How to find the slope intercept form of the line that passes through (-4,1) and perpendicular to y = 2x - 3

x best represent the width of the rectangle and x + 12 best represents the length of the rectangle.

The length of the rectangle is 12 inches more than it width.

The width of the rectangle can be found as follows:

The perimeter of the rectangle is 42 inches.

Therefore,

perimeter of a rectangle = 2(l + w)

where

Hence,

perimeter of a rectangle = 2(l + w)

The length of the rectangle is 12 inches more than it width.

Therefore,

let

x = width

Hence,

length = 12 + x

learn more on rectangle here: https://brainly.com/question/23241351

#SPJ1

In quartic equation, The player will catch the ball on its way down, at about 4.346 seconds. .

What is the quartic equation's formula?

h  =  -16t2 + 70t + 4

We want to know how many seconds it takes for the ball to be 6 feet above the ground.

We want to know the value of  t  when  h = 6 .  So plug in  6  for  h  and solve for  t .

6  =  -16t2 + 70t + 4       Subtract  6  from both sides of the equation.

0  =  -16t2 + 70t - 2        Let's solve this quadratic equation using the quadratic formula.

t = -70 ± √70² - 4( -16)(-2)/2(-16)

t = -70 ± √4900 -128/ -32

t = -70 ± √4772/ -32

t = -70 + √4772/ -32 ≈ 0.029

t = -70 - √4772/ -32  ≈ 4.346

So we know that

(a) at 0.029 seconds, the ball is 6 feet above the ground and on its way up,  and

(b ) at 4.346 seconds, the ball is 6 feet above the ground and on its way down.

The player will catch the ball on its way down, at about 4.346 seconds.

Learn more about quartic equation

brainly.com/question/13741193

#SPJ1

The probability distribution for X in a day care center where each child takes three classes and either passes or fails each class will be:

0 = 1/4

1 = 1/4

2 = 1/4

It should be noted that from the information, the grades are shown in the table below.

P represents a passed class.

F represents a failed class.

X represent the number of classes failed by a child.

The probability that the number of classes failed by a child is 0 will be:

= 2/8

= 1/4.

The probability that the number of classes failed by a child is 1 will be:

= 4/8

= 1/2

The probability that the number of classes failed by a child is 2 will be:

= 2/8

= 1/4.

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

Answer:Zero-0 divided by 8 3

Step-by-step explanation:

Answer:

What digital/technological features will your futuristic bath/shower time utilize?

The two numbers are 20 and 40

Let n represent the unknown

Next is to find the the products of both numbers

n × 2n= 800

2n²= 800

n²= 800/2

n²= 400

n= √400

n= 20

The first number is 20

The second number 2(20)= 40

Hence the two number are 20 and 40

Read more on products here

https://brainly.com/question/14690350

#SPJ1

The order of the magnitude of the given number is a 5.

According to the statement

We have to find that the order of the magnitude.

So, For this purpose, we know that the

An order of magnitude is an exponential change of plus or minus 1 in the value of a quantity or unit. The term is generally used in conjunction with power-of-10 scientific notation.

From the given information:

The number are 1.25 x 105

To find the order firstly solve it then

1.25 x 105

1.25 x 105 = 131.25

And in this according to the definition of the order of the magnitude:

The order is of the 5 numbers.

So, The order of the magnitude of the given number is a 5.

Learn more about order of magnitude here

https://brainly.com/question/24468862

#SPJ9

Finding m∠2 is c. 44°.

First step is to find the Measure of angle 1 which is m∠1

Measure of angle 1 = (68° + 68°) or (68°×2)

Measure of angle 1 = 136°

Second step is to find  m∠2

Since we have find the measure of angle 1 in order for us to find or determine m∠2 we would have to deduct or subtract m∠1 from 180°

Now let find m∠2

m∠1 = 136°

m∠1 + m∠2 = 180°

136° + m∠2 = 180°

m∠2 = 180° - 136°

m∠2 = 44°

Therefore finding m∠2 is c. 44°.

Learn more about Measure of angle here:https://brainly.com/question/25716982

#SPJ1

Answer:

Step-by-step explanation:

Because 8 2/3 is basically 8.66666666... (you can find this out by doing division 2÷3)

There's an infinite amount of 6's at the end and so the answer got rounded up to 8.67.

Anything above 5 when rounding will be rounded up.

The column vector is discussed below.

In order to write a vector as a column vector: Work out the horizontal component ( x component). Work out the vertical component ( y component). Write the column vector.

Given:

a + b- c

So, If the number is positive, the direction is to the right.  

If the number is negative, the direction is to the left.

Also, If the number is positive, the direction is upwards.  

If the number is negative, the direction is downwards.

So, according to that 'a' will be in right ( upward) direction and 'b' also be in right ( upward) direction.

Then, 'c' is negative in left ( downward ) direction.

Learn more about column vector here:

https://brainly.com/question/14582477

#SPJ1

I'll use x in place of θ

Let's isolate the sine term and then square both sides

3sin(x) + 4cos(x) = 5

3sin(x) = 5-4cos(x)

(3sin(x))^2 = ( 5-4cos(x) )^2

9sin^2(x) = 25-40cos(x)+16cos^2(x)

9sin^2(x) = 25-40cos(x)+16(1-sin^2(x))

9sin^2(x) = 25-40cos(x)+16-16sin^2(x)

9sin^2(x)+16sin^2(x) = 25-40cos(x)+16

25sin^2(x) = 41-40cos(x)

25(1-cos^2(x)) = 41-40cos(x)

25-25cos^2(x) = 41-40cos(x)

Now let w = cos(x), so we now have the following

25-25w^2 = 41-40w

25w^2-40w+41-25 = 0

25w^2-40w+16 = 0

(5w - 4)^2 = 0

5w-4 = 0

w = 4/5

Therefore cos(x) = 4/5

Use the pythagorean theorem or unit circle to find that if cos(x) = 4/5, then it leads to sin(x) = 3/5. This is exactly because of the 3-4-5 right triangle.

Then lastly,

tan(x) = sin(x)/cos(x)

tan(x) = sin(x)  ÷  cos(x)

tan(x) = (3/5)  ÷  (4/5)

tan(x) = (3/5)  *  (5/4)

tan(x) = (3*5)/(5*4)

tan(x) = 3/4

The equation that can be used to find z in the right triangle is sin 28° = 20 / z

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The side and angles of a right angle triangle can be found using trigonometric ratios.

The triangle XMI is a right angle triangle.

where

∠M = 90 degrees

∠X = 28 degrees

∠I = ?

Therefore, the side z can be found as follows;

sin ∅ = opposite / hypotenuse

where

opposite side = 20

∅ = 28°

Hence,

sin 28° = 20 / z

learn more on right triangle here: https://brainly.com/question/12817082

#SPJ1

Answer: a

Step-by-step explanation:

a

Answer:

35

Step-by-step explanation:

-a +5y

-(-5) +5(6)

5 + 30

35

Answer:

(6, -31)

Step-by-step explanation:

Answer:

I think (6, -31)

The set which represents whole numbers but are not natural numbers is:{0,1,2,3 }

Given, we have the following sets:

{₋2,₋3,₋4} = Integers

Negative numbers and all entire numbers are both considered integers. A number without a decimal or fractional element is known as an integer, which encompasses both positive and negative numbers, including zero.

{0,1,2,3} = whole numbers

Whole numbers refer to all natural numbers, including zero (0). We are aware that the term "natural numbers" refers to a group of counting numbers beginning with 1, 2, 3, and so forth. Simply said, a collection of numbers that are whole numbers are those that do not contain any fractions, decimals, or even negative integers. There are zeroes and a group of positive integers in it. whereas all positive integers from 1 to infinity are included in the number system, which also contains natural numbers, which are also used for counting. There is no zero included.

{√₋1 , √₋4 , √₋5 }= Irrational numbers

We are aware that the only numbers that cannot be stated in the form of p/q, where p and q are integers and q 0, are real numbers. For instance, the numbers √5, √3, and so on are irrational.

hence we get the set which represents whole numbers but not natural numbers is {0,1,2,,3,4}

Learn more about Number system here:

brainly.com/question/16612919

#SPJ9

1. The child's height after age 6 is a linear function of his age because it grows at a constant rate annually.

2. The child's growth rate is 5% with an initial value of 40 inches.

3. A linear function that represents the scenario is , H(t) = 40 + 2t.

A linear function is a mathematical expression with variables multiplied by constants appearing in the first degree.

The mathematical operations involved in a linear function are addition and subtraction.

A linear function represents a straight line on the coordinate plane.

Initial height at age 6 = 40 inches

The annual growth rate in inches = 2 inches

Growth rate in percentage = 5% (2/40 x 100)

H(t) = 40 + 2t

Where t = years after age 6

Learn more about linear functions at https://brainly.com/question/17646089

#SPJ1

Using t for the time in years since age 6 and H for height in inches, find a formula for H as a linear function of t.

Answer:

x∈(−25,25)

4x2−25<0

Add 425 to both sides.

x2<425

Calculate the square root of 425 and get 25. Rewrite 425 as (25)2.

x2<(25)2

Inequality holds for ∣x∣<25.

∣x∣<25

Rewrite ∣x∣<25 as x∈(−25,25).

x∈(−25,25)

Answer:  x > 5/4

First, add 25 to both sides

4x² < 25

Then take the square root

4x < 5

Finally, isolate the variable by dividing by 4

x < 5/4

Because you divided, the sign gets flipped

x > 5/4

Hope this helps!

Answer:

$567.88

Step-by-step explanation:

Start with the beginning balance.

Add all the mounts of checks and subtract the total from the beginning balance.

Add the amount of the deposit to the balance.

Beginning balance: $887.43

Withdraw: $435, $58.27, $127.96

Total withdrawals:  $435 + $58.27 + $127.96 = $621.23

Deposit: $301.68

Final balance = beginning balance - total of checks + amount of deposit

Final balance: $887.43 - $621.23 + $301.68 = $567.88

Answer: $567.88

The scholarship money used by Hector  to purchase books is $990

Hector earned $2640 through an academic scholarship.

Hector used three-eighths of his  earned academic scholarship of $2640 to buy books

This is a problem of fractions

In simple words, Fractions means the parts of a whole. The whole can be an object or a group of objects. For example, when we cut a piece of cake from the whole of it, then the portion is the fraction of the cake.

The fraction is also termed as a portion or section of any quantity.

Money used for buying books = 3/8 of $2640

= 3/8 × 2640

= 7920/8

= 990

Hence, the scholarship money used by Hector  to purchase books is $990

To know more about Fractions - https://brainly.com/question/10354322

# SPJ1

A table which could be used with Table A to verify that the function modeling Fahrenheit temperature, F(C), based on a given Celsius temperature, C, is the inverse of C(F) is: option A.

C           -20      -15      -5

F(C)        -5         4       23

Temperature can be defined as a measure of either the degree of hotness or coldness of a physical body (object).

In Science, temperature can be measured by using a thermometer and its units of measurement include the following:

In Mathematics, an inverse function can be defined as a type of function that is obtained by reversing (undoing) the operation of a given function f(x). In Mathematics, a given function f(x) and its inverse function has the following property f⁻¹(f(x)) = x.

Based on the given function which models the Fahrenheit temperature, F(C) and Celsius temperature, C, the inverse of C(F) is as follows:

C           -20      -15      -5

F(C)        -5         4       23

Read more on inverse function here: https://brainly.com/question/12672838

#SPJ1

Answer:

A

Step-by-step explanation:

Hope this helps! Pls give brainliest!

10 percent of the students failed in all three subjects.

Let the us assume that the total number of students in the school are 100.

Thus, according the the information given-

number of students who passed in all three subjects = 20

⇒ number of students who failed in at least one subject = 100 - 20 = 80

Let the number of people who failed in all three subjects be a

Then, as per the given information, we can make a venn diagram as shown in the figure below.

Now, the sum of all the terms in the venn diagram must be 80 since 80 people failed in at least 1 subject. Thus, we get the following equation-

a -3 + 35 - a + 25 - a + a + a - 4 + 15 - a + 2 + a = 80

a + 32 + 25 + 11 + 2 = 80

a + 70 = 80

a = 80 - 70

a = 10

Thus, the percentage of the students who failed in all 3 subjects will be-

10/100 × 100

= 10%

Hence, 10 percent of the students failed in all three subjects.

Learn more about Venn diagrams here-

https://brainly.com/question/1605100

#SPJ9

After excavating and inserting bushes, the hole's elevation in feet is 1 1/10 feet.

3/5 feet per 10 minutes are dug up on average.

After 30 minutes, the elevation or depth of the hole:

3/5 × (30/10) = (3/5 × 3) = 9/5 feets

Consequently, after 30 minutes, the hole's height will be 9 1/2 feet.

Elevation after planting bushes in half of the hole:

After 30 / 2 minutes, the hole's elevation was 2/ (9/5)

=2/(9 /5 )

= (9 /5 ) × 1/2

= 9/10 feet.

Consequently, the hole is elevated by 1 1/10 of a foot above the surrounding ground.

To learn more about elevation from given link

https://brainly.com/question/24823344

#SPJ9

Answer: no

Step-by-step explanation: hope this helps

The quadratic equation is y = x^2 - x - 6

The given parameters are

x-intercepts: x=-1 and x=3

Rewrite properly as

x1 = -2 and x2 = 3

By zero product property, the quadratic equation is

y = (x - x1) * (x - x1)

This gives

y = (x + 2) * (x - 3)

Expand

y = x^2 + 2x - 3x - 6

Evaluate the difference

y = x^2 - x - 6

Hence, the quadratic equation is y = x^2 - x - 6

Read more about quadratic equation at

https://brainly.com/question/1214333

#SPJ1

After 7 years, the total amount accumulated is $13,691.43.

For the given question;

The formula for compound interest is;

CI = P(1 + r/n)∧nt

The rate rate of interest is according to APR; r = 4.4% = 0.044

P = principal amount ($5800).

t  = time in years (7 years)

n = number of times interest given per time period

n = 7×12 = 84 (as compounded monthly)

CI = 5800( 1 + 0.044/84)∧(84×7)

CI = 5800×(1.36)

CI = 7891.43

Thus, the total interest formed after 7 years.

Total amount in bank = principal amount + CI

                                   = 5800 + 7891.43

                                   = 13,691.43

Therefore, the total amount accumulated after 7 years is $13,691.43.

To know more about the compound interest, here

https://brainly.com/question/12325365

#SPJ1