receives based on the number of chores he does, is y = 0.5x + 9. Here, the slope of 0.5 represents the amount Hari earns per chore, and 9 is the base amount Hari receives irrespective of the chores.

The given scenario provides us with two points (22, $20) and (6, $12) where the number of chores is the x-coordinate and the allowance is the y-coordinate. We can use these points to find the slope of the line:

Slope (m) = (y2 - y1) / (x2 - x1)= ($20 - $12) / (22 - 6) = $8 / 16 = $0.5,

Next, we use the slope and one of the points to find the y-intercept: y = mx + b so $20 = ($0.5 * 22) + b, solving for b gives us b = $20 - $11 = $9, which is our y-intercept.

So, the equation of the line in slope-intercept form is y = 0.5x + 9

This equation states that Hari earns $0.5 per chore and gets a guaranteed $9 even if he does no chores.

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Answer:

BD = 8 cm

Step-by-step explanation:

Diagonals of trapezoid divides each other in equal ratio.

if ABCD is a trapezoid and the diagonals AC and BD  intersect at point O

then we have

[tex]\frac{AO}{OC} =\frac{OB}{OD}[/tex]

it is given that

[tex]\frac{AO}{OC} =\frac{3}{1}[/tex] and BO=6 cm

so we can write

[tex]\frac{3}{1} =\frac{6}{OD}[/tex]

cross multiply

[tex]3 OD=6[/tex]

divide both side by 3

OD= 2 cm

now we have

BD = BO +OC

BD = 6 cm + 2 cm

BD= 8 cm

Step-by-step explanation:

The ratios of the sides is the same.

3OD=OB

Let y be the length of OD

Therefore,

3y=6

y=2,

meaning OD is 2.

OB+OD=DB

BD=6

ANSWER:

BD=8

Answer:

Yes, they are similar. The answer you would click is Yes, the corresponding sides are proportional.

Step-by-step explanation:

The second figure is a dilation of the first, making them similar. The dilation is by a factor of 2 and a half.

Answer:

m = 35/3  or 11 2/3

Step-by-step explanation:

1/3=12-m

Subtract 12 from each side

1/3 - 12 = -m

Get a common denominator

1/3 - 12*3/3 = -m

1/3 - 36/3 = -m

-35/3 = -m

Multiply by -1

-1* -35/3 = -1 *-m

35/3 = m

Changing to a mixed number

3 goes into 35    11  times with 2 left over

11 2/3

[tex]12-m=\dfrac{1}{3}\qquad\text{subtract 12 from both sides}\\\\-m=-11\dfrac{2}{3}\qquad\text{change the signs}\\\\\boxed{m=11\dfrac{2}{3}}[/tex]

Answer:

<DAB= 98

Step-by-step explanation:

Remark

I think you are supposed to assume that this is a parallelogram. In that case the two labeled angles are intended to be equal (one of the properties of a parallelogram).

Equation

2x + 36 = 3x - 5                    Add 5 to both sides

2x + 36 + 5 = 3x  - 5 + 5      Combine

2x + 41 = 3x                          Subtract 2x from both sides

2x - 2x + 41 = 3x - 2x           Combine

41 = x

Answer

<DAB = 2x + 36

<DAB = 2*41 + 36

<DAB = 82 + 36

<DAB = 98

Answer:

D

Step-by-step explanation:

The common difference d, between the terms is

d = - 9 - 3 = 3 - 15 = 15 - 27 = - 12

To find the next term in the sequence subtract 12 from the previous term

⇒ - 9 - 12 = - 21 ← is the next term in the sequence

The next term of the sequence after -9 is -21

∴ Common difference of the given problem = (15 - 27) = -12

∴ Each term of the sequence gets decreased by 12

∴ The term after -9 will be ( -9 - 12) = -21

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Answer: (x+1)^2=10

Step-by-step explanation:

Answer:

Neither

Step-by-step explanation:

y = 5/3 x + 3, this line has slope = 5/3

20x + 12y = 12

12y = -20x + 12

y = -20/12 x + 1

y = - 5/3 x + 1, this line has slope = - 5/3

Parralel ; same slopes

Perpendicular; slopes are opposite and reciprocal

So answer is neither pair parallel nor perpendicular

The pair of equations y = 5/3x + 3 and 20x + 12y = 12 are parallel because they both have the same slope of 5/3 once the second equation is put into slope-intercept form.

To determine if the pair of equations y = 5/3x + 3 and 20x + 12y = 12 are parallel, perpendicular, or neither, we must first put both equations into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. The equation y = 5/3x + 3 is already in slope-intercept form with a slope of 5/3. To convert the second equation into slope-intercept form, we can rewrite it as 12y = -20x + 12, and then y = (-20/12)x + 1, which simplifies to y = -5/3x + 1.

Now, comparing the slopes of these two lines, we see that both slopes are equal, meaning the lines are parallel to each other since they have the same slope but different y-intercepts.

To simplify the expression, find the common denominator, distribute the 'a' to each term, and combine like terms.

To simplify the expression  a/5x-10 + a/6x-12, we need to find a common denominator for the two terms. The common denominator is 30x(x-2). We then multiply each term by the appropriate factor to get a common denominator. This simplifies the expression to:

a(6x-12) + a(5x-10) / 30x(x-2)

Now, we can distribute the 'a' to each term:

6ax - 12a + 5ax - 10a / 30x(x-2)

Combining like terms, we get a(11x - 22) / 30x(x-2).

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To calculate 1/3 ÷ 4/5, switch the division operation to multiplication by flipping the second fraction. This gives us 1/3 * 5/4, which simplifies to 5/12.

In mathematics, when we're asked to divide fractions, we often use the method of multiplying by the reciprocal of the second fraction.

In this case, the question asks you to perform the division operation of 1/3 ÷ 4/5.

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Answer: travis can afford the compact car but not the coupe

Step-by-step explanation:

Answer:

Travis can afford the compact car.

Step-by-step explanation:

The EMI formula is :

[tex]\frac{p*r*(1+r)^{n} }{(1+r)^{n}-1 }[/tex]

In first case:

p = 10800

r = 6/12/100=0.005

n = 4*12 = 48

Putting values in the formula we get:

[tex]\frac{10800*0.005*(1+0.005)^{48} }{(1+0.005)^{48}-1 }[/tex]

= $254

We can see that Travis can afford the compact car because the EMI is less than $260.

In second case:

p = 11300

r = 6/12/100=0.005

n = 4*12 = 48

Putting values in the formula we get:

[tex]\frac{11300*0.005*(1+0.005)^{48} }{(1+0.005)^{48}-1 }[/tex]

= $265.75

We can see that the coupe will have an EMI of $265.75 which is higher than the amount that Travis can afford.

Hence, Travis can afford a compact car.

Answer:

( x - 6 ) ( x - 3 ) (x + 4)

Step-by-step explanation:

6 is in the tenths place.

Written Form: 0.6

Answer:

10 ounces

Step-by-step explanation:

10 ounces of iodine are worth 30 cents so the mixture can be sold for 20 cents an ounce.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

Let n be the ounces of 30 cents worth of iodine.

To determine the mixture to be worth 20 cents per ounce.

The value of 50 ounces of 18-cent iodine is

⇒ (50)(18) = 900 cents of iodine.

A (50+n) mixture of iodine is produced by combining 50 ounces of 18-cent iodine with n ounces of 30-cent iodine.

Similarly, n ounces of 30-cent iodine is worth 30n.

So, the price of 50+n ounces of 20-cent iodine (50+n)20

⇒ 30x + 900 = 1000 + 20x

Rearrange the likewise terms and apply the arithmetic operations,

⇒ 10x = 100

⇒ x = 10

We can estimate that in order to sell the mixture for 20 cents per ounce, we should combine 10 ounces of iodine worth 30 cents.

Hence, 10 ounces of iodine are worth 30 cents so the mixture can be sold for 20 cents an ounce.

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Answer:

2 out of 4.  2/4

Step-by-step explanation:

There are 2 sides to each coin, there are two coins so all sides add up to 4.

The probability that both coins will display tails is:

P = 0.25

A fair coin has two possible outcomes, tails and heads, both with the same probability.

Then the probability of getting tails is:

p = 0.5

So, the probability for each coin (of getting tails) is:

p₁ = 0.5

p₂ = 0.5

The joint probability (this is, the probability that both of the above events happen at the same time) is the product between the individual probabilities:

P = p₁*p₂ = 0.5*0.5 = 0.25

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Answer:

0.14 s

Step-by-step explanation:

s = -2.7 t² + 40t + 6.5

Let s = 12

12 = -2.7t² + 40t + 6.5     Subtract 12 from each side

-2.7t² + 40t + 6.5 - 12 = 0

      -2.7t² + 40t - 5.5 = 0

Apply the quadratic formula

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

a = -2.7; b = 40; c = -5.5

[tex]x = \frac{-40\pm\sqrt{40^2 - 4\times (-2.7) \times (-5.5)}} {2(-2.7)}[/tex]

[tex]x = \frac{-40\pm\sqrt{1600-59.4}}{-5.4}[/tex]

[tex]x = \frac{-40\pm\sqrt{1540.6}}{-5.4}[/tex]

[tex]x = \frac{-40\pm 39.25}{-5.4}[/tex]

x = 7.41 ± 7.27

x₁ = 0.14; x₂ = 14.68

The graph below shows the roots at x₁ = 0.134 and x₂ = 14.68.

The Moon’s surface is at -12 ft. The ball will be 12 ft above the Moon’s surface (crossing the x-axis) in 0.14 s.

The second root gives the time the ball will be 12 ft above the Moon’s surface on its way back down.

100% --> 14

30% --> x

100x = 420

x= 420/100

x=4.2

Answer:

The answer is 4.2

Step-by-step explanation:

Always remember that when they use the word of, it means you have to multiply. So 14 times 0.3 is 4.2

Suki rode her bike a longer distance than Claire because when comparing each of their distances to the benchmark of 1/2 mile, Suki's distance (4/5 mile) is greater than the benchmark (1/2 mile), while Claire's distance (1/3 mile) is less than the benchmark. Therefore, Suki rode a longer distance than Claire in relation to the benchmark.

Suki's Distance with Benchmark (1/2):

Suki rode her bike for 4/5 miles.

The benchmark is 1/2 mile.

Comparison: [tex]\frac{4}{5} > \frac{1}{2}[/tex]

Interpretation: Suki's distance ( 4/5 miles) is greater than the benchmark 1/2 mile.

Claire's Distance with Benchmark (1/2):

Claire rode her bike for 1/3 mile.

The benchmark is 1/2 mile.

Comparison: [tex]\frac{1}{3} < \frac{1}{2}[/tex]

Interpretation: Claire's distance ( 1/3 mile) is less than the benchmark 1/2 mile.

Overall Comparison:

Suki's distance (4/5) is greater than Claire's distance (1/3).

Interpretation: Suki rode her bike a longer distance than Claire.

In summary, both Suki and Claire are comparing their distances to the benchmark of 1/2 mile. Suki's distance is greater than the benchmark, while Claire's distance is less than the benchmark. Therefore, Suki rode a longer distance than Claire.

Answer:

Q 1 = answer is B

Q 2 = answer is A

Step-by-step explanation:

Answer: $1200 profit

Step-by-step explanation: $3200 - $2000 = $1200

Answer: 18.8%

Step-by-step explanation:

   [tex]\dfrac{\text{quantity of APPLE pies}}{\text{quantity ot TOTAL pies}}[/tex]

[tex]=\dfrac{3}{3+2+5+6}[/tex]

[tex]=\dfrac{3}{16}[/tex]

= 0.1875

= 18.75%

≈ 18.8%   rounded to one decimal place

Answer:

6 feet above the deck

Answer:

True

Step-by-step explanation:

Answer:

Step-by-step explanation:

If a then b is true  then not b = not a is true. This is called the contrapositive.

Answer:

You would use a = 12

Step-by-step explanation:

The b value is the coefficient that is in front of the x term, that does not have an exponent of 2. It's simply the x term (not the x^2 term)

We're told that b = 15 is used, but we see that -15 is in front of the x term. To fix this contradiction, add 15x to both sides so that you move the x term to the right side

-15x+22 = 12x^2

-15x+22+15x = 12x^2+15x

22 = 12x^2+15x

Now subtract 22 from both sides to move that term over as well

22-22 = 12x^2 + 15x - 22

0 = 12x^2 + 15x - 22

12x^2 + 15x - 22 = 0

12x^2 + 15x + (-22) = 0

The last equation is in the form ax^2 + bx + c = 0 with

a = 12, b = 15, c = -22