In expanded form, we write the numbers by showing the value of each digit
Consider the following figure.A circle, four points on the circle, two interior line segments, and two angles are given.Point R is on the top left.Point S is on the lower left.Point T is on the upper right.Point V is on the right, just below center.Segment R V goes from R down and right to V.Segment S T goes from S up and right to T, intersecting the first segment inside the circle.The angle left of the intersection point, formed below R V and above S T, is labeled 1.The angle under the intersection point, formed below R V and below S T, is labeled 2.Given:m∠1 = 55°mRS$\frown{\hspace{25px}}$ = (5x + 2)°mVT$\frown{\hspace{25px}}$ = x°Find: mRS$\frown{\hspace{25px}}$ in degreesWrite an equation relating m∠1 to mRS$\frown{\hspace{25px}}$ and mTV$\frown{\hspace{25px}}$ in terms of x.55° =°Find x°.x° =°Find mRS$\frown{\hspace{25px}}$ in degrees.mRS$\frown{\hspace{25px}}$ =°
Solution:
Given a circle;
Where
[tex]\begin{gathered} m\angle1=55\degree \\ Arc\text{ RS}=(5x+2)\degree \\ Arc\text{ VT}=x\degree \end{gathered}[/tex]Applying the secant theorem for an interior case,
It states that the measure of an angle whose vertex lies in the interior of a circle is equal to half the sum of the angle measures of the arcs intercepted by it and its vertical angle.
[tex]m\angle1=\frac{1}{2}(arc\text{ RS}+arc\text{ TV})[/tex]The equation becomes
[tex]55\degree=[\frac{1}{2}((5x+2)+x)]\degree[/tex]Hence,
[tex]55\operatorname{\degree}=\frac{1}{2}[(5x+2)+x]\degree[/tex]Solving for x
[tex]\begin{gathered} 55\degree=\frac{1}{2}(5x+2+x)\degree \\ 55\degree=\frac{1}{2}(6x+2) \\ Crossmultiply \\ 55\degree\times2=6x+2 \\ 110=6x+2 \\ Collect\text{ like terms} \\ 6x=110-2 \\ 6x=108 \\ Divide\text{ both sides by 6} \\ \frac{6x}{6}=\frac{108}{6} \\ x\degree=18\degree \end{gathered}[/tex]Hence, x is 18°
For arc RS
[tex]\begin{gathered} mRS=5x+2=5(18)+2=8=90+2=92\degree \\ mRS=92\degree \end{gathered}[/tex]Hence, mRS is 92°
multiple (-1s^2)(-3r^2)
multiple (-1s^2)(-3r^2) = 3 s^2 r^2
Answer:
[tex]3s^2r^2[/tex]Answer:
= 3r²s²
Step-by-step explanation:
(-1s²)(-3r²)
(-1)(-3) = +3 = 3
(s²)(r²) = s²r² = r²s²
Then:
(-1s²)(-3r²) = 3r²s²
IXL - Angle-Side relationships in trianglesList the angle measures of STU in order from smallest to largest. Assume that V is a positive number.
We know that the sum of the internal angles of a triangles must be equal to 180º, so in this cas we know that one of the angles are 92º then the sum of the other two angles will be 88º
so the bigger angle is S, then the other two angles we can see that U is bigger than T so the solution is:
[tex]m\angle TUse the diagram and give information to match the angle measure with the angle
Given the triangle below:
It can be observed that
[tex]m\angle ION=m\angle GOT(vertically\text{ opposite angles are equal)}[/tex][tex]\begin{gathered} \text{if,m}\angle GOT=168^0,then \\ m\angle ION=m\angle GOT=168^0 \\ m\angle ION=168^0 \end{gathered}[/tex]It can also be observed that
[tex]\begin{gathered} m\angle AON+m\angle AOI=m\angle ION(given) \\ m\angle AOI=90^0(given,right-angle) \\ m\angle ION=168^0(derived\text{ earlier)} \\ So, \\ m\angle AON+90^0=168^0 \\ m\angle AON=168^0-90^0 \\ m\angle AON=78^0 \end{gathered}[/tex]It can as well be observed that
[tex]m\angle NOG=180^0(angle\text{ on a straight line)}[/tex]Hence,
m∠ION = 168°
m∠AON = 78°
m∠NOG = 180°
(G.11c, 1 point) The minute hand on a clock is 6 centimeters long and travels through an arc of 108° every 18 minutes. Calculate which measure is closest to the length of the arc the minute hand travels through during this 18 minute period? 1 12 11 10 1080 -9 2 3 8 4 7 6 5 O A. 3.67 cm O B. 10.87 cm C. 67 cm D. 127 cm
Let's find the Arc length:
[tex]\begin{gathered} L=r\theta \\ \text{where:} \\ r=6 \\ \theta=108=\frac{3}{5}\pi \\ L=(6)(\frac{3}{5}\pi)=3.6\pi cm \end{gathered}[/tex]Solve for x.12x + 7 < -11 or 5x - 8 > 40
Given:
[tex]\begin{gathered} 12x+7<-11 \\ \\ \text{ Or} \\ \\ 5x-8>40 \end{gathered}[/tex]Find-:
To solve for "x"
Explanation-:
Solve for "x" is:
[tex]\begin{gathered} 12x+7<-11 \\ \\ 12x<-11-7 \\ \\ 12x<-18 \\ \\ x<-\frac{18}{12} \\ \\ x<-\frac{3}{2} \end{gathered}[/tex]The vale of "x" is:
[tex]\begin{gathered} 5x-8>40 \\ \\ 5x>40+8 \\ \\ 5x>48 \\ \\ x>\frac{48}{5} \end{gathered}[/tex]The final value of "x" is:
[tex]\begin{gathered} x<-\frac{3}{2} \\ \\ \text{ Or} \\ \\ x>\frac{48}{5} \end{gathered}[/tex]Can you please help me I’m confused how to turn my answer cos B = 13/43
Given:
[tex]\begin{gathered} a=13\text{ cm} \\ \\ c=43\text{ cm} \end{gathered}[/tex]Find-:
The angle of B.
Sol:
The angle of B is:
[tex]\begin{gathered} \text{ Base =}a=13\text{ cm} \\ \\ \text{ Hypotenuse =}c=43\text{ cm} \end{gathered}[/tex]Angle "B"
[tex]\cos\theta=\frac{\text{ Base}}{\text{ Hypotenuse }}[/tex][tex]\begin{gathered} \cos B=\frac{\text{ Base}}{\text{ Hypotenuse }} \\ \\ \cos B=\frac{13}{45} \end{gathered}[/tex]So the angle "B" is:
[tex]\begin{gathered} \cos B=\frac{13}{45} \\ \\ B=\cos^{-1}(\frac{13}{45}) \\ \\ B=73.21 \\ \\ B\approx73 \end{gathered}[/tex]The angle of "B" is 73
Write the inequality that represents the following sentence.The sum of a number and 7 is less than - 6.Choose the correct answer below.O A. X-7> -6O C. X-75-6O E X-7<- 6O G. -72-6OB. x + 75 -6D. x + 7 = -6OF. x + 72 -6H. x+7> -6
we have the following:
[tex]x+7<-6[/tex]Therefore, the answer is D. x + 7 < -6
Alexander is building an enclosure in the shape of a regular polygon. If the enclosure has a certain number of sides, n, and has exterior angles, each with a measure of 32.7 degrees, determine how many sides the garden has. 9 sides 10 sides 11 sides 12 sides
To calculate the measure of the external angles of a regular polygon, you have to divide 360º by the number of sides:
[tex]\angle\theta=\frac{360º}{n}[/tex]If the external angles have measure ∠θ=32.7º
Replace this measure in the expression and calculate for n
[tex]\begin{gathered} 32.7=\frac{360}{n} \\ 32.7n=360 \\ n=\frac{360}{32.7} \\ n=11.009 \end{gathered}[/tex]The regular polygon has 11 sides and is called hendecagon
if it was 3:54 p.m. then it turned 5:00 a.m. how much time would pass
To calculate how much time has passed from 3:54 pm to 5:00 am is best to do it by parts.
First, calculate how much time is between 3:54 pm to the next hour, that is 4:00pm
Each hour has 60 minutes, to determine how much time is left for the 60minutes to be complete you have to subtract 54min from 60 min
[tex]60\min -54\min =6\min [/tex]Between 3:54 pm and 4 pm there are 6 minutes
Second, let's calculate the time between 4 pm and the last hour of the day, that is 12:00am, to do so you have to calculate the difference between both times:
[tex]12-4=8[/tex]Between 4:00 pm and 12:00am there are 8 hours.
Third, calculate the time between 12:00am and 5:00am. Midnight can be also be written as 00:00am. Using this expression, calculate the amount of hours between both times as:
[tex]5-0=5[/tex]Between midnight and 5:00am there are 5 hours.
The final step is to add all calculated times to determine how much time passed between 3:54 pm and 5:00 am
8hours
5hours
[tex]8+5=13[/tex]+6minutes
The total time is 13 hours and 6 minutes
what is the distance between point a and point B where a equals 70, 10 and b equals 4, 30
I need help with this assignment that I am not understand.
The set of the graph below can be writen as,
[tex]\mleft\lbrace x|-4The equation y= ax describes the graph of a line. If the value of a is negative,the lineA. is horizontalB. is verticalC. goes up and to tight,D. goes down and to the right,SUSM
We certainly have a line when we have an equation (or a function) like:
[tex]y=ax[/tex]In this case, a, represent the slope of the line. If the slope of the line is negative, -a, the line will present the next representation (see the green and blue lines):
As we can see, the line goes down from left to right. As the values for x increase (from left to the right) the values for y decrease (from left to the right).
Therefore, the correct option is D (the one that fits better) ---> The line goes down and to the right.
(As I can see, this is the option that fits better from the explanation I wrote above ---and from the given options.)
Note: the graph for a line with positive slope, a, is of the form:
(As the values for x increase, the y values also increase.) ---> The line goes up and to the right.
hello I seem to be stuck on this math problem and could use some help thank you so much
$1400 bonus
5 year CD investment
interest rate = 1.47%
compounded annually
Compound interest formula:
A = P (1 + r/n)^ nt
Where:
• A = future value
,• P= principal = 1400
,• r= interest rate = 1.47 % = 1.47 / 100 = 0.0147 (decimal form)
,• n= compounding periods = 1
,• t = years = 5
Replacing:
A = 1400 ( 1 + 0.0147)^5
A = $ 1,505.970059 = $ 1,505.97
Answers:
(a) = $ 1,505.97
(b) = 1,505.970059 - 1400 = $105.97
Evaluate the expression. Write your answer in scientific notation.(9×10^−3)+(2.4×10^−5) ÷ 0.0012The answer is 2.9 times 10^-2 I just don't know how to get that.
We are given this expression:
[tex](9*10^{-3})+(2.4*10^{-5})\div.0012[/tex]Let's first evaluate 9 * 10^(-3) by moving the decimal place of 9 to the left 3 times.
[tex]9*10^{-3}=.009[/tex]Now, let's evaluate 2.4 * 10^(-5) by moving the decimal place of 2.4 to the left 5 times.
[tex].000024[/tex]Now, we have this expression:
[tex].009+.000024\div.0012[/tex]Start by dividing .000024 and .0012 because we must divide before adding.
Now, we have this expression:
[tex].009+.02[/tex]Add these terms together to get:
[tex].029[/tex]This number, .029 in scientific notation, is 2.9 * 10^(-2) since if we move the decimal place to the left in 2.9 two times, we get .029.
Solve the right triangle. Select the correct measure of each part of the triangle
Given:
Given that a right angle triangle.
[tex]\begin{gathered} \theta=52.4\degree \\ h=16.7 \end{gathered}[/tex]Required:
To measure the each part of the triangle.
Explanation:
Let the the two sides of triangle are a and o.
Now,
[tex]\begin{gathered} \cos\theta=\frac{a}{h} \\ \\ \cos52.4=\frac{a}{16.7} \\ \\ 0.6101=\frac{a}{16.7} \\ \\ a=0.6101\times16.7 \\ \\ a=10.188 \end{gathered}[/tex]Now we have to find the other side of the triangle.
Clearly the given triangle is right angle, therefore,
[tex]\begin{gathered} h^2=a^2+o^2 \\ \\ 16.7^2=10.188^2+o^2 \\ \\ 278.98=103.795+o^2 \\ \\ o^2=175.184 \\ \\ o=13.23 \end{gathered}[/tex]Final Answer:
The other two sides of triangle are,
[tex]\begin{gathered} 10.188 \\ 13.23 \end{gathered}[/tex]Solve the triangle below without using either the cosine or tangent ratios
Given
To solve the triangle, without using either the cosine or tangent ratios.
Explanation:
It is given that,
[tex]\theta=23\degree[/tex]By using the sine ratio, we get,
[tex]\begin{gathered} \sin23=\frac{a}{16} \\ a=16\times\sin23 \\ a=6.25 \end{gathered}[/tex]That implies,
[tex]\begin{gathered} a^2+b^2=16^2 \\ 6.25^2+b^2=16^2 \\ 39.0625+b^2=256 \\ b^2=256-39.0625 \\ b^2=216.9375 \\ b=14.73 \end{gathered}[/tex]Hence, the answer is,
[tex]a=6.25,b=14.73[/tex]how do I factor polynomials(2x+1) (x-1)
(2x+1) (x-1)
If we distirbute the terms we have this:
2x^2 -2x +x -1
And if we simplify we got:
2x^2 -x -1
the tutor i had before explained it all but the answer wasn’t loading. that’s all!
Explanation:
The expression f(0) represents the value of the function at x=0 which means the y-intercept of the function.
the y-intercept of the graph is the point that crosses the y-axis.
From the given graph,
The y-intercept of the graph does not define.
Answer: f(0) = not defined
This year consumers purchased 5,234,267,990 bottles of water. Last year consumers purchased 1,000,900,999 bottles of water. Which is the best estimate of the number of bottles sold this year and last year?A.4,000,000,000B.6,000,000,000C.6,235,168,989D.7,000,000,000
This years consumers purchased 5,234,267,990 bottles of water, let's called it X.
Last year consumers purchased 1,000,900,999 bottles of water, let's called it Y.
You need to find the best estimate of the number of bottles sold this year and last year, then you need to add both x and y:
[tex]\begin{gathered} X+Y=5,234,267,990+1,000,900,999 \\ X+Y=6,235,168,989 \end{gathered}[/tex]Thus, the answer is option C. 6,235,168,989
how is regrouping thousands show in the problem above show your work
The operation is:
Because, the 2 from 4002 is less than the 3 in 2153 we have to borrow from the new number.
In this case before the 2 in 4002 we have two zeros than can not borrow to 2, so the 4 will borrow an unit to the next number (the zero in this case), and the zero will convert in a 10 and the 4 in a 3. Now we have a zero taht convert in a 10 and can borrow an unit to the zero next to it, so the 10 convert in a 9 and the zero in a 10.
Finally, now we have a 10 before the 2, so it can borrow an unit and it will convert in a 9 and the 2 in a 12. Now, 12 is greater than 3, so we can substrac.
In the picture you can see how the numbers borrow a unit between them and convert.
5. The video store has a basic charge for a 3 day rental and a different charge per day late fee. Nate returned his video one day late and paid $5.50, Gina was four days late and paid $10,00 for her rental. What is the basic fee and the per day late fee the store charges?solve for x and y
Problem
5. The video store has a basic charge for a 3 day rental and a different charge per day late fee. Nate returned his video one day late and paid $5.50, Gina was four days late and paid $10,00 for her rental. What is the basic fee and the per day late fee the store charges?
Solution
For this case we can use the following notation:
y = 3 day payment x = per-day late fee
And we can set up these equations:
x+y = 5.50
4x +y= 10.00
From the first equation we can solve for x and we got:
x= 5.50 -y
We can replace this into the second equation and we got:
4(5.50-y) +y= 10.00
If we distribute the terms we got:
22 - 4y + y= 10.00
And solving for y we got:
22-10 = 3y
y= 4
and then we can solve for x and we got:
x= 5.50-4= 1.50
So our final solution would be x =1.5 and y= 4.00
886 billion and standard form
886 billion in standard form
We moved the decimal point 11 places to the left (886,000,000,000)
8.86 x10^11
I did 2600= 55% *X I got 4727.27I’m not sure if this correct
You know that 55% of the students of the school are female, and there are 2,600 students at the school.
To determine how many students are female, multiply the percentage by the total number of students and divide the result by 100:
[tex]\frac{55\cdot2600}{100}=\frac{143000}{100}=1430[/tex]There are 1430 female students at the school.
Abril likes to read. Right now, she has 60 books on herbookshelf and she would like buy some more books,Her bookshelf has space for a maximum of 180 books,Let B represent the number of new books Abrilpurchases.Which inequality represents the situation?60+ B 18060+ B 18060+ B 18060 B 180P
60 + B ≤ 180
The number of new books (B) plus the number of books she already has (60) must be equal to or less than the total number of books the bookshelf can contain (180)
what is k so that k-3,k+2,k+3 form a geometric sequence.
Given:
The sequence is,
[tex]k-3,k+2,k+3[/tex]Suppose that the given sequence is in the geometric sequence. The common ratio will be the same.
[tex]\begin{gathered} \frac{k+2}{k-3}=\frac{k+3}{k+2} \\ (k+2)(k+2)=(k+3)(k-3) \\ k^2+4k+4=k^2-9 \\ 4k=-9-4 \\ 4k=-13 \\ k=-\frac{13}{4} \end{gathered}[/tex]Answer: option c) -13/4
Report to the standard deck of playing cards if you are unfamiliar with playing cards see the description hereDuring a game of blackjack three players are dealt five cards each and the dealer has five cards. No one has a car that is worth 10 or 11 which would be a 10 a face card or an ace. What is the probability that the next player dealt a car would get a car worth 10 or 11? Express your answer in simplest form.
Answer:
Probability:
[tex]\frac{5}{8}[/tex]Explanation:
Teh formula to calculate probability of and event A of happening is:
[tex]P(A)=\frac{favorable\text{ }outcome}{total\text{ }outcome}[/tex]In this case, the favorable outcome is the amount of cards worth 10 or 11. The cards that worth 10 or 11 are:
4 Jacks
4 Queens
4 Kings
4 10's
4 Aces
This is a total of 4 * 5 = 20
The total outcome are all the cards remaining in the deck. Since 5 cards were dealt to 3 players, and 5 to the dealer, 20 cards were dealt from the deck of 52 cards.
. The total of cards in the deck is:
[tex]52-20=32[/tex]Now we can write:
[tex]P(worth\text{ }10\text{ }or\text{ }11)=\frac{20}{32}[/tex]In simplified form:
[tex]\frac{20}{32}=\frac{5}{8}[/tex]WXYZ is translated 6 units to the left and then reflected in the x-axis to create W'X'Y'Z'. Write an ordered pair to show the location of each vertex of the transformed figure.
Step 1: Write out the coordinates of W,X,Y, and Z
[tex]\begin{gathered} \text{ The coordinates of W }=(5,9) \\ \text{ The coordinates of X }=(7,8) \\ \text{ The coordinates of Y }=(9,2) \\ \text{ The coordinates of Z }=(2,5) \end{gathered}[/tex]Step2: Write out the rule to translate a point (x,y) by k units to the left, where k is a positive number
[tex](x,y)\to(x-k,y)[/tex]Step 3: Translate the coordinates of W,X,Y, and Z to the left by 6 units
[tex]\begin{gathered} \text{The coordinates of W translated 6 units to the left }=(5-6,9)=M(-1,9) \\ \text{The coordinates of X translated 6 units to the left }=(7-6,8)=N(1,8) \\ \text{The coordinates of Y translated 6 units to the left }=(9-6,2)=O(3,2) \\ \text{The coordinates of Z translated 6 units to the left }=(2-6,5)=P(-4,5) \end{gathered}[/tex]Step4: Write out the rule to reflect a point (a,b) over the x-axis
[tex](a,b)\to(a,-b)[/tex]Step 5: Reflect the coordinates of M,N,O, and P over the x-axis to get the coordinates of W', X', Y', and Z' respectively
[tex]\begin{gathered} \text{The coordinates of M reflected over the x-axis }=W^{\prime}(-1,-9) \\ \text{The coordinates of N reflected over the x-axis }=X^{\prime}(1,-8) \\ \text{The coordinates of O reflected over the x-axis }=Y^{\prime}(3,-2) \\ \text{The coordinates of P reflected over the x-axis }=Z\prime^{}(-4,-5) \end{gathered}[/tex]Step 6: Write an ordered pair to show the location of each vertex of the transformed figure
The location of W' = (-1, -9)
The location of X' = (1, -8)
The location of Y' = (3, -2)
The location of Z' = (-4, -5)
5. Trey plays on his school's basketball team. His points scored in eachgame are shown.15, 10, 20, 5, 25, 15, 40, 15, 20, 15What does the number 35 represent in relation to this data set?the maximum number of points scored in any of the gamesthe variation in the number of points he scored in these gamesthe sample size showing the number of games in which hescored points© the measure of center showing the number of points he usually scored
We have to find what 35 represent in relation to the data set.
We can discard some options:
- Is not the maximum score, as 40 is the maximum score.
- Is not the sample size, as the sample size is 10 games.
- Is not the measure of center, as most of the values are under 35 except for 40.
Then it should be the variation in the number of points he scored in these games. But we can try to calculate a measure of variation (there are more than one).
If we look at the minimum and maximum values, we have 5 and 40. The difference between the maximum and minimum values, called range, is equal to 35 and it is one of the measures of variation in a data set.
Answer: The variation in the number of points he scored in these games.
More precisely, 35 is the range of the data set (difference between maximum and minimum score)
Find (f • g)(4) for the following functions.f(x) = -x - 1 and g(x) = x^3 + x^2