To find the length of pole C, we can set up a system of equations using the given information. Solving the system of equations will give us the values of the lengths of poles A, B, and C. The length of pole C is found to be 14.5 inches.
Explanation:We can solve this problem by setting up a system of equations. Let's represent the length of pole A as 'a', the length of pole B as 'b', and the length of pole C as 'c'. We are given that pole B is 1 3/4 times as long as pole A, so we can write the equation b = 1.75a. We are also given that pole C is 2 1/2 inches longer than pole A, so we can write the equation c = a + 2.5.
Since the total combined length of the three poles is 47 1/2 inches long, we can write the equation a + b + c = 47.5. Now we have a system of three equations:
We can solve this system of equations to find the length of pole C. Substituting equation 1 and equation 2 into equation 3, we get:
a + 1.75a + (a + 2.5) = 47.5
Combining like terms, we get:
3.75a + 2.5 = 47.5
Subtracting 2.5 from both sides, we get:
3.75a = 45
Dividing both sides by 3.75, we get:
a = 12
Now that we know the length of pole A, we can substitute it into equation 1 to find the length of pole B:
b = 1.75 * 12 = 21
Finally, we can substitute the length of pole A and pole B into equation 2 to find the length of pole C:
c = 12 + 2.5 = 14.5
Therefore, the length of pole C is 14.5 inches.
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A card is drawn from a standard deck and a letter is chosen from the word incredible. What is the probability of drawing a king then getting an i?
Step-by-step explanation:
A card is drawn from a standard deck. A standard deck of cards has 52 cards. Its been asked if it is a king. There are 4 kings in a deck, so probability is = [tex]\frac{4}{52}[/tex] or [tex]\frac{1}{13}[/tex]
Simultaneously, a word is chosen from 'incredible' that has 10 letters. We have been asked if the letter is 'i'. In the given word, we have 2 'i's. So, probability is [tex]\frac{2}{10}[/tex] or [tex]\frac{1}{5}[/tex]
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Susan can buy 312312 lb of strawberries for $7.00. How many pounds of strawberries can she buy for $1.00? Express you answer as a fraction in simplest form
Answer:
are you sure it is that large number and not 3 1/2
Step-by-step explanation:
The The graph of g(x) is the result of translating the graph of f(x) = 3x six units to the right. What is the equation of g(x)?
g(x) = 3x – 6
g(x) = 3x + 6
g(x) = 3x – 6
g(x) = 3x + 6
Mark this and return
Answer:
The graph of g(x) is the result of translating the graph of f(x) = 3x six units to the right
When a graph is shifted 'a' units to the right f(x) becomes f(x-6)
Given f(x)= 3x
When graph is shifted 6 units to the right , then g(x)= f(x-6)
Replace x with x-6
g(x)= 3(x-6)= 3x-12
so g(x)= 3(x-6)
Step-by-step explanation:
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Two examples that have a gcf of 8
Which statement is true
The drama club is selling short-sleeved shirts for $5 each, and long-sleeved shirts for $10 each. They hope to sell all of the shirts they ordered, to earn a total of $1,750. After the first week of the fundraiser, they sold 1/3 of the short-sleeved shirts and 1/2of the long-sleeved shirts, for a total of 100 shirts.
This system of equations models the situation.
5x + 10y = 1,750
1/3x + 1/2y = 100
Let x represent the number of short-sleeved shirts ordered and let y represent the number of long-sleeved shirts ordered.
How many short-sleeved shirts were ordered?
How many long-sleeved shirts were ordered?
Answer:
150 short-sleeved shirts and 100 long-sleeved shirts.
Step-by-step explanation:
We will use elimination to solve this system of equations. We will make the coefficients of x the same in order to eliminate them; to do this, we must multiply the bottom equation by 15 (1/3 of 15 is 5, so 15(1/3) = 5):
[tex]\left \{ {{5x+10y=1750} \atop {15(\frac{1}{3}x+\frac{1}{2}y=100)} \right. \\\\\left \{ {{5x+10y=1750} \atop {5x+7.5y=1500}} \right.[/tex]
Subtract the second equation from the first one:
[tex]\left \{ {{5x+10y=1750} \atop {-(5x+7.5y=1500)}} \right. \\\\2.5y=250[/tex]
Divide both sides by 2.5:
2.5y/2.5 = 250/2.5
y = 100
Substitute 100 in for y in the first equation:
5x+10(100) = 1750
5x+1000 = 1750
Subtract 1000 from both sides:
5x+1000 - 1000 = 1750 - 1000
5x = 750
Divide both sides by 5:
5x/5 = 750/5
x = 150
Which value for x makes the sentence true?
5(9x-6) + 15 = 210
A. 8
B. 10
C. 2 11/17
D. 5
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Final answer:
To find the number of sugar packets from 40 pounds, divide by the weight per packet (1/16 pound). The calculation is 40 divided by 1/16, resulting in 640 packets.
Explanation:
To determine how many packets of sugar you can make from 40 pounds of sugar when each packet is 1/16 pounds, you would divide the total amount of sugar by the amount each packet contains. This is a basic math problem involving division.
Here's the calculation:
First, we establish that there are 40 pounds of sugar that need to be divided into packets.
Next, since each packet will contain 1/16 of a pound of sugar, we divide the total pounds of sugar by the weight of each packet.
The calculation is 40 pounds \/ (1/16) pounds per packet, which simplifies to 40 × 16 packets.
After performing the multiplication, the result is 640 packets of sugar.
Therefore, you would have a total of 640 packets of sugar if you repackage 40 pounds of sugar into 1/16 pound packets.
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Answer:
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