Answers
Given:
We're given two sections right and left and we need to match the correct options relating to each other.
Step-by-step solution:
1) We're given a diagram of a line passing through the circle and cutting two points on the circle.
Answer: Secant
2) A segment between the center of the circle and the point on the circle:
Answer: Radius
3) The distance along the circle, between two points of the circle:
Answer: Arc length
4) A figure of line cutting on one point of the circle:
Answer: tangent
5) The distance around a circle:
Answer: Circumference
6) A figure of a line joining two points of the circle (not passing through the circle):
Answer: Chord
Related Questions
I need help on this!Greater than, less than or equal to?number 28
Answers
Explanation:
We can draw a number line to see the numbers and check which one is greater:
2.5 is on the left of 3, so it is less than 3.
Answer:
2.5 < 3
2.5 < 3
Solve the right triangle. Round decimal answers to the nearest tenth. find RSfind RTfind angle T
Answers
Δ RST shown in the picture is a right triangle, we know the measure of ∠R and ∠S, and the length of side ST.
To determine the length of the missing angle, you have to remember that the sum of the inner angles of a triangle add up to 180º
Then we can calculate the measure of ∠T as follows:
[tex]\begin{gathered} \angle R+\angle S+\angle T=180 \\ 57+90+\angle T=180 \\ 174+\angle T=180 \\ \angle T=180-174 \\ \angle T=33º \end{gathered}[/tex]The measure of the missing angle is ∠T=33º
To determine the lengths of the missing sides RS and RT, you have to use the trigonometric ratios of sine, cosine, and tangent. These ratios are defined as follows:
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypothenuse} \\ \cos \theta=\frac{adjacent}{hypothenuse} \\ \tan \theta=\frac{opposite}{adjacent} \end{gathered}[/tex]"θ" represents the angle of interest.
Using ∠R as a point of reference, side ST is across this angle so it is the side of the triangle "opposite" to it.
Side RS is next to ∠R, so it is the side "adjacent" to it.
The trigonometric ratio that shows the relationship between the opposite and adjacent sides to an angle is the tangent. Using the definition of the tangent you can determine the length of RS as follows:
[tex]\tan R=\frac{RS}{ST}[/tex]-First, write the expression for RS, which means that you have to pass "ST" to the left side of the equal sign by applying the opposite operation to both sides of it.
[tex]\begin{gathered} ST\tan R=ST\cdot\frac{RS}{ST} \\ ST\tan R=RS \end{gathered}[/tex]-Replace the expression with the values of ∠R and ST:
[tex]\begin{gathered} 15\cdot tan57=RS \\ 23.09=RS \\ RS\approx23.1 \end{gathered}[/tex]Side RS measures 23.1
Side RT is the longest side of the triangle, and thus, its hypothenuse. To determine its length using ∠R and side ST, you have to apply the definition of the sine:
[tex]\sin R=\frac{ST}{RT}[/tex]-Pass the term RT to the other side of the equation to take the term out of the denominators place:
[tex]\begin{gathered} RT\cdot\sin R=RT\frac{ST}{RT} \\ RT\cdot\sin R=ST \end{gathered}[/tex]-Next, divide both sides by the sine of R to write the expression for RT
[tex]\begin{gathered} RT\cdot\frac{\sin R}{\sin R}=\frac{ST}{\sin R} \\ RT=\frac{ST}{\sin R} \end{gathered}[/tex]-Now replace the expression with the values of ∠R and ST to determine the length of RT
[tex]\begin{gathered} RT=\frac{15}{\sin 57} \\ RT=12.58 \\ RT\approx12.6 \end{gathered}[/tex]Side RT measures 12.6
35) Use a formula to find the area of the figure.a15 in.7 in.20 in.
Answers
Given
height = 7 inches
base = 20 inches
Recall the formula for finding the area of the triangle
[tex]\begin{gathered} A_{\text{triangle}}=\frac{1}{2}bh \\ \text{where} \\ b\text{ is the base} \\ h\text{ is the height} \end{gathered}[/tex]Substitute the given dimensions of the triangle and we have
[tex]\begin{gathered} A=\frac{1}{2}bh \\ A=\frac{1}{2}(20\text{ in})(7\text{ in}) \\ A=\frac{1}{2}\cdot140\text{ in}^2 \\ A=70\text{ in}^2 \\ \\ \text{Therefore, the area of the triangle is }70\text{ in}^2. \end{gathered}[/tex]The length of a rectangle is 97 m and the width is 14 m find the area give your answer without units
Answers
The area of the rectangle is 1358
Explanation:length of the rectangle = 97m
width of the rectangle = 14m
Area of a rectangle = length × width
[tex]\begin{gathered} \text{Area = 97m }\times\text{ 14m} \\ Area\text{ }of\text{ the rectangle = }1358m^2 \end{gathered}[/tex]The area of the rectangle is 1358 (without units)
A rocket is fired from the ground. Its height, in feet, is represented by the function h(t)=-16^2 +48t, where t(in seconds) represents the amount of time in the air since takeoff. When does the rocket land on the ground?A. 2 secondsB. 3.5 secondsC. 3 secondsd. 4.5 seconds
Answers
Given the height to be represented by the function
[tex]h(t)=16^{(2+48t)}[/tex]For a field trip 22 students rode in cars and the rest filled 5 buses how many students were in each bus if 317 students were on the trip.
Answers
We have to find how many students were in each bus.
We can call this quantity "x".
The total number of students is 317.
This quantity can be divided in the number of students that rode in cars, 22, and the rest went in 5 buses.
The quantity that rode in bus can be expressed as 5x.
Then we can write:
[tex]22+5x=317[/tex]We can solve this as:
[tex]\begin{gathered} 22+5x=317 \\ 5x=317-22 \\ 5x=295 \\ x=\frac{295}{5} \\ x=59 \end{gathered}[/tex]Answer: there were 59 students in each bus.
4 numbers that are divisible by both 2 and 9
Answers
A Number to be divisible by 2, the last digit must be even.
divisible by 9 = sum of the digits must be divisible by 9:
So, 4 numbers:
18,36,54,72
An equilateral triangle and a square have equal perimeters. The side of the triangle measures 8cm. What is the area of the square, in square centimeters?
Answers
Answer
Area of the square = 36 square cm
Step-by-step explanation:
Given:
The perimeter of an equilateral triangle = the perimeter of a square
In an equilateral triangle, all sides are equal
Each side of the equilateral triangle = 8cm
Perimeter of the equilateral triangle = 3 * 8cm
Perimeter of the equilateral triangle = 24cm
Since, perimeter of square = perimeter of an equilateral triangle
Perimeter of a square = 24cm
We need to find each side of the square
Perimeter of a square = 4s
24 = 4s
Divide both side by 4
24/4 = 4s/4
s = 6cm
Since the length of each side of the square is 6cm
Therefore, area = l^2
Area = 6 * 6
Area of a square = 36 square cm
: + = 27 = + 3. (15,12). (12,15). (6,21).
Answers
(12, 15) (option B)
Explanation:x + y = 27 ..equation 1
y = x + 3 ...equation 2
Using substitution method:
We would substitute for y = x + 3 in equation 1
x + (x + 3) = 27
x + x + 3 = 27
2x + 3 = 27
2x = 27 - 3
2x = 24
x = 24/2
x = 12
Substitute 12 for x in equation 2:
y = 12 + 3
y = 15
The solution to both equations (x, y):
(12, 15) (option B)
Quicy has 1/2 box of cereal to eat over 6 days if he splits the 1/2 box into equal portions how much will he eat each day
Answers
ANSWER:
1/12 of the cereal box
STEP-BY-STEP EXPLANATION:
In this case we must divide the amount that we have, that is, half a box of cereal by the number of portions that are desired equal, that is, 6
Therefore, we are left with:
[tex]\frac{\frac{1}{2}}{6}=\frac{1}{2\cdot6}=\frac{1}{12}[/tex]That is, for each day, you will have to eat 1/12 of the cereal box
Suppose there is a simple index of three stocks, stock X, stock Y, and stock Z. Stock X opens the day with 5000 shares at $4.10 per share. Stock Y opens the day with 2000 shares at $4.50 per share. Stock Z opens the day with 4000 shares at $3.60 per share. The simple index rises 3.4% over the course of the day. What is the value of the index at the end of the day? Round your answer the nearest hundred. A. $45,100 B. $43,900 C. $45,400 D. $44,800
Answers
Solution:
Step 1:
Calculate the total value of stock X
[tex]\begin{gathered} =5000\times\text{ \$}4.10 \\ =\text{ \$}20,500 \end{gathered}[/tex]Step 2:
Calculate the total value for Stock Y
[tex]\begin{gathered} =2000\times4.5 \\ =\text{ \$}9000 \end{gathered}[/tex]Step 3:
Calculate the total value for stock Z
[tex]\begin{gathered} =4000\times\text{ \$}3.60 \\ =\text{ \$}14,400 \end{gathered}[/tex]Step 4:
Calculate the total value of the shares but without the increase yet
[tex]\begin{gathered} 20,500+9000+14,400 \\ =\text{ \$}43,900 \end{gathered}[/tex]Step 5:
Calculate the increase in the simple index
[tex]\begin{gathered} =\frac{3.4}{100}\times43900 \\ =\text{ \$}1,492.60 \end{gathered}[/tex]Step 6:
Add the increase in the simple index to the total value of the shares
[tex]\begin{gathered} 43,900+1,492.60 \\ =\text{ \$}45,392.60 \\ \approx\text{ \$}45,400 \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow\text{\$}45,400[/tex]OPTION C is the right answer
Answer:
45,400
Step-by-step explanation:
just took test AP3
What is the volume of a cylinder whose base diameter is 10 cm and whose height is 12 cm? Round your answer to the nearest tenth.
Answers
Solution
We are given the following
Diameter = 10cm
Radius = 10/2 = 5cm
Height = 12cm
Therefore, the Volume will be
[tex]\begin{gathered} Volume=\pi r^2h \\ \\ Volume=\pi(5^2)(12) \\ \\ Volume=\pi\times25\times12 \\ \\ Volume=300\pi \\ \\ Volume=942.5cm^3\text{ \lparen to the nearest tenth\rparen} \end{gathered}[/tex]Therefore, the answer is
[tex]\begin{equation*} 942.5cm^3\text{ } \end{equation*}[/tex]f (t) = 44 – 5 g(t) = 2t - 1 Find (f - g)(t)
Answers
To solve the given problems, we have to subtract the functions.
[tex](f-g)(t)=4t-5-(2t-1)[/tex]Then, we simplify
[tex](f-g)(t)=4t-5-2t+1=2t-4[/tex]Hence, the resulting function is 2t-4.Yolanda is riding in a bike race that goes through a valley and a nearby mountain range,The table gives the altitude (in feet above sea level) for the five checkpoints in the race,Use the table to answer the questions,CheckpointAltitude(feet above sea level)12,2242- 13731,5714-305218(8) How much lower is Checkpoints than check out 2909 i lower
Answers
Step 1
Write the given checkpoint altitude
Checkpoint 1 = 2224
Checkpoint 2 = -137
Checkpoint 3 = 1571
Checkpoint 4 = -39
Checkpoint 5 = -218
Step 2:
a) How much lower is checkpoint 5 than checkpoint 2
You will subtract checkpoint 5 altitude from checkpoint 2
[tex]\begin{gathered} =\text{ -137 - (-218)} \\ =\text{ -137 + 218} \\ =\text{ 81 f}eet \end{gathered}[/tex]b) Altitude of the top hill that is 365 above checkpoint 5.
[tex]\begin{gathered} \text{Altitude of the top hill = 365 - 218 } \\ \text{Altitude of the top hill 365 above checkpoint 5 = 147} \end{gathered}[/tex]need this asap What is the x-coordinate of the solution to this system of equations: 4x + y = 2 x - y = 3
Answers
Given the following system of equations:
[tex]\begin{cases}4x+y=2 \\ x-y=3\end{cases}[/tex]to find the x-cooridnate of the solution, we can solve for 'y' the first equation to get the following:
[tex]\begin{gathered} 4x+y=2 \\ \Rightarrow y=2-4x \end{gathered}[/tex]next, we use this value on the second equation to get the following expression:
[tex]\begin{gathered} x-y=3 \\ \Rightarrow x-(2-4x)=3 \end{gathered}[/tex]simplifying we get the following:
[tex]\begin{gathered} x-(2-4x)=3 \\ \Rightarrow x-2+4x=3 \\ \Rightarrow x+4x=2+3 \\ \Rightarrow5x=5 \\ \Rightarrow x=\frac{5}{5}=1 \\ x=1 \end{gathered}[/tex]therefore, the x-coordinate of the solution to the system of equations is x = 1
Which of the following describes the image of the transformation graphed to the right?A.) T(x,y)=(x+7,y-7)B.) T(x,y)=(x-7,y-7)C.) T(x,y)=(x+7,y+7)D.) T(x,y)=(x-7,y+7)
Answers
Answer:
D.) T(x,y)=(x-7,y+7)
Step-by-step explanation:
Function f(x,y).
Transformation along the x axis:
Moving a units to the left: We have f(x+a,y).
Moving a units to the right: We have f(x - a,y).
Transformation along the y axis:
Moving a units up: We have f(x, y-a).
Moving a units down: We have f(x, y+a).
In this question:
The function is moved 7 units to the right among the x-axis(x - 7) and 7 units down along the y axis(y + 7).
So the answer to this question is:
D.) T(x,y)=(x-7,y+7)
It’s given that the shape is not a parallelogram but why?
Answers
They are two congruent triangles.
Draw the circle ( x − 3 ) 2 + y 2 = 1 .
Answers
A drawing of this equation of a circle (x − 3)² + y² = 1 is shown in the image attached below.
What is the equation of a circle?Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r² ....equation 1.
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.From the information provided, we have the following equation of a circle:
(x − 3)² + y² = 1 .........equation 2.
By comparing equation 1 and equation 2, we can logically deduce the following parameters:
Coordinate at the center, h = 3.Coordinate at the center, k = 0.Radius of circle, r = 1.In conclusion, the given equation of a circle (x − 3)² + y² = 1 was plotted by using an online graphing calculator.
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Complete Question:
Draw the circle (x − 3)² + y² = 1.
The area of the trapezoid is 14 square feet. Write an equation that you can use to find the value of x
Answers
Explanation
the area of a trapezoid is equal to half the product of the height and the sum of the two bases.
[tex]A=(\frac{base1+base2}{2})\cdot\text{heigth}[/tex]then
Step 1
Let
base1=2x
base2=x
height= 2 ft
area= 14 square feet
replace,
[tex]\begin{gathered} A=(\frac{base1+base2}{2})\cdot\text{heigth} \\ 14=(\frac{2x+x}{2})\cdot\text{2 } \\ 14=(\frac{3x}{2})\cdot2 \\ 14=3x\rightarrow equation \\ divide\text{ both sides by 3} \\ \frac{14}{3}=\frac{3x}{3} \\ \frac{14}{3}=x \\ x=\frac{14}{3} \end{gathered}[/tex]then put 3x in the box.
I hope this helps you
use the information given to answer the question.consider the textbook and its mathematical label.part Awhich statement is true?the answer questions is in the image
Answers
Solution:
Given the textbook and its mathematics label as shown below:
From the above shape of the book and label, the textbook takes the shape of a rectangular prism, while its label is rectangular in shape.
Thus, the textbook is best represented by a rectangular prism, while the label is best represented by a rectangle.
The third option is the correct answer.
Assume that a varies directly as b.When the value of a is 5,the value of b is 18.When the value of a is 22,what is the value of b?
Answers
In this case we have the proportion 18:5, then we have the equation
[tex]\begin{gathered} \frac{18}{5}=\frac{b}{22} \\ b=\frac{18}{5}\times22 \\ b=\frac{396}{5} \end{gathered}[/tex]Then, when a is 22, the value of b is 396/5 that is also equal to 79.2 or
[tex]79\frac{1}{5}[/tex]the table shows the number of hours worked and the total amount that each of the four people earned one weekendwhose pay rate was the best whose pay rate was the worst Based on the chart.
Answers
pay rate = money earned/hours worked
Gary's pay rate: $37/4 = $9.25 per hour
Tara's pay rate: $54.9/6 = $9.15 per hour
Lamont's pay rate: $27.6/3 = $9.2 per hour
Darius' pay rate: $46.5/5 = $9.3 per hour
best pay rate: Darius
worst pay rate: Tara
Determine whether each data set has a positive relationship, negative relationship or no relationship.
Answers
Two groups of numbers have a positive relationship, when we can identify a pattern where the two variables increase together, a negative relationship when the two variables decrease together and no relationship when we can't identify any pattern.
For the first graph we can identify that as the temperature grows, the number of chirps also grows, therefore they have a positive relationship.
For the second graph we can't clearly identify any relationship between the two variables, therefore it has no relationship.
round to the nearest ten-thousandth -7(10^x)=-54
Answers
The value x in the given expression is 0.8873.
Define logarithm.The power to which a number must be raised in order to get additional values is known as the logarithm. This is the simplest way to express really large numbers. The fact that addition and subtraction logarithms can also be expressed as multiplication and division of logarithms is shown by a number of significant properties of a logarithm.
The other technique to write exponents in mathematics is using logarithms. The base-based logarithm of a number equals another number. The exact opposite function of exponentiation is carried out by a logarithm.
Given expression -
-7(10^x)=-54
We can also write it as
7(10^x) = 54
Using the concept of logarithm, apply the log on both sides
log(7*[tex]10^{x}[/tex]) = log 54
Applying the identity of logarithm,
log 7 + log [tex]10^{x}[/tex] = log 54
x log 10 = log 54 - log 7
x log 10 = 0.8873
As value of log 10 = 1,
x = 0.8873
Hence the value x in the given expression is 0.8873.
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5x+10=-25solving for x
Answers
start by substracting 10 on both sides
[tex]\begin{gathered} 5x+10-10=-25-10 \\ 5x=-35 \end{gathered}[/tex]divide by 5 on both sides
[tex]\frac{5x}{5}=-\frac{35}{5}[/tex][tex]x=-7[/tex]using the values from the graph, compute the values for the terms given in the problem. Choose the correct answer. Age of car = 4 years Original cost = 13,850 The current market value is $ _
Answers
The current market value is $9086.98
In this problem, supposing a decay of 10% a year, and the original value of $13,850, the parameters are A(0) = 13850, r = 0.1.
Using exponential decay formula, the value of the car in 4 years is given by:
A(t) = A(0)(1 - r)^t
A(4) = 13850(1 - 0.1)^4
A(4) = 13850 * (0.9)^4
A(4) = 9086.98
Therefore, The current market value is $9086.98
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two angles of a triangle measure 59° and 63°. if the longest side measures 28 cm find the length of the shortest side. round answers to the nearest tenth
Answers
The two angles of triangle are : 59 and 63 degrees.
Length of the longest side of traingle is 28cm.
In a triangle,
the smallest side is always opposite to the smallest angle of the triangle,
and the largest side is always opposite to the largest angle
The sum of all the angles in atriangle is 180 degree
let the other angle is x so,
x+63+59=180
x=180-59-63
x=58
So, the longest side of traingle is in the opposite of angle 63
the smallest side of triangle is in opposite of angle 58
Apply the Sine rule to find the side of the traingle which has an opposite angle of 58.
Sine formula is expressed as:
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}^{}=\frac{c}{\sin C}[/tex]Let a be the smallest side and b be the longest side of triangle so,
A=58, B=63, b=28cm
Substitute the values, and solve for a,
[tex]\begin{gathered} \frac{a}{\sin58^{\circ}}=\frac{28}{\sin63^{\circ}} \\ a=\frac{28\times\sin58^{\circ}}{\sin63^{\circ}} \\ a=\frac{28\times(0.84804809)}{0.89100652} \\ a=\frac{23.74534652}{0.89100652} \\ a=26.6500 \\ a=26.7\operatorname{cm} \end{gathered}[/tex]The shortest length is 26.7cm
Find MK. ML = 8, LK = x + 2, MK = 4x - 2
Answers
From the given description, it appears that M, L, and K are collinear and the length of MK is equal to the sum of ML and LK.
To be able to find the length of MK let's first find the value of x using the equation of the sum of the lines.
[tex]\text{ }\bar{\text{ML}}\text{ + }\bar{\text{LK}}\text{ = }\bar{\text{MK}}[/tex]Let's plug in the values given in the description.
[tex]\text{ (8) + (x + 2) = 4x - 2}[/tex][tex]\text{ 8 + x + 2 = 4x - 2}[/tex][tex]\text{ x + 10 = 4x - 2}[/tex][tex]\text{ x - 4x = -2 - 10}[/tex][tex]\text{ -3x = -12}[/tex][tex]\text{ }\frac{\text{-3x}}{-3}\text{ = }\frac{\text{-12}}{-3}[/tex][tex]\text{ x = 4}[/tex]Let's plug in x = 4 in the equation for the length of MK = 4x - 2.
[tex]\text{ }\bar{\text{MK}}\text{ = 4x - 2}[/tex][tex]\text{ }\bar{\text{MK}}\text{ = 4(4) - 2}[/tex][tex]\text{ }\bar{\text{MK}}\text{ = 16 - 2}[/tex][tex]\text{ }\bar{\text{MK}}\text{ = 1}4[/tex]Therefore, the length of MK is 14.
Given the expression: 6x^10 - 96x^2Part A: Rewrite the expression by factoring out the greatest common factor.Part B: Factor the entire expression completely. Show the steps of your work.
Answers
According to factorization method, we have find out that by factoring out the greatest common factor, we can rewrite the expression as [tex]6x^{2}(x^{8}-16)[/tex] and by factoring the entire expression by difference of squares concept, we can rewrite the expression as [tex]6x^{2}(x^{4}+4)(x^{2}+2)(x^{2} -2)[/tex].
The given expression is -
[tex]6x^{10}-96x^{2}[/tex] ---- (1)
We have to -
A: Rewrite the expression by factoring out the greatest common factor.
B: Rewrite the expression by factoring the entire expression completely.
Solving for Part A:
From equation (1), we have
[tex]6x^{10}-96x^{2}[/tex]
Applying the distributive property, we can rewrite this as -
[tex]6x^{10}-96x^{2}\\=6x^{2} x^{8}-6x^{2}*16\\=6x^{2}(x^{8}-16)[/tex]------- (2)
This is the expression obtained by factoring out the greatest common factor that is [tex]x^{2}[/tex].
Solving for Part B:
From equation (2), we have
[tex]6x^{2}(x^{8}-16)[/tex]
Applying the difference of squares concept, we can rewrite this as -
[tex]6x^{2}(x^{8}-16)\\=6x^{2}[(x^{4} )^{2} -4^{2} ]\\=6x^{2}(x^{4}+4)(x^{4}-4)\\=6x^{2}(x^{4}+4)[(x^{2} )^{2}-2^{2} ]\\=6x^{2}(x^{4}+4)(x^{2}+2)(x^{2} -2)[/tex]
This is the expression obtained by factoring the expression completely.
Therefore, according to factorization method, we have find out that by factoring out the greatest common factor, we can rewrite the expression as [tex]6x^{2}(x^{8}-16)[/tex] and by factoring the entire expression by difference of squares concept, we can rewrite the expression as [tex]6x^{2}(x^{4}+4)(x^{2}+2)(x^{2} -2)[/tex].
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The function f(x)= 4x is one to one Find A and B
Answers
Given:
[tex]f(x)=4x[/tex]a)
[tex]\begin{gathered} x=4f^{-1}(x) \\ f^{-1}(x)=\frac{x}{4}\text{ , for all x} \end{gathered}[/tex]Option C is the final answer.
b)
[tex]\begin{gathered} f(f^{-1}(x))=f(\frac{x}{4}) \\ =4(\frac{x}{4}) \\ =x \end{gathered}[/tex][tex]\begin{gathered} f^{-1}(f(x))=f^{-1}(4x) \\ =\frac{4x}{4} \\ =x \end{gathered}[/tex][tex]f(f^{-1}(x))=f^{-1}(f(x))=x[/tex]