Solve each equation by factoring. Then solve the quadratic formula. (Show all work)

Answer:

3584

Step-by-step explanation:

[tex]896[/tex]×[tex]4[/tex] =[tex]3584[/tex] (refer as table of 896).

hope it help :)

Answer:

  176 yd²

Step-by-step explanation:

You want the shaded area of a parallelogram that has a trapezoid-shaped white area.

The area of a parallelogram is given by the formula ...

  A = bh

The parallelogram shown has a base of 17 yd and a height of 7 yd +6 yd. Its area is ...

  A = (17 yd)(7 yd +6 yd) = 221 yd²

The area of the white space cut from the parallelogram is given by the formula ...

  A = 1/2(b1 +b2)h

where b1 and b2 are the parallel bases of the trapezoid, and h is the distance between them.

  A = 1/2(7 yd +8 yd)(6 yd) = 45 yd²

The shaded area is the difference of these two areas:

  shaded area = 221 yd² -45 yd² = 176 yd²

The area of the shaded region of the parallelogram is 176 yd².

Answer:

B. the answer is 4

Step-by-step explanation:

Start by dividing miles by gallons.

So for Mitra: Divide 469.8 and 14.5 --- 469.8/14.5= 32.4

For Adira: Divide 355 and 12.5 355/ 12.5 = 28.4

Now, we just subtract the answers to find the difference.

32.4-28.4 = 4.

4 is the difference.

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 _____.

She uses 1/2 cup in each batch.

So, if she has 3 1/4 cups in total, we have to divide this total by 1/2 to know how many batchs she can make:

She can make 6 1/2 batches.

using the normal distribution, the warranty period of motor last at 6.24 years.

According to given question , the average life of motor = 10 years and standard deviations = 2 years .

let X be the time period in which the warranty period of motor last . X ~ N( μ, σ²) where u is mean and s is standard deviations. X ~ N( 10, 2²) ⁼ N(μ, σ²)

it is given that only 3% number of motors are replaced and 3% = 0.03

Using normal distribution , P( X≤ x)= P(( X - μ )/ σ ≤ (x- μ)/σ ) = P ( Z ≤ (x- μ ) / σ ) =0.03

Z = (X- μ) / σ => X = Z (σ) + μ

p (Z ≤ -1.88) = 0.03 so, Z-value is - 1.88..

put all the value of variables in above formula we get , -1.88 ( 2) + 10 = X => X = - 3.76 + 10

=> X = 6.24

Thus , the motor's warranty period lasted about 6.24 years.

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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:

John is 16 years old now.

Check:

1) 16+5 = 21

2) 16-9 = 7

3) 21 = 7*3

Step-by-step explanation:

Hope it helps! =D

Answer:

• score with two questions wrong = 18

• score with x questions wrong = (20 - x)

Step-by-step explanation:

The question is divided into two parts.

The first part asks us to calculate the marks that would be scored out of 20 if someone got 2 questions wrong. To do this we simply have to subtract 2 from 20 to get the score:

score = 20 - 2

         = 18

Therefore, Yasmin's score would be 18.

The second part asks us to calculate the marks that would be scored if someone got x questions wrong instead. As we did in the first part, we have to take away x from 20 in order to get the score:

score = 20 - x,

where x can be any whole number.

Therefore, Yasmin's score would be (20-x).

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.

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)

:]

Shelley's cup of tea is cooling down at the rate of 1.2 degree per minute.

According to the question,

We have the following information:

Shelley's cup cooled down 12 degrees in 10 minutes.

In order to find the rate of cooling down of the cup of tea, we will divide the degrees of the cooling by the total number of minutes.

So, we have the following expression:

Rate of cooling down of Shelley's cup = Total degrees the cup cooled down/total time taken

Rate of cooling down of Shelley's cup = 12/10

Rate of cooling down of Shelley's cup = 1.2 degree per minute

Hence, the rate of cooling down of Shelley's cup is 1.2 degree per minute.

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Answer:

1/20

Step-by-step explanation:

Find the rate in degrees per minute. Divide

1

2

of a degree by 10 minutes.

To divide by 10, multiply by its reciprocal,

1

10

.

1

2

÷10

=

1

2

1

10

=

1

20

Shelley's tea is cooling down at a rate of

1

20

of a degree per minute.

Sanjay a is making punch. he uses 1/3 c of pineapple juice for every 3/4 c of orange juice Then 4/3 cups of pineapple juice does he need if he uses 3 c of orange

equation of direct proportion between x and y

x1/y1 = x2/y2

as per given ,

let x= quantity of pineapple juice and y= quantity of orange juice

x1= 1/3 , y1 = 3/4

x2 = ?  and y2 =3

x1/y1 = x2/y2

(1/3)/ (3/4) = x2/3

4/9= x2 /3

4/3 = x2

Hence ,Sanjay a is making punch. he uses 1/3 c of pineapple juice for every 3/4 c of orange juice Then 4/3 cups of pineapple juice does he need if he uses 3 c of orange

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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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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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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:

a = - 1

Step-by-step explanation:

given the zeros of a parabola x = a and x = b , then the factors are

(x - a) and (x - b) , then the equation is

y = a(x - a)(x - b) ← a is a multiplier

here the zeros are x = - 3 and x = 3 , then factors are

(x - (- 3) ) and (x - 3) , that is (x + 3) and (x - 3) and the equation is

y = a(x - 3)(x + 3)

to find a substitute any other point on the curve into the equation

using (0, 9 ) , then

9 = a(0 - 3)(0 + 3) = a(- 3)(3) = - 9a ( divide both sides by - 9 )

- 1 = a

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 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:

Answer down below!

Step-by-step explanation:

y = 2

By taking a product, we can see that the total energy consumed by the console is 42,504 watt-hours.

Here we know that the console uses 154 watt-hours of energy each hour.

So, if you use it for x hours, the energy consumed is given by the product:

E = ( 154 watt-hours)*x

In this case, we know that the console is used for 276 hours, then we can write:

E = (154 watt-hours)*276 = 42,504 watt-hours.

Which is the product between the hourly consumption and the number of hours used.

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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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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:

Answer:

s:{4}

Step-by-step explanation:

4(4)+6<2(4)+12

16+6<8+12

32<20

which is the only false one

Answer:

5,067

Step-by-step explanation:

9,379-4,312=5,067

Answer:

5,067

sometimes writing the problem like this

9,379

- 4,312

can help. :)

Answer: |J|= -16

Step-by-step explanation:

The value of ∣J∣ is -16.

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the numbers.

Given:

[tex]J = \left[\begin{array}{ccc}-1&4\\2&8\end{array}\right][/tex]

To find the value of ∣J∣:

We have to find the determinant of matrix J.

Multiply the numbers along the diagonal from top-left to bottom-right.

Multiply the numbers along the diagonal from bottom-left to top-right.

The second product is subtracted from the first.

Get the 2-by-2 determinant's value via simplifying.

∣J∣ = {(-1x8) - (2x4)}

∣J∣ = {-8 - 8}

∣J∣ = -16

Therefore, the value of ∣J∣ is -16.

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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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The first law is called the Law of Detachment. The law states that if p → q and p is true, then q is true.

The second law is the Law of Syllogism. It states that If p → r and q → r, then p → r is true.

It is to be noted that the Law of Detachment is the most often employed deductive reasoning theory.

In other words, if a conditional statement and its hypothesis are true, the conclusion is likewise true. In other words, the conclusion may be "separated" from the conditional.

In the above instance, p is synonymous with having a cat; while q is synonymous with it chasing a rat.

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2.33 is the student's GPA using the average weighted mean.

So, the weighted average is calculated by multiplying each grade by its weight and dividing the result by the total weights.

It is as follows:

[tex]M=\frac{3 \times 3 \times 3+1(3)+2(4)+2(2)}{9+3+4+2}=\frac{12}{18}=2.33[/tex]

Therefore, 2.33 is the student's GPA using the average weighted mean.

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We can calculate the perimeter of the rectangular yard to find out how much fence Joshua needs:

since the perimeter of the yard is 264 yards, then Joshua does not have enough fence for his yard, since he only has 245 t of fence, and he needs 264ft