The length of a rectangle is 5 cm longer than its width.
If the perimeter of the rectangle is 54 cm, find its length and width.

Answer:

$14.25 for 3 bags

Step-by-step explanation:

First of all, the question is stating that 2 bags of cat food cost $9.50. This means each bag (1 bag) would cost ($4.75) So u would multiply that by 3, which is easy!

The height of the tree in 30 months given the linear equation is 16m.

The given equation is a linear equation. A linear equation is an equation that changes at a constant rate. The change can either be an increase or a decrease. A linear equation usually has an intercept and a slope. The intercept is the value of the equation when x is zero. The slope is the rate of change of the equation.

H (x) = 10 + 0.20x

10 = intercept

0.20 = slope

In order to determine the height of the tree after 30 months, substitute for x in the above linear equation.

H(x) = 10 + (0.2 x 30)

H(x) = 10 + 6

H(x) = 16

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The information that is not needed to determine the total bill after tax is is the tax was 7%.

The total bill is $11.

The total bill paid is the sum of the cost of the meal, tax and the tip paid. The tip and tax would increase in the total amount that is paid by the customers.

Tax is a compulsory amount that is levied by the government on certain goods and services.

Percentage is the fraction of an amount expressed as a number out of hundred. To convert a number from percentage to a number, divide the percentage by 100.

Tax paid = 10% x total bill

$1.10 = 0.1 x b

1.10 = 0.1b

b = 1.10 / 0.1

b = $11

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a. The information that is needed to solve the problem is D. All of this information is needed to solve the problem.

b. The total bill is $117.

It should be noted that an expression shows the relationship between the numbers or the variables

The total bill will be:

Tip = $1.10

Tax = 7%

Tip = 10% of cost:

$10 = 10% × c

0.1c = $10

c = $10/0.1 = $100

Cost = $100

The total bill. = Cost + Tip + Tax

= $100 + $10 + (7% × $100)

= $100 + $10 + $7

= $117

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Answer:

y = mx + b

y = 3/2x - 2

m = 3/2

b = -2

The solution of the inequality in the variable x <0.

Any monotonically rising function can, by definition, be applied to both sides of an inequality without violating the asymmetry connection (provided that both expressions are in the domain of that function). The inequality relation is flipped when a monotonically decreasing function is applied to both sides of an inequality. In the criteria for the basic inverse and the multiplicative inverse for positive values, a monotonically decaying function is utilized.

The given inequality is

4x + 2 <2

subtracting 2 from both sides

4x+2-2<2-2

or,4x < 0

or, x < 0

If the inequality is strict (a< b, a > b) and the function is strictly monotonic, the inequality remains strict. If only one of the preceding conditions is met, the ensuing imbalance does not exist. Indeed, the rules for addition and multiplicative exponentiation use a monotonically decreasing function.

Hence the solution of the inequality in the variable x <0.

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Answer:She can make 16 pitchers of lemonade

Step-by-step explanation:

1. Divide the amount of ounces needed for one pitcher of lemonade by the amount of ounces she has to get 16 pitchers of lemonade.

Answer:

x ≈ - 3.9 , x ≈ 5.9

Step-by-step explanation:

x² - 2x - 23 = 0 ( add 23 to both sides )

x² - 2x = 23

using the method of completing the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(- 1)x + 1 = 23 + 1

(x - 1)² = 24 ( take square root of both sides )

x - 1 = ± [tex]\sqrt{24}[/tex] ( add 1 to both sides )

x = 1 ± [tex]\sqrt{24}[/tex]

then

x = 1 - [tex]\sqrt{24}[/tex] ≈ - 3.9 ( to 1 dec. place )

x = 1 + [tex]\sqrt{24}[/tex] ≈ 5.9 ( to 1 dec. place )

The average rate of change is D. 2.

The average rate of change simply means the measure of how the function will change let unit of time.

In this case, it is important to look at the input and the output that wee given. It can seen that the difference between the output is given as:

13 - 11 = 2

15 - 13 = 2

In this case, the average change is 2.

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Brock is at a distance of 621/40 miles away from home.

Here, we are given that Brock rides his bike 22 1/8 miles to the nature preserve.

This means that he is now 22 1/8 miles away from his home. Now, he starts on his way home and after 16 1/5 miles, he stops at a deli for lunch.

Thus, he is now 22 1/8 - 16 1/5 miles away from his home.

To subtract the fractions we need to convert the mixed fractions into improper fractions, which can be done as follows-

22 1/8 = (22*8 + 1)/8

= 177/8

and 16 1/5 = (16*5 + 1)/5

= 33/5

Thus, the expression becomes-

177/8 - 33/5

now, we need to make the denominators of each fraction so that we can subtract them.

= (177*5)/40 - (33*8)/40

= 885/40 - 264/40

= 621/40

Thus, Brock is at a distance of 621/40 miles away from home.

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In the given figure,

line a is parallel to line b,

Therefore,

∠1 + ∠90° = 180° ............... (Since they are Linear pairs)

⇒ ∠1 = 90°

∠1 = ∠3 and ∠2 = ∠90°............. (Vertically opposite angles)

⇒ ∠1 = ∠3 = ∠2 = ∠90°

∠2 = ∠4 and ∠3 = ∠5 ................ (Alternate interior angles)

⇒ ∠4 = ∠5 = ∠90°

∠4 = ∠6 and ∠5 = ∠7 ............. (Vertically opposite angles)

⇒ ∠6 = ∠7 = ∠90°

So,

∠1 = ∠2 = ∠3 = ∠4 = ∠5 =∠6 = ∠7 = 90°

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x = 19 is the value of x in triangle .

What is triangle explain?

angle R + angle S + angle T = 180

(5+ 2x) + (7x - 16) + (x + 1) = 180

10x - 10 = 180

10x = 190

x = 19

Therefore

angle R = 5 + 2(19) = 43 degrees

angle S = 19 + 1 = 20 degrees

angle T = 7(19)-16 = 117 degrees

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Answer:

the percentage is 100g divided by 5 to get 20

Answer:

Step-by-step explanation: a rate per 100 g packet

Answer:

Step-by-step explanation: you would use point form slope in the equation and plug it in like this

y+2= 2/3(x+3)

y+2=2/3x+2

y= 2/3x

and whatever point goes through this line is your answer

Remember the y-intercept is 0!

Answer:

< 3 = 90°, < 8 = 43° and < 4 = 146°

Step-by-step explanation:

Since < 1 and < 3 are on the same straight line, < 3 = 180° - 90°.

Since < 6 = 137° and < 6 and < 8 are on the same straight line, < 8 = 180° - 137° = 43°.

Since < 2 = 34° and < 2 and < 4 are on the same straight line, < 4 = 180° - 34° = 146°.

The radius of the pond is found to be 17.32m.

What is angle of elevation?

The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.

Given;

Length of the pole above= 30m

Angle of elevation = 60°

From the given information we can draw the diagram as the pole becomes the opposite of the angle of elevation and radius becomes the base.

Therefore,

Opposite / Base = tan 60°

=> base = 30 / √3

=> base = 17.32m

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We have a relationship between temperature and chirp rate, such that the input in this case is the temperature.

We define a relation as an operator that maps elements from one set (the domain, set of the inputs) into elements of another set (the range, set of the outputs).

Particularly, the relations are written as:

x → y

Where y is the output and x is the input.

In this case, we have two pairs of the relation, these are:

So we are giving the temperature as the input, and the output is the chirp rate of the crickets at that particular temperature.

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Answer:

f'(x) = 15(5x + 3)²

Step-by-step explanation:

using the chain rule to differentiate

f(x) = g(h(x) , then

f'(x) = g'(x) × h'(x)

f(x) = (5x + 3)³

f'(x) = 3(5x + 3)² × [tex]\frac{d}{dx}[/tex] (5x + 3)

      = 3(5x + 3)² × 5

      = 15(5x + 3)²

[tex]1 - 3 < x < 4 - 3 \\ - 2 < x < 1[/tex]

WHAT YOU DO ON OTHER SIDE OF THE INEQUALITY YOU HAVE TO DO IT ON EVERY SIDE TO BALANCE THE INEQUALITY

GOODLUCK.

Answer:

75

Step-by-step explanation:

Answer: 11/4

Step-by-step explanation:

11/4x60/60=11/4

The required transformation of the regular polygon to onto itself is a rotation by the angle of 360° around its own center or any point in the plane.

Given that,
To determine which transformation carries the given regular polygon onto itself.

Here,
According to the question as asked.
There are only 2 usual possible ways of transforming a regular polygon that will onto itself as,
(1) A perfect rotation of 360° around its own center.
(2) A rotation of 360° around any point in the space and plane containing the regular polygon.

Thus, the required transformation of the regular polygon to onto itself is a rotation by the angle of 360° around its own center or any point in the plane.

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Answer:

4/5, 0.8 decimal form

Step-by-step explanation:

Hope this helps

Answer: = 8.54166666667

Step-by-step explanation:

15 2/3 - 7 1/8

Line AB is always skew to line CD as the two lines are in different planes.

Line AB will sometimes intersect line EF as the two planes intersect at some point.

We know that a plane represents a 2 dimensional surface in a 3 dimensional area.

Now it is given that planes x and y are parallel to each other, therefore they will never intersect at any place.

Now two separate lines on these two separate planes will also not intersect with each other as  they are on different planes and the ploanes do not meet.

Hence Line AB is always skew to line CD as the two lines are in different planes.

Again for Line AB it will intersect EF as the plane z intersects the plane x on which the line AB is located.

We know that the lines can still be skew lines but there is a possibility that they will meet.

Hence Line AB will sometimes intersect line EF as the two planes intersect at some point.

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Answer:

Slope-intercept form: y = 9/4x - 53/4

Point-slope form: y + 2 = 9/4(x - 5)

Yannick paid $9.25 as sales tax on the bicycle.

Here, we are given that Yannick bought a bicycle and paid $194.25 for it, including tax.

Let the cost of the bicycle without tax be x

We are given that the rate of sales tax is 5%

Thus, the amount of tax on bicycle will be-

5% of x

= (5/100)*x

= 0.05x

Thus, we can form an equation as follows-

x + 0.05x = 194.25

1.05x = 194.25

x = 194.25/ 1.05

x = 185

Thus, the cost of bicycle without tax is 185

Therefore, the tax paid will be-

0.05x

= 0.05*185

= 9.25

Thus, Yannick paid $9.25 as sales tax on the bicycle.

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Let X be the weight of fish in the lake.

Given that the mean and standard deviation as 20 and 6 respectively,

Consider the formula,

The proportion of fish weighing less than 15 pounds is calculated as,

Substitute the value,

Mulyiply by 100 to get the equivalent percent,

Thus, 20.33% of fish in the lake will weigh less than 15 pounds.