Write an equation in slope - intercept form for the line that passes through the given paint andis perpendicular to the given equation.7.(-5, 2), y =1/2x-3

The end behavior of the given function will be given by Down on the left down on the right.

A function may be defined as the expression in which for one value of input variable there is only one value of output variable. The input variable or the independent variable is x, and the output variable or the dependent variable is y. In the given function f(x) = -3x⁴ + 7x² - x + 13 we will use the Power and Polynomial Functions features. For final behavior of power functions of the form f(x) = axⁿ where n is represented as a non-negative integer depends on the power and the constant. Here, the leading coefficient is -3x⁴. So, when x → ∞ the value of f(x) → -∞ and when x → -∞ then the value of f(x) → -∞. So, the final answer for the behavior will be given by "Down on the left, down on the right".

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PROBLEM:

To find the point-slope form of the equation of the line passing through points (0, 0) and (-4, 7)

METHOD:

The point-slope form of the equation of a line is given to be:

Step 1: Find the slope of the line.

The formula to calculate the slope of a line is given to be:

We can use the two points provided to find the slope of the line such that:

Therefore, the slope is given to be:

Step 2: Pick a point on the line to use for the equation.

Step 3: Use the values gotten from Steps 1 and 2 to write out the equation of the line in the point-slope form:

ANSWER:

The slope-intercept form of the line is given to be:

The correct inequality sign for the first number expression is > and for the second number, the expression is <.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The mixed fractions are:

-19 5/6 = -119/6 = -19.83

-20 1/6 = -121/6 = -20.166

-19 5/6 > -20 1/6

|-19 5/6| = |-119/6| = 19.83

|-20 1/6| = |-121/6| = 20.166

|-19 5/6| < |-20 1/6|

Thus, the correct inequality sign for the first number expression is > and for the second number, the expression is <.

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First, find the slope of the line using the slope formula:

Provided two points (a,A) and (b,B) on a line, its slope is given by:

For the points (-6,7) and (4,-2), we have:

The equation of a line in slope-intercept form, of a line with slope m and y-intercept b is:

Substitute m=-9/10 and the coordinates of one point to find the y-intercept. Use, for instance, the point (-6,7):

Substitute b=8/5 and m=-9/10 to find the equation of line Q:

Side of cube = 8 ft

Volume of cube = Side x Side x Side

Volume of cube = 8 x 8 x 8

Volume of cube = 512 feet^3

A cylinder with diameter 8feet is cute form the cube

Height of cylinder = Side of cube

Height of cylinder = 8 feet

Diameter of cylinder = 8 feet

Radius of cylinder = 4feet

The volume of resulting shape = Volume of cube - Volume of cylinder

Volume of resulting shape = 512 - 401.92

Volume of resulting shape = 110.08 ft^3

Answer: 110.08 ft^3

The arrows indicate that the graph of the function continues beyond what can be seen in the image.

Notice that the graph does not appear to have asymptotes; then, the domain of the function is:

And the range is:

Since the graph seems to continue towards the +y-direction and the -y-direction

Finally, notice that for each value of x, the graph has only one value of y. This is the key characteristic of a function; the graph is a function.

we can make a relation

where x is the missing value

if she bikes 2/3km in 4 minutes how much kilometers she bike on 1 minute?

we solv using cross multiplication

we multiply 1 and 2/3 and the divide by 4

she will bike 1/6km in one minute

Answer:

0

Step-by-step explanation:

2(3x -1)  + 2(4x + 5) = 8  Distribute the 2's

2(3x) + 2(-1) + 2(4x) + 2(5) = 8

6x - 2 + 8x +10 = 8  Combine like terms

14x + 8 = 8    Subtract 8 from both sides of the equaion

14x = 0  Divide both sides by 14

x = 0

The costs of repairing iPads in UAE are normally distributed with a standard deviation of 73 Dhs. If 8% of the costs exceed 279 Dhs, then the mean of the costs is 1.405072

The mean of the Costs stands for the typical sum of money spent on a product's production. Depending on how many units are made, this amount may change.

Let X be the price of fixing iPads in the UAE (in Dhs)

X ~ N (μ, σ = 73)

if 8% of the costs are greater than 297 Dhs.

P (X > 297) = 8%

P(X > 297) = 0.08

We must determine the mean value (μ)

P (X > 297) = 0.08

P [(X - μ) / σ > (297 - μ) / 73] = 0.08

P [Z < (297 - μ) / 73] = 0.08

P [Z < (297 - μ) / 73] = 1 - 0.08

P [Z < (297 - μ) / 73] = 0.92

(297 - μ) / 73 = Z⁻¹(0.92)

(297 - μ) / 73 = 1.405072    (Using R software)

297 - μ = 73 * 1.405072

μ = 297 - (73 * 1.405072)

μ = 297 - 102.5702

μ = 194.4298

μ ≅ 194

Therefore, the mean of the cost (μ) = 194 dhs.

Using R Software, we can compute;

Z⁻¹ (0.92) is,

=qnorm(0.92) ` → (Command)

'1.405072 → (Output)

⇒ Z⁻¹ (0.92) = 1.405072

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A non-zero matrix A with A² = 0 is A = [tex]\left[\begin{array}{cc}0&1\\0&0\end{array}\right][/tex].

We need to find a 2 x 2 non- zero matrix with A² = [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]

A² = A x A

If A = [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex], then A x A =  [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex] x  [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]

                                          = [tex]\left[\begin{array}{cc}a^2+bc&ab+bd\\ac+dc&bc+d^2\end{array}\right][/tex]

This is called matrix multiplication.

Now consider the matrixes of the form A = [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex]

Then A² =   [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex]  x  [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex]

              =  [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]

Also Consider a matrix A = [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex]

Then A² =    [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex] x  [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex]

              =  [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]

So any matrix of the form  [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex] and   [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex] with x any number, will give A² = 0

In particular, A =  [tex]\left[\begin{array}{cc}0&1\\0&0\end{array}\right][/tex] is a non-zero matrix with A² = 0.

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The formula for exponential growth is expressed as

y = a(1 + r)^t

where

y is the population after t years

ais the initial population

r is the growth rate

t is the number of years

From the information given,

a = 350

r = 14% = 14/100 = 0.14

By substituting these values into the equation, the function to model th growth rate is

y = 350(1 + 0.14)^t

y = 350(1.14)^t

We would substitute values of t into the equation to determine corresponding values of y. We have

For t = 2, y = 350(1.14)^2 = 454.86

For t = 6, y = 350(1.14)^6 = 768.24

For t = 10, y = 350(1.14)^10 = 1297.52

We would plot these values of y on the y axis and the corresponding values of t on the x axis. The graph is shown below

The time when the population will reach 20000 would be the value of x at the point where y = 20000 on the graph. It is around y = 30.87

Thus, the population will reach 20000 in approximately 31 years

We can confirm this by solving the equation. We have

20000 = 350(1.14)^t

20000/350 = 1.14^t

57.14 = 1.14^t

Taking natural log of both sides, we have

ln 57.14 = ln1.14^t = tln1.14

t = ln 57.14/ln1.14

t = 30.87505

Answer:

Step-by-step explanation:

You have to assume each roll is independent. The probability of rolling a fair die is 1/6. When you roll the die, you only care about 2,4,5, and 6 since you do not want to get 1 or 3. So the probability is of getting a 2,4,5 and 6 is 4/6.

You could of also see it as the probability of NOT getting a 1 or 3 is:

[tex]1-\frac{2}{6} =\frac{4}{6}=\frac{2}{3}[/tex]

Now you roll the die 4 times with each success being 2/3

[tex]\frac{2}{3} \cdot \frac{2}{3} \cdot \frac{2}{3} \cdot \frac{2}{3} =(\frac{2}{3})^4=.197530864[/tex]

Answer:

• $250

• y=200+50x

• Graph A

• Yes

Explanation:

(a)Han cellphone's plan costs a fixed fee of $200 and an extra $50 per month.

Therefore:

(b)If Han uses the phone for x months

Extra Cost = 50x

Therefore:

(c)Since the number of months = x; and

Total cost for x months = y

When x=24

The graph that shows the cost of the cell phone plan over a period of two years using months as the units of time is Graph A.

(d)We see that the equation y=50x+200 has a proportional constant (50).

Another approach is to say that it is a linear equation.

Therefore, there is a proportional relationship between time and the cost of the cell phone plan.

a) Perimeter =  17.4 cm

b) Perimeter   =210.6 cm

How are the perimeters calculated?

a) The perimeter of an irregular polygon = Sum of all the sides of the polygon.

Converting value of all sides to centimetres.

Perimeter = 3.4 +3.2 +4.3 +3.7+2.8

                 = 17.4 cm

b) The perimeter of an irregular polygon = Sum of all the sides of the polygon.

Converting value of all sides to centimetres.

Perimeter = 29.1+25.3+30+28.6+32.6+36.5+28.5

                 =210.6 cm

What is the perimeter of a polygon?

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Part b.

If we want to dilate a figure we simply multiply each x- and y-coordinate with the scale factor we want to dilate with. Therefore:

Factor of 3

Multiply:

Answer:

Answer:

x=12

Step-by-step explanation:

(4x + 7) + 35 = 90

(4x+7)=90-35
4x+7=55
4x=55-7
4x=48

x=12

Answer:

x=12

Step-by-step explanation:

it just is.,...........

Answer:

4x>13

Step-by-step explanation:

4 × X=4x

>=more than symbol

The line is given by 3x + 6y = 8

To find the slope and the y-intercept, we must rewrite the equation in the form y = ax + b, where a is the slope and b is the y-intercept.

The first step is subtract 3x from both sides of the equation:

3x + 6y - 3x = -3x + 8

6y = -3x + 8

Then, we divide both sides by 6:

6y/6 = (-3x + 8)/6

y = -x/2 + 4/3

Therefore, the slope is -1/2 and the y-intercept is 4/3

Remember the following transformations of a function:

This transformation stretches the function over the vertical axis if c>1 and shrinks it if 0

If c is positive, the orientation is mantained, and if c is negative, the function is also flipped over (it shrinks if -1

This transformation moves the function vertically c units. It goes up if c>0 and down if c<0.

Therefore, starting with the absolute value function:

Multiply the function by 2:

Since 2>1, then this is a vertical stretching by a factor of 2.

Next, add 1:

This will translate the stretched absolute value function one unit upwards.

Therefore, the complete description of the transfromation would be:

Is a vertical stretching of the absolute value function by a factor of 2, translated 1 unit upwards.

The mean absolute deviation is 2.5.

The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data collection. A measure of variance in a data collection is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation.

How to calculate the mean deviation from the mean:

Given data:1, 1, 3, 5, 5, 6, 8, 11

So, mean of the data is

= 1+ 1 +3 +5 +5+ 6+ 8 +11 / 8

= 40 /8=

5

Now, Mean absolute deviation is

= | 1-5| + |1-5| + |3-5 | + |5-5| + |5-5| + |6-5| + |8-5| + |11-5|/ 8

= 4 + 4 + 2+ 0 + 0+ 1 + 3 +6 /8

= 20/8

=2.5

Hence, the mean absolute deviation is is 2.5.

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Answer: We have to find the volume of the pool and the number of pit balls that can fill it.

(1) We can find the volume of the pool with the following formula:

Using the equation (1) the volume of the pool is determined as follows:

(2) The number of ball pits that can fill the pool is as follows:

Therefore the answer is:

1 trillion to the tenth power is (10¹⁴)¹⁰ or  (10¹³)¹⁰.

So, 1 trillion to the tenth power:

Therefore, 1 trillion to the tenth power is (10¹⁴)¹⁰ or  (10¹³)¹⁰.

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the inverse function = f^-1(x) is option C

First let's state what we are given:

f(x) = x^3 - 5

We are to find the inverse of f(x).

To do this, first let's represent f(x) with y

y = = x^3 - 5

Then, we would interchange x and y

From the answer we got, the inverse function = f^-1(x) is option C

The polygon EFGH is a polygon.

What is polygon?

A polygon is a form of planar figure in geometry and is defined as a closed polygonal chain made up of a finite number of straight line segments. A region that is enclosed by a bounding plane, a bounding circuit, or both is referred to as a polygon. The portions of a polygonal circuit are referred to as its edges or sides.

To check the polygon EFGH is a square or not, first to find the length of each side of polygon.

If the length of each side is equal then the polygon EFGH is a square.

(Since length of each side of square is equal).

We know,

[tex]d \sqrt{(x_2-x_1)^2 + (y_2 - y_1)^2}[/tex]

where,

d = distance

[tex](x_1, x_2)[/tex] = Coordinates of the first point.

[tex](x_2, y_2)[/tex] = Coordinates of the second point.

So,

[tex]EF = \sqrt{(3-(-2))^2 + (3.5-3.5)^2} = \sqrt{25 + 0} = 5[/tex]

[tex]FG = \sqrt{(3-3)^2 + (-1.5-3.5)^2 } = \sqrt{0 + 25} = 5[/tex]

[tex]GH = \sqrt{(-2-3)^2 + (-1.5-(-1.5))^2} = \sqrt{25 + 0} = 5[/tex]

[tex]EH = \sqrt{(-2-(-2))^2 + (-1.5-3.5)^2} = \sqrt{0 + 25} = 5[/tex]

From above the length of each side is equal.

Therefore, given polygon EFGH is a square.

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Answer:

(x,y)->(x+4,y-5)

Step-by-step explanation:

Find a set of common points first, for example, A and A', or B and B'
Then, find the coordinates of the two points. I'm choosing B and B'.
B: (1,8) x = 1, y = 8
B':(5,3) x = 5, y = 3
from B to B', we see that the x increases by 4 and the y decreases by 5. So, the third option, (x,y)->(x+4,y-5) is correct

Solution

a + b = (-2, -1)

Using Parallelogram method

Given

While sailing a boat offshore, Bobby sees a lighthouse and calculates that

the angle of elevation to the top of the lighthouse is 3°.

When she sails her boat 700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.

To find:

How tall, to the nearest tenth of a meter, is the lighthouse?

Explanation:

It is given that,

While sailing a boat offshore, Bobby sees a lighthouse and calculates that

the angle of elevation to the top of the lighthouse is 3°.

When she sails her boat 700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.

That implies,

Also,

Therefore,

Then,

Hence, the height of the light house is, 91.5m.

Given that the illuminator 100 plus bulb movies onto larger screen farther away as shown in the diagram attached then;

Illuminator 100 plus bulb

It movies onto screens ;

108 ft wide

180 ft away from the projector

Illuminator 100 bulb

81 ft wide

? : from the projector

Here apply the idea of similarity ratios where;

The ratio

The actual distance is 90 miles between the town and the state capital based on the scale of the map

1/2 inch on the map = 10 miles

So, 1 inch = 20 miles

Distance between the town and state capital = 4 1/2 inches

The mathematical relationship between a small unit of measurement on a map, such as an inch or centimetre, and the corresponding real-world unit of distance, such as a kilometre or a mile, is known as a map scale.

The actual distance in miles between the town and the state capital is given by:

Distance between town and state capital* Scale of the map

= 4.5*20

= 90 miles

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Hello there. To solve this question, we have to remember some properties about conversion of values.

1. How many 2-liter bottles of soda will you need to fill ten 500 mililiter containers?

First, multiply the number of containers by its capacity, that is

Notice that 1000 mililiters is equivalent to 1 liter, hence

To fill these containers with 2-liter bottles of soda, you'll need at least 3 bottles.

The answer to the first question is 3.

2. How many mililiter are 1/5 liter?

Considering 1 liter = 1000 mililiters, we have that

Hence the answer to this question is 2. 200