y-intercept of y=3/2|x-2|

Answer:

Slope = 4

Step-by-step explanation:

The slope of a line can be calculated using the following formula:

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

From the question can put the points as:

(2, -5) as (x1, y1)

and

(4, 3) as (x2, y2)

Therefore, we can put in the values into the formula to solve for the slope.

[tex] \frac{3 - ( - 5)}{4 - 2} \\ = \frac{3 + 5}{2} \\ = \frac{8}{2} \\ = 4[/tex]

y=mx+b

replacing y=4, m=2, x=3 in the equation:

4=2(3)+b

then

Answer:

Explanation:

Given the values of the variables below:

• D = 116,870

• E=1/3

• L =15

• M = 20

• O = 10.4

• Y = 6,808

We are required to evaluate:

Substitute the given values:

We simplify using the order of operations PEMDAS.

First, evaluate the parentheses in the denominator.

Next, evaluate the exponent(E): 10.4²

Next, we take multiplication and division together:

Finally, take addition and subtraction and then simplify.

The result of the evaluation is:

The angle measures

m WXZ = 180 - 90 - 24

mWXZ = 66°

we have that

The area of the composite figure is equal to the area of a rectangle plus the area of a right triangle

so

step 1

Find out the area of the rectangle

A=L*W

A=8*5

A=40 cm2

step 2

Find out the area of the right triangle

A=(1/2)(b)(h)

where

b=8-(2+1)=8-3=5 cm

h=5 cm

A=(1/2)(5)(5)

A=12.5 cm2

therefore

the total area is

A=40+12.5=52.5 cm2

Given the inequality:

Solve for x:

so, the answer will be:

ANSWER

y = -3x

EXPLANATION

We have to determine the slope-intercept form of the equation of the line.

The slope-intercept form of a linear equation is given as:

y = mx + c

where m = slope

c = y intercept

First, we have to find the slope:

where (x1, y1) and (x2, y2) are two points the line passes through.

Therefore:

Now, we have to use the point-slope method to find the equation:

y - y1 = m(x - x1)

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

y + 3 = -3x + 3

y = -3x + 3 - 3

y = -3x

That is the slope intercept form of the equation.

⇒It is way more appropriate if I use the product rule. That states that:

⇒f(x)g(x)=f'(x)g(x)+f(x)g'(x)

[tex]t^{4} In(8cos(t))\\=4t^{3}In(8cos(t))+t^{4} \frac{1}{8cos(t)} *(0cos(t)+8*(-sin(t))*1)\\=4t^{3}In(8cos(t))+\frac{t^{4}-8sin(t)}{8cos(t)}[/tex]

Note:

Given F(x)=In(x)

⇒[tex]F'(x)=\frac{1}{x}[/tex]

Goodluck

Answer:

t^3 (4 ln(cos8t) - t tant)

Step-by-step explanation:

Using the Product Rule:

dy/dt = t^4 * d(ln(8cost) / dt + ln(8cost) * d(t^4)/dt

         = t^4 * 1/ (8cost) * (-8sint) + 4t^3 ln(8cost)

         = -8t^4 sint / 8 cost + 4t^3 ln(8cost)    

         = -t^4 tan t + 4t^3 ln(8cost)  

          = t^3 (4 ln(cos8t) - t tant)

test

some text with formatting

0. primo

1. secondo

2. terzo

• good

• better

• the best

∛

pl

lkp

ok

=)

1 mile= 1.609 km

Then,

2*1.609=3.218 km

He walked 3.218 kilometers

The correct volume of the rectangular prism as calculated by Betty is 108 cubic yards

A rectangular prism is cuboid and an hexahedron that has 6 faces.

The formula for finding the volume of the rectangular prism is V = l•w•h

Where;

l = Length

w = Width

h = Height

The measurement of the prism, for which Karen is calculating the volume gives;

w = h

The amount larger Karen found that she made the width, which gives;

Width of the cube Karen used = (1 + 1/3) × w

Therefore;

h = (1 + 1/3) × w

The volume becomes;

V' = l × (1 + 1/3) × w × (1 - 1/3) × w = l•w²•(1²-1/3²)

V' = l•w²•(8/9)

The amount by which the volume increased, dV = 12 yd³

Which gives;

l•w²•(8/9) = l•w•h - 12 = l•w² - 12

l•w²•(8/9) - l•w² + 12 = 0

l•w²•(8/9) - l•w² + 12 = 0

l•w²/9 = 12

V = l•w² = 12 × 9 = 108

The correct volume of the prism is 108 cubic yards

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From the question the following can be derived:

(a)

Let x cans of juice and y cans of soda be purchased for the dorm. Then the cost of the juice and soda is 0.60x + 0.75y. The equation of all the combinations of juice and soda is 0.60x + 0.75y = 24.

(b)

The cost of exactly 24 cans of juice is $24 * 0.60 = $14.40. After this purchase, the remaining sum of money available is $24 - $14.40 = $9.60. This will suffice to buy 12 cans of soda, leaving a balance of $0.80. Thus. the entire money cannot be spent if exactly 24 cans of juice are purchased.

(c)

Below is a graph of the line 0.6x + 0.75y = 24 or 4x + 5y = 160 is plotted. All possible cimbinations of juice and soda will lie on this line. The x-intercept is 40 and the y-intercept is 32. Since neither of x and y can be negative, hence the lower and upper bounds for x are 0 and 40 and the lower ad upper bounds for y are 0 and 32. Also , x has to be multiple of 5 and y has to be a multiple of 4. As may be observed from the graph, only 9 combinations are possible which are (x, y):

(0, 32), (5, 28), (10, 24), (15, 20), (20, 16), (25, 12), (30, 8), (35, 4), (40, 0).

Graph:

The approach is to find the area of the individual sides and add all up

Besides the base, we can identify about 6 rectangles.

area of a rectangle, A = base x height

Given the following functions;

f(x) = x^2 + 2

g(x) = 3x - 2

(g+h)(x) = g(x)+h(x)

(g+h) = x^2 + 2 + 3x - 2

(g+h) = x^2+3x + 2-2

(g+h) = x^2 + 3x

To get (g+h) (-3), we will subtitute x = -3 into the resulting function as shown;

(g+h) (-3) = (-3)^2+3(-3)

(g+h) (-3) = 9 - 9

(g+h) (-3) = 0

Hence the value of the expression (g+h) (-3) is 0

Given that:

- The office building contains 96,000 square feet of space.

- There will be at most 15 one-bedroom units with an area of 800 square feet. The rent of each unit will be $650.

- The remaining units have 1200 square feet of space.

- The remaining units will have two bedrooms. The rent for each unit will be $900.

Let be "x" the number of one-bedroom apartments and "y" the number of two-bedroom apartments.

• The words "at most 15 one-bedroom units" indicates that the number of these apartments will be less than or equal to 15 units:

• You know that the remaining units are two-bedroom apartments. And the number of them is greater than or equal to zero. Then, you can set up the second inequality to represent this:

• You know the area of each one-bedroom apartment, the area of each two-bedroom apartment, and the total area that the office building contains. The sum of the areas of the apartments must be less than or equal to the total area of the office building.

Then, the inequality that represents this is:

• Therefore, you can set up this System of Inequalities to represent that situation:

Hence, the answer is: Last option.

Explanation

To find the percentage of the tip we will use the formula below.

Answer: 13%

Given

The bacteria in a dish triples every hour. At the start of the experiment there

were 400 bacteria in the dish. When the students checked again there were

32,400 bacteria. How much time had passed? (Write your equation and solve for

x; y= a • bx)

Solution

The variable of interest is

X: sodium consumption of an American male.

a) This variable is known to be normally distributed and has a mean value of μ=9.6grams with a standard deviation of δ=0.8gr

Any normal distribution has a mean = μ and the variance is δ², symbolically:

X~N(μ ,δ²)

For this distribution, we have established that the mean is μ=9.6grams and the variance is the square of the standard deviation so that: δ² =(0.8gr)²=0.64gr²

Then the distribution for this variable can be symbolized as:

X~N(9.6,0.64)

b. You have to find the probability that one American man chosen at random consumes between 9.7 and 10.6gr of sodium per day, symbolically:

The probabilities under the normal distribution are accumulated probabilities. To determine the probability inside this interval you have to subtract the accumulated probability until X≤9.7 from the probability accumulated probability until X≤10.6:

Now to determine these probabilities, we have to work under the standard normal distribution. This distribution is derived from the normal distribution. If you consider a random variable X with normal distribution, mean μ and variance δ², and you calculate the difference between the variable and ist means and divide the result by the standard deviation, the variable Z =(X-μ)/δ ~N(0;1) is determined.

The standard normal distribution is tabulated. Any value of any random variable X with normal distribution can be "converted" by subtracting the variable from its mean and dividing it by its standard deviation.

So to calculate each of the asked probabilities, you have to first, "transform" the value of the variable to a value of the standard normal distribution Z, then you use the standard normal tables to reach the corresponding probability.

So we have to find the probability between the Z-values 1.25 and 0.125

Using the table of the standard normal tables, or Z-tables, you can determine the accumulated probabilities:

And calculate their difference as follows:

The probability that an American man selected at random consumes between 10.6 and 9.7 grams of sodium per day is 0.344

c. You have to determine the two sodium intake values ​​between which the middle 10% of American men fall. If "a" and "b" represent the values we have to determine, between them you will find 10% of the distribution. The fact that is the middle 10% indicates that the distance between both values to the center of the distribution is equal, so 10% of the distribution will be between both values and the rest 90% will be equally distributed in two tails "outside" the interval [a;b]

Under the standard normal distribution, the probability accumulated until the first value "a" is 0.45, so that:

And the accumulated probability until "b" is 0.45+0.10=0.55, symbolically:

The next step is to determine the values under the standard normal distribution that accumulate 0.45 and 0.55 of probability. You have to use the Z-tables to determine both values:

The value that accumulates 0.45 of probability is Z=-0.126

To translate this value to its corresponding value of the variable of interest you have to use the standard normal formula:

You have to write this expression for X

Replace the expression with a=-0.126, μ=9.6gr, and δ=0.8gr

The value of Z that accumulates 0.55 of probability is 0.126, as before, you have to translate this Z-value into a value of the variable of interest, to do so you have to use the formula of the standard normal distribution and "reverse" the standardization to reach the corresponding value of x:

Replace the expression with b=0.126, μ=9.6gr, and δ=0.8gr and calculate the value of X:

The values of sodium intake between which the middle 10% of American men fall are 9.5 and 9.7gr.

By algebra properties, the sum of four mixed numbers is equal to the mixed number [tex]8\,\frac{37}{40}[/tex].

In this problem we find a sum of four mixed numbers. The simplification process consists in transforming each mixed number into a fraction and apply algebra properties. Then,

[tex]9 \,\frac{1}{2}[/tex] = 9 + 1 / 2 = 18 / 2 + 1 / 2 = 19 / 2

[tex]3\,\frac {7}{8}[/tex] = 3 + 7 / 8 = 24 / 8 + 7 / 8 = 31 / 8

[tex]4\,\frac{4}{5}[/tex] = 4 + 4 / 5 = 20 / 5 + 4 / 5 = 24 / 5

[tex]1 \,\frac{1}{2}[/tex] = 1 + 1 / 2 = 2 / 2 + 1 / 2 = 3 / 2

(19 / 2 - 31 / 8) + (24 / 5 - 3 / 2)

(76 / 8 - 31 / 8) + (48 / 10 - 15 / 10)

45 / 8 + 33 / 10

450 / 80 + 264 / 80

714 / 80

357 / 40

320 / 40 + 37 / 40

8 + 37 / 40

[tex]8\,\frac{37}{40}[/tex]

The sum of mixed numbers is equal to [tex]8\,\frac{37}{40}[/tex].

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To change decimal or fraction to percent multiply them by 100

Example: 1/4 x 100% = 25%, 0.2 x 100% = 20%

Let us check the answer of the 3 students

Maggie wrote 75% = 3/5

Since

Then 3/5 = 60%, not 75%

Maggie is wrong

Bieber wrote 0.05 = 50%

Let us check

0.05 x 100% = 5%, not 50%

Bieber is wrong

Yung wrote 3/8 = 0.375

Let us check

Since 0.375 x 100% = 37.5%

Yung is right

The answer is Lee Yung only

The answer is D

We know that

• Each protective coat is 2/27 inches thick.

• We need to fill 2/3 inches of this protective coat.

To solve this problem, we need to know the total number of the application needed to fill 2/3 inches. We can form the following expression

We solve for x

the slope can be calculated using the next formula

where

(5,-14)=(x1,y1)

(-14,0)=(x2,y2)

then we substitute the values

the answer is -14/19

Answer

Option C is correct.

v = (20, 36)

Explanation

If the initial and terminal points of a vector are given, the vector itself is obtained, per coordinate, by doing a terminal point coordinate minus initial point coordinate.

u = [(5 - 15), (4 - 22)]

u = (-10, -18)

Then, we are told that vector v points in the opposite direction as that of vector u and its magnitude is twice that of vector u too.

In mathematical terms,

v = -2u

v = -2 (-10, -18)

v = (20, 36)

Hope this Helps!!!

A: height is increasing from 0-2 interval.

B: Height remains the same on 2-4

C: 4-6 the height is decreasing the fastest, because the slope is the steepest on that interval.

D: Baloon would be on the ground at 16 seconds, and will not fall down further. that is the way it is in real-world (constraint).

Okay, here we have this:

Considering the provided table, we are going to find the corresponding linear equation, so we obtain the following:

To do this we will start using the information in the slope formula, then we have:

m=(y2-y1)/(x2-x1)

m=(190-(-30))/(19-9)

m=220/10

m=22

Now, let's find the y-intercept (b) using the point (9, -30):

y=mx+b

-30=(22)9+b

-30=198+b

b=-30-198

b=-228

Finally we obtain that the linear equation is y=22x-228

Answer:

Step-by-step explanation:

These are the two methods to finding the equation of a line when given a point and the slope: Substitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b. Use the m given in the problem, and the b that was just solved for, to create the equation y = mx + b.

we have the equation

y=-4

This is a horizontal line (parallel to the x-axis) that passes through the point (0,-4)

see the graph below to better understand the problem

Let x be the number of peanut bags Jeff sells. Since he earns $1.75 per bag the total amount he earns for selling x bags is:

Now, to this we have to add the $12 he gets paid, then the total amount he earns is:

To find out how many bags he has to sell to earn $52 we equate the expression above with the amount and solve for x:

therefore he has to sell 24 bags to earn $54.

The number of times that pat pulse rate maintains the given ratio in 3/4 of a minute is 60 times.

The ratio is the division of the two numbers.

Proportion is the relation of a variable with another. It could be direct or inverse.

For example, a/b, where a will be the numerator and b will be the denominator.

As per the given,

Pat's normal pulse rate is 80 beats per minute.

So, 80 beats → 1 minute

Multiply both sides by 3/4

80 × 3/4 beats  → 1 × 3/4  minute

(3/4) minute → 60 beats.

Hence "The number of times that pat pulse rate maintains the given ratio in 3/4 of a minute is 60 times".

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