Interpreting the parameters of a linear function that models a real-world situation

In order to determine the ratio of the perimeters for the given rectangles, first calcualte their perimeters. Use the following formula:

P = 2w + 2l

w: width

l: length

For the smaller rectangle you have:

w = 2cm

l = 4 cm

P = 2(2cm) + 2(4cm) = 4cm + 8cm = 12cm

For the bigger triangle you have:

w' = 4cm

l' = 8cm

P' = 2(4cm) + 2(8cm) = 8cm + 16cm = 24cm

Then, you have:

P/P' = 12cm/24cm = 1/2

Hence, the ratio is 1:2

In order to solve this quadratic equation by factoring, we can do the following steps:

Therefore the solution is {-2, 5}. Correct option: third one.

You have that y is proportional to x. Futhermore, you have y = -0.6 when x = 0.24.

Due to y is proportional to x, you have the following equation:

where k is the constant of proportionality. In order to find the value of x when y = -31.5, you first calculate k.

k is calculated by using the information about y=-0.6 and x=0.24. You proceed as follow:

y = kx solve for k

k = y/x replace by known x and y values

k = -0.6/0.24

k = -2.5

Hence, the constant of proportionality is -2.5.

Next, you use the same formula for the relation between y and x to find the value of x when y = -31.5. You proceed as follow:

y = kx solve for x

x = y/

From the statement of the problem we know that:

• the principal amount of money invested is P = $85000,

• the rate per year is 7.5%, in decimals r = 0.075,

• the time is t = 5 years.

The interest earnt I is equal to the difference between the total accrued amount A and the principal amount P:

Replacing by the data of the problem we find that the simple interest is:

Answer

The simple interest is $31875.

As per given by the question,

There are given that a table of x and f(x).

Now,

The genral for of the equation is,

Then,

For the value of x and f(x).

Substitute 0 for x and -2 for f(x).

So,

Now,

For the value of b,

Substitute 1 for x and -1/3 for f(x),

So,

Now,

Put the value of a in above result.

So,

Now,

Put the value of a and b in the general form of f(x).

Hence, the exponential function is ,

As the triangle AEF has 2 angles with the same measure, triangle AEF is isosceles.

The right angled triangle is given with reference angle theta.

The opposite side (facing the reference angle) is 3, while the hypotenuse (facing the right angle) is 5. The adjacent shall be calculated using the Pythagoras' theorem as follows;

Therefore, the trigonometric functions of angle theta are shown as follows;

It is given that AB = CB from this information we conclude that <A=<C by reason :angles opposite equal sides.

<A+<B+<C=180°(Sum of angles in a triangle)

[tex](4x - 13) + (5x - 2) + (4x - 13) = 180 \\ 4x + 5x + 4x - 13 - 2 - 13 = 180 \\ 13x - 28 = 180 \\ 13x = 180 + 28 \\ 13x = 208 \\ \frac{13x}{13} = \frac{208}{13} \\ x = 16[/tex]

x=6°

ATTACHED IS THE SOLUTION

GOODLUCK

Problem

144 grapefruits in 4 boxes, How many grapefruits in 100 boxes?​

Solution

for this case we can do the following proportional rule:

4/144 = x/100

And solving for x we got:

x= 100 (4/144)= 2.77

So between 2 and 3 grape fruits are expected

If the line is parallel to y = -3/4 x + 1/4 then the slope is -3/4

the form of an equation is y = mx +b

In this case m = -3/4

Using the point given (4, -2) we will find the value of b:

y = mx + b

y = -3/4 x + b

Using the values of the point (4, -2).... x = 4 and y = -2

-2 = (-3/4)(4) + b

Solving for b:

-2 = -3 + b

-2 + 3 = b

1 = b

b = 1

Therefore the equation would be:

y = (-3/4)x + 1

Answer:

y = (-3/4)x + 1

The decibel value for this cats purr round to the nearest decibel is; 25

Decibel (dB) is a unit for expressing the ratio between two physical quantities, such as measuring the relative loudness of sounds. One decibel (0.1 bel) is equal to 10 times the common logarithm of the power ratio.

Decibels are a unit of measure used to describe how loud a sound is. Now, I₀ is the intensity of threshold sound, which is sound that can barely be perceived by the human ear.

The loudness of a sound, in decibels, with intensity I is given by;

dB = 10 log₁₀(I/I₀)

We are given the intensity of a cat’s purr as I = 320I₀

Thus;

dB = 10 log₁₀(320I₀/I₀)

dB = 10 log₁₀(320)

dB = 25.05 ≈ 25

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SOLUTION

From the question, the Perimeter of the rectangle is 19.4 cm and we want to find the width. The perimeter of a rectangle is given by

Applying this, we have

Hence the width is 3.7 cm, option C

Solution:

In the figure;

Thus;

Thus;

The number of bacteria that weighs 1 gram are,

Determine the number of bacteria in a sample that weighs 21 grams.

So answer is,

The expression is simplified to negative 23 over 14 times j plus negative 1 over 15. Option C

An algebraic expression can be defined as an expression mostly consisting of variables, coefficients, terms, constants and factors.

Such expressions are also known to be composed or made up of some mathematical or arithmetic operations, which includes;

From the information given, we have that;

Substitute the values

- 1/7j + 2/5 - 3/2j - 7/15

collect like terms

- 1/7j - 3/2j + 2/5 - 7/15

-2j - 21j /14 + 6  7 /15

-23j/14 + -1/15

Hence, the correct option is negative 23 over 14 times j plus negative 1 over 15

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The question requires us to find how many ways we can select 6 children from a total of 46.

The formula for combinations is given as follows;

Where n = total number of children, and r = number of children to be selected. The combination now becomes;

Let

x -------> the time in hours

y -------> the distance in miles

we know that

To find the average rate of change, we divide the change in the output (y) value by the change in the input value (x)

so

For x=2 h ------> y=140 mi

For x=7 h ------> y=480 mi

rate of change=(480-140)/(7-2)

rate of change=340/5=68 mi/h

The average rate of change is equal to the speed in this problem

Option C

Points: A, B, C, D

Line segments: AB, AD, AC, DC, BC

ANSWER

1987 and 1995

EXPLANATION

The revenue is modeled by:

To find the years that the revenue was $722 million, we have to solve for x when R is 722.

That is:

We can split the absolute value equation into two different equations because the term in the absolute value is equal to both the positive and the negative of the term on the other side of the equality.

That is:

Solve for x in both:

That is to say 7 and 15 years after 1980.

Therefore, in the years 1987 and 1995, the revenue was $722 million.

The acute triangle is defined by the condition,

Here, we have,

Thus, the triangle is an obtuse triangle.

To complete the table you evaluate the equation by the given value of x to find the corresponding value of y:

To put those (x,y) points in the plane;

the frist coordinate x is the number of units you move to the left (if x is negative) or to the right (if x is positive)

the second coordinate y is the number of units you move down (if y is negative) or up (if y is positive)

Then, using the points (0,4), (4,8), (8,12), (12,16) and (16,20) you get the next graph for y=x+4:

Answer:

√52

Step-by-step explanation:

[tex] \sqrt{ {(4 - ( - 2))}^{2} + {(1 - ( - 3))}^{2} } [/tex]

[tex] \sqrt{ {6}^{2} + {4}^{2} } = \sqrt{36 + 16} = \sqrt{52} [/tex]

Find the next two numbers in the pattern -243, 81, -27, 9​

Notice that all the values in the series are value of 3 raise to the power of a number.

-243 =

Answer:

it is C) find the coordinated of two x intercept is

The breakdown of fees paid by the Caldwell family are calculated and shown below;

The total cost of the order will now be

Total cost of clothing = $823.59

Shipping cost = $7.85

Sales tax = $61.77

TOTAL = $823.59 + $7.85 + $61.77 = $893.21

Therefore, the total cost of the order is $893.21

The given equation is

First, we need to elevate each side to the third power.

Second, subtract x and 1 on both sides.

Third, we elevate the equation to the square power to eliminate the root

Now, we use the formula to solve the squared binomial.

Now, we solve this quadratic equation

We need to find two number which product is 48 and which difference is 16. Those numbers are 12 and 4, we write them down as factors.

So, the possible solutions are

However, we need to verify each solution to ensure that each of them satisfies the given equation. We just need to evaluate it with those two solutions.

As you can observe, the solution 12 doesn't satisfy the given equation.

From the first diagram shown, we can see that 1 cupcake costs $1.5

To get the price of 5 cupcakes

Since 1cupcake = $1.5

5 cupcakes = $x

cross multiply

1 * x = 5 * 1.5

x = $7.5

Hence 5 cupcakes will cost $7.5

Since 1cupcake = $1.5

18 cupcakes = $x

cross multiply

1 * x = 18 * 1.5

x = $27

Hence 5 cupcakes will cost $27

To get the number of cupcakes priced $18

Since 1cupcake = $1.5

x cupcake = $18

1.5x = 18

divide both sides by 1.5

1.5x/1.5 = 18/1.5

x =

Since we know the ratio is 2:1, then to find the number of students who like iced tea we convert the ratio to a fraction:

this means that one of two students preferred iced tea.

To find the number of students who prefer iced tea we multiply the total number of students by the fraction, then:

Since we can't have a fraction of a student, we conclude that 19 students prefer iced tea and 20 prefer lemonade.

Answer:

1728 cm ^ 3.

Step-by-step explanation:

we are given 12 cm

As we know formula of volume of cube = s ^3 ( side * side * side ) So = 12 * 12* 12 = 1728 cm ^ 3.

Find the Volume cylinder (8cm) (12cm) h = 8cm r = 12cm h = 8 cm r = 12 cm. The volume of a cylinder is equal to the area of the base πr2 π r 2 times the height. π⋅(radius)2 ⋅(height) π ⋅ ( r a d i u s) 2 ⋅ ( h e i g h t) Substitute the values of the radius r = 12 r = 12 and height h = 8 h = 8 into the formula to find the volume of the cylinder

P.s hopes this helps

Given

An independent third party found the cost of a basic car repair service for a local magazine.

The mean cost is $217.00 with a standard deviation of $11.40.

To find: The repair costs which would be considered an “unusual” cost.

Explanation:

It is given that, the mean is 217.00, and the standard deviation is 11.40.

Consider, the distribution as a Normal distribution.

Then, the first range is defined as,

And, the second range is defined as,

Hence, the answer is option a) 192.53 since it does not belongs to the above ranges.