what is the solution to the following system?
5x+2y+z=4
x+2z=4
2x+y-z=-1
A. x = 0, y = 1, z = 2
B. x = 1, y = –1, z = 2
C. x = 1, y = 0, z = –1
D. x = 2, y = 1, z = 0
Answers
1) Write two of the variables in terms of the third variable. For this case we write x, y in terms of z.
2) Substitute the expressions in the first equation since it relates all the variables.
3) Clear z.
4) with the value of z, find x, y
Answer:
A. x = 0, y = 1, z = 2
See attached image.
Related Questions
For the following geometric sequence find the recursive formula and the 5th term in the sequence. In your final answer, include all of your work.
{-4, 12, -36, ...}
Answers
the formula is a(r)^(n-1)
a------------- >a is the first term------------ > -4
r--------------- > is the common ratio------- > 12/(-4)=(-36/12)=-3
n--------------- > is the number of terms
The fifth term is -4[(-3)^(5-1)]=-4[(81]=-324
the answer is -324
r = [tex] t_{n+1} / t_{n} [/tex]
where r is the common ratio
[tex] t_{n} [/tex] is any term in the sequence
[tex] t_{n} [/tex] is the term preceding [tex] t_{n} [/tex]
In your case the common ratio will be
12/-4 = -3
The recursive formula of a geometric sequence is:
An = [tex] A_{n-1} [/tex] x r
Where : An is the nth term
[tex] A_{n-1} [/tex] is the erm preceding the nth term
r = common ratio
For this case it is:
An = [tex] A_{n-1} [/tex] x -3
Now let us use this formula to find the 5th term:
[tex] A_{5} [/tex] = [tex] A_{5-1}[/tex] x -3
[tex] A_{5} [/tex] = [tex] A_{4}[/tex] x -3
Since you do not know the 4th term, you can use that by using our reclusive formula:
[tex] A_{4} [/tex] = [tex] A_{4-1} [/tex] x -3
[tex] A_{4} [/tex] = [tex] A_{3} [/tex] x -3
[tex] A_{4} [/tex] = [tex] -36 [/tex] x -3
[tex] A_{4} [/tex] = [tex] 108 [/tex]
Now that you know your fourth term, you can use the same formula:
[tex] A_{5} [/tex] = [tex] A_{5-1} [/tex] x -3
[tex] A_{5} [/tex] = [tex] A_{4} [/tex] x -3
[tex] A_{5} [/tex] = [tex] 108 [/tex] x -3
[tex] A_{5} [/tex] = [tex] -324 [/tex]
What is the total number of rectangles and triangles used for the net of this solid?
a. 3
b. 4
c. 5
d. 6
Answers
The total number of rectangles and triangles used for the net of this solid is 4.
Explanation:To find the total number of rectangles and triangles used for the net of a solid, we need to examine the shape of the solid. If the given solid has 4 faces, like a regular tetrahedron or a pyramid, then it will have 3 triangles and 1 rectangle. Hence, the total number of rectangles and triangles used for the net of this solid is 4, so the answer is option b.
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The table below shows data from a survey about the amount of time students spend doing homework each week. The students were either in college or in high school:
High Low Q1 Q3 IQR Median Mean σ
College 50 5 7.5 15 7.5 11 13.8 6.4
HS 16 0 9.5 14.5 5 13 . 10.7 5.3
Which of the choices below best describes how to measure the spread of this data? (Hint: Use the minimum and maximum values to check for outliers.) (2 points) A:Both spreads are best described with the IQR.
B:Both spreads are best described with the standard deviation.
C:The college spread is best described by the IQR. The high school spread is best described by the standard deviation.
D:The college spread is best described by the standard deviation. The high school spread is best described by the IQR.
Answers
Answer:
Option A is correct
Step-by-step explanation:
Given is a table which shows data from a survey about the amount of time students spend doing homework each week.
College HS
High 50 16
Low 5 0
Q1 7.5 9.5
Q3 15 14.5
IQR 7.5 5
Median 11 13
Mean 13.8 10.7
Std dev 6.4 5.3
1.5IQR 11.25 7.5
Q1-1.5IQR -9.38 -12
Q3+1.5IQR 37.5 29.5
WE find that there is only one outlier in college with 50 as high.
Except that all others are well within IQR range. Hence outliers are minimum
So option A is right.
Final answer:
To determine the spread of data on student homework hours, IQR and standard deviation are used. The college data's spread is best described by IQR, while the high school data's spread is best described by standard deviation, making Option C the most suitable choice.
Explanation:
To measure the spread of the data for the amount of time students spend doing homework each week, we have two primary measures: the Interquartile Range (IQR) and the standard deviation (σ). IQR represents the difference between the third quartile (Q3) and the first quartile (Q1) and describes the spread of the middle 50% of the data. The standard deviation indicates how much the values in the dataset deviate from the mean, which can help in understanding the overall spread including potential outliers.
When dealing with outliers, it's important to consider that potential outliers are typically identified as values that are more than 1.5 × IQR above Q3 or below Q1. We would use the minimum (Low) and maximum (High) values provided alongside the IQR to check for outliers. For the college data, with a High of 50 and a Low of 5, the range is 45. For high school, the range is 16. Outliers could potentially affect the standard deviation significantly, making IQR a better measure for the middle spread of data.
Based on this, the college data with a wider range may be more affected by outliers, whereas the high school data with a smaller range may not. Therefore, the spread for the college data can be better described by the IQR, while the standard deviation can be a good measure for the high school data. This suggests that Option C: "The college spread is best described by the IQR. The high school spread is best described by the standard deviation." is the most suitable choice.
Select the problems which show the correct answers. (1.12 x 105) (6.06 x 105) Answer: 6.79 x 1010 (2 x 101)(3.0 x 101) Answer: 6.0 x 101 (2.775 x 10−4) (4.775 x 104) Answer: 1.325 x 100 5 8.14 x 102 Answer: 6.14 x 10−3
Answers
Answer:
[tex](1.12 x 10^5) (6.06 x 10^5) = 6.787 x 10^{10}\\[/tex]
[tex]\frac{0.5 x 10 ^ 1}{8.14 x 10 ^ 2} = 6.14 * 10 ^ {-3}\\[/tex]
Step-by-step explanation:
To solve this problem we must solve all 4 operations.
For the first one we have:
[tex](1.12 x 10^5) (6.06 x 10^5)[/tex]
When we have multiplication of powers of equal base (10) the same base is placed and the exponents are added
So:
[tex]1.12 * 6.06 x 10^{5+5} = 6.787 x 10^{10}\\[/tex]
Therefore the answer to this question is correct.
For the second question we have:
[tex](2 x 10^1) (3.0 x 10^1)[/tex]
Then following the same procedure as in the previous question we have:
[tex]2 * 3.0 x 10 ^ {1 + 1} = 6 x 10 ^ 2\\[/tex]
Then the answer shown in the statement is not correct, because 10 must be squared, product of the sum of its exponents (1 + 1)
For the third question we have:
[tex](2,775 x 10^{-4}) (4,775 x 10^4)\\2.775 * 4.775 x 10 ^{(- 4) +4} = 13.251 x10 ^ 0\\[/tex]
Then it is verified that the answer for this operation is no correct
[tex]13.25\neq 1.325[/tex]
Finally, for the fourth question we have:
[tex]\frac{5}{(8.14 x 10 ^ 2)}\\[/tex]
This we can write it as:
[tex]\frac{0.5 x 10 ^ 1}{8.14 x 10 ^ 2}\\[/tex]
In division of powers of equal base (10 in this case) the same base is placed and the exponents are subtracted:
[tex]\frac{0.5}{8.14 x 10 ^ {1-2}} = 0.0614 x 10 ^ {-1} = 6.14 * 10 ^ {-3}\\[/tex]
Finally, the problems that show correct answers are:
[tex](1.12 x 10^5) (6.06 x 10^5) = 6.787 x 10^{10}\\[/tex]
[tex]\frac{0.5 x 10 ^ 1}{8.14 x 10 ^ 2} = 6.14 * 10 ^ {-3}\\[/tex]
Jacqueline's piggy bank contains $6.20 in dimes and quarters. There are 32 coins in all. How many of each kind are there?
Answers
Someone pleaser help me !
Answers
.. $80,000 * 4/(3 +4) = 45,714.29
The closest answer is the 4th selection, but it doesn't really agree with the conditions of the problem statement.
_____
If Steve invests the balance after Elizabeth contributes 45,600, the ratio of their contributions will be 43:57, about 0.7544, not 3:4 = 0.7500.
Factor the quadratic equations W^2-W-12
Answers
W^2-W-12 = w^2+bW+c
b=-1,
c=-12
We look for m, n so that m+n=b=-1, m*n=c=-12, where m,n are integer factors of -12.
Now enumerate all possibilities for m*n=12
m n m*n m+n
1 -12 -12 -11
2 -6 -12 -4
3 -4 -12 -1 ....... so m*n=-12, m+n=-1
The factorization is then
W^2-W-12=(W+3)(W-4)
can someone answer this?
Answers
All the right triangles are similar, so
.. hypotenuse/(short side) = x/6 = 6/(x -9)
Multiplying by the product of denominators gives
.. x(x -9) = 36
Two factors of 36 that differ by 9 are 12 and 3, so we have
.. x = 12
For y, we can use the Pythagorean theorem.
y^2 +6^2 = 12^2
y^2 = 144 -36 = 108
y = √108 = √(36*3)
y = 6√3
Which answer represents the series in sigma notation?
Answers
[tex]\sum^5_{j=1} (5j-12)[/tex] represents the series in sigma notation.
What is sigma notation?The symbol Σ (sigma) is generally used to denote a sum of multiple terms. This symbol is generally accompanied by an index that varies to encompass all terms that must be considered in the sum.
Given is a series (-7 + (-2) + 3 + 8 + 13), we need to define it in sigma notation,
Therefore,
For j = 1 up to j = 5
j = 1
(5j - 12) = (5(1) - 12) = 5 - 12 = - 7
j = 2
(5j - 12) = (5(2) - 12) = 10 - 12 = - 2
j = 3
(5j - 12) = (5(3) - 12) = 15 - 12 = 3
j = 4
(5j - 12) = (5(4) - 12) = 20 - 12 = 8
j = 5
(5j - 12) = (5(5) - 12) = 25 - 12 = 13
This gives us the given series,
(-7 + (-2) + 3 + 8 + 13)
Hence, [tex]\sum^5_{j=1} (5j-12)[/tex] represents the series in sigma notation.
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solve the right triangle shown in the figure BC = 1.6in< A=48.8 C =90
Answers
180 - 90 - 48.8 = 41.2
m∠B = 41.2°.
We can use the angles and the one side we're given to find the remaining sides. Since we do not know the length of the hypotenuse, AB, we cannot use sine or cosine. We must use tangent (the ratio for tangent is opposite/adjacent):
[tex]\tan 41.2 = \frac{x}{1.6}[/tex]
Multiply both sides by 1.6:
[tex]1.6 \tan 41.2 = x \\ 3.67 = x[/tex]
This is the length of side AC, which is opposite to angle B.
To find the length of AB we can use the Pythagorean Theorem:
[tex](1.6)^2+(3.67)^2=c^2 \\ 2.56+13.4689=c^2 \\ 16.0289=c^2 \\ \sqrt{16.0289} = \sqrt{c^2} \\ 4=c[/tex]
The length of side AC, the hypotenuse, is 4 inches.
I think your answer is A
A sidewalk forms the diagonal of a square park. The sidewalk is 30 meters long. To the nearest tenth of a meter, how long are the sides of the park ?
Answers
900 = 2A²
A^2 = 450
Taking the square root of 450, we find that the lengths of A and B are roughly 21.2 meters.
Length of the Diagonal l = 30 m
Formula for the length of the diagonal of a square l = square root of 2 x s; s being the side.
Therefore square root of 2 x s = 30 => s = 30 / square root of 2 = 30 / 1.414 Side of the Square s = 21.21 m
If f is differentiable at x = c, then f is continuous at x = c.
True
False
Answers
Answer:
This is true!
Step-by-step explanation:
P.S: keep in mind that the opposite is not true! If f is continuous at x = c, then f is NOT differentiable at x = c.
:)))
If f is differentiable at x = c, then f is continuous at x = c is not true.
What is differentiable?Any point inside the range of a function's purview has a derivative, making it a computable function of one real variable. In these other phrases, each interior site in the domain of an invertible method's graph does indeed have a non-vertical line segment.
F is NOT differentiable at x = c if it is continuous at x = c.
When working with units, this quality is highly helpful since, if a curve is discrete, we automatically infer that it is indeed continuous.
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The sum of the roots of the equation 1/2x^2-5/4x-3=0
Answers
Multiplying all the terms by 4 to remove fractions
2x²-5x-12=0
we can use factorization method;
product = -24
sum = -5
numbers= -8 and 3
Threfore; 2x²-8x+3x-12 =0
2x(x-4) +3(x-4) =0
= (2x+3)(x-4) =0
thus 2x +3= 0 or x-4 =0
therefore; x = -3/2 and x =4
Thus the sum of the roots will be (-3/2 +4) = 2.5
Ginny has a sheet of plywood that is 4 feet by 8 feet. She wants to saw the plywood into pieces 1 foot high and 2 feet long for signs. How many signs can she make with the sheet of plywood?
Answers
Answer: 16 signs
Step-by-step explanation: i not saying this cause the other person said it i am saying it because i tookthe question
how would I solve for x?
Answers
Acute scalene triangle.Sides: a = 15 b = 13 c = 14
Area: T = 84
Perimeter: p = 42
Semiperimeter: s = 21
Angle ∠ A = α = 67.38° = 67°22'49″ = 1.176 rad
Angle ∠ B = β = 53.13° = 53°7'48″ = 0.927 rad
Angle ∠ C = γ = 59.49° = 59°29'23″ = 1.038 rad
Height: ha = 11.2
Height: hb = 12.923 <- Answer
Height: hc = 12
Median: ma = 11.236
Median: mb = 12.971
Median: mc = 12.166
Inradius: r = 4
Circumradius: R = 8.125
Vertex coordinates: A[14; 0] B[0; 0] C[9; 12]
Centroid: CG[7.667; 4]
Coordinates of the circumcenter: U[7; 4.125]
The expression below is the factorization of what trinomial?
(2x + 7)(4x - 3)
A. 8x2 + 22x + 4
B. 8x2 + 28x - 21
C. 8x2 + 28x + 4
D. 8x2 + 22x - 21
Answers
= (2x)(4x) + (2x)(-3) + (7)(4x) + (7)(-3)
= 8x^2 - 6x + 28x - 21
= 8x^2 + 22x - 21 (Answer D)
A right triangle has legs that are 15 feet and 25 feet long.
What is the length of the hypotenuse?
Answers
15^2 + 25^2 = X62
225 + 625 = x^2
850 = x^2
x = 5sqrt(34)
if you need it as a decimal = 29.1547
Answer: The length of the hypotenuse is 5√34 units.
Step-by-step explanation: Given that a right-angled triangle has legs of length 15 ft and 25 ft.
We are to find the length of the hypotenuse.
As shown in the attached figure, AB and BC are the legs of the right-angled triangle ABC. AC is the hypotenuse of the triangle.
Also, AB = 15 ft and BC = 25 ft.
From Pythagoras theorem, we have
[tex]AC^2=AB^2+BC^2\\\\\Rightarrow AC^2=(15)^2+(25)^2\\\\\Rightarrow AC^2=225+625\\\\\Rightarrow AC^2=850\\\\\Rightarrow AC=\sqrt{850}\\\\\Rightarrow AC=5\sqrt{34}.[/tex]
Thus, the length of the hypotenuse is 5√34 units.
In the two triangles below, all angles equal 60 degrees and ab = ef. are the two triangles congruent?
Answers
Eric borrowed $1,800 for 9 months at 13.5% simple interest under an
add-on plan. What was his monthly payment?
a. $15.63
b. $220.25
c. $187.50
d. $1,982.25
ANSWER IS NOT C
Answers
You know the monthly repayment of $1800 over 9 months will be at least $200 per month. Since the interest is about 10% of the loan amount (3/4 of 13.5%), the amount added on for interest will be on the order of $20 per month.
If you work out the math, you find the payment is exactly $220.25 (selection B). You don't need to do that to make a sensible choice.
_____
Payment = ($1800 + 9/12*0.135*1800)/9 = $220.25.
Which of the following shows 2 + (x + 3y) rewritten using the Associative Property of Addition?
A. 2 + x + 3y
B. (2 + x) + 3y
C. 2x + (3 + y)
D. x + (2 + 3y)
Answers
(2 + x) + 3y ...>Associative Property of Addition
hope it helps Plz give Brainliest
B. (2 + x) + 3y
Step-by-step explanation:
First of all you must know how the associative property of addition looks like. Example: (1 + x) + y = 1 + (x + y)
Ok so now really we have to make the two ( ) on the outside of 2+x so then it looks like these ( ) have been reversed. So then (2+x)+3y would be your answer. Also I did this on FLVS so I know that the answer I said is correct. I hope this helps you.
Write and solve an equation to find the value of each variable
Answers
as you can see in the picture, the "near arc" is x°, and the "far arc", is the leftover from subtracting the arc of 120° and x°, therefore then
[tex]\bf 44=\cfrac{\stackrel{far~arc}{(360-x-120)~~-~~\stackrel{near~arc}{x}}}{2}\implies 88=240-2x \\\\\\ 2x=152\implies x=\cfrac{152}{2}\implies x=76[/tex]
Write an expression for the following situation and solve it. Mr. Simms bought 20 pencils. He used 1/4 of the pencils and then gave 4 to his students.
Answers
1/4 of 20 pencils are 5 pencils.
Since he gave away 4 pencils,
Total = 5 + 4 = 9
Mr. Simms use and give away total 9 pencils.
Consider the polynomial: x/4– 2x^5 + x^3/2 + 1 Which polynomial represents the standard form of the original polynomial?
a.x^3/2 – 2x^5 + x/4 + 1
b.–2x^5 + x^3/2 + x/4 + 1
c. –2x^5 + x/4 + x^3/2 + 1
d. 1 – 2x^5 + x^3/2 + x/4
Answers
Answer:
b. –2x^5 + x^3/2 + x/4 + 1
Step-by-step explanation:
In the given expression, the degrees of the terms, in the order given, are ...
1, 5, 3, 0
When the terms are properly arranged in standard form, they will be ...
5, 3, 1, 0 . . . . descending order
The standard form of this expression is ...
-2x^5 +x^3/2 +x/4 +1 . . . . . . matches choice B
Answer: b.–2x^5 + x^3/2 + x/4 + 1
Step-by-step explanation:
The three angle bisectors of ΔABC meet at P. Drag the vertices around to form different triangles, and then make a conjecture. Which segments appear to be equal in length? Check all that apply. XP = YP for an acute triangle XP = ZP for an acute triangle YP = ZP for an obtuse triangle ZP = XP for a right triangle XP = YP for an obtuse triangle
Answers
XP=YP for an acute triangle
YP=ZP for an obtuse triangle
XP=YP For an obtuse triangle
YP=ZP for an obtuse triangle
XP=YP for an obtuse triangle
this is right
What is 4 equal parts
Answers
Suppose there are 7 dimes, and someone gives you 4 of them. Each dime they gave you represents a part of the whole amount of dimes, and each of those dimes is equal to the others in size, weight, color, value. They are 4 equal parts of the whole amount of dimes. (The four equal parts don't have to add up to the whole--except when we say the whole is divided into 4 equal parts.)
Usually, we talk about equal parts when we are dividing something into shares. If we have a pizza that four people want to share in such a way that each person gets as much as possible without any fighting, it would usually be divided into four equal parts. Each share would be the same as the others in every aspect that matters. Each of those parts would be 1/4 of the pizza. The "4" in that fraction tells you the number of equal parts. The "1" tells you the number of those parts any one person gets in this scenario.
_____
Each of the words in that phrase "4 equal parts" has its usual dictionary meaning.
helpppppppppppppppppppppp
Answers
Second Option
Solution:
A geometric series converges when the value of its common ratio is between -1 and 1. Else the series will diverge. So we find the common ratio for each of the given options, the series with common ratio between -1 and 1 will be converging series.
For first option, common ratio = 1/3 divided by 1/9 = 3
Common ratio is not between -1 and 1, so this series is diverging.
For second option, common ratio = 1/2 divided by 1 = 1/2
Since the common ratio is between -1 and 1, this series is converging.
For third option, common ratio = -4
This series is also diverging.
For Fourth option, common ratio = 2
This series is also diverging.
find the inverse of y=x2-10x
Answers
y = x^2 - 10x + 25 - 25
y = (x-5)^2 - 25
y+25 = (x-5)^2
x-5 = +/-sqrt(y+25)
And you get TWO inverses:
x = 5 + sqrt(y+25), for x>=5
x = 5 - sqrt(y+25), for x<=5
Answer:
[tex]y=5\pm \sqrt{(25+x)}[/tex]
Step-by-step explanation:
We are asked to find the inverse for the function [tex]y=x^2-10x[/tex].
We know that to find inverse, we interchange x and y values and then solve for y.
After interchanging x and y values, we will get:
[tex]x=y^2-10y[/tex]
Switch sides:
[tex]y^2-10y=x[/tex]
[tex]y^2-10y-x=x-x[/tex]
[tex]y^2-10y-x=0[/tex]
Now, we will use quadratic formula to solve for y.
[tex]y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]y=\frac{-(-10)\pm \sqrt{(-10)^2-4(1)(-x)}}{2(1)}[/tex]
[tex]y=\frac{10\pm \sqrt{100+4x}}{2}[/tex]
[tex]y=\frac{10\pm \sqrt{4*25+4x}}{2}[/tex]
[tex]y=\frac{10\pm \sqrt{4(25+x)}}{2}[/tex]
[tex]y=\frac{10\pm 2\sqrt{(25+x)}}{2}[/tex]
[tex]y=5\pm \sqrt{(25+x)}[/tex]
Therefore, the inverse function for our given function would be [tex]y=5\pm \sqrt{(25+x)}[/tex].
Lindsay and Lorraine are trying to match the jump rope world record. Together, they need to jump 48 times in a row. Lindsay has gotten 14 jumps in a row, and Lorraine has gotten 13. How many more jumps (j) do they need to match the record? Show your work!
Answers
We have then:
Lindsay has gotten 14 jumps in a row and Lorraine has gotten 13:
14 + 13 = 27
Then, we must find the remaining amount:
j = 48-27
j = 21
Answer:
they need 21 more jumps to match the record
7. What is the angle measure that is vertical to an 83° angle?
Answers
30 POINTS!!! WILL MARK BRAINLIEST! : )
1. Name the property the equation illustrates.
8 x 1/8 = 1
A) Multiplication Property of –1
B) Inverse Property of Addition
C) Inverse Property of Multiplication
D) Identity Property of Division
2. Name the property the equation illustrates.
–5 + (8 + 10) = (–5 + 8) + 10
A) Multiplication Property of –1
B) Inverse Property of Addition
C) Inverse Property of Multiplication
D) Identity Property of Division
3. Name the property the equation illustrates.
-4 x -1/4 = 1
A) Multiplication Property of –1
B) Inverse Property of Addition
C) Inverse Property of Multiplication
D) Identity Property of Division
4. Name the property the equation illustrates.
(ab)3 = a(b3)
A) Multiplication Property of –1
B) Inverse Property of Addition
C) Inverse Property of Multiplication
D) Identity Property of Division
Answers
2. B) Inverse Property of Addition
3. C) Inverse Property of Multiplication
4. Your answer is not listed (The answer is Associative Property of Multiplication)
Answer:
1. C) Inverse Property of Multiplication
2. None of these. The answer is Associative property of Addition
3. C) Inverse Property of Multiplication
4. None of these. The answer is Associative property of Multiplication
Step-by-step explanation:
1.
Given a number a , the inverse property of multiplication states that
a * 1/a = 1
and 1/a is called the multiplicative inverse of a.
So 8 * 1/8 = 1 features the inverse property of multiplication where a = 8.
2.
Given three numbers a,b,c , the associative property of addition states that a + (b + c) = (a + b) + c
In this case, a = -5, b = 8 and c = 10
3.
-4 x -1/4 = 1 features the inverse property of multiplication where a = -4.
4.
Given three numbers a,b,c , the associative property of multiplication states that (a * b) * c = a * (b * c)
In this case, a = a, b = b and c = 3