in the diagram, RP bisects SRQ. if SRP =5x-10 and QRP=3x+20, what is the measure in degrees of SQR
Answers
When a line bisect an angle this means that it divide the total angle in two equal angles.
Then we can conclude than
[tex]m\angle SRP=m\angle QRP[/tex]But we know that
[tex]\begin{gathered} m\angle SRP=5x-10 \\ m\angle QRP=3x+20 \end{gathered}[/tex]Then, plugging this in the first equation
[tex]\begin{gathered} 5x-10=3x+20 \\ 5x-3x=20+10 \\ 2x=30 \\ x=\frac{30}{2} \\ x=15 \end{gathered}[/tex]Once we have the value of x we can determine the value of the angles SRP and QRP
[tex]\begin{gathered} m\angle SRP=5x-10=5(15)-10=75-10=65 \\ m\angle QRP=3x+20=3(15)+20=45+20=65 \end{gathered}[/tex]Finally, to find the angle SRQ, we only add both angles. Then
[tex]m\angle SRQ=65+65=130[/tex]So the angle SRQ is 130 degrees.
Related Questions
1/5 -> B A Are these triangles congruent? {circle YES or NO} D C С If you circled YES, is it SSS or HL? {circle one}
Answers
Yes. SSS
1) Examining those triangles, we can see that we have two congruent triangles their sides measure the same and their angles as well.
2) And since the leg, AC≅CA (by the reflexive property) we can state that they are Side, Side, Side (SSS).
3) So the answer is Yes. SSS
If you can’t see the photo ask for another one
Answers
Given
Find
the value of x and y
Explanation
to find the value of x and y, we apply angle bisector theorem
[tex]\begin{gathered} \frac{6}{9}=\frac{8}{x} \\ x=12 \end{gathered}[/tex]now,
[tex]\begin{gathered} \frac{y-3}{3}=\frac{4}{6} \\ y-3=2 \\ y=5 \end{gathered}[/tex]Final Answer
x = 12 and y = 5
5a - 14 = 80 + 4 and 9C - 3C = 48Product of a and c?
Answers
The first equation is 5a - 14 = 80 + 4
5a - 14 = 8a+4
collect the like terms
5a - 14 = 8a + 4
5a - 8a = 4 + 14
a(5-8) = 18
a(-3) = 18
-3a = 18
to find a divide both sides by -3
-3a/-3 = 18/-3
a = 18/-3
a = -6
second equation
9c - 3c = 48
c is common, so we can factorize out c
c(9 - 3) = 48
c(6) = 48
6c = 48
divide both sides by 6
6c / 6 = 48/6
c = 48/6
c = 8
the answer is a = -6 and c = 6
what does 3 × 1,000 + 400 x 100 + 6 × 1 + 1 ( 1 / 100) + 7 × (1/100) equals in standers form?
Answers
Suppose Elsa borrows $6500 at an interest rate of 8% compounded each year.Assume that no payments are made on the loan.Follow the instructions below. Do not do any rounding.
Answers
Answer:
(a) At the end of one year, the amount is $7020
(b) At the end of 2 years, the amount is $7581.6
Explanation:
To solve this problem, we need to use the compound interest formula:
[tex]A=P(1+r)^t[/tex]Where:
• P is the initial amount
,• r is the rate of annual compounding in decimal
,• t is the time in years
,• A is the amount after t years
In this case,
P = $6500
r = 0.08 (to convert 8% to decimal, we divide by 100. 8/100 = 0.08)
To solve (a), t = 1 (one year of compounding):
[tex]\begin{gathered} A=6500(1+0.08)^1 \\ A=6500\cdot1.08 \\ A=7020 \end{gathered}[/tex]After 1 year, the amount is %7020
To solve (b), t = 2:
[tex]\begin{gathered} A=6500(1+0.08)^2 \\ A=6500\cdot1.1664 \\ A=7581.6 \end{gathered}[/tex]After 2 years, the amount is $7581.6
The price for 8 ducks is $23.6.What is the price per duck?
Answers
This is a matter of division.
We are asked how much a duck should cost so that 8 of them together make $23.6.
In order to answer this question, we need to divide the price of 8 ($23.6) ducks in 8 ducks!
The price of one duck is
[tex]\frac{23.6}{8}=2.95.[/tex]The price of one duck is $2.95.
Need help on number 10 on this page. Use graph to answer this.
Answers
Answer:
[tex]22[/tex]Explanation:
Firstly,let us get the number of students that chose board games and puzzles
We can get this information from the picture graph
For puzzles, we have 5 red towers and that makes a total of 5 * 4 = 20 students
For board games, we have 6 towers and that makes a total of 6 * 4 = 24 students
The question says more students chose computer games than puzzles. This mean the number that chose it is greater than 20 students
But the number is lesser than board game of 24.
This means the number of students that chose computer games is between 20 and 24
The number between this two is 22
It is greater than puzzle number (20) but less than board game (24)
twice the sum of -2 and a number is the same as the number decreased by 7/8 find the number
Answers
We will have that the expression is:
[tex]2(n-2)=n-\frac{7}{8}[/tex]Now, we operate:
[tex]\Rightarrow2n-4=n-\frac{7}{8}\Rightarrow n=-\frac{7}{8}+4[/tex][tex]\Rightarrow n=\frac{25}{8}\Rightarrow n=3.125[/tex]So, the number is 3.125.
***Explanation***
We are told that twice the sum of -2 and a number equals something, now, the sum of a number [That we are going to call "n"] and -2 is the following:
[tex]n-2[/tex][Remember that when we add a number and a negative number we will write the negative value in the sum, subtraction is the sum of a negative number]. Now, we are told that is twice that number, so it is then:
[tex]2(n-2)[/tex]We are also told that that expression is equal to the number "n" decrease by 7/8, that is:
[tex]n-\frac{7}{8}[/tex]Finally, we equal both expressions and obtain the value that is described in the text:
[tex]2(n-2)=n-\frac{7}{8}[/tex]And to determine the value of "n" we simply operate like terms and leave "n" alone on one side.
i need help to solve a one step equation:-21 = k - 8
Answers
1. You add 8 in both sides of the equation:
[tex]-21+8=k-8+8[/tex]You get:
[tex]-21+8=k[/tex][tex]-13=k[/tex]Give the following numbers correct to the number of significant figures indicated in the brackets:(a) 478.831 06 (4 s.f.)(b) 58.073 02 (3 s.f.) (c) 0.000 068 2 (2 s.f.) (d) 0.048 851 (1 s.f.)
Answers
Solution
For this case we can do the following:
(a) 478.831 06 (4 s.f.)
478.8311
(b) 58.073 02 (3 s.f.)
58.073
(c) 0.000 068 2 (2 s.f.)
0.00
(d) 0.048 851 (1 s.f.)
0.01
If the scale factor of a dilation 1/3, what is the length of line segment E'F'?
Answers
Let's find the length of EF:
[tex]\begin{gathered} |EF|=\sqrt[]{(15-6)^2+(3-3)^2} \\ |EF|=9 \end{gathered}[/tex]In order to find E'F', multiply EF by the scale factor, so:
[tex]\begin{gathered} |E^{\prime}F^{\prime}|=\frac{1}{3}|EF| \\ |E^{\prime}F^{\prime}|=\frac{1}{3}\cdot9 \\ |E^{\prime}F^{\prime}|=3 \end{gathered}[/tex]Answer:
3
A drawbridge will sometimes open up to let boats and other water traffic pass through. As it opens, the surface of the drawbridge raises above the level of the roadway, as modeled by the function: If the length of the drawbridge, r, is 20 meters, and the point P is 16 meters above the roadway, what is the distance d? A.19.6 metersB.25 metersC.12 metersD.36.6 meters
Answers
Given that
The relation between r, h, and d is given as
[tex]r=\sqrt{h^2+d^2}[/tex]Also, r = 20m and h = 16m
Explanation -
We have to find the value of d and by substituting the values we have
[tex]\begin{gathered} 20=\sqrt{16^2+d^2} \\ On\text{ squaring both sides we have} \\ 20^2=16^2+d^2 \\ 400-256=d^2 \\ d^2=144 \\ d=\sqrt{144} \\ d=12\text{ meters} \end{gathered}[/tex]So the correct option is C.
And the final answer is 12 meters.The graph below shows triangle L’M’N’ , after a 90 counterclockwise rotation about the origin. What were the coordinates of pre-image point L ? A. (-8,5) B. (-5,8) C. (5,-8) D. (8,-5)
Answers
First we have to identify the coordinates of L' which are ( -8,-5) then we are rotate our point 90 degrees clockwise. Doing that we obtain the original coordinates. (-5,8). So, the answer would be B.
Solve for B A =1/2 b*h
Answers
Given that A = 1/2 b*h
A = b*h/2
Cross multiply
2A = b*h
Divide both sides by h
2A/h = b*h/h
2A/h = b
b = 2A/h
Which fraction and decimal forms match the long division problem? 9) 4.000 361 40 36 40 36 4 O A. 9 and 0.444 4 OB. and 0.4 O C. 9 4 and 0.4 OD. and 0.4
Answers
In the given division, you have that number 9 left side is the denominator of the corresponding fraction and numerator is number 4.000 right side.
Then, the associated fraction to the given division is 4/9 (because zeros right side decimal point of 4.000 are not significant digits).
The decimal number of the fraction 4/9, as it can be noticed in the division is 0.444...
Hence, 4/9 and 0.4 match with the given division
Given the toolkit function f(x) = 2x, find the equation of the transformation g(x) after a shift to the right 2 and a reflection across the y-axis.Group of answer choicesg(x) = 2-x - 2g(x) = 2-(x -2)g(x) = 2-x - 2g(x) = -2x - 2
Answers
1) Given that the g(x) function is the result of transforming f(x) by shifting to the right 2 units and reflecting across the y-axis, we can tell that:
2) So, let's shift to the right 2 units:
g(x)=f(x-2)
[tex]g(x)=f(x)=2(x-2)=2x-2[/tex]
3) Now, let's reflect it across the y-axis. To do that let's multiply by -1
[tex]g(x)=-2x-2[/tex]Which parabola has the graph shown? 5 O A. (1-2) = (1-1) O B. (1 - 1) = (x - 2)² O c. (x-1)=- (v - 2)² OD. O d. (x+1) = (-2)
Answers
Answer:
Choice D: ( x + 1) = ( y - 2) ^2
Explanation:
The parabola given is left to right, meaning it curves towards the right.
Therefore, its equation must look like:
[tex](x+c)=(y+a)^2[/tex]For a second, we notice that the point ( - 1, 2) is the vertex of the parabola. This means that the parabola is shifted 1 unit to the left and 2 units upwards. Therefore, The equation of the parabola must be:
[tex](x+1)=(y-2)^2[/tex]Hence, choice D is the correct answer.
-3/10+7/3=I have to simplify these( I'm awful with fractions, I have a whole packet but these are my most confused ones)3/3 - 5/4=- 5/9 - 1/9=3/6-5/6=5/8 - 7/8
Answers
1 Drag the tiles to the correct boxes. Not all tiles will be used. Consider the exponential functions f g and h, defined as shown. function f function g function h YA h X g(x) -1 1 0 4 fx) = -2(3)X + 6 -2 11 16 2 اسم 2. 64 -2. 3 256 Determine which function or functions have each key feature.
Answers
We have three functions and we have to identify some properties.
1) x-intercept at (1,0).
This means that when y=0, x is 1.
We start by testing this with f(x):
[tex]\begin{gathered} f(x)=0=-2(3)^x+6 \\ -6=-2\cdot3^x \\ \frac{-6}{-2}=3^x \\ 3=3^x \\ \ln (3)=x\cdot\ln (3) \\ 1=x \\ x=1 \end{gathered}[/tex]The function f(x) has the x-intercept at (1,0).
The table for g(x) shows us that when x=1, y=16 so it does not have a x-intercept at (1,0).
In th graph for h(x), we can see that the line intercepts the x-axis at point x=1, so the function has a x-intercept at (1,0)
Answer: f(x) and h(x)
2) Approaches an integer as x approaches minus infinity.
We can calculate this limit for f(x):
[tex]\lim _{x\to-\infty}-2(3^x)+6=0+6=6[/tex]The funtion f(x) approaches an integer when x approaches minus infinity.
For g(x), we estimate that there is a common ratio of 4, so when x approaches minus infinity, the function approaches 0. then, g(x) also approaches an integer as x approaches minus infinity.
In the graph of h(x) can also be estimated that there is an horizontal assymptote when x approaches minus infinity, so h(x) also satisfies this condition.
Answer: all three functions.
3) Increasing on all intervals of x.
f(x) and h(x) decrease when x increases, so they don't satisfy this condition.
The function g(x) increases when x increases for all values of x, so it satisfies this condition.
Answer: g(x)
4) y-intercept at (0,4)
This can be calculated as the values of the functions when x=0.
For f(x) we have:
[tex]f(0)=-2(3^0)+6=-2\cdot1+6=-2+6=4[/tex]f(x) has the y-intercept at (0,4).
In the table, we can see that g(0)=4, so it also satisfies this condition.
The function h(x) intercepts the y-axis at (0,3) so it does not satisfy this condition.
Answer: f(x) and g(x)
One says she doesn't feel well, she wants a soft drink and volunteers the remaining money to the others. How much do the other four sisters have to spend? Each sister has 10 dollars
Answers
Answer:
$12.11
Explanation:
From the menu:
• The cost of a Sprite = $1.55
Since she initially has $10 and volunteers the remaining money to the others:
[tex]10-1.55=\$8.45[/tex]Thus, the amount the other four sisters has in total will be:
[tex]4(10)+8.45=48.45[/tex]An inequality for the scenario will be:
[tex]4x\le48.45[/tex]We solve for x:
[tex]\begin{gathered} x\le\frac{48.45}{4} \\ x\le\$12.11 \end{gathered}[/tex]Each of the other four sisters has at most $12.11 to spend.
write 7/9 as a decimal use a bar to repeating decimals
Answers
Explanation:
The result of 7/9 using a calculator = 0.777777.....
This shows 7/9 is a repeating decimal
Using a bar to represent the repeating decimals above:
[tex]\frac{7}{9}=0.\bar{7}[/tex]Communication: Explain how knowledge of expanding is useful whenfactoring.
Answers
Explanation:
The knowledge of expanding is useful when factoring as it enables us check by doing the reverse of factorization. When a term has some common factors, we begin by noting the common factor(s) and then distribute the factor with the terms inside the parenthesis.
The factored form of a quadratic for example is useful for finding the roots and other properties but sometimes it is useful to expand in order to simplify the equation.
For example,
Expanding from factored form uses the distributive property of real numbers which states for real numbers x and y,
c (a + b) = ac + bc.
Another example will be:
[tex]\begin{gathered} (x-a)(x+b) \\ Distributing \\ x(x+b)-a(x+b) \\ x^2+bx-ax-ab \end{gathered}[/tex]What is the domain of the square root function graphed below? a)x>= -4b) x>-4c)x>=0d)x>0
Answers
Solution:
Given the graph of the function:
[tex]f(x)=\sqrt{x+4}[/tex]to be:
The domain of a function is the set of input values or arguments for which the function is real and defined.
Thus, the domain of the function is
[tex]x\ge-4[/tex]Answer:
Step-by-step explanation:
Use algebra to solve your equation. Show your work. Then check your answer in the Gizmo.
Answers
ANSWER
h = 10 hours
EXPLANATION
D) We have that the equation that describes the situation is given as:
2h = 3h - 10
We need to solve for h, the number of hours that Chris spent working.
Do that by collecting like terms:
=> 2h - 3h = -10
-h = -10
Divide both sides by -1:
=> h = -10/ - 1
h = 10 hours
Therefore, Chris worked for 10 hours.
The American Ballet Theatre opened at 5:30 p.m. In the 1st hour, 225 people purchased admission tickets. In the 2nd hour, 30% more people purchased admission tickets than in the 1st hour. Each ticket costs $22.25. What is the total amount of money that the ballet made from ticket sales after the first 2 hours?
Answers
Percentage is expressed in terms of 100
We were told that in the 1st hour, 225 people purchased admission tickets and in the 2nd hour, 30% more people purchased admission tickets than in the 1st hour. This means that the number of extra tickets purchased in the 2nd hour is
30/100 * 225 = 67.5
Thus, the number of people that purchased tickets in the 2nd hour is
225 + 67.5 = 292.5
Since the number of people must be whole number, it is appoximately 293 people. Thus, the total number of ticket sales after the first two hours is
225 + 293 = 518
If each ticket costs $22.25, then the total amount of money that the ballet made from ticket sales after the first 2 hours is
518 * 22.25 = $11525.5
When condensing logarithms with the same base that are being added, what do you do with the arguments? Forexample log3(2)+ log;(5) + log3(x)
Answers
The logarithm has the same base . If we are ask to add logarithm with the same base we just have to multiply the log values. If we are ask to subtract logarithm with same base we have to divide the logarithm values. For example
[tex]undefined[/tex]How to do powers of 10
Answers
Answer:
Explanation:
Here, we want to know how to work out the powers of 10
What is different amongst each is the number of zeros after the initial 1
Now, to get this, let us look at some examples
[tex]\begin{gathered} 10^{1\text{ }}=\text{ 10} \\ 10^2\text{ = 100} \\ 10^3\text{ = 1000} \\ 10^4\text{ = 10000} \\ 10^5\text{ =100000} \\ 10^6\text{ = 1000000} \\ 10^7\text{ = 10000000} \end{gathered}[/tex]We can see that the number of zeros after the inital 1 for each is the power to which it is raised
an 8 pack of marbles cost $1.12. What is the cost per orange?
Answers
Since we want to know the cost of one orange,we have to divide 1.12 by 8 to get the following:
[tex]\frac{1.12}{8}=0.14[/tex]therefore, the cost per orange is $0.14
Using the Product Rule, use the Product Rule to find the derivative of the function.
Answers
Given the following function:
[tex]g(x)=\sqrt{x}*sin\text{ }x[/tex]We will use the Product Rule to find the derivative of the function.
The product rule is as follows:
[tex]\begin{gathered} g(x)=m*n \\ g^{\prime}(x)=m^{\prime}*n+m*n^{\prime} \end{gathered}[/tex]For the given function:
[tex]\begin{gathered} m=\sqrt{x}\rightarrow m^{\prime}=\frac{1}{2\sqrt{x}} \\ \\ n=sin\text{ }x\rightarrow n^{\prime}=cos\text{ }x \end{gathered}[/tex]So, the derivative of the function will be as follows:
So, the answer will be
[tex]g^{\prime}(x)=\frac{sin\text{ }x}{2\sqrt{x}}+\sqrt{x}\text{ }cos\text{ }x[/tex]In 2012-2013 NBA season (82 games) Kevin Durant made 90.5% of his free throw attempts. He attempts a total of 792 free throws.How many did he make?
Answers
Answer:
717
Explanation:
If Kevin Durant made 90.5% of his free throw attempts and he attempted a total of 792 free throws, let's go ahead and find how many free throws he made;
[tex]\frac{90.5}{100}\times792=0.905\times792=716.76\approx717[/tex]