Which of the following represent x=1/2y written in general form
1/2x-y=0
2x-y=0
x-1/2y=0
Answer:
Option 2 - [tex]2x-y=0[/tex]
Step-by-step explanation:
Given : Expression [tex]x=\frac{1}{2}y[/tex]
To find : Write the given expression in general form?
Solution :
Step 1 - Write the given expression
[tex]x=\frac{1}{2}y[/tex]
Step 2 - Multiply 2 both side,
[tex]2x=\frac{2}{2}y[/tex]
Step 3 - Solve the expression
[tex]2x=y[/tex]
[tex]2x-y=0[/tex]
Therefore, The general form of given expression is [tex]2x-y=0[/tex]
Hence, Option 2 is correct.
Amelia receives a treat bag. the treat bag contains 10 gumballs, 5 pixie sticks, 2 bracelets, and 3 chocolates. If Amelia selects 3 items from her treat bag without looking and gives them to her sister, which could not represent a possible outcome for the items Amelia selects?
F. gumball, gumball, gumball
G. pixie stick, gumball, chocolate
H. bracelet, bracelet, bracelet
J. gumball, gumball, pixie stick
900 students attended the school concert. There were twice as many adults as children in the audience. How many children attended the concert? which let statement would you use?
To solve for the number of children at the concert with twice as many adults present in a total of 900 attendees, we let the number of children be x, set up the equation x + 2x = 900, and solve for x to find that there were 300 children.
Explanation:The question pertains to solving a problem involving proportions in a total population. Assuming there are twice as many adults as children at the school concert, we can use a 'let' statement to express the number of children as 'x'. Thus, the number of adults would be '2x' because there are twice as many adults as children. Since the total number of attendees is 900, we can set up the equation: x + 2x = 900.
To find the number of children, we combine like terms to get 3x = 900, and then divide both sides by 3 to find x. Thus, x = 900 / 3, which means x = 300. So, there were 300 children at the concert.
Step-by-Step Solution:Let the number of children be 'x' (let statement).Write the number of adults as '2x' because there are twice as many adults as children.Set up the equation for the total attendees: x + 2x = 900.Combine like terms: 3x = 900.Divide both sides by 3 to solve for x: x = 300.Conclude that there were 300 children at the concert.what is 3/20 as a decimal equivalent
The ratio of m∠PQR to m∠PQS is 5:9. What is m∠RQS?
10°
40°
50°
80°
A boat moves 60 kilometers east from point A to point B. There, it reverses direction and travels another 45 kilometers toward point A. What are the total distance and total displacement of the boat?
The total displacement of the boat is therefore 15 kilometers east.
The student is asking about calculating the total distance and displacement of a boat after it has traveled in two opposing directions. To find the total distance, we simply add up the lengths of both trips the boat makes. Since the boat moves 60 kilometers east from point A to point B and then reverses direction to travel another 45 kilometers towards point A, the total distance traveled by the boat is the sum of these two trips:
Distance from A to B = 60 kilometersDistance from B to A = 45 kilometersTotal distance = 60 km + 45 km = 105 kilometersThe total displacement, however, is the vector difference between the final and starting positions. Since displacement is directional, we calculate it by subtracting the westward trip from the eastward trip:
Displacement = 60 km (east) - 45 km (west)Since east is the positive direction, the displacement is 60 km - 45 km = 15 km towards the eastThe total displacement of the boat is therefore 15 kilometers east.
work out the value of 5x-2y when x=-2 and y=-3
A rectangle is transformed according to the rule R0, 90º. The image of the rectangle has vertices located at R'(–4, 4), S'(–4, 1), P'(–3, 1), and Q'(–3, 4). What is the location of Q?
(–4, –3)
(–3, –4)
(3, 4)
(4, 3)
The location of Q in the rectangle is D. (4, 3).
How to illustrate the information?
Graph images undergo transformations, one of the types of transformations is rotations. Rotation is done when each point of the image rotates 90° around a point in a counterclockwise manner.
When rotation is done, (x,y) -> (-y,x), therefore when taking points from image to original then the reverse is done (-y,x) --> (x,y)
The coordinates of image point q' is (-3,4), hence, before rotation then the coordinates are (4,3).
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Carolyn is building a pen for her dog. The perimeter of the pen is 52 ft
a) Explain how you can use a proportion to convert the perimeter into yards and feet.
b) The fencing material is sold by the yard. It costs 10.99 per yard. What is the cost of material before taxes
Carolyn's dog pen with a 52 ft perimeter is approximately 17.33 yards in length. Fencing material costs $10.99 per yard, making the total cost before taxes around $190.44.
Carolyn is constructing a dog pen with a perimeter of 52 feet. To convert the perimeter from feet to yards, we can use the fact that 1 yard equals 3 feet. Since she is purchasing fencing material by the yard, Carolyn needs to know the total length of fencing in yards. This requires setting up a proportion:
1 yard / 3 feet = x yards / 52 feet
Multiplying both sides by 52 gives us x = 52 / 3 yards. Upon calculating, we find that the pen's perimeter is approximately 17.33 yards.
Since the fencing material costs $10.99 per yard, to find the total cost before taxes, we multiply the number of yards needed by the price per yard:
17.33 yards × $10.99/yard = $190.4367
The cost for the fencing materials before taxes is approximately $190.44.
The area of a rectangle painiting is given by the trinomial x^2-9x-36. what are the possible dimensions of the painting ? use factoring
The first term is, x2 its coefficient is 1 .
The middle term is, -9x its coefficient is -9 .
The last term, "the constant", is -36
Step-1 : Multiply the coefficient of the first term by the constant 1 • -36 = -36
Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is -9 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and 3
x2 - 12x + 3x - 36
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-12)
Add up the last 2 terms, pulling out common factors :
3 • (x-12)
Step-5 : Add up the four terms of step 4 :
(x+3) • (x-12)
Which is the desired factorization
A software company startes with 2 employees. in 6 months, the company has u employees. the number of employees increased at a steady rate. which equation models the relationship between the number of employees n and the number of months m since the company started?
PTG has side lengths of 18 cm, 14 cm, and 16 cm. which type of triangle is PTG? right, obtuse, acute, isosceles
Final answer:
Triangle PTG is an acute triangle because the sum of the squares of the shorter sides (196 + 256 = 452) is greater than the square of the longest side (324). It is not a right or obtuse triangle, nor is it isosceles.
Explanation:
To determine which type of triangle PTG is, we can use the lengths of its sides (18 cm, 14 cm, 16 cm). A well-known method to identify the type of triangle based on side lengths is by using the Pythagorean theorem, which applies to right triangles.
Specifically, the theorem states that for a right triangle with legs 'a' and 'b', and hypotenuse 'c', the relationship a2 + b2 = c2 holds true.
First, we can check if PTG is a right triangle by ordering the sides in ascending order and assigning the longest side as 'c'(18 cm), and the other two as 'a'(14 cm) and 'b'(16 cm). If PTG were a right triangle, we would expect to see that 142 + 162 equals 182.
Let's perform the calculations:
142 = 196
162 = 256
182 = 324
Adding together the squares of the shorter sides, we get:
196 + 256 = 452
Since 452 is not equal to 324 (182), the triangle is not a right triangle. Next, we can determine if PTG is an obtuse or acute triangle. For an obtuse triangle, we should have a2 + b2 < c2, and for an acute triangle, we should have a2 + b2 > c2. Since 452 is greater than 324, PTG is an acute triangle.
a magazine costs 3.50 how much can you buy with 100$
Greatest common factor of 12, 60, and 68
What is the equation in point slope form of the line that passes through the point (2, 6) and has a slope of 5?
y−2=5(x−6)
y+2=5(x+6)
y−6=5(x−2)
y+6=5(x+2)
Answer:
The answer is Y-6=5(x-2)
Every ten years, the Bureau of the Census counts the number of people living in the United States. In 1790, the population of the U.S. was 3.93 million. By 1800, this number had grown to 5.31 million. Write an exponential function that could be used to model the U.S. population y in millions for 1790 to 1800. Write the equation in terms of x, the number of decades since 1790.
Carla's plant was 10 2/3 inches tall. Yolanda's was 8 3/4 inches tall.
How much taller was Carla's plant than Yolanda's?
A.
1 11/12 in.
B.
2 1/12 in.
C.
2 5/12 in.
D.
2 11/12
Answer: 128/12 > 105/12
Step-by-step explanation:
10 2/3 inches=32/3 inches
8 3/4 inches= 35/4 inches
Find the common denominator, in this case, 12.
128/12 inches is Carla's plant
105/12 inches is Yolanda's plant.
128/12 > 105/12. Therefore, Carla's plant is taller than Yonlanda's
Factor each completely.
7x^2- 31x-20
5p-p-18 Factor each completely.
7x^2- 31x-20
5p-p-18
A grocery store bought milk for $2.70 per gallon and stored it in two refrigerators. During the night, one refrigerator malfunctioned and ruined 13 half gallons. If the remaining milk is sold for $4.04 per half gallon, how many half gallons did the store buy if they made a profit of $62.72?
If is equal to 0.73, then is equal to ______.
0.73
0.50
0.33
0.27
What two numbers multiply to 80 and add to 28
Final answer:
The task is to find two numbers that multiply to 80 and add to 28. However, after checking possible factors, no such pair of numbers satisfies both conditions. A re-evaluation of the problem may be necessary as the conditions may have been stated incorrectly.
Explanation:
We are looking to find two numbers that when multiplied together equal 80, and when added together equal 28. To solve this problem, we set up a system of equations based on the information given:
By factoring the number 80, we look for factor pairs that also add up to 28. We notice that 16 and 5 are such numbers because:
However, this doesn't meet our second criterion, so we continue searching. Further examination reveals that 20 and 4 are the correct pair because:
In this case, we have not found two numbers meeting both conditions exactly. Therefore, it appears there has been a mistake as no pair of numbers both multiply to 80 and add up to 28. Thus, we either reconsider our pair list or recheck the conditions given.
Two acute triangles are similar. Which of the following must the similar triangles have?
every pair of sides and angles congruent
at least one pair of congruent sides and one pair of congruent angles
congruent corresponding angles and proportional side lengths
a right angle and a hypotenuse
factor the expression. -x^2+3x+40
To factor the expression -x^2 + 3x + 40, use the method of expanding binomials by comparing coefficients.
Explanation:To factor the expression -x^2 + 3x + 40, we need to find two binomials whose product equals the given expression. Let's set up the expression in the form of (a - b)(c - d) and expand it to compare coefficients.
-x^2 + 3x + 40 = (a - b)(c - d)
By comparing coefficients, we can determine that a, b, c, and d are -x, 5, -8, and 8, respectively. Therefore, the factored form of -x^2 + 3x + 40 is (-x + 8)(x + 5).
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What is the general form of the equation for the given circle?
x2 + y2 − 8x − 8y + 23 = 0
x2 + y2 − 8x − 8y + 32 = 0
x2 + y2 − 4x − 4y + 23 = 0
x2 + y2 + 4x + 4y + 9 = 0
Answer:
A ) x² + y² - 8 x - 8 y + 23 = 0
Step-by-step explanation:
hope i helped
Which pairs of angles below are alternate interior angles? Check all that apply.
A. ∠1 and ∠3
B. ∠7 and ∠2
C. ∠4 and ∠5
D. ∠8 and ∠2
E. ∠6 and ∠4
F. ∠7 and ∠1
A copy machine makes 32 copies per minute. How long does it take to make 120 copies?
Anne Katz, owner of Katz Sport Shop, loans $8,000 to Shelley Slater to help her open an art shop. Shelley plans to repay Anne at the end of 8 years with interest compounded semiannually at 8 percent. At the end of 8 years, Anne will receive:
What is the time 23 hours after 8:00 pm
A pack with 6 cans of juice costs 3.48. What it the unit price?
A.0.49 per can B.0.50 per can C.0.58 per can D.0.60 per can**my answer??**
The unit price of one can of juice, when a 6-pack costs $3.48, is $0.58 per can.
The question asks us to calculate the unit price of a juice can when a pack of 6 cans costs $3.48.
To find the unit price, we divide the total cost of the pack by the number of cans in a pack.
In this case, we divide $3.48 by 6, which gives us $0.58.
$3.48 / 6 = $0.58
Therefore, the unit price per can is $0.58.
Using the figure above, if< A = <D, then< B ___ <E.
Choose the relationship symbol that makes the statement true.
Answer:
The relationship symbol that makes the statement true is '>'.
Step-by-step explanation:
Given,
In triangles ABC and EDF,
∠A = ∠D
Since, the sum of all interior angles of a triangle is supplementary,
⇒ ∠A + ∠B + ∠C = 180° and ∠D + ∠E + ∠F = 180°
⇒ ∠A = 180° - ∠B - ∠C and ∠D = 180° - ∠E - ∠F,
By substituting the values,
180° - ∠B - ∠C = 180° - ∠E - ∠F
- ∠B - ∠C = - ∠E - ∠F
∠B + ∠C = ∠E + ∠F
∠B + 20° = ∠E + 30° ( given ∠C = 20° and ∠F = 30° )
∠B = ∠E + 10°
⇒∠B > ∠E
Hence, the relationship symbol that makes the statement true would be '>'.