A basketball court is shaped like a rectangle. It has a perimeter of 288 feet. The width of the court is 50 feet. What is the length of the court? Use the following formula to help you decide: Pr = 2l + 2w where Pr is the perimeter of a rectangle, l is the length, and w is the width

Answer:

B,C, D ) angle 2, ,3,4 are exterior angles.

Step-by-step explanation:

Given  : A figure .

To find : Which of the following are exterior angles.

Solution : We have given a figure of triangle

Exterior angle : An angle which are formed outside the closed figure,

We can see from the given figure angle 6 angle 5 , angle 1 are lies inside the triangle .

But Angle 2 , 4 ,3 are outside the triangle .

Therefore, B,C, D ) angle 2, ,3,4 are exterior angles.

It will take the man [tex]\( \frac{qx}{p} \)[/tex] minutes to run q miles at the same rate he runs p miles in x minutes.

Time = [tex]\frac{\text{Distance}}{\text{Rate}}[/tex]

where Time is the time taken, Distance is the distance traveled, and Rate is the rate of running.

Distance = q miles  

Rate = [tex]\( \frac{p}{x} \)[/tex] miles per minute.

Therefore,

Time = [tex]\frac{q}{\frac{p}{x}}[/tex]

Time = [tex]\frac{qx}{p}[/tex]

Answer:

9 students ride the bus.

Step-by-step explanation:

Given: The total number of students in gregs class is 24 and [tex]\frac{3}{8}[/tex] ride the bus to school.

To find how many students ride the bus;

Let x be the number of student ride the bus.

Proportional is simply a statement that the two ratios are equal.  

It can be written in two ways i.e,   [tex]\frac{a}{b} = \frac{c}{d}[/tex] or

[tex]a : b :: c :d[/tex]

Then, as per the given conditions;

x : 24 = 3 : 8 or

[tex]\frac{x}{24} = \frac{3}{8}[/tex]

Multiply both sides by 24 we get;

[tex]\frac{x}{24} \times 24 =\frac{3}{8} \times 24[/tex]

Simplify:

x = 9

Therefore, the student ride the bus is, 9

Answer:

Option D is correct .i.e., Vertical translation down 9 units

Step-by-step explanation:

Given Function is y = cosec x - 9

Here basic function or parent function is y = cosec x

1. When constant ' a ' is added to to parent function or basic function then the function is translated vertically upward by a units.

2.  When constant ' a ' is subtracted from parent function or basic function then the function is translated vertically downward by a units.

Therefore, Option D is correct .i.e., Vertical translation down 9 units

Answer:

1. D. irrational

2. A. 5

3. A. 16 and 25

4. A.  3 and four

Step-by-step explanation:

Hope this helps

Answers

0.25 ⇒ It is rational

√0.25 ⇒ It is rational

√0.33 it is irrational

Explanation

a rational number is one that can be written as a ration. Or we can say that a rational number can be written as a/b where a and b are integers and b ≠0.

0.25 = 25/100

          = 1/4

0.25 ⇒ It is rational.

√0.25 = 0.5

          = 5/10

           = 1/2

√0.25 ⇒ It is rational

√0.33 = 0.5744562664.......

           This can not be written as a/b. So,√0.33 it is irrational

Final answer:

0.25 and √0.25 are rational numbers because they can be represented as ratios of integers, while √0.33 is an irrational number due to its inability to be precisely expressed as a fraction.

Explanation:

The question asks to classify each number (0.25, √0.25, √0.33) as either rational or irrational. The distinctions between rational and irrational numbers can be understood by recalling that rational numbers are those that can be expressed as a ratio of two integers, while irrational numbers cannot be exactly expressed as a fraction of two integers.

0.25: This can be expressed as the fraction 1/4, which is a ratio of two integers. Therefore, it is a rational number.

√0.25: The square root of 0.25 is 0.5, which can also be expressed as the fraction 1/2. Hence, this is also a rational number.

√0.33: This cannot be expressed as a precise fraction of two integers and its decimal representation is non-repeating and non-terminating. Therefore, it is an irrational number.

To classify, 0.25 and √0.25 are rational numbers because they can be represented as ratios of integers. √0.33 is considered an irrational number as it cannot be exactly expressed as a fraction.

To find the total number of books on a topic when 9 are available and 55% are signed out, set up a proportion and solve for 'x.' The calculation reveals there are a total of 20 books available on the topic.

The student is asking how many books on a certain topic the library has available if 9 books are found and 55% of all the books on that topic have been signed out. To find the total number of books on the topic, we need to understand that the 9 books on the shelf represent 45% of the total books (100% - 55% = 45%). We can set up a proportion where 9 books is to 45% as the total number of books (let's call it 'x') is to 100% (the whole set of books on the topic).

Setting up the proportion, we have:

9 / 45% = x / 100%

To solve for 'x,' we cross-multiply and divide as follows:

9 * 100 = x * 45

900 = 45x

Now we divide both sides of the equation by 45 to find 'x':

x = 900 / 45

x = 20

Therefore, the library has a total of 20 books available on the topic.

Answer:

[tex]\$\,1.19[/tex]

Step-by-step explanation:

Quantity of apples bought by the student = 8.9 pounds

Amount paid by the student for apples bought by the student = [tex]\$[/tex] 10

If cost of one pound of apples is [tex]\$[/tex] 0.99  then cost of  8.9 pounds = 0.99 × Quantity of apples bought by the student = [tex]8.9\times 0.99=8.811[/tex]

Therefore,

Amount of change that the student receive if the apples are .99 per pound = Amount previously paid by the student for apples bought by the student when the student pays [tex]\$[/tex] 10 - Amount  paid by the student for apples if the apples are .99 per pound = [tex]\$ \,10-\$ \,8.811=\$\,1.19[/tex]

Final answer:

Spreadsheet software can be used to determine the amount of simple interest owed on a 30-day note by using the formula for simple interest: Principal (P) × Interest Rate (R) × Time (T).

Explanation:

In spreadsheet software, you can determine the amount of simple interest owed on a 30-day note using mathematical operations. The mathematical operations involved are multiplication and addition.

The formula for simple interest is:

Simple Interest = Principal (P) × Interest Rate (R) × Time (T)

For example, if you have a principal of $100, an interest rate of 5%, and a time period of 30 days, you can calculate the simple interest as:

$100 × 0.05 × (30/365) = $1.23

Therefore, the amount of simple interest owed on the 30-day note would be $1.23.

Answer:

only 3 lines of symmetry does an equilateral triangle have.

Explanation:

Since a triangle can have 3 or 1 or no lines of symmetry.

In a equilateral triangle:

*All sides are equal

*All angles are equal i.e each of 60 degree.

Symmetry is  when there is an exact replica or reflection of a shape or a line.    

Line of symmetry: It is an imaginary line that runs through the center of a line or shape creating two perfectly identical halves.

A line of symmetry for a given triangle must go through each vertex as shown in figure;

Therefore, the equilateral with 3 sides equal has 3 lines of symmetry.

An equilateral triangle has [tex]\fbox{\begin\\\ 3\text{lines}\\\end{minispace}}[/tex] of reflection symmetry.

Further explanation:

A triangle is a two dimensional closed figure which is formed when three non-collinear points are joined. There are three sides, three angles and three vertices of a triangle.

On the basis of sides and angles triangles are classified as follows:

1) Scalene triangle: A triangle in which all the sides and the angles have a unique value is called a scalene triangle.

2) Isosceles triangle: A triangle in which any two sides or two angles are equal then the triangle is called an isosceles triangle.

3) Equilateral triangle: A triangle in which all the sides and the angles are equal then the triangle is called an equilateral triangle.

A line of reflection is defined as a line across which the image of a figure or an object is reflected.

The reflected image is of same size as of the original image.

In case of an equilateral triangle if we drop a median from one of the vertex of the triangle to its opposite side then it is observed that the median divides the equilateral triangle into two equal halves.

From figure 1 (attached in the end) it is observed that the median AD of an equilateral trinagle [tex]\triangle \text{ABC}[/tex] divides the triangle into two equal halves.

As per the above statement it is concluded that the median AD is the line of reflection symmetry for the equilateral triangle [tex]\triangle \text{ABC}[/tex].

Now, similarly if we drop a median form the vertex B or C to its opposite side then it is observed that the triangle into two equal halves.

Figure 2 (attached in the end) shows that the median dropped from the vertex B and C divides the triangle into two equal halves.

This implies that the median BD and CD are also the line of reflection symmetry for the equilateral triangle ABC.

So, the total number of lines of reflection symmetry for an equilateral triangle is [tex]3[/tex].

Thus, an equilateral triangle has [tex]3[/tex] lines of reflection symmetry.

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2. A problem to determine the slope intercept form of a line https://brainly.com/question/1473992

3. Inverse function https://brainly.com/question/1632445  

Answer details

Grade: High school

Subject: Mathematics  

Chapter: Triangles

Keywords: Triangle, isosceles, scalene, equilateral, angles, vertex, non-collinear, reflection, symmetry, line of reflection, line of symmetry, median, reflected image.

Answer:

Part 1) The sum of the roots is [tex]4/3[/tex]

Part 2) The product of the roots is [tex]-7/3[/tex]

Step-by-step explanation:

Step 1

Find the roots

we have

[tex]3x^{2}-4x-7=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]3x^{2}-4x-7=0[/tex]

so

[tex]a=3\\b=-4\\c=-7[/tex]

substitute in the formula

[tex]x=\frac{-(-4)(+/-)\sqrt{-4^{2}-4(3)(-7)}} {2(3)}[/tex]

[tex]x=\frac{4(+/-)\sqrt{16^{2}+84}} {6}[/tex]

[tex]x=\frac{4(+/-)10} {6}[/tex]

[tex]x1=\frac{4+10} {6}=7/3[/tex]

[tex]x2=\frac{4-10} {6}=-1[/tex]  

Step 2

Find the sum of the roots

[tex]x1+x2=(7/3)-1=4/3[/tex]

Step 3

Find the product of the roots

[tex]x1*x2=(7/3)*(-1)=-7/3[/tex]

The factored type is the product of constants and two-dimensional terms, that is the root of a function as well as the graph's x-intercepts, and the further calculation can be defined as follows:

Given:

[tex]\bold{f(x)=x^3+5x^2+4x-6}[/tex]

To find:

factored form=?

Solution:

[tex]\bold{f(x)=x^3+5x^2+4x-6}[/tex]

putting the value x=-1,-2,-3...... to find the function value 0.

[tex]\to \bold{f(-1)=-1^3+5(-1)^2+4(-1)-6}\\\\[/tex]

              [tex]\bold{=-1+5\times 1+4 \times (-1)-6}\\\\ \bold{= -1+5-4-6} \\\\ \bold{=-6}\\\\[/tex]

[tex]\to \bold{f(-2)=-2^3+5(-2)^2+4(-2)-6}[/tex]

              [tex]\bold{=-8+5\times 4+4 \times(- 2)-6}\\\\\bold{= -8+20-8-6}\\\\\bold{=-2}\\\\[/tex]

[tex]\to \bold{f(-3)=-3^3+5(-3)^2+4(-3)-6}[/tex]

              [tex]\bold{=-27+5\times 9+4 \times(- 3)-6}\\\\\bold{= -27+45-12-6}\\\\\bold{=0}\\\\[/tex]

Therefore, [tex]\bold{(x+3)}[/tex] is the factor of the function.

Let [tex]\bold{(x+3)}[/tex] divide by the function:

[tex]\to \bold{\frac{x^3+5x^2+4x-6}{(x+3)}= x^2+2x-2}[/tex]

compare the value [tex]\bold{x^2+2x-2}[/tex] by the standard equation [tex]\bold{ax^2+bx+c=0}[/tex] so,

[tex]\bold{a=1}\\\\\bold{b=2}\\\\\bold{c=-2}\\\\[/tex]

Putting value into the quadratic equation formula:

[tex]\bold{x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}}[/tex]

[tex]\bold{x=\frac{-(2) \pm \sqrt{(2)^2-4\times 1 \times -2}}{2\times 1}}\\\\\bold{x=\frac{-2 \pm \sqrt{4+8}}{2}}\\\\\bold{x=\frac{-2 \pm \sqrt{12}}{2}}\\\\\bold{x=\frac{-2 \pm 2\sqrt{3}}{2}}\\\\\bold{x=\frac{2(-1 \pm \sqrt{3})}{2}}\\\\\bold{x=(-1 \pm \sqrt{3})}\\\\\bold{x=(-1 + \sqrt{3}) (-1 -\sqrt{3})}\\\\[/tex]

Adding the factor value that is [tex]\bold{(x+3)}[/tex] so, the value is "[tex]\bold{(x+3)(-1+\sqrt{3})(-1-\sqrt{3}) }[/tex]"

So, the final answer is "[tex]\bold{f(x)=(x+3)(x-(-1+\sqrt{3}))(x-(-1-\sqrt{3}))}[/tex]"

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Answer:

They receive $4.68 as a commission

Step-by-step explanation:

The cost of stereo system = $275

Price after discount of 15% = 275 - (15% × 275)

                                             = 275 - ( 0.15 × 275)

                                             = 275 - 41.25

                                             = $233.75

2% commission of the sales person = 2% × 233.75

                                                           = 0.02 × 233.75

                                                           = $4.675 ≈ $4.68

They receive $4.68 as a commission