Answer:
Three linear equations that has a unique solution (1,2,-1) are:-
x+ y+ z =2
2x + y + 3z = 1
x+ 2y+ z = 4
Step-by-step explanation:
Linear equations in three variables:-
If a, b, c and r are real numbers (and if a, b, and c are not all equal to 0)
then ax + by + cz = r is called a linear equation in three variables. (The
“three variables” are the x, the y, and the z.)
The numbers a, b, and c are called the coefficients of the equation. The
number r is called the constant of the equation.
so from from above explanation we can write 3 linear equations with three variables as.
x+ y+ z =2
2x + y + 3z = 1
x+ 2y+ z = 4
Now to check if the given point (1,2,-1) is solution or not these equations must satisfy this point,
x+ y+ z =2
1+ 2- 1 = 2
2= 2
2x + y + 3z = 1
2×1 +2 - 3×1 = 1
1=1
x+ 2y+ z = 4,
1+ 2×2 -1 = 4
4=4
therefore all three equations satisfies the given point
hence these are the three linear equation having point (1,2, -1) as the unique solution
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Please help!!!
Consider the segment UV.
Type the correct answer in each box. Use numerals instead of words.
Solve the following compound inequality: (1 point)
-2(x+8) +6 > x-4 or -3x + 12 < 6(x-4)
0x<2 orx>4
Ox>2 orx<4
0x<-2 orx>4
Ox>-2 orx<44
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x < -2 \:\: or \:\; x >4[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \textsf{First Inequality :} [/tex]
[tex]\qquad \tt \rightarrow \: - 2(x + 8) + 6 > x - 4[/tex]
[tex]\qquad \tt \rightarrow \: - 2x - 16 + 6 > x - 4[/tex]
[tex]\qquad \tt \rightarrow \: - 2x - 10 > x - 4[/tex]
[tex]\qquad \tt \rightarrow \: - 10 + 4 > x + 2x[/tex]
[tex]\qquad \tt \rightarrow \: - 6 > 3x[/tex]
[tex]\qquad \tt \rightarrow \: - \cfrac{ 6}{3} > x[/tex]
[tex]\qquad \tt \rightarrow \: - 2 > x[/tex]
[tex]\qquad \tt \rightarrow \: \therefore x < - 2[/tex]
[tex] \textsf{Second Inequality :} [/tex]
[tex]\qquad \tt \rightarrow \: - 3x + 12 < 6(x - 4)[/tex]
[tex]\qquad \tt \rightarrow \: - 3x + 12 < 6x - 24[/tex]
[tex]\qquad \tt \rightarrow \: 12 + 24 < 6x + 3x[/tex]
[tex]\qquad \tt \rightarrow \: 36 < 9x[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{36}{9} < x[/tex]
[tex]\qquad \tt \rightarrow \: 4 < x[/tex]
[tex]\qquad \tt \rightarrow \: \therefore x > 4[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Which of the following statements must be true about parallelogram ABCD? A) angle B+ angle D=180^ B) angle ABC cong angle CDA C) overline AC || overline BD D) overline BC cong overline CD
What are the x-coordinates of the solutions to this system of equations?
x² + y² = 16
y = x + 4
The x-coordinates are -4 and 0.
A 2-column table with 5 rows. Column 1 is labeled Number of Apples with entries 0, 1, 2, 3, 4. Column 2 is labeled Number of Slices with entries 0, 6, 12, 18, 24.
Use the table to find the constant of proportionality and the equation that represents the relationship.
Let x = number of apples and y = number of slices.
The constant of proportionality is
.
The equation for this relationship is
Answer:
The constant of proportionality is 6. This makes the relation y = 6x.
Step-by-step explanation:
Concept: As the number of apples are increasing, the number of slices are also increasing. Given that x is the number of apples and y is the number of slices. This means that y is directly proportional to x.
y ∝ x
Let the constant of proportionality be k.
y = kx
For x = 1, y = 6. So, k = 6.
For x = 2, y = 12. So, k = 6.
This follows for all the values.
Clearly, the constant of proportionality is 6.
The relationship will become y = 6x.
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A roll of paper towels is wound around a hollow cardboard tube. the
cardboard tube in the middle of the roll has an outside radius of 2.4 cm. the
thickness of the paper is 0.3 mm. the sequence of distances of the loops of
paper away from the center of the roll (in centimeters) is the following:
21, 22, az, a4 a5, ... = 2.40, 2.43, 2.46, 2.49, 2.52, ..
what is the radius of the 85th loop of paper, starting from the center of the
tube?
a. 4.95 cm
b. 4.86 cm
c. 4.92 cm
d. 4.89 cm
The correct Option is Option C: The radius of the cardboard tube of 85th loop of paper is 4.92cm
The arithmetic sequence is the sequence where every term is increased or decreased by a fixed number from the previous number.
Here the outer radius of the tube is 2.4 cm
the thickness of the paper is 0.3mm= 0.03cm
i.e. in every loop the increase in the radius of the loop is 0.03cm
then the radius in every sequence will be 2.40, 2.43, 2.46, 2.49, 2.52, .....
so here it is clear that it is an arithmetic sequence with a common difference of 0.03.
nth term of the sequence, aₙ = a₁ + (n - 1)d where a₁ is the first term, n is the index of the loop, and d is a common difference.
here a₁ =2.40
d=0.03
n=85
the radius of tube of the 85th loop will be= r= 2.40+(85-1)0.03= 2.40+ 2.52= 4.92
Therefore The radius of the cardboard tube of the 85th loop of paper is 4.92cm
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A cell phone plan charges $38 a month, and an additional $12 a month for each gb of data used. write an equation for the monthly cost (y) of the cell phone plan in terms of the number of gb of data used (x).
Answer:
y = 38 + 12x
Step-by-step explanation:
38is fixed cost per month and since the charge is $12 per GB, the variable cost is 12x where x is the GB used
PLEASE HELP ASAP!! Kate is trying to convert an area from meters squared to centimeters squared. She multiplied the area she had by 100 and got the wrong answer. What should she have multiplied the original area by?
1,000
1,000,000
100
10,000
Answer:
1m=100cm
1m squared=100cm×100cm
1msquared= 10000cm squared
She has to multiply 10000 to convert square centimetres to square meters. Hence option D is correct.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
We know that 1 meter is equal to 100 cm now for a 1-meter square the centimetres will be calculated as,
1m=100cm
1m squared=100cm×100cm
1msquared= 10000cm squared
Hence option D is correct.
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Kate used 555 grams of wool to knit a sweater, hat, and scarf. She used 5 times less grams for the hat than for the sweater. She used 5 more grams for the hat than for the scarf. How many grams of wool did she use to knit for each?
(Give explanation)
Answer:
Sweater: 392 [tex]\frac{6}{7}[/tex]
Hat: 78[tex]\frac{4}{7}[/tex]
Scarf: 83[tex]\frac{4}{7}[/tex]
Step-by-step explanation:
Set the sweater = x
The hat = [tex]\frac{1}{5}[/tex] x
The scarf = [tex]\frac{1}{5}[/tex] x + 5
x + [tex]\frac{1}{5}[/tex] x + [tex]\frac{1}{5}[/tex] x + 5 = 555
Combine like terms
1[tex]\frac{2}{5}[/tex] x + 5 = 555
Subtract 5 from both sides
1[tex]\frac{2}{5}[/tex] x = 550
Divide by 1[tex]\frac{2}{5}[/tex]
x = 392 [tex]\frac{6}{7}[/tex] This is how much wool was used for the sweater.
Divide by 5 to get the hat = 78 [tex]\frac{4}{7}[/tex]
Add 5 to that to get the scarf: 83[tex]\frac{4}{7}[/tex]
You are working in a lab and you need a solution of 22% acid. In the cupboard, you find a 10% and a 30% solution, but not a 22% solution. You will have to make your own 22% solution. You will need liters of the 10% and liters of the 30% to make 15 liters of a 22% solution?
The volume of 10% solution will be 6 l and 9 litre of the 30 % solution will be taken.
What is Volume ?Volume is the space occupied by a three dimensional object .
The concentration of solution required is 22% acid
The concentration of solution available is 10% and 30%
The total volume required is 15 liters
The formula for making a mixture is
Concentration = ( m₁x₁ +m₂x₂) / (x₁+x₂)
22 = (10 * x + 30 *(15 -x))/( 15)
10 x + 450 - 30x =330
-20x = -120
x = 6
The volume of 10% solution will be 6 l
and 9 litre of the 30 % solution will be taken.
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What is
-8/15of21/12
Someone pls help I don’t really understand graphing
what is the inverse of f(x)=(-2x+2)/(x+7)?
By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).
How to find the inverse of a function
In this question we have a rational function f(x) and finding its inverse consists in clearing x in terms of f(x). Prior any algebraic handling, we need to apply the following substitutions:
[tex]x \to y[/tex]
[tex]f(x) \to x[/tex]
[tex]x = \frac{-2\cdot y + 2}{y+7}[/tex]
x · (y + 7) = - 2 · y + 2
x · y + 7 · x = - 2 · y + 2
2 · y + x · y = - 7 · x + 2
y · (2 + x) = - 7 · x + 2
[tex]g(x) = \frac{- 7\cdot x + 2}{x + 2}[/tex]
By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).
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According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 15x11 – 6x8 + x3 – 4x + 3?
All potential rational roots of f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3, going by the rational rots theorem are {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}.
The rational root theorem suggests that for a polynomial function
f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x¹ + a₀, all potential rational roots can be given by the formula p/q, where p is the set of all factors of ±a₀ and q is the set of all factors of ±aₙ.
In the question, we are asked to find the potential rational roots of
f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3.
Comparing the given polynomial function with the standard polynomial function f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x¹ + a₀, we can say aₙ = 15, and a₀ = 3.
By rational root theorem, we know that all potential rational roots can be given by the formula p/q, where p is the set of all factors of ±a₀ and q is the set of all factors of ±aₙ.
Therefore, we can say that p = {factors of ±3} and q = {factors of ±15},
or, p = {±1, ±3}, q = {±1, ±3, ±5, ±15}.
Now, we can write all potential roots by calculating p/q.
p/q = {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}
Therefore, all potential rational roots of f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3, going by the rational roots theorem are {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}.
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ignore the answer i clicked on, i did not mean to click it
Answer:
20√2Step-by-step explanation:
The diagonal of a square is given as, √2 × side. Rearranging this formula to calculate the side of the square, we get, side = diagonal/√2 = (√2 × diagonal)/2 . Thus, the perimeter of the square can be calculated using the formula, P = 2√2 × diagonal.
Diagonal = 5 * 2 = 10
P = 2√2 * 10
P = 20√2
An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so the equation to solve is 2a + b = 15.7.
Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet. She writes and solves the equation 2 l plus 2 w equals 62 to find the width of the run.
Which statements are true of the solution? Check all that apply.
The value of w is 10 feet.
The value of w can be zero.
The value of w cannot be a negative number.
Substitution is used to replace the variable l with a value of 20.
The subtraction property of equality is used to isolate the term with the variable w.
Answer:
[c] The value of w cannot be a negative number.
[d] Substitution is used to replace the variable l with a value of 20.
[e] The subtraction property of equality is used to isolate the term with the variable w.
Step-by-step explanation:
To figure out which steps of the solution are true, let us solve.
2 l plus 2 w equals 62 -> 2l + 2w = 62
----
2l + 2w = 62
2(20) + 2w = 62 <- Substitution is used to replace the variable l with a value of 20.
40 + 2w = 62
2w = 22 <- The subtraction property of equality is used to isolate the term with the variable w.
w = 11
This means that the value of w is not 10 feet so the first option is incorrect. This shape is a rectangle, so the value of w cannot be 0. Since we cannot have a negative measurement, option three is incorrect. This leaves us with the last three options as our answer, shown by the work above.
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3. Use the following diagram to solve for x.
The value of x from the given diagram is -6
Lines and anglesLine is defined as the distance between two points. Given the line RP with the following measures
RP = 17
RQ = x + 14
QP = x + 15
Using the expression
RP = RQ + QP
Substitute
17 = x + 14 + x + 15
17 = 2x + 29
Determine the value of x
2x = 17 - 29
2x= -12
x = -6
Hence the value of x from the given diagram is -6
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What is the distance between the points (4, 5) and (10, 13) on a coordinate
plane?
Answer:
10
Step-by-step explanation:
square root of 6^2 + 8^2
Help ASAP, really stuck
The total length of the wire needed to make this shape is 162cm
Perimeter of a triangleThe perimeter of a triangle is the sum of the external side of the triangle.
Given the following parameters
Length of one side of the outside shape = 24cm
The side length of the smaller triangle = 24/4 = 6cm
The perimeter of the smallest triangle 3(6) = 18cm
The perimeter of the smaller triangle (at the middle) = 12(3) = 36cm
Total length of wire needed. = 3(24) + 3(18) + 36
Total length of wire needed = 72 + 54 + 36
Total length of wire needed = 162cm
Hence the total length of the wire needed to make this shape is 162cm
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What is the vertex of the quadratic function below y=-x^-2x-5
Answer:
(-1, -4)
Step-by-step explanation:
y = -x² - 2x - 5
y = -1(x² + 2x + 5)
y = -1(x² + 2x + 1 - 1 + 5)
y = -1(x² + 2x + 1) - 4
y = -(x + 1)² - 4
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Determine each segment length in right triangle . Triangle ABC with right angle marked at vertex B. Side AC, opposite vertex B, is labeled 14. Dashed segment is drawn from vertex B to point D on side AC. Angle BDA is marked right angle. Angles A and C both marked 45 degrees. Segment AD is labeled 7. (dragged tiles) 7(squareroot)3 7(square root) 7. 14. 14(squareroot)3. 14(square root)2
The segment length is 14 (square root)2
Given that Triangle ABC is right angle triangle
The vertex marked is B where side AC is the hypotenuse
The side of AC is at Vertex B is 14
The dash segment from vertex B to point D on side AC
Angle BDA is marked right angle .
Angles A and C both marked 45 degrees.
As shown in diagram
Triangle ABC is drawn according to the statement where B is vertex
The side lengths are 14
Now to find Another side length that is x
So , the equation formed is
x*cos45 = 14
x/√2 = 14
x = 14√2
Hence the length of the segment is 14√2
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Answer:
Step-by-step explanation:
The segment length is 14 (square root)2
Given that Triangle ABC is right angle triangle
The vertex marked is B where side AC is the hypotenuse
The side of AC is at Vertex B is 14
The dash segment from vertex B to point D on side AC
Angle BDA is marked right angle .
Angles A and C both marked 45 degrees.
As shown in diagram
Triangle ABC is drawn according to the statement where B is vertex
The side lengths are 14
Now to find Another side length that is x
So , the equation formed is
x*cos45 = 14
x/√2 = 14
x = 14√2
Hence the length of the segment is 14√2
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*HELP**NEEDS IT RIGHT NOW*
Without using a calculator, match each expression to the correct point.
Answer:
a=-2π
b=-17/3
c=-sqrt18
Step-by-step explanation:
eyeball it.
-2π≈-6.28
-17/3 is less than -5 but more than -6, so it's between those 2
-sqrt 18 is between -sqrt 16 and -sqrt 25, so it's a little less than -4
Assume that A TUVE AWXY. Which of the following congruence statements
are correct? Check all that apply.
A. ZX=ZU
B. ZY ZV
C. VU = YX
D. TV = WY
E. ZWE ZV
F. ZTE ZX
Congruent triangles are exact copies of each other. The correct options are 1, 2, 3, and 4.
What are congruent triangles?Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]
(|AB| denotes the length of line segment AB, and so on for others).
The following details about the two given congruent triangles TUV and WXY can be written,
[tex]\rm m\angle T = m\angle W \: or \: \: \angle T \cong \angle W\\\\\rm m\angle U = m\angle X\: or \: \: \angle U \cong \angle X \\\\\rm m\angle V = m\angle Y \: or \: \: \angle V \cong \angle Y \\\\\rm |TU| = |WX| \: \: or \: \: TU \cong WX\\\\\rm |VU| = |YX| \: \: or \: \: VU \cong VU\\\\\rm |TV| = |WY| \: \: or \: \: TV \cong TV[/tex]
Hence, the correct options are 1, 2, 3, and 4.
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Answer: A,,B, C, D
Step-by-step explanation:
LK
2(x+2y-x-1⁄2y+3);
When 2(5
4
01x + 2 y +6
Ox+2y+6
07x+8y+6
0176x+4y+3
is simplified, what is the resulting expression?
I am a nine digit number. my tens place is 2. ones place is 3 more than tens place . hundreds place is between 7 and 9. ten thousands place is 3 multiplied by tens place . lakhs place is successor of tens place. ten lakhs place is predecessor of hundreds place . crores place is between 8 and 10. ten crores place is 7 more than tens place. what number am i
Answer:
nmj
e
w
w
w
w
w
w
w
w
w
wej i2v82v2ivw8q
Step-by-step explanation:
h2iwv282vw8wvq
If g(x)=4x^(2)-16 were shifted 7 units to the right and 3 down, what would the new equation be?
The equation of the transformed function is h(x) = 4(x - 7)² - 19 option (C) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
g(x) = 4x² - 16
The above function shifted 7 units to the right and 3 down.
Applying transformation:
x → (x - 7)
G(x) = 4(x - 7)² - 16
G(x) → G(x) - 3
h(x) = 4(x - 7)² - 16 - 3
h(x) = 4(x - 7)² - 19
Thus, the equation of the transformed function is h(x) = 4(x - 7)² - 19 option (C) is correct.
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A man 1.8 m tall observes the angle of elevation of a tree to be 26 degrees, if he is standing bf 16 m from the tree find the height of the tree
The height of the tree is the man's height plus x.
[tex]\tan 26^{\circ}=\frac{x}{16}\\x = 16 \tan 26^{\circ}[/tex]
So, the height of the tree is [tex]\boxed{(16 \tan 26^{\circ}+1.8) \text{ m}}[/tex]
which of the sentence is true?
Answer:
The graph of the circle is not a function
Which algebraic expression is a trinomial?
Answer:
?
Step-by-step explanation:
because there is no picture or option
does this function represent a function? yes or no
Answer:b
Step-by-step explanation:
