Answer:
15 ÷ 17
Step-by-step explanation:
Since our hypotenuse side is 17 cm, our opposite side is 8 cm and our adjacent side is 15 cm. Since the acute angle is x degrees,
From trigonometric ratios, cosx° = adjacent/hypotenuse
= 15 cm/17 cm
= 15/17
= 15 ÷ 17
What is -a-2 if a = -5?
Answer:
3
Step-by-step explanation:
-(-5) -2
5 - 2
3
Answer:
-7
Step-by-step explanation:
-a - 2 = -5 + -2 (different sign- keep the first number same, change the sign to addition and the additive inverse of the second number) -5 + -2 = -7Hope this helps
Does the boxplot represent the information given in the histogram?
A) Yes
B) No, the boxplot should be skewed right
C) No, the median should be in the middle of the box
D) No, the left whisker should extend to zero
E) No, the right whisker should extend to 55
To determine whether the boxplot represents the information given in the histogram, we need to examine the characteristics of both the boxplot and the histogram.
The boxplot provides a visual representation of the distribution of a dataset, showing the minimum, first quartile, median, third quartile, and maximum values. It also displays any outliers that may be present. On the other hand, a histogram provides a graphical representation of the frequency or count of data values within specified intervals or bins.
Without specific information or visuals of the boxplot and histogram in question, it is not possible to directly compare them and determine their compatibility. Therefore, it is not possible to answer the question based on the information provided.
Learn more about boxplot from
https://brainly.com/question/14277132
#SPJ11
Suppose we have a ring R and ideals I and J of R. (a) Denote the set {a+b:a e I and b E J} by I + J. Show that I + J is an ideal of R. (b) Let IJ denote the set of of all sums of the form n Laibi i=1 where ai e I and bi E J and neNt. Show that I J is an ideal of R. (c) Show that I n J is an ideal of R. (d) Show that IJ CINJ (e) The ideals I and J of R are called coprime if there exist a eI and b E J such that a+b = 1. You should check that if in the PID,Z we have ideals I = (m) and J = (v) then the ideals I and J are coprime if and only if m and n are coprime, that is relatively prime. Let I and J be coprime ideals of R. Show that INJ CIJ and thus by the preceding problem I J = I UJ ?
I + J is an ideal of R because it satisfies closure under addition and absorption of elements from R.
To show that I + J is an ideal of R, we need to verify two conditions: closure under addition and absorption of elements from R.
1. Closure under addition:Let x, y ∈ I + J. This means that x = a + b and y = c + d, where a ∈ I, b ∈ J, c ∈ I, and d ∈ J. We have:
x + y = (a + b) + (c + d) = (a + c) + (b + d)
Since a + c ∈ I and b + d ∈ J (as I and J are ideals), (a + c) + (b + d) ∈ I + J. Therefore, I + J is closed under addition.
2. Absorption of elements from R:Let r ∈ R and x ∈ I + J. This means that x = a + b, where a ∈ I and b ∈ J. We have:
rx = r(a + b) = ra + rb
Since ra ∈ I (as I is an ideal) and rb ∈ J (as J is an ideal), ra + rb ∈ I + J. Therefore, I + J absorbs elements from R.
Hence, we have shown that I + J satisfies the conditions of being an ideal of R.
To know more about closure under addition refer here:
https://brainly.com/question/29798490#
#SPJ11
Calculate the distance between point B (3,-7) and point C (0,8) on the coordinate grid
Answer:
Distance= 15.3
Step-by-step explanation:
Describe the translation in each function as it relates to the graph of f(x) = x.
g(x)=x-5
Answer:
f(x) was translated to the left by 5 units to form g(x)
Step-by-step explanation:
Given the function f(x) = x to g(x)=x-5, if you look at the g(x) function, you will see that 5 was subtracted from the abscissa x that is;
g(x) = f(x) - 5
This shows' that the function f(x) was translated to the left by 5 units to form g(x). This described the required translation
What is the value of x?
Enter your answer in the box.
Answer:
the answer is 4
Step-by-step explanation:
the bar graph shows the approximate average rainfall for different cities in Texas compare the total inches of rainfall to the average annual rainfall in san Antonio ?
Answer:
I don't know
Step-by-step explanation:
I don't know
A car can go 35 1/2 miles in 1 1/2 miles gallons. How many gallons does a car need to go 639 miles?
Need work please!!
Answer: 27 gallons
Step-by-step explanation:
Since the car can go 35½ miles in 1½ miles gallons, we need to first calculate the number of miles that the car can go in 1 gallon. This will be:
= 35½ / 1½
= 71/2 / 3/2
= 71/2 × 2/3
= 23⅔ miles per gallon.
Therefore, the amount of gallons that the car need to go 639 miles will be:
= 639 / 23⅔
= 639 ÷ 71/3
= 639 × 3/71
= 27
The car will need 27 gallons.
How do you expand (4x+2)2
Answer:
=8x+4
Step-by-step explanation:
=2(4x+2)
a=2,b=4x,c=2
=2 x 4x + 2 x 2
Simplify- 2 x 4x + 2 x 2: 8x + 4
Can you please help me?
Answer:
-3, -4, -4, 0, 16, 64, 192.
Step-by-step explanation:
I don't know for sure if this is correct, but when i did it theses are the answers i got. You do y=8*2^x. Meaning you substitute the x for the x values such as -3, -2, and -1.
Also if you have one there's a setting you can go to on an actual calculator and type in this on a Y/X chart. I didn't use one this time because i don't have one, but thought you'd find that information useful.
which expression is not equvialet to 28ax
2(19-7) im pretty sure
a rectangular window dimensions areX by X +2 and window has a 3 inch frame all the way around the total area of the window and frame is 195 in
Answer:
Length of window = 9 inch
Width of window = 7 inch
Step-by-step explanation:
Given;
Area of window and frame = 195 inch²
Frame width = 3 inch
Length of window = x + 2
Width of window = x
Find:
Value of x
Computation:
Length of window and frame = x + 2 + 3 + 3
Length of window and frame = x + 8
Width of window and frame = x + 3 + 3
Width of window and frame = x + 6
Area of window and frame = (l)(b)
(x + 8)(x + 6) = 195
x² + 6x + 8x + (8)(6) = 195
x² + 14x + 48 = 195
x² + 14x - 147 = 0
x² + 21x - 7x - 147 = 0
x(x + 21) - 7(x + 21) = 0
So,
x + 21 = 0 and x - 7 = 0
So,
X = 7
Value of x = 7
Length of window = 9 inch
Width of window = 7 inch
Given the data 4, y, 9, 5, 2, 7. Find y if the mean is 5
Answer:
3
Step-by-step explanation:
(4+y+9+5+2+7)/6=5
(27+y)/6=5
Y=3
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
Function 1 has the greatest rate of change.
Step-by-step explanation:
The rate of change is also known as the slope.
Slope is rise over run: change in y over change in x.
Function 1's slope: 3 / 2
Function 2's slope: (0 - (-4)) / (5 - (-5)) = 4/10 = 2/5
3/2 > 2/5
Function 1 has the greatest rate of change.
Write the Recursive form and next of the following sequence
8,10,12,14,16...
Answer:
Step-by-step explanation:
The recursive form is a(n + 1) = a(n) + 2, with a(1) = 8.
The next term is a(6) = a(5) + 2, which heere is a(6) = 16 + 2 = 18
use spherical coordinates. evaluate ∭E (x² + y²) dv, where e lies between the spheres x² + y² + z² = 9 and x² + y² + z² = 16.
The value of ∭E (x² + y²) dv over the region E between the given spheres.
To evaluate the integral ∭E (x² + y²) dv using spherical coordinates, we first need to express the volume element dv in terms of spherical coordinates.
In spherical coordinates, the volume element is given by dv = r² sin(φ) dr dφ dθ, where r represents the radial distance, φ represents the polar angle, and θ represents the azimuthal angle.
Since we are integrating over the region E between the spheres x² + y² + z² = 9 and x² + y² + z² = 16, the limits of integration for r, φ, and θ will be as follows:
r: from the lower sphere to the upper sphere, which corresponds to r = 3 to r = 4
φ: from 0 to π (since we are considering the entire range of polar angle)
θ: from 0 to 2π (since we are considering the entire range of azimuthal angle)
Now, let's substitute these values and evaluate the integral:
∭E (x² + y²) dv = ∭E (r² sin(φ) cos²(θ) + r² sin(φ) sin²(θ)) dr dφ dθ
Integrating over θ from 0 to 2π, and integrating over φ from 0 to π, we have:
∭E (x² + y²) dv = ∫[0,2π] ∫[0,π] ∫[3,4] (r² sin(φ) cos²(θ) + r² sin(φ) sin²(θ)) dr dφ dθ
Now, we can evaluate the integral by performing the integration step by step, starting from the innermost integral.
After evaluating the integral, the final result will give us the value of ∭E (x² + y²) dv over the region E between the given spheres.
Learn more about spheres here
https://brainly.com/question/31242763
#SPJ11
Verify the following properties of the Fourier transform 1. (Fu)(E) = 27 (F-\u) (-) 2. (F(t,0)) (E) - (FU)(8 + a)
The properties of the Fourier transform stated in (1) and (2) are incorrect.
How to find that are the given properties of the Fourier transform (1) and (2) accurate?The properties of the Fourier transform stated in (1) and (2) are incorrect.
Let's examine each property:
(1) (Fu)(E) = 27 (F-\u) (-):
The expression on the left side, (Fu)(E), represents the Fourier transform of a function u evaluated at frequency E.
However, the expression on the right side, 27 (F-\u) (-), is not a valid representation of the Fourier transform.
The notation (F-\u) (-) is unclear and does not align with the standard conventions of the Fourier transform.
(2) (F(t,0))(E) - (FU)(8 + a):
Similarly, the expression on the left side, (F(t,0))(E), suggests the Fourier transform of a function F evaluated at time t and frequency E.
However, the subtraction of (FU)(8 + a) is not a well-defined operation in the context of the Fourier transform. The relationship between F(t,0) and FU is not clear, and the addition of 8 + a lacks proper justification.
Therefore, both properties (1) and (2) provided for the Fourier transform are inaccurate.
Learn more about Fourier transform
brainly.com/question/1542972
#SPJ11
What is the surface area of the right prism below?
A. 360 sq. units
B. 384 sq. units
C. 432 sq. units
D. 336 sq. units
The surface area of the right prism cone is,
⇒ 1960 units²
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A right prism shown in image.
Now, We get;
Base area of cone = 14 x 10
= 140
And, Height of cone = 6
And, Perimeter of the base = 2 (10 + 14)
= 280
Thus, WE know that;
The surface area of the right prism cone is,
⇒ 2B + hP
⇒ 2 × 140 + 6 × 280
⇒ 280 + 6 × 280
⇒ 280 + 1680
⇒ 1960 units²
Thus, The surface area of the right prism cone is,
⇒ 1960 units²
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ7
Find all entire functions f where f(0) = 7, f'(2) = 4, and |ƒ"(2)| ≤ π for all z € C.
All entire functions f where f(0) = 7, f'(2) = 4, and |ƒ"(2)| ≤ π for all z € C are given by f(z) = 2z + 7.
Given that f is an entire function, which means that it is holomorphic on the entire complex plane C. Let us write the Taylor series for f(z) centered at z = 0. Since f is an entire function, its Taylor series has an infinite radius of convergence. Thus, we can write:
f(z) = a0 + a1z + a2z² + · · ·
Differentiating both sides of the above equation with respect to z, we get:
f′(z) = a1 + 2a2z + · · ·
Given that f(0) = 7 and f'(2) = 4, we get the following equations:
a0 = 7
a1 + 4 = f′(2)
Subtracting the second equation from the first, we get:
a1 = −3
Differentiating both sides of the above equation with respect to z, we get:
f″(z) = 2a2 + · · ·
Using the inequality |ƒ"(2)| ≤ π, we get the following inequality:
|2a2| ≤ π
Thus, we get the inequality:
|a2| ≤ π/2
Therefore, the Taylor series for f(z) is given by:
f(z) = 7 − 3z + a2z² + · · ·
where |a2| ≤ π/2.
However, we can further simplify the expression by observing that f(z) = 2z + 7 is an entire function that satisfies the given conditions. Therefore, by the identity theorem for holomorphic functions, we conclude that f(z) = 2z + 7 is the unique entire function that satisfies the given conditions.
Know more about functions here:
https://brainly.com/question/31062578
#SPJ11
PLSSSSSS HELPPPPP PLS I NEED HELPPP PLSS
Let equal the price of one smoothie. Complete the equation.
(5 smoothies) (price of 1 1 Smoothie)+tip= $23
Answer:
5x+3=23
Step-by-step explanation:
Answer:
$4 per smoothie
Step-by-step explanation:
5x+4=23
let . explain how to find a set of one or more homogenous equations for which the corresponding solution set is w
The homogeneous equation corresponding to W = Span(2, 1, -3) is 0.
To discover a set of one or more homogeneous equations for which the corresponding answer set is W = Span(2, 1, -three), we will use the idea of linear independence.
The set of vectors v1, v2, ..., vn is linearly unbiased if the only strategy to the equation a1v1 + a2v2 + ... + anvn = 0 (wherein a1, a2, ..., an are scalars) is a1 = a2 = ... = an = 0.
Since W = Span(2, 1, -3), any vector in W may be represented as a linear aggregate of (2, 1, -three). Let's name this vector v.
Now, to find a homogeneous equation corresponding to W, we need to discover a vector u such that u • v = 0, in which • represents the dot product.
Let's bear in mind the vector u = (1, -1, 2). To check if u • v = 0, we compute the dot product:
(1)(2) + (-1)(1) + (2)(-3) = 2 - 1 - 6 = -5.
Since u • v = -five ≠ zero, the vector u = (1, -1, 2) is not orthogonal to v = (2, 1, -3).
To discover a vector that is orthogonal to v, we can take the go product of v with any other vector. Let's pick the vector u = (1, -2, 1).
Calculating the cross product u × v, we get:
(1)(-3) - (-2)(1), (-1)(-3) - (1)(2), (2)(1) - (1)(1) = -3 + 2, 3 - 2, 2 - 1 = -1, 1, 1.
So, the vector u = (-1, 1, 1) is orthogonal to v = (2, 1, -3).
Therefore, the homogeneous equation corresponding to W = Span(2, 1, -3) is:
(-1)x + y + z = 0.
Note that this equation represents an entire answer set, now not only an unmarried solution. Any scalar more than one of the vectors (-1, 1, 1) will satisfy the equation and belong to W.
To know more about homogeneous equations,
https://brainly.com/question/30331454
#SPJ4
The correct question is:
Students in an Introductory Statistics class at BYU-Idaho were studying prices of cold cereal at grocery stores in Rexburg. To get a sample of cold cereal prices, they went to Albertson's and rolled a die to decide which box from the left of the top shelf they would start on. They then recorded every 6th cereal after the first, moving from left to right down the shelves, recording the name, size, and price of each cereal in their sample. Is this study an experiment or an observational study, and why
Answer: Observational study
Step-by-step explanation:
The study illustrated in the question is an observational study. It is referred to as an observational study, because in this case, the price of the individual cereals us not being controlled by the students. They've no control over it.
If it was an experiment, there'll have been a control group and the students will have control over the price. Also, the sampling methods used here is a systematic random sampling.
Find 8.76 - 10.91. Write your answer as a decimal.
Answer:
-2.15
Step-by-step explanation:
Plug it into the calculator and it should give you the same answer.
Answer:
The answer is -2.15.
Step-by-step explanation:
Hope this helped Mark BRAINLIEST!!!
Please help me with the answer!!!
5x = 7x - 8
7x - 5x = 8
2x = 8
x = 8 ÷ 2
x = 4
Increasingly, developers are using tools that can quickly create screen mockups, referred to as element. A) Protoypes B) Wireframes C) Forms D) Reports
Increasingly, developers are using tools that can quickly create screen mockups, referred to as element Wireframes
Wireframes:Wireframes is a type of tool which is allow designers to quickly and effectively mock up an outline of a design as easily as possible. Designers easily drag the images and drop to placeholder images , header and content also.
There are three types of wireframes, which is very useful :
Low-fidelity wireframes.Mid-fidelity wireframes.High-fidelity wireframes.Wireframes generally is used for visual designer, developer, business analysts, user experience designers and information architecture and user research.
Learn more about Wireframes at:
https://brainly.com/question/16347344
#SPJ4
In a simultaneous inspection of 10 units, the probabilities of getting a defective unit and non-defective unit are equal.
(a) Find the probability of getting at least 7 non-defective units. [5] [BTL-4] [CO02]
(b) Find the probability of getting at most 6 defective units. [5] [BTL-4] [CO02]
The probability of getting at least 7 non-defective units is 0.1718 and the probability of getting at most 6 defective units is 0.8282.In a simultaneous inspection of 10 units, the probabilities of getting a defective unit and non-defective unit are equal.
(a) Probability of getting a defective unit = P(D)Probability of getting a non-defective unit = P(N)P(D)
= P(N) (equal probabilities)P(D)
= 1/2P(N)
= 1/2Total number of units inspected
= 10(a)
Find the probability of getting at least 7 non-defective units
P(X = x) = nCx * P^x * q^(n-x)
Where nCx is the binomial coefficient
P is the probability of successq is the probability of failuren is the total number of trialsx is the number of successes
(a) The probability of getting at least 7 non-defective units
= P(X ≥ 7)P(X ≥ 7)
= P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)P(X = x)
[tex]= nCx * P^x * q^{(n-x)}P(X = 7)[/tex]
= 10C7 * (1/2)^7 * (1/2)^3 = 0.1172P(X = 8)
= 10C8 * (1/2)^8 * (1/2)^2 = 0.0439P(X = 9)
= 10C9 * (1/2)^9 * (1/2)^1 = 0.0098P(X = 10)
= 10C10 * (1/2)^10 * (1/2)^0 = 0.00098P(X ≥ 7)
= 0.1172 + 0.0439 + 0.0098 + 0.00098
= 0.1718
(b) Find the probability of getting at most 6 defective units
P(X = x) = [tex]nCx * P^x * q^{(n-x)}[/tex]
Where nCx is the binomial coefficient P is the probability of success
q is the probability of failuren is the total number of trialsx is the number of successes
(b) The probability of getting at most 6 defective units
= P(X ≤ 6)P(X ≤ 6)
= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)P(X = x)
= [tex]nCx * P^x * q^{(n-x) }\times P(X = 0)[/tex]
= 10C0 * (1/2)^0 * (1/2)^10
= 0.00098P(X = 1)
= 10C1 * (1/2)^1 * (1/2)^9 = 0.0098P(X = 2) = 10C2 * (1/2)^2 * (1/2)^8 = 0.044P(X = 3)
= 10C3 * (1/2)^3 * (1/2)^7 = 0.1172P(X = 4)
= 10C4 * (1/2)^4 * (1/2)^6 = 0.2051P(X = 5)
= 10C5 * (1/2)^5 * (1/2)^5 = 0.2461P(X = 6)
= 10C6 * (1/2)^6 * (1/2)^4 = 0.2051P(X ≤ 6)
= 0.00098 + 0.0098 + 0.044 + 0.1172 + 0.2051 + 0.2461 + 0.2051
= 1- P(X ≥ 7) = 1 - 0.1718= 0.8282
The probability of getting at least 7 non-defective units is 0.1718 and the probability of getting at most 6 defective units is 0.8282.
To know more about inspection visit:
https://brainly.com/question/15581066
#SPJ11
a child who is 44.39 inches tall is one standaer deviation above the mean. what percent of children are between 41.25 aand 44.29 inches tall?
A child who is 44.39 inches tall is one standard deviation above the mean. Approximately 50.58% of children are between 41.25 and 44.29 inches tall.
To find the percentage of children between 41.25 and 44.29 inches tall, we need to calculate the area under the normal distribution curve within this range.
Given that the child's height of 44.39 inches is one standard deviation above the mean, we can infer that the mean height is 44.39 - 1 = 43.39 inches.
Next, we need to determine the standard deviation. Since the child's height of 44.39 inches is one standard deviation above the mean, we know that the difference between the mean and 41.25 inches is also one standard deviation.
Let's denote the standard deviation as σ. We have:
43.39 - 41.25 = σ
Simplifying the equation:
σ = 2.14
Now, we can calculate the percentage of children between 41.25 and 44.29 inches tall using the z-scores.
The z-score formula is given by:
z = (x - μ) / σ
For the lower bound, x = 41.25 inches:
z₁ = (41.25 - 43.39) / 2.14 = -0.997
For the upper bound, x = 44.29 inches:
z₂ = (44.29 - 43.39) / 2.14 = 0.421
We need to find the area under the normal distribution curve between z₁ and z₂. Using a standard normal distribution table or a calculator, we can find the corresponding probabilities.
Let P₁ be the probability associated with z₁, and P₂ be the probability associated with z₂. Then, the percentage of children between 41.25 and 44.29 inches tall is given by:
Percentage = (P₂ - P₁) * 100
Using the z-score table or a calculator, we find that P₁ ≈ 0.1587 and P₂ ≈ 0.6645.
Substituting these values into the formula:
Percentage = (0.6645 - 0.1587) * 100 ≈ 50.58%
Therefore, approximately 50.58% of children are between 41.25 and 44.29 inches tall.
To know more about standard deviation, refer here:
https://brainly.com/question/29115611
#SPJ4
Lily likes to collect records. Last year she had 10 records in her collection. Now she has 11 records,
What is the percent increase of her collection?
The percent increase of her collection is %.
Answer:7
Step-by-step explanation:
A retired couple supplement their income by making fruit pies, which they sell to a local grocery store. During the month of September, they produce apple and grape pies. The apple pies are sold for $4.50 to the grocer, and the grape pies are sold for $3.60. The couple is able to sell all of the pies they produce owing to their high quality. They use fresh ingredients. Flour and sugar are purchased once each month. For the month of September, they have 2,100 cups of sugar and 3,000 cups of flour. Each apple pie requires 1½ cups of sugar and 3 cups of flour, and each grape pie requires 2 cups of sugar and 3 cups of flour. a. Determine the number of grape and the number of apple pies that will maximize revenues if the couple working together can make an apple pie in 6 minutes and a grape pie in 3 minutes. They plan to work no more than 60 hours b. Determine the amounts of sugar, flour, and time that will be unused. (Leave no cells blank - be certain to enter "0" wherever required. Round your intermediate calculations and final answers to the nearest whole number.
By plugging in the values of x and y obtained from the linear programming solution, we can calculate the unused amounts of sugar, flour, and time.
To determine the number of grape and apple pies that will maximize revenues, we can use linear programming. Let's set up the problem:
Let x be the number of apple pies produced.
Let y be the number of grape pies produced.
Objective function:
Maximize Revenue = 4.50x + 3.60y
Constraints:
1.5x + 2y ≤ 2100 (sugar constraint)
3x + 3y ≤ 3000 (flour constraint)
6x + 3y ≤ 60*60 (time constraint, converting hours to minutes)
The problem can be solved using linear programming software or a graphing calculator. The optimal values for x and y will provide the number of apple and grape pies that maximize revenue.
Regarding part b, to determine the amounts of sugar, flour, and time that will be unused, we can compare the amount used with the amount available.
Unused Sugar = 2100 - (1.5x + 2y)
Unused Flour = 3000 - (3x + 3y)
Unused Time = (60*60) - (6x + 3y)
By plugging in the values of x and y obtained from the linear programming solution, we can calculate the unused amounts of sugar, flour, and time. Remember to round the final answers to the nearest whole number.
For more questions on values
https://brainly.com/question/843074
#SPJ8
2
(
3
r
+
4
)
−
3
(
r
+
1
)
=
11
Hey there!
ASSUMING
2(3r + 4) - 3 (r + 1) = 11
IF SO
2(3r + 4) - 3 (r + 1) = 11
2(3r + 4) - 3 (1r + 1) = 11
DISTRIBUTE
2(3r) + 2(4) - 3(1r) - 1(1) = 11
6r + 8 - 3r - 1 = 11
COMBINE the LIKE TERMS
(6r - 3r) + (8 - 3) = 11
6r - 3r + 8 - 3 = 11
3r + 5 = 11
SUBTRACT 5 to BOTH SIDES
3r + 5 - 5 = 11 - 5
SIMPLIFY!
3r = 11 - 5
3r = 6
DIVIDE 3 to BOTH SIDES
3r/3 = 6/3
SIMPLIFY!
r = 6/3
r = 2
Therefore, the answer should be: r = 2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)