Answers
An angle bisector is a ray, segment, or line that divides a given angle into two angles of equal measure. Therefore, the correct answer is option C.
What is an angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
An angle bisector is defined as a ray, segment, or line that divides a given angle into two angles of equal measures.
Steps to Construct an Angle Bisector:
Step 1: Draw any angle, say ∠ABC.
Step 2: Taking B as the center and any appropriate radius, draw an arc to intersect the rays BA and BC at, say, E and D respectively. (Refer to the figure below)
Step 3: Now, taking D and E as centers and with the same radius as taken in the previous step, draw two arcs to intersect each other at F.
Step 4: Join B to F and extend it as a ray. This ray BF is the required angle bisector of angle ABC.
Step 2: Taking B as the center and any appropriate radius, draw an arc to intersect the rays BA and BC at, say, E and D respectively. (Refer to the figure below)
Therefore, option C is the correct answer.
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Related Questions
Find the distance between R (-1,1) and S (-4,-5) to the nearest tenth.
Answers
The distance between the points R (-1,1) and S (-4,-5) is [tex]3\sqrt{5}[/tex] units.
To find the distance between points R(-1, 1) and S(-4, -5), we can use the distance formula in a coordinate plane.
The distance formula is given by:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Using the given coordinates:
[tex]x_1 = -1, y_1 = 1[/tex](coordinates of point R)
[tex]x_2 = -4, y_2 = -5[/tex] (coordinates of point S)
[tex]d = \sqrt{(-4 +1 )^2 + (-5 - 1)^2}[/tex]
[tex]d = \sqrt{9 +36}[/tex]
[tex]d = \sqrt{45}[/tex]
[tex]d = \sqrt{9 \times 5}[/tex]
[tex]d = 3\sqrt{5}[/tex]
Hence, the distance between the points R (-1,1) and S (-4,-5) is [tex]d = 3\sqrt{5}[/tex] units.
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The line x+2y=9 intersects the curve xy+18=0 at the points A and B. Find the coordinates of A and B
Answers
Chris runs 7 miles in 80 minutes. at the same rate, how many miles would he run in 64 minutes?
Answers
80 minutes= 7 miles
1 minute= 7 / 80
= 0.875
64 minutes= 0.875 x 64
= 5.6 miles
Hope this helps :))
~Top
What is 4125 divided by 8
Answers
jdjdjdhfjdhfjdhfj
Which congruence theorems can be used to prove △EFG ≅ △JHG? Check all that apply.
HL
SAS
SSS
ASA
AAS
Answers
Answer:
ASA and AAS
Step-by-step explanation:
We do not know if these are right triangles; therefore we cannot use HL to prove congruence.
We do not have 2 or 3 sides marked congruent; therefore we cannot use SSS or SAS to prove congruence.
We are given that EF is parallel to HJ. This makes EJ a transversal. This also means that ∠HJG and ∠GEF are alternate interior angles and are therefore congruent. We also know that ∠EGF and ∠HGJ are vertical angles and are congruent. This gives us two angles and a non-included side, which is the AAS congruence theorem.
Since EF and HJ are parallel and EJ is a transversal, ∠JHG and ∠EFG are alternate interior angles and are congruent. Again we have that ∠EGF and ∠HGJ are vertical angles and are congruent; this gives us two angles and an included side, which is the ASA congruence theorem.
Answer: ASA and AAS
Step-by-step explanation:
Janet has a balance of 125 on a credit card on her next statement she wants to reduce her balance to no more than 60 how much does she need to pay off
Answers
Janet has to pay off $65 to reduce her balance to no more than $60.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Janet has a balance of 125 on a credit card on her next statement she wants to reduce her balance to no more than 60.
The amount to be paid will be calculated as,
Amount = 125 - 60
Amount = $65
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Find the length of AC. Use that length to find the length of CD. What is the length of CD? Round to the nearest tenth.
A) 2.3 cm
B) 4.0 cm
C) 10.7 cm
D) 18.6 cm
Answers
length of AC = 10 * sin(30) = 5 cm
Length of CD = 5 /tan(25) = 10.7cm
answer is C
Answer
Find out the what is the length of CD , AC .
To prove
By using the trignometric identity
[tex]sin B = \frac{Perpendicular}{Hypotenuse}[/tex]
As in ΔABC
∠ B = 30° , AB= 10 cm
put in the trignometric identity
[tex]sin 30^{\circ} = \frac{AC}{10}[/tex]
As
[tex]sin30^{\circ} =\frac{1}{2}[/tex]
[tex]\frac{1}{2} = \frac{AC}{10}[/tex]
[tex]AC = \frac{10}{2}[/tex]
AC = 5cm
Now in the ΔADC
[tex]tan D^{\circ} = \frac{Perpendicular}{Base}[/tex]
∠ D = 25° , AC = Perpendicular = 5 cm
[tex]tan 25^{\circ} = \frac{5}{CD}[/tex]
tan 25 ° = 0.46630765815 (approx)
[tex]CD = \frac{5}{0.46630765815}[/tex]
CD = 10 .7cm ( approx )
Option (C) is correct .
Traveling with a speed of 70 mph, a car covered a distance D miles in T hours. Write an equation that relates the distance D this car travels in T hours. Use the equation to find the distance the car travels between 3:30 p.m. and 5:00 p.m.
Answers
Answer:
i need the equation I know that the distance is 105 miles
Step-by-step explanation:
helppppp
Find the measures of the angles of a triangle if the measure of one angle is three times the measure of a second angle and the third angle measures 55 times the second angle decreased by 90
Answers
3x+x+55x-4950=180
59x=5130
x=84.94
Answer: First Angle= 254.7
Second Angle= 84.9
Third Angle= 4669.5
But I think that's wrong because a triangle only has 180 and there is no higher degree than 360.
I WILL GIVE BRAINLIEST. What is the justification for each step in solving the inequality?
75x+35≥7(11x+9)+4
75x+35≥7(11x+9)+4 Given
75x+35≥77x+63+4 Distributive Property
75x+35≥77x+67
−2x+35≥67 Subtraction Property of Order
−2x≥32
x≤−16
I just need the ones that don't have the justification next to it
Answers
75x - 35 ≥ 77x + 63 + 4 Distributive property.
75x -35 ≥ 77x + 67 Combine like terms.
-2x - 35 ≥ 67 Subtraction property of equality.
-2x ≥ 102 Addition property of equality.
x ≤ 51 Division property of equality.
Answer:
Combine like terms
Subtraction property of inequality
Division property of inequality
Step-by-step explanation:
We are given tnat
[tex]75x+35\geq 7(11x+9)+4[/tex]
We have to find the missing justification in given solution
[tex]75x+35\geq 7(11x+9)+4[/tex]
Reason:Given
[tex]75x+35\geq 77x+73+4[/tex]
Reason:Distributive property
[tex]75x+35\geq 77x+67[/tex]
Reason:combine ike terms
[tex]-2x+35\geq 67[/tex]
Reason:Subtraction property of order
[tex]-2x\geq 32[/tex]
Reason:Subtraction property of inequality
[tex]x\leq -16[/tex]
Reason:Division property of inequality
Find the average value of f(x) = 1/x over the interval [e, 2e].
ln(2)/e
-1/2e^
Ln2
Ln3
Answers
the average value of f(x) = 1/x over the interval [e, 2e] is, ln(2)/e.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
f(x) = 1/x over the interval [e, 2e].
i.e. we get,
[tex]\frac{1}{2e-e}[/tex] × [tex]\int\limits^{2e}_e {1/x} \, dx[/tex] =1/e. ln (x)[2e, e]
=ln(2e)/e - ln(e)/e
=[ln2+lne/e] - 1/e
=ln2/e +1/e -1/e
=ln(2)/e
hence, the average value of f(x) = 1/x over the interval [e, 2e] is, ln(2)/e.
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The combined age of three relatives is 120 years. James is three times the age of Dan, and Paul is two times the sum of the ages of James and Dan. How old is each person?
Answers
james age is 3x and 2(x + 3x) is Pauls age so we have:-
x + 3x + 2*4x = 120
12x = 120
x = 10
so Dans age is 10 , James's age is 30 and Paul's age = 80
The ages of James, Paul and Dan is required.
James is 30 years old, Paul is 80 years old and Dan is 10 years old.
Let the ages of James be [tex]j[/tex], Paul be [tex]p[/tex] and Dan be [tex]j[/tex].
James is three times the age of Dan
[tex]j=3d[/tex]
Paul is two times the sum of the ages of James and Dan
[tex]p=2(j+d)\\\Rightarrow p=2(3d+d)\\\Rightarrow p=2(4d)=8d[/tex]
The combined ages of the people is 120
[tex]j+p+d=3d+8d+d\\\Rightarrow 120=12d\\\Rightarrow d=\dfrac{120}{12}\\\Rightarrow d=10[/tex]
[tex]j=3d=3\times 10\\\Rightarrow j=30[/tex]
[tex]p=8d=8\times 10\\\Rightarrow p=80[/tex]
So, James is 30 years old, Paul is 80 years old and Dan is 10 years old.
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Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dogs. Recall the inequality that represents this situation: 15x + 10y ≥ 1100
Explain how to graph the solution set.
Answers
15x + 10y = 1,100
x-intercept:
15x + 0 = 1,100
x = 1,100/15 = 73.33
y-intercept:
0 + 10y = 1,100
y = 1,100/10 = 110
Now, plot points (73.33,0) and (0,110). Since the equality symbol is ≥, which has an equal sign to it, connect the points using a solid line.
Next, let's find a point on the graph. Suppose it is the origin at (0,0). Use this points to the equation.
15x + 10y ≥ 1,100
15(0) + 10(0) ? 1,100
0 ? 1,100
0 < 1,100
It makes the symbol ≥ false. Therefore, it means that the other region bounded by the line is the solution. So, you shade this area. The final graph is shown in the picture attached.
To graph the solution set of the inequality 15x + 10y ≥ 1100, find the intercepts of the graph and draw a line passing through them. Then, test a point not on the line to determine which side represents the solution set. The solution set of the inequality is the region below the line on the graph.
Explanation:To graph the solution set of the inequality 15x + 10y ≥ 1100, we can start by identifying the intercepts of the graph. An intercept is a point where the graph intersects either the x-axis or the y-axis. To find the x-intercept, we set y = 0 in the inequality: 15x + 10(0) ≥ 1100. Simplifying this equation, we have 15x ≥ 1100. Dividing both sides by 15, we get x ≥ 73.33. Therefore, the x-intercept is (73.33, 0).
To find the y-intercept, we set x = 0 in the inequality: 15(0) + 10y ≥ 1100. Simplifying this equation, we have 10y ≥ 1100. Dividing both sides by 10, we get y ≥ 110. Therefore, the y-intercept is (0, 110).
After finding the intercepts, we can draw a line passing through these two points. Since the inequality is ≥, the line will be solid (including the points on the line). Finally, we determine which side of the line represents the solution set. We can choose a test point not on the line, such as (0, 0), and substitute its coordinates into the inequality. If the inequality is true, the shaded region representing the solution set should be below the line.
If the inequality is false, the shaded region should be above the line. In this case, substituting (0, 0) into the inequality gives 15(0) + 10(0) = 0, which is less than 1100. Therefore, the shaded region should be below the line. The solution set of the inequality 15x + 10y ≥ 1100 is the region below the line on the graph.
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$1.80 in dimes and nickels. she has a total of 23 coins. how many of each kind does she have?
Answers
Since 10*5=50
and 13*10=130
They both add you to 180
t takes Audrey 35 hour to paint 25 square yards of wood to be used for making shelves. How many square yards can she paint in 1 hour?
Answers
3/5 hours / 2/5 square yards
1 hour / x square yards
simplify by cross multiplying
3/5x = 2/5(1).
3/5x = 2/5.
3/5/3/5x = 2/5/3/5
x = 10/15
x = 2/3
so she can paint 2/3 square yards in 1 hour. hope this helps!
3/5x = 2/5(1)
3/5x = 2/5
3/5/3/5x = 2/5/3/5
x = 10/15
x = ⅔
Hope this helps and have a great day! ;)
A camel can drink 15 gallons of water in 10 minutes. at this rate, how much water can the camel drink in 77 minutes?
Answers
To solve this problem, we simply have to use ratio and proportion.
We know that 15 gallons is consumed in 10 minutes therefore the conversion factor is:
15 gallons / 10 minutes
Therefore in 77 minutes:
water consumed = (15 gallons / 10 minutes) * 77 minutes
water consumed = 115.5 gallons
PLEASE HELP!!
What is the slope of the line represented by the equation 2x+3y= –12 ?
A)–3/2
B)–2/3
C)2/3
D)3/2
Answers
Answer:
the correct answer is B.-2/3
A fair coin is flipped six times. what is the probability that heads occurs exactly 4 times if it is known that heads occurs at least four times?
Answers
A fair coin is flipped six times. Then 1/22 is the probability that heads occurs exactly 4 times if it is known that heads occurs at least four times
What is Probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
The probability that heads occurs exactly 6 times if it is known that heads occurs at least four times is
P{H=6|H≥4}
= P{(H=6)∩(H≥4)}/P{H≥4}
= P{H=6}/P{H≥4}
We need to calculate P{H=6}
P{H=6} = C(6,6)(½)6
= (½)6
P{H≥4} = P{H=4} + P{H=5} + P{H=6}
= C(6,4)(½)4(½)2 + C(6,5)(½)5(½) + C(6,6)(½)6
= (½)6[C(6,4) + C(6,5) + C(6,6)]
= (½)6[15 + 6 + 1]
= (½)6(22)
Therefore,
P{H=6|H≥4} = 1/22
1/22 is the probability that heads occurs exactly 4 times if it is known that heads occurs at least four times
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Max rode his bike 40 miles in hours.
Which complex fraction can be used to calculate Max’s average speed?
Answers
this is the answer
Answer:
40 Miles.
5 hrs.
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2
A cylindrical rain barrel has a radius of 2 feet and holds a total of 30 cubic feet of water. How tall is the rain barrel? Use 3.14 for pi. Round your answer to the nearest hundredth.
Answers
lets use the equation (3.14)(2^2)=30. first we must do the 2 squared which gives us 4 resulting in (3.14)4=30 now we multiply pi with 4 resulting in 12.56=30 now we do the division... and my answer is 2.39 i am not sure if this is right though so take caution when using my response
The height of the rain barrel is required.
The height of the barrel is 2.39 feet.
r = Radius of barrel = 2 feet
V = Volume of barrel = 30 cubic feet
h = Height of barrel
Since, the barrel is cylindrical the volume of the barrel is
[tex]V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{30}{3.14\times 2^2}\\\Rightarrow h=2.3885\approx 2.39\ \text{feet}[/tex]
The height of the barrel is 2.39 feet.
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The county fair charges $1.25 per ticket for the rides. Jermaine bought 25 tickets for the rides and spent a total of $43.75 at the fair. Jermaine spent his money only on ride tickets and fair admission. The price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Define your variables.
(b) Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission.
(c) Explain your answer to Part b.
Answers
The equation would be y = 1.25x + ?
You would insert 25 for x which equals 31.25 and insert 43.75 for y.
43.75 = 31.25 + ? Then subtract 31.25 from both sides of the equation and you would get....
12.5 = ?
That is your flat rate to get in to the fair
Marjorie bought 24 bottles of juice. She drinks 2 bottles each day. Which of the following best represents the number of bottles she has left at the end of d days?
A.2d - 24
B.24d - 2
C.24 + 2d
D.24 - 2d
Answers
Answer: D.24 - 2d
Step-by-step explanation: I took the test Hope you have a good day. PEACE
what is the property of this equation? if 2x=8 then x=4
Answers
Find the equation of the line with slope = -5 and passing through (4,-17). write your equation in the form y = m x + b y=mx+b.
Answers
m= -5
Just substitute the values of the point into the equation to find c
-17=-5 x 4 +b
-70+20+b
3=b
y=-5x+3
Hope I helped :)
-17 = -5(4) + b
-17 = -20 + b
+20 +20
3 = b
y = -5x + 3
Jim got 30 questions correct out of a total of 35. what was the percentage he got correct?
Answers
correct questions / total questions....* 100 (multiply by 100 to get ur percent)
30/35 * 100 =
0.857 * 100 =
85.7% ....so Jim got 85.7% correct....and if u need it rounded, it is 86%
Jim answered 30 out of 35 questions correctly, which is 85.7% correct when calculated using the percentage formula.
Explanation:Jim got 30 questions correct out of a total of 35. To find the percentage of questions he got correct, you can use the formula for calculating percentages: Percentage = (Number of correct answers ÷ Total number of questions) × 100%. Applying this formula to Jim's case: Percentage = (30 ÷ 35) × 100% = 0.857 × 100% = 85.7%. Therefore, Jim got 85.7% of the questions correct.
If x represents time, the average rate of change of a function f(x) in the first two seconds is____.
Answers
(y2-y1)/(x2-x1)=(100-50)/(2-0)=25
the rate of change is 25
Answer:
The average rate of change of a function f(x) in the first two seconds is 25.
Step-by-step explanation:
Given : Graph , X represent the time , function f(x).
To find : the average rate of change of a function f(x) in the first two seconds is____.
Solution : The rate of change of f(x) with respect to x is the slope of the line.
slope : [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
In first two second ( 0, 50 ) , ( 2, 100).
slope : [tex]\frac{100-50}{2-0}[/tex].
slope : [tex]\frac{50}{2 }[/tex].
the average rate of change of a function f(x) in the first two seconds is 25.
Therefore,The average rate of change of a function f(x) in the first two seconds is 25.
60 POINTS
Which statement is true about this argument?
Premises:
If an angle measure is greater than 90°, then the angle is an obtuse angle.
The measure of ∠C is 102°.
Conclusion:
∠C is an obtuse angle.
Answers
match each point with one of the following fractions 5/6, 7/12, 1/8, 5/16
A=5/6 B= 5/16 C= 7/12 D= 1/8
A= 1/8 B= 5/16 C= 7/12 D= 5/6
A= 7/12 B= 5/6 C = 5/16 D = 1/8
A= 5/16 B= 1/8 C = 7/12 D= 5/6
Answers
7/12=0.583
1/8= 0.125
5/16= 0.3125
5/6= 0.83
The order for this is 0.3125, 0.125, 0.583, and 0.83. So the answer is last option
Answer:
The correct option is A= 1/8 B= 5/16 C= 7/12 D= 5/6
Step-by-step explanation:
Consider the provided fractions.
First convert each fraction into decimal form as shown:
5/6 = 0.833..
7/12 = 0.5833..
1/8 = 0.125
5/16 = 0.3125
The largest number among them is 0.833.. i.e 5/6 and the smallest number among them is 0.125 i.e 1/8
Arrange them in increasing order as shown:
0.125, 0.3125, 0.5833.., 0.833.. or 1/8, 5/16, 7/12, 5/6
Now consider the provided figure. The alphabets are showing the number are in increasing order
Thus, the correct option is A= 1/8 B= 5/16 C= 7/12 D= 5/6
There are 20 alligators in the swamp. Each year, the number of alligators increases by 25%. There are 25 crocodiles in the swamp. Each year, 10 new crocodiles join the swamp.
Part A: Write functions to represent the number of alligators and crocodiles in the swamp throughout the years. (4 points)
Part B: How many alligators are in the swamp after 4 years? How many crocodiles are in the swamp after the same number of years? (2 points)
Part C: After approximately how many years is the number of alligators and crocodiles the same? Justify your answer mathematically. (4 points)
Answers
Part B: f(x)=(5)(4)+20(alligators) and f(x)=(10)(4)+25(crocodiles)
Alligators: 40 and Crocodiles: 65
Part C: None because the rate of the alligators won't catch up with the rate of crocodiles.
Part A: Alligators: [tex]\(A(t) = 20 \times (1 + 0.25)^t\), Crocodiles: \(C(t) = 25 + 10t\).[/tex]
Part B: After 4 years: Alligators: ~38, Crocodiles: 65.
Part C: Alligators and crocodiles equal: Solve [tex]\(20 \times (1 + 0.25)^t = 25 + 10t\).[/tex]
Part A:
Let's define the functions to represent the number of alligators and crocodiles in the swamp over the years.
For alligators:
[tex]\[A(t) = A_0 \times (1 + r)^t\][/tex]
Where:
[tex]- \(A(t)\) is the number of alligators in the swamp after \(t\) years.\\- \(A_0\) is the initial number of alligators (20 in this case).\\- \(r\) is the growth rate per year (25% or 0.25).\\- \(t\) is the number of years.[/tex]
For crocodiles:
[tex]\[C(t) = C_0 + n \times t\][/tex]
Where:
[tex]- \(C(t)\) is the number of crocodiles in the swamp after \(t\) years.\\- \(C_0\) is the initial number of crocodiles (25 in this case).\\- \(n\) is the number of new crocodiles joining each year (10 in this case).\\- \(t\) is the number of years.[/tex]
Part B:
To find the number of alligators after 4 years, we use the formula:
[tex]\[A(4) = 20 \times (1 + 0.25)^4\][/tex]
To find the number of crocodiles after 4 years, we use the formula:
[tex]\[C(4) = 25 + 10 \times 4\][/tex]
Part C:
To find when the number of alligators and crocodiles are the same, we set [tex]\(A(t) = C(t)\) and solve for \(t\).[/tex]
[tex]\[20 \times (1 + 0.25)^t = 25 + 10 \times t\][/tex]
This equation can be solved numerically to find the value of \(t\) when the number of alligators and crocodiles are the same.
Which of the following statements does not describe the structure of an atom?
An atom has a small, dense center called the nucleus.
Inside the nucleus of an atom are protons and electrons.
Protons are positively charged sub-atomic particles.
Electrons are negatively charged sub-atomic particles.
Answers
Final answer:
The incorrect statement is that the nucleus of an atom contains protons and electrons; actually, the nucleus contains protons and neutrons, with electrons orbiting around it.
Explanation:
The statement that does not correctly describe the structure of an atom is 'Inside the nucleus of an atom are protons and electrons'. This statement is incorrect because the nucleus of an atom actually contains protons and neutrons, not electrons. Electrons are negatively charged sub-atomic particles that orbit around the nucleus. The nucleus itself is a small, dense center that is positively charged due to the presence of protons, which are positively charged. Neutrons, which have no electric charge, are also found within the nucleus.
Further expanding on atomic structure, the nucleus is very tiny compared to the rest of the atom, which is mostly empty space. The electrons residing in this space are in perpetual motion, creating a cloud-like region around the nucleus. Despite their small mass compared to protons and neutrons, the number of electrons equals the number of protons in a neutral atom, balancing the charge.