Which of the following triangles can be proven similar through AA?
Answer:
C (Your chosen answer) is correct
Step-by-step explanation:
AA (Angle-Angle) Similarity postulate is exactly what it sounds like: Two triangles can be proven similar if they have two congruent angles.
We can tell what angles are congruent through the markings:
(A) and (B) can be immediately be eliminated, because one or more tringle in the pair does not have enough markings to prove congruency, so therefor cant be proven to be similar.
(D) is a little more difficult to decipher, but when you look closely, you can tell that the markings are not identical, so therefor the angles are not congruent.
(C) is correct because it has identical markings which makes the angles congruent.
Hope this helps :)
Option C is correct because it has identical markings which makes the angles congruent by AA.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Two triangles can be proven similar if they have two congruent angles.
Option A and B are not similar through AA because one or more tringle in the pair does not have enough markings to prove congruency, so therefore they are not similar.
Option C is correct because it has identical markings which makes the angles congruent by AA.
Hence, Option C is correct because it has identical markings which makes the angles congruent by AA.
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Because their posters were so popular, Ms. Ironperson and Mr. Thoro decided to hold a class on how to make a super hero capes. Tickets were sold to cover the costs of the materials for each cape.
The admission fee for children was $2.00 and $4.50 for adults. 3250 people showed up and $9625 was collected.
How many adults and children attended the class?
If x denotes the number of children and y denotes the number of adults, what are the equations needed to solve this problem?
Answer:
2,000 children attended and 1,250 adults attended.
The equations needed to solve these problems are:
[tex]x+y=3250\\2.00x+4.50y=9625[/tex]
Step-by-step explanation:
First, set up a system of equations. Let "x" equal the number of children who attended the class and let "y" equal the number of adults who attended the class.
Our two equations to use to solve this problem are:
[tex]x+y=3250\\2.00x+4.50y=9625[/tex]
Then, I took the first equation and I isolated the x-variable:
[tex]x+y=3250\\x+y-y=3250-y\\x=3250-y[/tex]
Then, I substituted (3250-y) in for the x-variable in the second equation and I solved for "y":
[tex]2.00x+4.50y=9625\\2.00(3250-y)+4.50y=9625\\6500-2.00y+4.50y=9625\\6500+2.50y=9625\\6500-6500+2.50y=9625-6500\\2.5y=3125\\\frac{2.5y}{2.5}=\frac{3125}{2.5}\\ y=1250[/tex]
Next, I substituted the y-value that I got in for the y-variable in the first equation:
[tex]x+y=3250\\x+1250=3250\\x+1250-1250=3250-1250\\x=2000[/tex]
Finally, now that I have found both the x-value and the y-value, I will use the values to check in both of my equations:
Equation 1:
[tex]x+y=3250\\2000+1250=3250\\3250=3250[/tex]
It works for Equation 1.
Equation 2:
[tex]2.00x+4.50y=9625\\2.00(2000)+4.50(1250)=9625\\4000+5625=9625\\9625=9625[/tex]
It works for Equation 2.
Therefore, the values work.
That means that 2000 children attended the class and 1250 adults attended the class.
which of the following is a fragment sentence?
A. I scheduled my exam for Sunday; my plan is to spend four or five hours studying on Saturday.
B. When the neighbors have a party, it's difficult to find a place to park on the street.
C. The county animal shelter is having an adoption drive at the park this weekend.
D. Passengers should stay seated. Until the train comes to a complete stop in the station.
Answer: D
Step-by-step explanation:
they shouldn’t be two different sentences they should blend together. “Until the train comes to a complete stop in the station.” is not a complete sentence making it a dependent clause which means it needs its independent clause to complete that sentence
please help me with this
Answer: C
Step-by-step explanation:
The formula to find average rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]. Since the problem is asking for the average rate of change from the second to fifth year, we plug in a=2 and b=5.
[tex]\frac{f(5)-f(2)}{5-2}[/tex]
f(5)=420.4
f(2)=408.04
[tex]\frac{420.4-408.04}{5-2}=4.12[/tex]
Now, we get 4.12 dollars per year for the average rate of change.
seven less than the quotient of nineteen and a number
Step-by-step explanation:
Let the number is n. We need to write an expression for "seven less than the quotient of nineteen and a number"
The quotient of nineteen and a number is [tex]\dfrac{19}{n}[/tex] and 7 less than this is [tex]\dfrac{19}{n}-7[/tex]
Now if n = 2, put the value of n in above expression,
[tex]\dfrac{19}{n}-7=\dfrac{19}{2}-7\\\\=\dfrac{5}{2}\\\\=2.5[/tex]
So, the value of the above expression is 2.5 at n = 2.
Answer:
19/n-7
and 2.5
Step-by-step explanation:
If u actually read the other guy's work
I was born in the month of February, what is the probability that I was born in a non-Leap year) before
Valentine's Day?
Answer:
Hey there!
February has 28 days on a non leap year.
Valentine's day is February 14th.
Thus, in the 28 days, you can be born on any day between day 1 and day 13.
You have a 13/28 probability to be born before Valentine's day.
Let me know if this helps :)
6. For every 12 burpees Melinda did, she did 20 squats.
If Melinda did a total of 128 squats and burpees, how many did she do of each?
(20 Points)
48 burpees & 80 squats
48 burpees & 82 squats
46 burpees & 80 squats
46 burpees &. 82 squats
Answer:
48 burpees & 80 squats
Step-by-step explanation:
Let burpees= x
Let squat = y
For every 12 burpees Melinda did, she did 20 squats.
X/y =12/20
20x= 12y
X= 0.6y
Melinda did a total of 128 squats and burpees
X+y= 128
But x= 0.6y
0.6y +y= 128
1.6y= 128
Y= 128/1.6
Y= 80
X+y= 128
X+80= 128
X=128-80
X= 48
Solve for x x-23=17 NEED TO KNOW FAST PLEASE!!!!
Answer:
x = 40
Step-by-step explanation:
Adding 23 to both sides gives us:
x - 23 + 23 = 17 + 23
x = 40
Answer:
[tex] \boxed{ \bold{ \bold{ \sf{x = 40}}}}[/tex]Step-by-step explanation:
[tex] \sf{x - 23 = 17}[/tex]
Move constant to right hand side and change it's sign
[tex] \sf{x = 17 + 23}[/tex]
Add the numbers
[tex] \sf{x = 40}[/tex]
Hope I helped!
Best regards!!
Given P=0.15M +20. Is P a function of M? explain your choice using the definition of a function
Answer: Yes, this is a linear function between P and M.
Step-by-step explanation:
We can define a function as a relation between two or more variables, like y = f(x).
This function, maps the elements x (the input) into elements y (the output).
We have a rule for a function: Each input x can be mapped into only one output y.
In this case, we have:
P = 0.15*M + 20.
Let's prove that each value of M is related to only one value of P.
Suppose that, for a given M0, we have:
0.15*M0 + 20 = p1
and also for M0, we have:
0.15*M0 + 20 = p2
This means that p1 = p2, so we can not have different outputs for the same input.
This is a linear relation, so each value of M is related to only one value of P.
Then this is a function P(m) = 0.15*M + 20.
How do we find the perimeter?
Answer:
perimeter = 4z - 8
Step-by-step explanation:
perimeter of a square box = 4 times the side
P = 4 ( z - 2)
P = 4z - (4*2)
P = 4z - 8
please help I'm almost done
Answer:
-4x-7
Step-by-step explanation:
Add like terms, aka the Xs and the normal numbers
Can someone please help me
Answer:
D. -2/5
Step-by-step explanation:
Slope= [tex]\frac{delta Y}{Delta X} =\frac{-2}{5}[/tex]
Answer:
D
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (14, - 2)
m = [tex]\frac{-2-4}{14+1}[/tex] = [tex]\frac{-6}{15}[/tex] = - [tex]\frac{2}{5}[/tex] → D
6/x = 2x+4/5
Multiply each side by the common denominator to find the
quadratic equation equivalent to this equation.
Answer:
5x² + 2x - 15 = 0
Step-by-step explanation:
Given
[tex]\frac{6}{x}[/tex] = 2x + [tex]\frac{4}{5}[/tex]
Multiply through by 5x ( common denominator )
30 = 10x² + 4x ( subtract 30 from both sides )
0 = 10x² + 4x - 30 ( divide through by 2 )
0 = 5x² + 2x - 15 , that is
5x² + 2x - 15 = 0
Solve for x: -1 < x + 3 < 5
O 2 < X < 8
0-4 < x < 2
O 2 > >8
04 >x>2
Answer:
B) -4<x<2
Step-by-step explanation:
-1 < x + 3 < 5
-3 -3 -3
-4 < x + < 2
We have some unknown number x and we're adding 3 to it getting x+3
To isolate x, we need to undo the operation happening to it. So we need to undo the addition of 3. We'll subtract 3 from all sides
-1 < x+3 < 5
-1-3 < x+3-3 < 5-3 ... subtract 3 from all sides
-4 < x+0 < 2
-4 < x < 2 ... answer is choice BThe linear function f is defined by f(x)= cx + d, where c and d are constants. If f(50) = 27,000 and f(100)= 38,000, what is the value of c?
Answer:
c = 220Step-by-step explanation:
f(x) = cx + d
For the first equation
f(50) = 27,000
Substitute the value of x that's 50 into the expression
That's
50c + d = 27,000
For the second equation
f(100) = 38,000
Substitute the value of x that's 100 into the expression
We have
100c + d = 38,000
Subtract the first equation from the second one to eliminate d
That's
100c - 50c + d - d = 38,000 - 27,000
50c = 11,000
Divide both sides by 50
We have the final answer as
c = 220Hope this helps you
What is the value that of the expression when n=3
Answer:
We need to find the value of the expression when d=3. Substitute d=3 in the above expression. Hence, the value of the expression at d=3 is 73.
this is similar answer of your question
a manager of a clothing store always orders 2 small shirts and 3 large shirts for every 4 medium shirts ordered. the manager plans to order 24 medium shirts. How many small shirts and large shirts will the manager order? Show you work.
Answer:
He will have 12 small shirts and 18 large shirts.
Step-by-step explanation:
How I know this is because to get from 4 to 24 you have to multiply by 6, so I multiplied 6x2 and got 12, and I also multiplied 6x3 and got 18.
The manager plans to order 24 medium shirts. he will have 12 small shirts and 18 large shirts.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
It is given that a manager of a clothing store always orders 2 small shirts and 3 large shirts for every 4 medium shirts ordered.
The manager plans to order 24 medium shirts.
We need to get from 4 to 24.
So we have to multiply by 6,
so multiplied 6 x 2 = 12,
and multiplied 6 x 3 = 18.
Therefore, The manager plans to order 24 medium shirts. he will have 12 small shirts and 18 large shirts.
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The mean GPA of student in a course at UCDevis is 3.2 with a standard deviation of 0.3. What percent of student in a course have a GPA between 2.9 and 3.8?
Answer:
81.86%
Step-by-step explanation:
We are given that the mean GPA of students in a course at UC Davis is 3.2 with a standard deviation of 0.3.
Assuming that the data follows normal distribution.
Let X = GPA of students in a course at UC Davis
So, X ~ Normal()
The z score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = population mean GPA = 3.2
= standard deviation = 0.3
Now, the probability that the students in the course have a GPA between 2.9 and 3.8 is given by = P(2.9 < X < 3.8)
P(2.9 < X < 3.8) = P(X < 3.8) - P(X 2.9)
P(X < 3.8) = P( < ) = P(Z < 2) = 0.97725
P(X 2.9) = P( ) = P(Z -1) = 1 - P(Z < 1)
= 1 - 0.84134 = 0.15866
The above probability is calculated by looking at the value of x = 2 and x = 1 in the z table which has an area of 0.97725 and 0.84134 respectively.
Therefore, P(2.9 < X < 3.8) = 0.97725 - 0.15866 = 0.8186
Hence, 81.86% of students in the course have a GPA between 2.9 and 3.8.
what is x equal to: 3x=1
Answer:
x = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Step 1: Solve
We can divide 3 from both sides to get "x" by itself
[tex]3x=1\\\frac{3x}{3} =\frac{1}{3} \\x = \frac{1}{3}[/tex]
Therefore x = [tex]\frac{1}{3}[/tex]
Answer:
[tex]\large \boxed{x=\frac{1}{3} }[/tex]
Step-by-step explanation:
[tex]3x=1[/tex]
We need to solve for the x variable. It is best to isolate the variable on one side of the equation to find the value that makes the equation true.
Divide both sides of the equation by 3.
[tex]\displaystyle \frac{3x}{3} =\frac{1}{3}[/tex]
Simplify the equation.
[tex]\displaystyle x=\frac{1}{3}[/tex]
Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the coordinate planes and the plane 8x+y+z= 4.
Answer:
[tex]\displaystyle \int\limits^{\frac{1}{2}}_0 \int\limits^{4 - 8x}_0 \int\limits^{4 - 8x - y}_0 {} \, dz \ dy \ dx = \frac{4}{3}[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Multivariable Calculus
Integration
IntegralsFubini’s Theorem [Box]: [tex]\displaystyle \iiint_R{f(x, y, z)} \, dV = \int\limits^{b_1}_{a_1} \int\limits^{b_2}_{a_2} \int\limits^{b_3}_{a_3} {f(x, y, z)} \, dx \, dy \, dz[/tex]
Volume Formula: [tex]\displaystyle V = \iiint_D \, dV[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
Given: Tetrahedron Solid
Function: 8x + y + z = 4 and coordinate planes x, y, and z
Step 2: Find Volume Pt. 1
Find limits of integration for each variable.
[z] Solve for z: [tex]\displaystyle z = 4 - 8x - y[/tex][y] Set z = 0 [z coordinate plane]: [tex]\displaystyle 0 = 4 - 8x - y[/tex][y] Solve for y: [tex]\displaystyle y = 4 - 8x[/tex][x] Set y = 0 [y coordinate plane]: [tex]\displaystyle 0 = 4 - 8x[/tex][x] Solve for x: [tex]\displaystyle x = \frac{1}{2}[/tex]Define: [tex]\displaystyle \left[\begin{array}{ccc} 0 \leq z \leq 4 - 8x - y \\ 0 \leq y \leq 4 - 8x \\ 0 \leq x \leq \frac{1}{2} \end{array}[/tex]Step 3: Find Volume Pt. 2
Substitute in variables [Volume Formula]: [tex]\displaystyle V = \int\limits^{\frac{1}{2}}_0 \int\limits^{4 - 8x}_0 \int\limits^{4 - 8x - y}_0 {} \, dz \ dy \ dx[/tex][z Integral] Integrate [Integration Rules and Properties]: [tex]\displaystyle V = \int\limits^{\frac{1}{2}}_0 \int\limits^{4 - 8x}_0 {z \bigg| \limits^{4 - 8x - y}_0} \ dy \ dx[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle V = \int\limits^{\frac{1}{2}}_0 \int\limits^{4 - 8x}_0 {4 - 8x - y} \ dy \ dx[/tex][y Integral] Integrate [Integration Rules and Properties]: [tex]\displaystyle V = \int\limits^{\frac{1}{2}}_0 {\Big( 4y - 8xy - \frac{y^2}{2} \Big) \bigg| \limits^{4 - 8x}_0} \ dx[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle V = \int\limits^{\frac{1}{2}}_0 {\Bigg[ 4(4 - 8x) - 8x(4 - 8x) - \frac{(4 - 8x)^2}{2} \Bigg]} \ dx[/tex][Integrand] Simplify: [tex]\displaystyle V = \int\limits^{\frac{1}{2}}_0 {8(2x - 1)^2} \ dx[/tex]Integrate [Integration Rules and Properties]: [tex]\displaystyle V = \frac{4(2x - 1)^3}{3} \bigg| \limits^{\frac{1}{2}}_0[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle V = \frac{4}{3}[/tex]∴ the volume of the given tetrahedron solid is equal to 4/3.
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Topic: Multivariable Calculus
Unit: Triple Integrals
2. Apples cost $0.99 per pound. Aaliyah has a
coupon for $0.50 off her purchase. She pays
a total of $2.14 for apples. Let a represent
the pounds of apples that Aaliyah buys.
Equation:
Solve it to find how many pounds of apples she purchased.
Type here
Solve the equation and write the equation
Answer:
a= about 2.7 pounds of apples
Step-by-step explanation:
2.14=0.99a-0.50
2.64=0.99a
In Littletown, the probability that a baseball team goes to the city playoffs is 0.30. the probability that the team goes to the state playoffs given that the team goes to the city playoffs is 0.20.
Answer:
0.06
Step-by-step explanation:
The probability they go to the city playoffs is:
0.30 (or 30%)
Then assuming they have gone to the city playoffs, the probability they go to the state playoffs is 0.20 (or 20%)
The probability of both events is the product:
P(city then state) = 0.30 * 0.20 = 0.06
Answer:
0.06
Step-by-step explanation:
Donte is planning on repairing bikes and skateboards to save up money for
college. He can repair up to 2 bikes per day and 4 skateboards per day. If b
represents the number of bikes and s represents the number of
skateboards, write the expression that represents the total number of
things Donte can repair in a single day. *
Answer:
The expression is T = b+s
Step-by-step explanation:
If b represents the number of bikes and s represents the number of skateboards Donte is planning to repair to save up money for college, the total number of things he can repair in a day will be expressed as the sum of number of bikes and number of skateboards i.e b+s = T
Given that He can repair up to 2 bikes per day, the total and 4 skateboards per day this means that b = 2 and s = 4
Total number of thing's he can repair in a day given this amount T = 2 + 4 = 6 things
The Widget Manufacturing industry has approximately 123.2 thousand Jobs in 2020, but has expected to decline at an average annual rate of 4.4 thousand jobs per year from 2020 to 2030. Assuming this holds true, what will be the industry's percent of change from 2020 to 2030?
Answer:
35.71%
Step-by-step explanation:
So, let's determine the number of jobs the industry will have in 2030.
So, in 2020, the industry has 123,200 jobs.
Each year, the industry loses 4,400 jobs.
Thus, by 10 years in (2030), the industry would have lost (4,400)(10) or 44,000 jobs.
This means that in 2030, there will only be 123,200-79200 jobs left.
Now, percentage change is given by:
[tex]PC=\frac{New-Old}{Old}\cdot100\%[/tex]
The new value is 79200 and the old value is 123,200. Substitute them:
[tex]PC=\frac{(79200)-(123200)}{123200}\cdot100\%\\[/tex]
Use a calculator. Simplify:
[tex]PC=\frac{-44000}{123200}\cdot100\%\\ PC\approx-0.3571\cdot100\%\\PC\approx-35.71\%[/tex]
If the result is negative, then it's a decrease. Therefore, the percentage change from 2020 to 2030 is approximately 35.71%
Answer:
The answer is 35.71%
Step by step explanation
In 2020 the industry has 123,200 jobs.
Each year, the industry loses 4,400 jobs.
Thus, by 10 years in (2030), the industry would have lost (4,400)(10) or 44,000 jobs.
This means that in 2030, there will only be 123,200-79200 jobs left.
Now, percentage change is given by:
New−Old
⋅100%
The new value is 79200 and the old value is 123,200. Substitute
123200
(79200)−(123200)
⋅100%
Simplify:
PC≈−0.3571⋅100%
PC≈−35.71%
the percentage change from 2020 to 2030 is 35.71%
h.
R(x) = kx – 2x^2 ; R(1/4)
R(-1/4)
find k.
Answer:
k=0
Step-by-step explanation:
R(x)=kx-2x²
R(1/4)=k(1/4)-2(1/4)²=k/4-1/8
R(-1/4)=k(-1/4)-2(-1/4)²=-k/4-1/8
R(1/4)=R(-1/4)
k/4-1/8=-k/4-1/8
k/4+k/4=1/8-1/8
2k/4=0
2k=0
k=0
Describe a situation that could be modeled with the ratio 4: 1.
Answer:
Stacey wanted to build a model airplane to display in her room. The scale ratio she planned to use was for every 4 feet the airplane was, the model airplane would be 1 inch. If the plane was 250 feet long, how long would the model airplane be?
Here, I used the ratio 4 : 1 as a scale in the problem.
Any help? I don’t get this q can anyone help me do this
For number 5 - .3 ( 3.60 ÷ 12 = .3)
For number 6 - .32 ( 2.56 ÷ 8 = .32)
For number 7 - 2 ( 2.36 ÷ 2 = 1.18)
What is the solution to this equation? 4x = 124 A. X= 120 (B. x = 41 C. X= 496 D. X = 31
Answer:
D. X = 31
Step-by-step explanation:
[tex]4x = 124 \\ x = \frac{124}{4} \\ x = 31[/tex]
Lets say you have a bunch of pennies that you are dividing into different groups. How many pennies could you have when you break the pennies into groups of 2 , you have 1 penny left over
Answer: We have an odd number of pennies.
Step-by-step explanation:
So we have N pennies.
When we wan to divide the N pennies into groups of 2, we have a penny left over.
This means that N is not divisible by 2.
The problem is that there are infinite natural numbers that are not divisible by two, this is the set of odd numbers.
And remember that an odd number can be written as:
N = 2*k + 1.
where k is an integer.
Then we want to divide this by 2 (divide N into groups of 2)
we have:
N/2 = (2*k + 1)/2 = 2*k/2 + 1/2 = k + 1/2.
So we have k groups of 2 pennies, and a penny leftover that we can not divide into two.
David uses drawing software to rotate the regular hexagon about its center. Through which angle measures can he rotate the hexagon to map it onto itself? Select each correct answer. 30° 45º 60° 120° 180°
Answer:
60, 120 and 180.
Step-by-step explanation:
It maps onto itself every 60 degrees.
So as they are multiples of 60 it will map onto itself at 120 and 189 degrees also.
The measure of the angle by which David can rotate the hexagon to map it onto itself is 60°, 120°, and 180°. The correct options are C, D, and E.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
Given that David uses drawing software to rotate the regular hexagon about its center. Now, since the measure of the center angle of a hexagon made by any of its sides is 60°.
Further, if the hexagon is rotated by any angle that is divisible by 60° then it will result in the same hexagon.
Hence, the measure of the angle by which David can rotate the hexagon to map it onto itself is 60°, 120°, and 180°.
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