Answers
ANSWER
m∠RQS = 33.5°
EXPLANATION
As we can see in the diagram, RQ is the diameter of circle P. Angles RPS and QPS are supplementary angles, so if m∠QPS = 113°, then,
[tex]m\angle RPS=180\degree-113\degree=67\degree[/tex]Angle RPS is a central angle that intersects arc RS, so the measure of arc RS is also 67°.
We have to find the measure of angle RQS, which is an inscribed angle - note that the vertex is on the circle, and it intercepts arc RS, so its measure is half the measure of the intercepted arc,
[tex]m\angle RQS=\frac{1}{2}mRS=\frac{1}{2}\cdot67\degree=33.5\degree[/tex]Hence, the measure of angle RQS is 33.5°.
Related Questions
Simply The Expression 12+3(7y-8)
Answers
First we use the distributive property to eliminate the parenthesis:
[tex]\begin{gathered} 12+3(7y-8)=12+3(7y)+3(-8) \\ =12+21y-24 \end{gathered}[/tex]Now we add similar terms and we get the following:
[tex]12+21y-24=21y-12[/tex]Notice that 21 and 12 are divisible by 3, therefore, we have::
[tex]21y-12=3(7y-4)[/tex]Finally, the simplifed expression of 12+3(7y-8) is 3(7y-4)
write a coordinate rule for the composition
Answers
The coordinate rule for the composition is (x, y) ⇒ 2(-x, -y)
How to determine the coordinate rule?From the graph, the coordinates of the triangles are
Triangle ABC: A = (-2, 1), B = (-4, 1) and C = (-2, 4)Triangle DEF: D = (4, -2), E = (8, -2) and F = (4, -2)The triangles are in opposite quadrants
This means that the triangles are rotated by 180 degrees
This is represented as
(x, y) ⇒ (-x, -y)
Next, we can see that the side lengths of triangle DEF is twice the side lengths of triangle ABC
This means that the triangle ABC is dilated by 2
So, we have
(x, y) ⇒ 2(-x, -y)
Note that we assume that the triangle is transformed from ABC
Read more about transformation at
https://brainly.com/question/27224272
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which of the following are like terms?3y^5 ,2x^53y^5, 2y^56y^2, 2z3y^4, 4x^3
Answers
1) Like terms have the same variable and the same exponent. Therefore we can add, subtract, and combine them when operating polynomials.
2) Examining the options, we can state that:
3y^5, 2y^5
We can add those, subtract them, and so on.
3) So the answer is 3y^5, 2y^5 for they have the same variable,
“Five times the difference of -16 and 3 amounts to -95” written as an equation is
Answers
Problem
“Five times the difference of -16 and 3 amounts to -95” written as an equation is
Solution
For this case we can do the following:
5(-16-3) = 5* -19 = -95
Find the measure of each numbered angle and name the theorem or postulate that justify your work.
Answers
Answer:
m∠2 = 94
m∠3 = 94
Explanation:
Angle 2 and 3 are vertical angles. They are opposite and are formed when two lines cross. Since they are vertical angles, they have the same measure, so we can write the following equation:
[tex]\begin{gathered} m\angle2=m\angle3 \\ 4x-26=3x+4 \end{gathered}[/tex]So, solving for x, we get:
[tex]\begin{gathered} 4x-26+26=3x+4+26 \\ 4x=3x+30 \\ 4x-3x=3x+30-3x \\ x=30 \end{gathered}[/tex]Now, we can calculate the measure of angle 2 and 3 as:
[tex]\begin{gathered} m\angle2=4x-26=4\cdot30-26=120-26=94 \\ m\angle3=3x+4=3\cdot30+4=90+4=94 \end{gathered}[/tex]Therefore, the measures of angles 2 and 3 are 94
Each number in the table below represents the number of employees at different stores in two nearby malls.Part ADetermine the interquartile range for numbers of employees at each mall. Show your work or explain your reasoning.Part BWhich mall would you expect to have greater variability in regard to numbers of employees? Show your work or explain your reasoning.
Answers
Solution
Part A
For this case we need to remember that by deifnition the IQR is given by:
IQR= Q3-Q1
Where:
Q3= third quartile and Q1= First quartile
Then we can find the values for each mall and we have:
Vallet View Mall
Q3=24.5 , Q1= 6 IQR= 18.5
Lone Pines Mall
Q3= 21.5 , Q1= 8 IQR= 13.5
Part B
Greater variablity with higher IQR then the answer is:
Vallet View Mall
Since the IQR = 18.5 higher than the Lone Pines Mall IQR of 13.5
Expected ValveMar 08, 12:56:29 PMJacob owns a small business selling bagels. He knows that in the last week 65customers paid cash, 26 customers used a debit card, and 8 customers used a creditacard.If next week, he is expecting 600 customers, about how many would you expect topay with a credit card? Round your answer to the nearest whole number.Answer:Submit Answerattempt 2 out of 2
Answers
From the question given, we have the following information;
[tex]\begin{gathered} \text{Cash customers}=65 \\ \text{Debit card customers}=26 \\ \text{Credit card customers}=8 \end{gathered}[/tex]In order to determine the probability that the next customer would be a credit card customer, we shall calculate as follows;
[tex]P\lbrack E\rbrack=\frac{\text{Number of required outcomes}}{Number\text{ of all possible outcomes}}[/tex]Using the details we are given, the probability that the next customer would be using a credit card would be;
[tex]\begin{gathered} P\lbrack\text{credit card}\rbrack=\frac{8}{65+26+8} \\ P\lbrack\text{credit card}\rbrack=\frac{8}{99} \end{gathered}[/tex]Next, we are told that next week, 600 customers are expected. Therefore, the number that is expected to pay with a credit card would be;
[tex]\begin{gathered} \text{Expected value}=\frac{8}{99}\times600 \\ \text{Expected value}=48.4848\ldots \\ \text{Rounded to the nearest whole number;} \\ \text{Expected value}=48 \end{gathered}[/tex]ANSWER:
About 48 customers would be expected to pay with a credit card
Two linear functions are represented below , f(x) by a table , and g(x) by a graph .which function has the greater rate of change
Answers
The rate of change of a function is equal to the derivative of that function.
So, we can proceed by finding the derivative of functions f and g. The one with the greatest derivative will then have the greatest rate of change.
Function f(x).
From the table, we can observe that
x=0-->f(x)=4 and x=5-->f(x)=7
Let's see if this function is a line. Remember that to define a line we only need two points, we can take (x,f(x))=(0,4),(5,7) so as to facilitate the solution.
[tex]\begin{gathered} (0,4),(5,7) \\ f(x)-f(x_1)_{}=\frac{(f(x_2)_{}-f(x_1)_{})}{(x_2-x_1)}(x-x_1) \\ \Rightarrow f(x)-4=\frac{(7-3)}{(5-0)}(x-0) \\ \Rightarrow f(x)-4=\frac{4}{5}x \end{gathered}[/tex]Now, let's verify that this equation models the information displayed in the table:
x=-10-->f(x)=-2
I’m always getting the wring answer. Can you help. I know it’s a very long process.
Answers
To make the table of values we need to determine in which interval we need to use each of the expressions of the piecewise function. For any value less than zero we need to use the expression y=3. For any value greater or equal than zero we are going to use the expression x+1; with this in mind we have the following table:
Now that we have this table we plot the points given and graph the function:
Now, in here it is important to notice that the horizontal lines goes till x=0 BUT we draw a hollow point indicating that this line does not touch the zero, this measn that the function y=3 is defined for x<0 like the function stated.
Furthermore we have to draw a solid circle in the point (0,1) that indicates that the function takes that value when x=0.
Now from the graph we notice that the function is defines for all values of x then we have that the domain is:
[tex]\text{domf}=(-\infty,\infty)[/tex]Also from the graph we notice that the range is the interval:
[tex]\text{rangeF}=\lbrack1,\infty)[/tex]Describe howfactoring can help you find the x-interceptsof the graph of the quadratic functiony=x2 - 4x + 3.
Answers
hello
the quadratic equation given is
[tex]x^2-4x+3=0[/tex]now let's find two factors to the equation and proceed to solve the equation.
to do this, i'll write down the standard form of a quadratic equation out
[tex]ax^2+bx+c=0[/tex]to solve this by factorization, we need to find two numbers that when they're multiplied will give us the value of c but when added will give the value of b
in this case, our value of b = -4 and c = 3
two numbers that will give us the desired value are (-1, -3)
[tex]x^2-4x+3=(x-1)(x-3)[/tex]the factorized form of the equation would be (x - 1)(x - 3)
The total revenue for Dante's Villas is given as the function R(x)=700x−0.5x^2, where x is the number of villas rented. What number of villas rented produces the maximum revenue?
Answers
The revenue function is,
[tex]R(x)=700x-0.5x^2[/tex]For maximum and minimum value, the first derivative of function is equal to 0.
Determine the first derivative of revenue function.
[tex]\begin{gathered} \frac{d}{dx}R(x)=\frac{d}{dx}(700x-0.5x^2) \\ R^{\prime}(x)=700-0.5\cdot2x \\ =700-x \end{gathered}[/tex]For maximum and minimum value, R'(x) = 0. So
[tex]\begin{gathered} 0=700-x \\ 700=x \end{gathered}[/tex]Since x = 700 corresponds to maximum or minimum value of revenue.
Determine the second derivative of revenue function.
[tex]\begin{gathered} \frac{d}{dx}R^{\prime}(x)=\frac{d}{dx}(700-x) \\ R^{\doubleprime}(x)=-1 \end{gathered}[/tex]Since second derivative of revenue function is less than 0 for every value of x. So x = 700 corresponds to maximum value of revenue.
So 700 villas rented to produce maximum revenue.
Answer: 700 villas
If -1/2 is a root of the equation ^2+5 + 2 = 0, find .
Answers
Given:
-1/2 is a root of the following equation:
[tex]^2+5+2=0[/tex]First, we will find the value of k
substitute with a = -1/2
so,
[tex]\begin{gathered} k\cdot(-\frac{1}{2})^2+5\cdot(-\frac{1}{2})+2=0 \\ k\cdot\frac{1}{4}-\frac{5}{2}+2=0 \\ k\cdot\frac{1}{4}-\frac{1}{2}=0 \\ k\cdot\frac{1}{4}=\frac{1}{2} \\ k=2 \end{gathered}[/tex]So, the equation will be:
[tex]2^2+5+2=0[/tex]Now, factor the equation:
[tex]\begin{gathered} (2a+1)(a+2)=0 \\ 2a+1=0\rightarrow a=-\frac{1}{2} \\ or,a+2=0\rightarrow a=-2 \end{gathered}[/tex]So, the answer will be:
[tex]a=\mleft\lbrace-2,-\frac{1}{2}\mright\rbrace[/tex]Base on definition of the inverse, f(g(x))=x and vice versa. Given f(x)=1/2x+3 and g(x)=2x-6, write a composition (s) should be used to prove that f(x) and g(x) are inverses of each other.
Answers
To verifiy if these are inverses we need to calculate the expression "f(g(x))" which uses the expression for "g(x)" in place of x on the expression of "f(x)". We have:
[tex]\begin{gathered} f(g(x))=\frac{1}{2}(2x-6)+3 \\ f(g(x))=\frac{2x}{2}-\frac{6}{2}+3 \\ f(g(x))=x-3+3 \\ f(g(x))=x \end{gathered}[/tex]Since the result is f(g(x)) = x, they are inverses of each other.
Judy drew an isosceles triangle.One side of the triangle was 6 incheslong. The other side of the triangle was 9 inches long. What couldbe the length of the third side of the triangle Judy drew? Explainyour reasoning.
Answers
Isosceles triangles Have two sides that have the same measure, and one of them is different.
So, we can have two situations:
6 - 6 - 9
or
9 - 9 - 6
Hi yea thank you thank goodness for your help today please
Answers
Given:
[tex]h(t)=3300-54t-300e^{-0.18t}[/tex]Find-:
(1)
Velocity at the instant when t = 6 sec.
(2)
The time when velocity is -45 meter per sec
Explanation-:
Velocity is define as a:
[tex]\begin{gathered} v(t)=\frac{dh(t)}{dt} \\ \\ v(t)=h^{\prime}(t) \end{gathered}[/tex]The value of the h'(t) is:
[tex]\begin{gathered} h(t)=3300-54t-300e^{-0.18t} \\ \\ h^{\prime}(t)=-54-300(-0.18)e^{-0.18t} \end{gathered}[/tex]Value is:
[tex]\begin{gathered} h^{\prime}(t)=54e^{-0.18t}-54 \\ \\ v(t)=h^{\prime}(t) \\ \\ v(t)=54e^{-0.18t}-54 \end{gathered}[/tex]At t=6 velocity is:
[tex]\begin{gathered} v(t)=54e^{-0.18t}-54 \\ \\ v(6)=54e^{-0.18\times6}-54 \\ \\ v(6)=54e^{-1.08}-54 \\ \\ v(6)=54\times0.333-54 \\ \\ v(6)=18.333-54 \\ \\ v(6)=-35.66 \end{gathered}[/tex]At t=6 velocity is -35.66 meters per sec.
(b)
Velocity is -45 meter per second then time is:
[tex]\begin{gathered} v(t)=54e^{-0.18t}-54 \\ \\ v(t)=-45\text{ then time is:} \\ \\ -45=54e^{-0.18t}-54 \\ \\ 54-45=54e^{-0.18t} \\ \\ 9=54e^{-0.18t} \\ \\ \frac{9}{54}=e^{-0.18t} \\ \\ 0.166=e^{-0.18t} \end{gathered}[/tex]Taking log both side then,
[tex]\begin{gathered} \ln0.166=\ln e^{-0.18t} \\ \\ \ln0.166=-0.18t\ln e \\ \\ -1.79175=-0.18t \\ \\ t=\frac{-1.79175}{-0.18} \\ \\ t=9.95 \end{gathered}[/tex]So, the time is 9.95 second
A rock is thrown from the side of a ledge. The height (in feet), x seconds after the toss is modeled by: h (x) = -4(x-2)^2 +293 How high was the platform at the time of the launch?
Answers
Answer:
The platform was 277 feet high at the time of the launch
Explanation:
Given that the height is modeled by:
[tex]h\mleft(x\mright)=-4\mleft(x-2\mright)^2+293[/tex]To find how high the platform was at the time of the launch, we find h(0) by replacing x by 0 in the given equation.
[tex]\begin{gathered} h(0)=-4(0-2)^2+293 \\ =-4(-2)^2+293 \\ =-4(4)+293 \\ =-16+293 \\ =277 \end{gathered}[/tex]The platform was 277 feet high at the time of the launch
Find the simplest form, of C, starting with the further point where the graph of C crosses the y axis.
Answers
We are given the function f(x) = x^3 - 6x^2 + 10x - 3, where x is a real number. We are supposed to translate it by (-2, 3) which means that we are moving the entore graph 2 units to the right and 3 units up.
The first thing to do is write the cubic function in the form f(x) = a(x - h)^3 + k where h is the horizontal translation and k is the vertical translation.
So, f(x) = x^3 - 6x^2 + 10x - 3 moved 2 units to the right and 3 units up would be written as:
[tex]C=(x+2)^3-6(x+2)^2+10(x+2)-3+3[/tex]We can simplify this as:
[tex]\begin{gathered} C=(x+2)^{3}-6(x+2)^{2}+10(x+2)-3+3 \\ C=(x^3+6x^2+12x+8)-6(x^2+4x+4)+(10x+20) \\ C=x^3+6x^2+12x+8-6x^2-24x-24+10x+20 \\ C=x^3-2x+4 \end{gathered}[/tex]The graph crosses the y-axis when x = 0.
[tex]\begin{gathered} C=x^{3}-2x+4 \\ y=0^3-2(0)+4 \\ y=4 \end{gathered}[/tex]The point where the graph crosses the y-axis is (0, 4).
Instead of the installment plan, suppose the Sanchez family went to the bankand borrowed $273 with 8% interest.
Answers
8. Amount of interest: $273*8% = $21.84
9. Total amount: $273 + $21.84 = $294.84
I need help solving this math problem by using substitution method
Answers
To solve by substitution method:
1. Substitute the x in the first equation by the value of x given in the second equation:
[tex]-3(-5y)-6y=45[/tex]2. Solve y:
[tex]\begin{gathered} 15y-6y=45 \\ 9y=45 \\ \\ \frac{9}{9}y=\frac{45}{9} \\ \\ y=5 \end{gathered}[/tex]3. Use the value of y to find x:
[tex]\begin{gathered} x=-5y \\ x=-5(5) \\ x=-25 \end{gathered}[/tex]Then, the solution for the given system of equations is: x= -25 and y=5 (-25,5)find the missing angle measures of each polygon in 8
Answers
The sum of the interior angles of a pentagon is 540°
angle H +angle I + angle J + angle K +angle L=540°
we substitute the values
100+143+85+92 angle L= 540°
angle L= 540-100-143-85-92
angle L=120°
Evaluate the function [p - 25]+pf where p=10 and f=3
Answers
ANSWER
[tex]15[/tex]EXPLANATION
We want to evaluate the expression given:
[tex]\lbrack p-25\rbrack+pf[/tex]for:
[tex]p=10;f=3[/tex]To do this, we substitute the values of p and f into the expression and simplify it:
[tex]\begin{gathered} \lbrack10-25\rbrack+(10\cdot3) \\ -15+30 \\ \Rightarrow15 \end{gathered}[/tex]That is the answer.
Is this set of values a function? Yes or No
Answers
No, the set doesn't represent a function because the number 1 has two diferent images which are 3 and 8.
what is the product of 2x^2-3xy+y^2 and 2x-4y?
Answers
4x³ -14x²y +14xy²-4y³
1) Let's calculate it
(2x²-3xy+y²) (2x-4y) Applying the Distributive Property
4x³-8x²y-6x²y+12xy²+2xy²-4y³ Combining like terms
4x³ -14x²y +14xy²-4y³
Answer:
(2x²-3xy+y²) (2x-4y) Applying the Distributive Property
4x³-8x²y-6x²y+12xy²+2xy²-4y³ Combining like terms
4x³ -14x²y +14xy²-4y³
e Calculate the area of the regular hexagon. Round your answer to the nearest tenths. 3.4cm X. 20.4cm? .. 29.6cm? c.59.1cm? 4.9cm?
Answers
The side of hexagon is s = 3.4 cm.
The apothem is a = 2.9 cm.
The formula for the area of regular hexagon is,
[tex]A=\frac{1}{2}\cdot P\cdot a[/tex]Here, P is perimeter of hexagon.
Determine the perimeter of hexagon.
[tex]\begin{gathered} P=6s \\ =6\cdot3.4 \\ =20.4 \end{gathered}[/tex]Substitute the value in the area formula to obtain the area of regular hexagon.
[tex]\begin{gathered} A=\frac{1}{2}\cdot20.4\cdot2.9 \\ =29.58 \\ \approx29.6 \end{gathered}[/tex]So answer is 29.6 square centimeter.
Which pair of functions are inverses of each other?O A. f(x) = and g(x) = 6 x3B. f(x) = 1 + 6 and g(x) = 5x - 6C. f(x) = 7x- 2 and g(x) = x+2O D. f(x) = -2 and g(x) = 2+2SUBMIT
Answers
Explanation:
To find the inverse of a function, we need to replace f(x) by y, then solve the function for x, and finally interchange the variables x and y.
So, the inverse function for each option is:
Option A.
[tex]undefined[/tex]use the interactive tool to find the difference:1- 3/10 .Write the answer as a fraction
Answers
The given difference is
[tex]1-\frac{3}{10}[/tex]To find this difference we can use the following property.
[tex]\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}[/tex]So,
[tex]1-\frac{3}{10}=\frac{1\cdot10-1\cdot3}{1\cdot10}=\frac{10-3}{10}=\frac{7}{10}[/tex]Therefore, the answer is 7/10.Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value.n=3-3 and 5 + 5i are zeros f(-1)= 122
Answers
Given:
a.) n = 3
b.) -3 and 5 + 5i are zeros
c.) f(-1) = 122
Step 1: Let's determine the factors based on the zeros.
-3 and 5 + 5i are zeros
Therefore, the factors will be:
x + 3
5 + 5i = 5(1 + i)
x + 5(1 + i)
x - 5(1 + i)
0
The ones with the X’s are the only ones i cannot get the answer for. please help
Answers
Order the winning scores from least to greatest, and do so with the losing scores.
[tex]\begin{gathered} winning \\ 14,16,16,16,17, \\ 20,20,20,21,21,23,23,24,24,24,26,27,27,27,27,27,29 \\ 30,31,31,31,31,32,32,33,34,34,35,35,35,37,38,38,39 \\ 42,46,48,49, \\ 52,55 \end{gathered}[/tex]As for the losing scores,
[tex]\begin{gathered} losing\text{ } \\ 3,6,7,7,7,7,7,9 \\ 10,10,10,10,10,10,10,13,13,14,14,14,16,16,16,16,17,17,17,17,17,17,17,19,19 \\ 20,21,21,21,21,23,24,24,25,26,29 \\ 31 \end{gathered}[/tex]Therefore, the correct diagram for the losing scores is
As for the winning scores,
Please find the cumulative frequency of this question, if possible, according to class 9 ICSE.
Answers
The cumulative frequency is the sum of all simple frequencies.
So, to determine the cumulative frequency of each class, you have to add the simple frequency of the class to the cumulative frequency of the previous class.
The cumulative frequency of the first class is equal to the simple frequency since before the first category of the variable there is no observed frequency.
xi → value of the variable
fi → simple frequency of the i-class
Fi → cumulative frequency of the i-class
For the first class, the cumulative and simple frequencies are equal
[tex]F_1=f1=3[/tex]For the second class, the cumulative frequency is equal to the sum of the cumulative frequency of the previous class and the simple frequency of the second class:
[tex]F_2=F_1+f_2=3+4=7[/tex]The cumulative frequency for the third class is equal to the sum of the cumulative frequency of the second class and the simple frequency of the third class:
[tex]F_3=F_2+f_3=7+2=9[/tex]The cumulative frequency of the last class of the frequency table corresponds to the sample size of the data set used to construct the table.
Three friends went to a school play. Each ticket was$5. They each spent different amounts of money on food and drink. Chris$5, Ben $3 and Danica$6 which is these expression can be used to find out the total amount of money all three friends spent on tickets, food, and drink(3+5*(5+6) (3*5)+(5+3+6)(3+5)+(5*5*6)
Answers
Answer:
(3*5) + (5 + 3 + 6)
Explanation:
To know the total amount of money that they spend, we need to sum the amount that they spend on tickets to the amount that they spend on food and drink.
So, if each ticket cost $5 and they are 3 friends, the total amount that they spend on tickets can be calculated as:
3*5
On the other hand, if Chris spent $5, Ben $3, and Danice $6, the total amount that they spent on food and drink is:
5 + 3 + 6
Therefore, the expression to calculate the total amount that they spent is:
(3*5) + (5 + 3 + 6)