A number n plus 4.1 is less than or equal to 7 . Write this word sentence as an inequality.

Let's take a look at our triangle:

Using the law of cosines, we'll get that:

Solving for angle G, we'll get:

This way,

Step-by-step explanation:

x^y × x^3 = 1/(x^2) = x^(-2)

that means

y + 3 = -2

y = -5

the missing exponent is -5

x^(-5) × x^3 = 1/(x^2)

Answer:

Step-by-step explanation:

Hi Ashley,    this looks harder than it really is  :)

recall your powers rules

so  [tex]x^{2}[/tex]  *  [tex]x^{2}[/tex] = [tex]x^{2+2}[/tex]=[tex]x^{4}[/tex]

knowing that you can probably figure this out.  But I'll help anyway

[tex]x^{?+3}[/tex] = 1 / [tex]x^{2}[/tex]

now flip over the fraction to make this even easier

[tex]x^{?+3}[/tex] = [tex]x^{-2}[/tex]

ohhhh  I bet you can see it now, huh

we just need  3 plus something to equal -2

that's negative 5 ,  right???

[tex]x^{-5+3}[/tex] = [tex]x^{-2}[/tex]

ahh, nice  , now just break it back up

[tex]x^{-5}[/tex] * [tex]x^{3}[/tex] = 1 / [tex]x^{2}[/tex]

got it???

Answer:

A=151

B= 29

Step-by-step explanation:

Nick will write

Date i.e. 11/5/20XX, Description i.e. Pay James, Check Number i.e. 123, Debit i.e. $150.32, Balance i.e. $X - $150.32.

The New balance will be $X - $150.32, where $X is the previous balance.

Given, that Nick writes a check to his friend James Sloan for $150.32 on May 11.

Let suppose Nick had an 'X' amount in his bank account.

He will fill the check register like this

Date           Description       Check Number       Debit       Credit     Balance

11/5/20XX                                                                                                $X

11/5/20XX   Pay James              123                  $150.32              $X-$150.32

Hence, Nick will write

Date i.e. 11/5/20XX

Description i.e. Pay James

Check Number i.e. 123

Debit i.e. $150.32

Balance i.e. $X - $150.32

The New balance will be $X - $150.32 i.e. $150.32 subtracted from the previous balance.

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If all of the ratios of the variables are equal, then there is a proportional link between the two variables.

One variable is usually a constant value multiplied by the other in proportional interactions. The proportionality constant is the name given to the constant value.

A set of equal ratios connected to one another by a constant of proportionality make up a proportional relationship between two quantities. Different, related representations of proportional connections include tables, equations, graphs, and written descriptions.

We'll now look at a real-world illustration of a proportionate relationship: There is a correlation between the quantity of fuel we put in our car's tank and the price we will have to pay when we fill it up. In other words, we will pay more money the more gas we put in.

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Volume of the cylinder = πr²h

see explanation below

A cylinder comprises of two circles and a curved part.

To get the volume, we would multiply the area of the circle with the height of the cylinder

The height of the cylinder is the distance between the two circular ends

Area of a cirlce is pi multiplied by radius squared

Area of circle = π×r² = πr²

where r = radius

h = height of the cylinder

Volume of the cylinder becomes = πr² × h

Volume of the cylinder = πr²h

Let the three consecutive even number be,

x, x+2, x+4

Sum of the numbers is 1002.

Hence, the numbers are,

332, 332+2, 332+4

Hence, the answer is 332, 334, 336.

Answer: $5 for each vinyl,$4 for each CD,and $1 for each electronic download

Step-by-step explanation:

Answer:

$5 vinyl

$4 CD

$1 every electronic download

Step-by-step explanation:

good luck

About 3 full cones of water are needed to be added to the cylinder to completely fill it.

The radius of the right circular cone is 3cm and the slant height is 5 cm.

The height of the cone can be found as,

H = √(5)²- (3)²

H = 4cm

The volume of the cone is given by,

V = πR²H/3

R is the radius and H is the height of the cone,

Putting values,

v = π x 5 x 5 x 4/3

v = 104.71 cm³

Now, the height h of cylinder is given to be 6 cm and the radius r of the cylinder is 4cm.

The volume of the cylinder is given as,

V = πr²h

V = π x 4 x 4 x 6

V = 301.59

Let us assume that we have to add n full cones of water to completely fill the cylinder, so, we can write,

nv = V

Putting values,

n104.71 = 301.59

n = 2.85

So, we have to add roughly three full cones of water to completely fill the cylinder.

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The coordinates of a slope triangle that could be on the line shown include

A slope triangle is a hypothetical triangle that aids in determining a line's or line segment's slope.

The line whose slope you are interested in learning is the triangle's hypotenuse (the diagonal). The slope formula's "rise" and "run" values are the two "legs" of the triangle.

With this idea, the slope triangle is drawn and the image is attached.

The coordinates should be able to form a right triangle which is used in slope calculation

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Answer:

Step-by-step explanation:

By using properties of angles, it is obtained that

x = 18.5°, y = 37°

Angle

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.

Here,

[tex]\angle COF = 90^{\circ}\\[/tex]

By the problem,

4x + 90  + 16 = 180 [Angle on a straight line]

4x + 106 = 180

4x = 180 - 106

4x = 74

[tex]\\x = \frac{74}{4}\\x = 18.5^{\circ}[/tex]

AB and CD are straight lines

[tex]\angle DOB = 16^{\circ}[/tex]  [Vertically opposite angle]

By the problem,

90 + 2y + 16 = 180 [ Angle on a straight line]

2y  + 106 = 180

2y = 180 - 106

2y = 74

[tex]y = \frac{74}{2}\\y = 37^{\circ}[/tex]

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In 49 minutes the car will travel 2/147 miles

In 60 minutes the car will travel 1/90 miles

The concept of average speed is used here. The formula is

= distance covered / time

= 2 1/3 / 3 1/2

= 2.3333 / 3.5

= 2/3

= 0.6667 miles per minutes

In 49 minutes

2/3 = distance  / 49

distance = 2/3 / 49

distance  = 2/147

= 0.0136 miles

In one hour = 60 minutes

distance = 2/3 / 60

distance = 1/90

= 0.0111 miles

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th first pic is not a function because a function dont have to values for the same x

the second pic is a function because each value of x has a different result

the third pic is a function because each value of x has a different result

so the first relation is not a function

Answer:

:-f(x)=x²-2x-24

Step-by-step explanation:

according to the rules of polynomial

f(-4) is the same thing as (x+4)

f(6) is the same thing as (x-6)

how?

x+4=0; x=-4

x-6=0; x=6

(x+4)(x-6)

x²-6x+4x-24

x²-2x-24

:-f(x)=x²-2x-24

award me

Answer:

Top: y = x

Bottom: y = 0.8x - 3.2

Step-by-step explanation:

I can see the question is asking to write the equation in Slope-Intercept form.

Slope-Intercept Form:

y = mx+b

M is the slope or how much the y value increases every time the x value increases by one. b is the y-intercept or when x=0.

Because these lines are parallel, we know they have the same form.

Lets look at the top line. When x increases by one, how much does y increase by?

1

What is the y value of when the line's x-value is 0?

0

Now, we have,

y = 1x + 0

Because adding 0 keeps the equation the same, we can remove it.

y = 1x

Because multiplying a term by 1 leaves it the same, we can remove one.

y = x

Now, for the bottom line.

How much does y increase by when x increases by 1? Because the slope will be a fraction and is not easy to see, I will use the slope formula.

Slope Formula:

[tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

To find the slope, take any pair of points on the line and plug them in.

I'll use:

(0,-3.2)

(4,0)

Plug the y-values (the latter number, or the height of the point) into the formula. Do the same with the x-values. keep in mind it does not matter what y-value you plug in. For example, for [tex]y_2[/tex] and [tex]y_1[/tex] you can plug in -3.2 and 0 or vice versa. If you make [tex]y_2[/tex] -3.2, then make [tex]x_{2}[/tex] 0.

[tex]\frac{-3.2-0}{0-4}[/tex]

Simplify.

[tex]\frac{-3.2}{-4}[/tex]

Because a negative number multiplied or divided by another negative number is always a positive number, remove the negative signs.

[tex]\frac{3.2}{4}[/tex]

Divide.

3.2/4 = 0.8

Now we have m, the slope on the 2nd line, 0.8

y = 0.8x + b

What is the y-value of the line when the line has the x-value of 0? On the graph, it says -3.2.

y = 0.8x - 3.2

To calculate the periodic payment (PMT) we use the following formula:

Where "FV" is the Future Value, "i" is the interest rate, and "n" is the number of periods. Replacing the known values we get:

Solving the operations:

The formula for the monthly loan payment is given as

Where

P = loan amount ( initial principal) = $15000

A= Payment amount per period = ?

r = interest rate per period = (5/12) x (1/100) =0.0041667

n = total number of payments or periods = 4 years = 4 x 12 = 48 months

Substituting all these into the above equation gives

So each month he pays $345.44 to the nearest cent

B)

The total interest for the loan is given by

Total amount paid over the total period of time - Original amount borrowed

Total amount paid over the total period of time = 345.44 x 48 months = $16581.12

The total interest of the loan hence = $16,581.12 - $15,000 = $1,581.12

The total loan interest to the nearest cent = $1,581.12

ANSWER

Yes, it can.

EXPLANATION

First of all, let us sort the data according to increasing value:

Time (minutes) 18 20 20 22 22 23 25 30

Duration (minutes) 38 40 42 41 42 44 47 52

As we can already see, the duration of the ride seems to increase as the amount of time after 8 am that she got on the bus.

This means that the Duration of the ride and the time Layne got on the bus have a linear relationship and so, YES, the duration of the ride can be represented as a function of the time Layne got on the bus.

The given function is

This equation represents a parabola which is expressed in its vertex form

Where (h,k) is the vertex. Using this rule, the vertex of the given parabola would be (6,8).

Answer:

Your answer would be 7,600.

Step-by-step explanation:

7,605 rounded to the nearest hundred would be 7,600 because:

The 7 is the thousands.

The 6 is the hundreds.

The 0 is the tens

The 5 is the ones.

So, we need to find which number makes sense to round. Is 605 closer to 600 or 700? 600. So, we have: 7,600

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Answer:

5x-1y

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. (1.5x+3.5x)-(0.25y+0.75y)

2. 5x-y

3. The answer is 5x-y.

Given: X-3(x+2)=4X-3(x+2)=4

Find: the solution of the given equation

Explanation:

on solving equation (1) and (2) , we get

Answer:

x = -5

Step-by-step explanation:

    x - 3(x + 2)= 4

    x - 3x - 3*2 = 4     {Distributive property}

   x - 3x  - 6    = 4

Combine like terms in LHS,

         -2x - 6  = 4

Add 6 to both sides,

               -2x = 4 + 6

               -2x = 10

Divide both sides by (-2)

                   x = 10 ÷ (-2)

                   [tex]\sf \boxed{x= -5}[/tex]

Given the following expression:

notice that the right side of the equation has a decimal number that goes up to the thousandth, therefore, the missing exponent in the equation is 3, since:

The probability of the company's order from first-time customers with the sample proportion less than 0.28 will be 0.6103.

Total percent of company’s orders from first-time customers are 35%

Probability of the company's orders from first-time customers are 35/100 = 0.35.

Total number of customers in the random sample is 62.

Minimum given probability of company’s order from first time customers is 0.28

And the minimum probability of company’s order not from first time customers will be 1 - 0.28 = 0.72

Therefore,

As per the given question, Let P(z<0.28) is the required probability, where

Z = (0.28 - 0.35)/sqrt(0.28x0.72/62)

  = (0.28 - 0.35)/sqrt(0.28x0.0112)

  =(0.28 - 0.35)sqrt(0.003250)

  = (-0.07)/sqrt(0.003250)

  = -0.07/0.057

  = -1.228

From the z-score, we can get P( z<0.28 ) = 0.6103 ( From standard normal table )

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Number of women's are 9,078.83.

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

In​ 2005, 10.9 out of every 50 employees at a company were women.

Now,

Since, In​ 2005, 10.9 out of every 50 employees at a company were women.

Let number of women's in 41,646 total company​ employees = x

So, We can formulate by the definition of proportion as;

⇒ 10.9 / 50 = x / 41,646

Solve for x as;

⇒ 10.9 × 41,646 / 50 = x

⇒ x = 9,078.83

Thus, Number of women's are 9,078.83.

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This is a way we can organize a linear equation:

[tex]y=mx+b[/tex]

We're given:

[tex]12x + 4y = 8[/tex]

To organize this equation in slope-intercept form, we have to focus on isolating y:

[tex]12x + 4y = 8\\4y = - 12x +8\\y = - 3x +2[/tex]

[tex]y = - 3x +2[/tex]

The answer is y= negative 3 plus 2

The equation can be used for "the total cost of buying x chocolate bars, such that each one costs $3.50"

Here we have the linear equation:

y = 3.5*x

And we want to make a word problem that can be represented by this.

The simplest example would be something like "the total cost of buying x items of a cost equal to the constant of proportionality"

So let's suppose that there is a chocolate bar in a given store that costs $3.50 per unit.

So, if you buy x of these, the total cost will be modeled (in dollars) by the equation:

y = 3.50*x

Which is the same equation that we have above:

y = 3.5*x

Where the second 0 on the constant factor is trivial and can not be written.

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we have the points

A (1,-2) and B(5,3)

Find out the point (x,y) that divide the segment AB in a ratio 2:3

that means

AX/XB=2/3

step 1

Find out the horizontal distance AB

ABx=5-1=4 units

Find out the vertical distance AB

ABy=3-(-2)=5 units

step 2

we have that

the horizontal distance between A and x is

AX/XB=2/3

AX=(2/3)XB -----> equation 1

AX+XB=4 -----> equation 2

substitute equation 1 in equation 2

(2/3)XB+XB=4

(5/3)XB=4

XB=12/5

XB=2.4

the x-coordinate of X is

x=5-2.4=2.6

Find out the y-cpoordinate

AX=(2/3)XB -----> equation 1

AX+XB=5 ------> equation 2

substitute equation 1 in equation 2

(2/3)XB+XB=5

5/3(XB)=5

XB=3

the y-coordinate of X is

y=3-3=0

answer is

the coordinate of the point is (2.6,0)

Given function : g(x)=3log(x+7) -8

A function is said to be increasing if the derivative of the function is greater than 0,

and it said to be decreasing tof the derivative of the function is less than 0,

Differentiate the given function with respect to x,

at x >7 , the function g(x) will be decreasing

at x <7 the function g(x) will be increasing.