Find the zeros and the axis of symmetry of the parabola.PLEASE HELP PLEASE

Answer: C, D, E

Step-by-step explanation: sub in -3 for x and 6 for y in all equations. Only c and d are true. In the graphs, E is the only one that has the point (-3,6)

Answer:

c, d, and e

Step-by-step explanation:

By using Euclid's first book, we can prove that the quadrilateral produced by perpendicular, unequal, bisecting diagonals is a kite. A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. In this case, the two pairs of adjacent sides are formed by the diagonals bisecting the quadrilateral into four smaller triangles with equal areas.

According to Euclid's first book, when two lines intersect at a right angle (perpendicular), they form four right angles. In the case of a quadrilateral with perpendicular, unequal, bisecting diagonals, the diagonals intersect at a right angle and divide the quadrilateral into four smaller triangles with equal areas.

1. Draw a quadrilateral with perpendicular, unequal, bisecting diagonals.
2. Label the points where the diagonals intersect as A, B, C, and D.
3. Label the point where the diagonals intersect as E.
4. Use Euclid's first book to prove that the angles at E are all right angles.
5. Use Euclid's first book to prove that the four triangles formed by the diagonals are congruent (equal in area).
6. Use the definition of a kite to prove that the quadrilateral is a kite (two pairs of adjacent sides are equal in length).
7. Therefore, the quadrilateral produced by perpendicular, unequal, bisecting diagonals is a kite.

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The composite function that expresses the calories burned while swimming with flippers as a function of time is b(c(t)) = 915.2t.

Given:

Calories burned while swimming without flippers: c(t) = 704t

Calories burned while wearing flippers: b(c) = 1.3c

To find the composite function that expresses the calories David burns while swimming with flippers, we need to combine the given functions: c(t) = 704t and b(c) = 1.3c.

Let's break down the steps to derive the composite function:

Start with the function for calories burned while swimming without flippers: c(t) = 704t.

Substitute c(t) into the function for calories burned while wearing flippers: b(c) = 1.3c.

Replace c with the expression 704t from step 1: b(c(t)) = 1.3(704t).

Combining the functions, we get the composite function:

b(c(t)) = 1.3(704t)

Simplifying further:

b(c(t)) = 915.2t

Therefore, the composite function that expresses the calories David burns while swimming with flippers is b(c(t)) = 915.2t.

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Complete question =

David tracks his calories burned while training for a meet. The number of calories he burns is expressed by the function c(t) = 704t, where t is the number of hours spent swimming.

To burn more calories, David wears flippers while he swims. The number of calories he burns while wearing flippers is expressed by the function b(c) = 1.3c, where c is the number of calories burned while swimming without flippers.

Which composite function expresses the calories, as a function of time, David burns while swimming with flippers?

The equation of the line with slope -1/7 is (y-3) = -1/7(x-3).

According to the question,

We have the following information:

Slope of the line = -1/7

Points through which line is passing = (3,3)

We know that the following formula is used to find the equation of the line:

(y-y') = m(x-x') where m is the slope of the line

In this case, we have x' = 3 and y' = 3.

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

This expression can be solved further by multiplying -1/7 into the bracket and then by moving 3 from the left hand side to the right hand side. Then this equation will be in slope-intercept form.

Hence, the correct option is B.

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Answer:

4 feet

Step-by-step explanation:

I'll use ratios:

10 feet tall is to 5 foot shadow  as  x feet tall is to 2 foot shadow

 or

10 / 5 = x /2    Multiply both sides of the equation by 2

20 / 5 = x  = 4 feet tall

The height of other tree is 4 foot.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

10 feet tall cats a shadow of 5 foot.

let x feet casts a shadow of 2 foot.

Using proportion

10/ 5 = x / 2

2 = x/2

x = 4 feet.

Thus, the 4 feet tall tree casts a shadow of 2 foot.

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sin(t)cos(t)dt = -0.338 (approx.) by numerical integration,

and sin(t)cos(t)dt = 1/2 by the Fundamental Theorem of Calculus.

a. To find F"(t), we need to differentiate F(t) twice.

Since F(t) sin(t), we first need to use the product rule:

F'(t) = sin(t) + F(t) cos(t)

Next, we differentiate F'(t) using the product rule again:

F"(t) = cos(t) + F'(t) cos(t) - F(t) sin(t)

Substituting F'(t) from the first equation, we get:

F"(t) = cos(t) + (sin(t) + F(t) cos(t))cos(t) - F(t) sin(t)

Simplifying, we get:

F"(t) = 2cos(t)cos(t) - F(t)sin(t)

\(F"(t) = 2cos^2(t) - F(t)sin(t)\)

b.i. To find sin(t)cos(t)dt numerically, we can use numerical integration methods such as the trapezoidal rule or Simpson's rule.

For simplicity, we will use the trapezoidal rule with n = 4:

Δt = (π - 0)/4 = π/4

sin(t)cos(t)dt ≈ Δt/2 [sin(0)cos(0) + 2sin(Δt)cos(Δt) + 2sin(2Δt)cos(2Δt) + 2sin(3Δt)cos(3Δt) + sin(π)cos(π)]

sin(t)cos(t)dt ≈ (π/4)/2 [0 + 2(0.25)(0.968) + 2(0.5)(0.383) + 2(0.75)(-0.935) + 0]

sin(t)cos(t)dt ≈ -0.338

ii. To find sin(t)cos(t)dt using the Fundamental Theorem of Calculus, we need to find an antiderivative of sin(t)cos(t).

Notice that the derivative of sin^2(t) is sin(t)cos(t), so we can use the substitution u = sin(t) to get:

sin(t)cos(t)dt = u du \(= (1/2)sin^2(t) + C\)

where C is a constant of integration.

To find C, we can evaluate the antiderivative at t = 0:

sin(0)cos(0)dt \(= (1/2)sin^2(0) + C\)

0 = 0 + C

C = 0

Therefore, the antiderivative of sin(t)cos(t) is \((1/2)sin^2(t)\), and:

\(sin(t)cos(t)dt = (1/2)sin^2(t) + C\)

\(sin(t)cos(t)dt = (1/2)sin^2(t) + 0\)

\(sin(t)cos(t)dt = (1/2)sin^2(t)\)

Now we can evaluate this antiderivative at the limits of integration:

\(sin(t)cos(t)dt = [(1/2)sin^2(π)] - [(1/2)sin^2(0)]\)

sin(t)cos(t)dt = (1/2) - 0

sin(t)cos(t)dt = 1/2.

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If an invertible symmetric n×n matrix A has a nonzero vector v in R^n such that Av is orthogonal to v, then it means that the dot product of Av and v is equal to zero. In other words, Av . v = 0. Using th peroperties of the dot product, we can rewrite this equation as:
v . A^T v = 0

Since A is symmetric, A^T = A, and we can rewrite the equation as:
v . A v = 0
This equation can be further simplified using the properties of the dot product:
v . A v = (A v) . v = 0
From this equation, we can see that the eigenvalues of A must be either positive or negative. If the eigenvalues of A are all positive, then v . A v > 0, which contradicts the equation v . A v = 0. Similarly, if the eigenvalues of A are all negative, then v . A v < 0, which also contradicts the equation v . A v = 0.
Therefore, the only way for there to exist a nonzero vector v in R^n such that Av is orthogonal to v is if the eigenvalues of A are both positive and negative. In other words, A must have both positive and negative

eigenvalues.

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Answer:

12 square yards of carpet

Step-by-step explanation:

area is l x w so 3 x 4 = 12

pls vote me brainliest

Given that $OF = 9$ and $OF' = 12,$ where $F$ and $F'$ are the foci of the ellipse, we can determine the lengths of the major and minor axes.

In an ellipse, the sum of the distances from any point on the ellipse to the two foci is constant. This property is expressed by the equation:

$$PF + PF' = 2a,$$

where $P$ is any point on the ellipse and $a$ is the semi-major axis. In our case, $P = O,$ and since $OF = 9$ and $OF' = 12,$ we have:

$$9 + 12 = 2a,$$

$$21 = 2a.$$

Therefore, the semi-major axis $a$ is equal to $\frac{21}{2} = 10.5.$

The distance between the center of the ellipse and each focus is given by $c,$ where $c$ is related to $a$ and the semi-minor axis $b$ by the equation:

$$c = \sqrt{a^2 - b^2}.$$

We can solve for $b$ using the distance to one focus:

$$c = \sqrt{a^2 - b^2},$$

$$c^2 = a^2 - b^2,$$

$$b^2 = a^2 - c^2,$$

$$b = \sqrt{a^2 - c^2}.$$

Substituting the known values:

$$b = \sqrt{10.5^2 - 9^2},$$

$$b = \sqrt{110.25 - 81},$$

$$b = \sqrt{29.25},$$

$$b \approx 5.408.$$

Therefore, the semi-minor axis $b$ is approximately $5.408.$

Finally, we can determine the lengths of the major and minor axes:

The major axis $\overline{AB}$ is twice the semi-major axis, so $\overline{AB} = 2a = 2(10.5) = 21.$

The minor axis $\overline{CD}$ is twice the semi-minor axis, so $\overline{CD} = 2b = 2(5.408) \approx 10.816.$

Therefore, the major axis $\overline{AB}$ is $21$ units long, and the minor axis $\overline{CD}$ is approximately $10.816$ units long.

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The company cannot build  10 child bikes and 12 adult bikes No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 , Option A is the correct answer.

System of inequality represent system of inequalities that satisfies common condition.

It is given that

Each child bike requires 4 hours to build and 4 hours to test.

Each adult bike requires 6 hours to build and 4 hours to test.

Total building hours = 120

Total testing hours = 100

If c represents child bikes and a represents adult bikes, can the company build 10 child bikes and 12 adult bikes in a week.

6a + 4c ≤ 120

4a +4c ≤100

On solving this system of Inequality

a ≤ 10

which is less than required , and so

No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100

Therefore Option A is the correct answer.

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Answer:

3x + 11m + c

Step-by-step explanation:

Step 1) Write the Equation: 3x + 5m + 6m + c

Step 2) Add like Terms: 3x + 11m + c

The probability that a person arriving to use the machine will find it idle is 1/3 or 0.3333. Option a is correct.

Use the concept of an M/M/1 queue to calculate the probability, which models a single-server queue with exponential interarrival times and exponential service times.

In this case, the interarrival time follows an exponential distribution with a rate parameter of λ = 5 persons per hour (or 1/12 persons per minute). The service time (copying time) also follows an exponential distribution with a rate parameter of μ = 1/8 persons per minute (since each person uses the machine for an average of 8 minutes).

In an M/M/1 queue, the probability that the system is idle (no person is being served) can be calculated as:

P_idle = ρ⁰ × (1 - ρ), where ρ is the traffic intensity, defined as the ratio of the arrival rate to the service rate. In this case, ρ = λ/μ.

Plugging in the values, we have:

ρ = (1/12) / (1/8) = 2/3

P_idle = (2/3)⁰ × (1 - 2/3) = 1/3

Therefore, the probability is 1/3 or approximately 0.3333.

Thus, option (A) is the correct answer.

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The system of equations that could be used to determine the cost of 1 piece of fudge, f, and 1 piece of bubble gum , g is:

5f + 3g = 5.70

2f + 10g = 3.60

Chase bought 5 pieces of fudge and 3 pieces of bubble gum for $5.70:

5f + 3g = 5.70

Sara bought 2 pieces of fudge and 10 pieces of bubble gum for $3.60:

2f + 10g = 3.60

System of equations:

5f + 3g = 5.70

2f + 10g = 3.60

From the first equation:

5f + 3g = 5.70

5f = 5.70 - 3g

f = 5.7/5 - 3/5g

f = 1.14 - 0.6g

Replacing "f" in the second equation:

2f + 10g = 3.60

2(1.14 - 0.6g) + 10g = 3.6

2.28 - 1.2g + 10g = 3.6

8.8g = 3.6 - 2.28

8.8g = 1.32

g = 0.15

Replacing "g" in the first equation:

5f + 3g = 5.70

5f + 3(0.15) = 5.7

5f + 0.45 = 5.7

5f = 5.7 - 0.45

5f = 5.25

f = 5.25 / 5

f = 1.05

Fudge cost $1.05 and Bubble Gum cost $0.15

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To find the slope of the curve \(y=x^2-4x-5\) at the point P(3,-8) using the limit of the secant slopes, we need to calculate the slope between P and nearby point on curve as distance between points approaches zero.

The slope of a curve at a specific point can be approximated by calculating the slope of a secant line that passes through that point and a nearby point on the curve. In this case, we are interested in finding the slope at point P(3,-8). Let's choose another point on the curve, Q, with coordinates (x, y). The slope of the secant line passing through points P and Q is given by (y - (-8))/(x - 3). To find the slope of the curve at point P, we need to calculate the limit of this expression as the point Q approaches P.

To do this, we substitute the equation of the curve, \(y=x^2-4x-5\), into the expression for the slope of the secant line. We have (x^2-4x-5 - (-8))/(x - 3). Simplifying this expression gives \((x^2-4x+3)/(x-3)\). Taking the limit of this expression as x approaches 3, we get \((3^2-4(3)+3)/(3-3)\), which becomes (9-12+3)/0. Since we have a 0 in the denominator, we cannot directly evaluate the limit. However, this form suggests that we have a factor of (x-3) in both the numerator and denominator. Factoring the numerator further gives ((x-3)(x-1))/(x-3). Canceling out the common factor (x-3), we are left with (x-1). Substituting x=3 into this expression gives the slope of the curve at point P as (3-1), which is equal to 2.

Therefore, the slope of the curve \(y=x^2-4x-5\) at point P(3,-8) is 2.

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Answer: $246.31

Step-by-step explanation:

The monthly payment of $1,100.48 is going to be divided into interest and principal repayment which is the one that reduces her balance.

The interest payment is based on the interest rate which is 5%.

Monthly interest is:

= 205,000 * 5% * 1/12 months because it is monthly

= $854.17

The amount that goes towards reducing her balance is:

= Monthly payment - Interest payment

= 1,100.48 - 854.17

= $246.31

Answer:

Hey there!

Our equation can be: 2y+3=4y+2

Hope this helps :)

Answer:

2y+3=4y+2

I hope you got it..

Answer:

Step-by-step explanation:

Answer:

18 \(\sqrt{5\\}\)

Step-by-step explanation:

Answer:

Original: 40.249223595

Simplified: 40.2

Step-by-step explanation:

3√5 = 6.7 (simplified)

15√5 = 33.5 (simplified)

6.7 + 33.5 = 40.2

The fraction that Brian can iron in a minute is 5/81.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. It should be noted that in a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

Here, set up a proportion (shirt ironed/minutes = shirt ironed/minutes). I'll convert 3 3/5 to an improper fraction as well to set it up.

(2/9) / (18/5) = x / 1

Cross multiply

2/9 = (18/5)x

Multiply both sides by 5/81 to solve for x.

x = 10/162

In this case, it should be noted that we can reduce 10/162 to the lowest term. This will be 5/81

The clothes that Brian can iron will be 5/81.

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Complete question

Brian irons 2/9 of his shirt in 3 3/5 minutes. If Brian irons at a constant speed how much of his shirt does he iron in a minute

Answer:

Length is 30 and the width is 12

Step-by-step explanation:

5 : 2 is the same as 5x : 2x

Area = l x w

Area = 5x * 2x = 10x^2

10x^2 = 360

Divide 10 on both sides

x^2 = 36

x = 6

5x = 30

2x = 12

The length is 30 and the width is 12

Hope this helps :)

Have a nice day

Answer:

a=250 and b=10

Step-by-step explanation:

a=5*100/2=250

b=200*5/100=10

Answer:

a = 250

b = 10

Step-by-step explanation:

1) a = \(\frac{5x^2}{2}\)

Putting x = 10

a = 5(10)²/2

a = 5(100)/2

a = 250

2) b = \(\frac{2x^2(x-5)}{10x}\)

Putting x = 10

b = 2(10)²(10-5) / 10(10)

b = 2(100)(5) / 100

b = 1000 / 100

b = 10

Answer:

6

Step-by-step explanation:

First, evaluate the expressions. Y2= 10, 3y= 15. (Y=5)

10-15= 0

0+6=6

Hope this helps! Sorry if I'm incorrect :)

Answer:

1. 7

2. 3

3. 105

49/7 = 7 which means 7 shot equals 1 minute

Answer:

Y is less than or equal to 2/5x+1

Answer:

it is 100% b

Step-by-step explanation:

The length of arc QS is approximately 7.85 units. to explain, the length of an arc can be calculated using the formula: L = 2πr(m/360), where r is the radius and m is the measure of the central angle in degrees. In this case, the central angle measure is 78 degrees, and the radius is not given. Without the radius, we cannot determine the exact length of the arc.

To find the length of an arc, we need two pieces of information: the measure of the central angle and the radius of the circle. In this case, we are given the measure of the central angle, which is 78 degrees, but the radius is not provided. Without the radius, we cannot directly calculate the length of the arc. The formula to find the length of an arc is L = 2πr(m/360), where L is the length of the arc, r is the radius, and m is the measure of the central angle. If we had the radius, we could substitute the values into the formula and calculate the exact length of the arc. However, without the radius, we cannot provide an exact value and can only give a general explanation.

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The probability of exactly three bulbs being replaced before the end of March is approximately 0.0126 or 1.26%.

To solve this problem, we need to use the exponential distribution formula:
f(x) = (1/β) * e^(-x/β)
where β is the mean and x is the time period.
In this case, β = 6 months, and we need to find the probability of exactly three bulbs being replaced before the end of March, which is three months from New Year's Eve.
So, we need to find the probability of three bulbs being replaced within three months, which can be calculated as follows:
P(X = 3) = (1/6)^3 * e^(-3/6)
         = (1/216) * e^(-0.5)
         ≈ 0.011
Therefore, the probability that exactly three bulbs will be replaced before the end of March is approximately 0.011.
To answer this question, we will use the Poisson distribution since it deals with the number of events (in this case, lightbulb replacements) occurring within a fixed interval (the time until the end of March). The terms used in this answer include exponential lifetime, mean, Poisson distribution, and probability.
The mean lifetime of the lightbulb is 6 months, so the rate parameter (λ) for the Poisson distribution is the number of events per fixed interval. In this case, the interval of interest is the time until the end of March, which is 3 months.
Since the mean lifetime of the bulb is 6 months, the average number of bulb replacements in 3 months would be (3/6) = 0.5.
Using the Poisson probability mass function, we can calculate the probability of exactly three bulbs being replaced (k = 3) in the 3-month period:
P(X=k) = (e^(-λ) * (λ^k)) / k!
P(X=3) = (e^(-0.5) * (0.5^3)) / 3!
P(X=3) = (0.6065 * 0.125) / 6
P(X=3) = 0.0126
So the probability of exactly three bulbs being replaced before the end of March is approximately 0.0126 or 1.26%.

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Answer:

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

Use slope formula and solve for y:

The value of y is 4.