Given:
a.) The radius of a circle is 16 miles.
b.) Use 3.14 for π
For us to be able to determine the circumference of the circle using the radius, we will be using the following formula:
[tex]\text{ Circumference = 2\pi r}[/tex]Where,
r = radius of the circle
We get,
[tex]\text{ Circumference = 2\lparen3.14\rparen\lparen16\rparen = 100.48 miles}[/tex]Therefore, the circumference of the circle is 100.48 miles.
Explanation:
The circumference of a circle is equal to
π, which is a number ≈3.14, multiplied by the diameter of the circle.
Therefore, C=πd.
We know that the circumference, C, is 16π, so we can say that:
16π=πd
We can divide both sides by π to see that 16=d.
We now know that the diameter of the circle is 16.
We also know that the diameter has twice the length of the radius.
In equation form: 2r=d
2r=16
r=8
Note that since 2r=d, the equation C=2πr holds and can be used in place of C=πd.
RS is a chord of circle P, and TU is a chord of circle Q. Circle P is congruent to circle Q.Which statement cannot be verified from the information that is given?If RS TU, then RS = TU.RIf RS TU, then RS - TQ.If RS = TU, then RS = TU.If RS TU, then RS = TU.
The proposition that can not be verified using the given information is
[tex]If\text{ }\hat{\text{RS}}\cong\hat{TV,}\text{ then }\bar{\text{RS}}\cong\bar{TQ}[/tex]Because there is no result (regarding chords) relating a chord that doesn't go through the center Q with a chord going through it. Look at the conclusion of the proposition
[tex]\bar{RS}\cong\bar{TQ}[/tex]RS doesn't go through Q, and TQ does it.
8 PointsQuestion 15Find the standard form equation of the line that passes through (-1,-4) and (3.-6). For the answer, just enter the coefficient ofthe x-termBlank 1Blank 1Add your answerPointe
The form of the equation that passes through two points is
[tex]y=mx+b[/tex]m is the slope,
b is the y-intercept
The rule of the slope is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let (x1, y1) = (-1, -4) and (x2, y2) = (3, -6)
[tex]\begin{gathered} m=\frac{-6-(-4)}{3-(-1)}=\frac{-6+4}{3+1} \\ m=\frac{-2}{4} \\ m=-\frac{1}{2} \end{gathered}[/tex]The equation is
[tex]y=-\frac{1}{2}x+b[/tex]Substitute x by 3 and y by -6 to find b
[tex]\begin{gathered} -6=-\frac{1}{2}(3)+b \\ -6=-\frac{3}{2}+b \end{gathered}[/tex]Add 3/2 to both sides
[tex]\begin{gathered} -6+\frac{3}{2}=-\frac{3}{2}+\frac{3}{2}+b \\ -\frac{9}{2}=b \end{gathered}[/tex]The equation is
[tex]y=-\frac{1}{2}x-\frac{9}{2}[/tex]The standard form of the linear equation is
[tex]Ax+By=C[/tex]A, B, C are integers
Then multiply all terms in the equation by 2
[tex]2y=-x-9[/tex]Add x to both sides
[tex]\begin{gathered} x+2y=-x+x-9 \\ x+2y=-9 \end{gathered}[/tex]The equation in the standard form is x + 2y = -9
Find the coordinates of A if M(-1, 2) is the midpoint of AB and B has coordinates of (3,-5).
Hello there. To solve this question, we have to remember how to determine the coordinates of a point given the midpoint of a segment.
Given that M is the midpoint of the segment AB
[tex]M=(-1,\,2)[/tex]and that the point B has coordinates
[tex]B=(3,\,-5)[/tex]First, remember the formula for the distance between two points (x0, y0) and (x1, y1):
[tex]d((x_0,\,y_0),\,(x_1,\,y_1))=\sqrt{(x_0-x_1)^2+(y_0-y_1)^2}[/tex]So that we know that the midpoint of a segment has the same distance from its ends.
In this case, we determine first the distance between the points M and B:
[tex]\begin{gathered} d(M,\,B)=\sqrt{(-1-3)^2+(2-(-5))^2}=\sqrt{(-4)^2+7^2} \\ \\ \Rightarrow d(M,\,B)=\sqrt{16+49}=\sqrt{65} \\ \end{gathered}[/tex]Next step, remember the formula for the midpoint of a segment
If A and B are the endpoints of the segment AB and has coordinates
[tex]A=(x_A,\,y_A)\text{ and }B=(x_B,\,y_B)[/tex]Its midpoint is given by
[tex]M=\left(\dfrac{x_A+x_B}{2},\,\dfrac{y_A+y_B}{2}\right)[/tex]Such that we find
[tex]M=(-1,\,2)=\left(\dfrac{x_A+3}{2},\,\dfrac{y_A-5}{2}\right)[/tex]Hence we find that
[tex]\begin{gathered} \dfrac{x_A+3}{2}=-1\Rightarrow x_A=-5 \\ \\ \dfrac{y_A-5}{2}=2\Rightarrow y_A=9 \end{gathered}[/tex]So the coordinates of the point A are
[tex]A=(-5,\,9)[/tex]Complete equation for the circle with center (4,8) and radius 2.
We are asked to determine the equation of a circle centered at (h, k) = (4, 8) and radius 2. We will apply the following equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h, k) is the center of the circle and "r" is the radius. Replacing the values:
[tex](x-4)^2+(y-8)^2=4[/tex]and thus we get the equation of the circle.
MidpointPoint A is at (-6,8) and point B is at (6, -7).What is the midpoint of line segment AB?8+7+
Tell me what is the scale factor, and the length of the missing side
As given by the question
There are given that two rectangles, first is larg and second is smaller.
Now,
The larger triangle is twice the smaller triangle
So,
(A)
The scale factor is shown below :
[tex]\frac{1}{2}[/tex](B).
The length of the missing side is:
[tex]11\times\frac{1}{2}=5.5[/tex]Hence, the missing side is 5.5 feet.
Need help solving this step by step Not sure of the subject of mathematics however, if you can identify this and let me now as well :)
Solution
Given that;
A ferris wheel completes 7 revolutions in 14 minutes
[tex]\begin{gathered} \Rightarrow1\text{ revolution }=\frac{14}{7}\text{ minutes} \\ \\ \Rightarrow1\text{ revolution }=2\text{ minutes} \\ \\ \Rightarrow1\text{ revolutions }=2\times1\text{ minutes} \\ \\ \operatorname{\Rightarrow}1\text{ revolut}\imaginaryI\text{ons}=2\times60\text{ seconds} \\ \\ \Rightarrow1\text{ revolut}\mathrm{i}\text{ons}=120\text{ seconds} \\ \\ \Rightarrow\omega=\frac{1}{120}\text{ rev/sec}\times(2\text{ }\pi\frac{\text{ radians}}{1\text{ rev}}) \\ \\ \Rightarrow\omega=\frac{\pi}{60}\frac{radians}{sec} \end{gathered}[/tex]Given that radius is 30 feet;
30 feet = 360 inches
linear speed = angular speed x radius of the rotation
[tex]\begin{gathered} \Rightarrow v=\omega r \\ \\ \Rightarrow v=\frac{\pi\text{ radian}}{60}\times360\text{ inches/sec}=18.8\text{ inches/sec} \end{gathered}[/tex]Therefore, linear velocity is 18.8 inches/sec
Every week Mary swims 2.5 miles on Monday, 3 miles on Wednesday, and 4.4 miles on Friday. How many miles will Mary swim in 4 weeks?
The miles Mary will swim in a week is,
[tex]N=2.5+3+4.4=9.9[/tex]Then, the miles Mary will swim in 4 weeks is,
[tex]\begin{gathered} T=4N \\ T=4\times9.9 \\ T=39.6\text{ miles} \end{gathered}[/tex]Therefore, Mary will swim 39.6 miles in 4 weeks.
Point T is on line segment SU. Given TU = 4x+1, SU = 8, and ST = 3x, determine the numerical length of TU.
The numerical length of TU is 5
Here, we want to get the value of TU
Since T is on SU, we have the length of SU calculated as;
[tex]\begin{gathered} SU\text{ = ST + TU} \\ 8\text{ = 3x + 4x+1} \\ 8\text{ = 7x + 1} \\ 8-1\text{ = 7x} \\ 7\text{ = 7x} \\ x\text{ = }\frac{7}{7} \\ x\text{ = 1} \\ TU\text{ = 4x + 1 } \\ TU\text{ = 4(1) + 1 = 4+1 = 5} \end{gathered}[/tex]Use the examples above to write a paragraph proof proving the Triangle Sum Theorem.
First, start by drawing the line EC that passes through vertex C and is parallel to AB, as showed in the question's figure.
Since AB and EC are parallel, the pairs ∠4 and ∠1 and ∠4 and ∠3 are Alternate Interior Angles, which means that the pairs are congruent, that is:
[tex]\begin{gathered} \angle4\cong\angle1 \\ \angle5\cong\angle3 \end{gathered}[/tex]Also, the angles ∠1, ∠2 and ∠3 are adjacent angles that make a straight line. This means that the sum of these 3 angles is 180°.
[tex]m\angle1+m\angle2+m\angle3=180\degree[/tex]Since congruent angles have the same measure, we can substitute:
[tex]\begin{gathered} m\angle1=m\angle4 \\ m\angle3=m\angle5 \end{gathered}[/tex]To obtain the Triangle Sum Theorem:
[tex]m\angle4+m\angle5+m\angle2=180\degree[/tex]That is, the sum of the interior angle measures of a triangle is 180°.
Write a cosine function that has a amplitude of 3, an midline of 5 and a period of pi/2f(x)=
Recall that the general formula of a cosine function is of the form
[tex]A\cdot\cos (Bx-C)+D[/tex]where A is the amplitude, D is the midline, the number C/B is the phase shift and the number 2*pi/B is the period.
We are told that A=3 and D=5. Also, we are told that the period is pi/2. Since we don't have any information regarding the phase shift, we will asume that the phase shift is 0. Then we have the following equations:
[tex]\frac{C}{B}=0[/tex]and
[tex]\frac{2\cdot\pi}{B}=\frac{\pi}{2}[/tex]From the first equation we deduce that C should be zero. From the second equation by multiplying by B on both sides and dividing by pi on both sides, we get
[tex]2=\frac{B}{2}[/tex]If we multiply by 2 on both sides, we get
[tex]B=2\cdot2=4[/tex]so gathering our previous results, we get the formula
[tex]3\cos (4x)+5[/tex]So I fell behind in my last semester geometry class, so right now I’m working with Pythagorean Triples. Here’s the screenshot of the work I’m doing and I’m confused on what “DEF” is? I drew my vertices for “ABC” but then it starts talking about measurements etc.
First, we set the points on the graph ;
A = (1,6) , B= (1,1) and C= (5,1)
Join the points and you obtain the first triangle.
For the triangle DEF we know that sides AB= DE and EF= BC, so it is the same triangle but with different letters on the points. Make sure to have a 90° angle on E. ( the same as angle B on triangle 1 )
Find the solution to the following quadratic.2x^2 – 8x + 10 = 0
1) Solving the quadratic equation 2x²-8x +10=0
Let's solve this using the Resolutive form, let's start by finding the Discriminant
[tex]\begin{gathered} \Delta=b^2-4ac\rightarrow\Delta=(-8)^2-4(2)(10)\rightarrow\Delta=64-80\text{ } \\ \Delta=-16 \end{gathered}[/tex]1.2 Since the Discriminant is a negative value, we know that this equation has complex roots and the parabola does not intercept the x-axis
Let's carry on
[tex]undefined[/tex]I need help on a quetion
The given fuctions are:
[tex]\begin{gathered} f(x)=3^x \\ g(x)=f(x+1) \end{gathered}[/tex]this means that for the reference it is:
[tex]g(x)=3^{x+1}[/tex]now for the first coordinate it is:
[tex]g(0)=3^{0+1}=3[/tex]then:
[tex]g(1)=3^{1+1}=9[/tex]then:
[tex]g(2)=3^{2+1}=27[/tex]Finally
[tex]g(3)=3^{3+1}=81[/tex]How long antermg5. Mitch throws a ball over a 20-foot fence to a baseball field. The height, h(1), of the ball at time iseconds after it was thrown can be modeled by the equation h(t)=-161 +301 +6. Which statement(s)is/are true? Then explain why the others are false?
Option D is correct
Explanations:The model equation for the height of the ball at time t is given as:
h(t) = - 16t² + 30t + 6
Note:
The ball reaches a maximum height at a time when dh/dt = 0
The height of the ball at any time t is given by h(t) = - 16t² + 30t + 6
From h(t), dh/dt will be calculated as:
dh/dt = -32t + 30
At maximum height, dh/dt = 0
0 = -32t + 30
32t = 30
t = 30/32
t = 0.94 s
Therefore, the ball reaches the maximum height at 0.94 second
Let us find the position of the ball at t = 2 seconds
h(t) = - 16t² + 30t + 6
h(2) = -16(2)² + 30(2) + 6
h(2) = -64 + 60 + 6
h(2) = 2
At t = 2 seconds, the height of the ball is 2 feet
Let us find the position of the ball at t = 1.5 seconds
h(t) = - 16t² + 30t + 6
h(1.5) = -16(1.5)² + 30(1.5) + 6
h(1.5) = -36 + 45 + 6
h(1.5) = 15
At 1.5 seconds, the ball is 15 feet high
Since the height of the ball, h(t) is a function of time, the ball can clear the fence depending on the time, t, spent in the air
On day 1 at the Texas State Fathering loss stand had 500 people play. On day 2, the ring lossstand had 700 people play. What is the percent change in the amount of people who played ringtoss?
What are the factors of this expression? 2/5ab Drag all of the factors.
Recall that a factor of an expression is a number or algebraic expression that divides the given expression evenly.
Notice that:
[tex]\begin{gathered} \frac{\frac{2}{5}ab}{\frac{2}{5}}=ab, \\ \frac{\frac{2}{5}ab}{a}=\frac{2}{5}b, \\ \frac{\frac{2}{5}ab}{b}=\frac{2}{5}a. \end{gathered}[/tex]Therefore:
[tex]\frac{2}{5},a,\text{ and b}[/tex]are factors of the given expression.
Answer:
[tex]\frac{2}{5},a,b.[/tex]12-Write the domain in interval notation.(a) w(x)= lx+1l+4(b) y(x)= X ➗ lx+1l+4(c) Z(x)= X ➗ lx+1l-4
Explanation
Part A
We are told to obtain the domain of the given function:
[tex]w(x)=|x+1|+4[/tex]The domain of a function is the set of all possible inputs for the function.
we can use the graph to obtain the intervals of the domain
[tex]\mathrm{The\:domain\:of\:a\:function\:is\:the\:set\:of\:input\:or\:argument\:values\:for\:which\:the\:function\:is\:real\:and\:defined}[/tex]Thus, the solution is
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:For part B
[tex]y(x)=\frac{x}{|x+1|+4}[/tex]The domain will be
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:Part C
[tex]z(x)=\frac{x}{|x+1|-4}[/tex]The domain will be
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:x<-5\quad \mathrm{or}\quad \:-53\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-5\right)\cup \left(-5,\:3\right)\cup \left(3,\:\infty \:\right)\end{bmatrix}[/tex]What are the solutions to the equation x² – 5x = 14? A. x= -7.x = -2 B. X= -14,X = -1 C. x = -2, x = 7 D. x = -1, x = 14
ok
x^2 - 5x - 14 = 0
Factor the expression
(x - 7)(x + 2) = 0
x = 7 x = -2
Solutions: x = -2, x = 7
Letter C is the answer to your question.
The amount of money Chaz earned for walking dogs is given in the table. Can the relationship be described by a constant rate explain? I’m confused
The relationship can be described by a constant rate
Explanations:Let the dogs walked be represented by x
Let the amount of money earned be represented by y
From the table:
[tex]\begin{gathered} x_1=6,x_2=6,x_3=11 \\ y_1=112.50,y_2=150.00,y_3=\text{ 206.25} \end{gathered}[/tex]For the relationship to be described by a constant rate:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y_3-y_2}{x_3-x_2}[/tex][tex]\begin{gathered} \frac{y_2-y_1}{x_2-x_1}=\frac{150.00-112.50}{8-6} \\ \frac{y_2-y_1}{x_2-x_1}=\text{ }\frac{37.50}{2} \\ \frac{y_2-y_1}{x_2-x_1}=18.75 \end{gathered}[/tex][tex]\begin{gathered} \frac{y_3-y_2}{x_3-x_2}=\frac{206.25-150.00}{11-8} \\ \frac{y_3-y_2}{x_3-x_2}=\frac{56.25}{3} \\ \frac{y_3-y_2}{x_3-x_2}=18.75 \end{gathered}[/tex]Since:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y_3-y_2}{x_3-x_2}=18.75[/tex]The relationship can be described by a constant rate of 18.75
If you take out a single card from a regular pack of cards, what is the probability that the card is either a king or heart?
Given:
The total number of cards is 52.
[tex]n(S)=52[/tex]To find:
The probability that the card is either a king or heart.
Explanation:
The number of heart cards is 13.
The number of king cards is 4.
The number of cards that are both heart and kind is 1.
So, the total number of favourable outcomes is,
[tex]\begin{gathered} n(E)=13+4-1 \\ n(E)=16 \end{gathered}[/tex]Then, the probability is,
[tex]\begin{gathered} P(A)=\frac{n(A)}{n(S)} \\ =\frac{16}{52} \\ =\frac{4}{13} \end{gathered}[/tex]Final answer:
The probability is,
[tex]\frac{4}{13}[/tex]Solve the equation. Check for extraneous solutions. In(7x-4) = In(2x+11)
Question: Solve the equation:
[tex]\ln (7x-4)=\text{ ln(2x+11)}[/tex]Solution:
applying the laws of logarithms (applying the inverse function of the logarithm function) we get:
[tex]e^{\ln (7x-4)}=e^{\text{ ln(2x+11)}}[/tex]this is equivalent to:
[tex]7x-4=\text{ 2x+11}[/tex]putting similar terms together we get:
[tex]7x-2x=11+4[/tex]this is equivalent to:
[tex]5x\text{ = 15}[/tex]solving for x, we get:
[tex]x\text{ = }\frac{15}{5}\text{ = 3}[/tex]then, we can conclude that the solution of the equation is:
[tex]x\text{ = 3}[/tex]
Which expression is equivalent to 8x + 5x? a (8 + 5) b (8.5)x C 8 + 5(x) d (8 + 5)(2x)
8x + 5x
when you factor out x, the expression becomes;
x(8+5)
if one angle of a triangle is 100 and the other two are what is the measure of each unknown angle
The sum of the three internal angles of a triangle is always equal to 180°. Let's use x for the measure of each of the missing angles. Then the sum of the three angles of triangle ABC is expressed as x+x+100°=2x+100°. If we equalize this expression to 180° we obtain an equation for x:
[tex]2x+100=180[/tex]We can substract 100 from both sides of the equation:
[tex]\begin{gathered} 2x+100-100=180-100 \\ 2x=80 \end{gathered}[/tex]Then we divide both sides by 2:
[tex]\begin{gathered} \frac{2x}{2}=\frac{80}{2} \\ x=40 \end{gathered}[/tex]AnswerThen the answer is 40.
Choose all the cylindrical containers that will hold at least 50 cm but not more than 55 cm- of a liquid. (a)radius = 2 cm height = 4.1 cm (b)radius = 2.2 cm height = 3.2 cm(c)radius = 2.5 cm height = 2.7 cm (d)radius = 2 1 cm height = 3.8 cm
Volume, V, of a cylinder with base radius, r, and height, h
is given by:
[tex]\begin{gathered} V=\pi\times r^2\times h \\ \pi\approx3.142 \\ \text{Hence} \\ \text{If r=2 and h=4.1} \\ V=3.142\times2^2\times4.1\approx51.52 \\ if\text{ r=2.2 and h=3.2} \\ V=3.142\times2.2^2\times3.2\approx48.66 \\ \text{if r=2.5 and h=2.7} \\ V=3.142\times2.5^2\times2.7\approx53.01 \\ \text{if }r=2.1\text{ and h=3.8} \\ V=3.142\times2.1^2\times3.8\approx52.64 \end{gathered}[/tex]Therefore cylindrical containers with dimensions as shown in options (a), (b), and (c) satisfy the given condition
From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings? Answer choices: 1)Independent2)Dependent3)Exclusive4)Inclusive
In this case they tell us that that 2 cards are drawn from a deck. No matter what those cards are, they come out of the came deck, which means that it is an event dependent.
Since when drawing a card, the deck would be missing a card, which means that one event depends on the other
The answer is 2) Dependent
Which of the following polar functions does NOTproduce a conic section?
Let us begin by defining the equation of a conic section
The equation of a conic section usually takes the form:
For a conic with a focus at the origin, if the directrix is x =± p , where p is a positive real number, and the eccentricity is a positive real number e, the conic has a polar equation
[tex]r\text{ = }\frac{ep}{1\text{ }\pm ecos\theta}[/tex]For a conic with a focus at the origin, if the directrix is y =± p , where p is a positive real number, and the eccentricity is a positive real number e, the conic has a polar equation
[tex]r\text{ = }\frac{ep}{1\text{ }\pm\text{ esin}\theta}[/tex]Looking through the options, we can see that the function that does not produce a conic section is:
[tex]r\text{ =2 \lparen Option D\rparen}[/tex]please help ASAP!!!!!
The rational function is
[tex]\frac{2x+2}{x^2-1}[/tex]For calculate vertical asymptote we need to find which value of x make zero the denominator
[tex]\begin{gathered} x^2-1=0 \\ (x+1)(x-1)=0 \\ x=1 \\ x=-1 \end{gathered}[/tex]And for the numerator
[tex]\begin{gathered} 2x+2 \\ 2(x+1) \\ \end{gathered}[/tex]The whole expression
[tex]\begin{gathered} \frac{2(x+1)}{(x+1)(x-1)} \\ \frac{2}{(x-1)} \end{gathered}[/tex]In this case, the vertical asymptote is at -1
Solve the following inequality algebraically:4|x+9|-2>10
The Solution:
Given the inequality below:
[tex]4\mleft|x+9\mright|-2>10[/tex]We are required to solve the above inequality.
[tex]\begin{gathered} 4\mleft|x+9\mright|-2>10 \\ \text{ Add 2 to both sides, we get} \\ 4\mleft|x+9\mright|-2+2>10+2 \\ 4\mleft|x+9\mright|>12 \end{gathered}[/tex]Dividing both sides by 4, we get
[tex]\begin{gathered} \frac{4\mleft|x+9\mright|}{4}>\frac{12}{4} \\ \\ \mleft|x+9\mright|>3 \end{gathered}[/tex]Applying the absolute rule that states that:
[tex]\begin{gathered} \mleft|x\mright|>a,a>0\text{ means} \\ x<-a\text{ or } \\ x>a \end{gathered}[/tex]We have:
[tex]\begin{gathered} x+9<-3\text{ or} \\ x+9>3 \end{gathered}[/tex]Solving each of them, we have
[tex]\begin{gathered} x+9<-3 \\ x<-3-9 \\ x<-12 \end{gathered}[/tex]Or
[tex]\begin{gathered} x+9>3 \\ x>3-9 \\ x>-6 \end{gathered}[/tex]Therefore, the correct answer is:
[tex]\begin{gathered} x<-12\text{ or} \\ x>-6 \end{gathered}[/tex]please help me ASAP!!!