The cοst οf οne adult ticket is $12 and the cοst οf οne child ticket is $5.
What is system οf equatiοn?A system οf linear equatiοns can be sοlved graphically, by substitutiοn, by eliminatiοn, and by the use οf matrices.
The cοrrect system οf equatiοns tο sοlve fοr a and c is:
12a + 5c = 169 (equatiοn 1)
22a + 10c = 314 (equatiοn 2)
These equatiοns represent the tοtal ticket sales and revenue οn twο different days.
Tο sοlve this system, we can use the methοd οf eliminatiοn.
-24a - 10c = -338
22a + 10c = 314
-2a = -24
Dividing bοth sides by -2:
a = 12
Nοw we can substitute a = 12 intο equatiοn 1 tο sοlve fοr c:
12(12) + 5c = 169
144 + 5c = 169
5c = 25
c = 5
Therefοre, the cοst οf οne adult ticket is $12 and the cοst οf οne child ticket is $5.
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Which function has an average change of -4 over the interval [-2,2]
Answer: B
Step-by-step explanation:
Use y = 4* to graph log4 x - 3
Therefore , the solution of the given problem of graphs comes out to be curve of y = 4x – 3 can be plot by y=4x graph.
A graph is what?Graphs are used by theoretical physicists to analytically and graphically display assertions rather than values. Typically, a graph coordinate point shows the relationship between several distinct objects. A graph is a particular kind of pas e carrier construction composed of groups and lines. The borders, also known as the channels, should be joined together with glue.
Here,
The methods below can be used to plot y = log4 x - 3 as a graph:
Move the y-axis of the graph of
=> y = log4 x down 3 units, making the horizontal asymptote y = -3 the new x-axis.
To acquire the graph of
=> y = log4 x – 3, reflect the resulting graph across the line y = x.
Here is a detailed explanation of how to plot y = log4 x - 3:
Diagram y equals 4x:
Plot the following y = 4x key locations first:
=> Y = 40 = 1 when x = 0.
=> If x = 1, then y = 41 = 4.
=> Y = 4-1 = 1/4 when x = -1.
The graph of y = 4x can be easily drawn using just these three values.
The curve of y = 4x is now 3 units lower:
To do this, take each y-coordinate and deduct 3 from it spots on the y = 4x graph. We now have the curve of y = 4x – 3:
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- Challenge:
A line through the points (2, 8) and (-2, k) has a slope of ¾. What is the value of k?
A line passing through the coordinates (2, 8) & (-2, k) does have a 34 slope. As a result, k has a value of 5.
A slope is what?The slope of a line governs its steepness. Rise over fall is a mathematical formula that describes slope.
We can construct an equation & solve for k using the slope formula:
if (x1, y1) & (x2, y2) are indeed the provided locations, slope is defined as (y2 – y1)/(x2 - x1).
Inputting the specified values results in:
¾ = (k - 8)/(-2 - 2) (-2 - 2)
By condensing this equation, we obtain:
3/4 = (k - 8)/(-4) (-4)
The result of multiplying all sides by -4 is:
-3 = k - 8
5 Equals k when we add 8 to both sides.
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Simplify pleaseeee help I need to understand it
Answer:
hope this helps you a lot
b. Write a multiplication equation to show how the length is scaled. 4 This bar shows the length of 8 units scaled in a different way. a. Use words to describe how the length of 8 units is scaled. b. Write a multiplication equation to show how the length is scaled. 1s = 1 × Is X Use th Is 0 53 X Use the 0 Is ³/3 x
The length of the bar is doubled because it was stretched to twice the length of the original bar.
A multiplication equation that shows how the length is scaled is 2 × 8 = 16.
The length of the bar is halved because it was compressed to one-half the length of the original bar.
A multiplication equation that shows how the length is scaled is 1/2 × 8 = 4.
What is scale factor?In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the length of the image (new figure) by the length of the pre-image (original figure):
Since the original bar has a length of 8 units, we can logically deduce that its length became doubled because it was expanded to twice the length of the original bar. Therefore, a multiplication equation to model this expansion is given by:
2 × 8 = 16.
Conversely, the original bar has a length of 4 units, we can logically deduce that its length was halved because it was shrunk to one-half the length of the original bar. Therefore, a multiplication equation to model this compression is given by:
1/2 × 8 = 4.
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Dirk and Steve both plan to run to a spot on the school board in their city. They must each collect a certain number of signatures to get their name on the ballot. So far, Dirk has 20 signatures, but Steve just started and doesn't have any yet. Kirk is collecting signatures at an average rate of 6 per hour, while Steve can get 10 signatures every hour. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How many hours will have gone by?
Answer: 2.5 hours
Step-by-step explanation:
Let's call the number of signatures that Steve needs to collect "x". We know that Dirk has 20 signatures, so he needs to collect "x - 20" more signatures to have the same number as Steve.
We can set up an equation to represent this:
6h + 20 = 10h + x - 20
Simplifying this equation, we get:
x = 4h + 40
So, Steve needs to collect 4 signatures more per hour than Dirk to eventually collect the same number of signatures. We can solve for "h", the number of hours it will take for them to have the same number of signatures:
6h + 20 = 10h + (4h + 40)
6h + 20 = 14h + 40
8h = 20
h = 2.5
So, it will take 2.5 hours for Dirk and Steve to have collected the same number of signatures.
Find the perimeter of the composite figure.
Responses
33.4 cm
41.8 cm
70 cm
44 cm
9. Use the expression 32.6 ÷ 10-5 x 8-9.16 to create an expression that includes
a set of parentheses so that the value of the expression is 43.10.
Use the expression 6.3 x 15 ÷ 3+ 6.8-28.09 to create an expression that
includes a set of parentheses so that the value of the expression is 46.25.
The first parentheses, (10-5), will calculate to 5. The second parentheses, (8-9.16), will calculate to -1.16.
The first parentheses, (3 + 6.8), will calculate to 9.8. The second parentheses, (6.3 x 15), will calculate to 94.
What are Parentheses?Parentheses are symbols used to group numbers or variables together, usually for the purpose of making calculations easier. Parentheses are commonly used to group numbers within an equation or expression and to indicate that certain operations should be performed before or after others. They are also used to clarify the meaning of a mathematical expression or to help identify the parts of an equation.
To create an expression with parentheses so that the value of the expression 32.6 ÷ 10-5 x 8-9.16 is 43.10, the following equation can be used: (32.6 ÷ (10-5)) x (8-9.16) = 43.10. The parentheses are used to ensure that the values within them are calculated first. The first parentheses, (10-5), will calculate to 5. The second parentheses, (8-9.16), will calculate to -1.16. Then the resulting equation will be 32.6 ÷ 5 x -1.16, which will equal -43.10.
To create an expression with parentheses so that the value of the expression 6.3 x 15 ÷ 3 + 6.8 - 28.09 is 46.25, the following equation can be used: (6.3 x 15) ÷ (3 + 6.8) - 28.09 = 46.25. The parentheses are used to ensure that the values within them are calculated first. The first parentheses, (3 + 6.8), will calculate to 9.8. The second parentheses, (6.3 x 15), will calculate to 94.
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Exo math 30 page 229
19. Money's value resides in the paper or metal from which it was made.
False
True
False. The value of money does not reside solely in the physical materials (paper or metal) from which it is made.
Explaining the concept of MoneyIn modern economies, money has value because it is widely accepted as a means of exchange for goods and services. The value of money is derived from the trust people have in its ability to facilitate transactions and store value over time.
The physical materials used to make money (paper or metal) are simply a medium of exchange that represent the value of the currency. The value of a currency can fluctuate based on a variety of factors such as inflation, interest rates, and global economic conditions.
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willka can cover 13.5 m^2 with 3L of paint
Willka would need 6 liters of paint to cover an area of 27 square meters according to the ratio.
What is ratio?A ratio is a comparison of two or more values or quantities. It is a way of expressing the relationship between two or more quantities in a mathematical form. A ratio is typically expressed in the form of "a:b" or "a to b", where a and b are two values being compared.
According to question:
To find the coverage per liter of paint, we can divide the total area covered by the amount of paint used.
In this case, we can divide 13.5 m² by 3 L:
Coverage per liter = 13.5 m² / 3 L = 4.5 m²/L
This means that with 1 liter of paint, Willka can cover an area of 4.5 square meters.
If we know the area to be painted, we can use this ratio to determine how much paint is needed.
For example, if we want to paint an area of 27 square meters, we can calculate:
Paint needed = area to be painted / coverage per liter = 27 m² / 4.5 m²/L = 6 L
So Willka would need 6 liters of paint to cover an area of 27 square meters.
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Nasim is flying a kite, holding his hands a distance of 2.5 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 28 degrees. If the string from the kite to his hand is 105 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Please help!
Answer: The height of Nasim's kite above the ground is 51.79 feet
Step-by-step explanation
Let h represent the height from Nasim hand to the kite, hence:
sin(28) = h / 105
h = 49.29
Kite height above the ground = 2.5 + 49.29 = 51.79 feet
The height of Nasim's kite above the ground is 51.79 feet
Answer:
The height of Nasim kite above the ground is 51.79 feet
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
Let h represent the height from Nasim hand to the kite, hence:
sin(28) = h / 105
h = 49.29
Kite height above the ground = 2.5 + 49.29 = 51.79 feet
The height of Nasim kite above the ground is 51.79 feet
What is the Value of X?
The value of x is found by using the similarity theorem to create a proportion of the sides of the similar triangle, such that: x = 6 cm.
How to Find the Value of x Using Similarity Theorem?Both triangles in the image above are similar to each other based on the AA similarity theorem, which states if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. This means that the corresponding sides of the triangles are proportional.
Therefore, we will have:
x/42 = 4/28
Cross multiply:
28x = 168
x = 168/28
x = 6 cm
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Let f(x)=x^2+3. Find F(2)
Answer:
7
Step-by-step explanation:
When you put a value for x in a function, it means that you substitute all terms of x for that value you just substitute for x=2. The x term in the function is x^2, so that squared would be 4. You then add 3, yielding a total result of 7.
Answer:
f(2) = 7
Step-by-step:
Solution :Let f(x)=x^2+3. Find f(2)
[tex] \begin{gathered}{\longrightarrow{f(x)= {x}^{2} +3}}\end{gathered}[/tex]
[tex] \begin{gathered}{\longrightarrow{f(2)= {(2)}^{2} +3}}\end{gathered}[/tex]
[tex] \begin{gathered}{\longrightarrow{f(2)= {(2 \times 2)}+3}}\end{gathered}[/tex]
[tex] \begin{gathered}{\longrightarrow{f(2)= {(4)}+3}}\end{gathered}[/tex]
[tex] \begin{gathered}{\longrightarrow{f(2)= 4+3}}\end{gathered}[/tex]
[tex]\begin{gathered}{\longrightarrow{\underline{\underline{f(2)= 7}}}}\end{gathered}[/tex]
Hence, the value of f(2) is 7.
————————————————18.75 in 3 significant figures
Answer:
18.8
Step-by-step explanation:
consider rounding off 7 that becomes 8
Answer:
18.8
Step-by-step explanation:
Yes...Thats the ans...
Find 2 × 2 2 1/5. 1 1 1/5 [][][][] 1 1 1/5 [][][][] A. 2 2/5 B. 4 1/5 C. 4 2/5 D. 5
The solution of the arithmetic expression is 4 2/5.
option C.
what is arithmetic expression?An arithmetic expression is a combination of numbers, operators (such as addition, subtraction, multiplication, and division), and parentheses, which are used to indicate the order of operations. Arithmetic expressions can be evaluated or simplified using the rules of arithmetic, which specify how the various operations should be performed.
We can solve this arithmetic expression by performing the multiplication operation first and then adding the results.
(2 x 2) + (2 x 1/5)
= 4 + 2/5
= 20/5 + 2/5
= (20 + 2) / 5
= 22/5
= 4 2/5
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The complete question is below:
Find 2 × 2 + 2 1/5 = ?
A. 2 2/5
B. 4 1/5
C. 4 2/5
D. 5
Brainly pls help me with this question
The area of the triangles are
1. 105.84 cm²
2. 210 in²
3. 126 ft²
How to find the area of the triangles
The formula for the area of a triangle is:
Area = (1/2) * base * height
where
base is the length of one of the sides of the triangle, and height is the perpendicular distance from that side to the opposite vertex.Using the formula we have that
1)
base = 16.8 and height = 12.6
= 0.5 * 16.8 * 12.6
= 105.84 cm²
2)
base = 20 in + 8 in = 28 in and height = 15
= 0.5 * 28 * 15
= 210 in²
3)
base = 12 ft and height = 21 ft
= 0.5 * 12 * 21
= 126 ft²
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Ryan wishes to purchase a new boat and can afford monthly payments of up to $500 per month. Finance is available, and the terms are that the loan lasts for 10 years and the annual interest rate is 13%. What is the maximum price for a boat that Ryan's budget can afford? Round your answer to the nearest hundred dollars.
Answer:
First, we need to calculate the total number of payments Ryan will make over 10 years, which is 10 years x 12 months/year = 120 months.
Next, we can use the formula for the present value of an annuity to calculate the maximum price of the boat:
PV = PMT x [1 - (1 + r/n)^(-nt)] / (r/n)
where PV is the present value, PMT is the monthly payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.
Plugging in the values we have:
PMT = $500
r = 0.13
n = 12 (since the loan is monthly)
t = 10
PV = $500 x [1 - (1 + 0.13/12)^(-12x10)] / (0.13/12)
PV = $44,484.72
Therefore, the maximum price for a boat that Ryan's budget can afford, rounded to the nearest hundred dollars, is $44,500.
You have six good cigars, five different boxes of matches, and four vintage watches. Sometimes you want to show off your cigar and watch only, and sometimes you want to show off all three. How many possibilities for you to show off?
The possible ways of possibilities might refer to the different interpretations or perspectives that could be applied to a particular idea or concept. For instance, a philosopher might consider the different ways in which free will could be defined or understood.
What is the possible ways of possibilities?The possible ways of possibilities might refer to the different ways in which a particular artistic vision could be realized. For instance, a filmmaker might consider the different ways in which a particular scene could be shot or edited to convey a certain emotion or message.
There are three possible ways to show off:
Cigar only
Watch only
Cigar and watch
To show off a cigar only, you have six options. To show off a watch only, you have four options. To show off both, you have six options for the cigar and four options for the watch, giving a total of [tex]6 \times 4 = 24[/tex] options.
Therefore, So the total number of possibilities to show off is: 6 (cigar only) + 4 (watch only) + 24 (cigar and watch) = [tex]34[/tex] Possibilities.
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What is the solution to the system of equations?
3 x minus 4 y = 16. 2 x + 3 y = 5.
Answer:
It's 5
Step-by-step explanation:
i tootk the test
Step-by-step explanation:
To solve the system of equations:
3x - 4y = 16
2x + 3y = 5
We can use either substitution or elimination method. Here, we will use the elimination method:
Multiply the second equation by 4 to get:
8x + 12y = 20
Now we can add this equation to the first equation:
3x - 4y + 8x + 12y = 16 + 20
Simplifying the left side and adding the right side, we get:
11x = 36
Dividing both sides by 11, we get:
x = 36/11
Substituting this value of x into the second equation, we get:
2(36/11) + 3y = 5
Multiplying through by 11 to eliminate the fraction, we get:
72/11 + 3y = 55/11
Subtracting 72/11 from both sides, we get:
3y = -17/11
Dividing both sides by 3, we get:
y = -17/33
Therefore, the solution to the system of equations is:
x = 36/11, y = -17/33
or in decimal form,
x ≈ 3.27, y ≈ -0.52
Find the distance in units, between P and R.
Express your answer as a square root.
Therefore , the solution of the given problem of unitary method comes out to be P and R are separated by 5 units.
What is an unitary method?One may use this common convenience, already-existing variables, or all important elements from the original Bishop customizable question that adhered to a particular method to achieve the goal. If so, there will be another chance to get in touch with the object. If it doesn't, all of the crucial elements that make up an expression proof outcome will be lost.
Here,
The triangle formed by the points P, Q, and R in the provided diagram is right-angled.
We can determine the length of PR, the hypotenuse of this triangle, using the Pythagorean Theorem.
PQ² + QR² = PR²
The illustration shows that PQ and QR each equal four units.
By replacing these numbers, we obtain:
=> PR² = 4² + 3²
=> PR² = 16 + 9
=> PR² = 25
When we square the two edges, we obtain:
=> PR = √25
=> PR = 5
As a result, P and R are separated by 5 units.
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Lol please help me , cant get this right!!!
The solution of the quadratic equation x² + 10x -4 found using the quadratic formula is: x = -5 ± √29.
Explain about the quadratic formula?Sometimes, factoring the quadratic, setting its factor equal to zero, but then solving each factor is the quickest way to find the answer to "ax² + bx + c = 0" given the value of x.
Yet, there are situations when the quadratic is too complicated, it just doesn't factor in anyway, or you might not feel like factoring at all. The Quadratic Formula also can provide the solutions for you even when factoring sometimes isn't going to be successful.
The given equation:
x² + 10x -4
The general quadratic equation can be written as:
ax² + bx +c
Then, roots of the equation can be found using quadratic formula:
x = -b±√(b²-4ac))/(2a)
a = 1, b = 10 and c = -4
Put the values:
x = [ -10 ± √(10²- 4*1*(-4))]/ (2*1)
x = [ -10 ± √(100 + 16)]/ 2
x = [-10 ± √116] / 2
x = [-10 ± 2√29] / 2
x = -5 ± √29
Thus, the solution of the quadratic equation x² + 10x -4 found using the quadratic formula is: x = -5 ± √29.
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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(-4) = -11 B. g(0) = 2 C. g(7) = -1 D. g(-13) = 20
The statement that could be true for g is D. g(-13) = 20.
What statement could be true?
We are given that the function g has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45, and we also know that g(0) = -2 and g(-9) = 6.
We can use this information to eliminate the statements that are not true and find the one that could be true for g.
A. g(-4) = -11: Since the range of g(x) is between -5 and 45, and g(-4) is less than -5, this statement cannot be true.B. g(0) = 2: We are given that g(0) = -2, so this statement is not true.C. g(7) = -1: 7 is outside the domain of g(x), so we cannot determine the value of g(7).D. g(-13) = 20: Since g(-9) = 6 and the range of g(x) is between -5 and 45, we can see that g(x) increases as x decreases.Therefore, g(-13) is greater than g(-9) and could be 20, so this statement could be true.
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1. Write an inequality to represent “a number (n) is at least four"
2. Graph your inequality.
Answer:
From what I remember, words like "at least" mean that that's the minimum, so it can be more than that, but not less than. So I believe the inequality that would best represent this is n ≥ 4.
Answer:
n>=4
Step-by-step explanation:
A magician makes potions by combining maple syrup from a magical maple tree with ordinary water. The magician starts with a large supply of two potions: a red potion, which is 60% magical syrup by volume (and the rest is just water), and a blue potion, which is 30% magical syrup by volume. (Perhaps you're wondering how the same syrup can produce both red and blue potions. That's why it's magic syrup!)
(a) Find the amount of red potion (in mL) that must be added to 500 mL of blue potion in order to produce a potion that is 40% magical syrup by volume.
(b) Find the amounts of red potion and blue potion (in mL) that can be combined in order to produce 100 mL of a potion that is 54% magical syrup by volume.
(c) Does there exist a combination of red potion and blue potion that can produce a potion that is 75% magical syrup by volume?
Taking the quantities by volume of each potion into consideration, we can respectively answer 250ml (A), 40 mL of red and 60 mL of blue potion (B), and no (C).
How to find the solutionFor question A: Let x be the amount of red potion (in mL) that must be added to 500 mL of blue potion to produce a potion that is 40% magical syrup by volume. The amount of magical syrup in the red potion is 0.6x, and the amount of magical syrup in the blue potion is 0.3(500) = 150. The total amount of syrup in the final mixture is 0.4(500 + x), and the amount of magical syrup in the final mixture is 0.4x + 150. We can set up the equation:
0.4x + 150 = 0.4(500 + x)
Solving for x, we get x = 250 mL. Therefore, 250 mL of red potion must be added to 500 mL of blue potion to produce a potion that is 40% magical syrup by volume.
For question B: Let x be the amount of red potion (in mL) and y be the amount of blue potion (in mL) that must be combined to produce 100 mL of a potion that is 54% magical syrup by volume. The amount of magical syrup in the red potion is 0.6x, and the amount of magical syrup in the blue potion is 0.3y. The total amount of syrup in the final mixture is x + y, and the amount of magical syrup in the final mixture is 0.6x + 0.3y. We can set up the equations:
x + y = 100 (equation 1)
0.6x + 0.3y = 0.54(100) (equation 2)
Solving for x and y, we get x = 40 mL and y = 60 mL. Therefore, 40 mL of red potion and 60 mL of blue potion must be combined to produce 100 mL of a potion that is 54% magical syrup by volume.
For question C: No, there does not exist a combination of red potion and blue potion that can produce a potion that is 75% magical syrup by volume. The amount of magical syrup in the red potion is 60%, which is more than twice the amount of magical syrup in the blue potion (30%). Therefore, any combination of the two potions will always have less than 60% magical syrup by volume.
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In triangle PQR is equal to QR and angle R is equal to 50° then find the measure of Q
Answer:
Step-by-step explanation:
Since PQR is a triangle with QR = PQ, we have:
∠PQR = ∠QPR (since the angles opposite to equal sides are equal)
Let x be the measure of ∠QPR. Then:
∠PQR + ∠QPR + ∠R = 180° (sum of angles in a triangle)
x + x + 50° = 180°
2x = 130°
x = 65°
Therefore, the measure of ∠QPR is 65°.
if you divide 50 by half and add 20 what is the sum?
Answer: 120
Step-by-step explanation: When 50 is divided by half, which is 100, and added 20 to it, it is 120
Answer:
45
step by step explaination:
Think about what same 2 numbers that, when added together make fifty. 25! so when you divide 50 by half, if equals 25. Then, add 25+20 to equal 45 :)
How many 1/16 of an inch are in 4 inches
Answer:
There are 64 (4/ (1/16)) 1/16 of an inch in 4 inches.
A toddler is playing with his toys in the bathtub. He is using a toy shaped like a rectangular prism, filling it with water to the top, and filling his other toys to overflowing.
Rectangular prism toy:
a. What is the volume of the rectangular prism toy?
b. What formula did you use to calculate your answer?
C. What formula did you use to calculate the volume of the cylindrical toy?
help
Therefore , the solution of the given problem of volume comes out to be a) 30 cubic inches , b)rectangular prism and c) cylinder volume is 108.6 cubic inches.
Explain volume.A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The digits cm3 and in3 are two examples of cubic units. However, one can gauge an object's size using its bulk. Usually, the weight of an item is converted into mass measurements like kilogrammes or kilos.
Here,
a. By multiplying the rectangular prism toy's length, breadth, and height together, one can determine its volume:
Capacity is calculated using the formula LWH.
5 in. × 3 in. x 2 in.
thirty cubic inches of volume
Consequently, the rectangular prism toy has a capacity of 30 cubic inches.
b. I calculated the capacity of a rectangular prism using the following formula:
Capacity is calculated using the formula LWH.
c. The equation for a cylinder's volume is:
=> V = π x radius² x height
We can determine the radius using the following formula given that the cylindrical toy's height is 4 inches and its width, which is twice the radius, is 5.2 inches:
=> radius = circumference / 2.
=> radius=5.2 inches/two
=> radius: 2.6 inches
When we enter the numbers, we obtain:
Dimensions = 2.6 in x 2 in x 4 in
108.6 cubic inches of volume
Consequently, the cylindrical toy has a capacity of roughly 108.6 cubic inches.
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The area of a plane shape is given by A=(10x-2)cm square. The area is not greater or equal to 12cm square. It is however not less than 2cm. Find the smallest possible area of this shape
Answer:
Step-by-step explanation:
We know that the area of the plane shape is given by A = (10x - 2) cm^2, and we also know that:
A is not greater than or equal to 12 cm^2 (i.e., A < 12), and
A is not less than 2 cm^2 (i.e., A > 2).
To find the smallest possible area of the shape, we need to find the smallest possible value of x that satisfies these conditions.
From the given conditions, we have:
10x - 2 < 12
10x < 14
x < 1.4
and
10x - 2 > 2
10x > 4
x > 0.4
Therefore, the smallest possible value of x that satisfies both conditions is:
0.4 < x < 1.4
To find the smallest possible area, we can substitute the lower bound of x into the area formula:
A = (10x - 2) cm^2
A = (10 × 0.4 - 2) cm^2
A = 2 cm^2
Therefore, the smallest possible area of the shape is 2 cm^2.