A piece wise function is graphed below. Fill in all of the blanks to give an algebraic description of the function

Answer:

5 seconds

Step-by-step explanation:

d = 16t^2

You are given the distance, d, and you need to find the time, t. Replace d with the given distance, 400 ft.

d = 400

400 = 16t^2

Switch sides.

16t^2 = 400

Divide both sides by 16.

t^2 = 25

Take the square root of both sides.

t = 5

Answer: 5 seconds

It takes 5 seconds for the penny to hit the ground when it falls from a height of 400 feet.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

The distance d (in feet) a penny falls from the window of a building is represented by ;

[tex]d = 16t^2[/tex]

where t is the time (in seconds) it takes for a penny to hit the ground.

d = 400

[tex]400 = 16t^2\\\\16t^2 = 400\\t^2 = 25\\t = 5[/tex]

Therefore, It takes 5 seconds for the penny to hit the ground when it falls from a height of 400 feet.

Learn more about quadratic equations;

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A.)> 161 is the answer

Answer:

160 dollars

Step-by-step explanation:

So you would add 6.19 and 9.81 together. Then divide it by 2.  You would get 8. Then multiply it by 20 and you would get 160 dollars

Answer:

5 degrees

Step-by-step explanation:

measure of angle 1=1/2(20-10)

because the secants intersect outside of the circle.

measure of angle 1=1/2(10)

measuer of angle 1=5 degrees

Answer: 12.96

Step-by-step explanation:

3.14 or pi * radius ^2

3.14 *2^2

12.96

Answer:

h(f(x)) = 2x - 11

Step-by-step explanation:

h(f(x)) is a "composite function."  We use the function f(x) as the input to the function h(x):

h(x) = 2x + 3, or 2( x ) + 3; replacing x with f(x), or x - 7, we get:

h(f(x)) = 2(x - 7) + 3, or

h(f(x)) = 2x - 14 + 3, or

h(f(x)) = 2x - 11

Answer: h(f(x)) = 2x - 11

Step-by-step explanation:

Answer:

A quadrilateral is a polygon with four sides.

Practicly anything with 4 sides like square, Rectangle ,and rhombas

Im sorry if i didn't answer your question but i did not get what you were saying but here is an image that can maybe help you

The quadrilateral has includes 7 types that are parallelogram, rhombus, kite, rectangle, trapezoid, square, and isosceles trapezoid.

The quadrilateral is a four-sided polygon having four angles.

Types of quadrilaterals:

Find out more information about the Classify quadrilaterals here:

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You have to get y by itself and to do that you need to do the opposite of order of operations.

So the opposite of subtraction is addition so you would add 37 to both sides.

It would cancel out itself then leave y by itself while the other side of the equation is 55

Answer: y = 55

Step-by-step explanation: You want to get the variable or y by itself, so you cancel out what number is next to it which is 37, so you add  -37 + 37 and that   cancels it out.The reason you add  them together is because of opposite operations since it was minus you want to add, and what ever you do to one side you have to do to the other, so 18 + 37 is 55 so y is 55

Answer: could you please be more clear..?

Step-by-step explanation:

The probability of drawing a red marble followed by a blue marble, without replacement, is approximately 0.083.

The question is about probability in a scenario where there's no replacement after each draw. The total number of marbles is 7 (red) + 9 (white) + 5 (blue) = 21 marbles. If we are to draw two marbles without replacement, the total outcomes reduce by 1 with each draw.

Let's say we want to find the probability of drawing a red marble and then a blue marble. The probability of drawing a red marble on the first draw is 7/21. After drawing a red marble, we are left with 20 total marbles, so the probability of drawing a blue one is 5/20. Therefore, the probability of these two events happening in sequence is calculated by multiplying the separate probabilities: (7/21) * (5/20) = 7/84 ≈ 0.083.

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1st answer: 7j = 91

2nd answer: 13

First, write the statement as an equation.

7j= 91

Now, divide both sides of the equation by 7.

j = 13

Answer:

7 + j = 91

J = 84

16% is the most accurate answer

16% is the answer to this question

The percentage that the store has taken off would be 30%.

The price of the sofa was reduced by 30%.

To calculate the percentage reduction in price:

Find the difference between the original price and the reduced price: $800 - $560 = $240.

Calculate the percentage decrease: ($240 / $800) x 100% = 30%.

Therefore, the price of the sofa was reduced by 30%.

Answer:

$7.50

Step-by-step explanation:

Sara buys a sweater that costs $30

The store is having a 25% off sale.

To figure out what 25% is you do 25/100, which will give you 0.25,

Multiply 0.25 by $30

You should get $7.50.

The answer is $22.50.

Hope this helps!

Answer:

(x,y)= (-3,1)

Step-by-step explanation:

4x + 9y = -3  => eq(i)

8x + 12y = 12  => eq(ii)

We need to solve these equations to find the values of x and y.

Multiply eq (i) with 2 and then subtract both equations

8x + 18y = -6  

8x + 12y = 12

-     -          -

__________

6y = -18

y= -18/6

y = -3

Putting value of y in eq(i)

4x + 9y = -3

x = -3

4(-3) + 9y = -3

-12 + 9y = -3

9y = -3+12

9y= 9

y= 9/9

y = 1

So, the value of x = -3 and y = 1

(x,y)= (-3,1)

The cost of the unfurnished and furnished apartments for 1 year would be $8,650 and $9,880 respectively. Therefore, the unfurnished apartment is the better deal for Jonathan.

The cost for the unfurnished apartment for one year would be $600 (monthly rent) * 12 (months) + $600 (one month deposit) + $350 (security deposit) + $850 (furniture cost) = $8,650.

The cost for the furnished apartment for one year would be $190 (rent per week) * 52 (weeks in a year) = $9,880.

Therefore, the unfurnished apartment offers a better deal for Jonathan if he plans to stay for 1 year.

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Answer: B

Step-by-step explanation:

the sum of any two sides is bigger than the third side... so 5+9= 14, bigger than 6. 5+6=11, greater than 9. 9+6=15, bigger than 5.

Answer:

B

Step-by-step explanation:

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

So, let's test each of the points:

A) We have the points: 4, 8, 2. If we sum 4 and 2, the result is 6. Which is not greater than the third side which is 8. So it does not qualify for a triangle.

B) We have the points 5, 9, 6. If we sum 5+6 = 11 which is greater than 9. The sum of any two sides from this set is greater than the third side. It could create a triangle.

C) We have the points 6, 8, 16. If we sum  6+8 = 14 which is not greater than the third side 16. So it could not create a triangle.

D) we have the points 10, 4, 3. If we sum 4+3 = 7 which is not greater than 10. For that reason, it could not create a triangle.

Answer: 1.5 kilometers.

Step-by-step explanation:

You need to make the conversion from 500 meters to kilometers.

It is important to remember that:

[tex]1\ kilometer=1,000\ meters[/tex]

Then, 500 m to km is:

[tex](500\ m)(\frac{1\ km}{1,000\ m})=0.5\ km[/tex]

Now you know that he ran 0.5 kilometers in each of his last three track meets.

To calculate the total amount of kilometers ran in those three meets, you need to multiply 0.5 kilometers by 3. Then:

[tex]Total=(0.5\ km)(3)\\Total=1.5\ km[/tex]

Answer:

375 units

Step-by-step explanation:

"What will its maximum height be?"

The given equation, h(x) = -3x^2 + 30x + 300, is a quadratic with coefficients a = -3, b = 30 and c = 300.

The axis of symmetry of this parabola will go thru the max ht.  The equation of the axis of symmetry is

x = -b / (2a)

In this particular case, the axis of symm. is x = -(30) / (2·[-3]), or x = 5 time units.

The max height is thus h(5) = -3(5)^2 + 30(5) + 300 = 375 units.

The answer is:

The maximum height reached by the projectile is 375 units.

To know what's the maximum height that the projectile reaches, we need to use the information about the given quadratic equation (parabola) to calculate the y-coordinate of the vertex.

The vertex of a parabola is located at the lowest or highest point depending on if the parabola opens upwards or downwards.

We can calculate the vertex of a parabola using the following equation:

[tex]x_{vertex}=\frac{-b}{2a}[/tex]

Then, after calculating the x-coordinate of the vertex, we need to substitute the x-coordinate value into the equation of the parabola to find the y-coordinate value or the highest point of the parabola.

We are given the parabola:

[tex]h(x)=y=-3x^{2}+30x+300[/tex]

Where,

[tex]a=-3\\b=30\\c=300\\[/tex]

Now, calculating the vertex we have:

[tex]x_{vertex}=\frac{-b}{2a}[/tex]

[tex]x_{vertex}=\frac{-30}{2*(-3)}=5[/tex]

Then, calculating the y-coordinate value, we have:

[tex]y_{vertex}=-3x^{2}+30x+300[/tex]

[tex]y_{vertex}=-3*(5)^{2}+30*(5)+300[/tex]

[tex]y_{vertex}=-3*25+150+300[/tex]

[tex]y_{vertex}=-75+150+300[/tex]

[tex]y=-75+150+300[/tex]

[tex]y_{vertex}=375[/tex]

Hence, the y-coordinate value of the vertex is equal to 375, meaning that the maximum height reached by the projectile is 375 units.

Have a nice day!

Answer:

3/5

Step-by-step explanation:

Make it a fractiona and simplify. Add 8+12=20 knowing theres twelve girls it would be 12/20. then simplify

Answer:

P(green) = ⇒ 5/14

P(red) = ⇒ 2/14

P(green and red) = ⇒ 5/98

The probabilities are P(green) = [tex]\frac{5}{14}[/tex], P(red) = [tex]\frac{1}{7}[/tex] and P(green and red) = [tex]\frac{5}{98}[/tex].

The probability of an event is calculated as the number of favorable outcomes divided by the total number of outcomes.

In this case, Deepak is choosing two marbles one after the other with replacement, which means after drawing the first marble, he puts it back into the bag before drawing the second one.

Since these are independent events (drawing the first marble does not affect the probability of drawing the second), the probability of both events happening is the product of their individual probabilities.

So, the probability that Deepak will choose one green marble and then one red marble is [tex]\frac{5}{14} *\frac{1}{7} =\frac{5}{98}[/tex].

Complete Question:

A bag contains fourteen marbles. There are 4 purple marbles, 3 blue marbles, 5 green marbles, and 2 red marbles. Deepak randomly chooses two marbles from the bag, one at a time, and replaces the marble after each choice. What is the probability he will choose one green marble and then one red marble? Express the probabilities in fraction form.

4x - y = -6 ....(1)

5x + y = -21 ....(2)

(1) + (2)

9x = -27

x = -3

from (1)

4 * -3 - y = -6

we solve

y = -6

so the answer is

D ( - 3 , - 6 )

The solution to the system of equations is (-3, 6), which corresponds to option D, by using the elimination method to first find x = -3 and then substituting it back to find y = 6.So,option D is correct.

To solve the system of equations using addition (also known as the elimination method), we start with the two given equations:

4x - y = -6

5x + y = -21

Adding these equations together allows us to eliminate the y variable:

4x - y + 5x + y = -6 - 21

Combining like terms, we get:

9x = -27

Dividing by 9 to solve for x:

x = -3

Next, we substitute x = -3 into one of the original equations to solve for y. Using the first equation:

4(-3) - y = -6

-12 - y = -6

y = -6 + 12

y = 6

The solution of the system is the pair (-3, 6), which corresponds to option D.

As a quick check, we can substitute x = -3 and y = 6 into both original equations to ensure they satisfy both equations. Doing this confirms that the solution is correct.

To solve this problem, we find the side length of the square pool, find the inner perimeter of the sidewalk, and then calculate the difference between the outer and inner perimeters. The width of the sidewalk is 5 feet.

This is a Mathematics problem that involves some knowledge of geometry. Firstly, let's inspect the given information: The square swimming pool’s area is 225 square feet. Since the pool is square, the side length of the pool can be found by taking the square root of the area: √225 = 15 feet. So, the inside perimeter of the sidewalk is 60 feet (4*15).

However, the outside perimeter of the sidewalk is 80 feet. The difference between the outside and the inside perimeter (80 – 60) is 20. That value is twice the width of the sidewalk because the sidewalk extends around all four sides. Therefore, each side of the sidewalk must cover extra 5 feet (20 / 4). So, the width of the sidewalk is 5 feet.

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Answer: Option C)

[tex]a_n = 2.5 + 2.5n[/tex]

Step-by-step explanation:

Note that the sequence increases by a factor of 2.5, that is, each term is the sum of the previous term plus 2.5.

[tex]7.5 - 5 = 2.5\\\\10 -7.5 = 2.5\\\\12.5 -10 = 2.5[/tex]

therefore this is an arithmetic sequence with an increase factor d = 2.5

The linear formula for the sequence [tex]a_n[/tex] is:

[tex]a_n = a_1 + d(n-1)[/tex]

Where

[tex]d = 2.5\\\\a_1 = 5[/tex]

[tex]a_1[/tex] is the first term of the sequence

So

[tex]a_n = 5 + 2.5(n-1)[/tex]

[tex]a_n = 2.5 + 2.5n[/tex]

The answer is the option C)

ANSWER

C)

[tex]a_n=2.5+2.5n[/tex]

EXPLANATION

The given sequence is:

5, 7.5, 10, 12.5, 15,...

where

[tex]a_1=5[/tex]

The constant difference is:

[tex]d = 7.5 - 5 = 2.5[/tex]

The closed linear form is given by;

[tex]a_n=a_1+d(n-1)[/tex]

We substitute the values into the formula to get:

[tex]a_n=5+2.5(n-1)[/tex]

Expand to get;

[tex]a_n=5+2.5n - 2.5[/tex]

[tex]a_n=2.5+2.5n[/tex]

First you should simplify the inequality and get n by itself:

3n - 10 ≥ 2      Add 10 on both sides

3n ≥ 12       Divide 3 on both sides

n ≥ 4

When the sign is ≤ or ≥ (less/greater than or equal to), the line is a solid line.

When the sign is < or >, the line is a dotted line.

If the variable is > than the function (like y > 3x + 2, or x > 2y²) The shaded area is above the line (or going in the positive direction)

If the variable is < than the function (like x < 2, or x < 5z - 7), The shaded area is below the line.

Since we got n ≥ 4,

If n is an x value, or n = x, you would have a horizontal line at y = 4, but if n is a y value, n = y, you would have a vertical line at x = 4. The shaded area should be above the line, or to the right of the line since n is > 4. (Sorry, I don't know if n = y or n = x, hope this clarified things)

Answer:

n ≥4

Step-by-step explanation:

3n -10 ≥ 2

Add 10 to each side

3n -10+10 ≥ 2+10

3n ≥12

Divide by 3

3n/3 ≥12/3

n ≥4

To find the length of line AB, the distance formula √((x2 - x1)² + (y2 - y1)²) is used, with coordinates substituted. The calculated distance is approximately 13.6 units.

To calculate the length of the line AB, we use the distance formula which is derived from the Pythagorean theorem. The formula is:

d = √((x2 - x1)² + (y2 - y1)²)

Here, (x1, y1) are the coordinates of point A and (x2, y2) are the coordinates of point B.

Now, let's substitute the given coordinates into the distance formula:

d = √((7 - (-4))² + (-2 - 6)²)

d = √((7 + 4)² + (-8)²)

d = √(11² + (-8)²)

d = √(121 + 64)

d = √185

d ≈ 13.6

The length of the line AB is approximately 13.6 units.

I think the answer might be C

Answer: A

Step-by-step explanation:

Answer:14

Step-by-step explanation: 4+10=14

Answer: 4 + 10 = 14. So, the answer is 14 cats

Answer:

C

Step-by-step explanation:

The n th term formula of a geometric sequence is

[tex]a_{n}[/tex] = a [tex]r^{n-1}[/tex]

where a is the first term and r the common ratio

Using the second and fourth term, then

ar = 6 → (1)

ar³ = 54 → (2)

Divide (2) by (1)

[tex]\frac{ar^3}{ar}[/tex] = [tex]\frac{54}{6}[/tex] = 9

r² = 9 ⇒ r = [tex]\sqrt{9}[/tex] = 3 → C

The answer would be C.

Answer:  I and II.

Step-by-step explanation:

By definition, two solids are similar if their corresponding sides are in the same ratio.

Knowing this, let's find which solids are similar:

Corresponding sides ratio of solids I and II:

[tex]\frac{3}{2}=\frac{2}{\frac{4}{3}}=\frac{5}{\frac{10}{3}}[/tex]

[tex]\frac{3}{2}=\frac{3}{2}=\frac{3}{2}[/tex]

Corresponding sides ratio of solids I and III:

[tex]\frac{3}{\frac{9}{2}}=\frac{2}{3}=\frac{5}{8}[/tex]

[tex]\frac{2}{3}=\frac{2}{3}=\frac{5}{8}[/tex]

Corresponding sides ratio of solids II and III:

[tex]\frac{2}{\frac{9}{2}}=\frac{\frac{4}{3}}{3}}=\frac{\frac{10}{3}}{8}}[/tex]

[tex]\frac{4}{9}=\frac{4}{9}=\frac{5}{12}[/tex]

 You can observe that the solids  I and II are similar.

Answer:

k=(-7y+11)/4

Step-by-step explanation:

Given

11(k-1)= 7(k-y)

In order to find the value of K we have to separate k on one side, so

Multiplying 11 and 7 into the brackets on both sides

11k-11=7k-7y

Subtracting 7k on both sides

11k-11-7k=7k-7y-7k

11k-7k-11= -7y

Adding 11 to both sides

4k-11+11= -7y+11

4k= -7y+11

4k=-7y+11

k=(-7y+11)/4

So the value of K is (-7y+11)/4.