20 pts. Graph f(x)=3/4x+2. Use the line tool and select two points to graph the line.

Final answer:

We solved the algebraic equation to find that the solution is x = -10. Each step involved distributing, combining like terms, and isolating the variable.

Explanation:

Let's solve the algebraic equation step-by-step:

The solution to the equation is x = -10, which you can verify by plugging it back into the original equation.

Answer:

A) 30 cubes.

B) 30 units³.

Step-by-step explanation:

A) 1. Calculate the volume of the rectangular prism, as following:

[tex]Vr=(lenght)(width)(height)[/tex]

2. You have that:

- The length is: [tex]1^{\frac{1}{2}}ft=1.5ft[/tex]

- The width is: [tex]1ft[/tex]

- The heigth is: [tex]2^{\frac{1}{2}}ft=2.5ft[/tex]

3. Substitute these values into the formula:

[tex]Vr=(1.5ft)(1ft)(2.5ft)=3.75ft^{3}[/tex]

4. The volume of one cube is:

[tex]Vc=side^{3}[/tex]

5. The length of one side is: [tex]\frac{1}{2}ft=0.5ft[/tex]

6. Substitute this value into the formula:

[tex]Vc=(0.5ft)^{3}=0.125ft^{3}[/tex]

7. The number of small cubes that can be packed in the rectangular prism is:

[tex]cubes=\frac{Vr}{Vc}\\cubes=\frac{3.75ft^{3}}{0.125ft^{3}}\\cubes=30[/tex]

B) 1. The length, the width and the height of the rectangular prism in term of units cubes is:

[tex]Length=\frac{1.5ft}{0.5ft}=3units[/tex]

[tex]Width=\frac{1ft}{0.5ft}=2units[/tex]

[tex]Heigth=\frac{2.5ft}{0.5ft}=5units[/tex]

2. Therefore, the volume of the rectagular prism in terms of the small cube and a unit cube is:

[tex]Vr=(3units)(2units)(5units)=30units^{3}[/tex]

Answer:

30 cubes.

Step-by-step explanation:

The function represented by the graph is (b) the reciprocal, y = 1/x

From the question, we have the following parameters that can be used in our computation:

The graph

From the graph, we can see that

The function has horizontal and vertical asymptotes

Only rational functions have this property

This means that the function represented by the graph is (b) the reciprocal, y = 1/x

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[tex]a_n=5n-1\\\\a_1=5(1)-1=5-1=4\\\\a_2=5(2)-1=10-1=9\\\\a_3=5(3)-1=15-1=14\\\\a_4=5(4)-1=20-1=19\\\\Answer:\ B.\ \{4,\ 9,\ 14,\ 19\}[/tex]

3(3x - 8) + 4x = -2(12 - 7x) - x

9x - 24 + 4x = -24 + 14x - x    distributed 3 on the left and -2 on the right

   - 24 + 13x = -24 + 13x        added like terms on the left and the right

            -13x            -13x

   -24          =   -24

           TRUE

A true statement means infinitely many solutions (aka All Real Numbers)

Answer: C

[tex]ax^2+bx+c=0\\\\\text{From quadratic formula the roots are equal:}\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\ \text{and}\ x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\\text{We have}\ 2x^2+7x-15=0\\\\a=2,\ b=7,\ c=-15\\\\\text{and}\ r,\ s\ \text{are two solution}\\\\\sqrt{b^2-4ac}=\sqrt{7^2-4(2)(-15)}=\sqrt{49+120}=\sqrt{169}=13\\\\x_1=\dfrac{-7-13}{2(2)}=\dfrac{-20}{4}=-5\\\\x_2=\dfrac{-7+13}{2(2)}=\dfrac{6}{4}=\dfrac{3}{2}\\\\\dfrac{3}{2}>-5\ \text{therefore}\ r=\dfrac{3}{2}\ \text{and}\ s=-5.[/tex]

[tex]r-s=\dfrac{3}{2}-(-5)}=\dfrac{3}{2}+5=\dfrac{3}{2}+\dfrac{10}{2}=\dfrac{13}{2}\\\\Answer:\ \boxed{B)\ \dfrac{13}{2}}[/tex]

The expression for the cost of Taxi B is 0.40x + 2.  The expression for the cost of Taxi A is 0.20x + 4.  The inequality asks for when the cost of Taxi B will be greater than Taxi A, so you write it as 0.40x + 2 > 0.20x + 4,  or  0.20x + 4 < 0.40x + 2.

The answer is B) 0.20x + 4 < 0.40x + 2.

Answer: B. [tex]0.20x+4<0.40x+2[/tex]

Step-by-step explanation:

let x denotes the number of mile taxi runs.

Given : Taxi A charges $0.20 per mile and an initial fee of $4.

i.e. the expression to show total charge by Taxi A will be :[tex]0.20x+4[/tex]

Taxi B charges $0.40 per mile and an initial fee of $2.

i.e. the expression to show total charge by Taxi B will be :[tex]0.40x+2[/tex]

Now, the inequality that can determine when the cost of Taxi B will be greater than Taxi A will be :-

[tex]0.20x+4<0.40x+2[/tex]

Hence, B is the correct answer.

The system of linear inequalities that are graphed are {y≥3x−2  and x+2y≤4

In order to get the required system of inequalities, we need to get the equations of both lines.

For the line with having the coordinate points (0, 2) and (4, 0)

The standard form of the expression will be y = mx+b

m = 0-2/4-0

m = -2/4

m = -1/2

The y-intercept "b" is 2 (the point where the line cuts the y-axis)

The equation of the line will be y = -1/2x + 2

2y = -x + 4

x + 2y = 4

Since the line is a solid line and shaded towards the negative side of the graph, the given inequality expression will be x+2y ≤ 4

For the line with having the coordinate points (0, -2) and (2, 4)

The standard form of the expression will be y = mx+b

m = 4+2/2-0

m = 6/2

m = 3

The y-intercept "b" is -2 (the point where the line cuts the y-axis)

The equation of the line will be y = 3x-2

Since the line is a solid line and shaded towards the positive side of the graph, the given inequality expression will be y≥3x−2

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the value of x for which L is parallel to M :28 done

0.4 feet per second is the answer.

Answer:

A) x²/25 + y²/9 = 1

Step-by-step explanation:

The major axis length is the sum of distances to the foci from the ellipse, 10. So the semi-major axis has length 10/2 = 5. The foci are on the x-axis, so the ellipse is oriented horizontally.

The semi-minor axis is the other leg of the right triangle having the focus and center as one leg, and the semi-major axis as the hypotenuse. This is obviously a 3-4-5 triangle, so the semi-minor axis length is 3.

When the ellipse is horizontal, the formula for it is ...

... (x/(semi-major axis))² + (y/(semi-minor axis))² = 1

... (x/5)² + (y/3)² = 1

... x²/25 + y²/9 = 1

The fraction of those who are scared of spiders and also scared of snakes is 1/2.

A fraction is a way of representing a part of a whole or a division of quantities. It consists of two components: a numerator and a denominator, separated by a horizontal line called a fraction bar.

We have,

1/3 of the children are scared of spiders and 1/6 of both snakes and spiders, we can find the fraction of those who are scared of spiders and snakes by dividing the overlap by the total number scared of spiders.

Fraction scared of spiders and snakes

= (Overlap) / (Total scared of spiders)

Overlap = 1/6

Total scared of spiders = 1/3

Fraction scared of spiders and snakes = (1/6) / (1/3) = (1/6) * (3/1) = 1/2

Therefore, the fraction of those who are scared of spiders and also scared of snakes is 1/2.

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Final answer:

Half of the children who are scared of spiders are also scared of snakes, calculated by dividing the fraction of children scared of both by those scared of spiders.

Explanation:

To find the fraction of those who are scared of spiders that are also scared of snakes, we start with the information that 2/3 of the children are scared of snakes, 1/3 are scared of spiders, and 1/6 are scared of both snakes and spiders. Since we want to find out the fraction of those scared of spiders (1/3 of the total) who are also scared of snakes, we focus on the 1/6 portion that represents children scared of both. This fraction is relative to the whole group. To express it as a fraction of just those scared of spiders, we divide the fraction of both phobias (1/6) by the fraction scared of spiders (1/3).

Calculation: (1/6) ÷ (1/3) = (1/6) * (3/1) = 1/2.

Therefore, 1/2 of those who are scared of spiders are also scared of snakes.

Josh would be 15 years old

He would be 12 years old on 1 September, 2015.

Answer: red = 10, orange = 20

Step-by-step explanation:

Let R represent the # of red skittles and G represent the # of orange skittles

there are 10 less red skittles than orange skittles: R = G - 10

orange skittles are twice the red skittles: G = 2R

Use substitution to solve the system:

 R = (2R) - 10

-R   -R        

0  = R - 10

+10     +10

10 = R

G = 2R   = 2(10)   = 20

Answer:30

Step-by-step explanation:

20+10=30

Answer:

When P and Q are equal there is no solution exist.

For example - (0,0) , (1,1)  

Step-by-step explanation:

Given : Equation [tex]Px+40=Qx+20[/tex]

To find : Which values of P and Q result in an equation with no solutions?

Solution :

In the given equation [tex]Px+40=Qx+20[/tex]        

P, Q, x are variable.

We have to find the values at which the equation has no solutions.  

[tex]Px+40=Qx+20[/tex]

[tex]Px+20=Qx[/tex]

[tex]20=Qx-Px[/tex]

[tex]20=x(Q-P)[/tex]

If Q=P then (Q-P)x = 0 for all x

Thus the original equation has no solutions.

For example,

Put x=1 and Q=1

[tex]x+40=x+20[/tex]

[tex]40\neq 20[/tex]

There is no solution.

(28 mph) x (5,280 ft/mi) / (60 min/hr) / (60 sec/min) = 41 feet per second

Joseph made no error.

The answer is F) no error

Answer:

Option: F is the correct answer.

F) No error.

Step-by-step explanation:

We are given the steps that Joseph used while solving as:

Step 1: 85 – 30 = 55

Step 2: 80 – 55 = 25

Step 3: 140 – 80 = 60

Step 4: 60 – 30 = 30

Step 5: 25 + 30 = 55

Clearly the steps involves simple addition as well as subtraction of the mathematical numbers.

Hence all his steps are correct as he has not committed any wrong operation.He evaluated the expressions in the right manner.

          Hence, the answer is:

                    Option: F

*(The Answer)*= [tex]y = \frac{2}{3} x-2[/tex]

*(Equation)*= The equation for slope-intercept form is [tex]y=mx+b[/tex]

*(Additional Information)*=                                                                                                   m = slope, and b = y-intercept

Hope this helps

Person who answered: BangtanBoyScouts

Answer:  The correct option is

(C) [tex]y=\dfrac{2}{3}x-2.[/tex]

Step-by-step explanation:  We are given to select the equation of a line in slope-intercept form with slope [tex]\dfrac{2}{3}[/tex] and y-intercept at (0, -2).

We know that

the slope-intercept form of the equation of a line with slope m and y -intercept at the point (0, c) is given by

[tex]y=mx+c.[/tex]

For the given line, we have

[tex]\textup{slope, }m=\dfrac{2}{3},\\\\\\\textup{y-intercept},~(0,c)=(0,-2)\\\\\Rightarrow c=-2.[/tex]

Therefore, the equation of the line in slope-intercept form is

[tex]y=mx+c\\\\\Rightarrow y=\dfrac{2}{3}x+(-2)\\\\\\\Rightarrow y=\dfrac{2}{3}x-2.[/tex]

Thus, the required equation of the line in slope-intercept form is [tex]y=\dfrac{2}{3}x-2.[/tex]

Option (C) is CORRECT.

Answer: the first choice, |x − 18.25| > 0.36; x < 17.89 or x > 18.61

Explanation:

1. Target weight: 18.25 oz

2. Variability accepted: 0.36 oz

3. Range of accepted masses: 18.25 oz - 0.36 oz ≤ x ≤ 18.25 oz + 0.36 oz

4. Addition property of the inequalities (subtract 18.25 oz to the three parts of the inequality):

- 0.36 oz ≤ x - 18.25 oz ≤ 0.36 oz

5. Definition of absolute value inequality: | x - a | ≤ c equals - c ≤ x - a ≤ c

   ∴ - 0.36 ≤ x - 18.25 ≤ 0.36  equals | x - 18.25 | ≤ 0.36, which is the range of accepted masses.

6. The range of rejected masses is the complement, so it is:

          |x - 18.25 | > 0.36

7. Solve the inequality to find the range of rejected masses:

    a) x - 18.25 > 0.36 ⇒ x > 18.25 + 0.36 ⇒ x > 18.61

    b) x - 18.25 < 0.36 ⇒ x < 18.25 - 0.36 ⇒ x < 17.89

90

divide 45 cookies by 15 to obtain cookies per student then multiply this amount by 30 to obtain cookies for 30 students

15 students → 45 cookies

30 students → 45 × [tex]\frac{30}{15}[/tex] = 90 cookies

Solution is attached below

Answer:

200 CD's.

Step-by-step explanation:

Jake recorded a special album in honor of mother's day. His mom was so excited that she purchased 40% of the copies in the store.

we have tell the total number of CD's in the store.

Let total number of CD's available in the store was = A

Then 40% of the total numbers of CD's = A×40% = 0.04 A

Since 0.04A = 80

A = 80/0.04 = 200

Therefore there were 200 CD's in the store for the sale.

Final answer:

To find the dimensions of the field with a perimeter of 600 feet where the length is three times the width, solve the equation derived from the perimeter formula. The width comes out to be 75 feet and the length 225 feet.

Explanation:

The question is about finding the dimensions of a rectangular field that is three times as long as it is wide, with a total perimeter of 600 feet. First, let's denote the width of the field as W and the length as 3W since the length is three times the width. The formula for the perimeter of a rectangle is 2(length + width), which in this case is 2(3W + W) = 8W. Given that the perimeter is 600 feet, we can set up the equation 8W = 600. Solving this for W gives us W = 75 feet. Therefore, the length, being three times the width, is 225 feet.

So, the dimensions of the field are 75 feet in width and 225 feet in length.

[tex]x^2 + 10x + 24 = 0\\\\x^2+2x+12x+24=0\\\\x(x+2)+12(x+2)=0\\\\(x+12)(x+2)=0\\\\x=-12 \vee x=-2\Rightarrow \text{A}[/tex]

[tex]14-4y\geq38\qquad|\text{subtract 14 from both sides}\\\\-4y\geq24\qquad|\text{change the signs}\\\\4y\leq-24\qquad|\text{divide both sides by 4}\\\\y\leq-6\\\\Answer:\ \boxed{d.\ y\leq-6}[/tex]

400-100=300

300÷60=5

5 trips

Answer:- C) is the right answer. She can take 5 trips without exceeding her budget .

Explanation:-

Given: Budget for trips = $400

Amount needed by Kayla at the end of the trip= $100

Thus the exact amount she spends on trips= $400-$100= $300

Amount spend for each day trip = $ 60

Then The number of trips she can take[tex]=\frac{\text{Amount spend on trips }}{\text{Amount for each trip}}=\frac{300}{60}=5[/tex]

Thus she can take 5 trips without exceeding her budget .

Answer:

[tex]x^{2}-16x+64[/tex]

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. You have the following perfect square trinomial given in the problem:

[tex]x^{2}-16+[/tex]

2. To fill the missing term, you must divide the coefficient -16 by 2 and then you must square it, as following:

[tex](\frac{-16}{2})^{2}=(-8)^{2}=64[/tex]