Use the number line below, where RS = 6y + 2, ST = 3y + 7, and RT = 14y - 11.
a. What is the value of y?
b. Find RS, ST, and RT.

Answers

Answer 1

Answer:

a) y = 4

b) RS = 26, ST = 19, RT = 45

Step-by-step explanation:

From the line given, the following vector equation is true, RS + ST = RT since R, S and T lies in the same straight line.

Given RS = 6y + 2, ST = 3y + 7, and RT = 14y - 11

On substituting this values into the equation above we will have;

6y+2+(3y+7) = 14y-11

6y+2+3y+7 = 14y-11

Collect the like terms

6y+3y-14y = -11-7-2

9y-14y = -20

-5y = -20

y = 20/5

y = 4

Since RS = 6y + 2

RS = 6(4)+2

RS = 24+2

RS = 26

ST = 3y + 7

ST = 3(4)+7

ST = 12+7

ST = 19

Also, RT = 14y - 11

RT = 14(4)-11

RT = 56-11

RT = 45


Related Questions

#1: Simplify the expression below. Type your answer as an integer.
7 + 1 - 18 : 6

Answers

Answer:

5

Step-by-step explanation:

Steps of calculation:

7 + 1 - 18 : 6 = 7 + 1 - 3 = 8 - 3 =5

Answer is 5

Evaluate C 3y − esin(x) dx + 7x + y4 + 1 dy, where C is the circle x2 + y2 = 16. SOLUTION The region D bounded by C is the disk x2 + y2 ≤ 16, so let's change to polar coordinates after applying Green's Theorem: C 3y − esin(x) dx + 7x + y4 + 1 dy

Answers

By Green's theorem,

[tex]\displaystyle\int_{x^2+y^2=16}(3y-e^{\sin x})\,\mathrm dx+(7x+y^4+1)\,\mathrm dy[/tex]

[tex]=\displaystyle\iint_{x^2+y^2\le16}\frac{\partial(7x+y^4+1)}{\partial x}-\frac{\partial(3y-e^{\sin x})}{\partial y}\,\mathrm dx\,\mathrm dy[/tex]

[tex]=\displaystyle4\iint_{x^2+y^2\le16}\mathrm dx\,\mathrm dy[/tex]

The remaining integral is just the area of the circle; its radius is 4, so it has an area of 16π, and the value of the integral is 64π.

We'll verify this by actually computing the integral. Convert to polar coordinates, setting

[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dx\,\mathrm dy=r\,\mathrm dr\,\mathrm d\theta[/tex]

The interior of the circle is the set

[tex]\{(r,\theta)\mid0\le r\le4\land0\le\theta\le2\pi\}[/tex]

So we have

[tex]\displaystyle4\iint_{x^2+y^2\le16}\mathrm dx\,\mathrm dy=4\int_0^{2\pi}\int_0^4r\,\mathrm dr\,\mathrm d\theta=8\pi\int_0^4r\,\mathrm dr=64\pi[/tex]

as expected.

State whether the data described below are discrete or​ continuous, and explain why.

The widths (in centimeters) of different paintings in an art museum

nothing

Choose the correct answer below.

A. The data are continuous because the data can only take on specific values.

B. The data are discrete because the data can only take on specific values.

C. The data are discrete because the data can take on any value in an interval.

D. The data are continuous because the data can take on any value in an interval.

Answers

D) The data are continuous because the data can take on any value in an interval

32 to 34 Directions: Given the following set of
numbers find the mean, median, and mode.
12, 13, 15, 15, 16, 19, 19, 19, 20, 21, 25
39.
32. Mean =
a. 17.64
b. 19
c. 15
40. 1
33. Median
a. 17.64
b. 19
c. 15

Answers

Answer:

32. A

33. B

Step-by-step explanation:

32. Mean: In order to find the mean, add all of the #up which is 194 then divide by how many # there is

33. Start by crossing out the beginning # and the end # all the way till you get the # without another pair in the end

Which formula used in probability to find Independence question

Answers

Answer:

Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together.

Answer:

Events are independent if the outcome of one effect does not effect the outcome

Step-by-step explanation:

Choose the best answer
Question
Cube A has volume V The edges of cube Bare 3 times as long as the edges of cube A. What is the
volume of cube B, in terms of V?
1.3V
2.9V
3.18V
4.27V

Answers

Answer:

4). 27V

Step-by-step explanation:

Let the edge of the cube A be x

Volume of Cube A= V

Volume= x*x*x= x³

so V = x³

Edge of cube B = 3 times edge of cube A

Edge of cube B = 3x

Volume of cube B =( 3x)³

volume of cube B = 27x³

But x³= V

So volume of cube B = 27v

Daniella accidentally left the drain partially open as she began filling the bathtub. The amount of water, in gallons, pouring into the tub after x minutes is given by the function f. f( x )=12x The amount of water, in gallons, draining from the tub after x minutes is given by the function g. g( x )=6x What is the equation of a function k that gives the amount of water in the tub in this situation after x minutes?

Answers

Answer:

k(x) = 6x

Step-by-step explanation:

A function shows the relationship between two or more variables. It shows the relationship between an independent and a dependent variable.

Given that the amount of water being poured into the tube is given by f(x) = 12x, where x is in minutes and the amount of water draining out of the tub is given by the function g( x )=6x. The amount of water remaining in the tube after x minutes is gotten by finding the difference between the amount of water entering the tube and the amount leaving the tube after x minutes. If k is the function representing the amount of water in the tube after x minutes, it is given by:

k(x) = f(x) - g(x)

k(x) = 12x - 6x

k(x) = 6x

1. Solve the system of equations. y = –3x + 4 x + 4y = –6 A. x = –2,y = –1 B. x = –2,y = 10 C. x = 2,y = –2 D. x = 3,y = –5 E. x = 4,y = –8

Answers

Answer:

C. x = 2, y = -2

Step-by-step explanation:

y = -3x + 4

x + 4y = -6

x + 4(-3x + 4) = -6

x - 12x + 16 = -6

-11x = -22

x = 2

y = -3(2) + 4 = -2

The graph of the function f(x) = (x − 3)(x + 1) is shown.

On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1, negative 4), and goes through (3, 0).
Which describes all of the values for which the graph is positive and decreasing?

all real values of x where x < −1
all real values of x where x < 1
all real values of x where 1 < x < 3
all real values of x where x > 3

Answers

Answer:

  x < -1

Step-by-step explanation:

Since the parabola opens upward, it is positive and decreasing where the left branch is above the x-axis: all points to the left of x=-1.

  all real values of x where x < -1

Fertilizing bromeliads. Bromeliads are tropical flowering plants. Many are epiphytes that attach to trees and obtain moisture and nutrients from air and rain. Their leaf bases form cups that collect water and are home to the larvae of many insects. As a preliminary to a study of changes in the nutrient cycle, Jacqueline Ngai and Diane Srivastava examined the effects of adding nitrogen, phosphorus, or both to the cups. They randomly assigned 8 bromeliads growing in Costa Rica to each of 4 treatment groups, including an unfertilized control group. A monkey destroyed one of the plants in the control group, leaving 7 bromeliads in that group. Here are the numbers of new leaves on each plant over the seven months following fertilization:
Nitrogen Phosphorus Both Neither
15 15 14 14
14 17 18 19
18 13 14 11
16 13 15 16
14 14 15 13
11 17 14 15
13 12 15 15
(a) Give the degrees of freedom for the F statistic. numerator degrees of freedom denominator degrees of freedom
(b) Find the F-statistic. (Round your answer to two decimal places.)
(c) Find the associated P-value. (Round your answer to four decimal places.)

Answers

Answer:

Calculated value of F = 0.0535

The critical region is F >F ₀.₀₅ (6,21) = 2.575

Reject H0

Step-by-step explanation:

1. Null hypothesis

H0: µ Nitrogen = µ Phosphorus = µ Both = µ Neither

2. Alternative hypothesis

H1: Not all means are equal.

3. The degrees of freedom for the numerator of the F-ratio = k- 1= 7-1=6

4.The degrees of freedom for the denominator of the F-ratio = n-k= 28-7

= 21

5. The significance level is set at α-0.05

The critical region is F >F ₀.₀₅ (6,21) = 2.575

The test statistic to use is

F = sb²/ sw²

Which if H0 is true has an F distribution with v₁=k-1 and v₂= n-k degrees of freedom

Correction Factor = CF = Tj²/n = (410)²/28= 6003.57

Total SS ∑∑X²- C. F = 6108- 6003.57= 104.43

Between SS ∑T²j/r - C.F = 42036/ 7 - 6003.57 =  1.57286

Within SS = Total SS - Between SS= 104.43- 1.573= 102.86

The Analysis of Variance Table is

Source Of                 Sum of          Mean              Computed

Variation          d.f     Squares       Squares               F

Between

Samples          6         1.57286       0.2621               0.0535

Within

Samples         21       102.86           4.898

Calculated value of F = 0.0535

Pvalue = 2.575

Since it is smaller than 5 % reject H0.

How to simplify this expression??

Answers

Answer :

1

Step-by-step-explanation :

[tex] {x}^{2} + 4x + 5 - {(x + 2)}^{2} \\ {x}^{2} + 4x + 5 - ( {x}^{2} + 4x + 4) \\ [/tex]

[tex]{x}^{2} + 4x + 5 - {x}^{2} - 4x - 4 = {x}^{2} - {x}^{2} + 4x - 4x + 5 - 4 = 5 - 4 = 1[/tex]

Answer:

(x+1)  •  (x-5)

Step-by-step explanation:

The first term is,  x2  its coefficient is  1 .

The middle term is,  -4x  its coefficient is  -4 .

The last term, "the constant", is  -5  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -5 = -5  

Step-2 : Find two factors of  -5  whose sum equals the coefficient of the middle term, which is   -4 .

     -5    +    1    =    -4    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  1  

                    x2 - 5x + 1x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-5)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-5)

Step-5 : Add up the four terms of step 4 :

                   (x+1)  •  (x-5)

this person made an error. what is it, and what is the right answer?

Answers

Answer:

Base area (B) should not be added.

Step-by-step explanation:

Base area should not be added as cone is not solid. Only Lateral surface area is sufficient in order to find the required paper.

What does the tape measure say Measurement # 4 is?

Answers

Answer:

It looks like 6 and one eighth of an inch.

What is the value of x?

Answers

Answer:

  7

Step-by-step explanation:

The two angles created by the angle bisector are the same measure, so we have ...

  2x +y = 14 +y

  2x = 14 . . . . . . . subtract y

  x = 7 . . . . . . . . . divide by 2

Solve the system 2x + 3y = 3 and 3x − 2y = 11 by using graph paper or graphing technology. What is the solution to the system? (2 points) (−3, 3) (−1, −7) (1, −4) (3, −1)

Answers

Answer:

(3,-1)

Step-by-step explanation:

Graph boths functions (picture below)

PLEASE HELP ! (4/4) - 50 POINTS -

Answers

Answer:

The correct answer, again, is A; Z = -0.6

Answer:

im pretty sure its A; Z = -0.6 sorry if im wrong

Step-by-step explanation:

Find an equation of the tangent plane to the given surface at the specified point. z = ln(x − 8y), (9, 1, 0)

Answers

Answer:

x - 8y - z = 1

Step-by-step explanation:

Data provided according to the question is as follows

f(x,y) = z = ln(x - 8y)

Now the equation for the tangent plane to the surface

For z = f (x,y) at the point P [tex](x_0,y_0,z_0)[/tex] is

[tex]z - z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)\\[/tex]

Now the partial derivatives of f are

[tex]f_x(x,y) = \frac{1}{x-8y} \\\\f_y(x,y) = \frac{8}{x-8y} \\\\P(x_0,y_0,z_0) = (9,1,0)\\\\f_z(9,1,0) = (\frac{1}{x-8y})_^{(9,1,0)}[/tex]

[tex]\\\\=\frac{1}{9-8}[/tex]

= 1

Now

[tex]f_y(9,1,0)=(\frac{8}{x-8y})_{(9,1,0)}\\\\ = -\frac{8}{9 - 8}[/tex]

= -8

So, the tangent equation is

[tex]z - 0 = 1\times (x - 9) -8\times (y - 1)[/tex]

Now after solving this, the following equation arise

z = x - 9 - 8y + 8

z = x - 8y - 1

Therefore

x - 8y - z = 1

The equation of the tangent plane is [tex]x-8y-z=1[/tex]

Tangent Plane:

An equation of the tangent plane to the given surface at the point [tex]P(x_0,y_0,z_0)[/tex] is,

[tex]z-z_0=f_x(x_0,y_0)(x-x_0)+f_y(x_0,y_0)(y-y_0)[/tex]

The function is,

[tex]z = ln(x-8y)[/tex]

And the point is (9,1,0)

Now, calculating [tex]f_x,f_y[/tex]

[tex]f_x(x,y)=\frac{1}{x-8y}\\ f_y(x,y)=\frac{x-8}{x-8y}[/tex]

Now, substituting the given points into the above functions we get,

[tex]f_x(9,1)=\frac{1}{9-8(1)}=1\\ f_y(x,y)=\frac{-8}{9-8(1)}=-8[/tex]

So, the equation of the tangent plane is,

[tex]z-0=1(x-9)-8(y-1)\\z=x-8y-1\\x-8y-z=1[/tex]

Learn more about the topic tangent plane:

https://brainly.com/question/14850585

Let s1 = k and define sn+1 = √4sn − 1 for n ≥ 1. Determine for what values of k the sequence (sn) will be monotone increasing and for what values of k it will be monotone decreasing.

Answers

Answer:

The answer is "[tex]\bold{\frac{1}{4}<k\leq 2+\sqrt{3}}[/tex]"

Step-by-step explanation:

Given:

[tex]\ S_1 = k \\\\ S_{n+1} = \sqrt{4S_n -1}[/tex]   [tex]_{where} \ \ n \geq 1[/tex]

In the above-given value, [tex]S_n[/tex] is required for the monotone decreasing so, [tex]S_2 :[/tex]

[tex]\to \sqrt{4k-1} \leq \ k=S_1\\\\[/tex]

square the above value:

[tex]\to k^2-4k+1 \leq 0\\\\\to k \leq 2+\sqrt{3} \ \ \ \ \ and \ \ 4k+1 >0\\\\[/tex]

[tex]\bold{\boxed{\frac{1}{4}<k\leq 2+\sqrt{3}}}[/tex]

In 2014, the population of India1 was 1.236 billion people and increasing at a rate proportional to its population. If the population is measured in billions of people and time is measured in years, the constant of proportionality is 0.0125. Define P to be the population of India, in billions of people, in the year t, where t represents the number of years since 2014. (a) Write a differential equation to describe the relationship.\

Answers

Answer: i don’t kno I’m 6 years old

Step-by-step explanation:

Find
two consecutive numbers
odd numbers such that the
sum of the
greater number
and 5 times the smaller
number is 92. Please give detailed step by step answer​

Answers

Answer:

The two odd numbers are 15 and 17

Step-by-step explanation:

Given

Let the odd numbers be represented with x and y

Let x be the greater number

[tex]x + 5y = 92[/tex]

Required

Find x and y

Since x and y are consecutive odd numbers and x is greater, then

[tex]x = y + 2[/tex]

Substitute y + 2 for x in [tex]x + 5y = 92[/tex]

[tex]y + 2 + 5y = 92[/tex]

Collect Like Terms

[tex]y + 5y = 92 - 2[/tex]

[tex]6y = 90[/tex]

Divide both sides by 6

[tex]\frac{6y}{6} = \frac{90}{6}[/tex]

[tex]y = \frac{90}{6}[/tex]

[tex]y = 15[/tex]

Substitute 15 for y in [tex]x = y + 2[/tex]

[tex]x = 15 + 2[/tex]

[tex]x = 17[/tex]

Hence; the two odd numbers are 15 and 17

Answer:

Maths

Step-by-step explanation:

Answer:

The two odd numbers are 15 and 17

Step-by-step explanation:

Given

Let the odd numbers be represented with x and y

Let x be the greater number

Required

Find x and y

Since x and y are consecutive odd numbers and x is greater, then

Substitute y + 2 for x in  

Collect Like Terms

Divide both sides by 6

Substitute 15 for y in  

Hence; the two odd numbers are 15 and 17

x − 6 ≤ 3 solve for x please

Answers

Answer:

x  ≤ 9

Step-by-step explanation:

x − 6 ≤ 3

Add 6 to each side

x − 6+6 ≤ 3+6

x  ≤ 9

Answer:

x ≤ 9

I hope this helps!

Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 8 sin(xy), (0, 9)

Answers

Answer:

The maximum rate of change of f at (0, 9) is 72 and the direction of the vector is  [tex]\mathbf{\hat i}[/tex]

Step-by-step explanation:

Given that:

F(x,y) = 8 sin (xy) at (0,9)

The maximum rate of change f(x,y) occurs in the direction of gradient of f which can be estimated as follows;

[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (x,y) \hat i \ + \ \dfrac{\partial }{\partial y } (x,y) \hat j \end {bmatrix}[/tex]

[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (8 \ sin (xy) \hat i \ + \ \dfrac{\partial }{\partial y } (8 \ sin (xy) \hat j \end {bmatrix}[/tex]

[tex]\overline V f (x,y) = \begin {bmatrix} (8y \ cos (xy) \hat i \ + \ (8x \ cos (xy) \hat j \end {bmatrix}[/tex]

[tex]| \overline V f (0,9) |= \begin {vmatrix} 72 \hat i + 0 \end {vmatrix}[/tex]

[tex]\mathbf{| \overline V f (0,9) |= 72}[/tex]

We can conclude that the  maximum rate of change of f at (0, 9) is 72 and the direction of the vector is  [tex]\mathbf{\hat i}[/tex]

9. There are 50 pupils in a class. Out of this
number, 1/10 speak French only and 4/5 of the remainder speak both French and
English. If the rest speak English only,
i) find the number of students who speak​

Answers

Answer:

Step-by-step explanation:

50 : 10 = 5 speaks French only

50 -5= 45 the remainder

4/5 * 45= 36 speaks French and English

45 - 36= 9 speaks English only

The number of students who speak:

i) French only = 5 students,

ii) both French and English = 36 students,

iii) English only = 9 students.

Step 1: Find the number of students who speak French only.

Step 2: Find the remainder (students who speak both French and English) after subtracting the French-only speakers.

Step 3: Find the number of students who speak both French and English.

Step 4: Find the number of students who speak English only.

Let's calculate it step by step:

Step 1: Find the number of students who speak French only.

1/10 of 50 pupils speak French only:

French-only speakers = (1/10) * 50 = 5 students.

Step 2: Find the remainder (students who speak both French and English) after subtracting the French-only speakers.

Remaining students = Total students - French-only speakers

Remaining students = 50 - 5 = 45 students.

Step 3: Find the number of students who speak both French and English.

4/5 of the remaining students speak both French and English:

Both French and English speakers = (4/5) * 45 = 36 students.

Step 4: Find the number of students who speak English only.

To find the English-only speakers, subtract the total number of French-only speakers and both French and English speakers from the total number of students:

English-only speakers = Total students - (French-only speakers + Both French and English speakers)

English-only speakers = 50 - (5 + 36) = 50 - 41 = 9 students.

To know more about French:

https://brainly.com/question/34246494

#SPJ2

Complete question is:

There are 50 pupils in a class. Out of this number, 1/10 speak French only and 4/5 of the remainder speak both French and English. If the rest speak English only, find the number of students who speak​

i) French only,

ii) both French and English,

iii) English only,

Find the surface area of the triangular prism.

Answers

Answer:

169 [tex]cm^{2}[/tex]

Step-by-step explanation:

Surface area (SA) = 2B + PH

                       SA = 2 ([tex]\frac{1}{2}[/tex] x 9 x 6) + (7+7+9) 5

                             = 2 (27) + (23) 5

                             = 54 + 115

                        SA = 169 [tex]cm^{2}[/tex]

The Eastern and Western Major League Soccer conferences have a new Reserve Division that allows new players to develop their skills. Data for a randomly picked date showed the following annual goals for six different teams in each division.
Eastern Western
9 9
3 8
4 7
3 6
4 5
4 3
Does the data show there is a difference in the annual goals for the eastern and western divisions? Test the claim at the 0.05 significance level.
A) The null and alternative hypothesis would be:
1. H0: PE = Pw
H1: PE > PW
2. H0: PE - Pw
H1: PE Pw
3. H0: Ps Pw
H1: PE Pw
4. H0: ME MW
H1: MMW
5. H0: HEW
H1: TME > HW
6.H0: ME Hw
H1: EMW
B) Determine the test statistic.

Answers

Answer:

A)

2. H0: Pe = Pw

H1: Pe [tex]\neq[/tex] Pw

B) Test statistics 1.96

Step-by-step explanation:

Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. In the given scenario the test is to identify whether there is any difference in annual goals between western division and eastern division. The  null hypothesis will be the Goals of western are equal to eastern division and alternative hypothesis will be Goals of western are not equal to eastern division.

someone please help me

Answers

I’m pretty sure is 8.6 ML

A wheel on a race car has 21-inch diameter. To qualify for an upcoming race, cars must be able to travel a minimum of 130 miles per hour. The wheel on this car can turn at the rate of 36 revolutions per second. Determine the linear speed of a point on the rim of this wheel (nearest inch per second) and determine if this car with this wheel would qualify for the upcoming race. 5 To convert inches per second to miles per hour, multiply by 5/88.
A) The linear speed is 756 inches per second, so this car would not quality
B) The linear speed is 4750 inches per second, so this car would quality
C) The linear speed is 2375 inches per second, so this car would quality
D) The linear speed is 378 inches per second, so this car would not qualify.

Answers

Answer: B) The linear speed is 4750 inches per second, so this car would qualify.

Step-by-step explanation: To determine linear speed using revolutions per second, i.e., angular speed (ω):

v = ω.r

where r is radius.

As ω is in revolutions per second, transform into rad/s:

ω = 36 revolutions/s

1 revolution = 2π rad

ω = 36.2π rad/s

ω = 72π rad/s

Radius is 21 inches, which can be written as

r = 21 inches/rad

Linear speed is

v = [tex]\frac{72.\pi rad}{s} .\frac{21 in}{rad}[/tex]

v ≈ 4750 inches per seconds

Converting to miles per hour:

v = [tex]4750.\frac{5}{88}[/tex]

v = 270mph

At linear speed of 4750 inches per second, a car with wheel of radius 21-inch can qualify.

Answer:

Above is correct

Step-by-step explanation:

Marine ecologists estimate the reproduction curve for swordfish in a fishing ground to be f(p) = −0.01p2 + 9p, where p and f(p) are in hundreds. Find the population that gives the maximum sustainable yield, and the size of the yield.

Answers

Answer:

The population that gives the maximum sustainable yield is 45000 swordfishes.

The maximum sustainable yield is 202500 swordfishes.

Step-by-step explanation:

Let be [tex]f(p) = -0.01\cdot p^{2}+9\cdot p[/tex], the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)

First Derivative Test

[tex]f'(p) = -0.02\cdot p +9[/tex]

Let equalize the resulting expression to zero and solve afterwards:

[tex]-0.02\cdot p + 9 = 0[/tex]

[tex]p = 450[/tex]

Second Derivative Test

[tex]f''(p) = -0.02[/tex]

This means that result on previous part leads to an absolute maximum.

The population that gives the maximum sustainable yield is 45000 swordfishes.

The maximum sustainable yield is:

[tex]f(450) = -0.01\cdot (450)^{2}+9\cdot (450)[/tex]

[tex]f(450) =2025[/tex]

The maximum sustainable yield is 202500 swordfishes.

Please help helppp :((((

Answers

Answer:

m∠Q = 61°

m∠S = 61°

m∠R = 58°

Step-by-step explanation:

Since we have an isosceles triangle, we know that ∠Q and ∠S are congruent.

Step 1: Definition of isosceles triangle

2x + 41 = 3x + 31

41 = x + 31

x = 10

Step 2: Find m∠Q

m∠Q = 2(10) + 41

m∠Q = 20 + 41

m∠Q = 61°

Step 3: Find m∠S

Since m∠Q = m∠S,

m∠S = 61°

Step 4: Find m∠R (Definition of a triangle)

Sum of angles in a triangle adds up to 180°

m∠R = 180 - (61 + 61)

m∠R = 180 - 122

m∠R = 58°

how many feet are in 53 yards, 2 feet? enter only the number. Do not include units

Answers

There are 161 feet are in 53 yards, 2 feet.

What is unit conversion?

Unit conversion is the process of changing a quantity's measurement between various units, frequently using multiplicative conversion factors.

As we know that;

1 yard = 3 feet

53 yards = 3 ×53 feet

53 yards = 159 feet

53 yards, 2 feet = 159 feet + 2 feet

53 yards, 2 feet = 161 feet

Hence, there are 161 feet in 53 yards, 2 feet.

To learn more about the unit conversion, refer;

https://brainly.com/question/4736731

#SPJ2

Other Questions
6Select the correct answer.Which scientist is best known for presenting new observations on empiricism and inductive reasoning?A. Galileo GalileiB. Andreas VesaliusC. Francis BaconD. Robert BoyleE. Isaac Newton Write the equations, after translating the graph of y = |x+2|: one unit up, You have 9kg of oats and cup scales that gears of 50g and 200g. How in three weighings can you measure 2kg of the oats? A teacher took a group of 48 students to the movie theater. They have saved $353 in a fund for the students' tickets. How much money will they have left in the fund if the ticket for each student was $7 Question 1 (5 points)The line segment AB with endpoints A(-3, 6) and B(9, 12) is dilated with a scalefactor 2/3 about the origin. Find the endpoints of the dilated line segment.OA) (-2, 4), (6,8)B) (2, 4). (6,8)OC) (4, -2), (6,8)OD) (-2,4), (8,6) 15. Food chain always start witha. PhotosynthesisDecayb. Respirationd. N2 FixationC.Photosynthesis So how can you, as a citizen, make your community andcountry a better place? Don't wait until you are 18 andcan vote.Read the passage, and think about how the writerexpresses his ideas and attitude to motivate a younaudience.Which words help you understand what the author :encouraging kids to do?How would you describe the tone?If you and your friends put your heads together, you'llfind lots of ways to practice citizenship every day.Whenyoucollect canned goods for a food drive, you'rebeing a good citizen. If you attend a rally to protect theenvironment, you're being a citizen. Even speaking out ata city council or school board meeting is good citizenship.-Citizenship,Jason SkogWhy are the word choice and tone appropriate for thiaudience?chip definition-when the elements of a painting or drawing balance each other out. This could be the objects themselves, but it can also relate to colors and other compositional techniques. Read the following statements. The sum of the angle measures of a triangle is 180. Two angles of a triangle measure 40and60", so Juan concludes that the third angle measures 80. What do you notice about the how the conclusions were made fromthe statement above? Most cars have a coolant reservoir to catch radiator fluid that may overflow when the engine is hot. A radiator is made of copper and is filled to its 21.1 L capacity when at 12.2C. What volume of radiator fluid (in L) will overflow when the radiator and fluid reach a temperature of 95.0C, given that the fluid's volume coefficient of expansion is = 400 106/C? (Your answer will be a conservative estimate, as most car radiators have operating temperatures greater than 95.0C). This expression represents the average cost per game, in dollars, at a bowling alley, where n represents the number of games:3n+7/nWhat is the average cost per game if James bowls 4 games? PLEASE HELP!!!!!! URGENT!!!!!!!!! ALGEBRA! Hannah, Yu, and Becky went to buy groceries together. All three of them bought pasta, noodles, and split peas. Hannah bought 3 packs of pasta, 10 packs of noodles, and 2 packs of split peas. Yu bought 5 packs of pasta, 12 packs of noodles, and 1 pack of split peas. Becky bought 3 packs of pasta, 15 packs of noodles, and 2 packs of split peas. Hannah, Yu, and Becky spent $8.41, $9.42, and $9.66 respectively on these items. What are the costs of a pack of pasta, a pack of noodles, and a pack of split peas? A) Pasta: $0.69 per pack, Noodles: $0.25 per pack, Split peas: $0.99 per pack B) Pasta: $1.09 per pack, Noodles: $0.20 per pack, Split peas: $1.97 per pack C) Pasta: $0.99 per pack, Noodles: $0.25 per pack, Split peas: $1.47 per pack D) Pasta: $0.69 per pack, Noodles: $0.20 per pack, Split peas: $1.97 per pack The manager of Synergy Company's Stock Division projects the following for next year: Sales $195,000 Operating income 70,000 Operating assets 385,000 The manager can invest in an additional project that would require $50,000 investment in additional assets and would generate $9,000 of additional income. The company's minimum rate of return is 15%. What is the residual income for the Stock Division with the additional project Find n. A. 5 B. 53 C. 10 D. 103/3 What is the density of a 10 kg mass that occupies 5 liters? ( pls need help) A rectangular box with a square base contains 24 cubic feet. if the height of the box is 18 inches, how many feet are there in each side of the base? *PLEASE ANSWER, MAKE SURE YOU ANSWER CORRECTLY* What dimensions would you need to measure the volume of the following prism? QUESTION 4According to Jean-Paul Sartre, what do I realize when someone looks at me? What emotion does this give riseto? The owner of a leased property conveys possession of the property to the tenant providing them with uninterrupted us of the property without interference from the owner. This is known as Select a scene from any film with at least two characters in the scene, Re-tell the scene from each person's perspective.Please help!!!!!!!