Alina spent no more than $45 on gas for a road trip. The first gas station she used charged $3.50 per gallon and the second gas station charged $4.00 per gallon. Which inequality relates the number of gallons of gas she bought at the first station, x, the number of gallons of gas she bought at the second station, y, and the total amount she paid? What are the possible values of y?

[tex]\bf 3x+y=15\implies y=-3x+15\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-3\implies -\cfrac{3}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{1}{3}}\qquad \stackrel{negative~reciprocal}{\cfrac{1}{3}}}[/tex]

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The slope of a line perpendicular to 3x + y =15 is 1/3. Thus, the correct option is C.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

In the given equation 3x + y =15, the slope of the line will be,

3x + y = 15

y = 15 - 3x

y = -3x + 15

Thus, the slope of the equation is -3.

Now, the product of the slope of two perpendicular lines is always equal to -1. Therefore, the product can be written as,

-3 × m = -1

m = -1/-3

m = 1/3

Hence, the slope of a line perpendicular to 3x + y =15 is 1/3. Thus, the correct option is C.

Learn more about Equation of Line:

https://brainly.com/question/21511618

#SPJ2

Answer:

[tex]\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}[/tex]

Step-by-step explanation:

The explicit formula for a geometric sequence:

[tex]a_n=a_1r^{n-1}[/tex]

[tex]a_n[/tex] - n-th term

[tex]a_1[/tex] - first term

[tex]r[/tex] - common ratio

[tex]r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}[/tex]

We have

[tex]a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...[/tex]

The common ratio:

[tex]r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}[/tex]

If [tex]a_3=-\dfrac{1}{16}[/tex] then the common ratio is [tex]r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}[/tex]

Put to the explicit formula:

[tex]a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}[/tex]

Put [tex]a_n=\dfrac{1}{1024}[/tex] and solve for n :

[tex]-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1[/tex]

[tex]\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6[/tex]

Answer:

Step-by-step explanation:

Start with y=(2/3)x+1 . The slope of any line perpendicular to this is the negative reciprocal of 2/3:  -3/2.

Then we have y = mx + b, which, using the given data (12, -6), becomes

-6 = (-3/2)(12) + b, or

-6 = -18 + b, so b = 12 and y = (3/2)x + 12.

We must put this into standard form.  Mult. all three terms by 2:

2y = 3x + 24      

Answer:

Number of Black grapes = 32

Step-by-step explanation:

This is a problem related to ratio and proportion. We are given the number of Green Grapes and the ration of Green Grapes to the Black Grapes

The ratio is 3:4

This means

[tex]\frac{G_g}{G_b} = \frac{3}{4}[/tex]

Now assume that the number of Black Grapes = x

Given that [tex]G_g[/tex]=24

Substituting these values in [tex]\frac{G_g}{G_b} = \frac{3}{4}[/tex]

[tex]\frac{24}{x} = \frac{3}{4}[/tex]

[tex]24*4 = 3*x\\x=\frac{24*4}{3}\\x=\frac{8*4}{1}\\x=32[/tex]

Hence the number of Black Grapes are 32

Answer:

32

Step-by-step explanation:

If 3:4 then 24:x (x represent the unknown)

So you have to divide 24 by 3 and the answer you get, which is 8, you multiply with four to get 32.

So we can say that both types of grapes are 8 times the amount that they originally were.

Answer:

I get 9.2 but if the answer is rounded then 9 should be correct

Step-by-step explanation:

Plug in the 5 and solve.

Hope this helps a bit,

Flips

To calculate the GPA, convert each grade to its numerical equivalent, add these up, and then divide by the total number of grades given. For example, the GPA for grades 'A', 'A', 'B', 'C', and 'D' would be 2.8.

To find the grade point average (GPA), you add up all the grade points and then divide by the total number of grades. Let's imagine you received the following grades: 'A', 'A', 'B', 'C', and 'D'.

So your GPA would be 2.8.

https://brainly.com/question/32444235

#SPJ2

Final answer:

To calculate your grade point average (GPA), assign numerical values to each letter grade and average them. In this case, the GPA would be 2.5 for the given grades.

Explanation:

To calculate your grade point average (GPA), you need to assign the respective numerical value to each letter grade and then average them. In the given scenario, an 'A' is equal to 4.0, a 'B' is 3.0, a 'C' is 2.0, a 'D' is 1.0, and an 'F' is 0.0. Let's assume the grades for your first semester are A, B, C, and D. To calculate your GPA, add up the numerical values of the grades and divide by the number of grades you have.

So, the calculation would be: (4.0 + 3.0 + 2.0 + 1.0) / 4 = 2.5.

Therefore, your grade point average for the first semester would be 2.5.

Answer:

In the middle of 2 and 3.

Step-by-step explanation:

2 < 2.49 < 3.

Therefore, 2.49 would be located in the middle of 2 and 3, assuming that the scale is 1.

Hope this helps!

It exists located to the right of the 0 on the line, and as you can see, the numbers stand increasing proceeding from left to right. 2.49 exists located 2.49 from 0.

In math, a number line can be described as a straight line with numbers positioned at equivalent intervals or parts along its length. A number line can be expanded infinitely in any direction and exists usually expressed horizontally.

It exists located to the right of the 0 on the line, and as you can see, the numbers stand increasing proceeding from left to right. 2.49 exists located 2.49 from 0.

To learn more about number line

https://brainly.com/question/27744253

#SPJ2

[tex]|\Omega|=6^2=36\\|A|=1\cdot5\cdot2+1=11\\\\P(A)=\dfrac{11}{36}\approx30.6\%[/tex]

Answer:

[tex]P=\frac{13}{36}=0.361[/tex]

Step-by-step explanation:

There are six possible outcomes when rolling a die. Therefore the probability of obtaining a 3 is a given is

[tex]P = \frac{1}{6}[/tex].

When throwing the two dice together, the probability of obtaining a 3 is the same:

[tex]P_1 = \frac{1}{6} * \frac{5}{6} + \frac{5}{6} * \frac{1}{6}=\frac{5}{18}[/tex]

Since the events are independent then the probability of obtaining a three in both dice is:

[tex]P_2 = \frac{1}{6} * \frac{1}{6} = \frac{1}{12}[/tex].

Finally the probability of obtaining a 3 on a given or both is equal to the sum of the probabilities [tex]P_1[/tex] and [tex]P_2[/tex]

[tex]P=\frac{1}{12}+\frac{5}{18}=\frac{13}{36}=0.361[/tex]

Answer:

25 percent.

Step-by-step explanation:

1,000 would be 20% of 5,000

250 is 5% of 5,000

20+5=25

25% of Emma's monthly income goes towards rent.

To calculate the percentage of Emma's monthly pay that goes towards rent, we need to divide the amount spent on rent by the total monthly income, and then multiply that result by 100 to convert it to a percentage.

Emma spends $1,250 a month on rent and earns $5,000 per month. The calculation is as follows:

Divide the monthly rent by the monthly income: $1,250 / $5,000 = 0.25.

Convert the decimal to a percentage: 0.25 * 100 = 25%.

Therefore, 25% of Emma's monthly income goes towards rent.

I'll use arithmetic series to find it.

First two-digit number divisible by 3 is 12, last such number is 99. Every 3rd number is divisible by 3.

So,

[tex]a_1=12\\a_n=99\\d=3\\n=?\\\\a_n=a_1+(n-1)\cdot d\\99=12+(n-1)\cdot 3\\3n-3=87\\3n=90\\n=30[/tex]

There are 30 such numbers.

Answer:

100

Step-by-step explanation:

When being asked what is x% more than y (y is something), you can use the formula 25% * y + y. However, you must convert the percent into a decimal for it to be used mathematically.

25% = 0.25

Now we can plug all of the numbers in.

0.25 * 80 + 80

20 + 80

100

Answer:

See explanation. (Also you can write an equation several different ways so without the choices I cannot tell you which)

Step-by-step explanation:

Slope-intercept form is y=mx+b

So one way to write the equation is y=-3/4 x +3/2

There are more ways to write it.

Every line about to write is a way to write it.

Multiply both sides by 4:                 4y=-3x+6

Add 3x on both sides:               3x+4y=6

Subtract 6 on both sides:         3x+4y-6=0

There are a lot of ways to write an equation like this.

To better assist you I would need to see options.

ANSWER

x=-2

EXPLANATION

The given polynomial function is:

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

The polynomial has two factors, one with an odd multiplicity which is

[tex] {(x - 5)}^{3} [/tex]

and the other with an even multiplicity which is

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

The graph does not cross the x-axis at where the multiplicity is even.

Therefore the graph touches the x-axis at

[tex]x = - 2[/tex]

We got this by solving

[tex]{(x + 2)}^{2} = 0[/tex]

Answer:

(x-5)2

Step-by-step explanation:

you must solve the expression (x-5)2 as the form (a-b)2 = a2 -2ab + b2

So it becomes x2-10x+25

Answer: (x-5)(x-5) or (x-5)²

Step-by-step explanation:

(a-b)(a-b)= a² - 2ab + b²

→ x² - 10x - 25

→ √25 = 5

so a= x, b= 5

this gives us (x-5)(x-5)

Answer:

159

Step-by-step explanation:

Please see attachment

Answer:

x(t)=-t/4

y(t)=-t-2

(answer can vary)

Step-by-step explanation:

Many different ways to do... you are just introducing a different variable, t, to rewrite x and y.  We are rewriting x and y as functions of t.

So if we let -4x=t  then x=t/-4 or x=-t/4

So if -4x=t then t+y=-2 so y=-t-2

So you could write the following:

x(t)=-t/4

y(t)=-t-2

Answer: the answer is a)x=t,y=4t-2

Step-by-step explanation: I guessed and got it right so sorry i do not know how to explain anything but hopefully it helps someone in the future at least

Step-by-step explanation:

[tex]f(x)=\dfrac{2}{x}\ and\ g(x)=\dfrac{2}{x}\\\\(f\circ g)(x)=f(g(x))\to\text{substitute}\ 2-3x\ \text{instead}\ x\ \text{in}\ f(x):\\\\(f\circ g)(x)=\dfrac{2}{\frac{2}{x}}=2\cdot\dfrac{x}{2}=x[/tex]

Answer:

48

Step-by-step explanation:

Multiply 16 and 3 together! This isn't usually the case but for this question it is. Hope this helps and have a nice day!

Answer:

48

explanation:

prime factorisation of 16 and 3.

[tex]16 = 2 \times 2 \times 2 \times 2 = {2}^{4} [/tex]

[tex]3 = 1 \times 3[/tex]

taking the greatest power from both the equation for multiplication

[tex]2 \times 2 \times 2 \times 2 \times 3 = 48[/tex]

hence the L.C.M of 16 and 3 is "48"

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

First table:

(-4, 26), (0, 10) → b = 10

[tex]m=\dfrac{10-26}{0-(-4)}=\dfrac{-16}{4}=-4[/tex]

[tex]\boxed{y=-4x+10}[/tex]

Second table:

(-4, 14), (0, 2) → b = 2

[tex]m=\dfrac{2-14}{0-(-4)}=\dfrac{-12}{4}=-3[/tex]

[tex]\boxed{y=-3x+2}[/tex]

We have the system of equations:

[tex]\left\{\begin{array}{ccc}y=-4x+10&(1)\\y=-3x+2&(2)\end{array}\right\\\\\text{Put (1) to (2):}\\\\-4x+10=-3x+2\qquad\text{subtract 10 from both sides}\\-4x=-3x-8\qquad\text{add 3x to both sides}\\-x=-8\qquad\text{change the signs}\\x=8\\\\\text{Put the value of x to (2):}\\\\y=-3(8)+2\\y=-24+2\\y=-22[/tex]

The solution to the given system of equations is (8, -22). Therefore, option C is the correct answer.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

From the table 1.

Slope (m) = (18-26)/(-2-(-4))

= -8/2

m=-4

Substitute m=-4 and (x, y)=(-2, 18) in y=mx+c, we get

18=-4(-2)+c

18=8+c

c=10

So, the equation is y=-4x+10 -----(i)

From table 2:

Slope (m)=(8-14)(-2-(-4))

m=-3

Substitute m=-3 and (x, y)=(-2, 8) in y=mx+c, we get

8=-3(-2)+c

c=2

So, the equation is y=-3x+2 --------(ii)

From equation (i) and (ii), we get

-4x+10 =-3x+2

x=8

Substitute x=8 in equation (i), we get

y=-4(8)+10

y=-22

So, the solution is (8, -22)

Therefore, option C is the correct answer.

To learn more about the linear system of an equations visit:

https://brainly.com/question/27664510.

#SPJ7

Answer:

x = 2

Step-by-step explanation:

Note that the coordinates (2, 3) and (2, 5) both have the same x- coordinate.

This indicates that the points lie on a vertical line parallel to the y- axis.

The equation of a vertical line is

x = c

where c is the value of the x- coordinates the line passes through.

In this case the x- coordinate is 2, hence the equation of the line is

x = 2

this is what the graph look like

ANSWER

See attachment.

EXPLANATION

The given function is

[tex]f(x) = {x}^{3} + {x}^{2} + 4[/tex]

The degree of this function is odd and the leading coefficient is positive.

The graph of this function rises on the left and keeps rising on the right.

The y-intercept of this graph is 4.

The graph intersects the y-axis at 4.

The graph of this function is the one shown in the attachment.

Answer:

Another point is (3,1) and the vertex is (0,0)

Step-by-step explanation:

The vertex is still (0,0) since the parabola has only been stretched some way and not shifted from the parent function f(x)=x^2.

Enter in any x you like like 3 (I chose 3 because I see I'm going to multiply by 1/3). Anyways

g(3)=(1/3*3)^2=(1)^2=1  so another point on the parabola is (3,1)... Now just use the fact that all parabolas are symmetrical to graph it.

Answer:

y=-2/5 x -1 (It says check all that apply... I hope this equation hasn't been written in a different form in your choices-let me know)

Step-by-step explanation:

Rearrange 2x+5y=10 into slope-intercept form.

First step: Subtract 2x on both sides:  5y=-2x+10

Second step: Divide both sides by 5 giving: y=-2/5 x+2

The slope is -2/5.

Parallel lines have the same slope.

So we know the equation of our new line is in the form y=-2/5 x+b.

We need to find the y-intercept of our line... let's just use the point they have our line going through to find it. Plug in and solve for b.

1=-2/5 (-5)+b

1=2+b

-1=b

So the equation is y=-2/5 x -1

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 2x + 5y = 10 into this form

Subtract 2x from both sides

5y = - 2x + 10 ( divide all terms by 5 )

y = - [tex]\frac{2}{5}[/tex] x + 2 ← in slope- intercept form

with slope m = - [tex]\frac{2}{5}[/tex]

• Parallel lines have equal slopes, so

y = - [tex]\frac{2}{5}[/tex] x + c ← is the partial equation of the parallel line

To find c substitute (- 5, 1) into the partial equation

1 = 2 + c ⇒ c = 1 - 2 = - 1

y = - [tex]\frac{2}{5}[/tex] x - 1 ← in slope- intercept form

Multiply through by 5

5y = - 2x - 5 ( add 2x to both sides )

2x + 5y = - 5 ← in standard form

Answer:

5/96.

Step by Step explanation:

The volume = width * length * height

= 1/3 * 5/8 * 1/4

= 1*5*1 / 3*8*4

= 5 / 96.

=

Answer:

can't understand the question.

What do you need? The mean? Mode? Median?

Answer:

3789.00 loss

Step-by-step explanation: Well She sold the stock but for every stock she sold she had to pay commission which was 39 Dollars for every stock sold. She only Made 2.5% of the Stocks sold, Which is an L, So the answer would be 3789.00, Loss.

Answer:

  option 3

Step-by-step explanation:

Dilation by a scale factor of 3/2 multiplies each of the coordinate values by 3/2. For example, P' = (3/2)P = (3/2)(4, 4) = (6, 6).

The only choice with coordinates matching these is option 3.

Answer:

f(x) = 10² + 3 = 100 + 3 = 103

Final answer:

Without a specific definition of ƒ(x), we can't provide a precise evaluation at x = 10. However, if ƒ(x) is a constant function such as ƒ(x) = 20 for the range of 0 to 20, then ƒ(10) would be 20.

Explanation:

To evaluate the function ƒ(x) when x = 10, we need to know the specific form of the function. However, based on the information provided, which seems fragmented and from different contexts, I can assume that ƒ(x) is defined for certain ranges. There’s reference to a horizontal line graph representation of a function, which suggests that ƒ(x) could potentially be a constant function within a certain range. If the function ƒ(x) is indeed a constant function, such as ƒ(x) = 20 for 0 ≤ x ≤ 20, then evaluating it at x = 10 would simply give the constant value, which is 20.

From the other contexts provided, it's implied that there could be scenarios where ƒ(x) represents different mathematical or physics concepts, such as force, probability distribution, or equations of motion. Without a direct specification of ƒ(x) for the x value in question, the remaining information cannot be used to definitively evaluate ƒ(x) at x = 10.

ANSWER

Last option

EXPLANATION

The given equation is

[tex]4 {x}^{5} - 12 {x}^{4} + 6x = 5 {x}^{3} - 2x[/tex]

We can form a system of equations by equating each side of the equation to y.

Equating the left hand side to y, we get

[tex]y = 4 {x}^{5} - 12 {x}^{4} + 6x...(1)[/tex]

Equating the right hand side to y gives

[tex]y= 5 {x}^{3} - 2x...(2)[/tex]To find the solution to

[tex]4 {x}^{5} - 12 {x}^{4} + 6x = 5 {x}^{3} - 2x[/tex]

We graph the two equations and locate the x-values of their points of intersection.

The last option is the correct answer

Answer:

D

Step-by-step explanation: