Write the equation of the line that passes through the points (7,-6)(7,−6) and (3,8)(3,8). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer:

4 seconds

===========================

Given is the

quadratic function

, which has a graph of parabola.

It has two

x-intercepts

, with the greater one representing the

projectile on the ground, at h(t) = 0

.

Let's

solve

the equation:

- 16t² + 32t + 128 = 0

t² - 2t - 8 = 0

t² - 2t + 1 - 9 = 0

(t - 1)² = 9

t - 1 = 3 and t - 1 = - 3

t = 4

and t = - 2

The root with the greater value is

t = 4

, which represents the time we need.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:4 \:\: sec [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

height of an object projected in air with time is represented by the given equation :

[tex]\qquad\displaystyle \tt \rightarrow \: h(t) = - 16 {t}^{2} + 32t + 128[/tex]

The height when the object hits the ground will be 0

so, just equate the equation with 0, and we will get the value of t (time) when the projectile will be back to ground.

[tex]\qquad\displaystyle \tt \rightarrow \: - 16 {t}^{2} + 32t + 128 = 0[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: - 16( {t {}^{2} - 2t}^{} - 8) = 0[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: t {}^{2} - 2t - 8 = 0[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: t {}^{2} - 4t +2 t - 8 = 0[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: t(t - 4) + 2(t - 4) = 0[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: (t - 4)(t + 2) = 0[/tex]

So,

[tex]\qquad\displaystyle \tt \rightarrow \: t = 4 \: \: \: \: or \: \: \: \: t = - 2[/tex]

but since time can't be negative, t = 4 seconds

The object will be back on ground after 4 seconds.

The amount of cash that as kept in the bank is $937500.

Let's have x represent the amount of cash.

One portion of it pays 0.5%, so 0.005x; the other portion pays 3.5%, so 0.035x. This gives us:

0.005x + 0.035x = 37500

Combining like terms:

0.040x = 37500

Solve for x:

x = (37500)/(0.04)

x = 937500

Therefore, the company started with $937,500.

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Answer:

Step-by-step explanation:

[tex]3\sqrt{20} + 4\sqrt{5}[/tex]

1st: Split up the numbers under the radical into possible factors.

[tex]3\sqrt{5*4} + 4\sqrt{5}[/tex]

2nd: Take out the perfect square (in this case 4)

[tex]3*2\sqrt{5} + 4\sqrt{5}[/tex]

3rd: simplify

[tex]6\sqrt{5} + 4\sqrt{5}[/tex]

4th: Combine like terms

[tex]10\sqrt{5}[/tex]

Answer:

[tex]\sf 10\sqrt{5}[/tex]

Step-by-step explanation:

      Prime factorize 20 and simplify 3√20

[tex]\sf 3\sqrt{20} = 3\sqrt{2*2*5}=3*2*\sqrt{5}=6\sqrt{5}[/tex]

[tex]\sf 3\sqrt{20}+4\sqrt{5}=6\sqrt{5}+4\sqrt{5}[/tex]

                   [tex]\sf = 10\sqrt{5}[/tex]

Total number of possible outcomes:

From those 36 possible outcomes the next 10 sum of at least 9 ( a number greather than or equal to 9):

Then, the probability of obtaining a sum of at least nine when rolling a pair of dice is:

Based on the gross pay for Melika Yasin, and the fact she claims no allowances and is married, the amount withheld from her pay for Federal Income Tax is $43.

Melika Yasin had a gross pay of $355.00 for the week. This amount is more than $350 but less than $360.

Melika Yasin therefore falls into the bracket of "At least $350 but less than $360."

She also claims no allowances in this bracket. This means that the amount that would be withheld for Federal Income Tax according to the table would be $43.

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Considering Justin's serve, it is found that:

a) The ball traveled 21.4 feet, which means that Justin's estimate is correct.

b) An assumption regarding the angle of Justin's serve was made.

c) The Pythagorean Theorem was used to solve this mathematical problem.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle(triangle which has an angle of 90º between the two legs) with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:

[tex]h^2 = l_1^2 + l_2^2[/tex]

Assuming that the ball was served at an angle of 90º, the situation can be summarized as follows:

Hence the Pythagorean Theorem is applied and the distance is calculated as follows:

d² = 7.5² + 20²

d = sqrt(7.5² + 20²)

d = 21.4 feet.

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A square has 4 congruent side lengths. This means that each side will be the same length. Therefore, we can set the two lengths equal to each other.

[tex]S=S[/tex]

[tex]7x-15=2x[/tex]

Isolating a variable: rearranging an equation so that the variable is by itself

3 Step Solving process:

1. Collect like terms

2. Perform inverse operations

3. Simplify if necessary

[tex]7x-2x-15=0[/tex]

[tex]5x=15[/tex]

[tex]\frac{5x}{5}=\frac{15}{5}[/tex]

[tex]x=3[/tex]

The value of x =  3

The perimeter can be found by adding all of the side lengths. A square has 4 sides.

a + a + a + a = P

However, we know that a square has congruent sides so we can manipulate this formula:

4a = P - where a is equal to the side length

Using a previous equation we know that a side length is equal to 2x and we know the value of x, to be 3. Therefore, a side length must be 6.

we can now input the value of the side length into the formula.

[tex]4(6)=P[/tex]

[tex]24=P[/tex]

The perimeter of the square is 24.

Answer:

Answer down below!

Step-by-step explanation:

y = 2

The answer should be dragged and dropped into the box to match each point to its coordinates as follows;

Point A ⇔  (2 1/4 , 1 1/2).

Point B ⇔  (-1 1/4 , 1 1/2).

Point C ⇔ (-2 1/2 , 1/4).

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

In Mathematics and Geometry, a quadrant simply refers to the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate.

Based on the cartesian coordinate (grid) below, the coordinates points and quadrants should be identified as follows;

Point A ⇔  (2 1/4 , 1 1/2) → quadrant 1.

Point B ⇔  (-1 1/4 , 1 1/2) → quadrant 2.

Point C ⇔ (-2 1/2 , 1/4) → quadrant 2.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

y < 3

Step-by-step explanation:

Answer:

8.00340909

Step-by-step explanation:

since 21129 was walked in one hour the in two hours 42258 wouldve been walked so that means mark walked a little over 8 miles

hope this helped

have a good day^^

def store_digits(n):

   """Stores the digits of a positive number n in a linked list.

   >>> s = store_digits(1)

   >>> s

   Link(1)

   >>> store_digits(2345)

   Link(2, Link(3, Link(4, Link(5))))

   >>> store_digits(876)

   Link(8, Link(7, Link(6)))

   """

   "*** YOUR CODE HERE ***"

   1 = Link.empty

   while n > 0:

       1 = Link(n % 10, 1)

       n //= 10

   return 1

Store Digits

In some programming languages you have to declare a variable before using them or define the information that will be stored in it, e.g., a number. However, in Python we just need to type the name of our variable, followed by an equals sign and a value to assign to it.

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Answer:

a. (2x−9)(x+3)

b. (2x+11)(2x−11)

c. (3x−2)(2x+5)

d. (3x+4)(x+1)

e. (5x+3)(x−9)

f. (2x+5)(2x−7)

g. 4(3x+5)(3x−5)

h. 3(2x+5)(2x+5)

Step-by-step explanation:

Answer:

Lol, I recommend you ask your teacher later how to factor :]

It's kinda hard to explain. Tell me if I got any wrong :]

Step-by-step explanation:

Ouch. Well, here I go:

a) (2x-9)(x+3)

b) (2x-11)(2x+11)

c) (3x-2)(2x+5)

d) (x+1)(3x+4)

e) (x-9)(5x+3)

f) (2x-7)(2x+5)

g) (6x-10)(6x+10)

h) (6x+15)(2x+5)

:]

We need to know how to write linear equation to solve the problem. The number of hours when they make the same amount is 2 hours.

Linear equation is when a value of one variable is dependent on only one other variable. In the given question we know that Greg charges a flat fee of $140 and another $25 for every hour and Greg charges a flat fee of $100 and $45 for every hour. We need to find out the number of hours when both of them have the same amount, we can consider number of hours to be x and form equations accordingly.

140+25x=100+45x

20x=40

x=2

Therefore both of them will make the same payment when number of hours is 2.

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Answer:70 cm

Step-by-step explanation:a^2+b^2=c^2

Answer: $2.96

Step-by-step explanation:

$18.75 - $3.95 = $14.80

$14.80 / 5 = $2.96

The approximate total of weight of the litter of  6 kittens 0.675kg

What is Weight ?

The force exerted on an object by gravity is known as its weight. The gravitational force acting on the item is referred to as weight in several common textbooks. Some people refer to weight as a scalar quantity that measures the gravitational force's strength.

Given,

The weight of one newborn kitten = 1/4 pounds
The value of pound in kilograms = 1pound = 0.45kg
convert the weight from  pound to kilograms = 1/4 x 0.45

                                                                              = 0.1125kg

Now, to find out total weight of litter of 6 kitten in kilograms

= 0.1125 x 6

= 0.675kg

Hence, The approximate total weight of the litter of 6 kittens in kilograms is 0.657kg
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The absolute value equation is |x - 70| = 0.02, while the minimum and maximum torque are 69.98 and 70.02 foot pounds

From the question, the given parameters are:

Specification = 70 foot pounds

Margin of error = 0.02 foot pounds

The absolute value equation of the scenario is then calculated as

|x - Specification| = Margin of error

Substitute the known values in the above equation

So, we have

|x - 70| = 0.02

Solving the equation, we have

x - 70 = 0.02 and x - 70 = -0.02

Add 70 to all sides

x = 70.02 and x = 69.98

Hence, the range is 69.98 to 70.02

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Answer:

x = - 1 / 24

Step-by-step explanation:

-6 ( 6x - 1 ) + 9 = 36x + 18

First, solve the brackets.

-36x + 6 + 9 = 36x + 18

Then, subtract 36x by both sides.

-36x - 36x + 6 + 9 = 18

-72x + 15 = 18

Now, Subtract 15 by both sides.

-72x = 18 - 15

-72x = 3

Now divide both sides -72 by both sides.

x = - 3 / 72

x = - 1 / 24

Answer:

D.

Step-by-step explanation:

7.99 is the basic fixed cost per month. this is charged, even if there are no songs (x = 0) downloaded.

and so, 1.75 is the cost per downloaded song in addition to the basic fixed cost. so, yes, the number of downloaded songs has to be multiplied by the cost for a single song to get the total.

and so, 1.75 is the change in the total cost for every automakers download (every time x is increased by 1).

The area of the rectangles A,B, C are 8 cm , 3cm and 15 cm , whereas  the area of the enlarged rectangle A,B,C are  32 cm ,12 cm and 60cm  

The relation between the area of the both original and the enlarged is the area of the enlarged rectangle is 4 times the area of the original rectangle.The problem we are dealing with is area what is referred to as the amount of space occupied by a two-dimensional figure, it is the amount that measures the number of unit squares that surround the surface of a closed figure. The standard unit of the region is square units which are generally spoken to as square inches, square feet. For the area of the rectangle we multiply the length of the rectangle by the width of the rectangle.

Area= l x b

for rectangle A : 4 x2 = 8 cm, for  B : 3 x 1 = 3 cm and for C: 5 x 3 = 15 cm  

As  we increase each dimension by 2 times:

For the enlarged rectangle A : 8 x4 = 32 cm ,B : 6 x 2 = 12 cm and C: 10 x 6 = 60 cm  .

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Answer: No, at least one segment length is not preserved, making this a nonrigid transformation.

Step-by-step explanation: A rigid transformation implies that both the shape and size are not changed. The second answer is right because the length of segment JK (2 units) is not preserved when mapped onto J'K' (5 units).

Based on the calculation below, the amount of cash that the Smith and Jones manufacturing company kept in the bank was $500,000.

Let x represents the amount of cash that Smith and Jones manufacturing company has.

Therefore, we have:

Interest amount from bank = Cash * A third * Bank interest rate = x * (1/3) * 0.5% = x0.0017

Interest amount from long-term investments = Cash * Two-third * Long-term investments interest rate = x * (2/3) * 3.5% = x0.023

Total interest earned = Interest amount from bank + Interest amount from long-term investments = $37,500 ...................... (1)

Substituting all the relevant values into equation (1) and solve for x, we have:

x0.0017 + x0.023 = $37,500

x0.025 = $37,500

x = $37,500 / 0.025

x = $1,500,000

Amount kept in the bank = Cash * A third = $1,500,000 * (1 / 3) = $500,000

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Answer:

A student writes the inequality representing the graph as y ≥ –2(x – 10)2 + 200.

The inequality is

✔ incorrect

because testing the point (5, 100) simplifies to the inequality

✔ 100 ≥ 150

.

Step-by-step explanation:

A student writes the inequality representing the graph as y ≥ –2(x – 10)2 + 200.

The inequality is

✔ incorrect

because testing the point (5, 100) simplifies to the inequality

✔ 100 ≥ 150

.

The inequality is incorrect because testing the point (5, 100) simplifies to the inequality 100 ≥ 150.

An inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an equation based on any of the following arguments (symbols):

Next, we would evaluate and simplify the given inequality in order to determine its solution as follows:

y ≥ –2(x – 10)² + 200.

At point (5, 100), we have:

100 ≥ –2(5 – 10)² + 200.

100 ≥ –2(-5)² + 200.

100 ≥ –2(25) + 200.

100 ≥ –50 + 200.

100 ≥ 150 (incorrect and false).

In conclusion, the given inequality is incorrect because 100 cannot be greater than or equal to 150.

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Compete Question;

A student writes the inequality representing the graph as y ≥ –2(x – 10)² + 200.

The inequality is ______ because testing the point (5, 100) simplifies to the inequality _____.

The expanded form of this number 14.702 will be  (1 × 10) + (4 × 1) + (7/10) + (2/1000)

It should be noted that expanded form simply means breaking down of the number given into different units.

Therefore, based on the information illustrated. This will be:

14.702 will be:

= (1 × 10) + (4 × 1) + (7/10) + (2/1000)

= 10 + 4 + 0.7 + 0.002

Note that your options aren't written well.

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Giv the table below:

Time (Months) 6 8 10 12

Money (Dollars) 476 606 736 866

(a) We are asked to find the amount that is alreafy in the account when Diane started depositing.

The amount that will be in the account before Diane started depositing will be

86 dollars.

(b) To get the rate if the money increase or decrease:

606 - 476

2

= 130/2

= 65

The money increases by 65

The tables that represent a proportional relationship are :

x 1 2 3 4 5

y 4 5 6 7 8

b 2 3 8 9 14

c 4 6 16 18 28

Two variables have a proportional relationship when the ratios of the rate of change of the variables are constant.

Ratio = change in the value of y / change in the value of x

First table:

(5 - 4) / (2 - 1) = 1

(6 - 5) / (3 - 2) = 1

(7 - 6) / (4 - 3) = 1

(8 - 7) / (5 - 4) - 1

Second table:

(5 - 3) / (3 - 2) = 2

(6 - 5) / (4 - 3) = 1

(8 - 6) / (5 - 4) = 2

(9 - 8) / (6 - 5) = 1

Third table:

(6 - 4) / (3 - 2) = 2

(16 - 6) / (8 - 3) = 2

(18 - 16) / (9 - 8) = 2

(28 - 18) / (14 - 9) = 2.

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The null hypothesis should not be rejected. There is insufficient evidence that the true diameter differs from 0.5 inches.

We are given that,

n = 15

t-value = 1.66

Significance level;α = 0.05

So, DF = n - 1 = 15 - 1 = 14

In the attached one-sample t-table, we can see that the p-value of 0.06

corresponds to a t-value of 1.66 and a DF of 14

Due to the P-value of 0.06, it is greater than the significance level of 0.05. Based on the results, we are not rejecting the null hypothesis. There is insufficient evidence to conclude that the true diameter in active attachment is different from 0.5

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Answer:

while using a calculator we need it for solving problems and practice and analysis of reference to be able to answer

Step-by-step explanation:

according to which unit are we calculating