Match the reasons to the statements in the proof.
1. m∠1 + m∠5 = 180° and m∠1 + m∠4=180°
Subtraction property of equality
2. m∠1 + m∠5 = m∠1 + m∠4
Substitution
3. m∠5 = m∠4
If alternate interior angles equal, then lines are ||.
4. Ray YZ is parallel to Ray UV
Given
Answer:
1. [tex]m\angle 1+m\angle 5=180^{\circ}[/tex] and [tex]m\angle 1+m\angle 4=180^{\circ}[/tex]; given
2. [tex]m\angle 1+m\angle5=m\angle 1+m\angle4[/tex]; substitution
3.[tex]m\angle5=m\angle4[/tex]; subtraction property of equality
4. Ray YZ is parallel to ray UV; if alternate interior angles equal , then lines are parallel.
Step-by-step explanation:
Given
[tex]m\angle1+m\angle5=180^{\circ}[/tex]
[tex]m\angle 1+m\angle4=180^{\circ}[/tex]
To prove that YZ is parallel to UV.
Proof:
1.Statement: [tex]m\angle 1+m\angle5=180^{\circ}[/tex] and [tex]m\angle1+m\angle4=180^{\circ}[/tex]
Reason; Given
2. Statement: [tex]m\angle1+m\angle5=m\angle 1+m\angle4[/tex]
Reason: By using substitution property
3.Statement: [tex]m\angle5=m\angle4[/tex]
Reason: Subtraction property of equality.
4.Statement: Ray YZ is parallel to Ray UV
Reason: If alternate interior angles equal, then lines are parallel.
For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).
Figure 1)
a) The area is A = 36( π - 2) ст²
b) The perimeter is P = 6 (π + 2√2) [tex]cm^2[/tex]
Figure 2)
a) The area is A = 576 cm²
b) The perimeter is P = 24(π+2) [tex]cm^2[/tex]
Figure 1)
a) To find the area of the figure 1 we have to do the substraction
The area of figure 1 is equivalent to the area of a triangle less the area of a quarter circle.
The area of quarter circle is equal to
A = 2
we have
r = 12 cm
Put the value r as given
A = (12)2
A = 36 [tex]cm^2[/tex]
Area of a triangle formula is
A = (b)(h)
Given information,
b=12 cm
h = 12 cm
substitute
A = (12) (12)
A = 72 cm²
therefore
The area of the figure is
A = (36π - 72) [tex]cm^2[/tex]
Simplify
A = 36(π -2) [tex]cm^2[/tex]
b)
The perimeter of the figure 1 is equal to the circumference of a quarter circle plus the side AC of triangle
The perimeter of a quarter of circle is formula
C = 2πr
simplify
C = r
we have
r=12 cm
substitute
C = (12)
C = 67 cm
Find the length side AC
Applying the Pythagorean Theorem
[tex]AC^2 = 12^2 + 12^2[/tex]
[tex]AC^2 = 144+ 144\\AC^2 = 288\\AC = \sqrt{288}[/tex]
AC = 12√2 cm
P = (6π +12√2) cm
Taking 6 as a common multiplier we get
P = 6(π+2√2)
The perimeter of the figure 1 is
P = 6(π+2√2) cm
Part 2)
a) As we can see,
The area of a semicircle plus the area of a square less the area of a semicircle equals the area of figure 2.
The figure's area and the square's area are equal.
A = [tex]24^2[/tex]
A = 576 cm²
b) Find the perimeter of the figure 2
we know that
The perimeter of the figure 2 is equal to the length side AB plus the length side DC plus the circumference of two semicircles
The perimeter of the figure 2 is equal to two times the length side AB plus the circumference of one circle
P = 2(AB) + π D
P = 2(24) + π(24)
P = 48 + π(24)
Take out 24
P = 24 (2 + π ) cm
What is the value of x?
Enter your answer, as a decimal, in the box.
The width of Maya’s poster is 2 inches shorter than the length. The graph models the possible area (y) of Maya’s poster determined by its length (x). Which describes what the point (2, 0) represents? The area is 2 if the length is 0. The area is 0 if the length is 2. The length is 2 if the width is 0. The width is 0 if the length is 2.
Sebuah prisma dengan alas berbentuk belah ketupat mempunyai panjang diagonal 24 cm dan 10 cm. jika tinggi prisma 8 cm , maka luas permukaan prisma adalah
helpppppppppppppppppppppppppppppppppppppp
Answer:
Option D is correct.
value of x is 48
Step-by-step explanation:
Solve: [tex]\frac{x}{64}=\frac{3}{4}[/tex]
Cross multiply in the given equation we get;
[tex]x \cdot 4 = 3 \cdot 64[/tex]
Simplify:
[tex]4x = 192[/tex]
Divide both sides by 4 we get;
[tex]\frac{4x}{4}=\frac{192}{4}[/tex]
Simplify:
[tex]x = 48[/tex]
Therefore, the value of x is 48
Which of the following is equal to the rational expression when x 2 or -4? 5(x-2)/(x-2)(x+4)
Answer: 5/x+4
Step-by-step explanation: a pex
HELP!!! Which of the following is not a perfect square trinomial? A. 169 – 26y + y2 B. 81 + 18y + y2 C. 64 + 8y + y2 D. 25 + 10y + y2
A recipe calls for 2/3 cup of water. You have a 1/6 cup measuring cup.
Which statements are true? Check all that apply.
The cup cannot be used to measure the amount of water needed.
2/3 can be rewritten as sixths.
Four full measuring cups are needed.
The numerator and denominator of 2/3 can be multiplied by 2 to get 4/6.
1/6 is equivalent to 2/3.
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Express the sequence given below as a recursively-defined function.
3, 11, 27, 59, 123
*u(0) = 3
u(n + 1) = u(n) + 8
for n = 0, 1, 2, ...
*u(0) = 3
u(n + 1) = 2u(n) + 5
for n = 0, 1, 2, ...
*u(0) = 3
u(n + 1) = 3u(n) + 2
for n = 0, 1, 2, ...
*u(0) = 3
u(n + 1) = 8u(n) + 1
for n = 0, 1, 2, ...
What is the sum of the first eight terms of the series?
(−600)+(−300)+(−150)+(−75)+(−37.5)+...
Round the answer to two decimal places.
−1200.50
−1195.31
−1190.63
−1181.25
The given sequence is a geometric series.
Common ratio can be found as :
(-300/-600) = 0.5
(-150/-300) =0.5
So common ratio is 0.5
First term is -600
The attachment shows the required calculations.
Answer: Sum of eight terms is (-1195.31).
Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12.
Can someone please help me
I would appreciate it please.
I would mark brainliest if its right only.
(Explain)
(Not adding)
Choose the best answer.
For a given distribution the average is 15.5 and the standard deviation is 1.5.
If a sample is taken at random, which value is most likely?
20.2
10.1
16.3
12.9
Answer:
The answer is 16.3
Step-by-step explanation:
For a random distribution with an specific mean and standard deviation, the most probable values are the ones that lie between the ( means + or - standard deviation)
so in this case, the confidence range is:
Low = 15.5-1.5= 14
High = 15.5+1.5= 17
Values that lie between this range are more probable. So in this case 16.3, which is the only value in this range, has higher chance of occuring.
Assume x = 5, y = 6, and z = 8. what is the value of the expression?
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Which solution to the equation 3/a+2 + 2/a = 4a-4/a^2-4 is extraneous?
a= -2
a= -2 and a= 4
neither a= -2 and a= 4
a= 4
Answer:
a=-2 is extraneous solution.
Step-by-step explanation:
Given the equation
[tex]\frac{3}{a+2}+\frac{2}{a}=\frac{4a-4}{a^2-4}[/tex]
we have to find the extraneous solution.
An extraneous solution is a solution to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem.
[tex]\frac{3}{a+2}+\frac{2}{a}=\frac{4a-4}{a^2-4}[/tex]
[tex]\frac{3}{a+2}+\frac{2}{a}=\frac{4a-4}{a^2-4}\\\\\frac{3a+2(a+2)}{a(a+2)}=\frac{4(a-1)}{a^2-4}\\\\\frac{5a+5}{a(a+2)}=\frac{4(a-1)}{a^2-4}[/tex]
On solving, we get
The solution is a=4 and a=-2
Here the solution a=-2 is the valid solution as it makes the denominator 0.
⇒ a=-2 is extraneous solution.
Option 1 is correct.
17+4h+2=1−5h solve for h
The value of h for the expression will be -2.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The given expression is 17+4h+2=1−5h. The value of "h" will be calculated as below:-
17+4h+2 = 1-5h
4h+5h = 1-2-17
9h = -18
h = -2
Therefore, the value of h for the expression will be -2.
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Rewrite this inequality so that one side is 0.
x2 − 2x + 1 < x − 1
To rewrite the inequality so that one side is 0, simply subtract x and add 1 to both sides, resulting in the inequality x² - 3x + 2 < 0.
To rewrite the inequality x² - 2x + 1 < x - 1 so that one side is 0, we follow these steps:
Bring all terms to one side of the inequality by subtracting x and adding 1 to both sides, resulting in x² - 3x + 2 < 0.
Now, the inequality is set up with one side equal to 0, and we can analyze or solve the inequality from here.
Which function represents a reflection of f(x) = 2(0.35)x over the y-axis? h(x) = 2(0.35)x h(x) = –2(0.35)x h(x) = 2(0.35)–x h(x) = 2(–0.35)–x
Answer:
Step-by-step explanation:
c
John Street Barber Shop pays $25 per month for water for the first 8,000 gallons and $3.50 per thousand gallons above 8,000. Calculate the total water cost when the barber shop uses 7,000 gallons, 10,000 gallons, and 13,000 gallons.
Final answer:
The John Street Barber Shop pays a flat rate of $25 for the first 8,000 gallons of water, with an additional charge of $3.50 per thousand gallons above this threshold. Accordingly, the total costs for using 7,000 gallons is $25, for 10,000 gallons is $32, and for 13,000 gallons is $42.50.
Explanation:
The John Street Barber Shop pays $25 per month for the first 8,000 gallons of water and $3.50 per thousand gallons above 8,000 gallons. To calculate the total water cost when the barber shop uses 7,000 gallons, 10,000 gallons, and 13,000 gallons, we follow this methodology:
For 7,000 gallons, since it's below 8,000 gallons, the cost is just the flat rate of $25.For 10,000 gallons, the cost is $25 for the first 8,000 gallons, plus $3.50 for each of the 2,000 gallons above 8,000. This gives $25 + ($3.50 * 2) = $32.For 13,000 gallons, the cost is $25 for the first 8,000 gallons, plus $3.50 for each of the 5,000 gallons above 8,000. This gives $25 + ($3.50 * 5) = $42.50.Thus, the total costs for using 7,000 gallons, 10,000 gallons, and 13,000 gallons are $25, $32, and $42.50 respectively.
What is reconciling your bank statement?
Answer:
Compare your personal records to the bank's statement
East Ascension High School is creating a rectangular parking lot behind the school. The width of the parking lot is 8 more yards than the length. The total area of the parking lot is 65 yds2. What are the length and the width of the parking lot?
A Not enough information
B length = 13 yards width = 21 yards
C length = 5 yards width = 13 yards
D length = 10 yards width = 6 yards
Which expression is equivalent to 6(2m – 1) – 4(m + 8)?
A. 8m – 38
B.8m + 7
C.2m – 38
D.8m + 31
Final answer:
To find the equivalent expression to 6(2m - 1) - 4(m + 8), we first expand and simplify the given expression to 8m - 38, making option A the correct answer.
Explanation:
The question asks which expression is equivalent to 6(2m – 1) – 4(m + 8). To find the equivalent expression, we first expand both terms and then simplify the resulting expression.
First, distribute the 6 in the first expression: 12m - 6.Next, distribute the -4 in the second expression: -4m - 32.Combine like terms: (12m - 4m) + (-6 - 32) which simplifies to 8m - 38.Therefore, the expression that is equivalent to 6(2m – 1) – 4(m + 8) is 8m - 38, which corresponds to option A.
The science club raised money to clean the beach the spent $29 on trashbags and $74 on waterproof boots I still have $47 left how much did they raise
Choose the option that correctly completes the statement.
A triangle has a total of ______ exterior angles.
six
nine
three
Answer:
The correct option would be 6 exterior angles in a Triangle.
NEED HELP ASAP PLEASE HELP
Find m
Select one:
a. 120°
b. 100°
c. 90°
d. 80°
Write an inequality to represent a number decreased by 15 is at least 4
The inequality that represents the number decreased by 15 is at least 4 will be equal to x - 15 ≥ 4.
What is inequality?Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values.
Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.
As per the given data in the question,
Let the number be x.
Number is decreased by 15 which is at least equal to 4.
Then, the inequality will be,
x - 15 ≥ 4
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Which statement is true about the parts of this expression?
7.5y-z/9+50+2y
he constant is 7.5.
The coefficients are 7.5 and -9
The variables are x and y.
the like terms are 7.5y and 2y
Answer:
The answer is, the like terms are 7.5y and 2y.
I just got a 100% on my test
Which expression is equivalent to 8+18a−2+6a? A.24a+6 B.24a + 10 C.8(1+2a)−(2+6a) D.30a
A circle has a radius of 6 in.
What is the exact length of an arc formed by a central angle measuring 45°?
Express your answer using π