m∠R = 110° and m∠S = 110°
Solution:
Given data:
RSWY is a parallelogram.
∠R = (5x – 90)° and ∠S = (2x + 30)°
In RSWY, ∠R and ∠S are opposite angles.
Opposite angles of a parallelogram are congruent.
m∠R = m∠S
(5x – 90°) = (2x + 30)°
5x° – 90° = 2x° + 30°
Add 90° on both sides of the equation, we get
5x° = 2x° + 120°
Subtract 2x° on both sides of the equation, we get
3x° = 120°
Divide by 3 on both sides of the equation.
x° = 40°
Substitute x = 40 in m∠R and m∠S.
m∠R = (5x – 90)°
= 5(40°) – 90°
m∠R = 110°
m∠S = (2x + 30)°
= 2(40°) + 30°
m∠S = 110°
Hence m∠R = 110° and m∠S = 110°.
Peter has 51 fruit chews to share with Josh and Jenny. The number of fruit chews Peter gives to Josh is 9 less than four times the number of fruit chews he gives to Jenny. If Peter has no fruit chews left over, how many fruit chews does Peter give to Jenny?
Henry divided his socks into five equal groups. Let s represent the total number of socks. Which expression and solution represent the number of socks in each group if s = 20?
Answer:
20/5=number in each group. It can also be S/5
Step-by-step explanation:
Answer:
I think its A
Step-by-step explanation:
sorry if im wrong but hope this helps :)
my math is horrible, please help me understand to solve
4/5 of 35=
Answer:
28
Step-by-step explanation:
divide 35 by 5 and multiply the product by 4
35 ÷ 5 = 7
7 × 4 = 28
solve for x 2(x+7)-3(2x+4)= -18
Answer:
x = 5
Step-by-step explanation:
Given
2(x + 7) - 3(2x + 4) = - 18 ← distribute both parenthesis
2x + 14 - 6x - 12 = - 18, that is
- 4x + 2 = - 18 ( subtract 2 from both sides )
- 4x = - 20 ( divide both sides by - 4 )
x = 5
The original equation 2(x+7) - 3(2x+4) = -18 simplifies to -4x = -20, which leads to the solution x = 5. This is confirmed by substituting x back into the original equation, resulting in an identity (-18 = -18).
The equation to solve is 2(x+7) - 3(2x+4) = -18. To solve for x, we first expand the equation:
2x + 14 - 6x - 12 = -18
Combining like terms, we get:
-4x + 2 = -18
Subtracting 2 from both sides gives us:
-4x = -20
Dividing both sides by -4, we find that x = 5.
To verify the solution, plug x back into the original equation:
2(5+7) - 3(2*5+4) = -18
Which simplifies to:
24 - 30 = -18
This confirms that the solution x = 5 is correct as it results in an identity after substitution.
Factor the expression completely. 9x+6
Answer:
3(3x+2)
Step-by-step explanation:
Answer:
3(3x+2)
Step-by-step explanation:
take out LCF of 3
Andre rents beach chairs and umbrellas to tourists visiting the beach. On one Saturday, he has 150 customers. If he rents 125 chairs and 72 people rent both chairs and umbrellas, how many people rent umbrellas?
A. 25
B. 72
C. 97
D. 125
Answer:
25
Step-by-step explanation:
First: 125+72-150 is 47
Chairs: 125-47 is 78 chairs
Umbrellas: 72-47 is 25 umbrellas
Hence, there is 25 people rented umbrellas
Hope this helps!!!
Have a nice day:)
By applying the principle of inclusion-exclusion, we determined that the number of people who rent umbrellas is 97, after accounting for the overlap of customers who rent both chairs and umbrellas.
Explanation:To solve this combinatorial problem, we can employ the principle of inclusion-exclusion. The principle is a way to count the number of elements of each collection, subtracting the overlaps (in this case, people who rent both chairs and umbrellas), and adding the elements that are in neither category if necessary.
Let's define the following terms:
According to the question:
C = 125 (chairs)
B = 72 (both chairs and umbrellas)
The total number of customers, T, is given by:
T = C + U - B
Since the total number of customers is 150, we have:
150 = 125 + U - 72
To find U (the number of people renting umbrellas), we just need to solve for U:
U = 150 - 125 + 72
U = 25 + 72
U = 97
Therefore, the number of people who rent umbrellas is 97.
Thirty one increased by fourteen
Answer:
Thirty-one increased by fourteen OR
31 + 14 is 45
Step-by-step explanation:
First- Line up the numbers
When you add, you want to line up the numbers. It makes it easier to add up.
[tex]\left\begin{array}{ccc}31\\&+\\14\end{array}\right\\---[/tex]
Second - Add the numbers
You want to do the ones side first
31 = Three tens and one
14 = One ten and four ones
So you do 1+4 first
[tex]1+4=5\\\\\mathrm{To\:check...}\:\\5-1=4\\5-1=4\\\\\mathrm{Fact\:Family!}\:[/tex]
Then you go on the tens side
Like I said before...
31 = Three tens and one
14 = One ten and four ones
So now we add 3+1
[tex]1+3=4\\\\\mathrm{To\:check...}\:\\4-3=1\\4-1=3\\\\\mathrm{Fact\:Family!}\:[/tex]
You add a 0 to the sum of the numbers because it is in the tens place...
So 4 becomes 40!
Finally - Add your sums up!
Now we add our 40 from our tens plus our 5from our ones and get
45!
So thirty-one increased by fourteen is...
45!
Hope this helps you!
Have a wonderful night!
How to divide fractions
Answer:
Step-by-step explanation:
When dividing fractions, I use a method called Keep Change Flip. Let's use the example 1/2 divided by 3/4 as an example. First, you have to keep the first fraction the same. This is what you currently have: 1/2 / 3/4. Next, you have to change the divison sign into a multiplication symbol. Now, this is what it should look like: 1/2 x 3/4. Then, you have to flip the fraction 3/4 into 4/3. Now, you have 1/2 x 4/3. Multiply the fraction. If you don't know how to, multiply numerator by numerator, denominator by denominator. You should get 4/6. However, this isn't your final answer. You can simplify this by dividing by 2 to get 2/3. So, your answer is 2/3. Hope this helped you and let me know if you need more help! :D
if a number cube is rolled once, what is the probability that it will stop with a composite number on top
Answer:
50%
Step-by-step explanation:
2, 4, 6 = 3 composite numbers
There are six numbers. Count the number of composite numbers.
Write it as a fraction.
3/6
Then convert it to a percent.
3/6 converts to 50%
To solve the problem, let's start by understanding what a number cube is and what a composite number is.
A number cube is typically a six-sided die, with each side having one of the numbers 1, 2, 3, 4, 5, or 6. Each number has an equal chance of appearing on the top when the cube is rolled.
A composite number is a whole number that has more than two distinct positive divisors. In other words, it can be divided evenly by numbers other than 1 and itself. The smallest positive composite number is 4 because it can be divided by 1, 2, and 4.
Let's list all the positive composite numbers that are on a standard number cube:
- 4 can be divided by 1, 2, and 4.
- 6 can be divided by 1, 2, 3, and 6.
The numbers 2 and 3 are not considered composite numbers, even though they are divisible by numbers other than 1 and themselves; this is because they are prime numbers, having exactly two distinct positive divisors (1 and the number itself).
Now, let's determine the probabilities.
The probability (P) of an event is given by the number of favorable outcomes (f) divided by the total possible outcomes (t), or P = f / t.
For a number cube, the total possible outcomes when rolling the cube are 6 (since there are 6 sides).
The favorable outcomes for rolling a composite number on a number cube are the outcomes where the top number is either 4 or 6.
Thus, f (favorable outcomes for rolling a composite number) = 2 (just the numbers 4 and 6).
Now, we can calculate the probability:
P(composite number) = f / t = 2 / 6
We can simplify this fraction by dividing both the numerator and the denominator by 2:
P(composite number) = 1 / 3
Hence, the probability of rolling a composite number on a standard number cube is 1/3.
What is the P(H,H,H,T,T) on 5 flips of a coin?
I need help
Answer:
The probability for Heads will be 60% or 3/5.
The probability for Tails will be 40% or 2/5.
Step-by-step explanation:
The coin flipped 5 times and landed on Heads 3 times. This shows that out of 5 situations, 3 situations were Heads. Therefore, the probability is 3/5.
The coin landed on Tails 2/5 times the coin was flipped, which is basically the probability.
The probability of getting 3 heads and 2 tails in 5 flips of a coin, in any order, is 0.3125 or 31.25%. This is calculated by figuring out the number of ways to get 3 heads and 2 tails out of 5 flips (10 ways) and dividing that by the total possible outcomes in 5 flips (32 outcomes).
Explanation:The question is asking about the probability of getting three heads and two tails in 5 flips of a fair coin. The order given in the question (H, H, H, T, T) doesn't matter in this case because the flips are independent events.
We calculate the probability by figuring out the number of ways we could get 3 heads and 2 tails out of 5 flips and divide that by the total number of outcomes in 5 flips of a coin. There are 10 ways to get 3 heads and 2 tails out of 5 flips, and there are 32 total possible outcomes in 5 flips of a coin (because 2^5 = 32, as each flip has 2 possibilities, heads or tails).
So, P(H, H, H, T, T) = 10 / 32 = 0.3125 or 31.25%
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A circular puzzle is 20 inches in diameter. All of the pieces are about the same size. You want to know about how many pieces there are in the puzzle.
The problem discusses a circular puzzle of 20 inches in diameter. Without further information on the dimensions of the individual pieces, an exact number of pieces cannot be determined.
Explanation:The subject of this question is Mathematics and it is relevant to a Middle School grade-level. It involves understanding the concept of a circular puzzle and its diameter. Although the information provided about the icosahedron, which is with 20 faces and 12 corners, is fascinating, it is not directly applicable to the question about the circular puzzle.
To solve this problem, you need to consider the size of the typical puzzle piece. Since we don't have that information, we can't provide a precise number of pieces. For example, if each puzzle piece is 2 inches wide then there would be a different number of pieces than if each piece was 1 inch wide.
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The largest possible circle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square feet, of the remaining board? ( where
Answer:
13.76ft²
Step-by-step explanation:
Side of square: d=8ft
Area of board: Sb=d×d=64ft²
Area of circle: Sc=pi×r²=pi×(d/2)²=pi×d²/4=pi×64/4= 16×pi=50.24ft²
Remainin area: Sb-Sc=64-50.24=13.76ft²
Answer:
Area of remaining board is 13.728 feet²
Step-by-step explanation:
Given; Square side length = 8 feet
Therefore, the diameter of the cut out circle = 8 feet, then Radius = 4 feet
The approximate area, in square feet, of the remaining board will be the are of the square minus the ares of the cut out circle.
Area of the square = S²
= (8 feet)²
= 64 feet²
Area of the cut circle = π(4 feet)²
= 3.142 x 16 feet²
= 50.272 feet²
Area of remaining board = Area of the square - Area of the cut circle
Area of remaining board = 64 feet² - 50.272 feet²
Area of remaining board = 13.728 feet²
What is the value of y for the linear equation,
x + x = 2x - 4y +16
Ona piece of paper usa protracter to construct right trangle ABC with AB = 4in. , m∠A90°, and m∠B= 45°
What statement is true about the triangle?
AC = 2 in.
BC = 8 in.
AC = 4 in.
BC = 4 in.
Answer:
AC = 4 in.
Step-by-step explanation:
Since m∠A = 90° and m∠B = 45°, you know that m∠C = 45° ( because you can tell it's an isosceles right triangle ).
This means that legs AB and AC both have to be congruent.
If leg AB is 4 in, then leg AC is 4 in.
How do you solve 3 over 4 •-3 -2.5
Answer:
(¾ * -3) -2.5
equals (-9/4) -2.5
equals -4.75
Step-by-step explanation:
If the mass of an object is 20 g and the volume is 2cm3 what is the density
Answer: 10cm^3 equals density please give briainliest
Step-by-step explanation: formula D=M/V
so D=20/2
D=10cm^3
ssignment
Active
Solving for Angle Measures of Isosceles Triangles
The vertex angle of an isosceles triangle measures 42°. A base angle in the triangle has a measure given by
(2x + 3)" What is the value of x? What is the measure of each base angle?
Each base angle measures
Part a: The value of x is 33°
Part b: The measure of each base angle is 69°
Explanation:
It is given that the vertex angle of an isosceles triangle measures 42°.
The base angle in the triangle has a measure of [tex](2x+3)^{\circ}[/tex]
Part a: To determine the value of x
Since, in an isosceles triangle the base angles are always equal.
Thus, the three angles in an isosceles triangle add up to 180°
Hence, we have,
[tex]42+2x+3+2x+3=180[/tex]
[tex]42+4x+6=180[/tex]
[tex]4x+48=180[/tex]
[tex]4x=132[/tex]
[tex]x=33^{\circ}[/tex]
Thus, the value of x is 33°
Part b: To find the measure of each base angle.
Base angle = [tex](2 x+3)^{\circ}[/tex]
Substituting [tex]x=33^{\circ}[/tex] , we get,
[tex]Base \ angle = (2(33)+3)^{\circ}[/tex]
[tex]=(66+3)^{\circ}[/tex]
[tex]=69^{\circ}[/tex]
Thus, the measure of each base angle is 69°
Answer:
33 and 69 lol funny number
Step-by-step explanation:
PLEASE ANSWER ASAP!!!
Prove the divisibility of the following numbers: 5^5−5^4+5^3 by 7
Answer:
Step-by-step explanation:
[tex]5^5-5^4+5^3 \: \: \:by \:\:\:\:7\\common factor\\\\\frac{5^5-5^4+5^3}{7}\\\\\frac{5^3(5^2-5+1)}{7}\\\\\frac{5^3(5^2-4)}{7}\\\\\frac{5^3(25-4)}{7}\\\\\frac{5^3(21)}{7}\\ \\Simplify\\\\5^3(3)\\[/tex]
what addition does the model below represent?
Answer:
It's the 5+(-3)
Step-by-step explanation:
If T=[23 -38]
[17 -6 ]
then what is –10(T)?
PLEASE HELP
Answer:
B
Step-by-step explanation:
Multiply each term by -10
The matrix in Option B is the value of the given expression.
What is a matrix?'In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.'
According to the given problem,
Given matrix = [tex]\left[\begin{array}{ccc}23&-38\\17&-6\\\end{array}\right] \left[/tex]
On multiplying -10 with this,
Matrix = [tex]\left[\begin{array}{ccc}(23*(-10))&(-38*(-10))\\(17*(-10))&(-6*(-10))\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}-230&380\\-170&60\\\end{array}\right][/tex]
Hence, we can conclude the matrix [tex]\left[\begin{array}{ccc}-230&380\\-170&60\\\end{array}\right][/tex] after multiplying -10 to [tex]\left[\begin{array}{ccc}23&-38\\17&-6\\\end{array}\right] \left[/tex].
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I need help please plot it
Which store is offering the best deal
A.8 for $6
B.10 for $10
C.2 for $3
D¢0.8 each
And why
Answer:
?
Step-by-step explanation:
Solve for x in the equation x - 4 = 7.
A. X = -3
B. x = 11
C. x = 28
D. x = 3
Answer:
B) x = 11
Step-by-step explanation:
Add 4 to both sides
x - 4 + 4 = 7 + 4
x = 11
Steps to solve:
x - 4 = 7
~Add 4 to both sides
x - 4 + 4 = 7 + 4
~Simplify
x = 11 (Option B)
Best of Luck!
i have 5 minss helppppp!!!!!
Answer:that's it
Step-by-step explanation:
Answer:
totalCost = 150 + 12x
$210
-3.25x + 4.1
40x-24y
4(x+5)
6(x+9)
Step-by-step explanation:
let x = day
foodCost = 100 + 5x
gameCost = 50+ 7x
totalCost = 100 + 50 + 7x + 5x
totalCost = 150 + 12x
5 days
150 +12(5) = 150 + 60 = 210
75x+6 -2.5x-1.9
-3.25x + 4.1
What are three numbers that have a sum of 44 if the greatest number is 11 more than the least
a. 1, 15, 12
b. 9, 14, 20
c. 8, 17, 19
d. 11, 16, 22
Find x, the missing side length of the right triangle. can anybody help
Answer:
16.64 units
Step-by-step explanation:
Use Pythagorean Theorem:
a^2+b^2=c^2
14^2+9^2=x^2
196+81=x^2
277=x^2
16.64=x
So the length is about 16.64 units
[tex]2a x 7b^{2}[/tex]
If that 'x' signifies multiplication, then,
[tex]2a * 7b^2 = (2*7)ab^2 = 14ab^2[/tex]
So,
[tex]2a*7b^2[/tex] simplifies to [tex]14ab^2[/tex]
Which of the following has no effect on the monthly payment?
where are the answer choices?
Answer: Vehicle's color
Step-by-step explanation: took the quiz.
Find the equation of the line specified.
The slope is 7, and it passes through ( 8, 6).
Answer:
The answer is A
Step-by-step explanation:
Given that the equation of line is y = mx + c and the slope is 7 :
y = 7x + c
By substituting the coordinate(8,6) into the equation, in order to find the value of c:
6 = 7(8) + c
6 = 56 + c
c = 6 - 56
= -50
y = 7x - 50
(Hope this can help)
What is y +4= -6(2 + 6) written in standard form?
Answer:
y = -52
Step-by-step explanation:
Step 1: Convert to Standard Form
y + 4 = -6(2 + 6)
y + 4 = -12 - 36
y + 4 - 4 = -48 - 4
y = -52
Answer: y = -52