You will purchase snacks for the painting class. You have abudget of $40. You want to buy fruit and granola bars. Fruit costs $4 perpound, and the granola bars are $1 each. You need at least 20 granolabars. What combinations of fruit and granola bars can you buy?My variables- f-fruits g-granola

You Will Purchase Snacks For The Painting Class. You Have Abudget Of $40. You Want To Buy Fruit And Granola

Answers

Answer 1
Writing inequalitiesWhat we know?

Budget: $40

Fruit: $4/pound

Granola bars: $1 each

At least 20 granolas

Let's call

f: number of pounds of fruit

g: number of granola bars

Therefore

The total cost of fruit is given by: $4 · f

The total cost of granola is given by: $1 · g

The total cost of everything is given by: $4 · f + $1 · g

Since budget: $40 then

$4 · f + $1 · g = $40

4f + g = 40

g > 20 means we have at least 20 granolas

4f + g > 20 means that we have at least 20 granolas, that cost $20, since 4f + g = 40 and 40 > 20


Related Questions

I need a run down on how to do multi step equations.Number 3 only

Answers

Answer:

x=-7

Explanation:

Given the equation:

[tex]8x-2=-9+7x[/tex]

To solve equations of this form, the goal is to try to bring all the terms containing the variable (letter x or any letter) to one side of the equation and the constants to the other side.

First, subtract 7x from both sides.

[tex]\begin{gathered} 8x\textcolor{red}{-7x}-2=-9+7x\textcolor{red}{-7x} \\ x-2=-9 \end{gathered}[/tex]

Next, add 2 to both sides.

[tex]\begin{gathered} x-2+2=-9+2 \\ x+0=-7 \\ \implies x=-7 \end{gathered}[/tex]

The value of x is -7.

I need to write to objective function and the constraints

Answers

Let's define:

x: number of Traveler bicycles made

y: number of Tourister bicycles made

The objective function is:

Maximize 300x + 600y

Subject to the following restrictions:

x + y ≤ 300

x + 3y ≤ 360

Two ropes are attached to a wagon, one horizontal to the west with a tension force of 30N, and the other east and at an angle of 30 degrees northward and a tension force of 40 N. Find the components of the net force on the cart. Show all work.

Answers

The net force on the cart is 62N

and the vertical component =36.64 N

the horizontal component= 50N

What is revolution of vector?

The process of splitting a vector into its components is called resolution of the vector. We resolve a vector into two components which are. component along the x-axis called horizontal component. component along the y-axis called vertical component

30N tension on the cart is westward which mean the vertical component will be 0 and the horizontal component will be 30N.

40N tension isN 30° E which means

the vertical component= 40 sin60=36.64N

Horizontal component= 40 cos 60= 20N

sum of vertical = 36.64N +0= 36.64N

sum of horizontal= 30N+20N= 50N

60° was used for tension 40N because the angle of vector must always lie on the horizontal axis

therefore the net force F is obtained by using Pythagoras theorem

F= √(50^2+36.64^2)

= 62N to the nearest whole number.

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Find two different ways to show that one third+ one fourth is not equal to 3/7. You can use numbers words and labels sketches.

Answers

We can show that one third + one fourth is not equal to 3/7 by following two ways.

By Calculation.By Analysis.

By Calculation.

We are given to prove that the one third and one forth combination of any object/value does not equals to the 3/7 of that same value/object.

let's Consider we have value as 1.

∴ one third of value will be [tex] \frac{1}{3} [/tex]

∴ one forth of value will be [tex] \frac{1}{4} [/tex]

∴ three of seven of value will be [tex] \frac{3}{7} [/tex]

Now we can do the mathematic calculation on one third and one forth of the value.

As given we have to calculate the addition of  one third and one forth of the value

∴ [tex] \frac{1}{3} + \frac{1}{4} [/tex]

= [tex] \frac{4}{12} + \frac{3}{12} [/tex] --(make base same )

= [tex] \frac{4\ + 3}{12}[/tex]

= [tex] \frac{7}{12}[/tex]

∴ By the calculation we clearly got that the addition of  one third and one forth of the value is equal to the seven of twelve of the value.

We can also prove it by analysis as follows ;

Proof by analysis:-

Consider a number say 120.

∴ 1/3 of 120 will be 40

∴ 1/4 of 120 will be 30

∴ 3/7 of 120 will be 51.42

Now Addition of 1/3 and 1/4 of 120 will be 40 + 30 = 70

Comparing it with 3/7 i.e 51.42 ≠ 70

Hence proved 1/3 + 1/4 ≠ 3/7 .

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Find the linear equation of the plane through the point (1, 3, 10) and parallel to the plane x+6y+2z+4=0

Answers

The most appropriate choice for equation of plane will be given by-

Required equation of plane is [tex]x + 6y +2z=39[/tex]

What is a plane?

A surface which is spanned by two linearly independent vectors is called a plane.

The general equation of plane is [tex]ax + by + c =d[/tex] where

[tex](a,b,c)[/tex] are the components of normal vectors.

Equation of the plane parallel to [tex]x + 6y +2z=-4[/tex] is

[tex]x +6y+2z=c[/tex] [As the perpendicular vector of two parallel planes are same]

The required plane passes through (1, 3, 10)

Putting [tex]x=1, y=3,z=10[/tex] in [tex]x + 6y+2z=c[/tex]

[tex]1 + 6 \times 3 + 2\times 10 = c\\1 + 18+20=c\\c=39[/tex]

So, Required equation of plane is [tex]x + 6y +2z=39[/tex]

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evaluate(if possible) the sine,cosine, and the tangent of the real number

Answers

[tex]\begin{gathered} t\text{ = }\frac{-3\pi}{2} \\ \pi=180^o \\ t\text{ = }\frac{-3\text{ x 180}}{2} \\ t\text{ = -270} \\ \\ \sin t\text{ = }\sin (-270)\text{ = 1} \\ co\sin e(t)\text{ = cos(-270) = 0} \\ \text{tangent t = tan(-270) = unknown or not possible} \end{gathered}[/tex]

Find the cos equation given amplitude: 6, period: 2π, vertical shift: 0, and horizontal shift:OA. y = 6 cos 0 + 2OB. y = 6 cos 0 - 2OC. y = 6 cos (0+²)OD. y = 6 cos (0-3)Reset Selection2T3

Answers

Given: A cosine function with amplitude: 6, period: 2 pie, vertical shift: 0, and horizontal shift-

[tex]\frac{2\pi}{3}[/tex]

Required: To determine the function.

Explanation: The cosine function is defined as-

[tex]y=Acos(Bx-C)+D[/tex]

where

[tex]\begin{gathered} A=Amplitude \\ \frac{2\pi}{B}=Period \\ \frac{C}{B}=Phase\text{ shift} \\ D=Verical\text{ shift} \end{gathered}[/tex]

Hence, the required function is-

[tex]y=6cos(x-\frac{2\pi}{3})+0[/tex]

Final Answer: The function is-

[tex]y=6cos(x-\frac{2\pi}{3})[/tex]

Hence, Option D is correct.

Sammy is 5 years younger than twice Lizzy's age. Sammy os 15 years old. How old is Lizzy?​

Answers

Answer:

Lizzy is 40

Step-by-step explanation:

15 + 5 + 20

20 x 2 = 40

Answer:

35

Step-by-step explanation:

15 x 2= 30 + 5=35

the five is because he is 5 years younger than lizzy

adding to her age

5
一堆
2
If log₁/2x = -1, then the value of x is
a) 2
b) 1/2
c)-1

Answers

The value of the variable 'x' in logarithmic expression is: 2

What is logarithm?

In mathematics, the term logarithmic expression can be explained as the exponent or the power which is raised on the base value of the logarithmic expression.

According to the question, the given logarithmic expression are as follows:

[tex]log_{1/2}x = -1[/tex]

Using standard logarithmic property, we get

x = (1/2)^-1

⇒x = 2

Hence, the logarithmic value of the variable 'x' is: 2

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Determine the distance between M(4, 0) and N(-2, -3).

Answers

[tex]\text{distance = }\sqrt[]{45}[/tex]

Explanation

Step 1

the distance between 2 points P1 and P2 is given by:

[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where} \\ P1(x_1,y_1)andP2(x_2,y_2) \end{gathered}[/tex]

Step 2

let

P1=M(4,0)

P2=N(-2,-3)

replace

[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{distance}=\sqrt[]{(-2-4)^2+(-3-0)^2} \\ \text{distance}=\sqrt[]{(-6)^2+(-3)^2} \\ \text{distance}=\sqrt[]{36+9} \\ \text{distance}=\sqrt[]{45} \\ \end{gathered}[/tex]

I hope this helps you

which representation shows y as a function of x?if you can't see c, is says: -1,0 -1,5-1,10-1,15

Answers

At first ,we should know that :

The relation between x and y will be a function when each value of x appeared one time

We will check the options:

A. for the figure of option A, each value of x connected one time to a value of y

B . there are 2 arrows from 0 and 1

C. the values of x = -1 , connected four times to the value of y

So, the answer is option A

What is g(f(x)) if f(x) = 3x + 2 and g(x) = -2x + 4?

Answers

⇒g(f(x)) means that in the function g(x) insert/plug in what f(x) is equal to in the place of x. f(x)= 3x+2 meaning in the place of x in g(x) insert 3x+2 and simplify.

[tex]g(f(x))=-2(3x+2)+4\\g(f(x))=-6x-4+4\\g(f(x))=-6x[/tex]

Attached is the solution of what g(f(x)) is equal to.

A total of $7000 is invested: part at 7 % and the remainder at 15 %. How much is invested at each rate if the annual interest is $510?

Answers

The total invested = $7000

Part of the money at 7% and the reminder at 15%

Let the part at 7% = x

So, the part at 15% = 7000 - x

Given the annual interest = $510

so,

7% of x + 15% of ( 7000 - x ) = 510

0.07 * x + 0.15 * ( 7000 - x ) = 510

0.07 x + 0.15 * 7000 - 0.15 x = 510

0.07 x + 1050 - 0.15x = 510

0.07 x - 0.15 x = 510 - 1050

-0.08 x = - 540

divide both sides by -0.08

x = -540/-0.08 = 6,750

7000 - x = 7000 - 6750 = 250

So, the part that is invested at a rate of 7% = $6,750

And the part that invested at a rate of 15% = $250

PLEASE HELP URGENT:
Graph the following function:

y=3sin(2x−π/2)−2


Drag the black dot to shift your graph in the desired direction. Use the blue draggable dot to change the period. Drag the orange dot to change the amplitude and/or reflect with respect to the x-axis. The horizontal distance between the vertical dotted green lines corresponds to one period.

Answers

A graph of this sine wave function y = 3sin( 2x + π/2) - 2.

A sine wave, also known as a sinusoidal wave or simply a sinusoid in mathematics, is a basic waveform that is frequently employed to describe periodic oscillations, with each interval's displacement amplitude being directly proportional to the sine of the displacement's phase angle.

This mathematical expression can be used to model or depict a sine wave mathematically:

y = asinbx

Where a represents the amplitude of a sine wave, b represents the periodicity.

After that, we would use the lowest common denominator (LCM) to solve the sine wave function given:

y = 3sin( 2x - π/2 ) - 2

y = 3sin( ( 2(2x) - π)/2) - 2

y = 3sin( ( 4x - π)/2 ) - 2

In conclusion, this sine wave function has an amplitude of 3 and a periodicity is 2.

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If there is more then one element in the set, separate them with commas

Answers

Answer:

Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}

Event that the number chosen is 2 = {2A, 2B, 2C}

Explanation:

The sample space is the set with all the possible outcomes, if she can select any number from 1, 2, or 3 and she can select any letter of A, B, or C, we get that the sample space is

Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}

Then, the outcome for the event that the select number is 2 is

Event that the number chosen is 2 = {2A, 2B, 2C}

Therefore, the answers are:

Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}

Event that the number chosen is 2 = {2A, 2B, 2C}

Analyze the graph of the function f(x)=4|x+7|+8 compared to the graph of the absolute value function g(x)=|x| .

Answers

Given:

The functions

[tex]\begin{gathered} g(x)=|x| \\ f(x)=4|x+7|+8 \end{gathered}[/tex]

Required:

Determine changes made in g(x) to get f(x).

Explanation:

The steps are:

[tex]\begin{gathered} f(x)=4|x+7|+8 \\ Shift\text{ the graph to the left }7\text{ units.} \\ Shift\text{ the graph upwards }8\text{ units.} \\ Apply\text{ a vertical stretch of }4\text{ units.} \end{gathered}[/tex]

So. fourth option is describing the f(x).

The graph

Answer:

Completed the answer.

discriminant of the equation x squared minus 5x equals -2 is

Answers

Recall that the "discriminat" of a quadratic equation of the form:

a x^2 + b x + c = 0

is given by the formula: b^2 - 4 a c

So for our equation:

x^2 - 5 x = -2, we start by adding 2 to both sides, in order to get the appropriate form equal to zero:

x^2 - 5 x + 2 = 0

Now we recognize:

a = 1

b = - 5

c = 2

and write the discriminant

b^2 - 4 a c = (-5)^2 - 4 (1) (2) = 25 - 8 = 17

Then, the discriminat of the equation is: 17.

Use the graph of the function below to answer the questions.i just need help with b and c

Answers

Answer:

a) Yes

b) -3, 0, 2

c) [-1, -3], [3, -4], [5, -1]

Explanation:

a) From the graph, we can see that f(3) = -4.

Therefore, f(3) is negative

b) From the graph, we can see that the values of x for which f(x) = 0 are -3, 0, and 2.

c) From the graph, we can see that the values of x for which f(x) < 0 are -1, 3, and 5.

Using the interval notation, we'll have [-1, -3], [3, -4], [5, -1]

Equation fraction X over 9 equals 7

Answers

Answer:

x/9= 7

×ing by 9 on both sides

x=9×7

x=63

Step-by-step explanation:

I need to know the answer for this question?

Answers

The probability of the first sock being blue is 1/3 and the second sock being white is 1/4.

What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

So,

Red socks: 10White socks: 6Blue socks: 8

Total number of socks: 10 + 8 + 6 = 24

Formula: P = favourable events/Total number of events

Probability of picking a blue sock first:

P = 8/24P = 1/3

Probability of picking a white sock at second:

P = 6/24P = 1/4

Therefore, the probability of the first sock being blue is 1/3 and the second sock being white is 1/4.

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Ben has a 6 3/5 pound bag of granola. He wants to give his friends 3/4 pound of granola each. To how many friends can Ben
give granola?

Answers

Answer:21 to each of his 3 friends

Step-by-step explanation:

solve the system of equations using elimination (1/2)x+(1/3)y=4(1/3)x+y=-2

Answers

EXPLANATION

Let's consider the system of equations:

(1) (1/2)x + (1/3)y = 4

(2) (1/3)x +

If ∆ABC is congruent to ∆PQR, find the length of QR.

Answers

If ∆ABC is congruent to ∆PQR, find the length of QR.

Given that If ∆ABC is congruent to ∆PQR:

The simplest way to prove that triangles are congruent is to prove that all three sides of the triangle are congruent.

When all the sides of two triangles are congruent, the angles of those triangles must also be congruent.

From the triangle ABC, the side BC = 4,

Hence the PQR, the side QR = 4 since they are congruent

my questions is about. latitude and longitude

Answers

Answer

Option B is correct.

The latitude and longitude of the point X is 42.5°N, 77.5°W

Hope this Helps!!!

5LATR이S20What is the value of sinEnter an exact value or round to the nearest hundredth.(5)

Answers

Sine:

[tex]\sin (x)=\frac{opposite}{hypotenus}[/tex]

Using the calculator (in radians), we can get the value:

[tex]\sin (\frac{\pi}{3})\approx0.87[/tex]

question will be in picture

Answers

ANSWER:

C. 50 fewer people will attend for every dollar the admission price increases.

STEP-BY-STEP EXPLANATION:

The equation in its slope and y-intercept form is as follows

[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is the y-intercept} \end{gathered}[/tex]

We have the following equation

[tex]n=800-50p[/tex]

We can see that in this case the slope is - 50, therefore the answer would be 50 fewer people will attend for every dollar the admission price increases.

find the radius of the circle given the central angle and the area of the Shaded sector

Answers

we have the following formula for the area of a sector of a circle:

[tex]A_s=\frac{\theta\cdot\pi}{360}\cdot r^2_{}[/tex]

In this case, we have the following information:

[tex]\begin{gathered} A_s=60\pi \\ \theta=24\degree \end{gathered}[/tex]

then, using the formula and solving for r, we get the following:

[tex]\begin{gathered} 60\pi=\frac{24\cdot\pi}{360}\cdot r^2 \\ \Rightarrow360\cdot60\pi=24\pi\cdot r^2 \\ \Rightarrow21600\pi=24\pi\cdot r^2 \\ \Rightarrow r^2=\frac{21600\pi}{24\pi}=900 \\ \Rightarrow r=\sqrt[]{900}=30 \\ r=30 \end{gathered}[/tex]

therefore, the measure of the radius is r = 30

Calculate the total loss after 4 years if 299000 is reduced by 4% per annum

Answers

The total loss after 4 years is $47840.

How to calculate the value?

From the information, we want to calculate the total loss after 4 years of 299000 is reduced by 4% per annum.

It should be noted that this simply means the calculation using the interest formula. In this case, the total loss will be gotten by knowing the interest.

In this case, the interest formula can be illustrated as:

Interest = PRT / 100

where P = Principal = 299000

R = Rate = 4%

T = Time = 4 years

Interest = (299000 × 4 × 4) / 100

Interest = 4784000 / 100

Interest = 47840

In this case, the calculation of the interest is the loss that the person gets.

Therefore, the loss is $47840.

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The functions rands are defined as follows.r(x)=32-4s(x) = -2x+4Find the value of s(r(-5)).s(r(-5)) = 00/0

Answers

With the use of factorization, we can state that s and r have values of -2 and 3, respectively.

What is factorisation?The process of breaking or decomposing an entity (such as a number, a matrix, or a POLYNOMIAL) into a product of another entity, Or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring.

The given values are

r(x)= 3x-4 s(x)= -2x+4

Solving with the help of factotisation.

s(r(-5))(2x-4)(3x-4-5)2x+4(3x-9)6x² - 6x - 36

Dividing the eqn by 6

x²-x-6taking common factors= x(x-3) + 2(x-3)(x+2)(x-3)x= -2,3

hence,from above solving we can say that values of s and r are: 2,3

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PLS HELP ME WITH THIS

Answers

Equation of the line in slope-intercept form = y = 8x − 1

How to calculate the equation of the line?

Given:

Co-ordinates of the first line (x, y)=(0,-1), (1,7), (2,15), (3,23),(4,31)

We know that,

[tex]\text{slope }=m=\frac{y_2-y_1}{x_2-x_1}\\\\= > \frac{7+1}{1-0}\\\\=8[/tex]

The slope - intercept form of a line is given by,

y = mx + b    ---(1)

Let us substitute ( x, y )= (0, -1) in (1)

-1 =(8)*0+b

-1= b

b = - 1 ----(2)

Let us substitute m and b in the slope-intercept equation (1)

y = 8x − 1

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