At a school supply store, binders cost $5 and pencil pouches cost $2. In one day, 42 of these items are sold for total sales of $144. Which system represents this (b represents binders and p represents pencil pouches), and how many binders were sold?

Answer:

y = (1/12)x^2

Step-by-step explanation:

The vertex of this parabola is halfway between (0, 3) and the directrix, y = -3; that is, it's at (0, 0).

The applicable equation for this vertical parabola is 4py = x^2, where p is the distance between the vertex and the focus.  Here that distance is p = 3.

Thus, 4py = x^2 becomes 4(3)y = x^2, or 12y = x^2, or y = (1/12)x^2.

The answer is: y = (1/12)x^2.

The equation of the parabola with focus (a,b) and directrix y=c is

(x−a)2+b2−c2=2(b−c)y

The equation for a parabola with its focus at (0, 3) and a directrix of y = -3 i.e:

The vertex of this parabola is halfway between (0, 3) and the directrix, y = -3; that is, it's at (0, 0).

The applicable equation for this vertical parabola is 4py = x^2, where p is the distance between the vertex and the focus.  Here that distance is p = 3.

Thus, 4py = x^2 becomes 4(3)y = x^2, or 12y = x^2, or y = (1/12)x^2.

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For this case we must find the solutions of the following equation;

[tex]5x = 30[/tex]

We clear the value of the variable "x", dividing by 5 on both sides of the equation:

[tex]x = \frac {30} {5}[/tex]

[tex]x = 6[/tex]

Answer:

[tex]x = 6[/tex]

We have a single solution of a linear equation.

Answer:

One solution

Step-by-step explanation:

We are given the following equation and we are to determine the number of solutions this equation has:

[tex] 5 x = 3 0 [/tex]

For that, we will solve it.

Dividing both the sides by 5 to get:

[tex] \frac { 5 x } { 5 } = \frac { 3 0 } { 5 } [/tex]

[tex] x = 6 [/tex]

Therefore, this equation has only one solution.

The right answer is b.I hope it helps

You can make one equation equal to t instead of y or x. I decided to make the equation y = t - 4 equal to t

y + 4 = t + (-4 + 4)

t = y + 4

Now in the other equation ( x = 3t + 1) you can replace t with y + 4 and solve for y

x = 3(y + 4) +1

x = 3y + 12 + 1

x = 3y + 13

x - 13 = 3y

y = x/3 -13/3

^^^I assume that's what you meant in the fourth opption when you wrote "y = x - 13/3"

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The correct option is C) [tex]y=\frac{x-13}{3}[/tex].    

Step-by-step explanation:

Consider the provided parametric equations.

[tex]x=3t+1......(1)[/tex]

[tex]y=t-4......(2)[/tex]

The equation (2) can be written as:

[tex]y+4=t[/tex]

Substitute the value of t in equation (1).

[tex]x=3(y+4)+1[/tex]

[tex]x=3y+12+1[/tex]

[tex]x=3y+13[/tex]

[tex]x-13=3y[/tex]

[tex]y=\frac{x-13}{3}[/tex]

Therefore, the correct option is C) [tex]y=\frac{x-13}{3}[/tex].

The formula for the volume of a sphere is:

[tex]v = \frac{4}{3} \pi {r}^{3} [/tex]

The formula for the surface area of a sphere is:

[tex]a = 4\pi {r}^{2} [/tex]

Since they have equal numerical values, we know that the two are equal and we can say:

[tex] \frac{4}{3} \pi {r}^{3} = 4\pi {r}^{2} [/tex]

Solving for r, pi cancels out and we get:

[tex]r = 3[/tex]

Now plug r = 3 into both of the formulas to make sure that they are equal (hint: they are)

Answer: r = 3

Answer:

11 ways

Step-by-step explanation:

10 crunchy

9 crunchy 1 crispy

8 crunchy 2 crispy

7 crunchy 3 crispy

6 crunchy 4 crispy

5 crunchy 5 crispy

4 crunchy 6 crispy

3 crunchy 7 crispy

2 crunchy 8 crispy

1 crunchy 9 crispy

10 crispy

As the question does not specify any order or arrangement for the boxes of Wake up cereal, the boxes can be organized in one single way: 10 boxes of crispy Wake up cereal and 10 boxes of crunchy Wake up cereal.

The question asks how many ways 10 boxes of crispy Wake up cereal and 10 boxes of crunchy Wake up cereal can be organized. This appears to be a problem of combinations or permutations. However, since there are only two types of cereal and the question only asks about the total number of boxes, not their order, the numbers of ways will be the same no matter how they're arranged. Therefore, the only answer in this case would be one single way: 10 boxes of crispy and 10 boxes of crunchy.

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Answer:

20 miles

Step-by-step explanation:

She traveled 4 miles in 15 minutes.

She went at the same speed for another hour.

1 hour is 60 minutes.

60 = 4 * 15

There are 4 15-minute periods in an hour.

Since she went 4 miles in 15 minutes, she went 4 * 4 miles in 1 hour.

4 * 4 miles = 16 miles.

She went 4 miles in 15 minutes and another 16 miles in an hour.

The total distance she traveled is 4 miles + 16 miles = 20 miles.

Answer: 20 miles

Answer:

Step-by-step explanation:

Going from (1, -2) to (3,6), x increases by 2 and y increases by 8.  Thus, the slope m of this line is m = rise / run = 8/2 = 4.

I think you meant, "What is the EQUATION of the line that passes through the point (-1, 1) and is parallel to a line that passes through

(3, 6) and (1, -2)?  We have seen that this slope is -4.  

Starting with the point-slope equation of a line, we have:

y - 6 = -4(x - 3)

ANSWER

[tex]y= {(x+ 1)}^{2}[/tex]

EXPLANATION

The given points are:

(1, 4), (2, 9), and (3, 16)

It is obvious that the function is not linear because there is no constant difference among the y-values.

We can however manipulate the y-values to quickly identify the function.

[tex]4 = {2}^{2} = {(1 + 1)}^{2} [/tex]

[tex]9= {3}^{2} = {(2 + 1)}^{2} [/tex]

[tex]16= {4}^{2} = {(3 + 1)}^{2} [/tex]

We can infer from the pattern that, the function is;

[tex]y= {(x+ 1)}^{2} [/tex]

Answer:

-4 <n <= 5

Step-by-step explanation:

Open at -4 and closed at 5 on number line so the inequality should be

-4 <n <= 5

Answer:

6, 13, 20, 27, 34

arithmetic sequence

Step-by-step explanation:

"Start with 6" means the first term is 6.

"Add 7 repeatedly" means each term is formed by adding 7 to the one before it:

6 +7 = 13

13 +7 = 20

20 +7 = 27

27 +7 = 34

So, the first 5 terms are ...

6, 13, 20, 27, 34

_____

Any sequence in which terms have a common difference is an *arithmetic* sequence. You know these terms have a common difference of 7, because that's the number you added to each term to get to the next term. 13-6 = 7; 20-13 = 7; 27-20 = 7; and so on.

[tex]x^{13}-2x^{12}-x^{11}+2x^{10}=0\\\\x^{10}\cdot\Big[x^3-2x^2-x+2\Big]=0\\\\x^{10}\cdot\Big[x^2\cdot(x-2)-(x-2)\Big]=0\\\\x^{10}(x-2)(x^2-1)=0\\\\\boxed{x^{10}(x-2)(x+1)(x-1)=0}[/tex]

So:

x = 0 with multiplicity 10 or

x = 2 or

x = 1 or

x = -1

Answer D)

Answer:

A

Step-by-step explanation:

The volume of a pyramid is one third the height times the area of the base.

V = ⅓ h A

The base is a square, so the area is the width times length.

V = ⅓ h wl

Problem is, we don't know the height, only the slant length.  But we can use this to find the height.

If we cut a cross section down the middle of the pyramid, we get an isosceles triangle.  The base of the triangle is 24, and the legs are 37.

If we cut this triangle in half, we get two right triangles.  Each right triangle has a base of 12 and a hypotenuse of 37.

Now we can use Pythagorean theorem to find the height of the triangle, which is also the height of the pyramid.

c² = a² + b²

37² = 12² + h²

h = 35

Now we can find the volume.  h = 35, w = 24, and l = 24:

V = ⅓ h wl

V = ⅓ (35) (24) (24)

V = 6720

So the volume is 6720 ft³, or answer A.

The correct answer is x = 3.

To solve the equation[tex]4x=8x-1\[/tex] we need to isolate the variable x on one side of the equation. Let's perform the necessary algebraic steps:

 First, subtract 4x from both sides of the equation to get all the x terms on one side:

[tex]4x=8x-1\\\8x-4x=1\\4x=1\\x=4-1\\3[/tex]

 However, the options provided are numerical values, and [tex]3[/tex] does not match any of the given options. It seems there was a mistake in the options provided or in the interpretation of the equation. The correct solution to the equation 4x = 8x - 1 is indeed x = 3

Answer:

[tex]112.25\ grams\ of\ carbohydrates[/tex]    

Step-by-step explanation:

we know that

using proportion

[tex]\frac{1}{44.9}\frac{serving\ of\ rice}{grams\ of\ carbohydrates} =\frac{2.5}{x}\frac{serving\ of\ rice}{grams\ of\ carbohydrates} \\ \\x=44.9*2.5\\ \\x=112.25\ grams\ of\ carbohydrates[/tex]

Answer:

WHAT IS THE ANSWER I CAN'T VEIR THE FILE

Step-by-step explanation:

Answer:

[tex]x=1.2528[/tex]

Step-by-step explanation:

Assuming the equation to solve is

[tex]1+2e^x+1=9[/tex]

We can first simplify as:

[tex]1+2e^x+1=9\\2+2e^x=9\\2e^x=9-2\\2e^x=7\\e^x=\frac{7}{2}[/tex]

to solve an equation with e and x as an exponent, we need to take "natural log (ln)" on both sides and also use the property:

[tex]ln(a^x)=xln(a)[/tex]

And also remember that ln e = 1

Now we have:

[tex]e^x=\frac{7}{2}\\ln(e^x)=ln(\frac{7}{2})\\xln(e)=ln(\frac{7}{2})\\x(1)=ln(\frac{7}{2})\\x=ln(\frac{7}{2})\\x=1.2528[/tex]

Answer:  [tex]x[/tex]≈[tex]1.252[/tex]

Step-by-step explanation:

Given the equation [tex]1+2e^x+1=9[/tex], add the like terms:

[tex]2e^x+2=9[/tex]

Subtract 2 from both sides:

[tex]2e^x+2-2=9-2[/tex]

[tex]2e^x=7[/tex]

Divide both sides by 2:

[tex]\frac{2e^x}{2}=\frac{7}{2}\\\\e^x=\frac{7}{2}[/tex]

Apply natural logarithm to both sides. Remember that

[tex]ln(e)=1[/tex] and  [tex]ln(m)^n=nln(m)[/tex]

Then, you get:

[tex]ln(e)^x=ln(\frac{7}{2})\\\\xln(e)=ln(\frac{7}{2})\\\\x=ln(\frac{7}{2})[/tex]

[tex]x[/tex]≈[tex]1.252[/tex]

Answer:

B. 1

Step-by-step explanation:

they only cross at one point... look below

ANSWER

B. 1

EXPLANATION

The given system of equations is;

–2x + 4y = –7

y= -1/2x + 5

We rewrite the first equation is slope intercept form:

4y = 2x–7

[tex]y = \frac{1}{2}x - \frac{7}{4} [/tex]

The two equations have different slopes.

This means that they will intersect at one point in the XY plane.

Hence the system has a unique solution.

Answer:

C

Step-by-step explanation:

The solution for the inequality 2x + 9/4 > 6 is x> 15/8 the all values of the x which is greater than the 15/8

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have inequality:

2x+9/4?6

Here the proper form of inequality is not given, but we can solve the inequality by assuming the inequality is:

2x + 9/4 > 6

2x > 6 - 9/4

2x > 15/4

x > 15/8

From the above procedures we can solve any inequality.

Thus, the solution for the inequality 2x + 9/4 > 6 is x> 15/8 the all values of the x which is greater than the 15/8

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Answer:

C. 1 7/8 of a pound

Step-by-step explanation:

We can use  a ratio to solve

2 1/2 pounds     x pounds

------------------ = ---------------

1 batch               3/4 batch

Change to improper fractions

2 1/2 = (2*2+1)/2 = 5/2

5/2 pounds     x pounds

------------------ = ---------------

1 batch               3/4 batch

Using cross products

5/2 * 3/4 = 1*x

15/8 = x

Changing from an improper fraction to a mixed number

8 goes into 15 1 time with 7 left over

15/8 = 1 7/8

Answer:

1  7/8

Step-by-step explanation:

For this case we have by definition, that the volume of a cone is given by:

[tex]V = \frac {1} {3} * \pi * r ^ 2 * h[/tex]

Where:

A: It is the cone radius

h: It's the height

They tell us that the diameter is 21 m, then the radius is half the diameter, that is: 10.5m. The height is 4m. Substituting the data:

[tex]V = \frac {1} {3} * \pi * (10.5) ^ 2 * 4\\V = \frac {1} {3} * \pi * 110.25 * 4\\V = 147 \pi[/tex].

Finally, the volume of the cube is[tex]147 \pi \ m ^ 3[/tex]

ANswer:

Option B

Answer:

147[tex]\pi[/tex]m^3

Step-by-step explanation:

Answer:

the solution is (-1, 2)

Step-by-step explanation:

Let's solve the system

(3x + 4y = 5)

(2x - 3y = -8)

using the method of elimination by addition and subtraction.  Notice that if we multiply all terms of the first equation by 3 and all terms of the second by 4, y as a variable will temporarily disappear:

  9x + 12y = 15

  8x - 12y  = -32

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

 17x       = - 17, so x = -1.  

Replacing x in the second equation by -1, we get:

2(-1) - 3y = -8, or

2 + 3y = 8,

or 3y = 6.  Thus, y = 2, and the solution is (-1, 2).

The solution to the given system of equations is x = -1 and y = 2. We found these values using the elimination method, first by making the coefficients of x in both equations the same, then eliminating x and solving for y, and finally substituting y = 2 into the first equation and solving for x.

To solve the given system of equations, we can use the elimination method. First, we need to make the coefficients of either x or y the same in both equations. We can do so by multiplying the first equation by 2 and the second equation by 3:

⟹ (3x * 2 + 4y * 2 = 5 * 2) and (2x * 3 - 3y * 3 = -8 * 3)

When simplified, we get:

⟹ 6x + 8y = 10 and 6x - 9y = -24

Now, we subtract the second equation from the first one to eliminate x:

⟹ (6x + 8y) - (6x - 9y) = 10 - (-24)

⟹ 17y = 34

Finally, we solve for y by dividing both sides of the equation by 17:

⟹ y = 34 / 17

⟹ y = 2

Substitute y = 2 into the first original equation:

⟹ 3x + 4 * 2 = 5

⟹ 3x + 8 = 5

⟹ 3x = -3,

On simplifying, we get x = -1. So, the solution to the system is x = -1, y = 2.

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Answer:

The triangle ABC is reflected over the line y = x ⇒ answer B

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

∴ Its image is (-y , -x)

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 90° clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180°

∴ Its image is (-x , -y)

* There is no difference between rotating 180° clockwise or  

anti-clockwise around the origin

* Lets find the vertices of ABC and A'B'C' to solve the problem

- In Δ ABC

# A = (5 , -5) , B = (5 , -4) , C = (2 , -4)

- In Δ A'B'C'

# A' = (-5 , 5) , B = (-4 , 5) , C = (-4 , 2)

∵ The image of (5 , -5) is (-5 , 5)

∵ The image of (5 , -4) is (-4 , 5)

∵ The image of (2 , -4) is (-4 , 2)

∴ The point (x , y) is (y , x)

- From the rule above

∴ The triangle ABC is reflected over the line y = x

Answer:

The triangle ABC is reflected over the line y = x ⇒ answer B

Step-by-step explanation:

Answer:

3/5

Step-by-step explanation:

There are 10 letters in the word "statistics".

Out of which, there are 3 s's and 3 t's.  

So, the question asks what's the probability to get a S or a T out of 10 letters.

Since the number of S's (3) and the number of T's equal 6, that means you have 6 chances out of 10 to pick an S or a T.

6/10 or if we simplify/reduce it... we get 3/5.

the correct answer is 3/5

The question is asking for the probability of selecting either an 's' or a 't' from the word 'statistics'. To solve this, we need to look at the total number of each letter and the total number of letters in the word. The word 'statistics' has 10 letters in total, with 3 's' letters and 3 't' letters.

To calculate the probability, we add the number of 's' letters to the number of 't' letters, which gives us 6. Then we divide this sum by the total number of letters in the word:

Probability('s' or 't') = (Number of 's' + Number of 't') / Total number of letters

Probability('s' or 't') = (3 + 3) / 10 = 6/10 = 3/5.

Thus, the correct answer is 3/5, meaning there is a 60% chance of picking either an 's' or a 't' from the word 'statistics'.

[tex]\bf (\stackrel{x}{2},\stackrel{y}{-2})\qquad y=2x+2\implies -2=2(2)+2\implies -2\ne 6~~\bigotimes \\\\\\ (\stackrel{x}{2},\stackrel{y}{-2})\qquad y = 2x-2\implies -2=2(2)-2\implies -2\ne 2~~\bigotimes \\\\\\ (\stackrel{x}{2},\stackrel{y}{-2})\qquad y=2x+6\implies -2=2(2)+6\implies -2\ne 10~~\bigotimes \\\\\\ (\stackrel{x}{2},\stackrel{y}{-2})\qquad y=2x-6\implies -2=2(2)-6\implies -2=-2~~\checkmark[/tex]

Answer:

x = 3

Step-by-step explanation:

A line of symmetry splits a figure into 2 exact, mirror images of one another.  The line here that does that is x = 3

Answer:

x=3

Step-by-step explanation:

For this case we have that by definition of trigonometric relations that the sine of an angle is equal to the opposite leg to the angle on the hypotenuse. That is to say:

[tex]Sin (43) = \frac {a} {26}[/tex]

Clearing the value of "a":

[tex]a = 26 * sin (43)\\a = 26 * 0.68199836\\a = 17.73195736[/tex]

Rounding off we have:

17.7

Answer:

Option B

1. [tex]x[/tex] in quadrant IV means [tex]\sin x<0[/tex], so

[tex]\cos^2x+\sin^2x=1\implies\sin x=-\sqrt{1-\cos^2x}=-\dfrac{\sqrt3}2[/tex]

2. [tex]x[/tex] in quadrant I means [tex]\cos x>0[/tex]. Then

[tex]\cos x=\sqrt{1-\sin^2x}=\dfrac{\sqrt2}2[/tex]

3. [tex]x[/tex] in quadrant II means [tex]\sin x>0[/tex]. Then

[tex]\tan x=\dfrac{\sin x}{\cos x}=\dfrac{\sqrt{1-\cos^2x}}{-\frac12}=\dfrac{\frac{\sqrt3}2}{-\frac12}=-\sqrt3[/tex]

4. If [tex]\sin x=-1[/tex], then [tex]\cos x=0[/tex], so [tex]\tan x[/tex] is undefined.

Answer:

56.07 degrees

Step-by-step explanation:

This is a classic problem involving right triangle trig.  We are looking for the angle that has a side opposite it with a measure of 55 m and a side adjacent to it with a measure of 37 m.  This is the tangent ratio of the missing angle.  Our equation then looks like this:

[tex]tan\theta=\frac{55}{37}[/tex]

To find a missing angle on your calculator in degree mode, hit 2nd then tan and you'll see "tan^-1(  " on your display.  After the open parenthesis, enter your fraction and hit the enter button to get the angle measure.  56.07°

Answer:47. 72°

Step-by-step explanation:

from the attached figure below; adjacent =37 hypotenuse=55

θ = ?

From trig. formular,

cos θ = adjacent / hypotenuse

cos θ = 37 / 55

cos θ =0. 6727

θ = cos⁻¹ (0. 6727)

θ = 47. 72°

The angle of elavation is 47. 72°

Answer: 16% as a fraction is 4/25

Step-by-step explanation:

convert 16% into a decimal then put it over 100 and simplify which gives you 4/25

Answer: [tex]=\frac{4}{25}[/tex]

Step-by-step explanation:

First, you need to convert 16% to decimal form. To do this, you must divide it by 100. Then, the numerator will be 16 and the denominator will be 100:

[tex]=\frac{16}{100}[/tex]

And finally, you need to simplify the fraction by reducing it. Notice that the numerator and the denominator can be both divided by 4. Then, dividing by 4 you get:

[tex]=\frac{4}{25}[/tex]

Since the numerator and the denominator cannot be divided by the same number anymore, then the fraction is simplified.

Therefore, the fraction equal to 16% (simplified) is:

[tex]=\frac{4}{25}[/tex]

Answer:

3

Step-by-step explanation:

12/4 = 3

so

(a^2/b^3)^4 = a^8 / b^12