Answers
The proposition can be proven by showing that the left and right cosets of H in G form a partition of G.
How to prove the proposition ?As H is a G subgroup, it comprises the identity element e within G. For any g element in G, the left coset gH comprises ge = g and the right coset Hg contains eg = g. Thus, there are non-empty left as well as right cosets.
G's each element belongs to both the left and the right cosets of H. Hence, all left (or right) cosets' union in G covers every G element. The left and right cosets of H in G build non-empty subsets that do not intersect with one another. Their union equals G; thus, they certainly construct a partition for G.
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Related Questions
A bacteria culture initially contains 2500 bacteria and doubles every half hour.
Find the size of the baterial population after 20 minutes.
Find the size of the baterial population after 4 hours.
Answers
Answer:
After half hour=30 min you have 2×2500=5000 bacteria so you can use this into your equation to write:
and:
Apply the natural logarithm ln to both sides and get:
so in units of
so your equation is now:
1] it t= 50 min substituting you get:
bacteria
2] if t= 8 h = 480 min you get:
bacteria
Step-by-step explanation:
I’m unsure where to plot the five points and shade in
Answers
The image is attached of the graph of the inequality y < 4x - 5.
What is the inequality equation?
An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
To graph the inequality y < 4x - 5 using the slope-intercept form, follow these steps:
Rewrite the inequality in slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.
y = 4x - 5
Plot the y-intercept on the y-axis.
The y-intercept is -5, so plot the point (0, -5).
Use the slope to find a second point on the line.
The slope is 4, so start at the y-intercept and move up 4 units and to the right 1 unit to find the point (1, -1).
Draw a dashed line through the two points.
Since the inequality is y < 4x - 5, use a dashed line to indicate that the line itself is not part of the solution.
Shade the region that satisfies the inequality.
To do this, pick a test point that is not on the line and plug its coordinates into the inequality. If the inequality is true for that point, shade the region that contains the test point. If the inequality is false for that point, shade the region that does not contain the test point.
Let's use the test point (0, 0). Plug its coordinates into the inequality to get:
0 < 4(0) - 5
This simplifies to 5 < 0, which is false. Therefore, we need to shade the region that does not contain the test point.
Since the inequality is y < 4x - 5, we need to shade the region below the dashed line.
Label the shaded region with the inequality symbol.
The inequality is y < 4x - 5, so label the shaded region below the dashed line with the symbol "<".
hence, The image is attached of the graph of the inequality y < 4x - 5.
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$900 is deposited in an account with 4%
interest rate, compounded continuously.
What is the balance after 10 years?
F = $[?]
Answers
Answer:
[tex]\$1342.64[/tex]
Step-by-step explanation:
We can represent the value [tex]A[/tex] of a quantity [tex]P[/tex] compounded continuously for [tex]t[/tex] years at [tex]r[/tex] rate of interest as:
[tex]A = P\cdot e^{rt}[/tex]
This formula uses the mathematical constant [tex]e[/tex] (approx. 2.72), which is the theoretical limit for continuous compounding.
Plugging the given values into the formula:
[tex]A = \$900 \cdot e^{(0.04 \, \cdot \, 10)}[/tex]
We can now solve for [tex]A[/tex].
↓ simplifying [tex]e[/tex]'s exponent
[tex]A = \$900 \cdot e^{0.4}[/tex]
↓ plugging into a calculator
[tex]A \approx \$1342.64222788[/tex]
↓ rounding to the nearest cent
[tex]\boxed{A \approx \$1342.64}[/tex]
4. Find the product
()
Answers
Answer: n^6-25
Step-by-step explanation:
Use the distributive property to obtain: n^6-5n^3+5n^3-25
Simplify: n^6-25
Answer: n^6-25
The product of the given expression [tex](n^{3} + 5) (n^{3} - 5)[/tex] will be the second option [tex]n^{6} - 25[/tex].
This is a simple math problem that can be solved using algebraic identities. Algebraic identities are mathematical formulas that hold true regardless of the value assigned to each of the variables. They can be used to resolve equations and simplify expressions.
In the above question, we have used the following identity:
[tex](a^{2} - b^{2} ) = (a + b) (a - b)[/tex]
In the given question, a = [tex]n^{3}[/tex] and b = 5
So putting values in the identity, we get
[tex][(n^{3})^{2} - 5^{2}] = (n^{3} + 5) (n^{3} - 5)[/tex]
On solving the left side of the equation, we get
[tex]n^{6} - 25[/tex] which is our answer to the given question.
Note: [tex](n^3)^2 = n^6[/tex] because the powers get multiplied.
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Calculating Loan Payments You want to buy a new sports coupe for $69,300, and the finance office at the dealership has quoted you a loan with an APR of 5.6 percent for 48 months to buy the car. What will your monthly payments be? What is the effective annual rate on this loan?
Input area:
Amount borrowed $69,300
APR 5.6%
# of years 4
# of times compounded per year 12
(Output area) Complete the following analysis. Do not hard code values in your calculations. All answers should be positive.
Loan Payment __________
Effective Intrest Rate ____________
Answers
The monthly payments will thus be $1,612.81.
The annual effective rate on this loan is 5.78%.
What is the loan payment formulae?We can use the following loan payment formula to determine the loan payment:
Loan Payment = [tex]\\\frac{p * \frac{r}{n} }{1 - (1 + \frac{r}{n} )^{-n *t} }[/tex]
where P = borrowed amount = $69,300
r = yearly interest rate (decimal) = 0.056
n = number of times compounded per year = 12
t = number of years = 4
When we plug in the values, we get:
Loan Payment = [69300 x (0.056/12)] / [1 - (1 + 0.056/12)^(-12*4)]
= $1,612.81 (to the nearest cent)
The monthly payments will thus be $1,612.81.
We can use the following calculation to obtain the effective annual rate:
Annual Effective Rate =[tex](1 + r/n)^{n-1}[/tex]
When we plug in the values, we get:
Annual Effective Rate =[tex](1 + 0.056/12)^{12 - 1}[/tex]= 0.0578 or 5.78%
As a result, the annual effective rate on this loan is 5.78%.
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math complementary angles
Answers
Answer: ∠BDA
Step-by-step explanation:
Complementary: Either of two angles whose sum is 90°.
Starting Angle: ∠BDC
Possible Complement: ∠BDA
Answer: ∠ACD
Step-by-step explanation:
Complementary angles are angles which have a sum of 90 degrees when added together.
Angle ∠ADB is 90°
So ∠BDC and another angle should give you ∠ADB
The angle that when added to ∠BDC give you ∠ADB is ∠ACD
Answer the following questions
Answers
To wrap gift boxes joelle uses 24 yards if ribbon which us 8% of her total amount of ribbon. How many ribbons does she gave jn all
Answers
Joelle gave a total of 300 yards of ribbon in all
How many ribbons does she gave in allLet's assume that the total amount of ribbon Joelle has is "x" yards.
We know that 24 yards of ribbon is 8% of her total amount of ribbon. So we can write an equation:
0.08x = 24
To solve for x, we divide both sides of the equation by 0.08:
x = 24 ÷ 0.08
x = 300
Therefore, Joelle has a total of 300 yards of ribbon.
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Answer:
Step-by-step explanation: the answer is 300 just divide and you’ll get the answer that simple
how exactly am i supposed to locate? please help
Answers
Answer:
We can use the vector addition property to find the coordinates of the points M, N, and I.
Let
[tex]\bold{ A = (x_1, y_1), B = (x_2, y_2), C = (x_3, y_3), and\: D = (\frac{x_2+x_3}{2}, \frac{y_2+y_3}{2})}[/tex]
To find M, we use the fact that MA + MB = 0. Therefore, we have:
MA = -MB
A - M = -(B - M)
A - M = -B + M
2M = A + B
M =[tex]\frac{A + B}{2}[/tex]
So, the coordinates of point M are
[tex]\bold{(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})}[/tex]
To find N, we use the fact that 3NA + NC = 0. Therefore, we have:
3NA = -NC
3A - N = -(C - N)
3A - N = -C + N
4N = 3A + C
N =[tex]\frac{ 3A + C}{4}[/tex]
So, the coordinates of point N are [tex]\bold{(\frac{3x_1+x_3}{4},\frac{ 3y_1+y_3}{4})}[/tex]
To find I, we use the fact that IM + 2IN = 0. Therefore, we have:
IM = -2IN
M - I = -2(N - I)
M - I = -2N + 2I
3I = M + 2N
I = [tex] \frac{(M + 2N)}{3} [/tex]
Substituting the values of M and N that we found earlier, we get:
I = (A + B + 2(3A + C)/4)/3
Simplifying this expression, we get:
I = [tex]\frac{(7A + 2B + 2C)}{12}[/tex]
So, the coordinates of a point I are[tex]\bold{(\frac{7x_1+2x_2+2x_3}{12}, \frac{7y_1+2y_2+2y_3}{12}).}[/tex]
Now, find the solution to the system of equations
Answers
The solution of equation is (2, 3).
We have,
x= 3y -7.........(1)
y= x + 1.........(2)
Solving equation (1) and (2) we get
y = 3y - 7 + 1
y - 3y = -7 + 1
-2y = -6
y = -6/(-2)
y = 3
and, x = 3(3) - 7
x = 9 - 7
x = 2
Thus, the solution of equation is (2, 3).
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7
7
?
?
Find the arc length of the partial circle.
Either enter an exact answer in terms of
π
πpi or use
3.14
3.14, point, 3.14 for
π
πpi and enter your answer as a decimal.
units
Answers
According to given information, the arc length of a partial circle is 14.67 units.
What is partial circle?A partial circle is a portion of a circle, usually defined by an angle that is less than 360 degrees.
According to given information:To find the arc length of a partial circle, we need to know the measure of the central angle, θ, in radians.
Let's say that the central angle of the partial circle is 2π/3 radians, which corresponds to an angle of 120 degrees.
Then, the arc length, denoted by L, can be calculated using the formula:
L = rθ
where r is the radius of the circle.
Plugging in the values we have, we get:
L = 7(2π/3)
L = (14/3)π
Using 3.14 for π, we get:
L ≈ 14.67 units (rounded to two decimal places)
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As seen in the diagram below, Dalvin is building a walkway with a width of x x feet to go around a swimming pool that measures 7 feet by 9 feet. If the total area of the pool and the walkway will be 143 square feet, how wide should the walkway be?
Answers
Answer: 2
Step-by-step explanation:
(7+2x)(9+2x)= 143 (area= length x width)
63+14x+18x+4x^2=143
4x^2+32x−80=0
x^2+8x−20=0
(x−2)(x+10)=0
x = 2 or -10
Since the length of the walkway can't be negative, the answer is 2.
Charlie made a start using 1/8 yards of red fabric and 1/3 yards of yellow fabric. How many yards of fabric did he use in all? Write your answer as a fraction in simplest form.
Answers
Answer:
[tex]\frac{11}{24}[/tex] yards
Step-by-step explanation:
[tex]\frac{1}{8}[/tex] + [tex]\frac{1}{3}[/tex] we need a common denominator which is 24
[tex]\frac{1}{8}[/tex] x [tex]\frac{3}{3}[/tex] = [tex]\frac{3}{24}[/tex]
[tex]\frac{1}{3}[/tex] x [tex]\frac{8}{8}[/tex] = [tex]\frac{8}{24}[/tex]
[tex]\frac{3}{24}[/tex] + [tex]\frac{8}{24}[/tex] = [tex]\frac{11}{24}[/tex] yards
Helping in the name of Jesus.
The mean score, overbar(x), on an aptitude test for a random sample of 5 students was 73. Assuming that σ = 15, construct a 95.44% confidence interval for the mean score, μ, of all students taking the test.
Question 14 options:
A)
67.0 to 79.0
B)
59.6 to 86.4
C)
43 to 103
D)
62.9 to 83.1
Answers
The 95.44% confidence interval for the mean score, μ, of all students taking the test is 59.6 to 86.4.
What is confidence interval?A confidence interval is a range of values that is calculated from a sample of data. It provides a level of certainty, usually expressed as a percentage, that a population parameter lies within this range. It is used to estimate a population parameter, such as a mean, a proportion, or a difference between two means.
The 95.44% confidence interval for the mean score, μ, of all students taking the test can be calculated using the formula:
Confidence Interval = overbar(x) ± (1.96 x (σ/√n))
where overbar(x) is the mean score on the aptitude test, σ is the standard deviation of the population (15 in this case), and n is the sample size (5 in this case).
Plugging in the given values, we get:
Confidence Interval = 73 ± (1.96 x (15/√5))
= 73 ± (1.96 x 3)
= 73 ± 5.88
Therefore, the 95.44% confidence interval for the mean score, μ, of all students taking the test is 59.6 to 86.4.
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Please answer this question, I’ll give brainliest, and no chat gpt
Q7. A 230 kg piano must be lifted onto a stage that is 1.7 m high.
(a) If the piano is lifted straight up by some very strong people, how much force must they apply? [2 marks]
(b) How much work have they done? [2 marks]
(c) If the stage-crew only need to apply a force of 300 N to get the piano onto the stage if they use a 15 m ramp. How much work is done using the ramp? [2 marks]
(d) What is the efficiency of the ramp? [2 marks]
(e) You should notice that the force needed to lift the piano in A is larger than the force needed to lift the piano in C. How is it possible that the piano can be raised with much less force when the incline is used? (In other words, what is the "trade-off" of using an inclined ramp?) [2 marks]
Answers
1. The force they must apply is 2256.3 N
2. The amount of work done = 3835.71 J
3. The work done using the ramp = 4500 J
4. The efficiency of the ramp = 85.24%
5. When the people use inclined ramp, they don't have worry about the gravitational force that is acting on the piano. The trade off with with less force, the ramp is able to cover more distance.
How do we find force applied, work done, and efficiency of ramp?1. To find force applied, used the formula; F = mg
230 x 9.8N
=2256.3N
2. To find the amount of work done, we use the formula;
W = Fd
2256.3 x 1.7 m
= 3835.71J
3. o calculate the work done using the ramp, you use the same formula you used in step 2
300N x 15m
= 4500J
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EASY POINTS!
A machine in a factory makes 2 1/4 pounds of nails in 1 1/2 hours. At this rate, in pounds per hour, does the machine make nails? Show your work!
A. 2/3
B. 3/4
C. 1 1/2
D. 3 3/4
Answers
The machine makes 2 1/4 pounds of nails in 1 1/2 hours.
To convert 2 1/4 to an improper fraction, we multiply the whole number (2) by the denominator (4) and add the numerator (1), then write the result over the denominator:
2 1/4 = (2 x 4 + 1)/4 = 9/4
To convert 1 1/2 to an improper fraction, we multiply the whole number (1) by the denominator (2) and add the numerator (1), then write the result over the denominator:
1 1/2 = (1 x 2 + 1)/2 = 3/2
Now we can divide the amount of nails by the time:
(9/4) ÷ (3/2) = (9/4) x (2/3) = 18/12 = 3/2
Therefore, the machine makes nails at a rate of 3/2 pounds per hour. The correct answer is C.
Look at the simultaneous equations below. (1) 18 = 7x - y (2) 3x + y = 2 a) Rearrange equation (1) to make y the subject. b) Using your answer to part a), solve the simultaneous equations ck to task Watch video
Answer:
Explanation:
Answers
The solution to the simultaneous equations is x = 2 and y = -4. To obtain these values, 18 = 7x - y is rearranged to y = 7x - 18, and then substituted into 3x + y = 2 to obtain the value of x and y.
Rearranging equation (1) to make y the subject
18 = 7x - y
Add y to both sides
18 + y = 7x
Subtract 18 from both sides
y = 7x - 18
Using the answer to part a) to solve the simultaneous equations
Substitute the expression for y from equation (1) into equation (2)
3x + (7x - 18) = 2
Simplify
10x - 18 = 2
Add 18 to both sides
10x = 20
Divide both sides by 10
x = 2
Substitute x = 2 into equation (1) to find y
18 = 7(2) - y
18 = 14 - y
Subtract 14 from both sides
4 = -y
Multiply both sides by -1
-4 = y
Therefore, the solution to the simultaneous equations is x = 2 and y = -4.
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Translate this sentence into an equation.
24 more than Craig's height is 68.
Use the variable c to represent Craig's height.
Answers
We can begin by focusing on c on one side of the equation to help us solve it. Craig's height is 44 as a result.
What is Equation?A mathematical equation is a claim that two expressions are equivalent. It is divided into two sections, the left and the right, by the equal sign (=). Equation's left and right sides each have the potential to include variables, constants, and operators.
Finding the value(s) of the variable(s) necessary to make an equation true is the aim of equation solving. Algebraic techniques like simplification, substitution, and elimination can be used to solve equations.
An equation can be used to represent the following sentence:
c + 24 = 68
Craig's height is represented by c in this equation. The equal sign (=) is used to symbolise the phrase "is 68," while the phrase "is 24 more than Craig's height" is symbolised by c + 24. The formula for the problem can be solved to find the value of c, which corresponds to Craig's height.
We can begin by concentrating c on just one side of the equation in order to solve it:
c + 24 - 24 = 68 - 24
c = 44
Therefore, Craig's height is 44.
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4. Mackenzie's dog can jump 2 1/2 feet off the ground. Jordyn's dog can
jump 1/2 foot off the ground. What is the difference in inches between
2how high Mackenzie's dog can jump and how high Jordyn's dog can
jump? Circle what to do to solve this problem.
Answers
The difference in the length of dogs jump is 24 inches.
Given that, Mackenzie's dog can jump [tex]2\frac{1}{2}[/tex] =5/2 feet off the ground. Jordyn's dog can jump 1/2 foot off the ground.
We know that, 1 feet = 12 inches
Here, 5/2 feet = 5/2 ×12
= 30 inches
1/2 foot = 1/2 ×12
= 6 inches
Now, difference = 30-6 = 24 inches
Therefore, the difference in the length of dogs jump is 24 inches.
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The following residual plot is obtained after a regression equation is determined for a set of data. Does the residual plot indicate that the regression equation is a good model or a bad model of the data? Why or why not?
Answers
The residual plot shows that the regression equation is a good model of the data because it shows a random scatter of points around a horizontal line at zero, with no pattern or trend
What makes a residual plot a good model?A residual plot is a scatter plot of the residuals against the predictor variable(s) or the fitted values. It is used to verify whether the regression equation fits the data well.
In the event that the residual plot shows a random scatter of points around a horizontal line at zero, with no pattern or trend, it shows that the regression equation is a good model of the data.
On the other hand, supposing the residual plot shows a pattern or trend, such as a curve, a U-shape, or a funnel shape, it shows that the regression equation is a bad model of the data.
Therefore, from the graph given, the residual plot shows that the regression equation is a good model of the data.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answers
Answer:
Step-by-step explanation:
1 -E (102/234) *100 =43.6%
2- F
3-C
4-A
18.
Simplify.
y²-6y +11
y-2
Oy-1
Oy³-8y² +23y - 22
none of the answer choices
Oy²-5y +9
O-y²-2y + 10
Answers
Answer:
the answer is none of the answer choices
Answer:
the answer is none of the answer choices
x^2+7x-9 + 2x-1 what is the polynomial and degree
Answers
Answer:
The given expression is a polynomial:
f(x) = x^2 + 7x - 9 + 2x - 1
Combining like terms, we get:
f(x) = x^2 + 9x - 10
The degree of the polynomial is 2, since the highest power of x is 2.
I need the area choices below
Answers
Answer:
Area of the shape is 244.98cm² is B
Step-by-step explanation:
Area of shape=Area of semi circle+Area of trapezoid
A=1/2 πr² + 1/2(a+b)h
A=1/2×3.142×7² + 1/2(14+18)10.5
A=1/2×3.142×49 + 1/2×32×10.5
A=76.98+168
A=76.98+168
A=244.98cm²
PLEASE HELP NOW ITS DUE TONIGHT!!!!
A zip line is constructed across a valley, as shown in the diagram. What is the width w of the valley? Round your answer to the nearest tenth.
w ≈__ft
Answers
Answer: 92.5
Step-by-step explanation:
Answer:
w = 92.5
Step-by-step explanation:
You cannot use Law of Sine in this case.
Use Law of Cosine.
They gave you 2 side length and one angle.
plug in your values into the equation and solve for w.
Let just use u, v, & w: Let u be 25 and v be 84.
[tex]w^2 = u^2 + v^2 - 2*u*v*cos(W)[/tex]
[tex]w^2 = 25^2 + 84^2 - 2*25*84*cos(102)[/tex]°
[tex]w^2=625+7056-4200*cos(102)[/tex]
[tex]w^2=7681-4200*(-0.2079116908)[/tex]
[tex]w^2=7681+873.2291014[/tex]
[tex]w^2=8554.229101[/tex]
[tex]w=\sqrt{8554.229101}= 92.48907558[/tex]
9. data was collected on houses currently for sale. based on a cubic modeling equation, which prediction about this data is the most reliable? a.
a $70k house would have 1,354 square ft
b. a $70k house would have about 1,460 square ft
c. a $400k house would have 492 square ft
d. a $400k house would have 4,328 square ft
10. suppose a scatterplot is created from the points in the following table. when x=7, what is the second coordinate in a scatterplot of the linearized data? round the answer to the tenth place.
a. 0.8
b. 2.1
c. 54.3
d. 112.8
11. the equation that best models the linearized data for a particular data set is log y= 0.75821x+0.03442. find the approximate value x=4. round your answer to the nearest whole number.
a. 3
b. 25
c. 1,168
d. 62,034
Answers
question 9.
Based on a cubic modeling equation, the prediction about this data that is most reliable is a $70k house would have 1,354 square ft.
Option A is correct.
Question 10.
The second coordinate in a scatterplot of the linearized data and rounding the answer to the tenth place is 0.8
Option A is correct.
Question 11.
The approximate value when x=4 and rounding the answer to the nearest whole number is 1,168
Option C is correct.
How do we calculate?The equation is given as
Log y= 0.75821x+0.03442
We substitute x = 4 into the given equation and solve for y:
log y = 0.75821(4) + 0.03442
log y = 3.07286 + 0.03442
log y = 3.10728
We take the antilogarithm of both sides,
y = 10^(3.10728)
y = 1,168.66
Rounding off, the closest answer is option (c) 1,168.
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Can someone explain to me how to find x?
Answers
Answer:
x° = 36°
Step-by-step explanation:
You want to find the angle between a secant and a tangent to a circle, where the intercepted arcs are 126° and 54°.
Exterior angleThe angle at D, labeled x°, is half the difference of the intercepted arcs:
x° = (126° -54°)/2 = 72°/2
x° = 36°
__
Additional comment
The same relationship applies for the angle between two secants.
This is easy to prove by considering triangle ADE. Angle DAE is half of arc CE. The exterior angle to the triangle at E is half of arc AE. That exterior angle is equal to the sum of the remote interior angles at D and A:
AE/2 = x° + CE/2 ⇒ x° = (AE -CE)/2
2x + y = 7
x + y = 1
Answers
Answer: x = 6 and y = -5.
Step-by-step explanation: Multiply the second equation by -2 to eliminate the y term:
-2(x + y) = -2(1) -> -2x - 2y = -2
Add the resulting equation to the first equation to eliminate the y term:
2x + y = 7
-2x - 2y = -2
0x - y = 5
Solve for y:
-y = 5
y = -5
Substitute y = -5 into either of the original equations and solve for x:
x + y = 1
x + (-5) = 1
x = 6
Therefore, the solution to the system of equations is x = 6 and y = -5.
What is the perimeter of the parallelogram?
units
Answers
Answer:
Step-by-step explanation:
Jenna threw a disc 18 yards to Karl, who threw it 11 yards in the same direction to Alice.
Start at 0 on the number line and move _____ to the right to represent Jenna throwing the disc to Karl.
Then move ______ to the right to represent Karl throwing the disc to Alice the result shows that.
Answers
Start at 0 on the number line and move 18 yards to the right to represent Jenna throwing the disc to Karl. Then move 11 yards to the right to represent Karl throwing the disc to Alice the result shows that.
To represent Jenna throwing the disc to Karl, we need to move 18 yards to the right on the number line. This is because Jenna threw the disc directly to Karl, so the distance between them is 18 yards. Therefore, we can start at 0 on the number line and move 18 yards to the right to represent Jenna throwing the disc to Karl.
To represent Karl throwing the disc to Alice, we need to move 11 yards to the right from Karl's position on the number line. This is because Karl threw the disc 11 yards in the same direction as Jenna threw it to him.
So, we can start at Karl's position on the number line (which is 18 yards to the right of 0) and move 11 yards to the right to represent Karl throwing the disc to Alice.
Overall, to represent the entire throwing sequence from Jenna to Karl and then to Alice, we can start at 0 on the number line and move 18 + 11 = 29 yards to the right.
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