Find the value of k the diagram is not to scale.
Answer:
[tex]k=73[/tex]
Step-by-step explanation:
We have been given a triangle. We are asked to find the value of k for our given triangle.
We will use angle sum property to solve for k. The angle sum property states that all angles of triangle add up-to 180 degrees.
[tex]k+62^{\circ}+45^{\circ}=180^{\circ}[/tex]
[tex]k+107^{\circ}=180^{\circ}[/tex]
[tex]k+107^{\circ}-107^{\circ}=180^{\circ}-107^{\circ}[/tex]
[tex]k=73^{\circ}[/tex]
Therefore, the value of k is 73.
The value of [tex]\angle{k}[/tex] is [tex]\fbox{\begin\\\ \bf 73^{\circ}\\\end{minispace}}[/tex].
Further explanation:
Consider, the given triangle as [tex]\triangle{ABC}[/tex] shown in figure 1.
Now, the value of [tex]\angle{A}[/tex] is 62 degree, the value of [tex]\angle{B}[/tex] is 45 degree and the value of [tex]\angle{C}[/tex] is [tex]k[/tex] .
From the property of the triangle, we know that sum of angles of a triangle is equal to 180 degree.
Now, for [tex]\triangle{ABC}[/tex] it can be written as follows:
[tex]A+B+C=180[/tex] ……(1)
Substitute 62 for [tex]A[/tex], 45 for [tex]B[/tex] and [tex]k[/tex] for [tex]C[/tex] in equation (1) to obtain the value of [tex]k[/tex].
[tex]\begin{aligned}62+45+k&=180\\107+k&=180\\k&=180-107\\k&=73\end{aligned}[/tex]
Thus, the value of angle [tex]k[/tex] is [tex]\fbox{\begin\\\ \bf 73^{\circ}\\\end{minispace}}[/tex].
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Answer Details:
Grade: Middle School
Subject: Mathematics
Chapter: Triangle
Keywords: triangle, similar, similarity, ratio of sides, right triangle, similar triangle, ratio of sides, equal angles, square of hypotenuse, sum, square of legs, sum of square of legs, sum of angle of triangle, property of triangle, triangle ABC.
How to work this out ?
Answer:
The solution is (-3, -2).
Step-by-step explanation:
Please note that if you simply add these 2 equations together, 9x - 9x = 0, and you are then left with -5y = 10. Thus, y = -2. Subbing -2 for y in the first equation, we get 9x - 8(-2) = -11, or 9x + 16 = -11.
Subtracting 16 from both sides, we get 9x = -27, so that x = -3.
The solution is (-3, -2).
Explain the differnce between function and relation and the relationship between the domain and the range of a function.
A relation is a set of numbers that have a relationship through the use of a domain and a range, while a function is a relation that has a specific set of numbers that causes there to be only be one range of numbers for each domain of numbers. All functions are relations, but all relations are not functions.
Given two sets [tex] A [/tex] and [tex] B [/tex], the "starting" set is called the domain, while the "landing" set is called the codomain.
With that being said, a relation is any way you can associate any number of elements in the domain with every number of elements in the codomain.
A function has more restriction: you can associate one and only one output for every input.
If you visualize this with arrows linking domain and codomain, in order for a relation to be a function, only one arrow can start from each point in the domain.
The domain is thus the set of elements from whence an arrow starts. The range is the subset of the codomain, given by the elements that are reached by at least one arrow.
BEST ANSWER GET TO BE BRAINLYEST+82pts
Estimate the area and perimeter. Each square represents 9 yd2.
area: about 22 yd2; perimeter: about 81 yd
area: about 22 yd2; perimeter: about 27 yd
area: about 198 yd2; perimeter: about 243 yd
area: about 198 yd2; perimeter: about 81 yd
d im pretty sure
hope this helps
To estimate the area and perimeter, multiply the number of 9 yd2 squares by 9 for the area and count the edge squares for the perimeter, considering that a square yard is 3 feet by 3 feet.
To estimate the area and perimeter of the figure where each square represents 9 yd2, we need to count the total number of squares for the area and the length of the edges in units of squares for the perimeter. If the figure has 22 full squares, then the area is 22 multiplied by 9 yd2, which equals 198 yd2.
To find the perimeter, count the number of squares along the outer edge of the figure, and multiply by the side length of each square. Assuming that the side length of each square is 3 yards (since a square yard is 3 feet by 3 feet, and 1 yard equals 3 feet), if the perimeter in squares is 27, then the perimeter in yards would be 27 yd.
The function f(x)=2×5x can be used to represent the curve through the points (1,10), (2,50) , and (3,250) what is the multplicative rate of change of the function?
f(x) = 2(5)ˣ
You can tell from the given equation that (5) is the multiplicative rate of change because 5 is the value being raised to the x-power.
Let's see if that is true:
x y
1 10 (10 x 5 = 50) so next y-value should be 50.
2 50 (50 x 5 = 250) so next y-value should be 250.
3 250
Can you calculate what the next ccordinate will be? (4, ____) (250 x 5 = 1250)
Answer: 5
You bought 5 pounds of hamburger meat, and you want to make quarter pounders (each weigh .25 of a pound). How many quarter pounders can you make? Show your work and explain your reasoning.
You can make 20 quarter pounders based on the information provided. You can show your work by dividing 5 by .25. You need to make both of these a fraction by doing 5/1 x 1/4. This leading you to get 20 making this your answer.
PL has endpoints P(4, −6) and L(−2, 1).
The segment is translated using the mapping (x, y) → (x + 5, y).
What are the coordinates of P’ and L’?
P’(9, -6), L’(-2, 1)
P’(4, -6), L’(3, 1)
P’(9, -6), L’(3, 1)☺
P’(9, -1), L’(3, 6)
i just took the assignment and the was correct
have a good day
Does This Table Represent a function? Why Or Why Not?
Answer: The correct option is
(A) No, because one x-value correspond to two different y-values.
Step-by-step explanation: We are given to check whether the table represent a function or not.
From the table, we note that
the corresponding values of x and y in form of ordered pairs are
(x, y) = (2, 1), (2, 4), (3, 4), (4, 2) and (5, 5).
We know that a set of ordered pairs (x, y) represents a function of no value of x correspond to more than one one value of y.
But, in the given table, when the value of x is 2, then we are getting two different values of y, 1 and 4.
That is, one value of x correspond to two different values of y.
Thus, the given table DOES NOT represent a function, because one x-value correspond to two different y-values.
Option (A) is CORRECT.
An expression is shown below:
square root of 18 plus square root of 2
Which statement is true about the expression?
It is rational and equal to 3.
It is rational and equal to 4.
It is irrational and equal to 3 multiplied by the square root of 2.
It is irrational and equal to 4 multiplied by the square root of 2.
The expression 'square root of 18 plus square root of 2' is irrational and equal to 3 multiplied by the square root of 2.
Explanation:The expression square root of 18 plus square root of 2 is irrational and equal to 3 multiplied by the square root of 2. To simplify the expression, we can't combine the square roots. Therefore, the expression remains in the form of irrational number multiplied by another irrational number.
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Multiply x5 by x2:
A. x7
B. x4
C. x10
D. x3
E. x2.5
A [tex]x^{7}[/tex]
add the exponents when multiplying
[tex]x^{5}[/tex]× [tex]x^{2}[/tex] = [tex]x^{5+2}[/tex] = [tex]x^{7}[/tex]
To multiply x5 by x2, you add the exponents, resulting in x7 (option A). This operation follows the laws of exponents in algebra.
When asked to multiply x5 by x2, you are performing an operation in algebra known as exponentiation. According to the laws of exponents, when you multiply two exponential terms with the same base, you add the exponents. Therefore, x5 multiplied by x2 is x7 because 5 + 2 equals 7. The correct answer is A. x7.
Solve x42=37 x 42 = 3 7 using two different strategies. Explain each strategy.
Given equation : [tex]\frac{x}{42}=\frac{3}{7}[/tex].
Strategy 1: We can cross mutiply both sides remove fraction form.
On cross multiplication, we get
x * 7 = 3 * 42
7x = 126.
Dividing both sides by 7, we get
x = 18.Strategy 2: We can find least common denominator(lcd) of both sides and multiplying both sides by that lcd to get rid denominators from both sides.
LCD of 42 and 7 is 42.
Therefore, multiplying both sides by 42, we get
[tex]42\times \frac{x}{42}=42\times\frac{3}{7}[/tex]
x = 6 * 3
x = 18.What do you call it when a plane comes down in garbage heap
It is called "trash landing". :)
This is a show of word play which sounds similar to “crash landing” (trash/crash), crash landing is actually an organized landing made by an airplane because of a crisis containing a fast approaching or continuous danger to the well being and activity of the flying machine, but in this case as the plane land in garbage the word “crash” is replaced by “trash” giving a humorous meaning to the phrase.
Hope this helped :)
A crash landing describes a plane coming down in a garbage heap, whereas a stall refers to the loss of lift on an airplane's wings, which may not lead to a crash. The term 'Vomit Comet' is used for an aircraft simulating weightlessness in a controlled fall, different from a crash scenario.
When a plane comes down in a garbage heap, it can be referred to as a crash landing in a less formal context, especially if the aircraft is damaged in the process. In aviation, a stall is a condition in which the airplane's wings lose lift due to an insufficient angle of attack, but it does not necessarily result in a crash. Engine failure, which people often confuse with a stall, does not always result in a plane coming down immediately; pilots are trained to handle such situations and aim for a safe landing. In training simulations, astronauts and pilots may experience controlled falls to mimic various scenarios, such as the 'Vomit Comet' used for simulating weightlessness. However, such controlled descents are carefully managed to avoid accidents.
Environmental aspects can also be considered when relating a plane's descent to garbage heaps. For example, the way resources are depleted and environmental sinks become overwhelmed, as mentioned in 'The Tragedy of the Commons,' can be analogous to how an overloaded trash can at a concert spills over, drawing a parallel to the ecological impacts of mishandled waste.
I'll Mark The First To Answer And Work Shown Brainliest!!!!!!!! PLEASE HELP ASAP
In 2005, there were 12,000 students at Beacon High. In 2010, there were 12,250. What is the rate of change in the number of students?
a. 250/yr
b. 50/yr
c. 42/yr
d. 200/yr
Answer:
Step-by-step explanation:
(2005, 12,000) (2005, 12,000)
x1 y1 x2 y2
m= (12,250-1200) / (2010-2005) = 250/5 = 50/1 = or 50
Use the fractions to write and evaluate a multiplication expression that represents 70% of 400. Compare the answer to the one you got using the model.
Answer:
[tex]70\% \text{ of } 400=280[/tex]
Step-by-step explanation:
To find : Use the fractions to write and evaluate a multiplication expression that represents 70% of 400.
Solution :
Expression 70% of 400 is written as,
[tex]70\% \text{ of } 400=\frac{70}{100}\times 400[/tex]
[tex]70\% \text{ of } 400=70\times 4[/tex]
[tex]70\% \text{ of } 400=280[/tex]
Therefore, [tex]70\% \text{ of } 400=280[/tex]
the price p of a clubs membership is $30 foran enrollment fee and $12 per week w tobe a member .Write a function
The function would be
p = $30 + $12w
or
p = $12w + 30
The function representing the total cost of the club membership is p(w) = 12w + 30, where 'w' is the number of weeks.
Explanation:The student is essentially asking to write a function which represents the cost of a club membership based on a fixed fee and a weekly cost. This is an example of a linear function in the form of y = mx + b. In this case, 'y' is the total cost 'p', 'm' is the weekly cost $12 (w), 'x' is the number of weeks, and 'b' is the fixed enrollment fee $30.
Thus, the function representing the total cost of the club membership is p(w) = 12w + 30. This equation can be used to find the total cost of the club membership for any number of weeks 'w'.
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Please help quickly thanks :)
(0, 0) → t = 0, w = 0 → w = 0 · 0
(1, 4) → t = 1, w = 4 → w = 1 · 4
(2, 8) → t = 2, w = 8 → w = 2 · 4
(3, 12) → t = 3, w = 12 → w = 3 · 4
Answer: w = 4tIsaac takes 5 minutes to ride his bike down the hill to school and 10 minutes to ride up the hill from school. He attends school monday through friday. How many minutes does he spend biking to and from school in two weeks? Write an equation to model your work.
Answer:150 minutes
Step-by-step explanation:
Given
Issac take 5 minutes to ride his bike down the hill to school
and 10 minutes to ride up the hill from school .
So it takes 15 min each day to and from school
He attends school monday through friday
so 5 days in a week
for 5 days it takes [tex]15\times 5=75 minutes[/tex]
for 2 weeks
[tex]75\times 2=150 minutes [/tex]
How to solve this problem?
The answer should be 1y and -6y
Marcy job 0.8 mile on Wednesday and 0.9 mile on Thursday how far did she jog on the two days
Marcy jogged 1.7 miles total. Hope I could help!!
To solve the equation t² - t = 12 by factoring, you would use t(t - 1) = 12 t(t - 1) - 12 = 0 (t - 4)(t + 3) = 0
t^2-t=12
t^2-t-12=0
(t-4)(t+3)=0
t=4, -t^2-t=12
t^2-t-12=0
(t-4)(t+3)=0
t=4, -t^2-t=12
t^2-t-12=0
(t-4)(t+3)=0
t=4, -t^2-t=12
t^2-t-12=0
(t-4)(t+3)=0
What type of lines are these? Y = 2x + 4 and 2y = -4x + 10
ANSWER
The lines are two intersecting lines. They intersect` at the point [tex](\frac{1}{4}, \frac{9}{2})[/tex]
EXPLANATION
To determine which type of lines, we look for the slopes of the two lines and compare them to see whether they are parallel or perpendicular.
The first line is [tex]y=2x+4--(1)[/tex].
This line is already in the form;
[tex]y=mx+c[/tex], which is referred to as the slope intercept form, where [tex]m=2[/tex] is the slope.
The second line is
[tex]2y=-4x+10[/tex]
Dividing through by 2 gives;
[tex]y=-2x+5--(2)[/tex]
This implies that, this line also has a slope of [tex]-2[/tex].
Since the two slopes are not the same,the lines are not parallel.
Also the the product of the two slopes, [tex]-2\times 2 \ne -1[/tex], hence the two lines are not perpendicular.
Adding equation (1) and (2) gives;
[tex]2y=9[/tex]
[tex]\Rightarrow y=4.5[/tex]
Putting [tex]y=4.5[/tex] in equation (1) gives
[tex]4.5=2x+4[/tex]
[tex]\Rightarrow 0.5=2x[/tex]
[tex]\Rightarrow x=\frac{1}{4}[/tex].
Hence the two lines intersect` at the point [tex](\frac{1}{4}, \frac{9}{2})[/tex]
An electronis store had 20% off sale. If a sterreo originally cost 125, how much
A store clerk has 45 shirts to pack in boxes. Esch box hold 6 shirts what is the fewest boxes the clerk will need to pack akk the shirts
what expressions is the prime factorization of 360?
Answer,
Prime[1] = 2, Prime[2] = 3, Prime[3] = 5
Hope this helps :-)
A certain arithmetic sequence has this explicit formula for the nth term: an = 11 + (n – 1)(4) The same sequence has this recursive formula: an = an–1 + What number belongs in the blank space in the recursive formula?
a.15
b.11
c.3
d.4
Answer:
I would say D
Answer:
4
Step-by-step explanation:
A certain arithmetic sequence has this explicit formula for the nth term:
[tex]a_n = 11 + (n- 1)(4)[/tex]
Substitute n = 1
[tex]a_1 = 11 + (1- 1)(4)[/tex]
[tex]a_1 = 11 [/tex]
Substitute n =2
[tex]a_2 = 11 + (2- 1)(4)[/tex]
[tex]a_2 = 15[/tex]
[tex]d= a_2-a_1=15-11=4[/tex]
So,[tex]a_2=a_1+d=11+4=15[/tex] --1
Substitute n = 3
[tex]a_3 = 11 + (3- 1)(4)[/tex]
[tex]a_3 = 19[/tex]
[tex]a_3=a_2+d=15+4=19[/tex] ---2
So, with 1 and 2
Recursive formula : [tex]a_n=a_{n-1}+d[/tex]
Since d is 4
So, the number belongs in the blank space in the recursive formula is 4.
Subtract the following fractions.6/11 - 3/11=
Note that they have the same denominator (11). Because of this, just subtract across
6/11 - 3/11 = 3/11
3/11 is your answer
hope this helps
The answer is 3/11. Because of the common denominators it is 6-3.
Write 5 numbers that round to 360 when rounded to the nearest ten
Look at the diagram and the following information to find the value of x.
Note: T is the midpoint of .
PT = 5x + 3 and TQ = 48.
A:x=9
B:x=10
C.x=10.2
D.x=8
Answer: x=9
Step-by-step explanation:
Customer buys 17.01 in gas and requests one five dollar [$5] lottery ticket, two one dollar [$1] lottery tickets, and one [$3] lottery ticket. He gives you two winning tickets to be redeemed: one for ($5) and the other for ($2). How much change would he receive from a $100 bill?* $20.01 $72.01 $74.99 $79.99 have 1 case of soap bars and there are 150 bars in a case. You use 300 bars of soap per day. How many cases do you need to order to have enough for 7 days?* 11 12 13 14
#1
Answer:
$79.99
Step-by-step explanation:
Add Up All Charges
17.01 + 5 + 2 + 3 = 27.01
Subtract For Winning Lottery Tickets
27.01 - 5 - 2 = 20.01
Subtract Total From $100
100 - 20.01 = 79.99
#2
Answer:
14.
Step by Step Explanation:
Find Out How Many Bars You Use In 7 Days
300 * 7 = 2100
Divide By The Number Of Cases
2100 / 150 = 14
PLEASE Help!! 20 Points!
Explain the difference between algebraic expressions and equations.
An Expression is a group of numbers, variables, and operators. An equation is described as a mathematical statement.
Hope this helps