AB ll CD and EF ll GH use the figure above to find the value of each angle
Answers
Answer:
[tex]x=k=117\°[/tex]
Step-by-step explanation:
Givens
AB || CD
EF || GH
These parallels gives us certain pair of angles which are congruent.
The given angle 63° is congruent with its corresponding angles. The image attached shows all corresponding angles that are equal to 63° (red angles).
Basically,
[tex]x+63=180[/tex] and [tex]k+63=180[/tex], by suplementary angles and straight angle definition.
Then, solving for [tex]x[/tex] and [tex]k[/tex], we have
[tex]x=180-63\\x=117\°[/tex]
[tex]k=180-63\\k=117\°[/tex]
Therefore, both angles are equal to 117°.
The measure of each angle are:
<m = 63 <n = 117<k = 63 <x = 63 <w = 63 <p = 63Given:
AB || CD
EF || GH
As, the lines are parallel and parallel line have following properties
Corresponding angleAlternate Interior angleAlternate Exterior angleCo- interior angleSo, <m = 63 {Corresponding angle}
Now, <m + <n = 180 {Linear pair}
63 + <n =180
<n =180 - 63
<n = 117
and, <k = 63 {Vertical opposite angle}
and, <k = <x = 63 {Corresponding angle}
and, <w = <x = 63 (alternate Interior angle}
and, <p = <w = 63 {Vertical opposite angle}
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Related Questions
an engine manufacturer discovered that .05 of a certain production run was defective. What fraction of the run does this represent?
Answers
Simplest form: 1/20
[tex]\huge{\boxed{\frac{1}{20}}}[/tex]
Explanation:To convert from a decimal to a percentage, multiply the decimal by [tex]100[/tex]. [tex]0.05*100=5[/tex], so the percentage equivalent is [tex]5\%[/tex].
Percentages are fractions when you use a denominator of [tex]100[/tex], so [tex]5\%[/tex] is the same as [tex]\frac{5}{100}[/tex]. Divide the numerator and denominator each by [tex]5[/tex] to get the fraction in simplest form, which is [tex]\frac{1}{20}[/tex].
What is the length of the hypotenuse of the triangle below?
Answers
Answer:
C
Step-by-step explanation:
Since the triangle is right with hypotenuse h
Use Pythagoras' identity to solve for h
The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is
h² = ( 5[tex]\sqrt{2}[/tex] )² + ( 5[tex]\sqrt{2}[/tex] )²
= 50 + 5 0 = 100
Take the square root of both sides
h = [tex]\sqrt{100}[/tex] = 10 → C
Do you prefer to express solutions to inequalities using interval notation or as an inequality? Do you think it is important to know both formats? How could each be used?
Answers
Answer:
I prefer to express solutions to inequalities using interval notation. Both formats are are important but I think interval notation is easier to understand and represents better the solutions.
For example, if you have the following inequation:
x-2> 1
x>3
Therefore, the solution could be written either x>3 OR (3, +inf). But what happens if the solution to the system of equation is x>3 or x<-3? The solution can be easily written as: (-inf, -3) U (3, inf) instead of 'x>3 or x<-3' which can be confusing.
To express solutions to inequalities using interval notation.
I prefer to express solutions to inequalities using interval notation. Both formats are important but I think interval notation is easier to understand and represents better the solutions.
For example, if you have the following inequation:
x-2> 1
x>3
Therefore, the solution could be written either x>3 OR (3, +inf). But what happens if the solution to the system of equation is x>3 or x<-3? The solution can be easily written as: (-inf, -3) U (3, inf) instead of 'x>3 or x<-3' which can be confusing.
Hence, To express solutions to inequalities using interval notation.
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if u=1+3 i and v=-2-i what is u+v
Answers
1+3=4
4-2=2
2-i=2-i
The answer is:
[tex]u+v=-1+2i[/tex]
Why?To solve the problem, we just need to consider that the variable "u" and "v" represents different expressions, and then, perform the operation and add the like terms.
We must remember that the like terms are the terms that share the same variable and the same exponent.
We have that:
[tex]u=1+3i\\v=-2-i[/tex]
So, calculating we have:
[tex]u+v=(1+3i)+(-2-i)=(1-2)+(3i-i)=-1+2i[/tex]
Hence, we have that:
[tex]u+v=-1+2i[/tex]
Have a nice day!
Question number 8 please please fast
Answers
Answer:
[tex]a_n=-\frac{1}{n}[/tex]
[tex]a_6=-\frac{1}{6}[/tex] is our sixth term.
[tex]a_7=-\frac{1}{7}[/tex] is our seventh term.
[tex]a_8=-\frac{1}{8}[/tex] is our eighth term.
Step-by-step explanation:
So every number in this sequence is -.
If you write 1 as 1/1, then you should see the numerator is constant one while the denominator is going up by 1 each time.
So the patter is
[tex]a_n=-\frac{1}{n}[/tex]
Test if you like:
n=1 gives us [tex]a_1=-\frac{1}{1}=-1[/tex] which is our first term.
n=2 gives us [tex]a_2=-\frac{1}{2}[/tex] which is our second term.
n=3 gives us [tex]a_3=-\frac{1}{3}[/tex] which is our third term.
n=4 gives us [tex]a_4=-\frac{1}{4}[/tex] which is our fourth term.
n=5 gives us [tex]a_5=-\frac{1}{5}[/tex] which is our fifth term.
Now we are going to use [tex]a_n=-\frac{1}{n}[/tex]
to write our next three terms:
n=6 gives us [tex]a_6=-\frac{1}{6}[/tex] which is our sixth term.
n=7 gives us [tex]a_7=-\frac{1}{7}[/tex] which is our seventh term.
n=8 gives us [tex]a_8=-\frac{1}{8}[/tex] which is our eighth term.
If f(x) = 3* + 10 and g(x) = 2x - 4, find (f - g)(x).
Answers
Answer:
(f - g)(x) = 3ˣ - 2x + 14Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
We have f(x) = 3ˣ + 10 and g(x) = 2x - 4. Substitute:
(f - g)(x) = (3ˣ + 10) - (2x - 4) = 3ˣ + 10 - 2x - (-4) = 3ˣ + 10 - 2x + 4
(f - g)(x) = 3ˣ - 2x + 14
Match the following items.
Answers
1. Commutative property of adfition
2. Multiplicative inverse
3. Associative property of addition
4. Distributive property
5. Additive identity
Answer:
1-------------- Commutative property of addition
You can commute the terms in a addition, so doesn't matter wat therm goes left or right,
2 ------------ is multiplicative inverse
Each number X has another number Y so X*Y=1
3-------------- Associative property of addition
When you have parentheses in this type of addition, the order in what you do te equation doesn't matter
4 ------------- distributive property
You can distribute the multiplication here, so x(a +b) = x*a + x*b
5 ------------ Additive identity
There exist one number a so for every number x, x+a = x, and the number a is te zero.
On Tuesday you use your debit card for 3 separate transactions, $5 each, and pay 2 ills for $20 each from your checking account. If you had a starting balance of $50, what is the ending balance in your checking account?
Answers
Answer: -5
Step-by-step explanation:
You start with 50.
Then subtract the 3 transactions: 50-(3×5)=50-15=35
Then you subtract the 2 ills: 35-(2×20)=35-40=-5
And that's how get the answer!
how much must you deposit in an account that pays 6.25% interest compounded annually to have a balance of $700 after 2 years
Answers
Answer:
[tex]\$620.07[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=2\ years\\A=\$700\\ r=0.0625\\n=1[/tex]
substitute in the formula above and solve for P
[tex]700=P*(1+\frac{0.0625}{1})^{2}[/tex]
[tex]700=P*(1.0625)^{2}[/tex]
[tex]P=700/(1.0625)^{2}[/tex]
[tex]P=\$620.07[/tex]
Nick is researching a possible link between cosmetic surgery and depression.
Which of the following would likely be a credible source for him to use?
O
A. A blog written by a popular actress
O
B. An online photo gallery of before and after pictures
O
c. A medical journal published in 1982
O
D. A news interview with a psychologist
Answers
Answer:
Step-by-step explanation:So to me I would trust the medical journal published in 1982. Back then they were more people that studied those kind of things. And back then there was like people finding out different types of plants and medical resources. (hope this helps you)..:)
Answer:
The correct answer will be option- C
Step-by-step explanation:
A research journal is considered as the reliable or credible source of the research as the research articles published in the journal are always verified by the peer-group which includes the scientists.
The peer-group verifies the credibility of the research paper by checking and correcting the steps of the scientific method and checking the eligibility of the collected data and the conclusions drawn from it.
Therefore, Nick should use a medical journal published in 1982 as the credible source for him and thus option- C is the correct answer.
A 26 foot rope is used to brace a tent pole at the county fair. the rope is anchored 10 feet from the box of the pole. How tall is the pole? (answers above^^)
Answers
Using the Pythagorean theorem a^2 + b^2 = c^2 where a and b are the side and bottom of the triangle and c is the hypotenuse ( length of rope).
Let the tent pole = a
Lhe distance from the pole be b = 10 ft.
The length of rope would vce c = 26 ft.
Now you have:
a^2 + 10^2 = 26^2
Simplify:
a^2 + 100 = 676
Now subtract 100 from each side:
a^2 = 576
To get a, take the square root of both sides:
a = √576
a = 24
The tent pole is B. 24 ft
the equation of a line in the point slope form is show below.
Answers
Answer:
A 3
Step-by-step explanation:
y-9 = 3(x-9)
This is in point slope form
y-y1 = m(x-x1)
where (x1,y1) is the point and m is the slope
A point on the line is (9,9) and the slope is 3
Study the triangle. What can you conclude about the angle measures? The angle measures are 30°, 60°, and 90°. The angle measures are 45°, 45°, and 90°. The triangle has a 90° angle, but the other angle measures cannot be determined.
Answers
Answer:
A. The angle measures are 30°, 60°, and 90°.
on edge
Step-by-step explanation:
If the question provides the angles of a triangle as 30°, 60°, and 90°, or 45°, 45°, and 90°, we are dealing with a right triangle. Depending on the measures of the angles, the triangle can be classified as either a 30-60-90 triangle or a 45-45-90 isosceles right triangle. Without sufficient information, the exact measures of the angles cannot be determined.
Explanation:When considering a triangle with angle measures provided as options, we recall the fundamental property that the sum of internal angles in any triangle is 180 degrees. The question presents three possible sets of angle measures:
30°, 60°, and 90°45°, 45°, and 90°A 90° angle, with unspecified other anglesBoth of the first two options include a 90° angle, indicating that we are dealing with a right triangle. Right triangles have specific properties and can be classified as either 30-60-90 or 45-45-90 triangles, depending on the measures of the other two angles. A 30-60-90 triangle has angles in the ratio of 1:2:√3, and a 45-45-90 triangle, also called an isosceles right triangle, has two angles of 45° each. The third option implies insufficient information to determine the exact measures of all angles.
f(x)=3x-7 and g(x)=2x-4 find (f+g)(x) and (f-g)(x)
Answers
Answer:
(f+g)(x)= 5x-11
(f-g)(x)= x-3
The value of the functions (f + g)(x) and (f - g)(x) will be 5x - 11 and x - 3.
It is required to find the value of (f+g)(x) and (f-g)(x).
What is function?A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
Given:
The functions are
f(x) = 3x - 7
g(x) = 2x - 4
We have to find the value of the function (f + g)(x) and (f-g)(x) we get
According to given question we have,
The value of the function (f +g)(x)
(f + g)(x) = f(x) + g(x)
(f + g)(x) = 3x - 7 + 2x - 4
(f + g)(x) = 5x - 11
The value of the function (f - g)(x)
(f - g)(x) = f(x) - g(x)
(f - g)(x) = 3x - 7 - (2x - 4)
(f - g)(x) = 3x - 7 - 2x + 4
(f - g)(x) = x - 3
Therefore, the value of the functions (f + g)(x) and (f - g)(x) will be 5x - 11 and x - 3.
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9m=4.5? 3v=-105? 17m=85? please help me:)
please show work:
please show work:
please show work:
thank you
Answers
9m = 4.5
divide by 9 for 9m and 4.5
9m/9= 4.5/9
m= 0.5
3v= -105
divide by 3 for 3v and -105
3v/3=- 105/3
v= -35
17m = 85
divide by 17 for 17m and 85
17m/17= 85/17
m= 5
Answers: 0.5,-35 and 5
divide 9 on both sides to get m alone
m= .5
2. 3v=-105
divide 3 on both sides to get v alone
v=-35
3. 17m= 85
divide 17 on both sides to get m alone
m= 5
This kind of transformation can change the _________.
A. The lengths of some or all of the sides
B. The area of the shape
C. Both A and B
Answers
Answer:
The correct answer option is C. Both A and B.
Step-by-step explanation:
We are given a figure of a rectangle which when transformed changes it length of two sides AB and DC to AB' and DC'.
By looking at the figure, we can conclude that the transformation has changed the lengths of some sides of the given figure as well as changed the area of the figure.
Therefore, the correct answer option is C.
II. Using Radians to Measure Arcs and Angles
A. Convert each radian measure to degrees
2."
4. 18
B. Convert each degree measure to radians
1. 100°
3. 30°
5. 10
C. Determine each arc length
Carnegie Learning, Inc.
1. The radius of a circle is 1 centimeter. What is
the length of an arc intercepted by an angle
of radians?
2. The radius of a circle is 4 inches. What is
the length of an arc intercepted by an angle
of radians?
4 in.
1 cm
Answers
A
1) 180/3=60
2) 270
3) 45
4) 3240
B
1) 100/180=5/9
3) 30/180=3/18
5) 1/180
C
1) (pi) cm
2) 2pi
Use parallelogram ABCD What are the values of X and
y?
Answers
Based on parallelogram ABCD shown below, the values of x and y include;
x = 17 units.
y = 10 units.
In Euclidean Geometry, a parallelogram is a type of quadrilateral and two-dimensional geometrical figure that has two equal and parallel opposite sides.
Generally speaking, a parallelogram has both pairs of opposite sides parallel to each other and the opposite angles (vertical angles) are congruent:
AB ║ CD
AB = CD
3x - 9 = 42
3x = 42 + 9
3x = 51
x = 51/3
x = 17 units.
Next, we would determine the value of y as follows;
4y - 3 = 37
4y = 37 + 3
4y = 40
y = 40/4
y = 10 units.
Complete Question:
Use parallelogram ABCD. What are the values of x and y?
Solve for x: −7 < x − 1 < 8
Answers
Answer:
−6 < x < 9
Step-by-step explanation:
−7 < x − 1 < 8
Add 1 to all sides
−7+1 < x − 1+1 < 8+1
−6 < x < 9
Answer: [tex]-6<x<9[/tex]
Step-by-step explanation:
You have the following expression provided in the exercise:
[tex]-7 < x - 1 < 8[/tex]
Then, in this case, in order to solve the expression, it is necessary to add 1 to both sides.
Therefore, applying the procedure mentioned before, you get that the solution is the following:
[tex]-7 < x - 1 < 8\\\\-7 +(1)< x < 8+(1)\\\\-6<x<9[/tex]
A baseball player has 546 plate appearances in his first year, 627 plate appearances in his second year, and 712 plate appearances in his third year. How many plate appearances has the player had in three years?
Answers
Answer:
1885 plate appearances
Step-by-step explanation:
546 plate appearances + 627 plate appearances + 712 plate appearances = 1885 plate appearances
Answer:
1885
Step-by-step explanation:
546+627+712=1885
[tex]4c - d - c - 3d[/tex]
Answers
[tex]\tt 4c-d-c-3d=3c-4d[/tex]
Answer:
3c -4d
Step-by-step explanation:
4c -d -c -3d
Combine like terms
4c -c -d -3d
3c -4d
Solve x - (-9) = -14. -23 23 -5 5
Answers
Answer:
-23 = x
Step-by-step explanation:
-(-9) = 9
The thing with double negatives is that they form a plus sign, so that is really a POSITIVE nine. Therefore you do the inverse to find x: -14 - 9 = -23.
I am joyous to assist you anytime.
Answer:
[tex]\Huge \boxed{X=-23}[/tex]
Step-by-step explanation:
[tex]\displaystyle x+9=-14[/tex]
[tex]\Large\textnormal{First, subtract by 9 from both sides of equation.}[/tex]
[tex]\displaystyle x+9-9=-14-9[/tex]
[tex]\Large\textnormal{Simplify, to find the answer.}[/tex]
[tex]\displaystyle -14-9=-23[/tex]
[tex]\Large\textnormal{x=-23, which is our answer.}[/tex]
1. A retirement account is opened with an initial deposit of $8,500 and earns 8.12% interest compounded monthly. What will the account be worth in 20 years? What if the deposit were compounded monthly with simple interest? Could you see the situation in a graph? From what point one is better than the other?
Answers
Answer:
Part A) [tex]\$42,888.48[/tex]
Part B) [tex]A=\$22,304[/tex]
Part C) The graph in the attached figure
Step-by-step explanation:
Part A) What will the account be worth in 20 years?
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=20\ years\\ P=\$8,500\\ r=0.0812\\n=12[/tex]
substitute in the formula above
[tex]A=8,500(1+\frac{0.0812}{12})^{12*20}[/tex]
[tex]A=8,500(1.0068)^{240}[/tex]
[tex]A=\$42,888.48[/tex]
Part B) What if the deposit were compounded monthly with simple interest?
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=20\ years\\ P=\$8,500\\r=0.0812[/tex]
substitute in the formula above
[tex]A=8,500(1+0.0812*20)[/tex]
[tex]A=\$22,304[/tex]
Part C) Could you see the situation in a graph? From what point one is better than the other?
Convert the equations in function notation
[tex]A(t)=8,500(1.0068)^{12t}[/tex] ------> equation A
[tex]A(t)=8,500(1+0.0812t)[/tex] -----> equation B
using a graphing tool
see the attached figure
Observing the graph, from the second year approximately the monthly compound interest is better than the simple interest.
The retirement account will be worth $27,627.24 after 20 years with compound interest and $23,180 with simple interest. Compound interest grows at a faster rate and becomes better than simple interest when the compounding periods are more frequent.
Explanation:To calculate the value of the retirement account after 20 years with compound interest, we can use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal deposit, r is the interest rate, n is the number of times compounded per year, and t is the number of years. In this case, P = $8,500, r = 8.12%, n = 12 (monthly compounding), and t = 20. Plugging in these values, we get A = $8,500(1 + 0.0812/12)^(12*20) = $27,627.24.
If the deposit were compounded monthly with simple interest, we can use the formula A = P + (P*r*t), where A is the final amount, P is the principal deposit, r is the interest rate, and t is the number of years. In this case, P = $8,500, r = 8.12%, and t = 20. Plugging in these values, we get A = $8,500 + ($8,500 * 0.0812 * 20) = $23,180.
To compare the two situations on a graph, we can plot the value of the retirement account over time for both compound and simple interest. We would see that the compound interest account grows at a faster rate and reaches a higher value compared to the simple interest account. Compound interest becomes better than simple interest when the compounding periods are more frequent, as it allows the interest to be reinvested more often and generate additional earnings.
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Determine the input that would give an output value of 2/3
Answers
Answer:
x = 19
Step-by-step explanation:
Question: find x such that f(x) = 2/3
Given f(x) = (-1/3) x + 7
equate the value of f(x) to be 2/3
hence,
(2/3) = (-1/3)x + 7 (multiply both sides by 3)
(3) (2/3) = (3) (-1/3)x + (3) 7
2 = -x + 21
x = 21 - 2
x = 19
So to get the output value 2/3 we will input x = 19
What is a function?A mathematical relationship from a set of inputs to a set of outputs is called a function.
What are equations?An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression.
How to find the input that would give an output value of 2/3 ?The function used here is f(x) = [tex]-\frac{x}{3} + 7[/tex]Clearly, all the values of x and f(x) are satisfying it.
Now, the output is given as 2/3.
So, we can write,
[tex]\frac{2}{3} = -\frac{x}{3} + 7[/tex]
⇒ [tex]\frac{2}{3}-7 = -\frac{x}{3}[/tex] ( changing the side of 7)
⇒ [tex]-\frac{19}{3} = - \frac{x}{3}[/tex]
⇒ x = 19
So to get the output value 2/3 we will input x = 19
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Find an equation for the inverse of the function. f(x)=2x-3x/4
Answers
Answer:
f⁻¹(x) = (4x)/5
Step-by-step explanation:
f(x) = 2x - 3x/4.
Assume y=f(x). Therefore:
y = 2x - 3x/4.
Make x the subject in the above equation.
y = (2x(4) - 3x)/4.
y = 5x/4.
4y = 5x.
(4y)/5 = x.
x = (4y)/5.
Therefore:
f(y) = (4y)/5.
Replace y with x.
f⁻¹(x) = (4x)/5.
Therefore, the inverse of f(x) = 2x - 3x/4 is f⁻¹(x) = (4x)/5!!!
Triangle HAM is reflected over the y-axis using the rule (x, y) → (−x, y) to create triangle H′A′M′. If a line segment is drawn from point A to point A′, which statement would best describe the line segment drawn in relation to the y-axis?
Answers
The line segment drawn from point A to point A′, after reflecting the triangle over the y-axis, is perpendicular to the y-axis. This is because the reflection mirrors the image across the y-axis resulting a right-angle formation between the line segment and the axis.
Explanation:The line segment drawn from point A to point A′, after a reflection of Triangle HAM over the y-axis, would be perpendicular to the y-axis. This is because in a reflection over the y-axis, the x-coordinates of the points change sign and the y-coordinates stay the same. This procedure mirrors the image over the y-axis and creates a segment from A to A′ that is perpendicular to the y-axis and bisects the distance between A and A′.
This idea correlates to the vector concept in physics where components of the vector may be viewed as sides of a right triangle. Much like in that context, the line segment from A to A′ and the y-axis form a right angle, hence they are perpendicular.
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If triangle DEC congruent to triangle BEC, which is true by CPCTC?
Answers
Answer:
The correct answer is the second one
Step-by-step explanation:
Line BE and ED are congruent because they are the same length and E is the mid line.
Answer:
second option is correct
Step-by-step explanation:
By the given
ΔDEC≅ΔBEC
which means triangle DEC is congruent to triangle BEC
then by CPCTC (corresponding parts of congruent triangle are congruent)
there every side and angle of DEC will be equal to BEC
⇒BE= DE (by CPCTC)
hence second option is correct
40 POINTS!!!!
graph the function g(x) = x3 − x2 − 4x + 4. (an actual graph that you can attach)
Answers
Answer:
see below
Step-by-step explanation:
g(x) = x^3 − x^2 − 4x + 4
We know the graph will have up to 3 zero's because it is a cubic
g(x) = x^3 − x^2 − 4^x + 4
I will factor by grouping, taking an x^2 from the first 2 terms and -4 from the last 2 terms
g(x)= x^2(x-1) -4(x-1)
Now factor out x-1
g(x)= (x-1)(x^2 -4)
We can factor the (x^2-4) as a difference of squares
g(x) = (x-1) (x-2)(x+2)
Using the zero product property
0= (x-1) (x-2)(x+2)
x-1 =0 x-2 =0 x+2=0
We have zeros at x=1 x=2 and x=-2
Then we can plot points to determine where the function is between the points We will pick negative infinity 0 1.5 and infinity
at g(-inf) = -inf because x^3 dominates and that goes to -infinity
at g(0) = 0+000+4 =4
at g(1.5) =-.875
at g(inf)=because x^3 dominates and that goes to infinity
Find the num
The sum of a number and its reciprocal 10/3. find the number 5
Answers
Answer:
x=3 or x= 1/3
Step-by-step explanation:
Let the number = x
The reciprocal of the number = 1/x
According to the given statement:
x+1/x=10/3
x²+1/x=10/3
3(x²+1)=10x
3x²+3=10x
Move 10x to the L.H.S
3x²-10x+3=0
Break the middle term:
3x²-9x-x+3=0
3x(x-3)-1(x-3)=0
(x-3)(3x-1)=0
x-3=0 , 3x-1=0
x=0+3 , 3x=0+1
x=3 , 3x=1
x=3 ,x = 1/3
So x=3 or x= 1/3 ....
In △ABC, m∠A=16°, m∠B=49°, and a=4. Find c to the nearest tenth.
Answers
Answer:
c=13.2 units
Step-by-step explanation:
step 1
Find the measure of angle C
Remember that the sum of the internal angles of a triangle must be equal to 180 degrees
so
A+B+C=180°
substitute the given values
16°+49°+C=180°
65°+C=180°
C=180°-65°=115°
step 2
Find the measure of c
Applying the law of sines
c/sin(C)=a/sin(A)
substitute the given values and solve for c
c/sin(115°)=4/sin(16°)
c=4(sin(115°))/sin(16°)
c=13.2 units