The sale price of every item in a store is 80% of its usual price.


A: The usual price of a backpack is $30, what is its sale price?


B: The usual price of a sweatshirt is $18, what is its sale price?


C: The usual price of a soccer ball is $24.80, what is its sale price?

the measure of the angle formed by the beam and the ground is approximately 57.76 degrees. the measure of the angle formed by the beam and the ground is approximately  \(57.76^\circ\) degrees.

What is Right triangles?

A right triangle is a type of triangle that has one angle measuring 90 degrees (a right angle). The side opposite to the right angle is called the hypotenuse, and the other two sides are called the legs.

The Pythagorean theorem is a fundamental concept in mathematics that relates to right triangles, stating that the square of the length of the hypotenuse is equal to the sum of the squares of  lengths of  two legs.

To solve this problem, we can use trigonometry and the properties of right triangles.

First, let's draw the picture:

In this diagram, we have a right triangle formed by the beam, the wall, and the ground. The height of the triangle is given as 16 feet, and the length of the hypotenuse (the beam) is 30 feet.

We need to find the length of the base of the triangle (the distance between the wall and the bottom of the beam), which we can call d.

Using the Pythagorean theorem, we can find the length of the opposite side of the triangle:

length = √(beam² - wall²)

length = √(30² - 16²)

length = √(900 - 256)

length = √644

length ≈ 25.37 feet

Now we can use the tangent function to find the angle θ:

tan(θ) = opposite/adjacent

tan(θ) = ground/wall

tan(θ) = 25.37/16

tan(θ) ≈ 1.586

To find θ, we need to take the inverse tangent (or arctangent) of 1.586:

\(\Theta = tan-1(1.586)\)

 \(\Theta \approx 57.76^\circ\) degrees

Therefore, the measure of the angle formed by the beam and the ground is approximately  \(57.76^\circ\) degrees.

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Step-by-step explanation:

I hope this answer is helpful ):

The dimensions of the circles are as follows

1. Chord AB = 9

2. Chord FG = 6

3. Chord KM = 8

4. Arc length XY = 105 degrees

5. Arc length TU = 85 degrees

6. Arc length TU = 130 degrees

7. QS is the diameter because it bisects the chord and perpendicular to the chord

8. QS is not a diameter because it does not bisect the chord

9. QS is not a diameter because it is not perpendicular the chord

Chords with matching measurements share congruence due to being equidistant from the circle's center.

Congruent radii stem from each chord midpoint, indicating two equivalent right triangles are created; therefore, their respective intercepted arcs also equal in degree measurement.

Therefore, if two chords possess uniform lengths, they will intercept equal degrees along the circle.

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Answer:

  see below

Step-by-step explanation:

First of all, you want to find the data set the matches the extreme values of 5 and 35. That eliminates the 2nd and 4th choices.

Then you want to find the data set that has a median of 15. The first data set has a middle value (median) of 20, so that choice is eliminated.

The data set of the 3rd choice matches the box plot extremes, median, and quartile values.

Answer:

The third choice, (5, 6, 10, 12, 13, 15, 17, 25, 30, 35) would be your best answer.

Step-by-step explanation:

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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A first course in differential equations with modeling applications ninth edition is a textbook that covers the basics of differential equations and their applications in mathematical modeling.

It begins with an introduction to the concepts of differential equations, including the definition, solution methods, and the concept of modeling. It then covers topics such as first-order linear equations, higher-order linear equations, systems of linear differential equations, and nonlinear equations. It also has a chapter on boundary-value problems, which is a type of differential equation that involves a set of boundary conditions that must be satisfied for the solution to be valid.

In order to solve differential equations with boundary-value problems, we must first define the boundary conditions that must be satisfied for the solution to be valid. This involves setting up the boundary conditions in terms of the dependent and independent variables of the equation. We then solve the equation using the boundary conditions and the equation itself. The solution is then used to calculate values for the independent and dependent variables at the boundary points. Finally, we can verify the solution by substituting the calculated values into the equation and seeing if the solution is valid.

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Answer:

Step-by-step explanation:

Bottom row on the left.

A function assigns the values. The (f·g)(x) equals 5x³ + 5 + 5x²+15x.

A function assigns the value of each element of one set to the other specific element of another set.

Given the value of the functions f(x)=5x³ and g(x)=x+1. Therefore, the value of (f·g)(x) is,

(f · g)(x) = f(g(x))

             = 5(x+1)³

             = 5(x³+1+3x²+3x)

             = 5x³ + 5 + 5x²+15x

Hence, the (f·g)(x) equals 5x³ + 5 + 5x²+15x.

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Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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Part a: total number of boxes carried by the forklift = 60.

Part b: Total weight carried by forklift is "less than" 3000 pounds.

Both mathematical phrases, equations and inequalities, are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols  >, <, ≤ or ≥. or indicate that the two expressions in an inequality are not always equal.

Given data:

in equality formed are:

x + y ≤ 60 number .....eq1

45x + 70y ≤ 3000 pounds ...eq 2

Part a: total number of boxes carried by the forklift = 60.

Part b: Total weight carried by forklift is "less than" 3000 pounds.

Part c: inequality for number of boxes carried by the forklift.

From eq 1, x + y ≤ 60

Part d:  inequality for amount of weight carried by the forklift.

From eq 2;  x + y ≤ 60

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Answer:

Step-by-step explanation:

The answer is B

Answer:

constant is - 19

Step-by-step explanation:

the constant is the term in an expression with no variable attached to it.

12r + \(\frac{r}{2}\) - 19

the only term without the variable r attached to it is - 19

then the constant term is - 19

Answer:

Step-by-step explanation:

Short answer 2/3 if you need more just text bcak I will be happy to explain

Answer:$ 24,679.20 or 514.15 a month

Step-by-step explanation: 565(.09) is 50.85 which needs to be deducted from the payment of 565 because he needs to be able to pay for interest. 514.15 is then multiplied by 48 months which will bring you to 24,679.20

ANSWER

y = 6x

EXPLANATION

Sam wants to write an equation to represent a proportional relationship.

The constant of proportionality is 6.

A proportional relationship is one where one value is related to another by a certain factor such that a change in one value will result in a proportional change in the other.

It is generally represented as:

Therefore, for Sam, the constant of proportionality is 6.

The equation to represent it will be:

y = 6x

So, Sam is wrong.

9514 1404 393

Answer:

  C.  (1, -1)

Step-by-step explanation:

Dilation by a factor of 1/3 multiplies each coordinate value by 1/3.

  (x, y) ⇒ (x/3, y/3)

  K(3, -3) ⇒ K'(3/3, -3/3) = K'(1, -1)

Answer:

3.

\( \frac{28}{3} \)

Step-by-step explanation:

number 1 equals 8 1/5

number 2 equals 5

number 3 equals 9 1/3

Answer:

D. 25.7 sq.ft

Step-by-step explanation:

Area of the Figure = Area of Rectangle - Area of Semi Circle

Area of Rectangle = LW = 8*4 = 32 sq.ft

Area of Semicircle = 0.5*π*r² = 0.5*3.14*2² = 6.28 sq.ft

Area of the Figure = 32-6.28 = 25.72 ≈25.7

Answer:4

Step-by-step explanation:

tbh because i said so

Answer:

433 in.²

Step-by-step explanation:

Divide the figure into 2 rectangles

Area of the figure = area of the bigger rectangle + area of smaller rectangle

✔️Area of bigger rectangle = L*W

L = 29 in.

W = 13 in.

Area of the bigger rectangle = 29*13

= 377 in.²

✔️Area of the smaller rectangle = L*W

L = 7 in.

W = 8 in.

Area of the bigger rectangle = 7*8

= 56 in.²

✅Area of the figure = 377 + 56 = 433 in.²

Answer:

The rate of change is 28.

Step-by-step explanation:

The equation is in slope-intercept form,  y = mx + b, where m is the slope, and b is the y-intercept.

Answer:

$0.64 per cup

Step-by-step explanation:

There are 16 cups in 1 gallon, so the number of cups in 2 gallons is:

1 gallon: 16 cups

2 gallon = 2 x 1 gallon = 2 x 16 cups = 32 cups

So we need to find the price of each cup:

1 cup = ($20.48 / 32 cups) = $0.64 per cup.

I have no idea what this question is about