Find the area of a circle with a diameter of 8.
if ABC and GEF are congruent by the ASA criterion, which pair of angles must be congruent
The pair of angles that must be congruent for the given pair of congruent triangles are ∠CAB and ∠GEF.
The ASA criterion states that two triangles are congruent if two angles and the included side of one triangle are equal to the two angles and the included side of the other triangle.
In the figure, we have:
∠ABC = ∠GEF (given)
∠ACB = ∠EGF (included angles)
AC = EG (included side)
Therefore, by the ASA criterion, triangles ABC and GEF are congruent.
The other possible pairs of congruent angles are:
∠ACB and ∠FEG
∠CAB and ∠EGF
∠ABC and ∠GFE
However, none of these pairs of angles are included angles.
Therefore, the only pair of congruent angles that must be congruent is ∠CAB and ∠GEF.
learn more about angles here
brainly.com/question/30147425
#SPJ3
The above question is incomplete, the complete question is:
if ABC and GEF are congruent by the ASA criterion, which pair of angles must be congruent
Attached figure.
the length of a rectangular garden is 5 feet longer than its width. The garden is surrounded by a 2-foot-wide sidewalk. The sidewalk has an area of 76 square feet. Find the dimensions of the garden.
Final answer:
By setting up equations based on the given information about the garden and the sidewalk around it, and then solving for the width, we find that the width of the garden is 5 feet, and its length is 10 feet.
Explanation:
Let's denote the width of the garden as w feet. Therefore, the length of the garden can be represented as w + 5 feet, since it is mentioned that the length is 5 feet longer than its width. Surrounding the garden, there is a 2-foot-wide sidewalk which affects the overall dimensions of the combined area (garden plus sidewalk). The width and length of this entire area would thus be w + 4 and w + 9 respectively, adding 2 feet on each side for the sidewalk.
To find the area of just the sidewalk, which is given as 76 square feet, we first calculate the area of the entire (garden plus sidewalk) rectangle, and then subtract the area of the garden. The equation for the area of the entire rectangle is (w + 4)(w + 9), and for the garden alone, it's w(w + 5). The difference between these areas gives us the area of the sidewalk:
(w + 4)(w + 9) - w(w + 5) = 76
Expanding and simplifying this equation gives us a quadratic equation to solve for w. Simplifying further:
w^2 + 13w + 36 - w^2 - 5w = 76
8w + 36 = 76
8w = 40
w = 5
Therefore, the width of the garden is 5 feet and the length is 10 feet (5 + 5).
Shortest distance from the base of parallelogram to its opposite side is the
Please help me asap will give brainliest
meagan has $1.10 in dimes nickels and pennies she has three times as many nickels as pennies and the number of dimes is two less than the number of pennies how many dimes nickels and pennies dose she have please help
What is the surface area of the triangular prism shown?
A. 860 ft 2
B. 920 ft 2
C. 1,040 ft 2
D. 760 ft 2
The Answer to the problem is B. 920 ft 2
a dinner plate has a diameter of 7 in approximately how many inches is a circumference of the plate
A dinner plate having a diameter of 7 in approximately is given.
The distance around a circle is called the circumference.It is the perimeter of the circle.
The circumference of a circle can be found by multiplying pi ( π = 3.14 ) by the diameter of the circle.
Circumference is a special case of perimeter.
Circumference =[tex] \pi .d [/tex]
Given dinner plate has a diameter of 7 in.
Substituting d=7in we have:
Circumference = [tex] \pi (7)=3.14 (7)=21.98 in [/tex]
A window that is in the shape of a semicircle has a diameter of 28inches. find the area of the window. Round to the nearest tenth
Final answer:
The area of the semicircle shaped window is approximately 307.7 square inches when rounded to the nearest tenth.
Explanation:
The student has asked to find the area of a window in the shape of a semicircle with a diameter of 28 inches. To calculate the area of a semicircle, we first find the radius of the full circle, which is half the diameter, and then apply the formula for the area of a circle, A = πr², before halving it since we want the area of a semicircle.
Find the radius (r) of the semicircle: r = diameter/2 = 28 inches / 2 = 14 inches.
Calculate the area of the full circle: A = πr² = π * (14 inches)².
Halve the area to get the semicircle's area: Semicircle area = A/2.
Using the value of π as 3.14 and rounding to the nearest tenth: Semicircle area ≈ (3.14 * [tex](14)^2[/tex])/2 = (3.14 * 196)/2 = 307.72 inches².
Hence, the area of the semicircle shaped window is approximately 307.7 square inches when rounded to the nearest tenth.
Rachel is packing up some og her old stuff into a box.A box can hold eight pounds.but she only filled ot up two quarters full.how much weight was in the box
the perimeter of an equilateral triangle is 63 inches. if the length of each side is (4x-3), find the value of x
A hiker walks an average rate of 2 miles per hour. Write a multiplication equation to find how long it will take for the hiker to walk 11 miles?
Stephanie is going to summer camp. There are three cabins to which she could be assigned: Pine Cabin, Maple Cabin, or Spruce Cabin. She can be assigned either a top bunk bed or bottom bunk bed.
Answer: The probability of Stephanie being on a top bunk is 50%
The probability of Stephanie being in Spruce Cabin is 3333.3%
The probability of Stephanie being in Pine cabin on bottom bunk is 80%
Step-by-step explanation:
The probability of Stephanie being assigned to the Pine Cabin and a bottom bunk bed is 1/6.
We have,
To find the probability of Stephanie being assigned to a specific cabin and a specific bunk, we need to know the total number of possible outcomes.
In this case, there are 6 possible outcomes because there are 3 cabins and 2 bunk bed options for each cabin:
Pine Cabin, top bunk
Pine Cabin, bottom bunk
Maple Cabin, top bunk
Maple Cabin, bottom bunk
Spruce Cabin, top bunk
Spruce Cabin, bottom bunk
Let's say we want to find the probability of Stephanie being assigned to the Pine Cabin and a bottom bunk bed.
There is only one outcome that satisfies this condition (Pine Cabin, bottom bunk),
So the probability is:
1 outcome / 6 possible outcomes = 1/6
Therefore, the probability of Stephanie being assigned to the Pine Cabin and a bottom bunk bed is 1/6.
We can similarly calculate the probability for any other combination of cabin and bunk bed by counting the number of outcomes that satisfy the condition and dividing by the total number of possible outcomes.
Thus,
The probability of Stephanie being assigned to the Pine Cabin and a bottom bunk bed is 1/6.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ2
The complete questions:
Stephanie is going to summer camp. There are three cabins to which she could be assigned: Pine Cabin, Maple Cabin, or Spruce Cabin. She can be assigned either a top bunk bed or bottom bunk bed.
Find the probability of Stephanie being assigned to the Pine Cabin and a bottom bunk bed.
100 POINTS PLEASE 1. Yared and Luke are wrapping presents. Yared is able to wrap presents at a constant rate of 3 presents every 15 min. Luke is able to wrap presents at a constant rate of 5 presents every 20 min. Each boy has 20 presents to wrap, and the boys started wrapping presents at the same time. (a) How many presents will Yared still need to finish wrapping when Luke has finished wrapping all 20 of his presents? Explain. (b) What percent of his presents will Yared still need to wrap when Luke has finished wrapping presents? Explain.
2. A researcher collected data about the favorite car color of a particular population. He asked 250 people about their favorite vehicle color and the survey revealed the following: 32% of people said blue, 24% of people said white, 20% of people said red, 18% of people said black, and 4% of people said silver.
(a) How many people said their favorite vehicle color was red? Explain.
(b) How many more people said their favorite vehicle color was blue compared to those who said white? Explain.
(c) How many people said their favorite vehicle color was either black or silver? Explain.
3. Haruto was the starting pitcher for his baseball team. In his last two games, the coach kept a close eye on the number of pitches, balls, and strikes he threw.
(a) In the first game recorded, the coach wrote 60%, or 54 pitches, were strikes. Find the total number of pitches Haruto threw in this game.
(b) In the second game recorded, the coach recorded 40%, or 34 pitches, were balls. Find the number of strikes and the total number of pitches he threw in this game.
Answer:
Yared takes 15 minutes to wrap 3 presents, and Luke takes 20 minutes to wrap 5 presents.
I divided 15 by 3 to get 5, and did the same with Luke, and I got 4. Both boys have a total amount of 20 presents to wrap, so I multiplied 5 by 20, to get 100, and I multiplied 4 by 20, and got 80.
I subtracted 100 by 80, and got a 20. Since I am finding information for Yared, I’m going to use 5, I divided 20 by 5, and got 4.
(b) Yared still needs to wrap 20% of his presents when Luke has finished wrapping presents.
Since the total amount of
presents to wrap is 20, I divided that by the total amount of presents that
Yared still needs to finish wrapping, which is 4. 4 divided by 20 is 0.2, and I
multiplied 0.2 by 100, 100 is the whole, and I got 20.
2. (a) 50 people said their favorite color was red.
Since there is 250 people in total, I used the percentage of the color red, which is 20%, and multiply it by 250. 20 divided by 100 is 0.2, and I multiply 0.2 by 250, which got me 50.
(b) The number of strikes and the total number of pitches he threw in this game is 80 total pitches.
Hoped I helped!
Answer:
so have I
1. (a)Yared will still need to finish wrapping 4 presents when Luke finished wrapping all of his own presents.
Yared takes 15 minutes to wrap 3
presents, and Luke takes 20 minutes to wrap 5 presents.
I divided 15 by 3 to get 5, and
did the same with Luke, and I got 4. Both boys have a total amount of 20
presents to wrap, so I multiplied 5 by
20, to get 100, and I multiplied 4 by 20, and got 80.
I subtracted 100 by 80, and got a
20. Since I am finding information for
Yared, I’m going to use 5, I divided 20 by 5, and got 4.
(b) Yared still needs to wrap 20%
of his presents when Luke has finished wrapping presents.
Since the total amount of
presents to wrap is 20, I divided that by the total amount of presents that
Yared still needs to finish wrapping, which is 4. 4 divided by 20 is 0.2, and I
multiplied 0.2 by 100, 100 is the whole, and I got 20.
2. (a) 50 people said
their favorite color was red.
Since there is 250 people in total, I used the percentage of the color red, which is 20%, and multiply it by 250. 20 divided by 100 is 0.2, and I multiply 0.2 by 250, which got me 50.
(b) 20 more people said their favorite vehicle color was blue compared to those who said white.I used the same formula as (a). The percentage of blue is 32%, so I divided 32% by 100, and I got 0.32. I multiplied the total amount of people, which is 250, by 0.32, and I got 80. The total amount of people who said they liked blue is 80. The percentage of people who said they like white is 24%, so I divided 24% by 100, and I got 0.24. I multiplied that to 250, and got 60. The total amount of people who said they liked white is 60. I subtracted 80 to 20, to get 20.
(c) 45 people said their favorite vehicle color was black. I divided 18 by 100, and got 0.18. I multiplied 0.18 by 250. I got 45.
3. (a) The total number of pitches Haruto threw in this game is 90 pitches.
(b) The number of strikes and the total
number of pitches he threw in this game is 80 total pitches.
Hoped I helped!
BRAINLIEST IF CORRECT PLEASE SHOW WORK:)
Evaluate. 8 2/9 −7 1/6
A: 1/18
B: 1 7/18
C: 1 1/3
D: 1 1/18
Draw a picture to show how to find12+37
Find the arc measure ML.
Simplify the following and write your answer in simplest form
Which of the following represents the most accurate estimation of 719 - 348?
A line segment has one endpoint on a circle and one endpoint at the center of the circle. What is the segment called?
A. Diameter
B. Radius
C. Chord
D. Arc
Briana surveys five students from four different classrooms. She asks them about the number of hours they spend on the Internet every day. This is the data from her survey: classroom A: 0, 0, 0, 1, 1 classroom B: 1, 1, 1, 2, 2 classroom C: 2, 3, 3, 3, 4 classroom D: 1, 2, 2, 2, 3 Which classroom's data has the highest center of distribution?
classroom A
classroom B
classroom C
classroom D
Thank you!
Answer:
Classroom C
Step-by-step explanation:
all you do is add it then divide it by 5 and boom
Two numbers are in the ratio of 2 to 3 if the smaller number is 18 the lager number is ___ 21 27 36 54
PLEASE HELP!
Drag a reason to each box to complete this proof.
If 5x-4+13=5 , then x=1/2
Answer:
Combine like terms
Addition property of equality
Division property of equality
Step-by-step explanation:
13x+5x=18x
18x-4=5 negative 4 would become positive and you will as it to 5 to get 9
18x=9 simply divide
The reasons required to complete this question are;
Addition property of equalityCombine like termsDivision property of equalityThis is an equation in which we just need to write the accurate steps on each required side.
We are asked to prove x = 1/2 from 5x - 4 + 13x = 5
Step 1On the statement side, we are given an equation
[tex]5x -4 + 13x = 5[/tex]
On the reason side, we already have our answer as Given
Step 2On the statement side, we have an equation
[tex]18x-4=5[/tex]
On the reason side, we should write down addition property of equality
Step 3
we have an equation
[tex]18x = 9[/tex]
On the reason side, we should write Combine like terms
Step 4
On the statement side, we have an equation
[tex]x = \frac{1}{2}[/tex]
On the reason side, we should write down Division property of equality.
Within the four steps above, we were able to justify and prove how x = 1/2.
The key operations performed are
Addition property of equalityCombine like termsDivision property of equality.Learn more about equations here;
https://brainly.com/question/13729904
circle O has a circumference of 132 feet. what is the approximate area of the circle?
You can use the given circumference of 132 feet to find the radius using the formula C=2πr. Once the radius is found to be approximately 21 feet, use the formula for the area of a circle, being A=πr², to calculate an area of approximately 1386 square feet.
Explanation:To find the area of a circle when you know the circumference, you can use the formula for the circumference of a circle, which is C = 2πr (C is the circumference and r is the radius). From the circumference, we can find the radius.
Let's rearrange the formula for r: r = C / 2π . Plugging in the given value, r = 132 / 2π approximately equals 21 feet.
Next, we use the area of a circle formula A = πr² and plug in the radius to calculate the area. Here, A = π * (21)^2 that gives us an area of approximately 1386 square feet.
Learn more about Area of Circle here:https://brainly.com/question/28642423
#SPJ12
Which number is equivalent to 43/12?
A fraction is a way to describe a part of a whole. The correct option is B.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
What is Mixed Fraction?A mixed fraction is a fraction that contains a whole number and a fraction whose denominator is greater than the numerator. A mixed fraction can be converted as,
2 1/2
= (2×2 + 1)/2
= 5/2
= 2.5
Given that the number that is equivalent to 43/12 can be found as shown below.
43/12
= 3 ⁷/₁₂
= 3 + 7/12
= 3 + 0.58333333
= 3.58333333
[tex]= 3.58\overline3[/tex]
Hence, the correct option is B.
Learn more about Fraction here:
https://brainly.com/question/1301963
#SPJ2
Janica’s lucky number (36) is her birth month multiplied by her birth day. What are some possibilities for her birthday (month and day)? Write an equation that shows the relationship.
How does the volume of a cone change if its radius and height are both tripled? A. B. C. D.
The volume of the cone changes by a factor of 27
How does the volume of the cone change
From the question, we have the following parameters that can be used in our computation:
Volume of a cone
The volume of a cone is calculated using
[tex]V = \frac13\pi r^2h[/tex]
When the radius and height are both tripled, we have
R = 3r
H = 3h
So, the new volume is
[tex]V_2 = \frac13\pi R^2H[/tex]
Substitute the known values into the equation
[tex]V_2 = \frac13\pi (3r)^2 * 3h[/tex]
Evaluate
[tex]V_2 = \frac13\pi 9r^2 * 3h[/tex]
So, we have
[tex]V_2 = \frac13\pi r^2h * 27[/tex]
Recall that
[tex]V = \frac13\pi r^2h[/tex]
So, we have
[tex]V_2 = 27V[/tex]
This means that the volume of the cone changes by a factor of 27
Question
How does the volume of a cone change if its radius and height are both tripled? A. 3 B. 9 C. 27 D. 81
15 POINT QUESTION
Francine solves the system of equations using the linear combination method. 4x+3y=−1
3x−5y=4
Which steps would allow her to eliminate the x terms in the system of equations?
A) Multiply 4x+3y=−1 by 4. Multiply 3x−5y=4 by 3. Add the resulting equations together.
B) Multiply 4x+3y=−1 by −4 . Multiply 3x−5y=4 by 3. Add the resulting equations together.
C) Multiply 4x+3y=−1 by 3. Multiply 3x−5y=4 by −4. Add the resulting equations together.
D) Multiply 4x+3y=−1 by 5. Multiply 3x−5y=4 by 3. Add the resulting equations together.
How to find the surface area of certain 3 dimensional shapes
A bicyclist was traveling from the village to the railroad station with a speed of 15 mph and he was coming back to the village with a speed of 10 mph. Find the distance from the village to the railroad station, if it’s known that it took 1 more hour for the bicyclist to get back to the village.
Since, a bicyclist was traveling from the village to the railroad station with a speed of 15 mph and he was coming back to the village with a speed of 10 mph.
Let the time taken in traveling from village to the railroad station be 't' hours
Distance is calculated by the formula:
[tex] d= s \times t [/tex]
So, the distance traveled from village to the railroad station is:
[tex] d=15 \times t [/tex]
Since, the time taken in traveling from railroad station to the village is 1 hour more = 't+1' hours
So, the distance traveled from railroad station to the village is:
[tex] d=10 \times (t+1) [/tex]
Therefore, distance traveled from village to railroad station is equals to the distance traveled from railroad station to the village.
So, [tex] 15 \times t=10(t+1) [/tex]
[tex] 15t=10t+10 [/tex]
[tex] 5t=10 [/tex]
So, t=2
Therefore, distance from village to railroad station = [tex] 15 \times t [/tex]
= [tex] 15 \times 2 [/tex]
= 30 miles.
Therefore, the distance from village to railroad station is 30 miles.
The distance from the village to the railroad station is 30 miles
Speed is the ratio of distance to time taken. It is given by:
Speed = distance/time
Let d represent the distance from the village to the rail station.
When Going at a speed of 15mph, let us assume he spent a hour, hence:
15 = d/a
d = 15a
When coming at a speed of 10mph, let us assume he spent b hour, hence:
10 = d/b
d = 10b
Therefore:
15a = 10b
But it took 1 more hour for the bicyclist to get back to the village, hence b = a + 1, hence:
15a = 10(a + 1)
15a = 10a + 10
5a = 10
a = 2 hours
d = 15a = 15(2) = 30 miles
Therefore, the distance from the village to the railroad station is 30 miles
Find out more at: https://brainly.com/question/22610586