Elizabeth bought 4 drinks and some nachos. The nachos cost $6, and she spent a total of $18. How much did each drink cost? Use d to represent the cost of each drink. A. ; each drink cost $4. B. ; each drink cost $6. C. ; each drink cost $2. D. ; each drink cost $3.
Answer:
D. ; each drink cost $3
Step-by-step explanation:
Given that Elizabeth bought 4 drinks and some nachos.
Total amount spent = [tex]18[/tex]$
She can buy only in integers the drinks i.e.1,2,or 3
Nachos also she can buy 1,2...
If x is the no of nachos and d the cost of drink, we get
[tex]6x+4d=18[/tex]
If x=1, d =3
x=2, d = 1.50
d=3, d=0 (which is not possible)
Hence d can take values either as 3 or 1.50
Out of the options given 3 is only there.
D. ; each drink cost $3
Prove algebraically that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.
After 2 months of living at his new apartment, Henry had 2 cats. Six months later, Henry still had 2 cats. Which of the graphs below models Henry's cat population?
I know it is just a straight line but I need to know if its horizontal or vertical..
Answer:
The graph with the horizontal line.
which graph represents a circle with equation x2 + y2 = 9
Answer: The correct option is (B). Its image is attached below.
Step-by-step explanation: We are given to select the graph that represents the circle with equation as follows:
[tex]x^2+y^2=9~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that the standard equation of a circle with center at the point (h, k) and radius r units is given by
[tex](x-h)^2+(y-k)^2=r^2.[/tex]
From equation (i), we have
[tex]x^2+y^2=9\\\\\Rightarrow(x-0)^2+(y-0)^2=3^2.[/tex]
Comparing the above equation with the standard equation of a circle, we get
Center, (h, k) = (0, 0) and radius, r = 3 units.
We draw the graph of the circle with center at the origin (0, 0) and radius 3 units in the attached figure below.
We see that the graph of the circle is same as the one provided in option (B).
Thus, option (B) is CORRECT.
Jack wants to fill a rectangular box with sand. The length of the sand box is 3 feet, width is 6 inches, and height is 2.4 inches. Each bag of sand contains 0.15 cubic foot of sand. How many bags of sand will Jack need to fill the box completely?
[1 foot = 12 inches]
Numerical Answers Expected!
The number of bags of sand that Jack need to fill the box completely are:
2
Step-by-step explanation:The length(l) of the sand box is 3 feet, width(w) is 6 inches, and height(h) is 2.4 inches.
Also,
1 foot=12 inches
This means that:
1 inch=1/12 foot
i.e.
6 inches=0.5 feet
i.e.
w=0.5 feet
and
h=2.4 inches
i.e. h=0.2 feet
Now, we find the volume of the rectangular box.
The volume of the rectangular box is given by:
Volume=lwh
Hence,
Volume=3×0.5×0.2
i.e.
Volume=0.3 cubic feet.
Also, the volume of one bag of sand= 0.15 cubic feet
This means that the number of bags of sand that will fill the box completely is:
(Volume of rectangular box) / (Volume of one bag of sand)
= 0.3/0.15
=2
Hence, number of bags =2
If the sum of six consecutive even integers is 390 what is the smallest of the six integers
use the image above to write a conjecture about regular polygons and lines of symmetry
find the perimeter of ABC with vertices A (1,1), B (7,1), and C (1,9)
Answer:
24 unit
Step-by-step explanation:
Given,
The vertices of the triangle ABC are,
A (1,1), B (7,1), and C (1,9),
By the distance formula,
[tex]AB=\sqrt{(7-1)^2+(1-1)^2}=\sqrt{6^2}=6\text{ unit}[/tex]
[tex]BC=\sqrt{(1-7)^2+(9-1)^2}=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10\text{ unit}[/tex]
[tex]CA=\sqrt{(1-1)^2+(1-9)^2}=\sqrt{8^2}=8\text{ unit}[/tex]
Thus, the perimeter of the triangle ABC = AB + BC + CA = 6 + 10 + 8 = 24 unit
A bakery has prepared 320 ounces of bread dough. a machine will cut the dough into a loaf. the amount of d dough left after m minutes is given by the function d (m)=-5m+320. how many minutes will it take the machine to use all the dough? find a reasonable domain and range for this situation.
A. how many minutes will it take the machine to use all the dough?
We are given the formula:
d (m) = - 5 m + 320
To find for the value of m when all dough is used, we set d (m) = 0:
0 = - 5 m + 320
m = 320 / 5
m = 64 minutes
B. The domain is time and time can never be negative so it always starts at zero, so at time = 0, the range d (m) is:
d (m) = - 5 (0) + 320
d (m) = 320
The other domain and range is already described in (A.), when all dough is used up.
So the pair of reasonable domain and range is:
(0, 320), (64, 0)
Using the formula for volume of a cone, express r in terms of V, h and pi
The volume of the cone is one-third of the volume of the cylinder which is equal to the product of area of the base and the height. The equation is,
V = (1/3)(pi)(r^2)h
Dividing both sides of the equation by (1/3)(pi)(h) will give us,
3V/(pi)(h) = r^2
Taking the square-root of both sides,
r = sqrt(3V/(pi)(h))
Answer:
[tex]r = \sqrt{\displaystyle\frac{3V}{h\pi}}[/tex]
Step-by-step explanation:
We are given the following information in the question.
Using the formula for volume of cone, we have to express r in terms of V, h and pi.
Formula:
[tex]\text{Volume of cone, V} = \displaystyle\frac{1}{3}\pi r^2 h\\\\\text{where r is the radius of cone, h is the height of radius}[/tex]
Now, we have to evaluate r, the radius of cone.
Rearranging the terms, we have,
Working:
[tex]V = \displaystyle\frac{1}{3}\pi r^2 h\\\\r^2 = \frac{3\times V}{\pi\times h}\\\\r^2 = \frac{3V}{h\pi}\\\\r = \sqrt{\frac{3V}{h\pi}}[/tex].
Thus, r in form of V, h and pi can be written as:
[tex]r = \sqrt{\displaystyle\frac{3V}{h\pi}}[/tex]
Solve 81^x = 27^x+2
X=1
X=2
X=5
X=6
What key would you use is 10 students chose cartoons
?/48=7/8 what is the numerator
Suppose a coin is tossed 12 times and there are three heads and nine tails. how many such sequences are there in which there are at least five tails in a row?
Solve 6e^(x)-4e^(-x)=5. Solve for x and please describe how you got your answer.
For the given equation 6eˣ-4e⁻ˣ=5 the value obtained after solving the equation will be x =0.29.
What is an exponential function?It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x, where a is a constant and a>1
It is given that,
6eˣ-4e⁻ˣ=5
Multiplying complete equation by eˣ
eˣ(6eˣ-4e⁻ˣ)=5(eˣ)
6(eˣ)(eˣ) - 4(e⁻ˣ)(eˣ) =5(eˣ)
6e²ˣ-4 = 5(eˣ)
6e²ˣ-5eˣ -4 = 0
Suppose y = eˣ
6y² - 5y -4 = 0
After solving the equation we get y = 4/3 and y = -1 / 2.As a result,
eˣ = 4/3
x = log(4/3)
x = 0.29
Thus, for the given equation 6eˣ-4e⁻ˣ=5 the value obtained after solving the equation will be x =0.29.
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Approximately 55% of the 750 pupil student body voted for Suresh for student body president. How many students voted for him?
Maria started with $10. She has been saving $3 dollars each week to buy a softball bat. The amount of money Maria has depends on how many weeks she has been saving. Which expression represents Maria after x weeks?
A) f(x) = 10x + 3
B) f(x) = 3x + 10
C) f(x) = 10x - 3
D) f(x) = 3x - 10
what times what equals 108
12 times 9 = 108, 18 times 6 = 108, 27 times 4 = 108 and 36 times 3 = 108.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number.
Given that, what times what equals 108,
Below is a list of all the different ways that what times what equals 108.
12 times 9 equals 108
18 times 6 equals 108
27 times 4 equals 108
36 times 3 equals 108
54 times 2 equals 108
108 times 1 equal 108
Hence, 12 x 9 = 108. 18 x 6 = 108. 27 x 4 = 108. 36 x 3 = 108.
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There are multiple pairs of numbers that multiply to 108, such as 1 × 108, 2 × 54, 3 × 36, 4 × 27, 6 × 18, and 9 × 12. Therefore, any pair of these factors will correctly answer the question.
To determine what times what equals 108, we need to identify the factors of 108.
1 × 108 = 108
2 × 54 = 108
3 × 36 = 108
4 × 27 = 108
6 × 18 = 108
9 × 12 = 108
There are multiple pairs of numbers that, when multiplied together, equal 108. Therefore, any of these factor pairs are valid answers to the question.
For example, 9 times 12 or 6 times 18 are pairs that satisfy this condition.
Find the distance between A (0,1) and B (-4,6) to the nearest tenth
An auditor performs attribute sampling to test for proper cancellation of payment vouchers. in a sample population of 100, two vouchers are missing the proper cancellation, while one simply cannot be located. the error rate of the sample is
how do i factor x^3+3x^2
what 3 digits are in the ones/units period 4,083,817
twenty-two pencils cost $0.60 less than $5 what is the cost per pencil?
Isa's calculator displays a number as 7.3579 E8. What is this number in standard form? Enter your answer in the box.
Karli's shadow is 60 inches long. A nearby fire hydrant casts a shadow 40 inches long. If Karli is 48 inches tall, what is the height of the fire hydrant?
∠E∠E and ∠F∠F are vertical angles with m∠E=9x+12m∠E=9x+12 and m∠F=3x+24m∠F=3x+24 .
What is the value of x?
Since ∠E and ∠F are vertical angles, they are congruent, meaning that m∠E = m∠F
Plugging in the equations that were originally given, we can form the equation 9x + 12 = 3x + 24
Subtract both sides of the equation by 3x
6x + 12 = 24
Subtract 12 from both sides
6x = 12
Divide both sides by 6
x = 2
This should be your answer. Have an awesome day! :)
Assume that you own a ruby. Apply the law of detachment to the following conditional statement:
If you have a ruby, then it you have at least $1000.
Which of these statements is true, according to the law of detachment?
You have a ruby.
Someone buys the ruby for $1000.
You sell the ruby.
You have at least $1000.
The statement fourth "You have at least $1000" is correct if you have a ruby, then it you have at least $1000.
What is the law of syllogism?Legal syllogism is a legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.
We have:
Assume that you own a ruby. Apply the law of detachment to the following conditional statement:
The statement is:
If you have a ruby, then it you have at least $1000.
As we know, the law of detachment, we must let go of attachment to both the desired end and all possible routes to get there in order to actualize our wants.
Thus, the statement fourth "You have at least $1000" is correct if you have a ruby, then it you have at least $1000.
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Given the statement 'If you have a ruby, then you have at least $1000.' and the fact that you have a ruby, the Law of Detachment leads to the conclusion 'You have at least $1000.'
Explanation:The Law of Detachment (also known as Modus Ponens) in logic says that if a conditional statement ('if p then q') is true and the first part of the statement (p) is true, then the second part of the statement (q) is true. Let's apply it to your statement.
The original statement is 'If you have a ruby, then you have at least $1000.' You confirmed the first part 'You have a ruby.' So, according to the Law of Detachment, the resulting correct statement would be 'You have at least $1000.' The other statements about selling or someone buying the ruby are irrelevant to the Law of Detachment.
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Which gas is plotted using the y-axis on the right?
divide using synthetic division (2x^3 + 14x^2 - 58x) / (x + 10) 58 POINTS!!!!
algebra- you make a large pot of soup. You freeze the soup in small and medium containers. A small container holds 4 ounces and a medium container holds 6 ounces. The soup can fill 6 small containers and 10 medium containers.
A.Write an equation in standard form that models the possible combinations of small and medium containers that the soup can fill.
B. Graph the equation from part (a)
C. Find four possible combination.
A. Let us say that:
s = number of small containers
m = number of medium containers
From the given data, the total volume of soup is:
total soup = 4 ounces * 6 + 6 ounces * 10 = 84 ounces
So the equation is:
4s + 6m = 84
B. We rewrite the equation explicit to one variable, here we choose s:
4s = 84 – 6m
s = 21 – 1.5m
Then we assign several values for m starting at 0 to get the corresponding value of s then plot the graph. See the graph attached.
C. From the graph, we choose the pair of s and m that are whole numbers. The four possible combinations are:
21 small containers, 0 medium containers
15 small containers, 4 medium containers
9 small containers, 8 medium containers
3 small containers, 12 medium containers