The value of w, x, y, and z will be 57°, 57°, 66°, and 57°. Then the value of the expression will be 237°.
What is the triangle?
A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The diagram is given below.
Given ΔABC with BA extended to D, AB = AC and AE bisects ∠DAC.
x = ∠DAE = ∠EAC = 57°
The sum of linear angles is 180 degrees.
∠DAE + ∠EAC + ∠CAB = 180°
57° + 57° + ∠CAB = 180°
∠CAB = 66°
y = 66°
Then the triangle is an isosceles triangle. Then the angle z and w will be equal.
w = z
Then we have
Angle sum of triangle is 180 degrees.
z + w + 66° = 180°
2z = 114°
z = w = 57°
Then the value of the expression will be
⇒ w + x + y + z
⇒ 57° + 57° + 66° + 57°
⇒ 237°
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solve for r a= pi r squared
A farm lets you pick 3 pints of raspberries for $12.00.
a. What is the cost per pint?
b. How many pints do you get per dollar?
c. At this rate, how many pints can you afford for $20.00?
d. At this rate, how much will 8 pints of raspberries cost?
Answer:a.4 dollars per pint
b.4th a pint/ 1 cup per dolllar
c. 5 pints
d.32 dollars
Step-by-step explanation:
2 inequalities that compare -6 and 3
Answer:
Step-by-step explanat ion-6< 3 :
find the mean of the first six multiples of 4
Answer: 14.
Step-by-step explanation:
a circular pizza with a diameter of 8 inches. The pizza is in a square box with side lengths of 8 inches. In square inches, how much of the box is empty?
Use π = 3.14 and round your answer to the nearest hundredth.
Step-by-step explanation:
13.70 square inches of the box is empty
A number is 9 more than another number. Twice the sum of the two numbers is 10. Find the two numbers.
Answer:
7, -2
Step-by-step explanation:
we call the first number "X" and the second one "Y"
X is 9 more than Y! which means we need to add 9 to Y so it'll be equal to X. so: Y+9=X
also 2×(X+Y)=10
you can also write this down as: 2X+2Y=10
now we have:
X=Y+9
2X+2Y=10
you can now put what equals to X in the second Equation:
2(Y+9)+2Y=10 => 2Y+18+2Y=10 => 4Y=10-18 =>Y= -2
the only thing left to do is to put Y= -2 in the first equation:
X= -2+9 => X=7
An algebraic equation is an equation with unknown variables which can be represented using any number of the alphabet.
The two numbers are 7 and -2
Let's represent the unknown numbers which are the unknown variables with the letters
Let the first number = m
The second number = n
A number is 9 more than another number. This statement is represented by the algebraic equation:
m = 9 + n .......... Equation 1
Twice the sum of the two numbers is 10. This statement is represented by the algebraic equation:
2 (m + n) = 10
2m + 2n = 10...................Equation 2
We substitute 9 + n for "m" in Equation 2
2(9 + n) + 2n = 10
18 + 2n + 2n = 10
Subtract 18 from both sides
18 - 18 + 2n + 2n = 10 - 18
4n = -8
Divide both sides by 4
4n/4 = -8/4
n = -2
We solve for m using Equation 1
m = 9 + n
m = 9 + (-2)
m = 9 - 2
m = 7
Therefore, the two numbers are 7 and -2
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Zynga and Walmart which balance sheet items does the two have in common
The State Education Department requires local school districts to keep these records on all students: age, race or ethnicity, days absent, current grade level, standardized test scores in reading and mathematics, and any disabilities or special educational needs the student may have.
Which of the following are categorical (or qualitative) variables in these records?
Current Grade Level
Mathematics Test Score
Disabilities or Special Needs
Reading Test Score
Days Absent
Age
Race or Ethnicity
Answer:
Disabilities or Special Needs, Race or Ethnicity
Step-by-step explanation:
these are categories, while the rest are numbers
According to the given data, the categorical (or qualitative) variables are Disabilities or Special Needs, Race or Ethnicity.
What is categorical (qualitative) variables?A qualitative variable is a categorical variable which is not numerical, it is based on quality that describes the characteristic of an individual.
What is Disability or Special Need?"In clinical diagnostic and functional development, special needs refers to individuals who require assistance for disabilities that may be medical, mental, or psychological."
What is Race?"The belief that some races of people are better than others; unfair ways of treating people of different races"
What is Ethnicity?"An ethnic group or an ethnicity is a grouping of people who identify with each other on the basis of shared attributes that distinguish them from other groups."
As we know each discussed variable Disability or Special Needs, Race, and Ethnicity describes the characteristics of an individual. Hence, Disabilities or Special Needs, Race or Ethnicity are the qualitative variables.
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center =
3. A diameter of a circle has endpoints P(-7,-4) and Q (3,2).
a. Find the center of the circle (hint use midpoint formula)
b. Find the radius. If your answer is not and integer, express in radical form. (hint use
distance formula)
c. Write an equation for the circle.
17
radius=
equation of the circle:
work:
< 2/3
I
>
a. The center of the circle is (-2, -1).
b. The radius of the circle is √136.
c. The equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.
a. To find the center of the circle, we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
In this case, the endpoints of the diameter are P(-7, -4) and Q(3, 2).Applying the midpoint formula:
Midpoint = ((-7 + 3)/2, (-4 + 2)/2)
= (-4/2, -2/2)
= (-2, -1)
Therefore, the center of the circle is at the coordinates (-2, -1).
b. To find the radius of the circle, we can use the distance formula, which calculates the distance between two points (x1, y1) and (x2, y2). The radius of the circle is half the length of the diameter, which is the distance between points P and Q.
Distance = √\([(x2 - x1)^2 + (y2 - y1)^2]\)
Using the distance formula:
Distance = √[(3 - (-7))^2 + (2 - (-4))^2]
= √\([(3 + 7)^2 + (2 + 4)^2]\)
= √\([10^2 + 6^2\)]
= √[100 + 36]
= √136
Therefore, the radius of the circle is √136.
c. The equation for a circle with center (h, k) and radius r is given by:
\((x - h)^2 + (y - k)^2 = r^2\)
In this case, the center of the circle is (-2, -1), and the radius is √136. Substituting these values into the equation:
\((x - (-2))^2 + (y - (-1))^2\) = (√\(136)^2\)
\((x + 2)^2 + (y + 1)^2 = 136\)
Therefore, the equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.
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The original plan for assigning telephone numbers that you investigated in
Applications Task 4 was implemented in
1947. At that time, the supply of numbers was expected to last for 300 years. However, by the 1970s the numbers were already starting to run out. So, the numbering plan
had to be modified. In this task, you will count the number of different phone numbers that were available in 2012.
a. For three-digit area codes, the first digit cannot be a 0 or a 1. Assuming no additional restrictions, how many three-digit area codes are possible under
this plan?
b. Certain area codes are classified as "Easily Recognizable Codes" (BRCs).
ERCs designate special services, like 888 for toll-free calls. The requirement for an ERC is that the second and third digit of the area code must be the same. The first digit again cannot be a 0 or a 1. How many ERCs are there?
c. Consider the seven digits after the area code. As with the area code, the first digit of the three-digit local prefix cannot be a 0 or a 1. The remaining six digits for the local number have no restrictions. How many of these seven-digit phone numbers are possible?
d. Assuming only the 0 and 1 restrictions in Parts a and c, how many ten-digit phone numbers are possible?
a. Assuming no additional restrictions, there are 800 possible three-digit area codes.
b. Considering ERCs, there are 80 ERCs.
c. For the seven digits after the area code, there are \(8 \times 10^6 = 8,000,000\) possible seven-digit phone numbers.
d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers is 800 \(\times\) 8,000,000 = 6,400,000,000.
a. For three-digit area codes, the first digit cannot be 0 or 1.
Assuming no additional restrictions, there are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining two digits (0-9). Therefore, the total number of three-digit area codes possible under this plan is \(8 \times 10 \times 10 = 800.\)
b. For an ERC (Easily Recognizable Code), the second and third digits of the area code must be the same, and the first digit cannot be 0 or 1. There are 8 possibilities for the first digit (2-9) and 10 possibilities for the third digit (0-9).
Since the second digit must be the same as the third digit, there is only 1 possibility.
Therefore, the total number of ERCs is \(8 \times 1 \times 10 = 80.\)
c. For the seven digits after the area code, the first digit of the three-digit local prefix cannot be 0 or 1.
There are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining six digits (0-9).
Therefore, the total number of seven-digit phone numbers possible is 8 * \(10\times 10 \times 10 \times 10 \times 10 \times 10 = 8,000,000.\)
d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers can be calculated by multiplying the number of possibilities for each digit position.
For the area code (part a), there are 800 possibilities.
For the seven digits after the area code (part c), there are 8,000,000 possibilities.
Therefore, the total number of ten-digit phone numbers possible is 800 * 8,000,000 = 6,400,000,000.
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Score: 7.5/50
13/50 answered
Question 15
Annette and Rose went to an orchard to pick pears. Annette picked 8
1
pounds of pears and Rose picked 6
1
pounds. How much more did Annette pick than Rose? Write your answer as a reduced mixed number.
10
Submit Question
Complete Question:
Annette and Rose went to an orchard to pick pears. Annette picked \(8\frac{1}{6}\)
pounds of pears and Rose picked\(6\frac{1}{8}\) pounds. How much more did Annette pick than Rose? Write your answer as a reduced mixed number.
Answer:
Annette picked \(2\frac{1}{24}\) pounds of pears more than Rose
Step-by-step explanation:
Pounds of pears picked by Annette = \(8\frac{1}{6}\)
Pounds of pears picked by Rose = \(6\frac{1}{8}\)
To get the difference in the pounds of pears picked by Annette and Rose, we will do a simple subtraction:
Difference in the pounds of pears picked = \(8\frac{1}{6} - 6\frac{1}{8}\)
\(= 2(\frac{1}{6} - \frac{1}{8})\\= 2\frac{4 - 3}{24} \\= 2\frac{1}{24}\)
825 use each digit once. make the smallest 3digit number
Step-by-step explanation:
Given: To make smallest 3-digit number of 825.
To find: The smallest 3-digit number of 825.
Solution: We can make the smallest 3-digit number of 825 by separating the numbers and arranging it to ascending order. The given number is 825. ...
Final answer: The smallest 3-digit number of 825 is 258.
hope it helps
Answer:
258
Step-by-step explanation:
We are given 3 numbers:
8 2 5
And we are asked to find the smallest 3 digit number using those 3 digits above.
To make the smallest number, place the numbers in value from least to greatest:
2 5 8
This is your 3 digit number: 258.
Hope this helps! :)
If the following data were transformed and points with the coordinates
(x, log(y)) were plotted, what points would be plotted? Round log(y) to three
decimal places.
X
1
2
3
y
12
83
580
If the data were transformed and points with the coordinates
(x, log(y)) were plotted then the points (1, 1.079), (2, 1.919), (3, 2.763) were plotted.
To plot the points with the coordinates (x, log(y)), we need to take the logarithm of the y-values.
Let's calculate the logarithms for the given data:
x y log(y)
1 12 log(12) = 1.079
2 83 log(83) = 1.919
3 580 log(580) = 2.763
Therefore, the points that would be plotted are (1, 1.079), (2, 1.919), (3, 2.763)
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A group of friends is sharing 25 pounds of berries. Type the answer to each question in the boxes below. If each friend received of a pound of berries, how many friends are shar berries? 2 friends If 5 friends are sharing the berries, how many pounds of berries does each receive? pound(s)
Help pls!! I’ll give points and brainliest!!!
Maggie is standing in her front yard and measures the length of the shadow she casts, as well as the shadow, cast by her house. Her shadow is 8 feet long and the shadow of the house is 60 feet, long. If Maggie is 5 feet 2 inches tall how tall is her house to the nearest foot?
Answer:
the answer is 57
Step-by-step explanation:
because you round to the nearest foot which it means that the answer good luck hope this helps
Find the intercepts and the vertical and horizontal asymptotes
The x and y-intercepts of the rational function are; (-3, 0) and (0, -3/25).
The vertical asymptotes of the function are; x = ± 5.
The horizontal asymptotes of the function is f(x) = 0.
What are the intercepts?For x-intercept; let f (x) = 0;
0 = (x + 3) / (x² - 25)
x + 3 = 0; x = -3 or (-3, 0).
For the y-intercept; let x = 0.
f (0) = (0 + 3) / (0² - 25)
= -3/25 or (0, -3/25).
For the vertical asymptotes;
x² - 25 = 0
x² = 25
x = ±5.
For the horizontal asymptote;
Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is; f (x) = 0.
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find the inverse of f(x) =3/x -10
Explanation:
f(x) = 3/x -10
To get the inverse, let's make f(x) = y
y = 3/x -10
interchange y and x:
x = 3/y - 10
make y the subject of formula:
\(\begin{gathered} x\text{ =3/y - 10/1} \\ x\text{ = }\frac{3\text{ - 10y}}{y} \\ \text{cross multiply: } \\ xy\text{ = }3\text{ - 10y} \end{gathered}\)\(\begin{gathered} xy\text{ + 10y = 3} \\ y(x\text{ + 10) = 3} \\ y\text{ = }\frac{3}{x+10} \\ f^{-1}(x)\text{ = }\frac{3}{x+10} \end{gathered}\)1.2 Generate a three-column table where you evaluate how learning takes place according to: • Piaget • Vygotsky • Bruner (15)
While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.
Here's a three-column table evaluating how learning takes place according to Piaget, Vygotsky, and Bruner:
Theorist Approach to Learning Key Concepts
Piaget Constructivism 1. Schema: Individuals actively construct their knowledge through assimilation and accommodation, organizing information into mental structures called schemas. 2. Stages of Development: Learning occurs through cognitive development stages, from sensorimotor to formal operational, where individuals progressively acquire more complex mental abilities. 3. Active Exploration: Children learn best through hands-on exploration and interactions with the physical world.
Vygotsky Sociocultural Theory 1. Zone of Proximal Development (ZPD): Learning takes place within the gap between a learner's actual developmental level and their potential level with guidance from a more knowledgeable other. 2. Social Interaction: Learning is facilitated through social interactions with peers and adults, such as cooperative learning and scaffolding. 3. Cultural Tools: The use of language, symbols, and cultural artifacts plays a central role in cognitive development and learning.
Bruner Constructivism 1. Scaffolding: Instruction should provide support and guidance tailored to the learner's current abilities to help them progress to higher levels of understanding. 2. Discovery Learning: Learners construct knowledge by actively exploring and discovering concepts and relationships on their own. 3. Spiral Curriculum: Learning is organized in a spiral manner, revisiting key concepts and building upon previous knowledge in a progressive and interconnected way.
While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.
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Rewrite as a product of the GCF and another sum 36 + 48
Answer:
72+12
Step-by-step explanation:
Find the next number in the sequence.
25, 36, 49, 64, ...
Answer:
81
Step-by-step explanation:
25, 36, 49, 64, ...
36 - 25 = 11
49 - 36 = 13 = 11 + 2
64 - 49 = 15 = 13 + 2
64 + 15 + 2 = 81
I will show you the question
The given system is
\(\begin{cases}3x+6y=12 \\ x+2y=4\end{cases}\)First, we multiply the second equation by -3.
\(\begin{cases}3x+6y=12 \\ -3x-6y=-12\end{cases}\)Then, we combine the equations
\(\begin{gathered} 3x-3x+6y-6y=12-12 \\ 0=0 \end{gathered}\)This means the system has infinitely many solutions.
Hence, the answer is D.On January 1, 2021, Princess Corporation leased equipment to King Company. The lease term is 12 years. The first payment of $716,000 was made on January 1, 2021. The equipment cost Princess Corporation $5,188,466. The present value of the lease payments is $5,588,516. The lease is appropriately classified as a sales-type lease. Assuming the interest rate for this lease is 9%, how much interest revenue will Princess record in 2022 on this lease? (Round your answer to the nearest whole dollar amount.)
The amount of the interest revenue that Princess will record in 2022 on this lease is:$413,553.82.
Interest revenue
First step
Lease value payments after first payment:
Lease value payments= $5,588,516- $716,000
Lease value payments= $4,872,516
Second step
Lease value payments after second payment:
Lease value payments=$4,872,516+ ($4,872,516×9%) - $716,000
Lease value payments=$4,872,516+$438,526.44-$716,000
Lease value payments=$4,595,042.44
Third step
2022 Interest revenue=$4,643,787.6×9%
2022 Interest revenue=$413,553.8196
2022 Interest revenue=$413,553.82 (Approximately)
Therefore the amount of the interest revenue that Princess will record in 2022 on this lease is:$413,553.82.
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Answer this question as soon as possible please. Thanks!
Step-by-step explanation:
36/6 or it is just 6 depends on if you need it as a fraction or not
60% of 72 is what? Round to the nearest tenth.
Answer:
The answer is 43.2
One die, numbered 1, 2, 3, 4, 5, 6 is rolled. What is the probability of rolling a 1 or a 6?
Answer:
1/3
Step-by-step explanation:
There are 2 different options to get a 1 or a 6 out of 6 total options, so:
2/6 = 1/3.
Where are all the classifications of square root 12
Answer:
Real, irrational/ R, I
Sidenote: Mark me brainliest? Do you agree that anime girls are cute?
Suppose that a scarf company estimates that its monthly cost is
C(a)=500x2 + 300 and its monthly revenue is
R(x) = -0.523 +6002-200+300, where x is in thousands of
scarves sold. The profit is the difference between the revenue and the cost.
What is the profit function, P(x)?
The profit function is P(x) = -500.523x^2 + 600x - 200.
To find the profit function, P(x), we need to subtract the cost function, C(a), from the revenue function, R(x).
Given:
Cost function: C(a) = 500x^2 + 300
Revenue function: R(x) = -0.523x^2 + 600x - 200 + 300
Profit function, P(x), is obtained by subtracting the cost function from the revenue function:
P(x) = R(x) - C(a)
P(x) = (-0.523x^2 + 600x - 200 + 300) - (500x^2 + 300)
Simplifying the expression:
P(x) = -0.523x^2 + 600x - 200 + 300 - 500x^2 - 300
P(x) = -500x^2 - 0.523x^2 + 600x + 300 - 200 - 300
P(x) = -500x^2 - 0.523x^2 + 600x - 200
Combining like terms:
P(x) = (-500 - 0.523)x^2 + 600x - 200
Simplifying further:
P(x) = -500.523x^2 + 600x - 200
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How can you best rearrange the terms in the following expression to create an equivalent expression that would be easier to simplify?
−4(y−5)+2y−77
Answer:
-4y + 20 + 2y - 77
Step-by-step explanation:
Apply the distributed property, so it now looks like this: -4y -(-20) + 2y-77Simplify: -4y + 20 + 2y - 77I hope this helps!
Find the equation of the line that contains the points (2,1) and (6,3). Write the equation in the form y=mx+b and identify m and b
Answer:
y=1/2x+0 m=1/2 b=0
Step-by-step explanation:
You first need to find the slope of this line, the equation for this is.
(y2-y1)/(x2-x1)
In this case it is (3-1)/6-2)
This simplifies to 1/2.
This graph also does not have a +b as when you graph y=1/2x, it already passes through the 2 points shown.