Irunt
Amanda only has $30 to buy pens and notebooks. Each pen costs $2. Each
notebook costs $3. Which of the following graphs represents the possible
combinations of pens and notebooks that she may purchase?

Answer:

The x-intercept is (6,0).

The y-intercept is (0,-21/2).

Step-by-step explanation:

So we are told this is a line.

Linear equations in the form y=mx+b tell us the slope,m, and the y-intercept,b.

So we are going to write our equation in this form to determine x- and y- intercept.

Let's begin.

First thing I'm going to is compute the slope.  The slope can be found by lining up the points vertically and subtracting them vertically then put 2nd difference over 1st difference.

Let's do that:

 (   -10  ,  -28)

- (    -6  ,   -21)

-----------------------

   -4             -7

So the slope is -7/-4 which is 7/4.

Now we know our equation to be in this form

y=(7/4)x+b

Use one of the points along with y=(7/4)x+b to find b.

Doesn't matter which one, you get to choose.

How about (-2,-14)?

-14=(7/4)(-2)+b

-14=-7/2+b

Add 7/2 on both sides:

-14+7/2=b

-21/2=b

So our equation is

[tex]y=\frac{7}{4}x-\frac{21}{2}[/tex]

So we already know the y-intercept is (0,-21/2).

We knew this because we were putting into slope-intercept form.

Now to find the x-intercept, set y=0 and solve for x:

[tex]0=\frac{7}{4}x-\frac{21}{2}[/tex]

Clear the fractions; multiply both sides by 4:

[tex]0=7x-42[/tex]

Add 42 on both sides:

[tex]42=7x[/tex]

Divide both sides by 7:

[tex]\frac{42}{7}=x[/tex]

So x=6

The x-intercept is (6,0).

Answer:

The correct answer is f(x) =1/2 x + 6

Step-by-step explanation:

We have to convert the equation of line in the form of a function to compare with the options

Given equation of line is:

[tex]y-8=\frac{1}{2}(x-4)\\ Distributing\ 1/2\\y-8=\frac{1}{2}x-(4)(\frac{1}{2})\\y-8=\frac{1}{2}x-2\\y=\frac{1}{2}x-2+8\\y=\frac{1}{2}x+6[/tex]

Therefore, the correct answer is f(x) =1/2 x + 6  ..

Answer:

Step-by-step explanation:

The given equation is √2x+1+3=0

And we have been given that x= 4

I do not agree with the solution because it does not give any real solution. It only gives possible solution. If you plug the value 4 in the original equation you will get 8 and the square root of 8 is a complex number.  Thus 4 is an extraneous solution....

Answer:

I do not agree with the student because there is no real solution.

Solving the equation only gives possible solutions, but you must check them in the original equation.

Checking the solution in the original equation shows that 4 is an extraneous solution.

Step-by-step explanation:

2a. 14,9; 2b. 15,4; 2c. 30,8; 3. 32

For 2a., you have to set it up like this: csc 48° = 20⁄x [OR sin 48° = ˣ⁄20]. Then you would have to isolate the variable by getting rid of the denominator. The cosecant function has an extra step because you will get xcsc 48° = 20. As stated, isolate the variable; this time, divide by csc 48°. This is what 20 will be divided by to get your x, whereas the other side cancels out. Then you have to round to the nearest tenth degree.

For 2b., you have to set it up like this: sec 39° = ˣ⁄12 [OR cos 39° = 12⁄x. Then you would have to isolate the variable by getting rid of the denominator. The cosine function has an extra step because you will get xcos 39° = 12. As stated, isolate the variable; this time, divide by cos 39°. This is what 12 will be divided by to get your x, whereas the other side cancels out. Then you have to round to the nearest tenth degree.

For 2c., you have to set it up like this: cot 64° = 15⁄x [OR tan 64° = ˣ⁄15]. Then you would have to isolate the variable by getting rid of the denominator. The cotangent function has an extra step because you will get xcot 64° = 15. As stated, isolate the variable; this time, divide by cot 64°. This is what 15 will be divided by to get your x, whereas the other side cancels out. Then you have to round to the nearest tenth degree.

Now, for 3., it is unique, but similar concept. In this exercise, we are solving for an angle measure, so we have to use inverse trigonometric ratios. So, we set it up like this: cot⁻¹ 1⅗ = m<x [OR tan⁻¹ ⅝ = m<x]. We simply input this into our calculator and we get 32,00538321°. When rounded to the nearest degree, we get 32°.

WARNING: If you use a graphing calculator, you have to input it uniquely because most graphing calculators do not have the inverse trigonometric ratios programmed in their systems. This is how you would write this: tan⁻¹ 1⅗⁻¹. You set 1⅗ to the negative first power, ALONG WITH the inverse tangent function, because without it, your answer will be thrown off. Since Cotangent and Tangent are multiplicative inverses of each other, that is the reason why the negative first power is applied ALONG WITH the inverse tangent function.

**NOTE: 1⅗ = 8⁄5

Take into consideration:

sin θ = O\H

cos θ = A\H

tan θ = O\A

sec θ = H\A

csc θ = H\O

cot θ = A\O

I hope this helps you out alot, but if you are still in need of assistance, do not hesitate to let me know and subscribe to my channel [username: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

1) Find the unit rate

$18/6 attendees = 3

2) Apply the unit rate to find the answer

$48/$3= 16 attendees

Therefore, there can be 16 attendees if the budget is $48.

Hope this helps!

Answer:

y - 9 = 1/2(x + 3)

Step-by-step explanation:

For the equation y = -2x + 8, your slope, m, is -2. To find the slope for a line perpendicular to the original line, we do the opposite reciprocal of this number. The slope of the perpendicular line is 1/2.

Point-slope form is: y - y1 = m(x - x1) where x1 and y1 are the x- and y-coordinates of an ordered pair.

With this new slope for the perpendicular line, and the point we are given, we just plug in the info.

Your equation is: y - 9 = 1/2(x + 3)

Answer:

D. x=-6 y= -11

Step-by-step explanation:

y= x -5

y= 2x +1

2y=2x- 10

y=2x+1

y= -11

-11= x-5

+5 +5

-6=x

Answer:

  A)  125 inches squared

Step-by-step explanation:

The lateral area is the product of the perimeter of the base, and the height:

  (25 in)(5 in) = 125 in²

__

If you draw the net for the object, you will see that the rectangle representing the lateral area has these dimensions.

Answer:

D. -2, -1

Step-by-step explanation:

[x + 1][x + 2] = 0

Additive Inverses always result in 0, so straight off the bat, you know that your zeros are the above answers.

I am joyous to assist you anytime.

Answer:

6n = 18p

Step-by-step explanation:

Answer: n=3p

Step-by-step explanation:

Answer:

108 feet cubed

Step-by-step explanation:

i think its 24 because you do l*w*h so 4 times 6 equals 24, times 4.5 and its 108.

Answer : The volume of the swimming pool is, [tex]142ft^3[/tex]

Step-by-step explanation :

In the given figure, there are two figures are included which are cuboid and 2 hemisphere.

As we know that 2 hemisphere combine to form a sphere.

Volume of swimming pool = Volume of cuboid + Volume 2 hemisphere

Volume of swimming pool = Volume of cuboid + Volume sphere

Volume of swimming pool = [tex](l\times b\times h)+(\frac{4}{3}\pi r^3)[/tex]

where,

l = length of cuboid = 6 ft

b = breadth of cuboid = 4 ft

h = height of cuboid = 4.5 ft

r = radius of sphere = [tex]\frac{Diameter}{2}=\frac{4ft}{2}=2ft[/tex]

Now put all the given values in the above formula, we get:

Volume of swimming pool = [tex](l\times b\times h)+(\frac{4}{3}\pi r^3)[/tex]

Volume of swimming pool = [tex](6ft\times 4ft\times 4.5ft)+(\frac{4}{3}\times 3.14\times (2ft)^3)[/tex]

Volume of swimming pool = [tex]108ft^3+33.49ft^3[/tex]

Volume of swimming pool = [tex]141.49ft^3[/tex]

Volume of swimming pool ≈ [tex]142ft^3[/tex]

Therefore, the volume of the swimming pool is, [tex]142ft^3[/tex]

Answer:

see explanation

Step-by-step explanation:

x = 54° corresponding angle to 54° and congruent )

y = 46° ( alternate angle to 46° and congruent )

w and x form a straight angle and are supplementary, hence

w = 180° - x = 180° - 54° = 126°

--------------------------------------------------------

The angle adjacent to z = 32° ( alternate angle to 32° and congruent )

z = 180° - 32° ( straight angle and supplementary )

z = 148°

The equation (x+5)^2 + (y+7)^2=81 is a variation of a circles standard formula (x - h)^2 + (y - k)^2 = r^2

The center of the circle is found by (h, k)

In this case:

h = -5

k = -7

Therefore the center is:

(-5, -7)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

(16x^2-1) can be factored over integers so, Option C is correct.

Step-by-step explanation:

Given: 256x^4y^2-y^2

Factorizing the given expression:

Taking y^2 common

=y^2(256x^4-1)

Using formula: a^2-b^2 = (a-b)(a+b)

=y^2((16x^2)^2-(1)^2)

y^2(16x^2+1)(16x^2-1)

y^2(16x^2+1)((4x)^2-(1)^2)

y^2(16x^2+1)(4x-1)(4x+1)

Since (16x^2-1) can be factored over integers so, Option C is correct.

Answer:

d no is correct

I hope it will help you

The equivalent Pythagorean identity is [tex]-cos^2 \theta - 1 = -sin^2 \theta[/tex]

According to the theorem;

[tex]x^2 + y^2 = r^2[/tex]

Given the following

x = [tex]r cos \theta[/tex]

y = [tex]r sin \theta[/tex]

Substitute into the formula

[tex](rcos \theta)^2 + (r sin \theta)^2 = r^2\\cos^2 \theta + sin^2 \theta =1[/tex]

Multiplying through by minus, the equivalent Pythagorean identity is [tex]-cos^2 \theta - 1 = -sin^2 \theta[/tex]

Learn more on Pythagoras theroem here: https://brainly.com/question/343682

Answer:

x can be 0, -1/3, 8 or -2

Step-by-step explanation:

the equation is already expressed in factor form:

-2x(3x+1)(x-8)(x+2)=0​

Simply equate each of the factors to zero

i.e

-2x = 0 ----------> x = 0

3x+1 = 0 ----------> x = -1/3

x-8 = 0 ----------> x = 8

x+2 = 0 ----------> x = -2

Answer:

r = ∛(3V/4π)

Step-by-step explanation:

The formula for the volume of a sphere is V = (4/3)πr³.

We want to solve this first for r³ and then for r.

Multiplying both sides of V = (4/3)πr³ by 3 yields an equation without fractions:  3V = 4πr³.

Dividing both sides of this equation by 4π isolates r³:

       3V

r³ = -------

       4π

To find r, take the cube root of both sides of

       3V

r³ = -------

       4π

obtaining r = ∛(3V/4π)

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=113 \end{cases}\implies 113=\cfrac{4\pi r^3}{3}\implies 339=4\pi r^3 \\\\\\ \cfrac{339}{4\pi }=r^3\implies 26.98\approx r^3\implies \sqrt[3]{26.98}=r\implies 2.999 \approx r\implies \stackrel{\textit{rounded up}}{3=r}[/tex]

Step-by-step explanation:

Tally means you write the number of marks of terms that fall in between every range you see.

Ex: Age 40 [36 - 40]; Tally: I; Frequency: 1

What I just did was find one term that fell in between the range of 36-40. See if you can do the rest using this example, and as always, I am joyous to assist anyone at any time!!!

1. Total teachers: 38

2. Teachers older than 35: 9

3. Teachers aged 31-40: 7

4. Most populated age range: 21-25 and 26-30 (5 teachers each)

5. Teachers younger than 31: 7

To complete the frequency table, we count the number of occurrences of each age within the given ranges:

Age Range        Tally                     Frequency

-----------------------------------------------------------

16-20                ||                           2

21-25                |||||                    5

26-30                |||||                    5

31-35                |||||                    5

36-40                ||                           2

41-45                ||                           2

46-50                |||||                    5

-----------------------------------------------------------

Now, let's answer the questions:

1. There are 38 teachers at Accelerate Education. (Count the total frequency)

2. To find the number of teachers older than 35, we sum the frequencies of the age ranges 36-40, 41-45, and 46-50. 2 + 2 + 5 = 9.

3. To determine the number of teachers between the ages of 31 and 40, we sum the frequencies of the age ranges 31-35 and 36-40. 5 + 2 = 7.

4. The age range with the highest frequency is 21-25 and 26-30, each with 5 teachers.

5. To find the number of teachers younger than 31, we sum the frequencies of the age ranges 16-20 and 21-25. 2 + 5 = 7.

The question probable maybe:

(Given in the attachments)

Answer:

-1

Step-by-step explanation:

2x-10

-------------- = 3x

4

Multiply each side by 4

     2x-10

4*-------------- = 3x*4

      4

2x-10 = 12x

Subtract 2x from each side

2x-10 -2x = 12x-2x

-10 = 10x

Divide each side by 10

-10/10 =10x/10

-1 =x

Answer:-1

Step-by-step explanation:GOT it right on my quiz (FLVS)

Answer:

C. A=1/2bh

The formula for the area of a triangle is 1/2bh

Answer:

6!

or

6*5*4*3*2*1

or

720

Step-by-step explanation:

The word 'PLANTS' contains no letter more than once.

It is say 6 letter word.

_  _  _ _ _ _

There are 6 ways to choose the first blank (after than there are 5 letters left to choose from)

After the first blank, there are 5 letter left to choose from so there are 5 ways to choose the second blank.

Then 4 ways for the third blank.

3 ways for the fourth blank.

2 ways for the fifth blank.

1 way for the sixth blank.

Now to figure out the number of permutations you must multiply the number of different ways we have above for each blank.

That is we are doing 6*5*4*3*2*1 or 6!

There are 720 different permutations of the letters in the word 'PLANTS' when used without repetition. This is calculated as the factorial of the number of letters, which is 6. Therefore, 6 factorial (6!) equals 720.

The subject of the question falls under the topic of permutations in Mathematics. The question is asking for the number of different ways that the letters in the word 'PLANTS' can be arranged if all letters are used without repetitions. This is a concept in combinatorics, a subject of discrete mathematics that deals with counting and arranging objects.

To solve this, we need to calculate the factorial of the number of letters in the word 'PLANTS'. There are 6 letters in the word. The factorial of a number (denoted as n!) is the product of all positive integers less than or equal to that number. Therefore, the number of permutations is 6!, which equates to 6 x 5 x 4 x 3 x 2 x 1 = 720.

So, there are 720 different permutations of the letters in the word 'PLANTS' if all the letters are used without repetition.

https://brainly.com/question/23283166

#SPJ11

This question is solved using a system of equations. I am going to say that:

Doing this, we get that: There are 4 nickels and 12 dimes.

There are 8 more dimes than nickels in the bank.

This means that: [tex]y = x + 8[/tex]

There is a total of $1.40.

Thus, for the nickels:

[tex]0.05x + 0.1y = 1.4[/tex]

Since [tex]y = x + 8[/tex]

[tex]0.05x + 0.1(x + 8) = 1.4[/tex]

[tex]0.05x + 0.1x + 0.8 = 1.4[/tex]

[tex]0.15x = 0.6[/tex]

[tex]x = \frac{0.6}{0.15}[/tex]

[tex]x = 4[/tex]

For the dimes:

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

There are 4 nickels and 12 dimes.

A similar question is found at https://brainly.com/question/24342899

Final answer:

To solve the problem, we use algebra to express the relationship between the number of dimes and nickels and their total value in pennies. We find that there are 4 nickels and 12 dimes in the piggy bank.

Explanation:

Calculating the Number of Dimes and Nickels

Let's denote the number of nickels as N and the number of dimes as D. According to the problem, there are 8 more dimes than nickels, which means D = N + 8. Now, we need to convert the total value of coins into pennies because there are 100 pennies in one dollar.

The value of nickels and dimes in pennies is 5N (for nickels) and 10D (for dimes), respectively. Since the total amount is $1.40 or 140 pennies, we can express this as the equation 5N + 10D = 140.

Replacing D in the equation with N + 8 we get 5N + 10(N + 8) = 140. Simplifying this, we get 5N + 10N + 80 = 140, which simplifies further to 15N + 80 = 140.

Subtracting 80 from both sides gives us 15N = 60, and dividing both sides by 15 yields N = 4. This means there are 4 nickels.

To find the number of dimes, we substitute N with 4 in the earlier expression for D (D = N + 8) giving us D = 4 + 8, which equals 12.

Therefore, there are 4 nickels and 12 dimes.

Answer:

You can use photo math it does all the math for you and explains why.

Hope this helps!

Step-by-step explanation:

Final answer:

For creating rectangular shaped fractions, Adobe Photoshop or Illustrator can be utilized for graphic designs, while EquatIO is fitting for educational materials involving math. Microsoft Word is another option that includes a built-in equation editor for such purposes.

Explanation:

If you are looking for an app that allows you to create graphics featuring rectangular shaped fractions, there are a few different tools that may be useful depending on your specific needs. For instance, graphic design apps like Adobe Photoshop or Illustrator have the capability to create almost any shape including rectangles, allowing you to design custom graphics that include fractions in any way you desire. If your goal is specifically to create educational materials, a math-oriented tool like EquatIO might be more suitable. This particular app is designed to help create mathematical equations, graphs, and shapes which can then be inserted into documents, making it very useful for educational purposes.

Additionally, if you're just looking to type fractions in a rectangular format for reports or presentations, you might consider using a word processor with good equation support, such as Microsoft Word, which includes a built-in equation editor that allows for the creation of rectangle shaped fractions and other mathematical notations. Always be sure that you have the appropriate licenses and access to these pieces of software before using them for any purpose.

Answer:

[tex]g(x)=x+6[/tex]

Step-by-step explanation:

we have

[tex]f(x)=x+8[/tex]

If f(x) is shifted 2 units to the right

then

The rule of the translation is

[tex]g(x)=f(x-2)[/tex]

so

[tex]g(x)=(x-2)+8[/tex]

[tex]g(x)=x+6[/tex]

Answer:  The correct option is

(D) [tex]g(x)=x+6.[/tex]

Step-by-step explanation:  Given that the following function is shifted 2 units to the right :

[tex]f(x)=x+8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We are to write the equation when the function (i) is shifted 2 units to the right.

We know that

if a function is shifted 2 units to the right, then its x co-ordinate is reduced by 2 units.

Therefore, the equation of the new function is given by

[tex]g(x)=f(x-2)=(x-2)+8=x+6.[/tex]

Thus, the required function is [tex]g(x)=x+6.[/tex]

Option (D) is CORRECT.

Answer:

y=px^2/4

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

3^-4 x 2^3 x 3^2/2^4 x 3^-3

base 3 will be numerator and base 2 will be denominator:

3^-4 * 3^2 * 3^3 / 2^4*2^-3

Now add the exponents of the base:

3^-4+2+3/ 2^4-3

3^-4+5/ 2^1

3/2

The correct option is 3/2 ....

Step-by-step explanation:

the correct answer is c

Area of a circle is found using the formula: Area = π * r^2

Using 3.14 for π

Area of the bull'e eye = π * 2^2 = 4π = 4 * 3.14 = 12.56 square inches.

This is 20% of the entire target.

To find the area of the entire target, divide the area of the bull's eye by the percentage:

Area = 12.56 / 0.20 = 62.8 square inches.

Round the answer as needed.

Answer:

Area of target = 62.8 inch²

Step-by-step explanation:

A bull’s-eye with a 4-inch diameter covers 20 percent of a circular target.

Diameter of bull's eye = 4 inch

[tex]\texttt{Area of bull's eye = }\frac{\pi\times 4^2}{4}=12.56inch^2[/tex]

Given that  bull’s-eye covers 20% of circular target.

[tex]\texttt{Area of bull's eye = }\frac{20}{100}\times \texttt{Area of target}\\\\\texttt{Area of target}\times 0.2=12.56\\\\\texttt{Area of target}=\frac{12.56}{0.2}=62.8inch^2[/tex]

Area of target = 62.8 inch²