Answers
First, let's complete the angles in the triangle. Remember that the sum of the angles in a triangle is 180 degrees.
73 + 90 + x = 180
163 + x = 180
x = 17
So, the angle that completes the triangle is 17 degrees. If we look at that angle in the triangle and the one adjacent to it, we can see that those two angles form a linear pair (or are supplementary, both meaning that they add up to 180 degrees).
17 + x = 180
x = 163
So, 17's supplement is 163 degrees. The 163 degree angle corresponds with angle r, and corresponding angles are congruent.
Therefore, angle r is 163 degrees. The correct answer is option C.
Hope this helps!
Step-by-Step Solution:
In the Right Triangle formed to the extreme right, lets mark the angles as
∠1, ∠2 and ∠3.
Therefore, from the Figure :-
∠1 = 73°
∠2 = 90°
By Angle Sum Property :-
∠3 = 180 - (73 + 90)
∠3 = 180 - 163
=> ∠3 = 17°
The Angle which forms a Linear Pair with ∠3 is the Corresponding Angle of ∠r, and Corresponding Angles are Equal.
Therefore,
=> 180 - ∠3
= 180 - 17
=> 163°
Therefore, the Angle that forms the Linear Pair with ∠3 is 163°
This Angle is Corresponding to ∠r and hence they are Equal ie. ∠r = 163°
Hence, ∠r = 163°
Related Questions
I need to know The value of f(1/2)
Answers
[tex]\huge\boxed{\textsf{a.)}\ 10}[/tex]
Substitute [tex]\frac{1}{2}[/tex] for [tex]x[/tex].
[tex]f\left(\frac{1}{2}\right)=5\cdot4^\frac{1}{2}[/tex]
Use [tex]a^\frac{m}{n}=\sqrt[n]{a^m}[/tex].
[tex]\begin{aligned}f\left(\frac{1}{2}\right)&=5\cdot\sqrt[2]{4^1}\\&=5\cdot\sqrt[2]{4}\\&=5\cdot2\\&=\boxed{10}\end{aligned}[/tex]
h(t)=t^4+3t^2-t+3
h'?
Answers
Answer: [tex]h'(t)=4t^3 + 6t-1[/tex]
Step-by-step explanation:
Use the power rule for differentiation.
FAST HELPPPPPPP
The point at which three or more lines intersect is the point of
A.equality.
B.concurrency.
C.parallelism.
D.tangency.
Answers
Answer:
B.concurrency.
Step-by-step explanation:
Three or more lines when met at a single point are said to be concurrent and the point of intersection is point of concurrency.
This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Answers
Answer:
Step-by-step explanation:
Question
64^m
--------
4^2m
Solution
(64)^m = (4^3)^m = 4^3m
4^3m/4^2m = 4^(3m - 2m) = 4^m
Answer
2^2m = (2^2)^m = 4^m Equivalent
16^0.5m = (16^0.4) ^m = 4^m Equivalent
4^m Equivalent
All three of these are equivalent. The catch is in splitting the powers apart. In this top one (2^2m) you move the brackets so that the right bracket is after the two which gives (2^2)^m = 4m
You do the same thing with (16^0.5)^m. 16^0.5 = 4 So the answer is 4^m
The last one is 4^m which is the answer you got from the division.
Given expression: [tex]64^{m} /{4^{2m} }[/tex]
We can rewrite the expression (in the numerator and the denominator) as the product of multiple fours. Then, we can apply the exponent rule to simplify the expression to its simplest form. The simplest form will be the required simplified expression (solution to the provided expression).
[tex]\implies (4^{3}) ^{m} /{4^{2m} } \\[/tex][tex]\implies 4^{3m} /{4^{2m} }[/tex]We can apply the following exponent rule to simplify the expression:
[tex]\boxed{\text{Exponent rule:} \ 4^{m} /4^{n} = 4^{m - n}}[/tex]
The exponent rule states that the "base" must be the same when subtracting exponents. If we divide a term with same bases, we can reduce work time by subtracting the exponent to simplify the expression.
[tex]\implies 4^{3m} /{4^{2m} }[/tex][tex]\implies 4^{3m - 2m} = 4^{m}[/tex]Step-2) Equivalent or Non-equivalent?Now, let us look at all the options to verify which term matches our simplified term, and which expressions do not match our simplified term.
First option:Given term: [tex]2^{2m} \\[/tex]
Can be re-written as:
[tex]=2^{2m} \\[/tex][tex]= [2^{(2)}]^{m}[/tex]Simplifying the expression inside the long brackets:
[tex]\\= [4]^{m}[/tex][tex]\\= 4^{m} \ ( \text{matches})[/tex]Therefore, the first option is equivalent to our simplified term.
Second option:Given term: [tex]16^{0.5m}[/tex]
Can be re-written as:
[tex]= 16^{0.5m}[/tex][tex]\\= (4^{2}) ^{0.5m}[/tex]Exponent Rule: (xᵃ)ᵇ = xᵃᵇ
[tex]= (4^{1}) ^m[/tex][tex]= (4^{1m})[/tex][tex]= 4^m[/tex]Therefore, the second option is equivalent to our simplified term.
Third option:Given term: [tex]4^{m}[/tex]
This term already matches our simplified term.
Therefore, the third option is equivalent to our simplified term.
Step-3) Conclude/verify your answerWe can conclude that all the options provided are equivalent to the given expression. We proved it by applying exponent rules and formulas.
6(m + 2 + 7m)
Part A: Write two expressions that are equivalent to the given expression. (3 points)
Part B: Show that one of your expressions in Part A is equivalent to the given expression using algebraic properties. Explain which properties you used. (4 points)
Part C: Show that your other expression from Part A is equivalent to the given expression by substituting a number for m. (3 points)
Answers
Part A: 6 ( 8m + 2) and 48m + 12
Part B: 48m - 48m = 12 - 12
Part C: 6 (10) = 6(10)
How to determine the expressions1. The two expressions could be gotten thus;
6(m + 2 + 7m)
Collect like terms in the bracket
6 ( 8m + 2) ⇒ first expression
6(m + 2 + 7m)
Expand the bracket
6m + 12 + 42m
Collect like terms
6m + 42m + 12
48m + 12 ⇒ second expression
Part B:
6(m + 2 + 7m) = 48m + 2
Expand the bracket
6m + 12 + 42m = 48m + 2
Collect like terms
48m - 48m = 12 - 12
0 = 0
Part C:
Let the expression from A be 6 ( 8m + 2)
6(m + 2 + 7m) = 6 ( 8m + 2)
Let the number be m = 1
Substitute the values
6(1 + 2 + 7(1) ) = 6 (8(1) + 2)
6 ( 1 + 2 + 7) = 6 (10)
6 (10) = 6(10)
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I have tried this problem multiple times now and don't get the correct answer. Please help!
Answers
The confidence interval is (-1.1059, 7.70459).
What is confidence interval in statistics?Image result for what is confidence interval
A confidence interval is the mean of your estimate plus and minus the variation in that estimate.
The sample mean is M=3.3
The sample size is N=44
So, σM= s/√N = 16.6/ √44
= 16.6/ 6.633
= 2.621
and, the degree of freedom
df= n-1
=44-1
=43
So, The t-value for a 90% confidence interval and 43 degrees of freedom is t=1.681.
Now, Margin of error = 2.261* 1.681 = 4.4059
Now, the lower and upper bound of the confidence interval are:
LL = 3.3- 4.40459 = -1.1059
UL = 3.3+ 4.40459 = 7.70459
Hence, the confidence interval is (-1.1059, 7.70459).
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Cost of a CD: $17.50
Markup: 45%
Answers
Answer:
25.375
Step-by-step explanation:
17.50×45%=7.875
17.50+7.875=25.375 new price
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.)
{2, 6, 10, 14, 18, . . . }
Answers
The formula for the general term of the sequence is Tn = 4n - 2
How to determine the formula?The sequence is given as:
{2, 6, 10, 14, 18, . . . }
The above sequence is an arithmetic sequence with the following features:
First term, a = 2Common difference, d = 4 i.e. 6 - 2The formula for the general term is calculated using:
Tn = a + (n - 1) * d
This gives
Tn= 2 + (n - 1) * 4
Expand
Tn = 2 + 4n - 4
Evaluate the like terms
Tn = 4n - 2
Hence, the formula for the general term of the sequence is Tn = 4n - 2
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Giving brainliest :)
Answers
Answer:
I think it would be D the last answer on the page I am pretty confident in the answer but if for some reason it's wrong then I'm sorry.
Step-by-step explanation:
A data set is summarized in the frequency table below. Using the table, determine the number of values less than or equal to 6.
Answers
Based on the data set given in the frequency table, the number of values that are less than or equal to 6 is 18.
How many values are less than or equal to 6?The value that will be less than or equal to 6 are those that are valued at 6 or below.
The sum of these values are:
= 2 + 3 + 6 + 4 + 3
= 18
In conclusion, 18 values are less than or equal to 6.
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If y is inversely proportional to x and y=−54 when x=38, find y if x=30. (Round off your answer to the nearest hundredth.)
Answers
Answer:
-68.4
Step-by-step explanation:
answer explained on the photo !
Brian has earned 65%, 80% and 92% on his three pre-final exams. These exams are not weighed equally: the lowest counts for only 20% of his overall grade, while the other two count for 25% each. If the final exam is the remainder of the overall grade and there are no opportunities for extra credit, what is the highest grade Brian can earn in the class? Express your answer to the nearest whole percent.
Answers
Answer:
89.25%
Step-by-step explanation:
65 is the lowest so it only counts for 20% of the grade
65*0.2=16.25
80*0.25=20
92*0.25=23
There is 30% left and 100% is the highest score
100*0.3=30
16.25+20+23+30=89.25
Answer:
86%
Step-by-step explanation:
From the information give:
Exam 1
Exam result = 65%
Overall grade weighting = 20%
⇒ Credit = 65% of 20% = 0.65 × 0.2 = 0.13 = 13%
Exam 2
Exam result = 80%
Overall grade weighting = 25%
⇒ Credit = 80% of 25% = 0.8 × 0.25 = 0.2 = 20%
Exam 3
Exam result = 92%
Overall grade weighting = 25%
⇒ Credit = 92% of 25% = 0.92 × 0.25 = 0.23 = 23%
Final Exam
The highest grade Brian can earn = 100%
Overall grade weighting = 100% - 20% - 25% - 25% = 30%
⇒ Credit = 100% of 30% = 1 × 30% = 30%
Highest potential class grade
Sum of each exam credit:
⇒ 13% + 20% + 23% + 30% = 86%
Therefore, the highest grade possible that Brian can earn in the class is 86%.
[tex]212 \times 5 + 5222 \div 45 + 63 - 34[/tex]
this question i want
Answers
Divide first
5222/45 = 116.04
Multiply
212x5= 1060
Then add & subtract
1060 +116.04+63-34= 1205.04
If 7 spiders make 7
webs in 7 days, then 1
spider will make 1
web in how many
days?
Answers
Answer:
1 day
Step-by-step explanation:
since 7 spider =7 days
1 spider =? day
cross multiply
7 days × 1 spider = 7 spider × ? days
7 spider = 7 spider × ? days
7 spider 7 spider
= 1 days
Please help me. NO LINKS!!
Answers
The domain (input values) of the cosine function is all negative and positive angle measures.
Let the function be f(x) = cos(x)
The domain of cos(x) is -∞ < x < ∞
The range is -1 ≤ f(x) ≤ 1
Hence, domain of cos(x) is all (+) and (-) angle measures.
Same goes with sine function as well
For function f(x) = sin(x)
The domain is -∞ < x < ∞ and range -1 ≤ f(x) ≤ 1
However for f(x) = tan(x) the same is not applicable.
Answer:
A. all negative and positive angle measures.
Step-by-step explanation:
The domain of a function is the set of input values (x-values).
The cosine function is a continuous function, and therefore has no restrictions throughout its domain.
Therefore, its domain is all real numbers.
Set notation: { x | x ∈ R }
Interval notation: (-∞, ∞)
2b^3+5=2(3)^3+5
I will mark u brainliest if u get the question right
ALSO I NEED THE ANSWER AS SOON AS POSSIBLE
Answers
Answer:
B=3
Solution in photo
I hope this helped :)
8. determine the shape:
Melissa: Does your shape have exactly one right angle?
Keya: Yes
Melissa: Does your shape have opposite congruent sides?
Keya: No
Melissa: Does your shape have any parallel sides?
Keya: Yes
Melissa: The shape is a _____________________
How did you rule out other shapes?
b) Michelle: Does your shape have 2 pairs of congruent opposite sides?
Olga: Yes
Michelle: Does your shape have right angles?
Olga: No
Michelle: Does your shape have 2 pairs of opposite parallel sides?
Olga: Yes
What is the shape?
Is there an additional question Michelle should ask to be sure? If so, what should she ask?
Answers
Quadrilaterals are plane shapes with four sides. Thus, the required answers are:
a) The first shape is a right trapezoid.
b) The second shape is a parallelogram.
The given properties are that of a quadrilateral, thus both shape is a quadrilateral. A quadrilateral is a family of shapes that have four straight sides. Examples include squares, rhombus, kites, etc.
A. Given that the shape has one right angle and parallel sides. Then considering the given properties, the most likely shape is a right trapezoid.
A right trapezoid is a type of trapezium that has one right angle, and a pair of parallel sides. Thus the shape here is a right trapezoid.
Other shapes could be ruled out by comparing their properties with the properties of the shape given in the question.
B. The properties of the required shape as given are: it has two pairs of congruent opposite sides, and 2 pairs of opposite parallel sides. Thus the most likely shape required here is a parallelogram. A parallelogram is a shape with parallel and congruent opposite sides, and no right angle.
Other shapes could be ruled out by comparing their properties with the properties of the shape given in the question.
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Kindly contact a 1-on-1 tutor if more explanations are required.
Given: f(x) = 4x+1 and g(x)= x2+1, find (f g)x.
Answers
Answer:
given
fx = 4x+1
gx= 2x+1
Step-by-step explanation:
fg x = ?
we know ,
f g x = (4x+1) ( 2x+1)
= 4x ( 2x+1) +1 (2x+1)
= 8x² +4x +2x+1
= 8x² + 6x +1
The equation y minus 1 = negative 7 (x minus 3). is written in point-slope form. What is the y-intercept of the line?
Answers
Answer:
(0, 22)
Step-by-step explanation:
So you have the equation:
[tex]y-1=-7(x-3)[/tex]
So first let's define what the "y-intercept" is. The y-intercept, of a line is like the name implies, when the line intercepts or "passes" the y-axis. And if you were to take any point on the y-axis, the y-value may vary, but there is one value that doesn't change, and that's the x-value. the x-value is always going to be zero, no matter where you are on the y-axis. So to find the y-intercept simple plug 0 in as x. This gives you the equation:
[tex]y-1 = -7(0-3)[/tex]
[tex]y-1 = -7(-3)[/tex]
[tex]y-1=21[/tex]
[tex]y=22[/tex]
So the y-intercept is at (0, 22)
1. What is the remainder when x³+4x2-2x+1 is divided by x+2 1. What is the remainder when x³ + 4x2-2x + 1 is divided by x + 2
Answers
Answer:
Remainder is 13
Step-by-step explanation:
You can apply the remainder theorem here. You just equate the divisor to 0, then substitute the x-value in the expression.
[tex]x^3 + 4x^2 - 2x + 1 \\[/tex] then, [tex]x+2=0\\x=-2[/tex]
substitute:
[tex]-2^3 + 4(-2)^2-2(-2) + 1 =13[/tex]
Therefore, the remainder is 13
Find k. ..................
Answers
Answer:
k = -10
Explanation:
f(x) = 4x³ - 3kx² + 44x - 30
The divisor is:
(x - 2)Set divisor to zero:
(x - 2) = 0x = 2Insert this into equation.
⇒ 4(2)³ - 3k(2)² + 44(2) - 30 = 210
⇒ 32 - 12k + 88 - 30 = 210
⇒ -12k + 90 = 210
⇒ -12k = 210 - 90
⇒ -12k = 120
⇒ k = 120/-12
⇒ k = -10
Answer:
k = -10
Step-by-step explanation:
From the remainder theorem, we know that the remainder, 210, is equal to f(2).
∵ [tex]f(2) = 210[/tex] ,
⇒ [tex]4(2)^3 - 3 k(2)^2+44(2) - 30 = 210[/tex]
⇒ [tex]32 -12k + 88 - 30 = 210[/tex]
⇒ [tex]90 - 12k = 210[/tex]
⇒ [tex]-12k = 120[/tex]
⇒ [tex]k = -10[/tex]
The sum of 8 times a number and 10 is 34. Find the number.
Answers
Explanation: 8 * 3 = 24 + 10 = 34
Answer: 3
8x+10=34
sub 10
8x=24 divide by 8
x=3
Step-by-step explanation:
4(4 - x) - 8(-2 + 4x)
Answers
If you want the answer simplified, its
-36x + 32
AADF, AB = 16,
mZB = 59° mZD = [?]
Answers
Answer:
59°
Step-by-step explanation:
ABC and ADF are congruent (that is the meaning of that symbol).
that means all their associated angles and side lengths are the same.
it is relatively clear to see that
A corresponds to A.
D corresponds to B.
F corresponds to C.
therefore, the angle D = angle B = 59°.
FYI - it also means that AD = AB = 16. but this information was actually irrelevant for this question.
Can someone answer this
Answers
We can see that the unit rate of y = 6.5*x is larger than the unit rate on the graph.
How to get the unit rate of the line?
The unit rate is the equal to the slope of the line.
In the written line, y = 6.5*x, the unit rate is 6.5
On the graphed line we can see that it passes through the points (0, 0) and (1, 3), so the unit rate is:
[tex]r = \frac{3 - 0}{1 - 0} = 3[/tex]
Then we can see that the unit rate of y = 6.5*x is larger than the unit rate on the graph.
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Latesha justifies whether the expression 4x – 3 is equivalent to one-half (4 x minus 6) minus 2 x (1 minus 3) by letting x = 2 in both expressions. which values should latesha compare to justify whether the expressions are equivalent? 2 and 5 5 and 9 5 and 5 9 and 9
Answers
Answer:
5 and 9
Step-by-step explanation:
Answer:b
Step-by-step explanation: took the test
465 draws will be made at random with replacement from the box [0 0 1]. The number of 1’s among the draws will be around…
Answers
The number of 1’s among the draws will be 155.
How to find that a given condition can be modelled by binomial distribution?Binomial distributions consist of n independent Bernoulli trials.
The expected value is given as
E(X) = np
465 draws will be made at random with replacement from the box [0 0 1].
The number of 1’s among the draws will be
p = 1/3
n = 465
Then the expected value is given as
E(x) = 465 × 1/3
E(x) = 155
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2+2*+456+5367+63784+464749=
Answers
Answer:534360
Step-by-step explanation:
I did have to remove the multiplication though
the sum of two numbers is 24 and the quotient is 3. what are the to numbers
Answers
Answer:
18 and 6
Step-by-step explanation:
18+6=24
18/6=3
please mark brainliest
Help plsss there’s a timer
Answers
Answer:
[tex]a=27, b=81[/tex]
Step-by-step explanation:
Plug in the values
[tex]a=3^3\\b=3^4\\\\a=27\\b=81[/tex]