[someone help] The speed of the object 7 seconds after it is dropped is ___m/sec

Answer:

Option A:

y = 3*(x - 5)^2 - 4

Step-by-step explanation:

For a quadratic equation:

y = a*x^2 + b*x + c

with the vertex (h, k), we can rewrite the function as:

such that:

h = -b/2*a

y = a*(x - h)^2 + k

Here we have the function:

y = 3*x^2 - 30*x + 71

the x-value of the vertex will be:

h = -(-30)/(2*3) = 30/6 = 5

And k is given by:

k = y(5) = 3*(5)^2 - 30*5 + 71 = -4

Then the vertex is:

(5, - 4)

And we can rewrite the equation in the vertex form as:

y = 3*(x - 5)^2 + (-4)

y = 3*(x - 5)^2 - 4

Then the correct option is A.

The angle m∠D of the triangle is 78 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

The ΔKDT and ΔKPQ are isosceles triangle.

Isosceles triangle is a triangle that has two sides and angles equal to each other.

Therefore,

∠D + ∠T + ∠k = 180

∠D  = 6x + 6

∠T = 6x + 6

∠K = 2x

Therefore,

6x + 6 + 6x + 6 + 2x = 180

14x + 12  = 180

14x = 180 - 12

14x = 168

divide both side by 14

x = 168 / 14

x = 12

Therefore,

m∠D = 6x + 6 = 6(12) + 6 = 72 + 6 = 78 degrees.

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The speed of the carts after collision is  3 m/s.

We have to note that in this case, we would need to apply the principle of the conservation of linear momentum. This implies that the momentum before collision would have to be the same as the momentum after collision.

Then we have;

Momentum before collision = Momentum after collision thus;

(3 * 4) + ( 1 * 0) = (3 + 1) v

Note that the two carts are said to stick together and move with a common speed

Hence;

12 = 4v

v = 12/4

v = 3 m/s

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Answer:

$7

Step-by-step explanation:

Answer:

pretty sure its 7

Step-by-step explanation:

Alright I got it.

So first what I did was I made an equation that match did the word problem.

The equation was 15x=250+10x

When I solved it the answer was 50.

so they would need to sell 50 Tshirts (x=50)

Answer:

100

Step-by-step explanation:

Multiply two of the side lengths

10×10 = 100

If they leave the money from the first 8 years in the account and continue to contribute $200 at the end of each quarter for the next 19 years, the future value in the account to help with their child's college is $215,293.42.

The future value for this investment is computed in two separate solutions.

We have used an online finance calculator to facilitate the process.

The future value denotes the present deposits compounded at an interest rate.

Initial Deposits:

N (# of periods) = 32 quarters (8 years x 4)

I/Y (Interest per year) = 7.6%

PV (Present Value) = $0

PMT (Periodic Deposit) = $1,000

Results:

FV = $43,489.87

Sum of all periodic payments = $32,000.00

Total Interest = $11,489.87

Subsequent Deposits:

N (# of periods) = 76 quarters (19 years x 4)

I/Y (Interest per year) = 7.6%

PV (Present Value) = $43,489.87

PMT (Periodic Payment) = $200

Results:

Future Value (FV) = $215,293.42

Sum of all periodic payments = $15,200 ($200 x 76 quarters)

Total Interest = $156,603.55

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9514 1404 393

Answer:

  D.  0, 1, or 2 solutions

Step-by-step explanation:

The line represented by g(x) may intersect the parabola represented by f(x) in 0, 1, or 2 places, as illustrated in the attachment. The curves are different shapes, so cannot overlap to give infinite solutions.

The system may have 0, 1, or 2 solutions.

The probability that they include at least five persons having blood of type O is given as follows:

0.1075 = 10.75%.

The number of donors needed so that the probability of including at least one student donor of type O shall be 0.9 or more is of 184 donors.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The values of the parameters for this problem are given as follows:

n = 200, p = 1/80 = 0.0125.

The probability of less than five is given as follows:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).

Using a binomial distribution calculator, these probabilities are given as follows:

Hence the probability of less than five successes is given as follows:

P(X < 5) = 0.0808 + 0.2046 + 0.2576 + 0.2153 + 0.1342 = 0.8925.

Hence the probability of at least five is given as follows:

P(X >= 5) = 1 - P(X < 5) = 1 - 0.8925 = 0.1075.

The probability of at least one is given as follows:

P(X >= 1) = 1 - P(X = 0)

P(X >= 1) = 1 - (1 - 0.0125)^n.

This probability is of 0.9 when:

1 - (1 - 0.0125)^n = 0.9

(0.9875)^n = 0.1

log((0.9875)^n) = log(0.1)

nlog(0.9875) = log(0.1)

n = log(0.1)/log(0.9875)

n = 183.1.

Rounding up, at least 184 donors must be surveyed.

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The tax rate of an Item that costs $450 Before tax. and the sales tax is $31.50 is 7%

The tax rate is the percentage of an income or an amount of money that has to be paid as tax.

To find the tax rate of $31.50 from $450

The formula is

Amount taxed/Principal amount x 100

= $31.50/$450 x100

=$3150/450

=7%

Hence, the tax rate is 7%

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Tee welding joints are formed when two members intersect at a 90-degree angle that makes the edges come together in the center of a plate or component

h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).

A graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of a function. It is a way to visualize the behavior of the function and its relation to the x and y axes.

Here,

We can draw the graph as

h(x) = 3x - 5 can be written in terms of f(x) by adding 5 to the output of f(x)

h(x) = f(x) + 5

The transformation from the graph of f(x) to the graph of h(x) is a vertical shift of 5 units down. This is because the original function f(x) is shifted down by 5 units to get h(x). The slope of the two lines is still the same, 3, but the y-intercept of f(x) is (0,0) and the y-intercept of h(x) is (-5/3,0). The transformation causes the graph of h(x) to be shifted down 5 units along the y-axis, while the slope and x-intercept of the graph remain the same.

Hence, h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).

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Answer:

10y^2-3xy+6x

Step-by-step explanation:

Answer:

U add 1 then add 2 for each number

Answer:

+1 then +2

Step-by-step explanation:

We are given a sequence of 1, 2, 4, 5, 7, 8, 10 and are asked to find the pattern.

To solve, we need to see how much is being added into every single number.

1, 2

+1

2, 4

+2

4, 5

+1

5, 7

+2

We see that there is a repetition of +1 and then +2.

Therefore the pattern is +1 then +2

Answer:

x=2, y=3. (2, 3).

Step-by-step explanation:

2x+4y=16

-2x-3y=-13

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

y=3

2x+4(3)=16

2x+12=16

2x=16-12

2x=4

x=4/2

x=2

Answer:

Step-by-step explanation:

60

8x10x3/4

Answer: 12x^3 y^3 (x − 4y)

(GCF is: 12x^3 y^3)

Step-by-step explanation:

This is the best I can do, sorry that I don't have an explanation.

The conditions of the line to be intersecting, parallel, and coincident are explained below.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The types of lines are as follows:

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Answer:

12

Step-by-step explanation:

The linear equation can be written in point-slope form as:

y + 7 = (3/8)*(x - 15.2)

So the correct option is A.

A linear equation with a slope M and a known point (h, k), can be written in the point-slope form as:

y - k = m*(x - h)

Here we know that the slope of the line is 3/8, then we get:

y - k = (3/8)*(x - h)

And we also know that this line must pass through the point (15.2, -7), then we know that:

h = 15.2

k = -7

Replacing these values we get:

y + 7 = (3/8)*(x - 15.2)

Thus the correct option is the first one, A.

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Answer: Gloria will need 14 cups of flour

Step-by-step explanation: 2 1/3 x 6 = 14

Answer:

Interval: [0,∞), solution: x≥0.

Answer:

Domain: (0,+∞)

Step-by-step explanation:

negative numbers cannot have a square root taken unless your working with imaginary numbers.

Answer: 2.25 grams

Step-by-step explanation:

In this problem, we are given the ratio of grams to weight. Since we are trying to find how many grams to give to a person with a specific weight, we can use proportions to solve.

[tex]\frac{150mg}{5kg} =\frac{x}{75kg}[/tex]               [cross multiply]

[tex]11250=5x[/tex]                  [divide both sides by 5]

[tex]x=2250mg[/tex]

We are almost done with the problem. The problem is asking for grams, not mg, so we can use unit conversions to change that.

[tex]\frac{1000mg}{1g}=\frac{2250mg}{y}[/tex]          [cross multiply]

[tex]1000y=2250[/tex]               [divide both sides by 1000]

[tex]y=2.25[/tex]

Therefore, we need to give 2.25 grams.

Answer:

m arc 1 = 65°, m arc 3 = 129°, m ∠9 = 25.5°, m ∠ 10 = 57.5°

Step-by-step explanation:

m arc 1 => 180 - 115 = 65°

m arc 3 => 180 - 51 = 129°

m ∠9 => 51 ÷ 2 = 25.5°

m ∠ 10 => 115 ÷ 2 = 57.5°

The Correct answer while simplifying the given algebraic expression is: 4a²+1/2a+7

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Method to simplify any algebraic Expressions are :

Given:

=3a²+1/4a+3+a²+4+1/4a

=(3a²+a²)+(1/4a+1/4a)+(3+4)

=4a²+1/2a+7

So the Answer is

=4a²+1/2a+7

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Answer:

Answer: 35 would be the median

Step-by-step explanation: Put the numbers in order and whichever one is the middle value is the median

Answer:

35

Step-by-step explanation:

The median is the middle price when listed from smallest to largest

31, 34,   35,    48, 50

The middle price is 35

The median is 35

Answer:

line is negative, so -3/4

Step-by-step explanation:

Using the given function and the ordered pairs, we observed that Mr. Poppen pays more initially, to join the club

From the question, we are to determine who pays more initially to join the club between Mr. Poppen and Mrs. Zagorski  

From the given information,

"Mr. Poppen joins a fitness club which has a cost represented by the function y = 10x + 70"

The initial amount paid by Mr. Poppen is the value of y when x is 0

y = 10x + 70

y = 10(0) + 70

y = 0 + 70

y = 70

From the given ordered pairs

(0, 50)

(1, 60)

(2, 70)

(3, 80)

We can conclude that the initial amount paid by Mrs. Zagorski is 50

Hence, Mr. Poppen pays more initially

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Answer:

[tex]\frac{27}{1024}[/tex]

Step-by-step explanation:

So the chance of getting yellow is 0.25

Getting it once is 0.25

Getting it twice is 0.25 • 0.25

Not getting it is 0.75

So we have 0.25 • 0.25 • 0.75 • 0.75 • 0.75 = [tex]\frac{27}{1024}[/tex]