Answers
Because angles 1 and 2 are adjacent, we will see that the measure of angle 2 is 77°.
How to find the measure of angle 2?Here we know that m∠1 = 103°, and we want to find the measure of angle 2, which is an angle adjacent to angle 1.
That means that if we add their measures, then we will get a plane angle, this means that:
m∠1 + m∠2 = 180°
Then we can write:
103° + m∠2 = 180°
m∠2 = 180° - 103° = 77°
That is the measure of angle 2.
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Related Questions
Steve repairs elevators. When he is called to a job he uses the stairwell to go to the floor on which the elevator is located. In the Modis building, he climbs 22 steps for every 15 ft of horizontal travel. In Sears Tower, he climbs 17 steps for every 7 ft of horizontal travel
Part A: What is the rate of change for each stairwell?
Part B: Which stairwell will be easier to climb? Explain your reasoning
Answers
The rate of change for Modis building stairwell is 0.68 feet per step.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Part A: In the Modis building, he climbs 22 steps for every 15 ft of horizontal travel.
Now, rate = 15/22
= 0.68 feet per step
In Sears Tower, he climbs 17 steps for every 7 ft of horizontal travel
Here, rate 7/17
= 0.41 feet per step
Part B: Sears Tower steps are easy to climb, because rate is lesser than Modis building steps.
Therefore, the rate of change for Modis building stairwell is 0.68 feet per step.
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-3k2g - [8kg2 -(6k2g - 2kg2)]
Answers
Answer:
Step-by-step explanation:
ghjhkvfgfgnfdgn
The function ƒ (x) = (x − 2)³ is transformed to g (x) = (x + 1)³ − 2.
What transformations are performed from function f to function g?
Choose each correct answer.
Function f is translated down 2 units.
Function f is translated to the left 3 units.
Function f is translated to the left 2 units.
Function f is translated up 1 units.
Answers
Function g(x) is function f(x) translated 3 units to the left and 2 units down.
What is the transformation appllied?
Here we know that the function f(x) = (x − 2)³ is transformed to g(x) = (x + 1)³ − 2.
Remember that:
A vertical translation of N units is written as:
g(x) =f(x) + N
if N > 0, the translation is up.
If N < 0, the translation is down.
A horizontal translation of N units is written as:
g(x) =f(x) + N
if N > 0, the translation is left.
If N < 0, the translation is right.
Here we can see that:
g(x) = f(x + 3) - 2
Then we have a translation of 3 units to the right and 2 units downñ.
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For the following right triangle, find the side length A15 B20
Answers
Answer:
Step-by-step explanation:
you first take A15 and square it. Then you take B20 and square it also. Then you add them together and that is your answer. the hypotenuse of a triangle.
Answer: Side length C will be 25
Step-by-step explanation:
C^2 = A^2+B^2
15^2+20^2=C^2
225+400=625
Take square root of 625 to get side C
Solve this system of linear equations:
4x - 2y = 8
y=-2
Step 1: Plot the x-intercept of the first equation.
Equations by Graphing
d
-6-4-2
6
4
2
-2
4
-6
Y
2
4 6
x+
x
y
Answers
A solution to this system of linear equations is (1, -2).
How to graph the solution to this system of equations?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
4x - 2y = 8 ......equation 1.
y = -2 ......equation 2.
Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.
Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant IV and it is given by the ordered pair (1, -2).
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Let X and Y be the following sets:
X = {1, 2, 4, 8, 16, 32}
Y = {}
Which of the following is the set X Y?
Choose 1 answer:
A {}
B
{8, 16, 32}
{1,2,4}
{1, 2, 4, 8, 16, 32}
9
Answers
The set X ∪ Y is the union of sets X and Y, which is the set of all elements that are in either X or Y. In this case, X ∪ Y = X = {1, 2, 4, 8, 16, 32}.
Franny's suitcase weighs 35.7 pounds. Which statement is not true?
A. The 35 represents whole pounds. The 7 represents part of a
pound.
B. The 7 represents more weight than the 5.
OC. The suitcase weighs more than 35 pounds, but less than 36
pounds.
OD. All of these statements are true.
Answers
amit took part in an cycle race .he started at 1:25 pm and reached the finishing line at 1:50 . what was the duration of the race ?
amit took a part in cycle race .he started at 1:25 and he reached finishing lline at 1:50 pm what was the duration of the race .
Answers
Answer:
25 minutes
Explanation:
Subtract the two times to find the duration.
Chloe borrows 800 from the bank for 3 years at simple interest. The interest she is charged after 3 years is 168. Calculate the rate of simple interest charged at this bank. Give the answer as a percentage
Answers
After 3 years the rate of simple interest charged at this to Chloe bank is 7%
We can start by using the formula for simple interest:
Simple Interest = Principal * Rate * Time
where the principal is the amount borrowed, the rate is the interest rate as a decimal, and the time is the duration of the loan in years.
Plugging in the given values, we get:
168 = 800 * Rate * 3
Solving for the rate, we get:
Rate = 168 / (800 * 3) = 0.07
Hence,
The rate of simple interest charged at this bank is 0.07, or 7% as a percentage.
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a steel plate contains 20 bolts. assume that five bolts are not torqued to the proper limit. four bolts are selected at random, without replacement, to be checked for torque. (a) what is the probability that all four of the selected bolts are torqued to the proper limit?
Answers
The probability that all four of the selected bolts are torqued to the proper limit is approximately 0.28.
To calculate the probability that all four of the selected bolts are torqued to the proper limit, we need to find the number of combinations of 4 bolts out of 20 that have been torqued to the proper limit.
Let's call the number of proper bolts n = 20 - 5 = 15.
The number of combinations of 4 proper bolts out of 15 is given by the binomial coefficient nCk, where n is the number of bolts and k is the number of bolts selected.
nCk = n! / (k! (n - k)!).
So, the number of combinations of 4 proper bolts out of 15 is:
15C4 = 15! / (4! (15 - 4)!) = 15! / (4! 11!) = 1365.
Therefore, the probability of selecting all 4 proper bolts out of 20 is:
P = number of combinations of 4 proper bolts / number of combinations of 4 bolts = 1365 / 20C4 = 1365 / 4845 = 0.28
So, the probability that all four of the selected bolts are torqued to the proper limit is approximately 0.28.
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If , which equation describes the graphed function? A. y = f(-x) − 3 B. y = -f(x) + 3 C. y = -f(x) – 3 D. y = f(-x) + 3
Answers
The equation that describes the graphed function is -
g(x) = - f(x) - 3.
What is root function?A root function in mathematics is given as -
y = [tex]$\sqrt[n]{x}[/tex]
We can further write the function as -
y = [tex]$x^{\frac{1}{n} }[/tex]
Given is the graph of the function as shown in the image attached.
We can write the function f(x) as -
f(x) = √x
Inverting the f(x) across the {x} axis, we can write -
- f(x) = - √x
After downward translation, we can write g(x) as -
g(x) = - f(x) - 3
Therefore, the equation that describes the graphed function is -
g(x) = - f(x) - 3.
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Virat has 200 metres of wire, correct to the nearest metre.
he cuts the wire into n peices of length 3 metres, correct to the nearest 20 centimetres
Answers
The number of wires that cut from of 200 meters is 66 meters 66 centimeters.
What are the nearest two places?
The second place to the right of the decimal point, or the hundredth place, is used to round a decimal number to two decimal places. For instance, you can round 2.83620364 to two decimal places as 2.84 and 0.7035 to two decimal places as 0.70.
Given the length of the wire is 200 meters.
Assume that he cuts n pieces of length 3 meters.
The length of n pieces is 3n.
Therefore the equation is
3n = 200
n = 200/3
n= 66.66
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023) You are the owner of a AT&T store that
has two employees working at all times.
The first employee scheduled to work next
Wednesday makes $10.50 per hour and
averages $50 per day for commision. The
other person that is scheduled earns
$10.50 per hour and averages $60 per day
for commision.
i) Write a function that predicts your
expected payroll for the day.
+12
ii) Next Wednesday the store is going to
be open for 5 hours. How much do you
expect to pay your employees?
Answers
(i) The function that predicts your expected payroll for the day is,
For first person; y = $50 + $10.50x
For second person; y = $60 + $10.50x
Where, y is total amount and x is number of working hours.
(ii) In Wednesday; The amount expect to pay your employees is,
For first person;
⇒ y = $102.50
For second person;
⇒ y = $112.50
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The first employee scheduled to work next Wednesday makes $10.50 per hour and averages $50 per day for commission.
And, The other person that is scheduled earns $10.50 per hour and averages $60 per day for commission.
Let total amount earn = y
And, Number of working hours = x
Hence, We can formulate;
The function that predicts your expected payroll for the day is,
For first person;
⇒ y = $50 + $10.50x
For second person;
⇒ y = $60 + $10.50x
And, For 5 hours, the amount is,
For first person;
⇒ y = $50 + $10.50x
⇒ y = 50 + 10.50 × 5
⇒ y = 50 + 52.50
⇒ y = $102.50
For second person;
⇒ y = $60 + $10.50x
⇒ y = 60 + 10.50 × 5
⇒ y = 60 + 52.50
⇒ y = $112.50
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Describe a sequence of transformations that exhibits the similarity between the pair of figures shown.
Answers
Answer:
Reflection across the x-axis followed by dilation by a scale factor of with the center of dilation at the origin
Step-by-step explanation:
Rectangle EFGD has vertices at points E(-6,8), F(0,8), G(0,1) and D(-6,1).
1 transformation - reflection across the x-axis with the rule
So, the image rectangle E''F''G''D'' has vertices with coordinates
2 transformation - dilation by a scale factor of with the center of dilation at the origin. This transformation has the rule
Thus,
These are exactly vertices of rectangle E'F'G'D'.
2b (3a – c) + 12 ac –b^{2}[/tex]
Answers
The value of the equation is A = 6ab - 2bc + 12ac - b²
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = 2b ( 3a - c ) + 12ac - b² be equation (1)
On simplifying the equation , we get
A = 2b ( 3a ) - 2b ( c ) + 12ac - b²
On further simplification , we get
A = 6ab - 2bc + 12ac - b²
Hence , the equation is A = 6ab - 2bc + 12ac - b²
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Suppose the water level of a river is 34 feet and that it is receding at a rate of 0.5 feet per day. Write an equation for the water level, y, after x days. In how way days will the water level be 26 feet?
The equation is......
It will take.....days for the water level to be 26 feet.
Answers
The equation is y = (-0.5)x + 34 and it will take 16 days for the water level to be 26 feet.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
Let the number of days = x, and the water level = y.
Given that,
Water level of river = 34 ft (initial value/y-intercept)
Rate of change = -0.5 ft per day (slope)
The equation of the line is given as:
y = mx + c
where, m is the slope
c is the y-intercept.
Substituting the values we have:
y = (-0.5)x + 34
The number of days in which the water level will reduce to 26 ft is:
26 = (-0.5)x + 34
26 - 34 = -0.5x
x = 16 days.
Hence, it will take 16 days for the water level to be 26 feet.
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The isosceles right triangle reflection to prove ASA congruence
Answers
A line of reflection in a triangle can be any line that acts as a mirror image, such that the reflected image of the triangle is congruent to the original triangle.
This line is perpendicular to the plane of the triangle and bisects the angle between the two sides that are being reflected.
How we used the reflection ruleTo be sure that each point was reflected across this line, we apply the reflection rule.
The reflection rule states that the distance from a point to the line of reflection is equal to the distance from its reflection to the line of reflection. This ensures that the reflected image of the triangle is congruent to the original triangle.
In an isosceles right triangle, two of its sides are congruent. This means that it satisfies the Angle-Side-Angle (ASA) congruence theorem. The ASA theorem states that if two triangles have two congruent angles and a congruent side between them, then the two triangles are congruent.
In addition to satisfying the ASA congruence theorem, an isosceles right triangle also satisfies the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Finally, the reflection of a triangle is considered a rigid motion, as it preserves the size and shape of the triangle.
Rigid motions do not change the lengths of the sides or the angles between them. They only change the position of the triangle in space. In the case of reflection, the triangle is flipped over the line of reflection, but its size and shape remain unchanged
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Isosceles Right Triangle Reflection to prove ASA Congruence
Answer the following questions:
What line of reflection did you choose for your transformation?
How are you sure that each point was reflected across this line?
What reflection rule did you apply to your triangle?
What other properties exist in your triangle? Discuss at least two theorems you learned about in this module that apply to your triangle. Make sure to show evidence by discussing your triangle's measurements.
Did your triangle undergo rigid motion? Explain why.
If the _ of a parallelogram are perpendicular and a diagonal _opposite angles then the parallelogram is a _.
Answers
The distance between two towns is 600km,correct to the nearest 10km
A car takes 8 hours 40minute, correct to the nearest 10 minute, to travel this distance
Calculate the lower bound for the average speed of the car in km/h
Answers
Answer:
Below
Step-by-step explanation:
rate X time = distance
rate = distance / time <=====we want minimum of this so make denominator as large as possible and numerator as small as possible
distance = 595 KM ( rounds up to 600 km)
time = 8 hr 44 min rounds down to 8 :40 you could make it 8:44.99)
595 km / (8 + 44.99/60) hr = 68 km/hr
what expressions can be used to calculate the total price of a DVD that cost d dollars if the tax rate is 7.5%
Answers
total_price = d + (d * (7.5/100))
or
total_price = d * (1 + (7.5/100))
In the first expression, we calculate the cost of the tax by multiplying the cost of the DVD (d) by the tax rate (7.5/100) and then add that amount to the cost of the DVD to get the total price.
In the second expression, we express the total price as the cost of the DVD (d) multiplied by the sum of 1 and the tax rate (7.5/100). This is equivalent to the first expression and gives us the same result
10 x 10 divide 5.6 x 5
Answers
Answer: 4
Step-by-step explanation:
The function
y
=
f
(
x
)
y=f(x) is graphed below. Plot a line segment connecting the points on
f
f where
x
=
−
4
x=−4 and
x
=
1.
x=1. Use the line segment to determine the average rate of change of the function
f
(
x
)
f(x) on the interval
−
4
≤
x
≤
1.
−4≤x≤1.
Answers
The change in y is equal to f ( 1 ) − f ( − 4 ) f(1) - f(-4). The change in x is equal to 1 − ( − 4 ) = 5. 1-(-4) = 5.
Therefore, the slope of the line segment connecting the two points is f ( 1 ) − f ( − 4 ) 5 f(1) - f(-4)/5, which is equal to the average rate of change of the function f ( x ) f(x) on the interval − 4 ≤ x ≤ 1. −4≤x≤1.
The volume V (in cubic feet) of the pyramid is given by F(x)=-4
The function (x) = (3x) gives the volume (in cubic feet) of the pyramid when x is measured in yards. Write a rule for W.Find and interpret W(5)
Answers
The volume is 3315 cubic feet.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given polynomial function is V(x)=x³-4x.
Here, W(x)=V(3x)
Replace x by 3x in the function V(x)=x³-4x, we get
V(3x)=(3x)³-4(3x)
V(3x)=27x³-12x
W(x)=27x³-12x
Replace x by 5 in the function W(x)=27x³-12x, we get
Now, W(5)=27(5)³-12(5)
= 27×125-60
= 3375-60
= 3315 cubic feet
Hence, the volume is 3315 cubic feet.
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"Your question is incomplete, probably the complete question/missing part is:"
A polynomial function V(x)=x³-4x that represents the volume of the right triangle pyramid when measured in cubic feet.
The function (x) =(3x) gives the volume (in cubic feet) of the pyramid when x is measured in yards.
Find a function W(x) that gives us the volume when measured in yards also to find W(5).
The graph represents the amount of money, in thousands, that you make over a
time period of years. According to the graph, what is the original price you invested?
Answers
Answer:
$2,000
Step-by-step explanation:
The initial investment price is given by the y-value where the graph intersects the y-axis
This is at y = 2
Since the scale is in thousands of $, that would mean $2,000 as the original price
John brings $15 to the candy store. He buys a bag of jelly beans for $4 and plans to buy some chocolate that costs $5 per pound. He wrote the inequality 4+5x≤15 to solve for all the possible values of x , the number of pounds of chocolate John could buy
Answers
John can buy any amount of chocolate between 0 and 2.2 pounds (rounded to one decimal place) and still have enough money to buy the jelly beans.
John brings $15 to the candy store and buys a bag of jelly beans for $4. He plans to buy some chocolate that costs $5 per pound. Let x be the number of pounds of chocolate John could buy.
The cost of the chocolate John plans to buy is $5 per pound, so the total cost of x pounds of chocolate is 5x. John's total budget is $15, so he must have enough money to buy the jelly beans and the chocolate. Therefore, the inequality that represents this situation is:
4 + 5x ≤ 15
To solve for x, we can begin by isolating the variable on one side of the inequality. We can do this by subtracting 4 from both sides of the inequality:
5x ≤ 11
Next, we can isolate x by dividing both sides of the inequality by 5:
x ≤ 11/5
Therefore, the possible values of x, the number of pounds of chocolate John could buy, are all real numbers less than or equal to 11/5. However, since John cannot buy a negative amount of chocolate, we must also restrict x to be greater than or equal to 0. Therefore, the solution to the inequality is:
0 ≤ x ≤ 11/5
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Translate the following sentence into an equation "the sum of 8 times x and 4 is 68"
Answers
Answer:
The equation is:
8x + 4 = 68
and the solution is:
x = 8
Step-by-step explanation:
The equation is:
8 time x and 4 is 68
8x+4 = 68
Solve:
8x + 4 - 4 = 68 - 4
8x + 0 = 64
8x = 64
x = 64/8
x = 8
Check:
8*8 + 4 = 68
Question 6 of 10
The function a(b) relates the area of a trapezoid with a given height of 12 and
one base length of 9 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid.
a(b)=12.b+9
2
Which equation below represents the inverse function b(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
OA. b(a)=2-9
6
OB. b(a)=+9
6
O C. b(a)=8-6
O
D. b(a)= +6
Answers
Answer:96
Step-by-step explanation:
uwu yay
The required equation represents the inverse function b(a), which takes the trapezoid's area is B(a) = a/6 - 9.
What is a trapezoid?A trapezoid is a quadrilateral having two parallel bases and one set of other sides called as legs.
We have been given that the trapezoid's base is nine and its height is twelve.
As an outcome, 'b' is the base's parallel side.
The function that represents the trapezoid's area is given by:
A(b) = [12(b + 9)]/2
Let's consider A(b) = a
Then, a = [12(b + 9)]/2
Now solving for b, we get
2a = 12(b + 9)
a = 6(b + 9)/2
a = 6b + 54
6b = a - 54
b = (a - 54)/6
b = a/6 - 9
Assuming that the length of the side parallel to the base 'b' = B(a), the equation will be:
B(a) = a/6 - 9
Thus, the correct answer would be option A. B(a) = a/6 - 9.
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On a certain hot summer's day, 455 people used the public swimming pool. The daily prices are $1.75 for children and $2.50 for adults. The receipts for admission totaled $952.25. How many
children and how many adults swam at the public pool that day?
Answers
The number of children and adults that swam at the public pool are 247 and 208 respectively
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.
Represent the number of children by x and the number of adult by y
this means;
x+y = 455 equation 1
1.75x + 2.5y = 952.25 equation 2
using substitution method,
x = 455-y
substitute 455-y for x in equation 2
1.75(455-y) + 2.5y = 952.25
796.25-1.75y+2.5y = 952.25
0.75y = 952.25-796.25
0.75y = 156
divide both sides by 0.75
y = 156/0.75
y = 208
substitute 208 for y in equation 1
x = 455-208
x = 247
therefore the number of children and adults in the pool are 247 and 208 respectively.
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what is the solution to the number sentence k - 1.6 / 6 = 5.4
Answers
Answer:
k = 48.4
Step-by-step explanation:
[tex] \frac{k - 16}{6} = 5.4 \\ 6 \times \frac{(k - 16)}{6} = 5.4 \times 6 \\ k - 16 = 32.4 \\ k = 32.4 + 16 \\ k= 48.4 [/tex]
there are c different types of coupon, and each coupon obtained is equally likely to be any one of the c types. find the probability that the first n coupons which you collect do not form a complete se
Answers
The probability that the first n coupons which you collect do not form a complete set is (c^n - (c-1)^n) / c^n.
To find the probability that the first n coupons collected do not form a complete set, we need to count the number of ways in which the first n coupons can be collected so that they do not form a complete set and divide it by the total number of ways in which n coupons can be collected, which is c^n.
Let S be the set of all possible complete sets of coupons. The number of ways in which the first n coupons can form a complete set is the number of ways to choose any one of the complete sets in S, multiplied by the number of ways to order the coupons within that set. There are (c choose n) ways to choose n coupons out of c, and for each complete set of n coupons, there are n! ways to order them. Therefore, the number of ways to choose n coupons that form a complete set is (c choose n) * n!.
The total number of ways to choose n coupons out of c is c^n.
So, the probability that the first n coupons collected do not form a complete set is:
P = 1 - [(c choose n) * n! / c^n]
Alternatively, we can count the number of ways in which the first n coupons can be collected so that they do form a complete set. There are (c-1)^n ways to choose n coupons out of c-1 types of coupons, and for each set of n coupons, there is exactly one way to add the missing coupon to form a complete set. Therefore, the number of ways to choose n coupons that form a complete set is c^n - (c-1)^n.
So, the probability that the first n coupons collected do not form a complete set is:
P = (c^n - (c-1)^n) / c^n
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