Gerard bought 9 hamburgers and 3 orders of fries for 24.75. Chris bought 6 hamburgers and 4 orders of fries for 19.50. Each hamburger cost the same amount. Each Order of fries cost the same amount. Wrote a system of equations that can be used to find how much one hamburger and one Order of fries cost.

Answers

Answer 1

9 hamburgers and 3 fries for 24.75 and 6 hamburgers and 4 fries for 19.50 can be represented by 9h + 3f = 24.75 and 6h + 4f = 19.5 Multiply by 4 36h + 12f = 99 and multiply by -3 -18h -12f = -58.5 12f and -12f cancel each other out 36h - 18h = 99 -58.5 18h = 40.5 h = 2.25 hamburgers cost 2.25 9h + 3f = 24.75 9(2.25) + 3f = 24.75 3f = 24.75 - 20.25 = 4.50 f = 150 fries cost 1.50 One hamburger and one fries can be represented by : h + f 2.25 + 150 = 3.75

Related Questions

Find (3 × 104) − (5 × 102).

Answers

The answer is -198

(3*104) - (5*102)
312 - 510
-198

(3 × 10^4) − (5 × 10^2)
= 295 x 10^2
= 2.95 x 10^4

hope it helps

G write the equation in spherical coordinates. (a) 7z2 = 8x2 + 8y2

Answers

Answer:

[tex]\displaystyle 7 \cos^2 \phi - 8 \sin^2 \phi = 0[/tex]

General Formulas and Concepts:
Multivariable Calculus

Spherical Coordinate Conversions:

[tex]\displaystyle r = \rho \sin \phi[/tex][tex]\displaystyle x = \rho \sin \phi \cos \theta[/tex][tex]\displaystyle z = \rho \cos \phi[/tex][tex]\displaystyle y = \rho \sin \phi \sin \theta[/tex][tex]\displaystyle \rho = \sqrt{x^2 + y^2 + z^2}[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle 7z^2 = 8x^2 + 8y^2[/tex]

Step 2: Convert

[Equation] Substitute in Spherical Coordinate Conversions:
[tex]\displaystyle 7( \rho \cos \phi )^2 = 8( \rho \sin \phi \cos \theta )^2 + 8( \rho \sin \phi \sin \theta )^2[/tex]Simplify:
[tex]\displaystyle 7 \rho^2 \cos^2 \phi = 8 \rho^2 \sin^2 \phi \cos^2 \theta + 8 \rho^2 \sin ^2 \phi \sin^2 \theta[/tex]Factor:
[tex]\displaystyle 7 \rho^2 \cos^2 \phi = 8 \rho^2 \sin^2 \phi \bigg( \sin^2 \theta + \cos ^2 \theta \bigg)[/tex]Simplify:
[tex]\displaystyle 7 \rho^2 \cos^2 \phi = 8 \rho^2 \sin^2 \phi[/tex]Simplify:
[tex]\displaystyle 7 \cos^2 \phi = 8 \sin^2 \phi[/tex]Rewrite:
[tex]\displaystyle 7 \cos^2 \phi - 8 \sin^2 \phi = 0[/tex]

∴ we have found the given equation in terms of spherical coordinates.

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Topic: Multivariable Calculus

Unit: Triple Integrals Applications

The mass of a radioactive element at time x is given by the equation below, where c is the original mass and h is the half-life of the element. The half-life of a substance is 4.9 years. How long will it take for 36 grams to decay to 10 grams? (Round your answer to one decimal place.)
M(x)=c(.5^x/h)

Answers

[tex]\bf M(x)=c(0.5)^{\frac{x}{h}}\implies 10=36(0.5)^{\frac{x}{4.9}}\implies \cfrac{10}{36}=0.5^{\frac{x}{4.9}} \\\\\\ \cfrac{5}{18}=0.5^{\frac{x}{4.9}}\implies log\left( \frac{5}{18} \right)=log\left( 0.5^{\frac{x}{4.9}} \right) \\\\\\ log\left( \frac{5}{18} \right)={\frac{x}{4.9}}\cdot log\left( 0.5 \right)\implies \cfrac{4.9\cdot log\left( \frac{5}{18} \right)}{log(0.5)}=x[/tex]

A package of breadcrumbs to feed the ducks at the duck pond costs $0.25. How many packages of bread crumbs could be bought with $23.50

Answers

23.50 divided by .25 = 94

How you find that out would be by dividing $23.50 by $0.25.

23.50÷0.25=94

You would be able to buy 94 packs of bread crumbs with $23.50.

f (x) = x5 − 8x4 + 21x3 − 12x2 − 22x + 20 Three roots of this polynomial function are −1, 1, and 3 + i. Which of the following describes the number and nature of all the roots of this function?
f (x) has two real roots and one imaginary root.

f (x) has three real roots.

f (x) has five real roots.

f (x) has three real roots and two imaginary roots.

Answers

Answer:

It's D on edge.

The f(x) has three real roots and two imaginary roots option (D) is correct.

What is polynomial?

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have a polynomial:

f(x) = x⁵ − 8x⁴ + 21x³ − 12x² − 22x + 20

The three roots of this polynomial function are −1, 1, and 3 + i.

We can write the function in a factored form:

f(x) = (x - 1)(x⁴ - 7x³ + 14x² +2x - 20)

Again factoring the above polynomial:

f(x) = (x - 1)(x + 1)(x - 2)(x² -6x + 10)

The roots of the polynomial are

x - 1 = 0

x = 1

x + 1 = 0

x = -1

x - 2 = 0

x = 2

x² - 6x + 10 = 0

The above quadratic equation has two complex roots.

x = 3 + i

x = 3 - i

Thus, the f(x) has three real roots and two imaginary roots option (D) is correct.

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PLZ ANSWER I BEG U
An airplane flies to San Francisco from Los Angeles in 4 hours. It flies back in 3 hours. If the wind is blowing from the north at a velocity of 20 mph during both flights, what was the airspeed of the plane (its speed in still air)?

Answers

the plane's airspeed is 140:)

Divide m2n2/p3 by mp/n2 .

Answers

8n^2 / 3p^2

Hope it helped!

Answer:

The answer is 'm'.

Step-by-step explanation:

Here, the given expression,

[tex]\frac{\frac{m^2n^2}{p^3}}{\frac{mp}{n^2}}[/tex]

[tex]=\frac{m^2n^2\times n^2}{p^3\times mp}[/tex]

[tex]=\frac{m^2n^{2+2}}{p^{3+1}m}[/tex] ( [tex]a^m.a^n=a^{m+n}[/tex] )

[tex]=\frac{m^2p^4}{p^4m}[/tex]

[tex]=m^2p^4p^{-4}m^{-1}[/tex] ( [tex]a^{m}=\frac{1}{a^{-m}}[/tex] )

[tex]=m^{2-1}p^{4-4}[/tex]

[tex]=m^1p^0[/tex]

[tex]=m[/tex]

Can someone help me with this question?

State the Pythagorean Theorem and tell how you can use it to solve problems

Answers

The Pythagorean Theorem is [tex]a^{2} + b^{2} = c^{2} [/tex]

You can use the Pythagorean theorem to solve for the hypotenuse. For example lets say you have one side (a) equal to 3 and the other side (b) equal to 2. From there you can plug it in and find that the hypotenuse (c) is equal to 3.61

Hello, the Pythagorean Theorem states: the sum of the squares made on the sides is equivalent to the square made on the hypothenuse.

What does it mean? It may help you to draw a right triangle and to draw a square for each side. You can see that the sides of the triangle are the sides of the squares.

Then, if we sum the area of the squares on the sides (because they are equivalent = same area) we get the are of the square on the hypothenuse.

Call "a" and "b" the squares on the sides and "c" the squares on the hypothenuse.

a^2 + b^2 = c^2

Where can this Theorem be used? Of course, where you have to deal with geometry problems, in particular right triangles, rectangles and many more.

For example, we have to find the hypothenuse of a right triangle.

Let's follow the formula and we have that a = 4, b = 3...what's c?

4^2 + 3^2 = c^2

16+9 = c^2

25 = c^2

So, c^2 is 25.

We have c^2 but not c, so how do we solve it?

Simple, do the square root, c = square root of 25 = 5

Of course there are even inverse formulas:

a^2 = c^2 - b^2
b^2 = c^2 - a^2

The average annual income I in dollars of a lawyer with an age of x years is modeled with the following function I=425x^2+45,500x-650,000

Answers

You did not include the questions, but I will give you two questions related with this same statement, and so you will learn how to work with it.

Also, you made a little (but important) typo.

The right equation for the annual income is: I = - 425x^2 + 45500 - 650000

1) Determine the youngest age for which the average income of a lawyer is $450,000

=> I = 450,000 = - 425x^2 + 45,500x - 650,000

=> 425x^2 - 45,000x + 650,000 + 450,000 = 0

=> 425x^2 - 45,000x + 1,100,000 = 0

You can use the quatratic equation to solve that equation:

x = [ 45,000 +/- √ { (45,000)^2 - 4(425)(1,100,000)} ] / (2*425)

x = 38.29 and x = 67.59

So, the youngest age is 38.29 years

2) Other question is what is the maximum average annual income a layer can earn.

That means you have to find the maximum for the function - 425x^2 + 45500x - 650000

As you are in college you can use derivatives to find maxima or minima.

+> - 425*2 x + 45500 = 0

=> x = 45500 / 900 = 50.55

=> I = - 425 (50.55)^2 + 45500(50.55) - 650000 = 564,021. <--- maximum average annual income

Simone paid $12 for an initial years subscription to a magizine. The renewal rate is $8 per year. This situation can be represented by the equation y=8x+12, where x represents the number of years the subscription is renewed and y represents the total cost.

Answers

This is easy. Select different values for x to find y values.

For example, let x = 0.

y = 8x + 12

y = 8(0) + 12

y = 0 + 12

y = 12

On your table, you have x = 0 and y = 12.

Do the same using other values of x.

The table shows the solution for the linear equation.

What is linear equation?

"An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line".

For the given situation,

Cost for initial year subscription = $12

Cost for renewal = $8

The number of years the subscription is renewed be 'x' and

The total cost be 'y'.

This situation can be represented by the equation y = 8x+12.

For this linear equation, we need to make table by substituting different values of x to get y.

For [tex]x=1[/tex]

⇒[tex]y=8(1)+12[/tex]

⇒[tex]y=20[/tex]

For [tex]x=2[/tex]

⇒[tex]y=28[/tex]

For [tex]x=3[/tex]

⇒[tex]y=36[/tex]

For [tex]x=4[/tex]

⇒[tex]y=44[/tex]

For [tex]x=5[/tex]

⇒[tex]y=52[/tex]

The table below shows these interpretations.

Hence we can conclude that the table shows the solution for the linear equation.

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____ provides a greater degree of security by implementing port-based authentication. ieee 802.3ad ieee 802.11n ieee 802.1x ieee 802.1z

Answers

Hello!

The correct answer for the blank is: IEEE 802.1x

I hope you found this helpful! :)

4/25, 13%, 0.28, 7%, 21/100, 0.15 least to greatest

Answers

7%, 13%, 0.15, 4/25, 21/100, 0.28

Hello,

I think we should turn all of these numbers to decimals so that we can tell which one is least and greatest.

Let's start with 4/25. Let's get the divide 4 by 25 to get the decimal form. 4÷25=.16

Then 13%, move the decimal two places to the left to get it into percentage form. After you move the decimal, it is now .13

0.28 is already in decimal form, let's move to the next one.

7%, again let's move the decimal place two places to the left. After that, it i now .07

21/100, let's divide "21" from "100, 21÷100= 0.21

0.15 is already in decimal form, so now we are ready to order them from least to greatest.

Least to Greatest: 0.7 (7%), 0.13 (13%), 0.15, 0.16 (4/25), and lastly 0.21 (21/100).

Hope this helps!

May

For problems 2-3: data were collected on the contents of 1-kilogram sugar packets of brands 1 and 2. assume contents are normally distributed. let and be the true average and standard deviation of contents for brand ( = 1, 2). data summaries are given below. data summary brand 1: = 16, ̅ = 1.053, = 0.058 brand 2: = 16, ̅ = 1.071, = 0.062 2. we would like to determine if there is evidence that brand 1 has a lower average content that brand 2. what hypothesis test will we conduct?
a. : − = 0 versus : − ≠ 0
b. : − = 0 versus : − > 0
c. : − < 0 versus : − = 0
d. : − = 0 versus : − < 0 3. what is the value of the test statistic for testing : = ?
a. 0.9355
b. 0.8751
c. −0.018
d. −0.848

Answers

the answer d right answer

whats the awnser is it 600

Answers

the answer will be C 520

3600/300 = 12

4800/400 = 12

the common ratio is 12 so divide pounds of milk by 12 to get pounds pf ice cream

6000 / 12 = 500

Answer is B

explain...................

Answers

First you change it into slope intercept and get y=3x+7. To make it perpendicular you flip the slope so 3/1 becomes 1/3. Then you make it the opposite so it becomes -1/3. The answer is y=-1/3x+7

The slopes of perpendicular lines are negative reciprocals. That means that when you multiply then together, you get -1.

The slopes of all the choices are easy to see because all the choices are in y = mx + b form, slope-intercept form.

If we write our equation in slope-intercept form also, then we can see its slope easily.

We solve -3x + y = 7 for y.
Add 3x to both sides to get
y = 3x + 7
The slope is 3.
We need a negative reciprocal slope to 3, so we need -1/3.

Only choice A has a slope of -1/3.

Answer: Choice A, y = -1/3x + 7

A retangular box is 2 cm high, 4 cm wide and 6 cm deep. M packs the box with cubes, each 2 cm by 2 cm by 2 cm with no space left over . How many cubes fit in the box?

Answers

Sent a pic of the solution (s).

check the picture below.

how many times does 8 go into 48? well, that many cubes.

the quotient of a number and three is equal to negative eight

Answers

there are multiple answers to this

Compute r6r6, l6l6, and m3m3 to estimate the distance traveled over [0, 3] if the velocity at half-second intervals is as follows:

Answers

For R6 and L6, t= (3- 0) / 6= 0.5. For M3, t= (3- 0)/ 3 = 1. Then

For R6 we will add all the velocity given from 12 to 20 and then multiply it by 0.5 seconds

R6 = 0.5 s ( 12 + 18 + 25 + 20 + 14 + 20 ) m/ sec = 0.5 (109) m = 54.5 m,

For L6 we will add all the velocity given from 0 to 14 and then multiply it by 00.5 as well.

L6 = 0.5 sec ( 0 + 12 + 18 + 25 + 20 + 14 ) m/ sec = 0.5 (89 ) m = 44.5 m.

For M3:

M3 = 1 sec (12 + 25 + 14) m/ sec = 51 m.

Final answer:

The question relates to integral calculus and the concept of Riemann sum approximation. The values r6r6, l6l6, and m3m3 need to be calculated given they represent velocities at half-second intervals. The estimated distance travelled would be the sum of these velocities multiplied by their respective time intervals.

Explanation:

The task here is to compute the expressions r6r6, l6l6, and m3m3, and use those to estimate the distance traveled over the interval [0,3], if the velocity changes at half-second intervals. From the details, it is indicative this is a problem involving the mathematical concept of integral calculus, specifically the area under velocity-time curve. The overall distance travelled is given by the area under the curve which is the integral of the velocity function over the given interval.

Let's suppose the values r6r6, l6l6, and m3m3 represent velocities at different half-second intervals of time. In order to estimate the total distance travelled, you would need to sum these velocities and multiply by the duration of each interval (0.5 seconds). This concept is also known as Riemann sum approximation in integral calculus.

For example, if r6r6 = 10 m/s, l6l6 = 12 m/s, and m3m3 = 8 m/s, the estimated total distance travelled would be calculated as (10*0.5 + 12*0.5 + 8*0.5) = 5 m + 6 m + 4 m = 15 m.

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Payout Annuities:
1. You want to be able to withdraw $30,000 from your account each year for 15 years after you retire.

You expect to retire in 30 years.

If your account earns 5% interest, how much will you need to deposit each year until retirement to achieve your retirement goals?

Answers

If deposit made at beginning of each year, then $4,686.87 per year is required. If deposit made at end of each year, then $4,921.21 per year is required. Assuming you can continue to get the 5% interest when you start withdrawing money, then this problem consists of two parts. Part 1. How much money must you have in the account when you start withdrawing? Part 2. How much must you deposit in order to reach the figure for part 1? Part 1 is fairly easily calculated, just figure it out in reverse. For example At the beginning of year 15, you have to have $30,000 in the account. Since you're getting 5% interest, that means that after you've made the withdraw at the beginning of year 14, you need to have $30,000/1.05 = $28,571.43 in the account. And since you'll be withdrawing $30,000 at the beginning of year 14, you need to have $28,571.43+$30,000 = $58,571.43 in the account at the beginning of year 14. Continuing this process in reverse (add 30000 to sum, divide by 1.05, repeat), you'll determine that your retirement fund has to have $326,959.23 in it when you make your first withdrawal of $30,000. Now you need to figure out how much you need to invest each year for 30 years at an interest rate of 5% to get the sum of $326,959.23 Assuming that you make your contribution at the end of each year, then the formula for the worth of your investment is V=C(((1 + r)Y - 1) / r) where C = Contribution r = interest rate Y = number of years V = Value Solving for C, gives V=C(((1 + r)Y - 1) / r) V/(((1 + r)Y - 1) / r)=C Substituting known values into formula: 326959.23/(((1 + 0.05)^30 - 1) / 0.05)=C 326959.23/((1.05^30 - 1) / 0.05)=C 326959.23/((4.321942375 - 1) / 0.05)=C 326959.23/(3.321942375 / 0.05)=C 326959.23/66.4388475=C 4921.21=C So if you invest $4,921.21 for 30 years at the end of each year, you'll have the required amount for your retirement fund. But if you can make your investment at the beginning of each year, you'll have an extra interest period and the formula for that case is V=C(((1 + r)^(Y + 1) - (1 + r)) / r) Solving for C, gives V/(((1 + r)^(Y + 1) - (1 + r)) / r)=C Substituting known values 326959.23/(((1 +0.05)^(30 + 1) - (1 + 0.05)) / 0.05)=C 326959.23/((1.05^31 - 1.05) / 0.05)=C 326959.23/((4.538039494 - 1.05) / 0.05)=C 326959.23/(3.488039494 / 0.05)=C 326959.23/69.76078988=C 4686.87=C So if you can make your investment at the beginning of each year for 30 years, then $4,686.87 will be enough to reach your retirement goal.

Final answer:

To achieve your retirement goals of withdrawing $30,000 per year for 15 years, you will need to deposit approximately $121,200 each year until retirement.

Explanation:

To determine how much you need to deposit each year until retirement, you can use the formula for the present value of an annuity. The formula is:

PV = PMT x ((1 - (1 + r)^-n) / r)

Where:

PV is the present value of the annuity,PMT is the annuity payment amount,r is the interest rate per period, andn is the number of periods.

In this case, the annuity payment amount is $30,000, the interest rate is 5%, and the number of periods is 15 years. Plugging these values into the formula:

PV = $30,000 x ((1 - (1 + 0.05)^-15) / 0.05)

Simplifying the equation:

PV = $30,000 x ((1 - 1.798) / 0.05)

PV = $30,000 x (0.202 / 0.05)

PV = $30,000 x 4.04

PV = $121,200

Therefore, you will need to deposit approximately $121,200 each year until retirement to achieve your retirement goals.

What is the 4th term of the sequence?
a1 = 8 and an = 6 + an – 1
a4 =

Answers

[tex]\bf \begin{array}{ll} term&value\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ a_1&8\\\\ a_2&6+a_{n-1}\\ &6+a_{2-1}\\ &6+a_1\\ &6+8\\ &14\\\\ a_3&6+a_{3-1}\\ &6+a_2\\ &6+14\\\\ a_4&6+a_{4-1}\\ &6+a_3 \end{array}[/tex]

notice, is an arithmetic sequence, simply adding 6 to get the next term's value.

find the area of the figure (sides meet at right angles)

Answers

4mm + 2mm + 12mm
18mm
18mm

A right triangle has a hypotenuse of length 20 cm and another side of length 16 cm. what is the length of the third side of the triangle?

Answers

Apply the Pythagorean Theorem:

20^2 = 16^2 + x^2 => 400 = 256 + x^2 => 144 = x^2, or x = 12 cm (answer)

The veterinarian weighed Oliver’s new puppy, Boaz, on a defective scale. He weighed 46 pounds. However, Boaz weighs exactly 44.5 pounds. What is the percent of error in measurement of the defective scale to the nearest tenth?

Answers

The percent error is the absolute difference of the actual and measured values, divided by the actual value, multiplied by 100. In here, the actual value is 44.5 lb, while the measured value is 46 pounds.

Percent error = |44.5 - 46|/44.5 * 100 = 3.37%

A 7 pound bag of grass seed covers 2,000 square feet. How many pounds would be needed to cover 35,000 square feet? Round your answer to the nearest pound.

Answers

5,000 pounds..hope this helps

35000 / 2000 = 17.5

17.5 * 7 = 122.5 pounds round to 123 pounds are needed

Which choice is the GCF and LCM of 24 and 48? A) GCF = 12, LCM = 12 B) GCF = 24, LCM = 48 C) GCF = 12, LCM = 24 D) GCF = 12, LCM = 48 PLZ HELP FAST

Answers

GCF = 24, and LCM = 48

, the GCF 36 and 48 is 12

What percent of 43.75 is 70

Answers

62.5%
What I did was divided 43.75 by 70 to get 0.625.
Then I moved the decimal over two places to the right to get 62.5.

Which equations have a greater unit rate than the rate represented in the table?
Choose more than one
x y
-----
3 2
6 4
9 6

A. y=5/7x
B. y=3/5x
C. y=1/3x
D. y=7/9x
E. y= 7/11x

Answers

Table slope = (4-2)/((6-3) = 2/3

A. 5/7 > 2/3
B. 3/5 < 2/3
C. 1/3 < 2/3
D. 7/9 > 2/3
E. 7/11< 2/3

(a) y=5/7x and (d) y=7/9x have a greater unit rate than the rate represented in the table.

What is slope intercept form?

y=mx+c is the slope intercept form where m is the slope and c is y intercept.

The given table is

x 3 6 9

y 2 4 6

The formula to calculate slope is m =y₂-y₁/x₂-x₁

(3,2 ) and (6, 4) are two points.

x₁=3, y₁=2 , x₂=6 and y₂=4

m=4-2/6-3

m=2/3.

Now let us check the equation with greatest slope

(a) y=5/7x

5/7 > 2/3

(b) y=3/5x

3/5 < 2/3

1/3 < 2/3

(d) y=7/9x

7/9 > 2/3

(e) y= 7/11x

7/11< 2/3

Hence (a) y=5/7x and (d) y=7/9x have a greater unit rate than the rate represented in the table.

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In how many ways can 3 boys and 3 girls sit in a row if the boys and girls are each to sit together?

Answers

the answer would be 36 because theres 6 people and 6 seats so 6*6 = 36

Final answer:

The boys and girls are each to sit together, and there are 3 boys and 3 girls. The total number of ways to arrange them is 36.

Explanation:

The boys and girls are each to sit together, meaning that the boys should sit together in one group and the girls should sit together in another group. We can consider these two groups as two separate entities.

The number of ways to arrange the boys within their group is 3! (3 factorial), because there are 3 boys. Similarly, the number of ways to arrange the girls within their group is also 3!. Since these two groups can be arranged independently of each other, the total number of ways to arrange the boys and girls is 3! * 3! = 6 * 6 = 36.

the senior is having a car wash to raise money. They can wash about 35 cars in 5 hours. if they are washing the same number of cars each hour, how many cars do they wash in 1 hour

Answers

they wash about 8.6 cars in 1 hour

Hello!

your answer is 75 • $6 - $35

next time add the answers too for these questions that's why the other guy didn't give you the right answer

[tex]r \frac{8}{11} r \frac{10}{11} [/tex] Simplify. Write your answer using a single, positive rational exponent

Answers

hmmmm I take it you meant those rationals to be exponents, so hmmm asumming that,

[tex]\bf r^{^\frac{8}{11}}\cdot r^{^\frac{10}{11}}\implies r^{^{\frac{8}{11}+\frac{10}{11}}}\implies r^{^\frac{18}{11}}[/tex]

Other Questions

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