Answers
Answer:
x = -2 , y = 3 , z = -5 thus the answer is C.)
Step-by-step explanation:
Solve the following system:
{3 x + 2 y - 3 z = 15
-2 x + 4 y + 2 z = 6
4 z + 12 = -8
Express the system in standard form:
{3 x + 2 y - 3 z = 15
-2 x + 4 y + 2 z = 6
0 + 0 + 4 z = -20
Express the system in matrix form:
(3 | 2 | -3
-2 | 4 | 2
0 | 0 | 4)(x
y
z) = (15
6
-20)
Write the system in augmented matrix form and use Gaussian elimination:
(3 | 2 | -3 | 15
-2 | 4 | 2 | 6
0 | 0 | 4 | -20)
Add 2/3 × (row 1) to row 2:
(3 | 2 | -3 | 15
0 | 16/3 | 0 | 16
0 | 0 | 4 | -20)
Multiply row 2 by 3/16:
(3 | 2 | -3 | 15
0 | 1 | 0 | 3
0 | 0 | 4 | -20)
Divide row 3 by 4:
(3 | 2 | -3 | 15
0 | 1 | 0 | 3
0 | 0 | 1 | -5)
Subtract 2 × (row 2) from row 1:
(3 | 0 | -3 | 9
0 | 1 | 0 | 3
0 | 0 | 1 | -5)
Add 3 × (row 3) to row 1:
(3 | 0 | 0 | -6
0 | 1 | 0 | 3
0 | 0 | 1 | -5)
Divide row 1 by 3:
(1 | 0 | 0 | -2
0 | 1 | 0 | 3
0 | 0 | 1 | -5)
Collect results:
Answer: {x = -2 , y = 3 , z = -5
Related Questions
Antonio invests 3000 at .10 interest compounded semianually for 12 years. Use the compound interest formula to calculate the compound amount for his investment
Answers
Answer:
A=9675.299
Step-by-step explanation:
A=p(1+r)^t
A compound amount
P is the principle amount invested
r : rate ( semiannually is 0.5 )
t=years ( semiannually 12*2=24)
A=3000(1+0.10/2)^24
A=9675.299
Create two equations, one that will model a linear relation and one that will not (e.g., y = -3x +2, y = 4x2 -7). Describe the ways by which you could determine whether it is a linear relation. Include calculations, graphs, tables of values and anything else you feel will support your argument.
Answers
Answer:
linear: y = x + 1
non-linear: y = x² + 1
Step-by-step explanation:
In a linear relationship, from one pair (x1,y1) to other one (x2,y2) that satisfies the equation, there is a constant k, so that k = (y2 - y1)/(x2 - x1).
Equation: y = x + 1
Computing some points as an example:
x | y
0 | 1
1 | 2
2 | 3
3 | 4
(2-1)/(1-0) = (3-2)/(2-1) = (4-3)/(3-2) = 1. Therefore, the equation is linear.
Equation: y = x² + 1
Computing some points as an example:
x | y
0 | 1
1 | 2
2 | 5
3 | 10
(2-1)/(1-0) ≠ (5-2)/(2-1) ≠ (10-5)/(3-2). Therefore, the equation is not linear.
What else would need to be congruent to show that triangle ABC cong Triangle XYX by ASA?
Answers
Explanation:
AC = XZ shows that the horizontal pieces are congruent. This is the "S" of "ASA" as it stands for the pair of congruent sides. We are also given angle A = angle X. This is one of the "A"s in "ASA" as it stands for pair of congruent angles.
What we're missing is the other pair of angles. We must pick C and Z because they help sandwich the two sides mentioned above. ASA has the two angles surrounding the sides; or the sides are between the angles. We can't pick B and Y, unless we were doing AAS which is a similar related idea. The order matters when it comes to ASA and AAS. However, AAS is the same as SAA.
Answer:
AC=XZ
so the correct answer is D
PLZ HELP!!! BRAINLIEST AND POINTS!!!
Answers
The answer is for this question is c
2(3x+2)+2(2x-1)
=10x+2
This is a polynomial
So the answer is c
Tony is opening a pizza restaurant and needs to determine the amounts of ingredients he will use in his pizzas. He wants the amount of dough for a medium pizza to be 3/2 times the amount of dough for a small pizza. And, he wants the amount of dough for a large pizza to be 5/2 times the amount of dough for a small pizza. Also, the amount of dough used for one large pizza should to be equal to the amount of dough used for one medium and one small pizza. So, he needs to determine how much dough to use for a small pizza. Use this information to complete the following tasks.
Answers
Answer:
If the amount of dough for a small pizza is S, for a large pizza is L and for a medium pizza is M, we have the equations:
M = (3/2)*S
L = (5/2)*S
L = M + S
First, we can convine the second and third equation and get:
(5/2)*S = M + S
and now we can replace M by the first equation:
(5/2)S = (3/2)*S + S = 5/2 S
so we have a trivial equation, S can be any number, this means that the system of equation is not well constructed.
For example, if S = 1Kg then:
M = (3/2)kg
L = (5/2)kg = (3/2)kg + 1 kg = 5/2kg
Answer:
The equation for a small pizza is, 3/2s + s = 5/2s.
Next, to combine like terms the equation is, 5/2s = 5/2s.
After that, for opposite operations you write, 5/2s - 5/2s = 0.
When you combine the like terms for the last equation, you come up with,
0 = 0.
The small sized pizza does not have a specific size and is no longer part of the equation. Its' size can be anything, and the other sized pizzas will equal their equation towards the small pizza, still representing their same value.
Step-by-step explanation:
cheese + sauce + dough + lots of meat + fire = happiness/pizza
(HopE ThIs HeLPs)
Calculate the equation of the line if two points are (1,6) and (5,0) Hint, you will have to find the slope of the line and then sub it into the equation y=mx+b
PLEASE ANSWER
Answers
Answer:
The equation is [tex]y=\frac{-3}{2} x-9[/tex]
Step-by-step explanation:
First, you will have to find the slope of the two points.To do that, you will have to use the formula : [tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
Our points are [tex](1,6)[/tex] and [tex](5,0)[/tex]
We will have to substitute the points into the formula.
[tex]m=\frac{0-6}{5-1}[/tex]
Then, we will simplify
[tex]m= \frac{-6}{4}[/tex]
We could simplify that fraction into [tex]\frac{-3}{2}[/tex]
So, our slope is [tex]\frac{-3}{2}[/tex]
We will have to pick a coordinate point, and choose. I chose [tex](1,6)[/tex]
We will substitute the x-value and the y-value of the coordinate point, including our slope, to calculate the y-intercept.
The formula we will be using is [tex]y=mx+b[/tex]
We will substitute in our values which will make it look like:
[tex]6=\frac{-3}{2} (1)+b[/tex]
We will then multiply [tex]\frac{-3}{2}[/tex] by [tex]1[/tex] which will stay the same.
Then, we will multiply [tex]\frac{-3}{2}[/tex] by [tex]6[/tex] which will equal [tex]-9[/tex]
[tex]-9=b[/tex]
Hence, the equation for our line is [tex]y=\frac{-3}{2} x-9[/tex]
Hope it helped:D
-Jazz
Maya is signing her daughter up for summer activities. Some of the activities cost $10, and some of them cost $20. Maya pays a total of $130 for 9 activities. How many of each activity did she sign her daughter up for?
Answers
Answer:
(5,4)
Step-by-step explanation:
10x + 20y = 130
x + y = 9
you can solve by substitution
x = 9 - y
10 (9 - y) + 20y = 130
90 - 10y + 20y = 130
90 + 10y = 130 (subtract 90 from both sides)
10y = 40
y = 4
Plug the answer back in the original equations to solve for x
x + 4 = 9 (subtract 4 from both sides)
x = 5
The number of activities that cost $10 is 4.
The number of activities that cost $20 is 5.
What are the linear equations that represent the question?
10a + 20b = 130 equation 1
a + b = 9 equation 2
Where:
a = number of activities that cost $10b = number of activities that cost $20What is the number of activities cost $20?Multiply equation 2 by 10
10a + 10b = 90 equation 3
Subtract equation 3 from equation 2
$10b = $40
b = $40 / $10
b = 4
What is the number of activities cost $10?Subtract 4 from 9: 9 - 4 = 5
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
#SPJ2
If an apple has a mass of 25 kg and a momentum of 50 kg-m/s
south, what is its velocity?
O 5 m/s south
O 125 m/s north
0 0.2 m/s south
2 m/s south
Answers
Answer:
2m/s south
Step-by-step explanation:
p = mv
Where p is the momentum, m is the mass, while v is the velocity.
Given that
m = 25kg
v = ?
p = 50kgm/s
Substituting the values into the formula.
50kgm/s = 25×v
50kgm/s = 25v
Divide both sides by 25
v = 50/25
v = 2m/s
From the option list, the answer is
2m/s south
1)Find the third side of a triangle when two sides of the triangle is 4 and the included angle measuring 89 degrees
2)you were asked by your teacher to add up the numbers 1 to 100. Please show all work
3)determine if the foci for the following ellipse are correct and explain your reasoning 7x2 + 8y2 = 30; foci: (sqrt11, 0), (-sqrt11, 0)
Answers
Answer:
1) The length of the third side is 5.607 units
2) The sum of the numbers from 1 to 100 is 5050
3) For the x-axis, foci: ((√15/28), 0) and (-(√15/28), 0)
For the y-axis, foci: (0, (√15/28)) and (0, -(√15/28))
Step-by-step explanation:
1) When two sides of the triangle are equal to 4 then the triangle is an isosceles triangle
Given that the included angle (the angle between the two sides) is 89°, we have;
The other two base angles are equal to {180 - 89)/2 = 91/2 = 45.5°
Therefore, we have from cosine rule;
a² = b² + c² - 2·b·c·cos(A)
We note that the angle opposite the third side is the included angle 89°, therefore, when we put a as the third side in the above equation, we have;
a² = 4² + 4² - 2×4×4×cos(89°)
a² = 31.44
a = 5.607
The length of the third side is 5.607 units
2) The numbers 1 to 100 form an arithmetic series with the first term, a = 1 and the common difference, d = 1 with the number of terms n = 100
The sum of an arithmetic progression, Sₙ, is given as follows;
[tex]S_n = \dfrac{n}{2}\cdot (2 \cdot a + (n - 1) d)[/tex]
Therefore, by plugging in the values, we have;
Sₙ = 100/2*(2*1 + (100 - 1)*1) = 100/2*(101) = 5050
The sum of the numbers from 1 to 100 is 5050
3) The foci of an ellipse 7·x² + 8·y² = 30 is found as follows;
Dividing both sides of the equation by 30 gives;
7/30·x² + 8/30·y² = 30/30
7/30·x² + 8/30·y² = 30/30
7/30·x² + 4/15·y² = 1
Which is of the form;
x²/a² + y²/b² = 1
For the x-axis we have
c² = a² - b²
c² = 30/7 - 15/4 = 15/28
h = 0, k = 0
Foci: ((√15/28), 0) and (-(√15/28), 0)
For the y-axis, we have;
x²/b² + y²/a² = 1
The foci are then (0, (√15/28)) and (0, -(√15/28)).
Let ƒ(x) = x^2 + 2x and g(x) = 2x. Evaluate the composition (ƒ ∘ g)(2).
Answers
Answer:
The answer is option D.
Step-by-step explanation:
f(x) = x² + 2x
g(x) = 2x
To find (ƒ ∘ g)(2) first find (ƒ ∘ g)
To find (ƒ ∘ g) wherever you see x in f(x) replace it with g(x)
That's
(ƒ ∘ g) = (2x)² + 2(2x)
= 4x² + 4x
Substitute 2 into the expression
That's
(ƒ ∘ g)(2) = 4(2)² + 4(2)
= 4(4) + 8
= 16 + 8
= 24
Hope this helps you.
The equations 3 x minus 4 y = negative 2, 4 x minus y = 4, 3 x + 4 y = 2, and 4 x + y = negative 4 are shown on the graph below. On a coordinate plane, there are 4 lines. Green line goes through (0, negative 4) and (2, 4). Blue line goes through (negative 2, 2) and (2, negative 1). The pink line goes through (negative 2, negative 1), and (2, 2). The purple line goes through (negative 2, 4) and (0, negative 4). Which is the approximate solution for the system of equations 3 x + 4 y = 2 and 4 x + y = negative 4? (–1.4, 1.5) (1.4, 1.5) (0.9, –0.2) (–0.9, –0.2)
Answers
Answer:
(–1.4, 1.5)
Step-by-step explanation:
The blue line and the purple line are the lines corresponding to the equations of interest. Their point of intersection is in the 2nd quadrant, so is nearest to ...
(–1.4, 1.5)
__
It can be useful to understand that for equations in standard form:
ax +by = c
the x- and y-intercepts are ...
x-intercept: c/a . . . . value of x for y = 0y-intercept: c/b . . . . value of y for x = 0__
For the equations of interest, the first has intercepts of ...
x=2/3, y=1/2 . . . . graphed line makes a 1st-quadrant triangle with the axes (blue line)
And the second has intercepts of ...
x=-1, y=-4 . . . . graphed line makes a 3rd-quadrant triangle with the axes (purple line)
Since the purple line has a steeper slope, the point of intersection of the lines will be in the 2nd quadrant. There is only one 2nd-quadrant answer choice: (-1.4, 1.5).
Answer:
(–1.4, 1.5)
Step-by-step explanation:
Please can someone help I have tried many times
Answers
Answer:
My answer is in the attached picture
Step-by-step explanation:
Enlarged by a scale of 2 using P as the centre of enlangment.
Answer:
Step-by-step explanation:
All you should do is to draw lines that conect each node of the triangle with the center of enlargement .
Triangle J K L is shown. Angle J K L is 120 degrees and angle K L J is 40 degrees. The length of K L is 2 and the length of J L is k. Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction What is the approximate value of k? Use the law of sines to find the answer.
Answers
Answer:
[tex]k \approx 5$ units[/tex]
Step-by-step explanation:
In Triangle JKL
[tex]\angle K=120^\circ\\\angle L=40^\circ\\KL=2\\JL=k[/tex]
We want to determine the approximate value of k using the law of sines.
[tex]\angle J+\angle K+\angle L=180^\circ $ (Sum of angles in a \triangle)\\\angle J+120^\circ+40^\circ=180^\circ \\\angle J=180^\circ-(120^\circ+40^\circ)=20^\circ[/tex]
Using Law of Sines
[tex]\dfrac{k}{\sin K} =\dfrac{j}{\sin J} \\\dfrac{k}{\sin 120} =\dfrac{2}{\sin 20} \\k=\sin 120 \times \dfrac{2}{\sin 20}\\k=5.06\\k \approx 5$ units[/tex]
Answer:
5.1
Step-by-step explanation:
Right on EDU
Please help me! This is urgent!!!!!
Answers
Answer:
The first one would be reasonable, because the minutes late is 50, which is a little under 1 hour.
Explanation:
The 2nd one uses a negative value for m, you can't use a negative value when adding time.
The 3rd and fourth have fairly large numbers which are not typical for parents picking up their kids.
Can someone please help me please I really need help please help
Answers
Answer:
K'(4, -4)L'(8, -4)M'(8, 8)N'(4, 8)Step-by-step explanation:
Dilation centered at the origin multiplies every coordinate value by the scale factor.
K(1, -1) ⇒ K' = 4(1, -1) = (4, -4)
L(2, -1) ⇒ L' = 4(2, -1) = (8, -4)
M(2, 2) ⇒ M' = 4(2, 2) = (8, 8)
N(1, 2) ⇒ N' = 4(1, 2) = (4, 8)
Hello does anybody know what the answer to this question is : 32² x 4 Will give brainliest :)
Answers
Answer:
4096
Step-by-step explanation:
used a calculator but u always do indicies first due to bidmas
Answer:
4096
Step-by-step explanation:
The little two on top of the 32 means squared or that we need to multiply 32 by itself.
So 32*32 equals 1024
Then we multiply it by 4 to give us 4096.
The lengths of the sides of a triangle are in the ratio 3:4:5. Find the lengths of the sides of this triangle if its perimeter is 96 cm.
Answers
Answer: 16 one side 32 second side 48 third side
Step-by-step explanation:
16;32;48
3;4;5
Answer:
24, 32, 40
Step-by-step explanation:
We know that the ratio of the sides is 3:4:5, and that total is 96.
First I tested out some numbers by multiplying them by 3, 4, and 5
Eventually I got to 8;
8×3:8×4:8×5 --> 24:32:40 --> 3:4:5
24+32+40=96
Meaning, the sides were 24, 32, and 40
Hope this helps, and good luck!
Mrs Lim bought a number of plates at an average price of $6. She decided to buy another plate which cost $18. The average price of all the plates then became $8. What was the total number of plates Mrs Lim bought in all?
Answers
Answer: 6
Step-by-step explanation:
Let x represent the number of plates bought for $6
Let y represent the Total number of plates bought = x + 1
Remember that Mrs. Lim bought another plate for $18
Total cost ÷ Total plates = Average Cost
[tex]\dfrac{6x+18}{x+1}=8\\[/tex]
6x + 18 = 8(x + 1)
6x + 18 = 8x + 8
18 = 2x + 8
10 = 2x
5 = x
y = x + 1
= 5 + 1
= 6
The coordinates of the vertices of a polygon are shown below. D(–4, 5), E(–1, 5), F(1, 2), and G(–1, –1) What type of polygon is this figure? heptagon hexagon octagon quadrilateral
Answers
Step-by-step explanation:
Since the polygon has four vertices (D,E,F and G), it is a quadrilateral (4 vertices).
Answer:quadrilateral
Step-by-step explanation:
It has four points, so it has four sides which makes it a quadrilateral.
Tony has a hosepipe. The length of the hosepipe is 20 m. Tony stores the hosepipe on a reel. The weight of the reel is 1.4 kg. 1 ⁄ 2 metre of the hosepipe has a weight of 150 grams. Work out the total weight of the hosepipe and the reel.
Answers
Answer:
the total weight of the hosepipe and the reel is 7.4 kg
Step-by-step explanation:
First, we need to find the weight of the hosepipe, we know that 1/2 metre of the hosepipe has a weight of 150 grams, therefore we can conclude that 1 meter has a weight of (150)(2) = 300 grams.
If one meter weighs 300 grams, then 20 meters have a weight of [tex]20(300) = 6000[/tex] grams. But since 1000 grams are 1 kg, this would be equivalent to 6 kg.
Now, to find the total weight of the hosepipe and the reel we are going to sum up the 2 weights:
Total weight = hose pipe weight + reel weight
Total weight = 6 kg + 1.4 kg
Total weight = 7.4 kg.
Therefore, the total weight of the hosepipe and the reel is 7.4 kg
I’m confused can ya help me
Answers
Answer:
C & D
Step-by-step explanation:
x² + 3x - 3 = 0
a = co efficient of x² = 1
b= co efficient of x = 3
c = constant = -3
roots = (-b ± [tex]\sqrt{b-4ac}[/tex])/2a
= (-3±[tex]\sqrt{3^{2}-4*1*[-3]}[/tex] )/2*1
= (-3±[tex]\sqrt{9+12}[/tex])/2
= (-3±√21)/2
[tex]x = \frac{-3+\sqrt{21}}{2} ; x =\frac{-3-\sqrt{21}}{2}[/tex]
42. Carmen spends 5 minutes, correct to the nearest minute, preparing one meal. She spends a total time
of T minutes preparing 30 meals. Between what limits does lie?
[2]
Answers
Answer:
4.5 < T < 5.5
Step-by-step explanation:
Nearest 5 minutes could be 4.5 to 5.49
The computation of the limits in between is shown below:
Now Multiply these numbers by 30
4.5 × 30 = 135
5.4 × 30 = 162
5.5 × 30 = 165
We can easily round 5.5 would to 6, since we cannot use 5.5.
Therefore
135 < T < 162
Therefore If the correct answer is 135 < T < 165
So it must be 4.5 < T < 5.5
9:PLEASE HELP Evaluate the expression 2m+n for m=7 and n=2
Answers
Answer:
16
Step-by-step explanation:
Let's find out you're equation together!
You're equation could be turn into (2 * 7)+2.
And, that equation is equal to 14 + 2.
so, it is 16.
It would take an hour for plane A to meet plane B. If the distance between them will be 200 miles in 45 minutes, how far are they now?
Answers
Answer: 125 miles
if you do the math you will get the same answer.
Answer:
800 miles
Step-by-step explanation:
For the reaction of nitrogen gas and hydrogen gas to make methane, describe FOUR stresses would shift the equilibrium to the left toward the reactants? (10 points) N2(g) + 3 H2(g) ⇌ 2 NH3(g) + Energy
Answers
Answer:
1) decrease in pressure
2) increase in temperature
3) increase in volume
4) accumulation of the product in the reaction system
Step-by-step explanation:
Equilibrium is generally defined as a state in which there is no observable change in the system over a period of time. In chemical systems, equilibrium is dynamic, this implies that the toward and reverse reactions proceed at the same rate.
The Le Chateliers principle states that if an external constraint such as change in temperature, pressure or concentration is imposed on a reaction system in equilibrium, the equilibrium position will shift so as to annul the constraint.
For the system shown in the question, low pressure, increase in volume, increase in temperature and accumulation of the product in the reaction system will make the equilibrium position to shift towards the left (reactants side)
what's the answer to
1067×6740
Answers
Answer:
(1067)(6740)
=7191580
Step-by-step explanation:
I hope this help you :)
If you need another thing just let me know.
What is the area of the polygon below?
Answers
Answer:
28cm^2
Step-by-step explanation:
I find the area of the shape, simply add the square engulfed within it
I was able to find 28! So 28cm^2
Hope this helps
Answer: 28.5 square units
Step-by-step explanation: Count the whole squares in the figure then figure the areas of the triangular areas around the sides. Whole squares 3+5+5+5 = 18
Left side: 5/2 = 2.5
Top (2)( 3/2) = 3
Right: 4/2= 2
Bottom 6/2 = 3
Sum of triangular areas: 10.5
Add squares and triangles:
18+10.5= 28.5
It may be possible to compute the area by using the Pythagorean Theorem to get the lengths of the bases and height, but that's a bit more complicated!
what is the standard deviation of {0, 3, 1, 1, 0, 5, 1, 0, 3, 0},
Answers
Answer:
1.7
Step-by-step explanation:
Answer this as quick as possible please! (NO EXPLANATION REQUIRED!) <3
Answers
Answer: 9 Apples
Step-by-step explanation:
Given the following :
Total number of bags = 12
Mean of the distribution(m) = 8
Number of apples (x):
6 - - - - 7 - - - - 8 - - - - 9 - - - - 10
Frequency (f) :
1 - - - - 4 - - - - 2 - - - - 3 - - - - 1
Therefore :
Let number of apples in the 12th bag = y
Frequency of 12th bag : (12 - 11) = 1
Mean of distribution(m) :
Sum of ( f * x) / sum of f
Sum of (f * x) = (6*1)+(7*4)+(8*2)+(9*3)+(10*1)+(y*1)
Sum of (f * x) = (6+28+16+27+10+y) = 87 + y
Sum of f = 12
From :
m = Sum of ( f * x) / sum of f
8 = (87 + y) / 12
87 + y = 12 * 8
87 + y = 96
y = 96 - 87
y = 9
Number of apples in 12th bag is 9 apples
what is 1+1, is the answer a letter and why
Answers
Answer:
2
Step-by-step explanation:
Lets say John had 1 apple and Sarah gave him 1 more apple. John would now have 2 apples.
Hope this helps :)
Answer:
B
Step-by-step explanation:
1=a 2=b