At the beginning of a class period, half of the students in a class go to the library. Later in the period, half of the remaining students go to the computer lab. If there are eight students remaining in class, how many students were originally in the class?

No the negative slope means the line moves down from left to right.

Hope this helps.

r3t40

Answer:

It slopes upwards from right to left.

Step-by-step explanation:

A negative slope means that a line rises from right to left. Like a back slash \.

Answer:

If each linear function is given as a set of two ordered pairs, you need to use those points to find the equation of each line, and then solve the system of equations.

For example:

Let's say that f(x) has the following ordered pais: (a, b) and (c, d) and g(x) has the following ordered pais: (e, f) and (g, h). We know that the general equation of a line is the following:

(y - yo) = m(x-xo), where 'm' represents the slope and (xo, yo) any point from the line.

The slope will be given by: (y1 - yo)/(x1 - x0).

For example, the equation of the line of f(x) is:

f(x) = (y - b) = [(d - b)/(c - a)](x-a)

You do the same for the function g(x), and then you are all set to solve the system of equations!

Answer:

Sample response: Use the two points of a linear function to write an equation in slope-intercept form by first finding the slope of the function, and then using a point and the slope to determine the y-intercept. Write the equations in slope-intercept form.

Answer with Step-by-step explanation:

As we can clearly see from the graph the value of f(x)=0 at x=2 and x= -4

a. f(x)=|x-1|+3

at x=2

f(2)=|2-1|+3

    = 1+3

    =4

Hence, this function is not represented by the graph

c. f(x)=|x-1|-3

at x=2

f(2)= |2-1|-3

    = 1-3

    = -2

Hence, this function is not represented by the graph

d. f(x)=|x+1|+3

at x=2

f(2)= |2+1|+3

    = 3+3

    = 6

Hence, this function is not represented by the graph

Hence, Correct option is:

b. f(x)=|x+1|-3

Answer:

The answer is B

Step-by-step explanation:

the least possible quotient of the two numbers would be C.) 111

Answer:

[tex]\sqrt{85}[/tex] (about 9.2195) units

Step-by-step explanation:

The formula for the distance between two points is: [tex]\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

Substitute the values. [tex]\sqrt{(-5 - 4)^2 + (8 - 6)^2}[/tex]

Subtract. [tex]\sqrt{(-9)^2 + 2^2}[/tex]

Solve the exponents. [tex]\sqrt{81 + 4}[/tex]

Add. [tex]\sqrt{85}[/tex]

This is as simple as the solution can get without estimating, but we can use a calculator to estimate that the distance is about 9.2195 units.

Hey there! :)

Find the distance between (-5, 8) (4, 6)

The formula to find the distance is : d = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2[/tex]

Where : -5 = x1 , 4 = x2 , 8 = y1 , 6 = y2

Now, simply plug everything into our equation.

[tex]d = \sqrt{(4 + 5)^2 + (6 - 8)^2}[/tex]

Let's simplify this now.

[tex]d = \sqrt{9^2 - 2^2}[/tex]

Simplify again.

[tex]d = \sqrt{81 + 4} = \sqrt{85}[/tex]

Therefore, our distance is [tex]\sqrt{85}[/tex] OR 9.22

Hope this helped! :)

Answer:

x = 4

Step-by-step explanation:

hope this helps!!!

Answer:

right 2, up 3

Step-by-step explanation:

The original function is:

[tex]f(x) = x^2[/tex]

Translated to:

[tex]g(x)=(x-2)^2+3[/tex]

Lets look at the constants that are added or subtracted to determine the transformation.

As -2 is is added to x (grouped with x), the transformation is a horizontal transformation. The shift is of two to the right.

As +3 is not grouped with x, the transformation is vertical. The shift is vertical shift of 3 to upward direction.

So the correct answer is:

right 2, up 3 ..

Answer:

values of x,y and z are x = -2, y= -9 and z=5

Step-by-step explanation:

2x+4y+1z=−35    eq(1)

3x+7y+7z=−34    eq(2)

2x+10y+6z=−64  eq(3)

We can solve using elimination method

Subtracting eq (1) from eq(3)

2x + 10y +6z = -64

2x +4y +1z = -35

______________

6y + 5z = -29     eq(3)

Multiplying eq(2) with 2 and eq(3) with 3 and subtracting

6x + 14y +14z = -68

6x + 30y +18z = -192

-     -         -          +

_________________

-16y -4z = 124     eq(4)

Multiply eq(3) with 4 and eq(4) with 5 and add both equations

24y + 20z = -116

-80y - 20z = 620

______________

-56y = 504

y = -504/56

y= -9

Putting value of y in equation(3)

6y + 5z = -29

6(-9) + 5z = -29

-54 + 5z = -29

5z = -29+54

5z = 25

z = 25/5

z =5

Now, putting value of y and z in eq(1)

2x + 4y +1z = -35

2x + 4(-9) +1(5) = -35

2x -36+5 = -35

2x -31 = -35

2x = -35+31

2x = -4

x= -4/2

x=-2

So, values of x,y and z are x = -2, y= -9 and z=5

Answer:

-4

Step-by-step explanation:

mark branliest :))

Hello There!

The quotient of 32 and -8 is -8.

When dividing a positive number by a negative number, your final result will always end up with a negative number so 32 divided by 8 is 4 but it will be -4 instead of 4

Answer:

[tex]\large\boxed{y=\dfrac{5}{9}x+\dfrac{19}{9}}[/tex]

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\\text{We have the equation i the standard form.}\\\text{ Convert it to the slope-intercept form}\ y=mx+b:\\\\5x+9y=-9\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\9y=-5x-9\qquad\text{divide both sides by 9}\\\\y=-\dfrac{5}{9}x-1\to m_1=-\dfrac{5}{9}\\\\m_2=-\dfrac{1}{m_1}\to m_2=-\dfrac{1}{-\frac{5}{9}}=\dfrac{9}{5}[/tex]

[tex]\text{We have the equation:}\\\\y=\dfrac{5}{9}x+b\\\\\text{Put the coordinates of the point (-2, 1) to the equation:}\\\\1=\dfrac{5}{9}(-2)+b\\\\1=-\dfrac{10}{9}+b\qquad\text{add}\ \dfrac{10}{5}\ \text{to both sides}\\\\\dfrac{19}{9}=b\to b=\dfrac{19}{9}[/tex]

Y is the Audio Book.

"determine the price of one music album and one audio book"

"She lets x represent the cost of one music album."

According to this information "One Audio Book" should be the correct answer. Have a great day!

Answer:

y will represent the cost of one audio book.

Step-by-step explanation:

Here, the cost of 3 music albums and 5 audio books is $49.60 and 1 music album and 2 audio books is $20.50,

Since, there are two unknown values,

First one is the cost of one music album,

Second one is the cost of one audio book,

We know that, for finding an unknown value we take a variable,

If we have variables x and y in which x represent the cost of one music album, then y must represent the cost of one audio album.

Answer:

x = 20

Step-by-step explanation:

see attached

From Pythagoras, [tex]\(z^2 - y^2 = 369\)[/tex]. Solving, z - y = 19, z + y = 19, yielding z = 19. Substituting, x = 17.

Given that Triangle A and Triangle B are right angle triangles with similar heights 'x' and different perpendicular (say 'y' and 'z' respectively).

From the Pythagoras theorem, we know that:

[tex](Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2[/tex]

Substituting the given values, we get:

[tex]y^2 = 16^2 + x^2[/tex]

[tex]z^2 = 25^2 + x^2[/tex]

Subtracting the two equations, we get:

[tex]z^2 - y^2 = 25^2 - 16^2[/tex]

(z - y)(z + y) = 625 - 256 = 369

z - y = 19

z + y = 369 / 19 = 19

Adding the two equations, we get:

2z = 38

z = 19

Substituting the value of 'z' in the equation:

[tex]z^2 = 25^2 + x^2[/tex]

[tex]19^2 = 25^2 + x^2[/tex]

[tex]x^2 = 19^2 - 25^2 = 289[/tex]

[tex]x = sqrt(289)[/tex] = 17

Therefore, the value of 'x' is 17.

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Answer:

Part 1) The volume of pyramid A is two times the volume of pyramid B

Part 2) The new volume of pyramid B is equal to the volume of pyramid A

Step-by-step explanation:

we know that

The volume of a pyramid is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base of pyramid

h is the height of the pyramid

Part 1

The heights of the pyramids are the same

Find the volume of pyramid A

Find the area of the base B

[tex]B=10*20=200\ m^{2}[/tex]

substitute

[tex]VA=\frac{1}{3}(200)h[/tex]

[tex]VA=\frac{200}{3}h\ m^{3}[/tex]

Find the volume of pyramid B

Find the area of the base B

[tex]B=10^{2}=100\ m^{2}[/tex]

substitute

[tex]VB=\frac{1}{3}(100)h[/tex]

[tex]VB=\frac{100}{3}h\ m^{3}[/tex]

Compare the volumes

[tex]VA=2VB[/tex]

The volume of pyramid A is two times the volume of pyramid B

Part 2)

If the height of pyramid B increases to twice that of pyramid A

we have that

[tex]VA=\frac{200}{3}h\ m^{3}[/tex]

Find the new volume of pyramid B

we have

[tex]B=100\ m^{2}[/tex]

[tex]h=2h\ m[/tex]

substitute

[tex]VB=\frac{1}{3}(100)(2h)[/tex]

[tex]VB=\frac{200}{3}h\ m^{3}[/tex]

Compare the volumes

[tex]VA=VB[/tex]

The new volume of pyramid B is equal to the volume of pyramid A

Answer:

The volume of pyramid A is  twice the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is  equal to  the volume of pyramid A.

Step-by-step explanation:

Correct for plato :)

The missing value in the table is 38, obtained by using the concept of average rate of change which is consistent across the given values, suggesting that the function is linear.

In this question, the student needs to find the unknown value denoted by the "?" in the table of a function f(x), whose x-values are -2, 2, 5, 9, and the corresponding f(x)-values are 5, 17, 26, and unknown (?) respectively.

To predict the next value, we can use the concept of the average rate of change which is defined as the difference in the y-values divided by the difference in the x-values over the interval. This rate of change is the same between every pair of successive x-values in this table which suggests that the function might be linear.

We can calculate this using the formula, Average Rate of Change = Δf(x) / Δx. To illustrate, the average rate of change from x = -2 to x = 2 is (17-5) / (2 - (-2)) = 12 / 4 = 3. Similarly, the change from x = 2 to x = 5 is (26 - 17) / (5 - 2) = 9 / 3 = 3. Thus, the average rate of change is constant and equals 3.

If we follow the same pattern, then the missing f(x) value when x = 9 should be 26 (the last provided y-value) plus 4 (which is the next x interval) times 3 (the average rate of change) = 26 + 4*3 = 38. Hence, the missing value denoted by "?" is 38.

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Answer:

x = (C-By)/A

Step-by-step explanation:

Ax+ By = C

We want to isolate x

Subtract By from both sides

Ax+ By-By = C-By

Ax = C - By

Now divide both sides by A

Ax/A = (C-By)/A

x = (C-By)/A

[tex]Ax+ By = C\\Ax=C-By\\x=\dfrac{C-By}{A}[/tex]

Answer:

120°.

Step-by-step explanation:

The sum of all interior angles in a polygon with [tex]n[/tex] sides ([tex]n\in \mathbb{Z}[/tex], [tex]n \ge 3[/tex]) is equal to [tex](n - 2) \cdot 180^{\circ}[/tex]. (Credit: Mathsisfun.)

The polygon here has 6 sides. [tex]n = 6[/tex]. Its interior angles shall add up to [tex](6 - 2) \times 180^{\circ} = 720^{\circ}[/tex].

Consider the properties of a regular polygon. (Credit: Mathsisfun.)

There are six interior angles in a polygon with 6 sides. All six of them are equal. Thus, each of the six interior angle will be

[tex]\displaystyle \frac{1}{6}\times 720^{\circ} = 120^{\circ}[/tex].

Answer:

 [tex]f(-\frac{1}{2}) = 1[/tex]

[tex]g(-\frac{1}{2} ) = -\frac{3}{2}[/tex]

Step-by-step explanation:

Given the function [tex]f(x) = 4x + 3[/tex] and the function [tex]g(x) = 3x[/tex], to evaluate for [tex]x=-\frac{1}{2}[/tex], you need to substitute it into each function.

Then, for the function f(x), when  [tex]x=-\frac{1}{2}[/tex], you get:

 [tex]f(-\frac{1}{2}) = 4(-\frac{1}{2}) + 3[/tex]

 [tex]f(-\frac{1}{2}) = 4(-\frac{1}{2}) + 3[/tex]

 [tex]f(-\frac{1}{2}) = -\frac{4}{2}+ 3[/tex]

 [tex]f(-\frac{1}{2}) = -2 + 3[/tex]

 [tex]f(-\frac{1}{2}) = 1[/tex]

For the function g(x), when  [tex]x=-\frac{1}{2}[/tex], you get:

[tex]g(-\frac{1}{2} ) = 3(-\frac{1}{2})[/tex]

 [tex]g(-\frac{1}{2} ) = -\frac{3}{2}[/tex]

Answer:

f(-1/2) = 1

g(-1/2) =-3/2

Step-by-step explanation:

f(x) = 4x+3

Let x = -1/2

f(-1/2) = 4(-1/2) +3

f(-1/2) = -2 +3

f(-1/2) =1

g(-1/2) = 3(-1/2)

          = -3/2  

Answer:

2622

Step-by-step explanation:

The answer can be found by adding up the volume of the two parts of the composite figure, which consists of a triangular prism and  a rectangular prism

Volume of the rectangular prism=(Width)(Height)(Length)

=12*7*19

=1596

Volume of the triangular prism=(Base area)(Height)

If the triangle consisting of the sides 9, 12, 15 is a right angled triangle, 9²+12²=15²

The statement above is true

The triangle above is a right angled triangle, where 9 is the height and 12 is the base

Triangle area=(height)(base)(0.5)

=9*12*0.5

=54

Volume of triangular prism=54*19

=1026

Adding up both=1596+1026=2622

V = V1 + V2

V1 = 0.5 x 9 x 12 x 19

V1 = 1,026

V2 = 12 x 19 x 7

V2 = 1,596

V = V1 + V2

V = 1,026 + 1,596

V = 2,622

The answer is 2,622.

Answer:

- [tex]\frac{\sqrt{2-\sqrt{2} } }{2}[/tex]

Step-by-step explanation:

Note that [tex]\frac{5\pi }{8}[/tex] is in the second quadrant

where cos < 0 , hence overall sign will be negative

Using the half- angle formula

cos [tex]\frac{5\pi }{8}[/tex]

= - [tex]\sqrt{\frac{1+cos\frac{5\pi }{4} }{2} }[/tex]

= - [tex]\sqrt{\frac{1-\frac{\sqrt{2} }{2} }{2} }[/tex]

= - [tex]\sqrt{\frac{2-\sqrt{2} }{4} }[/tex]

= - [tex]\frac{\sqrt{2-\sqrt{2} } }{2}[/tex]

Answer:

x=0.76 or -5.26

Step-by-step explanation:

You can apply the completing square method to solve this ;

[tex]2x^2+9x=8\\\\[/tex]

Rewrite the equation with a zero like below

[tex]2x^2+9x-8=0[/tex]

This is by taking 8 to the left side of the equation

Divide the terms by 2 in x²

[tex]\frac{2x^2}{2} +\frac{9x}{2} -\frac{8}{2} =\frac{0}{2}[/tex]

[tex]=x^2+4.5x-4=0[/tex]

Move the number term to the right side of the equation

[tex]x^2+4.5x=4[/tex]

complete square on the lefts side of the equation, how?

[tex]=(\frac{b^}{2})^2 =(\frac{4.5}{2} )^2=5.0625[/tex]

balance the equation by adding this value to the right side , in this form

[tex]x^2+4.5x+5.0625=4+5.0625\\\\[/tex]

Factorize the left side

[tex](x+2.25)(x+2.25)=9.0625\\\\\\(x+2.25)^2=9.0625\\[/tex]

Eliminate the square on the left side

[tex]x+2.25=\sqrt{9.0625}[/tex]

x+2.25= ± 3.010

Solve for x

x=+3.010-2.25=0.76

or

x=-3.010-2.25=-5.26

Answer:

x = 0.76 or x= -5.26

Step-by-step explanation:

Points to remember

Solution of a quadratic equation ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/2a

It is given a quadratic equation,

2x² + 9x = 8

⇒ 2x² + 9x - 8 = 0

To find the solution

Here a = 2, b = 9 and c = -8

x = [-b ± √(b² - 4ac)]/2a

 = [-9 ± √(9² - 4*2*(-8))]/2*2

 = [-9 ± √(81 +64)]/4

 =  [-9 ± √(145]/4

 =  [-9 ± 12.04]/4

x =  [-9 + 12.04]/4 or x =  [-9 - 12.04]/4

x = 0.76 or x= -5.26

To rationalize the denominator and simplify the given expression, multiply both the numerator and denominator by the conjugate of the denominator. Simplify the resulting expression by applying the FOIL method and simplifying square roots. The final simplified expression is 72+24 √6+20 √12/84.

To rationalize the denominator and simplify √6+5 √2/4 √6-3 √2, we need to eliminate the square root from the denominator. To do this, we can multiply both the numerator and denominator by the conjugate of the denominator, which in this case is 4 √6+3 √2. The conjugate of a binomial in the form a+b is a-b. So, we will multiply the numerator and denominator by 4 √6+3 √2:

(3 √6+5 √2)(4 √6+3 √2)/[(4 √6-3 √2)(4 √6+3 √2)]

Next, we can apply the FOIL method in the numerator and the difference of squares in the denominator to expand the expression:

(3*4*6+3*4*2 + 5*4 √6 √2 + 3* √2 √6)/ (16*6 - 9*2)

Simplifying further, we get:

(72+24 √6+20 √12)/102 - 18

The final simplified expression is:

72+24 √6+20 √12/84

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Answer:

"The electrician charges an initial fee of $42", AND "The electrician charges $22 for every hour worked" is true.

Step-by-step explanation:

The equation is y=22x+42.

The formula is y=mx+b.

m is the slope, or is this case, the number of dollars for every "x", which is the number of hours worked. So you have to pay $22 for every hour the electrician works.

b is the y-intercept, or the amount it starts with, in this case, you have to pay a fee of $42 even when the electrician worked 0 hours. This is because $42 is the amount it starts with.

On a graph, the line will start at (0,42) because that is when you start paying. And then it will increase by 22 for each hour, so the next coordinate would be (1,64).

The equation y = 22x + 42 indicates that an electrician charges a base fee of $42, plus an additional $22 for every hour worked. Thus, the correct statements are 'The electrician charges an initial fee of $42' and 'The electrician charges $22 for every hour worked.'

The equation y = 22x + 42 is a linear function where the y-variable represents the total dollars the electrician charges and the x-variable represents the number of hours worked. From this equation, we can immediately discern two truths:

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Answer:

y = -3x+17

Step-by-step explanation:

1. Find the change in y corresponding to the change in x. In this case x is changing by +3 and y is changing by -3. That is your m in y=mx=b.

2. y= -3x + b

To find b substitute a set into the equation. I used 4 and 5.

5= -3(4) +b

3. 5= -12 +b ,add  12 to both sides.

17= b

4. y = -3x+17

Answer:

a y=  -x+9

Step-by-step explanation:

[tex]\bf (\stackrel{x_1}{8}~,~\stackrel{y_1}{-8})~\hspace{10em} slope = m\implies -\cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-8)=-\cfrac{5}{4}(x-8)\implies y+8=-\cfrac{5}{4}(x-8)[/tex]

The equation in point-slope form for this line is 4y = -5x + 8.

The equation of a straight line in the form y = mx + c where m is the slope of the line and c is its y-intercept is known as the point-slope form. Here both the slope (m) and y-intercept (c) have real values. It is known as point-slope form as it gives the definition of both the slope, y-intercept and the points mentioned in the line.

It is given that the line passes through the point (8.-8) and has a slope of -5/4.

The general representation for straight line is y = mx + c .

Here, m = -5/4 , x = 8 and y = -8 .

Thus we have ,

⇒ -8 = -5/4 * 8 + c

⇒  c = 10 - 8

∴   c = 2

The y-intercept is 2.

The equation of straight line becomes,

⇒ y = -(5/4)x + 2

∴  4y = -5x + 8

Therefore, the equation in point-slope form for this line is 4y = -5x + 8.

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Answer:

D

Step-by-step explanation:

It turns out from similar triangles, that 7/BD = BD / 18. Use triangles  ABD and BDC to show this relationship. Solving this equation will give you BD

BD^2 = 7*18

BD^2 = 126     Just leave it in this form. Do your rounding at the end.

Because triangle BDC is a right angle triangle, use the Pythagorean Theorem to solve for m

m^2 =  BD^2 + 7^2

m^2 = 126 + 49

m^2 = 175                         Take the square root of both sides.

sqrt(m^2) = sqrt(175)

m = 13.22

so the answer is D

Answer:

y ≈ 358.3 ft

Step-by-step explanation:

The angle in the right side of the triangle = 28° ( alternate angle )

Using the tangent ratio in the right triangle to solve for y

tan28° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{350}{y}[/tex]

Multiply both sides by y

y × tan28° = 350 ( divide both sides by tan28° )

y = [tex]\frac{350}{tan28}[/tex] ≈ 658.3 ft

y = 658.3ft. The value of the side y of the right triangle shown in the image is 658.3ft.

The key to solve this problem we have to use the trigonometric functions tan θ = opposite leg/adjacent leg

To find side y, where opposite leg = 350ft, adjacent leg = y, and θ = 28° by symmetry:

tan θ = opposite leg/adjacent leg

tan 28° = 350ft/y

Clear y:

y = 350ft/tan 28°

y = 658.254ft

Round to the nearest tenths y = 658.3ft

\frac{d}{dx}\left(\frac{1+x^4+x^6}{x^2+x+1}\right)=\frac{4x^7+5x^6+8x^5+3x^4+4x^3-2x-1}{\left(x^2+x+1\right)^2}

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