What are the missing parts that correctly complete the proof?
Drag the answers into the boxes to correctly complete the proof.
(Please refer to the images provided for the answer options and equation image.)
It has been proved that point A is equidistant from the sides of angle PQR.
What is a Bisector ?Any line or point that divides an angle or a side in equal parts is called a Bisector.
It is given that
Point A is the bisector of Angle PQR
Referring to the image
1. QA is the bisector of angle PQR : Given
2.Angle PQA = Angle RQA : Definition of Bisector
3.Angle QXA = Angle QYA : Definitions of Perpendicular
4. Angle QXA = Angle QYA : All right angles are congruent.
5. QA ≅QA : Reflexive Property of Congruence
6. ΔPQA ≅ΔRQA : AAS Congruence Postulate
7. AX ≅AY Corresponding parts of Congruent Triangles
8. Point A is equidistant from the sides of Angle PQR : Definition of equidistant.
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The list price of a commodity is RM420 and the percentage profit is 40%. If the commodity is sold at a discount of 10%, the profit is____.
Answer:
56
Step-by-step explanation:
you first had to get the marked price so t you can get the profit.
just as illustrated in the picture above.
Use properties of exponents to simplify the expression. First, express the
answer in exponential form. Then, evaluate the expression.
(1^3) ^4
Step-by-step explanation:
[tex] = { ({1}^{3} )}^{4} [/tex]
[tex] = {1}^{3 \times 4} [/tex]
[tex] = {1}^{12} [/tex]
[tex] = 1[/tex]
a researcher in north america discovers a fossil that contains 40% of its original amount of C-14
Using an exponential function, it is found that the substance is 7,535 years old.
What is the exponential function for the amount of a substance?
The function is given by:
[tex]A(t) = A(0)e^{-kt}[/tex]
In which:
A(0) is the initial amount.k is the rate of exponential decay.Carbon-14 has a half life of 5700 years, that is, A(5700) = 0.5A(0), hence we use this to find k.
[tex]A(t) = A(0)e^{-kt}[/tex]
[tex]0.5A(0) = A(0)e^{-5700k}[/tex]
[tex]e^{-5700k} = 0.5[/tex]
[tex]\ln{e^{-5700k}} = \ln{0.5}[/tex]
[tex]k = -\frac{\ln{0.5}}{5700}[/tex]
k = 0.00012160476
Hence:
[tex]A(t) = A(0)e^{-0.00012160476t}[/tex]
It was 40% of the amount when A(t) = 0.4A(0), hence we solve for t.
[tex]A(t) = A(0)e^{-0.00012160476t}[/tex]
[tex]0.4A(0) = A(0)e^{-0.00012160476t}[/tex]
[tex]\ln{e^{-0.00012160476t}} = \ln{0.4}[/tex]
[tex]t = -\frac{\ln{0.4}}{0.00012160476}[/tex]
t = 7535.
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Look at pictures attached for question and answer choices
The answers are a rhombus, bisect a pair of opposite angles, and SAS congruency postulate respectively.
What is a rhombus?A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.
We have a rhombus shown in the picture.
The intersection point is P
From the definition of the rhombus: JK ≅ KM
According to the SAS congruency postulate, two triangles are congruent if a triangle has two sides and an included angle that are congruent to the two sides and an included angle of another triangle.
Thus, the answers are a rhombus, bisect a pair of opposite angles, and SAS congruency postulate respectively.
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what is the inverse of f(x)=(-2x+2)/(x+7)?
By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).
How to find the inverse of a function
In this question we have a rational function f(x) and finding its inverse consists in clearing x in terms of f(x). Prior any algebraic handling, we need to apply the following substitutions:
[tex]x \to y[/tex]
[tex]f(x) \to x[/tex]
[tex]x = \frac{-2\cdot y + 2}{y+7}[/tex]
x · (y + 7) = - 2 · y + 2
x · y + 7 · x = - 2 · y + 2
2 · y + x · y = - 7 · x + 2
y · (2 + x) = - 7 · x + 2
[tex]g(x) = \frac{- 7\cdot x + 2}{x + 2}[/tex]
By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).
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Review the debate between former presidents, Jimmy Carter and Ronald Reagan. In a three paragraph essay of (4-5 sentences each), write an evaluation with evidence to support which candidate proposed a more compelling argument about inflation.
Support your claim with specific data presented by each of the candidates. Be sure to mention a minimum of one counterpoint, and refute this point with evidence.
Answer:
A key turning point in American politics was the election of 1980. It indicated the new electoral power of the suburbs. The success that Reagan had as a conservative would initiate a group of parties because liberals and conservatives would either leave politics or change party affiliations through the 1980s and 1990s. The research shows this caused the 1980 election to be recalled as one of America's best historical events.
Step-by-step explanation:
The League of Women Voters is pleased to welcome President Jimmy Carter, the Democratic Party's candidate for re-election to the Presidency, and Governor Ronald Reagan of California, the Republican Party's candidate for the Presidency. The candidates will debate questions on domestic, economic, foreign policy, and national security issues.
In the debate between sitting president Jimmy Carter and Republican challenger Ronald Reagan, Reagan's arguments and explanations best match the available evidence. Carter claims his policies had reduced the inflation rate by 10% in less than a year and points to the 9 million jobs he had provided to reduce unemployment rates. Reagan refutes this by mentioning that while Carter may have decreased the inflation rate from the beginning of the year, the inflation rate increased from 4.4% at the start of his presidency to almost 12% now. A graph provided by Ed Genuity proves this to be true, therefore current evidence supports Reagan's claim.
In the final week of the 1980 presidential campaign between Democratic President Jimmy Carter and Republican nominee Ronald Reagan, the two candidates held their only debate. And then, during the debate, Reagan posed what has become one of the most important campaign questions of all time: “Are you better off today than you were four years ago?” Carter’s answer was a resounding “NO,” and in the final, crucial days of the campaign, his numbers tanked.
On Election Day, Reagan won a huge popular vote and electoral victory. The “better off” question has been with us ever since. Its simple common sense makes it a great way to think about elections. And yet the answers are rarely simple.
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Which of the following is equal to m
Answer: tan^-1 (c/a)
Step-by-step explanation: An angle C ∈ ℝ such that angle C > 0 can be defined by the trigonometric ratio Arctangent (or rather tan^-1) where side "c" divided by side "a" ≠ 0.
Round 2
5. A Cadillac Escalade gasoline tank has a capacity of 24
gallons. The car uses approximately 1 gallon for every 25
miles it drives. If the tank starts full, write an equation that
describes the amount of gas, g, left in the tank after it has
been driven for m miles.
Answer:
g = 24 - 1/25m
Step-by-step explanation:
Since the Cadillac Escalade can travel 25 miles per gallon, each mile the Escalade travels is 1/25th of a gallon of gas.
This means that every mile the Escalade travels, 1/25th of a gallon is subtracted from the gas tank. Since the gas tank has a capacity of 24 gallons, the value of the gas tank is 24.
This leads us to the equation:
g = 24 - 1/25m
where g is the amount of gas left, and m is the number of miles driven.
what is the equation of x2 + 6x + 8 + 0 algebraically
Answer:
x = - 4 , x = - 2
Step-by-step explanation:
x² + 6x + 8 = 0
consider the factors of the constant term (+ 8) which sum to give the coefficient of the x- term (+ 6)
the factors are + 4 and + 2 , since
4 × 2 = 8 and 4 + 2 = 6 , then
(x + 4)(x + 2) = 0 ← in factored form
equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x + 2 = 0 ⇒ x = - 2
PLEASE HELP ME WITH THIS ASAP
Answer:
x=46
Step-by-step explanation:
4(x+1)-3x=50
first you gotta take care of the () so multiple by 4
(4x+4) -3x=50
combine like terms, subtract 4-3 to get 1 so you have 1x left
4 + x = 50
and then solve for x
x=46
( i checked it to make sure it was right so dw)
Ragan makes beaded jewelry. The graph below shows the number of beads on varying cord lengths.
Jewelry
A graph has cord length (inches) on the x-axis and number of beads on the y-axis. A line goes through points (16, 48) and (24, 72).
Which is the best estimate of the number of beads on a cord that is 16 inches long?
5
8
44
48
Answer:
48
Step-by-step explanation:
Answer:
48
Step-by-step explanation:
edge 2023
C
2
1
3
A. 21
B. 23
C.24
D. 25
b7
#
5
4
In the figure, which angle has the same measure as /2?
Answer:
the angle that has the same measure as /2 is A
Please help me with my math
Answer:
x = 72
y = 15
Step-by-step explanation:
m and n are parallel lines so we can write the following equation:
108 + x = 180 because these angles are supplementary
if we subtract 108 from both sides
x = 72 we can also write the following equation:
5y - 3 = x because these are alternate angles
5y - 3 = 72 add 3 to both sides
5y = 75 divide both sides by 5
y = 15
Karl’s math class is playing a number game. Each student is given a number card containing the numbers 1 to 6. The rules of the game are that each student must put a cross through two numbers on the card and hand it in to the teacher. The teacher has a bag containing six balls numbered 1 to 6. When all the number cards have been handed in the teacher draws out two balls from the bag. Every student who had chosen the same two numbers shown on the balls wins a prize. If there are 30 students in Karl’s class, how many students are likely to win a prize? Describe your reasoning
By finding the probability, we can expect that 2 out of the 30 students will win the prize.
How many of the 30 students will win the prize?
First, we should get the probability of winning this game.
Here the students select two numbers out of 6, just to make the calculations let's say that these numbers are 1 and 2.
Now, we need to get these two numbers in two balls. The probability of getting the ball with the number 1 out of the 6 balls is:
p = 1/6
The probability of getting the ball with the number 2 out of the remaining 5 balls (because we already got one) is:
q = 1/5
The joint probability is then:
P = 2*(1/6)*(1/5) = 1/15.
Where the factor 2 comes to take in account the permutations, for the case where we first draw the number 2 and then the number 1.
Then the expected number of students that will win is equal to the probability times the total number of students:
(1/15)*30 = 2
So out of the 30 students, we can expect that 2 will win.
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What is the slope of the linear relationship shown in this table of values?
Answer:
B
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 1) and (x₂, y₂ ) = (- 4, 11) ← 2 ordered pairs from the table
m = [tex]\frac{11-(-1)}{-4-2}[/tex] = [tex]\frac{11+1}{-6}[/tex] = [tex]\frac{12}{-6}[/tex] = - 2
Select the correct answer.
Which calculation correctly uses prime factorization to write √48 In simplest form?
OA √48 = √2-2-2-2-3-2√12
OB. √48√4 - 12 = 2√12
OC. √48 = √2-2-2-2-3= 4√3
OD. √48 =√16-3 = 4√3
D. √48 =√16*3 = 4√3
Simplify the radical by breaking the radicand up into a product of known factors.
16*3 = 48
this means that √48 = √16*3, but this can be simplified.
√16 = 4, √3 = √3 because it cannot be simplified farther
making the most simplified answer 4√3
Points
Find f(−2)
given f(x)=−x3−3x2+8
Answer:
12 :D
Step-by-step explanation:
First we substitute all x's for -2 :)
f(-2)=−-2^3−3(-2)^2+8
Now we solve :)
f(-2)=−-2^3−3(-2)^2+8
f(-2)=− -8 −3(-2)^2 + 8
f(-2) = -8 - 3(-4) + 8
f(-2) = - 8 + 12 + 8
f(-2) = 4 + 8
f(-2) = 12 :)
f will equal 12 :)
Have an amazing day!!
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Which is a rational function?
A. Y=5
B. Y=√x-3
C. Y=x²-3x+5
D.Y = x-5/x
I’m having trouble understanding how to solve this someone please help ASAP thank you!
Use the Law of Cosines to solve the problem. You must solve for BC first. Solve this problem in order.
A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position. To the nearest tenth of a degree, how many degrees north of west (x) did it
turn when it changed direction? Show your work.
Matt is trying to measure the height of a tree using
trigonometry. He is having trouble because of the
terrain around the tree. The horizontal distance
from the tree to Matt's eyes is 120 feet. The angle
of depression from the horizontal is 30°. Matt's
angle of sight to the top of the tree is 23°. What is
the height of the tree? (Round to the nearest foot.)
The height of the tree will be 18.35 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Matt is trying to measure the height of a tree using trigonometry.
He is having trouble because of the terrain around the tree.
The horizontal distance from the tree to Matt's eyes is 120 feet.
The angle of depression from the horizontal is 30°.
Matt's angle of sight to the top of the tree is 23°.
The diagram is given below.
Let x be the height of tree and AM be h.
The value of (h + x) will be
tan 30° = (x + h) / 120
x + h = 69.288
Then the value of h will be
tan 23° = h / 120
h = 50.94 feet
Then the height of the tree will be
⇒ h + x – h
⇒ 69.29 - 50.94.
⇒ 18.35 feet
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Find the following, giving your answers
to 1 decimal place.
10 cm/
6 cm
8 cm
a) The volume of the cone.
b) The curved surface area of the cone.
Answer:
a) 301.6 cm³
b) 188.5 cm²
Step-by-step explanation:
The volume and lateral surface area of the cone can be found using the given dimensions with the given formulas. All that is needed is to substitute the appropriate values and do the arithmetic.
__
a) volumeThe volume is given by the formula ...
V = 1/3πr²h
The dimensions are given on the diagram: r = 6 cm, h = 8 cm. Using these values in the formula, we find the volume to be ...
V = 1/3π(6 cm)²(8 cm) = 96π cm³ ≈ 301.6 cm³
The volume of the cone is about 301.6 cm³.
__
b) areaThe lateral area of the cone is given by the formula ...
A = πrl
The dimensions are given on the diagram: r = 6 cm, l = 10 cm (the slant height). Using these values in the formula, we find the area to be ...
A = π(6 cm)(10 cm) = 60π cm² ≈ 188.5 cm²
The area of the curved surface is about 188.5 cm².
what is the principle value of sin^-1(1)
The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. The principal value of sin⁻¹(1) is 90°.
What is Sine (Sinθ)?The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,
Sin(θ) = Perpendicular/Hypotenuse
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The hypotenuse is the longest side of the triangle.
The principal value of sin⁻¹(1) is,
θ = Sin⁻¹(1)
θ = 90°
Hence, the principal value of sin⁻¹(1) is 90°.
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Find the value of x.
5
X
11
y
The value of the variable is 4√5. Then the correct option is C.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The similar triangles are shown in the diagram.
16 / x = x / 5
x² = 16 × 5
x = 4 √5
Then the value of the variable is 4√5.
Then the correct option is C.
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same side interior angles are _____ congruent
A.always
B.never
C.sometimes
Answer:
B. Never
Step-by-step explanation:
that's just what my math teacher told us...
Squares are cut out of the corners of a piece of 18*18 graph paper so that the sides can be folded to make an open box. What is the largest possible number of cubic units in the volume of the box if we require that the length of each edge is a whole number?
Answer:
432 mm²
Step-by-step explanation:
We need to cut out 3x3 squares from corners and make an open box. It's height will be 3mm(see the plan). So volume will be:
V = 12 * 12 * 3 = 432mm²
Which function can be used to represent the graphed geometric sequence?
f(x) = 80(One-fourth) Superscript x minus 1
f(x) = 320(One-fourth) Superscript x minus 1
f(x) = 80(4)x – 1
f(x) = 320(4)x – 1
The function which is used to represent the graphed geometric sequence is
[tex]f(x) = 80{( \frac{1}{4}) }^{x - 1} [/tex]
Let a be first term and r common ratio of the Geometric progression.
The Geometric sequence is of the form a,ar,ar^2, ...
The common ratio will be ar/a.
From the graph, we can find out the sequence as 80,20,5, ...
Here we can see that the sequence is in Geometric Progression.
First term a=80
Common ratio r= ar/a
= 20/80
=1/4
General term of Geometric sequence is
[tex]f(x) = a {r}^{x - 1} [/tex]
Substituting the value a = 80 and r = 1/4,
we get,
[tex]f(x) =80 { (\frac{1}{4} )}^{x - 1} [/tex]
Hence, the correct answer is
[tex]f(x) =80 { (\frac{1}{4} )}^{x - 1} [/tex]
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What is the independent variable in the equation y=-5x+2?
Answer: x
Step-by-step explanation:
For this equation, the variable y is dependent on the value of x. The value of y changes depending on the value of x. This means that x is the independent variable for this equation.
On a number line, 2.5 would be located ______. Choose all answers that make a true statement.
2.5
《----|----|----|----|----|----|----|----|----|----|----》
A. to the right of 2.52
B. between 2.45 and 2.55
C. to the left of 2.3
D. between of 2.4 and 2.6
Answer:
It is both answers B and D
What is the volume of a cylinder, in cubic feet, with a height of 13 feet and a base
diameter of 4 feet? Round to the nearest tenths place.
Answer:
163.3
Step-by-step explanation:
3.14*r^2*h
h=13
4/2 = 2
r=2
2^2 = 4
3.14*4 = 12.56
12.56*13 = 163.28
Rounded = 163.3
I believe the answer is 163.3
