The cost of a movie ticket is $5. it costs a group of friends $105 to go to the movies. which equation describes the number of people that went to the movies?
The equation that describes the number of people that went to the movies could be 5x = 105
What is a solution to a system of equations?For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs,
So solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)
Given; The cost of a movie ticket is $5. it costs a group of friends $105 to go to the movies.
Each ticket cost is $5,
The tickets were $105.
So, multiplied 5 x 105 = 525.
Let x be the number of people that went to the movies.
So, 105 / 5 = x = 21
OR
5x = 105
Therefore, the equation that describes the number of people that went to the movies could be 5x = 105
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Solve x(−2) 2 =4(−2)
x(−2) 2 =4(−2) = -2
Explanation:To solve this equation, we first need to understand the order of operations in mathematical equations. The acronym PEMDAS is often used to remember the order: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
In this equation, we have parentheses and exponents. According to PEMDAS, we need to solve the parentheses first before moving on to the exponent. So, let's start by simplifying the parentheses on the left side of the equation.
x(-2)^2 = 4(-2)
= x(4) = -8
= 4x = -8
= x = -2
In the first step, we distributed the exponent of 2 to the -2 within the parentheses, resulting in (-2)^2 = (-2)(-2) = 4. This simplifies the left side of the equation to x(4) = 4x.
In the second step, we substituted the value of -2 on the left side of the equation, resulting in 4(-2) = 4x. This simplifies to -8 = 4x.
To isolate x, we divide both sides by 4, resulting in x = -2. This gives us our final answer.
In conclusion, when solving equations with multiple operations, it is important to remember the order of operations and follow it step by step. In this equation, we simplified the parentheses first, then solved for x by isolating it on one side of the equation. By following these steps, we were able to find the value of x, which is -2.
Five times a number is equal to the number increased by 12
The required expression is [tex]5n = n+ 12[/tex] and the unknown number is [tex]3[/tex]
Let the unknown number be "n"
Five times the number is expressed as 5nThe number increased by 12 is expressed as n + 12Equating both expressions will give:
[tex]5n = n + 12[/tex]
Solve for n:
[tex]5n - n = 12\\4n = 12\\n = 12/4\\n = 3[/tex]
Hence the required expression is [tex]5n = n+ 12[/tex] and the unknown number is [tex]3[/tex]
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A segment with endpoint M Left parenthesis 5 comma 9 right parenthesis and N Left parenthesis 4 comma 3 right parenthesis is rotated 270°. What are the coordinates of M prime and N prime?
The correct answer is : M prime (9,-5) and N prime (3,-4)
Look at the diagram. If RS= 8y + 4, ST = 4y + 8, and RT = 36, find the value of y.
Answer:
(A) y=2
Step-by-step explanation:
It is given that [tex]RS=8y+4[/tex], [tex]ST=4y+8[/tex]and [tex]RT = 36,[/tex] then
According to the figure given, we have
[tex]RT=RS+ST[/tex]
[tex]36=8y+4+4y+8[/tex]
[tex]36=12y+12[/tex]
[tex]24=12y[/tex]
[tex]y=\frac{24}{12}[/tex]
[tex]y=2[/tex]
Thus, the value of y will be 2.
Hence, option A is correct.
The length of a rectangle is twice its width. if the area of the rectangle is 162 m2 , find its perimeter.
The width of the rectangle is 9m and the length is 18m. The perimeter of the rectangle is 54m.
Explanation:Let's assume the width of the rectangle as 'w'. According to the given information, the length would be twice the width, so the length can be represented as '2w'.
The formula for the area of a rectangle is length multiplied by width, which can be written as 'A = lw', where 'A' is the area. By substituting the given area value of 162m2, the equation becomes '162 = 2w * w'.
Solving this equation, we get 'w = 9m' which represents the width. The length can be found by doubling the width, so the length is '2 * 9m = 18m'.
The perimeter of a rectangle can be calculated using the formula 'P = 2(l + w)', where 'P' is the perimeter, 'l' is the length, and 'w' is the width. Plugging in the values, the perimeter of the rectangle is 'P = 2(18m + 9m) = 54m'.
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In November 2010, ING Direct was offering 2.4% interest on its Orange Savings Account, with interest reinvested quarterly.† Find the associated exponential model for the value of a $3,000 deposit after t years
A particle's position is r⃗ =(ct2−2dt3)i^+(2ct2−dt3)j^,
where c and d are positive constants. Find expressions for times t > 0 when the particle is moving in the x-direction.
Evaluate the expression below when x = -1.
2x2 − 5
x + 9
-7
8
-3
8
-1
8
-1
Answer:
-3/8
Step-by-step explanation:
plato
Jeff wants to make an a in his math course this semester. To do so, he must have an average of 90 or above. If his test scores this semester or 88, 92 and 96 what is the score that he would need to make on his final test to attain an average on exactly 90
Points a, b, c, and d are collinear. in how many ways can the line be named using only these points
What is m∠D ?
Enter your answer in the box. __°
Answer
Find out the m∠D .
To proof
In Δ ABE
∠EAB + ∠ABE + ∠AEB = 180 °
(By using the angle sum property of a triangle.)
As given and shown in the diagram
∠EAB = 14° , ∠ABE = 45 °
Put in the above equation
14° + 45° + ∠AEB = 180 °
∠AEB = 180 °- 59°
∠AEB = 121 °
∠AEB = ∠DEC = 121°
(by using the vertical opposite angles property)
Now in ΔCED
∠DEC + ∠EDC + ∠ECD = 180 °
(Angle sum property of a triangle)
(as given ∠DEC = 121° ,∠ECD = 27° shown in the diagram )
∠EDC = 180 ° - 27 ° - 121 °
∠EDC = 32°
therefore
∠ D = 32 °
Hence proved
A right triangle has exterior angles at each of its acute angles with measures in te ratio 13:14. find the measures o the two acute angles of the right triangle.
10 more than the quotient of a number and 8 is at least 12
Which equation is related to the equation shown? x + 3 = 12
a. x = 12 + 3
b. x = 12 ÷ 3
c. x = 12 − 3
d. x = 12 • 3 open study?
There are 3 in. of snow on the ground when it begins to snow 0.5 in. /h.
Which linear equation represents the total depth of the snow, in inches, after x hours?
A. y=0.5x
B. 3+y=0.5x
C. y=0.5x+3
D. x=0.5y
Answer:
c. i took the test
Step-by-step explanation:
The required linear equation y = 0.5x + 3 represents the total depth of the snow, in inches, after x hours which is the correct answer would be option (C).
What exactly is a linear equation?A linear equation is one in which the greatest power of the variable is always one.
The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
We have been given that there is 3 in. of snow on the ground when it begins to snow 0.5 in. /h.
Let the total depth of the snow, in inches, after x hours
As per the given information, translate the phrase into an algebraic form:
y = 0.5x + 3
Here y represents the total depth of the snow.
Therefore, the correct answer would be option (C).
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Write an inequality for the given statement: The sum of y and 20 is more than 50.
Hey!
Hope this helps...
~~~~~~~~~~~~~~~~~~~~~~~~
We know that we will be using the greater than symbol...
By know this we can assume that the start of the problem looks like this:
> 50
This is because the answer of said question MUST be greater than 50...
We also know that the question states "the sum of y and 20"
So... that will look like this:
y + 20
We also know that it says "the sum of y and 20 is more than 50", so we set that up like this:
y + 20 > 50
So the inequality for this is: y + 20 > 50
luke scored 21 goals in 7 soccer games. if he scores goals at the same rate, how many goals will he score in 23 games
Answer:
69
Step-by-step explanation:
My bad if it's wrong
What is the common term for the set of all points with x- coordinate zero?
A. X axis
B. Y axis
C. Coordinate plane
D. Origin
Mikel creates the table below to help her determine 40% of 70
To Find: 40 % of 70
Solution:
x % of y means = [tex]\frac{x \times y}{100}[/tex]
40 % of 70= [tex]\frac{40 \times 70}{100}=\frac{2800}{100}=28[/tex]
This is the way Mikel can determine 40 % of 70.
The line segments are translated 2 units to the left to form J′K′ and M′N′. Which statement describes J′K′ and M′N′?
Answer:
Step-by-step explanation:
the line segments J'K' and M'N' do not intersect and are the same distance apart as JK and MN.
Point M is the midpoint of segment JK. Find JK when JM=6x-7 and MK=2x+3.
The value of JK will be 16.
It is given that M is the midpoint of segment JK.
We have to find out the value of JK.
What will be the value of x , if 4x + 12 = 8x + 4 ?
The value of x will be 2.
As M is the midpoint of JK.
JK = MK + JM
So,
MK = JM
2x + 3 = 6x - 7
4x = 10
x =2.5
So ,
MK = 2x + 3 = 8
JM = 6x - 7 = 8
Hence ,
JK = MK + JM = 8 + 8
JK = 16
Thus , value of JK will be 16.
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The product of some negative number and 3 less than twice that number is 209. find the number
if a right triangle has side lengths x + 9, x + 2, x + 10 is the hypotenuse, find the value of x
To determine the value of x for the right triangle, we applied the Pythagorean theorem to the side lengths and solved the resulting quadratic equation, revealing x to be -1.
Explanation:To find the value of x for the side lengths of a right triangle with side lengths x + 9, x + 2, and x + 10 as the hypotenuse, we use the Pythagorean theorem, which states that in a right triangle, a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the two other sides.
Here's the step by step solution:
Write the Pythagorean theorem with the given side lengths: (x + 2)² + (x + 9)² = (x + 10)².Expand the squares: x² + 4x + 4 + x² + 18x + 81 = x² + 20x + 100.Combine like terms and move all terms to one side: x² + 22x + 85 = 0.Solve the quadratic equation, which yields x = -1 or x = -85. However, since side lengths cannot be negative, the only logical value of x is -1.
Final answer:
To find the value of x in a right triangle with sides x + 9, x + 2, and hypotenuse x + 10, the Pythagorean theorem is used. After applying the theorem, we simplify and solve the resulting quadratic equation, which gives us a positive value of x = 3.
Explanation:
The student is asking how to find the value of x in a right triangle with sides x + 9, x + 2, and x + 10, where x + 10 is the hypotenuse. To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².
For this particular triangle:
Identify the legs and the hypotenuse of the triangle: Leg 1 is x + 9, Leg 2 is x + 2, and the Hypotenuse is x + 10.Apply the Pythagorean theorem: (x + 9)² + (x + 2)² = (x + 10)².Simplify and solve for x. Expand the squares: x² + 18x + 81 + x² + 4x + 4 = x² + 20x + 100.Combine like terms and move all terms to one side of the equation:(2x² + 22x + 85) - (x² + 20x + 100) = 0x² + 2x - 15 = 0Factor the quadratic equation: (x + 5)(x - 3) = 0Find the possible values for x: x = -5 or x = 3. Since a side length can't be negative, the value for x must be 3.Therefore, the value of x is 3.
Find the angle measure of the hands of a clock at the given time. 5:00
The angle measured by the hands of a clock at the given time at 5:00 will be 150°.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
We know that the hour hand will be on 5 and the minute hand will be on 12 at 5:00 o'clock.
Then the angle measured by the hands of a clock at the given time at 5:00 will be
⇒ (360° / 12) x 5
⇒ 30° x 5
⇒ 150°
The angle measured by the hands of a clock at the given time at 5:00 will be 150°.
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Can someone help me with 11? I’m confused on how to solve for the rest of the problem. I don’t know how to get rid of the 3
A box has dimensions of 17 inches long 1.3 feet wide and 8 inches high what is the volume of the box the formula of the volumes is v=l•w•h
Which would hold more water a teaspoon or a milliliter?
Write a story that matches the expression
42x - 5
Answer: Hello there!
The equation is: 42x - 5
That can be phrased as "the difference between 42 times a number x and 5"
And we want to write a story that matches this.
an example can be:
Suppose that Jon craft musical instruments and he sells them in the beach, then you could write:
"The revenue in a day for Jon is equal to $42 for each instrument that he sells, less a 5 dollar fee that he needs to pay every day"
where the number of instruments would be x.
what do you add 15/4 to make 4