Opposite angles in a parallelogram are equal. This is due to the property of parallel lines being crossed by a transversal line, which causes the corresponding angles to be equal.
Explanation:Yes, the opposite angles in a parallelogram always have the same measure. This happens because when lines are parallel and they get crossed by another line (called the transversal), the corresponding angles in the different parallel lines are equal.
In a parallelogram, the opposite sides are parallel. If you draw a diagonal inside the parallelogram, it acts as a transversal line crossing the parallel lines. Therefore, the angles it forms at the corners are equal to each other, meaning the opposite angles have the same measure.
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A rectangular prism has a base with side lengths x and x+3, and a height 2x. What is the surface area & volume of the prism?
Final answer:
The surface area of the rectangular prism is represented as [tex]2x^2 + 16x[/tex] square units, and the volume as [tex]2x^3 + 6x^2[/tex]cubic units, based on the dimension formulas where the side lengths of the base are x and x+3, and the height is 2x.
Explanation:
The question involves finding the surface area and volume of a rectangular prism with dimensions based on the variable x. Given, the side lengths of the base are x and x+3, and the height is 2x.
Surface Area Calculation
The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is length, w is width, and h is height. Substituting the given values, we get:
Top and Bottom Surface Area: 2(x)(x+3)
Front and Back Surface Area: 2(2x)(x+3)
Left and Right Surface Area: 2(x)(2x)
Adding these together yields the total surface area as [tex]2x^2 + 10x + 6x[/tex], which simplifies to [tex]2x^2 + 16x[/tex].
Volume Calculation
The volume of a rectangular prism is found using the formula V = lwh. For this prism, it translates to V = x(x+3)(2x), which simplifies to [tex]2x^3 + 6x^2.[/tex]
In conclusion, the surface area of the prism can be represented as [tex]2x^2 + 16x[/tex] square units, and the volume as [tex]2x^3 + 6x^2[/tex] cubic units.
The waiter places a bowl of soup in front of Caesar. In a counterclockwise direction, he passes the soup to Jada who then passes it to Haifa. Which two rotations about the center of the table describe passing the soup?
Answer:
We choose answer C) First 150° and then 60°
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.
The waiter places a bowl of soup in front of Caesar. In a counterclockwise direction, he passes the soup to Jada who then passes it to Haifa. Which two rotations about the center of the table describe passing the soup?
A) First 200° and then 80°
B) First 180° and then 72°
C) First 150° and then 60°
D) First 100° and then 40°
My answer:
From the photo, we can see that there are 12 people or 12 places in the circle. And each person has the same distance to other one.
Hence, we can find the the arch degrees between two members:
360 / 12 = 30 °
So from Caesar to Jada, we have to pass through 5 arches
=> the rotation counterclockwise in this situation is: 30 ° *5 = 150°
So from Jada to Haifa, we have to pass through 2 arches
=> the rotation counterclockwise in this situation is: 30 ° *2 = 60°
We choose answer C) First 150° and then 60°
Easy math question help asap
Answer:
3/4z-1/4z+1=2/4z+1
Combine like terms to get
1/2z+1=1/2z+1
Subtract one from both sides to get
1/2z=1/2z
Multiply both sides by 2 to get
z=z.
This is D, has infinitely many solutions because any number you enter as z will equal itself.
Ex. 5 as z would be 5=5 which is true with any number.
Given the function y-4=5/6(x-2), complete the table of values by entering the missing value.
Table:
X: -10 | -4 | -1 | ?
----------------------------
Y: -6 | -1 | 3/2 | 9
And how did you find the that Answer?
How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally
Each person will get 1/6 lb of chocolate.
Here,
Number of people = 3.
Quantity of chocolate = 1/2 lb
What is equally divide?
The law recognizes that both spouses contribute to child care, household management and financial support.
Now,
Quantity of chocolate dividing equally in 3 person = [tex]\frac{\frac{1}{2} }{3}[/tex]
= [tex]\frac{1}{6}[/tex]
Hence, Each person will get 1/6 lb of chocolate.
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. mc076-1.jpg If mc076-2.jpg and mc076-3.jpg, what is mc076-4.jpg?
Answer:
B
Step-by-step explanation:
Julia spent 1/3 of her birthday money then she lost half of the rest now she has only $10 left how much did she get for her birthday
Final answer:
Working backwards from the $10 Julia has left after spending and losing money, we calculate that she initially had $30 for her birthday.
Explanation:
To find out how much birthday money Julia initially had, we can work backwards from the $10 she has left. Julia lost half of her money after spending 1/3 of it, which means that the $10 is half of what remained after spending 1/3. Therefore, before she lost half, she must have had $20 (since $10 is half of $20). We can then calculate the original amount by understanding that $20 is 2/3 (the remaining amount after spending 1/3) of the original amount. To find the full amount, we divide $20 by 2/3.
Here's the calculation step-by-step:
Let the original amount of birthday money be X.
Julia spent 1/3 of X, leaving her with 2/3 of X.
She then lost half of the remaining money, leaving her with (1/2)(2/3)X, which equals $10.
Solving for X: (1/2)(2/3)X = $10 -> (1/3)X = $10 -> X = $10 / (1/3) -> X = $10 × 3 -> X = $30.
Julia originally had $30 for her birthday.
What is the degree of this polynomial 5y2+y+1
Answer:
Degree = 2
Step-by-step explanation:
Given: [tex]5y^2+y+1[/tex]
We are given a polynomial with variable y.
Polynomial: It is an expression with positive number exponent of same variable.
Degree: It is highest power of variable.
In the given polynomial, [tex]5y^2+y+1[/tex].
It has three term with variable y.
The highest power of y is 2.
Leading coefficient is 5
Hence, The degree of given polynomial is 2
The odds against a spinner showing an even number are 3:8. What is the probability of the spinner showing an even number?
Probability is the likelihood or chance that an event will occur. If the probability of the spinner showing an even number if the odds against a spinner showing an even number are 3:8 is 8/11
What is probability?Probability is the likelihood or chance that an event will occur. The formula for calculating probability is expressed as:
Probability = expected/total outcome
If the odds against a spinner showing an even number are 3:8, the total number of spins is 11 spins
From the ratio
Number of odd spin = 3
Number of even spin = 8
Find the probability of spinning even
pr(even spin) = 8/11
Hence the probability of the spinner showing an even number if the odds against a spinner showing an even number are 3:8 is 8/11
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Simplify: (64x^5y^9z^8)^3/7
The graph shows f(x) = (1/2)^x and its translation, g(x). Which describes the translation of f(x) to g(x)?
translation of four units up
translation of five units up
translation of four units to the right
translation of five units to the right
Translation of 4 units up
1.2, 3, 7.5, 18.75, ...
Which formula can be used to describe the sequence?
f(x) = 1.2(2.5)x – 1
f(x) = 2.5(1.2)x – 1
f(x) = 1.2(2.5)x
f(x) = 2.5(1.2)x
It's geometric sequence:
[tex]a_1=1.2,\ a_2=3,\ a_3=7.5,\ a_4=18.75,\ ....[/tex]
Calculate the common ratio:
[tex]r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{3}{1.2}=2.5[/tex]
The explicit formula of geometric sequence:
[tex]a_n=a_1r^{n-1}\to f(x)=a_1r^{x-1}[/tex]
Substitute:
[tex]a_1=1.2,\ r=2.5\\\\f(x)=1.2\left(2.5)^{x-1}[/tex]
Answer: "f(x) = 1.2(2.5)x-1"
Answer:
AStep-by-step explanation:
100% righttt
Chang is participating in a 4-day cross-country biking challenge. He biked for 70, 63, and 66 miles on the first three days. How many miles does he need to bike on the last day so that his average (mean) is
65miles per day?
Chang needs to bike 65 miles on the last day to have an average of 65 miles per day.
Explanation:To find how many miles Chang needs to bike on the last day, we need to find the total miles he has biked so far. So, we add up the miles he has biked on the first three days: 70 + 63 + 66 = 199 miles.
To find the average of 65 miles per day, we need to divide the total miles by the number of days: 199 / 4 = 49.75 miles per day.
Since Chang wants to have an average of exactly 65 miles per day, he needs to bike 65 miles on the last day. Therefore, he needs to bike 65 miles on the last day.
Question: In the diagram below, point O is the center of the given circle. What is the measure of arc DE.
Answer:
[tex]82^{o}[/tex]
Step-by-step explanation:
I assumed you are asking about the angle size of minor arc DE.
OD and OE are radii and therefore are equal.
So triangle ODE must be isosceles. That makes angle OED also 49 degrees.
Using sum of interior angles of a triangle DOE = 180 - (49+49)= 82 degrees.
Note: Your question is ambiguous. There are two arc DE's in this question:
The minor arc, straight from D to E along the circumference
The major arc, from D along the circumference to F then E. That is also arc DE
What number must you add to complete the square? x^2+14x=-7
a. 196
b.7
c. 49
d. 14
Write what the expressions below best represent within the context of the word problem How many quarts of water must be added to 4 quarts of an 80% mixture to obtain a 50% mixture?
Answer:
80%
50%
Step-by-step explanation:
Nancy and Gabe had a pizza with 12 pieces. Brent ate 1/3 of a pizza and Kayla ate 1/4 of a pizza. How much of the whole pizza is left? Explain how you got your answer please!
Brian needs to paint a logo made using two right triangles. The dimensions of the logo are shown below. What is the difference between the area of the large triangle and the area of the small triangle? 7.5 cm2 15.0 cm2 19.5 cm2 39.0 cm2
The graph below represents the price of sending picture messages using the services of a phone company.What is the constant of proportionality?
10
11
21
22
if x is equal 1 what number is y
Learning about system of equations, please give a VERY DETAILED explanation! I'm having a lot of trouble with this. :(
What are the solutions of the following equation? 5∣x+6∣+8=−6∣x+6∣+8
A $33$-gon $P_1$ is drawn in the Cartesian plane. The sum of the $x$-coordinates of the $33$ vertices equals $99$. The midpoints of the sides of $P_1$ form a second $33$-gon, $P_2$. Finally, the midpoints of the sides of $P_2$ form a third $33$-gon, $P_3$. Find the sum of the $x$-coordinates of the vertices of $P_3$.
What is the slope of a line that is perpendicular to the line whose equation is
2y = 3x - 1 ?????
Meg described four triangles as shown below:
Triangle P: All sides have length 7 cm.
Triangle Q: Two angles measure 55°.
Triangle R: Two sides have length 8 cm, and the included angle measures 60°.
Triangle S: Base has length 8 cm, and base angles measure 55°.
Which triangle is not a unique triangle? PLEASE HELP
The triangle which is not a unique triangle is:
Triangle Q.
Step-by-step explanation:As we know that with the help of given three side lengths a unique triangle is constructed.Hence, Triangle P will be unique.
Also, with the help of the given three angle measure infinite number of triangles could be constructed as the side lengths may be different.'Hence, Triangle Q is not unique.
( Since we are given two angles and the measure of the third angle could be known with the help of property that:
Sum of all the angles of a triangle is 180° )
Also, with the help of a given two side lengths and a included angle measure a unique triangle is constructed.( Since, we make a line segment of given length and then keep the compass at one of end point and make a 60 degree angle and cut that side into length 8 cm and finally join the other end point and the constructed line to get a triangle)
Hence, Triangle R is also unique.
Similarly Triangle S will also be unique by construction.( First draw a line segment of length 8 cm and at both the ends of the line make a 50 degree angle and extend the line over the arc of the angle and see where two lines intersects.
By such a way we obtain a unique triangle)
Nancy had 16 chocolate candies in a bag. Her mother put a handful of candies in the bag. When Nancy counts her chocolate candies, she discovers she now has 32 of them. Which of the following equations will help Nancy solve for the number of chocolate candies, c, that her mom put in the bag?
Jason has two bags with 6 tiles each.
Without looking, Jason draws a tile from the first bag and then a tile from the second bag. What is the probability of Jason drawing the tile numbered 2 from the first bag and the tile numbered 3 from the second bag?
assuming the tiles are numbered 1, 2, 3, 4, 5, 6
there is one tile with the number 2 on it in the first bag
and 1 tile with the number 3 on it in the second bag
so you have a 1/6 probability of picking the 2 and a 1/6 probability of picking the 3
so 1/6 * 1/6 = 1/36 probability of picking them both
Answer:
1/36
Step-by-step explanation:
first bag, 1/6 probability of taking 2 from the bag with 6 tabs
second bag, 1/6 probability of taking 3 from the bag with 6 tabs
Multiply 1/6 and 1/6 = 1/36
What is the value of y in the solution to the system of equations?
x + y = 1
2x – 3y = –30
Answer: The required value of y in the solution to the given system is 6.4.
Step-by-step explanation: We are given to find the value of y in the solution to the following system of linear equations :
[tex]x+y=1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x-3y=-30~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
To find the value of y, we will try to eliminate x from both the equations.
Multiplying equation (i) by 2, we have
[tex]2(x+y)=1\times2\\\\\Rightarrow 2x+2y=2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Subtracting equation (ii) from equation (iii), we get
[tex](2x+2y)-(2x-3y)=2-(-30)\\\\\Rightarrow 2y+3y=2+30\\\\\Rightarrow 5y=32\\\\\Rightarrow y=\dfrac{32}{5}\\\\\Rightarrow y=6.4.[/tex]
Thus, the required value of y in the solution to the given system is 6.4.
Determine which system below will produce infinitely many solutions.
−6x + 3y = 18
4x − 3y = 6
2x + 4y = 24
6x + 12y = 36
3x − y = 14
−9x + 3y = −42
5x + 2y = 13
−x + 4y = −6
Answer:
The answer is C
[tex]3x-y=14\\-9x+3y=-42[/tex]
Step-by-step explanation:
In order to determine the system, we have to know the condition to produce infinitely solutions. A solution of a system is the coordinate (x,y) which is common between two lines ( in a 2D plane). A system does not have solution when the lines do not intercept each other, that it means, they are parallele. When two lines are coincident in all points, there are infinitely solutions.
I have attached an image that shows different systems of two lines.
So, to find the system, we have to find two equal equation. If we multiply by 3 the third system:
[tex]3x-y=14\\-9x+3y=-42\\\\(-3)*(3x-y)=(-3)*14\\(1)*(-9x+3y)=(1)*-42\\\\-9x+3y=-42\\-9x+3y=-42[/tex]
This system has infinitely solutions.
Graph the following inequality. Then click to show the correct graph. 3x - 2y ≤ 6
Solution:
The given inequality is :
3 x - 2 y ≤ 6
To draw the graph we will first draw the graph of line : 3 x - 2 y = 6
The graph of this function i.e 3 x - 2 y = 6 will be a straight line.
Then we will check whether origin lies on which side of line .
Put x=0, and y = 0 in the inequality 3 x - 2 y ≤ 6, we obtain
LHS = 0 ≤ 6
It means the line will contain the Origin.
Equation of line in Intercept form is : [tex]\frac{x}{2} -\frac{y}{3}\leq 1[/tex]