Answers
Statement Problem: (3)
List the angles of the triangle in order from smallest to largest.
Solution:
First, let's use the Cosine Rule to find the angle B;
[tex]\begin{gathered} b^2=a^2+c^2-2ac\cos B \\ 2ac\cos B=a^2+c^2-b^2 \\ \cos B=\frac{a^2+c^2-b^2}{2ac} \end{gathered}[/tex]Where;
[tex]\begin{gathered} a=3,b=2.9,c=3.1 \\ \cos B=\frac{3^2+3.1^2-2.9^2}{2(3)(3.1)} \\ \cos B=\frac{9+9.61-8.41}{18.6} \\ \cos B=\frac{10.2}{18.6} \\ \cos B=0.5484 \\ B=\cos ^{-1}(0.5484) \\ B=56.74 \\ B=57^o \end{gathered}[/tex]Also, let's use the Cosine Rule to find the angle A;
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cos A \\ \cos A=\frac{b^2+c^2-a^2}{2bc} \end{gathered}[/tex][tex]\begin{gathered} \cos A=\frac{2.9^2+3.1^2-3^2}{2(2.9)(3.1)} \\ \cos A=\frac{8.41+9.61-9}{17.98} \\ \cos A=\frac{9.02}{17.68} \\ A=\cos ^{-1}(0.5102) \\ A=59.32 \\ A=59^o \end{gathered}[/tex]Lastly, let's use the sum of angles in a triangle theorem to get the third angle, Angle C;
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^o \\ \angle C=180^o-59^o-57^o \\ \angle C=64^o \end{gathered}[/tex]Hence, the angles of the triangle from the smallest to the largest are;
[tex]\angle B,\angle A,\angle C[/tex]Angle B,
Angle A,
Angle C
Related Questions
If a polynomial with real coefficients is of degree 3. Can we say there must be at least 1 real root?a. Yes, because complex roots must appear in conjugate pairs, leaving one root real. b. No. we can’t say anything about this casec. Yes, because if there is one real root, there must be two additional real rootsd. No, because such a curve never crosses the x-axise. Sometimes yes and sometimes no
Answers
Solution
If we have a polynomial odf degree 3 it must have 3 roots
And one of then should be real the answer is true
And the correct choice is:
a. Yes, because complex roots must appear in conjugate pairs, leaving one root real.
Since we have two possible options:
1) (x-i)(x+i) (x-a) with 2 factors conjugate and 1 root real a and two other complex numebrs
2) (x-a)(x-b)(x-c) with 3 real roots a,b and c
So then we must have at least one root assuming that the coeffcients of the polynomial are not complex
What’s the correct answer answer asap for brainlist
Answers
Answer:
B. There is not much to add to this answer
Answer:
Step-by-step explanation:
B.
The valence electrons are known as the outermost elections which are usually stored in something called "valence electron shel"
If you borrow $500 for 4 years atan annual interest rate of 6%, howmuch will you pay altogether?
Answers
Problem
If you borrow $500 for 4 years at an annual interest rate of 6%, how much will you pay altogether?
Solution
For this case we can use the following:
Solve 2(4x - 3) = 2(x + 2) + 8 for x.A) x = 3B) x = 4C) x = -2D) x = -5
Answers
Given: 2(4x - 3) = 2(x + 2) + 8
Required: The value of x
Explanation:
Opening the brackets
[tex]\begin{gathered} 2(4x-3)=2(x+2)+8 \\ 8x-6=2x+4+8 \end{gathered}[/tex]Further
[tex]\begin{gathered} 8x-2x=4+8+6 \\ 6x=18 \end{gathered}[/tex]So
[tex]x=3[/tex]Final Answer: Option A is correct.
Value of x = 3 that is option A
Here we are given with the equation as,
2(4x-3) =2(x+2) +8
Now solving both left hand side and right-hand side
taking left hand side,
2(4x-3)
2 X 4x + 2 X (-3)
8x - 6
Now solving right hand side,
2(x+2) +8
2x + 4 +8
2x+ 12
Now according to question equating both left hand side and right-hand side,
8x - 6 = 2x + 12
Now transposing variables and constants on left hand side and right-hand side respectively,
8x - 2x = 6 + 12
6x = 18
x= 12 / 6
x = 3
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Patty went to the shopping mall at 10:30 A.M. She shopped for 20 minutes. She spent 35 minutes eating lunch. Then she met a friend at a movie
Answers
Patty started shopping at 10:30 AM. It was for 20 minutes, then it lasted until 10:50. (30 min + 20 min = 50 min).
Then, we can say she starts lunch 10 minutes before 11:00 AM.
She spent 35 minutes eating lunch. Then, she ends at 11:25 AM. Ten minutes before 11:00 AM and 25 minutes after 11:00 AM, giving the 35 minutes.
After lunch she mets a friend, then it was about 11:25 AM.
PLS HELP!!! I GIVE BRAINLESS!!!! NOT FOR TEST!!!
Answers
Answer:D
Step-by-step explanation:
D (-1,-2)
6.25 ft7.14 am25 cm11 am8.9 m21.6 m
Answers
For figure 6
In figure 6 we have a circle and a rectangle. The shaded area will be the difference between the area of the rectangle of side 25ft and the area of the ciercle of diameter 25ft.
The radius of the circle will be 25ft/2 = 12.5ft
Then, the area will be:
[tex]\begin{gathered} \text{Area}=(25ft)\cdot(25ft)-\pi\cdot(12.5ft) \\ \text{Area}=625ft^2-490.87ft^2=134.13ft^2 \end{gathered}[/tex]For figure 7
In figure 7 we have a rectangle and a triangle. The shaded area will be the area of the rectangle minus the area of the triangle. The sides of the triange are 25cm and 14cm, while the triangle has a base of 25cm and a height of 11cm. We can say 11cm is the height because according to the figure this height forms a right triangle with the base.
Then, the area will be:
Area = 350cm^2 - 137.5cm^2
Area = 212.15cm^2
For figure 8
The figure 8 has a triangle and a semicircle. The shaded area will be the difference between the area of the semicircle and the area of the triangle.
We can say this is a righ triangle because his hypotenuse is the diameter of a circle and the hycks join in the circumference.
The hypotenuse is calculated with hicks 9m and 21.6m
[tex]h=\sqrt[]{(9m)^2+(21.6m)^2}=\sqrt[]{81m^2+466.56m^2}=\sqrt[]{547.56m^2}=23.4m[/tex]The area of the triangle could be calculated with the base 21.6m and the height 9m., and the area of the semicircle could be calculated considering his radius as the half of diameter: 23.4/2 = 11.7m
Then the area will be:
[tex]\text{Area = }\pi\cdot(11.7m)^2-\frac{(21.6m)\cdot(9m)}{2}[/tex][tex]\text{Area}=215.02m^2-97.2m^2=117.82m^2[/tex]What is the domain of this function? (assume there are arrows at the ends of the graph) The answer has the form [A, B] Where A = and B = What is the range of this function? The answer has the form Select an answer Where A = and B = On what interval is the function increasing? The answer has the form Select an answer Where A = and B = On what interval is f(x) >= 0? The answer has the form Select an answer Where A = and B =
Answers
SOLUTION
From the question, we want to find
(a) The domain of the function.
The domain is gotten from the x-values. Looking at the x-values from the graph whether the curve is expanded or not, it would satisfy infinitely the value of any x-values. That is whatever x-value will make the function defined.
So the domain is all real numbers or negative infinity to positive infinity Written as
[tex]\begin{gathered} (A,B) \\ where\text{ } \\ A=-\infty\text{ and B = }\infty \end{gathered}[/tex](b) The range is the y-values that satisfy the function. Looking at the curve, the y-values would have infinitely number of negative values, but does not exceed 1, which is the maximum value.
So the range is negative infinity to 1.
Written as
[tex]\begin{gathered} (A,B] \\ where\text{ } \\ A=-\infty\text{ and B = 1} \end{gathered}[/tex](c) The function is increasing from infinite negative values of x, up to where x is -3, before it starts decreasing of sloping downwards
Hence the function is increasing between negative infinity to negative 3, written as
[tex]\begin{gathered} (A,B) \\ where\text{ } \\ A=-\infty\text{ and B = -3} \end{gathered}[/tex](d) Interval where f(x) >= 0
For f(x), that is y to be greater than or equal to zero, this must take place at the x-intercept, that is where the graph cuts the x-axis plane. Looking at the graph, this is at -4 and -2
hence the answer is between -4 and -2, written as
[tex]\begin{gathered} [A,B] \\ where\text{ } \\ A=-4\text{ and B = -2} \end{gathered}[/tex]In the United States, 1 nautical mile
is officially 6076.10 feet. How much
longer is a nautical mile than a statute mile?
Answers
Answer:
796.1 feet
Step-by-step explanation:
The nautical mile is 6076.10 feet and the statute mile is 5280 feet.
Subtracting that yields 796.1 feet.
Geena's hair grew 1 1/8 inches in 3 months. How many inches will her hair grow in 1 month?
Answers
If Geena's hair grew 1 1/8 inches in 3 months then in one month Geena's hair grew 1 1/8 inches long.
What is Equation?Two or more expressions with an equal sign is called as Equation.
Given that,
Geena's hair grew 1 1/8 inches in 3 months.
We need to find how many inches grow in one month.
Let x be the hair grown in one month.
Let us convert 1 1/8 inches to improper fractions
1 1/8= 9/8
Let us form a equation with the given data.
nine by eight by three equal to x by 1.
9/8/3=x/1
Twenty seven by eight equal to x by one.
27/8=x/1
Apply cross multiplication
27=8x
x=27/8
x=3 3/8
Hence in one month Geena's hair grew 1 1/8 inches long.
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How many 1/4 pound pork chops can be cut from a 9 1/2 pound boneless pork loin.
For Culinary
Answers
Evaluate. [(1 1/5−2/5)⋅(− 3/4)3]÷(−9) What is the value of the expression? Enter your answer as a simplified fraction in the box.
Answers
The value of given expression [(1 1/5−2/5)⋅(− 3/4)3]÷(−9) is 1/5
In this question, we have been an expression [(1 1/5−2/5)⋅(− 3/4)3]÷(−9)
We need to evaluate given expression.
First we write an improper fraction as proper fraction.
1 1/5 = 6/5
So given expression becomes,
[(1 1/5−2/5)⋅(− 3/4)3]÷(−9)
= [(6/5 − 2/5) × (− 3/4) 3] ÷ (−9)
= [(4/5) × (-9/4)] ÷ (−9)
= (-9/5) ÷ (-9)
= 1/5
Therefore, the value of given expression [(1 1/5−2/5)⋅(− 3/4)3]÷(−9) is 1/5
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Which statement is true of both debit AND credit cards?
A. Both can help you in endless cycle of debt if you’re not careful
B. Both require you to pay a minimum monthly payment when your bill arrives
C. Both typically have interest rates between 10-30%
D. Both allow you to make purchase in a store or online
Answers
Both allow you to make purchase in a store or online.
D is the ideal choice.
What exactly are credit AND debit cards?While credit cards charge transactions using a line of credit, debit cards commonly withdraw money from a checking account. You use your own money to make purchases when using a debit card. By using a credit card, you are effectively borrowing the funds, which you will eventually have to return to the card's issuer along with any applicable interest.
A credit card against a debit card: Which is safer?When it comes to fraudulent purchases, credit cards typically provide consumers with better protections than debit cards. Purchases made using debit cards may not be as easily or liberally covered by these fraud protections.
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Use the data given to complete the table for your first bulb. DATA TABLE A Time (hours) Energy (kWh) X у Point (time, energy) (x, y) 3 10
Answers
Jourden, this is the solution:
a 100-watt light bulb operating for ten hours would use one kilowatt-hour.
Therefore, in three hours:
0.3 KwH
In ten hours:
1 kwH
A line passes through the point (-9,1) and has a slope of -4/3.
Write an equation in slope-intercept form for this line.
Answers
The equation of line is (y- 2)= 4/3(x- (-9)) or 3y = 4x + 42.
What is equation of line?The slope of the line and a point on the line may be used to create the equation of a line. To better comprehend how the equation for a line is formed, The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.
and, the point slope form of line for any point can be written as
(y- [tex]y_1[/tex] )= m(x- [tex]x_1[/tex])
Given:
A line passes through the point (-9,2) and has a slope of 4/3.
We know by point- slope form
(y- [tex]y_1[/tex] )= m(x- [tex]x_1[/tex])
Here the points are (-9, 2) and m=4/3
So,
(y- 2)= 4/3(x- (-9))
3y -6 = 4 (x+ 9)
3y - 6 = 4x+ 36
3y = 4x + 42
Hence, the equation of line is 3y = 4x + 42.
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Vijay earned some money doing odd jobs last summer and put it in a savings account that earns 6% interest compounded continuously. After 1 year, there is $400.00 in the account. How much did Vijay earn doing odd jobs? Round your answer to the nearest cent.
Answers
The interest is 6%, compounded continuously.
After 1 year there is $400.
The continuous compound formula is
[tex]A=P\times e^{i\times t}[/tex]Where P is the principal, A is the final amount, i is the interest and t is the time in years.
Replacing all the given information, we have.
[tex]\begin{gathered} 400=P\times e^{0.06\times1} \\ P=\frac{400}{e^{0.06}} \\ P\approx376.71 \end{gathered}[/tex]Hence, Vijay earned $376.71 doing odd jobs.Hello would u pls help me find the correct answer
Answers
As we can see in the graphic when we are going more to the left the negative number increase
the point that is closer to the -0.1 is the point C that is located in -0.095.
The correct answer is point C.
Find the volume of the sphere. Either enter an exact answer in terms of ar or use 3.14 for pi and round your final answer to the nearest hundredth.
Answers
We have a sphere of radius 4
r = 4
We know that the equation for the volume is:
[tex]V=\frac{4}{3}\pi r^3[/tex]We know that:
r = 4
and
π = 3.14
Then, we replace in the equation:
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \downarrow \\ V=\frac{4}{3}\cdot3.14\cdot4^3 \end{gathered}[/tex]Since
4³ = 64
then
[tex]\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot4^3 \\ =\frac{4}{3}\cdot3.14\cdot64 \\ =267.9467 \\ =\frac{4}{3}\cdot\pi\cdot64=\frac{256}{3}\pi \end{gathered}[/tex]We want to round our answer to the nearest hundredth (two numbers after the decimal point).
For this case we have two options:
267.94 or 267.95
Since
267.9500 is nearer to 267.9467
than
267.9400
then the answer is 267.95
Answer: the volume of the sphere is 267.95 units³ or (256/3)π units³
write this as a conditional statementMrs.smith has a dog that is not a poodle.
Answers
A conditional statement is used to implicate something, using if and then. Conditional statements are used in deductive reasoning to conclude something from initial evidence.
The given statement is: Mrs. Smith has a dog that is not a poodle.
The conditional statement is: if Mrs. Smith has a dog then it's not a poodle.
3) Yi-fei Wang inherited $20,000 which she invested in stocks and bonds. The stocks returned 6% and the bonds 8%. if the return on the bonds was $80 less than the return on the stocks, how much did she invest in each?
Answers
We know that
• The total amount of money invested is $20,000.
,• The stocks returned 6%.
,• The bonds returned 8%.
,• Bonds return $80 less than Stocks return.
Let's called x stocks and 20,000 - x bonds.
Using the given information, we can define the following equation.-
[tex]0.08(20,000-x)=0.06x-80[/tex]Now, we solve for x.
[tex]\begin{gathered} 1,600-0.08x=0.06x-80 \\ 1,600+80=0.06x+0.08x \\ 0.14x=1,680 \\ x=\frac{1,680}{0.14} \\ x=12,000 \end{gathered}[/tex]Stocks' investment was $12,000.Bond's investment was $8,000. (the difference).3.724x10^-12 convert into numerical form
Answers
A numerical expression is a mathematical statement that only consists of numbers and one or more operation symbols.
3.724x10^-12 = 3724/1000000000000000.
What is a numerical form?A numerical expression is a mathematical statement that only consists of numbers and one or more operation symbols. Thus, if someone gives you an expression, such as x + 2 - 3 + 8 = 11, and claims it is a numerical expression, you must deny it.Standard form refers to any number that can be written as a decimal number between 1.0 and 10.0 multiplied by a power of ten.A fraction is a numerical representation of a portion of something larger.A standard form is a method of writing a given mathematical concept, such as an equation, number, or expression, in a way that adheres to certain rules.3.724x10^-12 = 3.724/ 10^12
= 3.724/ 1000000000000
=3724/1000000000000000 (numerical form)
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please help me find the y-intercept in the graph!
Answers
Answer:
(0,9)
Step-by-step explanation:
can you help me with this, this is not for a test or quiz, i accept brainlys community guidelines.
Answers
The depth od the underwater camerais proportional to the time, this means that the depth varies the same amount of meters for every unit of time (second) that passes.
Let "y" represent the depth and "x" represent the time, you can express the relationship between both variables as
[tex]y=kx[/tex]Where k is the coefficient fo variation, ie. is the amount of meters the depth veries for every second that passes by.
Using the paired values (100, -5) we can calculate the coefficient of variation as
[tex]\begin{gathered} k=\frac{y}{x} \\ k=-\frac{5}{100} \\ k=-0.05 \end{gathered}[/tex]This means that fo every passing second the depth increases -0.05, we can establis the relationship as:
[tex]y=-0.05x[/tex]Now using this expression we can calculate the missing values of time and depth
For depth y= -1m
[tex]\begin{gathered} -1=-0.05x \\ x=-\frac{1}{-0.05} \\ x=20s \end{gathered}[/tex]For time x=60s
[tex]\begin{gathered} y=-0.05\cdot60 \\ y=-3m \end{gathered}[/tex]For time x=240s
[tex]\begin{gathered} y=-0.05\cdot240 \\ y=-12m \end{gathered}[/tex]In parallelogram STUV, VT bisects US and point G. If UG = x + 6 andGS = 2x + 6, find US.
Answers
Answer:
US = 12
Explanation:
The length of GS = UG (because TV bisected the line segment US) and
GS + UG = US
From GS = UG we have
[tex]x+6=2x+6[/tex]subtracting 6 from both sides gives
[tex]x=2x[/tex]subtracting x from both sides gives
[tex]0=x[/tex]With the value of x in hand, We now find the length of the line segment US.
[tex]US=UG+GS=x+6+2x+6=3x+12[/tex]Since x =0, the above gives
[tex]\begin{gathered} US=3(0)+12 \\ US=12 \end{gathered}[/tex]What is the range of the relation (-2,3) (0,3) (2,5) (2,9)
Answers
The range of a relation is given by the values of y the relation can assume.
Looking at the ordered pairs in the relation, the y-values that can be assumed are 3, 5 and 9.
Therefore the range is:
[tex]range=\mleft\lbrace3,5,9\mright\rbrace[/tex]change 0.31 to a fraction
Answers
Problem
change 0.31 to a fraction
Solution
For this case we can do the following:
31/100
And the final answer for this case would be 31/100 the most simplified form
A survey was conducted to determine the percentage ofcollege freshmen that planned to take a math course while in college. The results were given as 75% with a margin oferror of +/- 4%. What does the margin of error of +/- 4%mean?Select one:•4% of the students surveyed refused to participate in the poll.•4% of the students surveyed will most likely change theirminds.• Your guess can be up to 4% wrong and your confidenceinterval will still be correct•4% of the population was not included in the survey.
Answers
Recall that the a margin of error ir a way to do calculations under uncertainty. What the margin of error does is guarantee that the given calculation, under uncertainty, will still be valid within that range.
In our example, we are given that the calculation is 75% with a margin of error of 4%. That is, that the process of calculation that the real value would be with a high confidence between 71% and 79%. So, a value of 77% would be still correct, as it is between the admissible ranges.
So, the anwer would be option C.
The base of an 8-foot ladder is placed 2 feet away from a wall. How high up the wall will the ladder reach?
Answers
The height up the wall will be 7.74 feet the ladder reach when an 8-foot ladder is placed 2 feet away from a wall.
The base of an 8-foot ladder is placed 2 feet away from a wall.
This is a simplistic Pythagoras problem since the wall forms a right angle with the ground.
Let a be the height up the wall.
Let b be the distance from the wall.
Let c be the length of the ladder.
According to Pythagoras's theorem,
a² + b² = c²
Here b = 2 and c = 8
a² + 2² = 8²
a² + 4 = 64
a² = 64 - 4
a² = 60
a = √60
a = 7.74 feet
Thus, the height up the wall will be 7.74 feet the ladder reach.
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Question 1 (Multiple Choice Worth 2 points)
(04.02 MC)
Which graph represents the function of f(x) =
4x²-16?
2x-4
Answers
A graph of function that is a line passing through ( 0 , 4 ) and
( -2 , 0 )
What is function explain?
One input results in one output when using a function, which is a type of rule. This is illustrated by the equation y=x2. Any input for x results in a single output for y. The fact that x is the input value leads us to say that y is a function of x.First we simplify the given function.
Consider,
f(x) = 4x²-16/2x-4
f(x) = (2x)² - (4)²/2x-4
f(x) = [tex]\frac{(2x+4)(2x-4)}{2x-4}[/tex]
f(x) = 2x + 4
Obtained function represent a straight line whose slope is 2 and y-intercept is 4
Let say, y = 2x + 4
then when x = 0 we get, y = 4
when y = 0 we get, x = -2
So we get a graph of function that is a line passing through ( 0 , 4 ) and
( -2 , 0 )
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why does 90×5 and 50×9 equal the same product
Answers
There is a math rule that says the order in which we multiply the factors does not change the product, it's called commutative property.
