Answer:
Three cubes
Step-by-step explanation:
The cubes have to be indistinguishable and all orientations of one cube are also have to be indistinguishable.
All ways of connecting two cubes result in the same shape. So answer is larger than two.
After connecting two cubes, there are ten faces where the third cube can be attached, and two faces which are connected, accounting for all 12 faces of two cubes.
Of the 10 exposed faces, exactly two are on opposite ends, both leading to the same straight line figure. The other 8 faces all lead to an L shape, and all L shapes can be rotated to be identical.
Hence, three cubes can only make a straight shape or an angled shape.
Four cubes can make a straight shape, a L shape, a Γ shape (but flipping it over through 3 dimensions makes L and Γ identical), a T shape, and a square shape. That is either four or five different objects depending on if they can be lifted from the table. Anyway, it is more than two.
Which statement is true about the product square root of 2 (5 + square root of 8 )?
It is rational and equal to 7.
It is rational and equal to 9.
It is irrational and equal to 4 + square root of 10.
It is irrational and equal to 4 + 5 square root of 2.
Answer:
It is irrational and equal to 4 + 5 square root of 2.
Step-by-step explanation:
[tex]\sqrt{2}(5+\sqrt{8})=5\sqrt{2}+\sqrt{2\cdot 8}=5\sqrt{2}+\sqrt{16}\\\\=4+5\sqrt{2}[/tex]
The square root of 2 in the result makes the result irrational.
Answer:
It is irrational since the square root sign in the answer is present.
Step-by-step explanation:
We are given with two factors: square root of 2 and 5 + square root of 8. We use a scientific calculator that displays irrational answers. The product of the two factors is 4 + 5 square root of 2. The answer is irrational since the square root sign in the answer is present.
Standard FIF.2 DOK: 18. An outfielder throws a ball vertically upward with a velocity of 30 meters per second. Its distance from the ground after t seconds is approximately equal to 30t -5t2 meters. How many seconds will it take the ball to reach its maximum distance from the ground?
Answer:
t = 3
Step-by-step explanation:
y = - 5t^2 + 30t Take out - 5 as a common factory = -5(t^2 - 6t) Complete the squarey = -5(t^2 - 6t + (6/2)^2) Add (6/2)^2 outside the brackets. Why add?y = -5(t^2 - 6t + 9) + 9 Express the bracketed part as a perfect squarey = -5(t - 3)^2 + 9 The highest point reached will be nineThat occurs when -5(t -3)^2 = 0That happens when t = 3The ball thrown vertically upward reaches its maximum height after 3 seconds, as calculated by setting the derivative of the position function, which represents the velocity, to zero.
The question is about determining how many seconds it will take for a ball thrown vertically upward to reach its maximum height. The ball's position as a function of time is given by 30t - 5t2 meters. To find when the ball reaches its maximum height, we need to find the time at which the velocity is zero. The velocity function is the derivative of the position function, which is 30 - 10t. Setting the velocity equal to zero gives us the time when the ball reaches its maximum height:
0 = 30 - 10t
t = 3 seconds
The ball will reach its maximum distance from the ground after 3 seconds.
Jana paid a $75 initial fee to join a sports club and a monthly fee of $14 per month. Write an expression that shows how much Jana spends after x months of membership at the sports club.
Answer:
y=14x+75 where y is equal to 14x+75. Hope this helps.
Step-by-step explanation:
Answer:
y=14x+75
Step-by-step explanation:
y=mx+b is the slope intercept form which you will use for equations like these.
the M represents what it recurring, and in this case it is 14 dollars per month
The b represents your initial value and in this case it is 75 dollars
The 14x represents that it is 14 per, and the 75 represents the initial cost.
Which absolute value function, when graphed, represents the parent function, f(x) = |x|, reflected over the x-axis an Which absolute value function, when graphed, represents the parent function, f(x) = |x|, reflected over the x-axis and translated 1 unit to the right?d translated 1 unit to the right?
The absolute value function that represents the parent function f(x) = |x| reflected over the x-axis and translated 1 unit to the right is g(x) = -|x-1|.
The absolute value function that represents the parent function f(x) = |x|, reflected over the x-axis and translated 1 unit to the right is g(x) = -|x-1|.
Reflecting over the x-axis involves multiplying the function by -1 to get -|x|. Translating 1 unit to the right involves substituting (x-1) for x within the absolute value to get -|x-1|.
Therefore, the transformation involves two steps:
Reflection over the x-axis: Multiply the parent function f(x) by -1 to get -f(x).Translation to the right: Replace x with (x-1) to shift the graph 1 unit to the right.A cylindrical coffee can has a height of 14 centimeters. The radius of the base is 5 centimeters. What is the area of its label?
The area of the label for a cylindrical coffee can with a height of 14 cm and a radius of 5 cm is approximately 440 square centimeters.
Explanation:The subject in this case is Mathematics, and the question pertains to the use of geometry to determine the area of a label on a cylindrical coffee can. Specifically, the question asks to calculate the area of the cylindrical surface (lateral surface), which will be used as the label area. To calculate this, one needs to use the formula for the lateral surface area of a cylinder, which is 2πrh, where r is the radius and h is the height of the cylinder.
Given a cylinder with a height of 14 centimeters and a radius of 5 centimeters, the area of the label can be calculated as follows:
Area = 2π(5 cm)(14 cm) = 2π×5 cm×14 cm = 2×3.1416×5 cm×14 cm ≈ 440 cm².
Which situation would not be represented by the integer -10?
-You owe $10
-Temperature of 10 degrees
-a hole 10 feet deep
-a 10 yard penalty
Answer:Temperature of 10 degrees
Step-by-step explanation:
The others involve a decrease of 10 units, justifying use of a megative number.
The situation would not be represented by the integer -10 is Temperature of 10 degrees.
What are Integers?The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
Integers come in three types:
Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)Given:
The representation of integer -10.
first, You owe $10
Owning is taken which can be represented as -10.
Temperature of 10 degrees have no clear idea of above or below 0 degree.
and, hole 10 feet deep can be represented as -10.
if we take ground at 0 then the above will positive integer and depth will be negative integer.
Lastly, 10 yard penalty can be represented as -10.
Penalty means deduction which can be shown as negative integer.
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rusty burns 6 calories per minute swimming and 10 calories per minute jogging. In the morning Rusty burns 175 calories walking and swims for x minutes. In the afternoon Rusty will jog for x minutes. How many minutes must he jog to burn at least as many calories y in the afternoon as he did in the morning
Answer:
at least 43 1/4 minutes (or 44 rounded)
Step-by-step explanation:
I set up an equation:
175+6x=10x
Isolate x:
175=4x
x=43.25
is this a college question? (just curious)
Joshua read 1/6 of his book in 1/3 hour. At this rate, how much of his book will he read in an entire hour?
Answer:
1/2 of his book
Step-by-step explanation:
1/3 of an hour = 1/6 of the book
3/3 of an hour = 3/6 or 1/2 of the book read
Write a polynomial as the sum of the monomials and write it in standard form. For each of the above specify the degree of the resulting polynomial. 4a, −5b·b^2, −3c, +7b^3, +c, −2a, 1
Answer:
2b³ +2a -2c . . . . degree 3 polynomial
Step-by-step explanation:
The monomials are ...
... 4a . . . . degree 1 in a
... -5b·b² = -5b³ . . . . degree 3 in b
... -3c . . . . degree 1 in c
... 7b³ . . . . degee 3 in b (like term with -5b³)
... +c . . . . degree 1 in c (like term with -3c)
... -2a . . . . degree 1 in a (like term with 4a)
So, we have 3 pairs of like terms. The like terms can be combined by summing their coefficients.
The degree of the polynomial is that of the highest-degree term. (Here, the b³ term makes it a polynomial of degree 3.)
... 4a -2a = (4-2)a = 2a . . . . combining the "a" terms
... -5b³ +7b³ = (-5+7)b³ = 2b³ . . . . combining the b³ terms
... -3c +c = (-3 +1)c = -2c . . . . combining the "c" terms
In standard form, we write the highest-degree term first. Follwing terms are in order by decreasing degree. It is convenient, but perhaps not required, to then write the terms of the same degree in alphabetical order.
... = 2b³ +2a -2c . . . . a 3rd degree polynomial
The engine displacement of an automobile is the volume through which the piston moves from high to low position. If an engine has n cylinders, the displacement is D = pi(bore/2)^2 • stroke • n, where the bore is the diameter of the cylinder and stroke is the length of the piston's travel.
If bore = k/2 and stroke = h, simplify the expression, D, in terms of k and h for 8 cylinders.
If the bore is 4 inches, the stroke is 3.4 inches, and the engine has four cylinders, what is the displacement? Round your answer to the nearest tenth of a cubic inch.
Substituting the given expressions for bore and stroke and 8 cylinders, you have ...
... D = π((k/2)/2)^2 · h · 8
... D = (π/2)hk^2 . . . . simplified expression for 8 cylinders
_____
For bore = 4 in, stroke = 3.4 in, n = 4, the displacement is ...
... D = π(4 in/2)^2 · (3.4 in) · 4 = 54.4π in^3
... D ≈ 170.9 in^3
Answer:
[tex]85.4[/tex] cubic inch
Step-by-step explanation:
Given-
Displacement = [tex]\pi (\frac{bore}{2} )^2 * stroke * n[/tex]
Now,
bore is represented as [tex]\frac{k}{2}[/tex]
and stroke is represented as [tex]h[/tex]
and number of cylindres "n"[tex]= 8[/tex]
Substituting these values in above equation, we get -
Displacement [tex]= \pi (\frac{\frac{k}{2} }{2})^2*h*8\\= \pi \frac{k^2}{16} * h* 8\\= \frac{\pi* k^2*h}{2}[/tex]
Now substituting the given values, in above equation we get -
Displacement [tex]= \frac{\pi* 4^2*3.4 }{2}\\= \frac{\3.14* 16*3.4 }{2} \\ = 85.408\\= 85.41= 85.4[/tex]cubic inch
Cedar Point amusement park has some of the tallest roller coasters in the United States. The Mantis is 165 feet shorter than the Millennium Force. What is the height of the Mantis?
Answer:
The height of the Mantis is 145 feet
Step-by-step explanation:
There is a table with the roller coasters' heights at Cedar Point amusement park in the assignment that is missing from the post.
Looking up the info online, the Millennium Force is 310 feet tall.
The Mantis is 165 feet shorter than the Millennium Force.
So the height of the Mantis is 310 - 165 = 145 feet
To find the height of the Mantis roller coaster, subtract 165 feet from the height of the Millennium Force roller coaster.
Explanation:The problem states that the Mantis is 165 feet shorter than the Millennium Force. To find the height of the Mantis, we need to subtract 165 feet from the height of the Millennium Force.
If we let x represent the height of the Millennium Force, then the height of the Mantis would be x - 165 feet.
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HELP!!
Monette began heating a liquid with a starting temperature of 62.5°F. The temperature increased by 5° per minute.
What is the recursive rule that represents this situation?\
an=
a1=
Answer:
an = 65 + 5[tex]_{n - 1}[/tex]
a1 = 65
Step-by-step explanation:
If the begining value is 65, then a1 has to be itL
a1 = 65
Then, if this amount increased every minute then 5 has to be added to this value each time:
an = 65 + 5
But this means that 5 is added to 65 every time with no increase, so the five must me multiplied by the n value:
an = 65 + 5[tex]_{n}[/tex]
a2 = 65 + 10 = 75
But this value should be 70 because it is the first point after 65 so it should be +5 not +10
To do this we can simply subtract one from the n value that is being multiplied by 5:
an = 65 + 5[tex]_{n - 1}[/tex]
Which is the recursive rule!
15. convert the following values into scientific notation, a) 42,670,000 B) 0.0000008
Answer:
8x10^-7
Step-by-step explanation:
First one you have correct however the second one you were close lets figure it out:
0.0000008
In order to move the decimal in front of the eight we have to "jump" 7 times to the right. Furthermore since we have to move the decimal to the right our exponent will be negative. That means that we have:
[tex]0.0000008=8 \times 10^{-7}[/tex]
~~~Brainliest Appreciated~~~
To express in scientific notation, move the decimal so it is after the first non-zero digit, and count the number of steps as the power of 10. 42,670,000 becomes 4.267 * 10^7 and 0.0000008 becomes 8 * 10^-7.
Explanation:To convert a value to scientific notation, you need to express it as a product of a number between 1 and 10 and a power of 10.
For the value 42,670,000 we rewrite it as 4.267 * 10^7 which means first you move the decimal to the left until it is after the first digit and then count how many places you moved it to determine the power of 10. For the value 0.0000008, it's a similar process, but slightly different because it is less than one. We get 8 * 10^-7, the power of 10 is negative to reflect that we moved the decimal to the right.Learn more about Scientific Notation here:
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On a separate sheet of paper, use the graph of y = |x| to graph y+4=|x| In the answer box, explain how the new graph differs from the parent function.
See the attachment for graphs.
Step-by-step explanation:The new graph (solid blue) is shifted 4 units down from the parent function (dashed red).
You can get there a couple of ways:
Replacing y by y-k shifts the graph up by k units. Here, k=-4, so the graph is shifted down 4 units.Adding k to the function value shifts the graph vertically by k units. The equation y+4 = |x| can be rewritten to y = |x| -4, showing that -4 is added to the function value.Answer:
The new graph (solid blue) is shifted 4 units down from the parent function (dashed red).
You can get there a couple of ways:
Replacing y by y-k shifts the graph up by k units. Here, k=-4, so the graph is shifted down 4 units.
Adding k to the function value shifts the graph vertically by k units. The equation y+4 = |x| can be rewritten to y = |x| -4, showing that -4 is added to the function value.
Step-by-step explanation:
PLEASE HELP NEED ASAP!!!
(a) To make use of the forms of the equation for a line this problem requires, we must first calculate the slope (m) of the line between the two given points. That is computed by ...
... m = (change in y)/(change in x)
... m = (8 -3)/(2 -0) = 5/2
The second given point tells us the y-intercept (b) is 3, so the equation for the line is ...
... y = mx + b
... y = 5/2x + 3
(b) As in part (a), we must calculate the slope of the line. That is ...
... m = (change in y)/(change in x)
... m = (4 -3)/(1 -3) = 1/(-2) = -1/2
Using the first point (h, k) in the point-slope form of the equation of a line, we have ...
... y -k = m(x -h)
... y -4 = -1/2(x -1) . . . . . point-slope equation
Simplifying this, we get
... y = -1/2x +1/2 +4
... y = -1/2x +9/2 . . . . . slope-intercept equation
(c) The slopes of the two equations are different, so they must intersect at exactly one point. The equations are consistent.
(d) We can substitute the "y" from one equation into the other to give ...
... 5/2x +3 = -1/2x +9/2
... 3x = 3/2 . . . . . . . add 1/2x -6/2
... x = 1/2 . . . . . . . . divide by 3
Using the first equation to find y:
... y = (5/2)·(1/2) +3 = 5/4 +12/4
... y = 17/4
The point of intersection is (x, y) = (1/2, 17/4).
Suppose that 50 identical batteries are being tested. after 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30. what is the probability that greater than 40 batteries will last at least 8 hours?
about 0.04023
Step-by-step explanation:My probability calculator says that probability is about 0.04023.
Which is the graph of the equation y−2=0.5(x+3)?
Answer:
Step-by-step explanation:
First put the point slope form equation into slope intercept form.
y−2=0.5(x+3)
y - 2 = .5x + 1.5
y - 2 + 2 = .5x + 1.5 + 2
y = .5x + 3.5
With it in the slope intercept form we can see that the y intercept is at (0,3.5)
Find a graph that has this as the y intercept. Next we can graph it like the picture I have attached. You graph the equation by inserting numbers for x.
Answer:
Step-by-step explanation:
The given equation is y - 2 = 0.5(x + 3)
Since the equation is of a straight line so we further rewrite the equation in the form of intercept form.
y - 2 = 0.5x + 1.5
y = 0.5x + 1.5 + 2
y = 0.5x + 3.5
Now plot the graph for the points suitable for the equation
x 0 2 -2 4 -4
y 3.5 4.5 2.5 5.5 1.5
Now the graph which matches the graph plotted will be the graph of the equation.
Which function equation(s) does the sentence describe? Every y-value is the sum of one-half of x and 15.
Select each correct answer.
y=15/2x
y=15x/2
y=15+1/2x
y=1/2x−15
y=x/2+15
y=1/2+x+15
y=1/2x+15
Answer:
y=1/2x+15
y=x/2+15
Step-by-step explanation:
Every y-value is the sum of one-half of x and 15.
y = 1/2 x+15
We can rewrite this as
x/2 +15
A.) A diver descends 12 feet below sea level. She then ascends 4 feet. State the depth of the diver in terms of sea level. Explain how the depth was determined. B.) Suppose the diver now descends an additional 12 feet. State the new depth of the diver in terms of sea level. Explain how this depth was determined. C. ) Explain how the diver will reach sea level from the position found in part B.
22
-22
8
-8
-20
20
-4
4
Swim up 4 feet
Swim up 20 feet
Swim up 8 feet
Swim up 20 feet
Answer for part A:
Answer for part B:
Answer to part C:
Answer:
1: The diver is 8 feet below sea level.
2: -20
3: -20 + 20 = 0
Step-by-step explanation:
1: This is determined by adding 4 to negative 12. -12 +4 = -8
2: You get this by subtracting 12 from negative 8. -8 - 12 = -20
3: This is done by adding 20 to negative 20. -20 + 20 = 0
The diver's depth in relation to sea level is determined by subtracting the ascent from the initial descent and subsequent descents are added or subtracted accordingly. To reach sea level from a negative depth, the diver needs to ascend by swimming.
Explanation:Answer for part A:The depth of the diver in terms of sea level is -8 feet. This was determined by subtracting the ascent of 4 feet from the initial descent of 12 feet below sea level, resulting in -8 feet.
Answer for part B:The new depth of the diver in terms of sea level is -20 feet. This was determined by adding the additional descent of 12 feet to the previous depth of -8 feet below sea level, resulting in -20 feet.
Answer for part C:The diver will reach sea level from the position found in part B by swimming up 20 feet. This will bring the depth of the diver to 0 feet below sea level, which is equivalent to sea level.
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Receive 99 points if answered correctly with steps!
Point E is the midpoint of side BC of parallelogram ABCD (labeled counterclockwise) and AE ∩ BD =F. Find the area of ABCD if the area of △BEF is 3 cm2.
Answer:
36 cm²
Step-by-step explanation:
1. ΔBEF & ΔADF are similar; 2. the height of ΔABE is 3height of ΔBEF; 3. area of ΔABE is 3 area of ΔBEF; 4. area of ΔABE= area of ΔACE; 5. area of ΔABC = 2 area of ΔACE; 6. Area of ABCD = 2 area of ΔABC = 12 area of BEF.
36 cm²
Step-by-step explanation:
1. ΔBEF & ΔADF are similar; 2. the height of ΔABE is 3height of ΔBEF; 3. area of ΔABE is 3 area of ΔBEF; 4. area of ΔABE= area of ΔACE; 5. area of ΔABC = 2 area of ΔACE; 6. Area of ABCD = 2 area of ΔABC = 12 area of BEF.
WILL GIVE BRAINIEST!
Vito Melvins bank account has a balance of $9,669.26. The previous balance was $6,955.01. Vito made a Deposit of $2,815.85 and withdrew $100.00. how much did he earn in interest?
Please show all steps!
Answer:
negative $1.60 was the "interest" added to Vito's account
Step-by-step explanation:
new balance = old balance + deposits - withdrawals + interest
$9669.26 = $6955.01 + 2815.85 - 100.00 + interest . . . . fill in givens
$9669.26 = $9670.86 + interest . . . . . simplify
$9669.26 - 9670.86 = interest = -$1.60 . . . . . subtract 9670.86
_____
Comment on the problem
This result is "unexpected." Usually an interest amount will be positive. Please have your teacher work this problem for you and explain the result.
Vito Melvin started with $6,955.01 in his account, deposited $2,815.85, and withdrew $100. The expected balance was $9,670.86, but the actual balance was $9,669.26, meaning Vito earned $1.60 in interest.
Explanation:This problem is about calculating interest earned on a bank account. Let's start by looking at Vito Melvin's actions with his bank account.
He began with a previous balance of $6,955.01. He then made a deposit of $2,815.85 and then withdrew $100. This means his new balance should be his previous balance plus his deposit minus his withdrawal. In calculation, (($6,955.01 + $2,815.85) - $100) = $9,670.86.
However, Vito's actual balance is $9,669.26. The difference between the expected balance ($9,670.86) and the actual balance ($9,669.26) is the interest he earned. So, subtract the actual balance from the expected balance to find the interest: $9,670.86 - $9,669.26 = $1.60.
Therefore, Vito Melvin earned $1.60 in interest.
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segment LM is the mid-segment of trapezoid a b c d. Ab = 38 and cd = 78. what is lm?
Answer:
58
Step-by-step explanation:
The midsegment has a length that is the average of the lengths of the parallel sides it is halfway between.
... LM = (38 +78)/2 = 116/2 = 58
What is the quotient (6x4 − 15x3 − 2x2 − 10x − 4) ÷ (3x2 + 2)? (6 points)
2x^2 -5x -2
Step-by-step explanation:See the attached for the polynomial long division.
Susan has a credit card balance of $4000. Her annual interest rate is 18%. If she pays $366.72 a month she will pay the balance off in 1 year. If she pays $199.70 a month she will pay the balance off in 2 years. What is the overall financial benefit of Susan paying the credit card balance off in 1 year instead of 2?
$392.16 in interest saved
Step-by-step explanation:The payoff in 1 year costs a total of 12 × $366.72 = $4400.64.
The payoff in 2 years costs a total of 24 × $199.70 = $4792.80.
Paying off the balance in 1 year saves interest charges of ...
... 4792.80 -4400.64 = $392.16
Evaluate 3x – 2 if x = 6.
16
20
18
6
Answer:
16
Step-by-step explanation:
We need to evaluate the expression 3x-2
Plugging in x=6, we get
3(6)-2
=18-2
=16
Answer:
16
Step-by-step explanation:
3x – 2 if x = 6
To solve this we substitute the x with 6.
3x – 2 = 3(6) - 2
= (3×6) - 2
= 18 - 2
= 16
Determine if each function is linear or nonlinear.
Answer:
To see if a table of values represents a linear function, check to see if there's a constant rate of change. If there is, you're looking at a linear function!
Step-by-step explanation:
Answer:
linear: y = x+5; 5x +5y = 25nonlinear: everything elseStep-by-step explanation:
If it has an exponent, it's non-linear. (There are other ways it can be non-linear, too, but this is the one applicable here.)
(99 POINTS, ANSWER PROPERLY) What is 5 - 7, plus 2, minus 6, divided by 2, plus 24, to the power of 3, multiplied by 7000, minus 76?
96,767,921
Step-by-step explanation:5 - 7 + 2 - 6 ÷ 2 + 24^3 * 7000 - 76 = 96,767,921
Exponentiation is performed first, followed by multiplication and division in their order of appearance.
= 5 - 7 + 2 - 6 ÷ 2 + 13,824 · 7000 -76
= 5 - 7 + 2 - 3 + 96,768,000 -76
Then addition and subtraction are peformed in the order of appearance. (The commutative and associative laws apply.)
= (5 -7 +2) +96,768,000 -3 -76
= 96,767,921
_____
A Google or Bing search box will evaluate an arithmetic expression strictly according to the order of operations. Your result is attached. The preferred symbols are * (asterisk) for "times" and / (slash) for "divided by". The usual ^ (caret) is used for "to the power of." If you intend grouping, parentheses are required.
During a one-month sales contest, Joaquin sold 56 cars and Annette sold 49 cars. Which ratio is equivalent to the ratio of the number of cars Annette sold to the number of cars Joaquin sold? A. 56:49 B. 3:4 C. 8:7 D. 98:112
Answer:
D. 98:112
Step-by-step explanation:
We want to find Annette:Joaquin
49:56
Both of these numbers are divisible by 7. so we need to divide both of them by 7.
7: 8
Now multiply by each side by 14
7*14 : 8*14
98: 112
An art teacher has a total of 7/8 pound of clay. the teacher puts 1/16 pound of clay at each work station. The teacher sets up an equal number of work stations in each of 2 classrooms. How many work stations does the teacher set up in each of the classrooms?
There are 7 work stations.
This is because:
7/8 divided by 1/6 divided by 2 =
7/8 times 16/1 times 1/2 = 7
Hope this helps :)
Workstations the teacher set up in each of the classrooms is is mathematically given as,
⇒ x = 7
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
An art teacher has a total of 7/8 pound of clay.
And, The teacher puts 1/16 pound of clay at each workstation.
Since, The teacher sets up an equal number of workstations in each of 2 classrooms
Generally the equation for the workstations is mathematically given as,
1/16(x) = 7/8
x = 16 × 7/(8×2)
x = 7
Therefore, The workstations the teacher set up in each of the classrooms is, ⇒ x = 7
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five hamburgers and three orders of fries cost 9.90. three hamburgers and five orders of fries cost 8.50. find the cost of one hamburger
1.50
Step-by-step explanation:Let h and f represent the cost of 1 hamburger and 1 order of fries, respectively. Then you can write two equations for the cost of the orders.
... 5h +3f = 9.90
... 3h +5f = 8.50
Using Cramer's rule, the cost of a hamburger can be found to be ...
... h = (3·8.50 -5·9.90)/(3·3 -5·5) = (25.50 -49.50)/(9 -25)
... = -24/-16
... h = 1.50
The cost of one hamburger is 1.50.
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Formulation of Cramer's Rule
For equations ...
... ax +by = c
... dx +ey = f
The rule tells you ...
... x = (bf -ec)/(bd -ea)
... y = (cd -fa)/(bd -ea)
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Note that we have chosen this method of solution because we only needed the value of one of the variables. It is effectively the same as substitution (or elimination), but does all the steps in one formula.
Using the matrix solution methods on a calculator is another fast way to solve a pair of equations like this.