9514 1404 393
Answer:
(x, y) = (-1, 2)
Step-by-step explanation:
The augmented matrix for this system of equations is ...
[tex]\left[\begin{array}{cc|c}2&3&4\\5&8&11\end{array}\right][/tex]
Your graphing calculator or web solver will tell you the reduced row-echelon form of this matrix is ...
[tex]\left[\begin{array}{cc|c}1&0&-1\\0&1&2\end{array}\right][/tex]
The solution is (x, y) = (-1, 2).
_____
The determinant of the coefficient matrix is ...
(2)(8) -(5)(3) = 1
The inverse of the coefficient matrix is the transpose of the cofactor matrix, divided by the determinant. For a 2×2 matrix, that is the original matrix with the diagonal terms swapped, and the off-diagonal terms negated, then divided by the determinant. Since the determinant is 1, the inverse of the coefficient matrix is ...
[tex]\left[\begin{array}{cc}8&-3\\-5&2\end{array}\right][/tex]
Multiplying this by the constant vector gives the solution vector.
x = (8)(4) +(-3)(11) = 32 -33 = -1
y = (-5)(4) +(2)(11) = -20 +22 = 2
(x, y) = (-1, 2)
_____
Additional comment
Many modern calculators have so many functions that there are likely many you will never use. It is a good idea to learn to use the functions available for solving the kinds of problems you run across. Recent model calculators make it easy to enter matrices and perform various functions on them.
For solving systems of linear equations, the RREF (reduced row-echelon form) function is pretty useful. The bottom row of the result will tell you the kinds of solutions; the right column(s) will tell you what they are.
The graph represents the relationship between the number of rocks a child collects, r, over a number of weeks, w. Which function can be used to determine the number of rocks, r, a child will collect after w weeks? r = 15w + 5 r=115w+5 r = 5w + 15 r=15w+15
♡ The Question/Task(s)! ♡
-Which function can be used to determine the number of rocks, r, a child will collect after w weeks?
*୨୧ ┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Answer(s)! ♡
-The answer is, r = 5w + 15!
I apologize in advance if the answer is incorrect! ♡
*୨୧ ┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Explanation(s)/Step-By-Step! ♡
-No Explanation(s)/Step-By-Step provided!
*୨୧ ┈┈┈┈┈┈┈┈┈ ୨୧*
♡ Tip(s)! ♡
-No Tip(s) Provided!
Plz help I need help
Answer:
the ratio should be 4.754
Step-by-step explanation: ez kiddo i have the answer key
Use the fundamental trigonometric identities to simplify the expression. There is more than one correct form of the answer.
5 csc φ tan φ + 5 sec φ
Answer:
10sec φ
Step-by-step explanation:
5 csc φ tan φ + 5 sec φ
= 5 (1/sin φ) * (sin φ/cos φ) + 5 sec φ
= 5 (1/cos φ) + 5 sec φ
= 5 sec φ + 5 sec φ
= 10 sec φ
help please i can't find anything
Answer:
The answer is -40
Step-by-step explanation:
Answer: 19x - 216/6
Explanation: Hope this helps!
1. A sample of bacteria cells in a petri dish increases by 50% every hour. A scientist
starts with a sample of 30 bacteria cells. Write an equation that can be used to
determine the number of cells after x hours.
2. how many bacteria cells will be present in the dish after 3 hours?
3.how many bacteria cells will be present after 12 hours?
The equation is, [tex]\rm y = 30(1+0.50)^x[/tex] 101.25 bacteria cells after 3 hours, and 3892 bacteria cells after 12 hours will be present,
It is given that the sample of bacteria cells in a petri dish increases by 50% every hour, a scientist starts with a sample of 30 bacteria cells.
It is required to find the equation that can be used to determine the number of cells after x hours.
What is Exponential Growth?It is defined as increasing an amount by a definite percentage over the span of a time, the original amount increases exponentially.
We know the Exponential Growth equation written as:
[tex]\rm y= a(1+r)^t[/tex]
Where y = total amount,
a = starting amount
r = the growth rate/exponential decay rate as a decimal
t = number of growth periods.
We have a = 30
r = 50% = 0.50
t = x
Putting these values in the Exponential Growth equation, we get:
[tex]\rm y = 30(1+0.50)^x[/tex] this is the equation for Exponential Growth.
If x = 3 hours, then:
[tex]\rm y = 30(1+0.50)^3 \Rightarrow 30(1.50)^3\Rightarrow 30(3.375)\Rightarrow 101.25\\[/tex]
If x = 12 hours, then:
[tex]\rm y = 30(1+0.50)^1^2 \Rightarrow 30(1.50)^1^2\Rightarrow 30(129.746)\Rightarrow 3892.39\approx 3892[/tex]
Thus, the equation that can be used to determine the number of cells after x hours is, [tex]\rm y = 30(1+0.50)^x[/tex], that 101.25 bacteria cells will be present in the dish after 3 hours, and 3892 bacteria cells will be present after 12 hours.
Learn more about Exponential Decay here:
brainly.com/question/2193820
Answer:
1). y=30(1+.50)^x
2). 101.25
3). 3,892.39 Bacteria cells
Step-by-step explanation:
A paper airplane was thrown from the top of a tall building.The height of the paper airplane above the ground can be found using the function `y=-1.5x+60` , where `x` is the time in seconds the airplane has been in the air.
Jayden made this table to figure out how high the plane was at different times.
0 | 60
10 | 45
20 | 30
30 | 15
40 | 0
How would the equation `y=-1.5x+60` change if the height at 0 seconds was 75?
The new equation will be [tex]y=-1.5x+75[/tex]
Since the height at 0 seconds will be 75, it means that 15 has been added to the height at each time instant.
As a result, the gradient will remain [tex]-1.5[/tex], but the y-intercept will become 75. Therefore the equation will only change at the intercept.
The new equation will be [tex]y=-1.5x+75[/tex]
Learn more about slopes and intercepts: https://brainly.com/question/1201010
2 − 8 ÷ (24 ÷ 2)
............
............
Answer:
1.333333
Step-by-step explanation:
1) Simplify 24 / 2 to 12.
2 - 8 / 12
2) Simplify 8 / 12 to 0.666667.
2 - 0.666667
3) Simplify.
1.333333
what is the next three terms in this sequence -4, -2, 1, 5, 10...
Answer:
16, 23, 31, i think
Step-by-step explanation:
Answer:
16,23,31
Step-by-step explanation:
it is non linear because it it doesn't go up by the same amount of numbers each time however we can see that it goes up by 2 then 3 then 4 then 5 so from this we can infer that it will only go up 6 then 7 then 8 ,10 + 6 + 16 16 + 7 is 23 and 23 + 8 is 31
Hope it helps?
One side of a 216 square foot rectangular room is 18 feet. How long is the other side?
Answer:
216 -18-18= 180 /2= 90
Step-by-step explanation:
thus is how I figured it out cause 2 aides of a rectangle are the same so it would leave the other 2 sides as equal too
Simplify: ( 36-4 )*5
Answer:40
Step-by-step explanation:
[(√36-4)³]*5
[(6-4)³]*5
(2)³ * 5
= 2*2*2 = 8
8*5 = 40
Starting on the positive x-axis and moving 1/3 of the way around a circle that has radius 3 m, how far would one travel?
11.
Describe how the graph of y = |x| – 4 is like the graph of y = |x| and how it is different.
A. The graphs are the same shape. The y-intercept of y = |x| is 0 and the x-intercept of y = |x| – 4 is –4.
B. The graphs have the same y-intercept. The graph of y = |x| – 4 is steeper than y = |x|.
C. The graphs are the same shape. The y-intercept of y = |x| is 0 and the y-intercept oof y = |x| – 4 is –4.
D. The graph of y = |x| – 4 is the same as y = |x|.
Answer:
D. The graph of y = |x| – 4 is the same as y = |x|.
Step-by-step explanation:
The graph y=|x|-4 is obtained from the graph y=|x| dy moving down 4 units the graph y=|x| along the y-axis (see, if x=0, then for y=|x|, y=0 and for y=|x|-4, y=-4).
These two graphs have the same form.
...................................................................................................................................................
The graph of y=|x|-4 is the same as y=|x|.
......................
Answer:
The answer is A
Step-by-step explanation:
A store purchased a digital camera and marked it up 100% from the original cost of $863.57. A week later, the store placed the digital camera on sale for 40% off. What was the discount price?
Answer:
1,036.28
Step-by-step explanation:
what is the y intercept of the line that passes through the point 3, 4 and has a slope of 3
(0, -5)
Step-by-step explanation:
Since we are given the slope and a point on the line, we can use these to write the point-slope form of the equation of the line, which looks this this:
[tex]y - y_1 = m(x - x_1)[/tex]
where [tex](x_1, y_1)[/tex] is the point on the line and m is the slope. So the equation has the form
[tex]y - 4 = 3(x - 3)[/tex]
To find the y-intercept, set x = 0 to get
[tex]y - 4 = 3(0 - 3) \Rightarrow y - 4 = -9[/tex]
Solving for y, we get
[tex]y = -5[/tex]
Therefore, the coordinates of the y-intercept is (0, -5).
which one of these answers is the actual one
Jackson bought paint for $11.50 per can. How much would his total cost be if he needed 4 cans of paint?
Multiply number of cans by price per can:
4 x 11.50 = 46
They need $46
Answer:
$46
Step-by-step explanation:
Cuz im Smart
What is the Slope of the equation x = -4
A -4
B Undefined
C 0
D 1
Answer:
B
Step-by-step explanation:
Since x= −4 is a vertical line, the slope is undefined.
Answer:
B.) Undefined
Step-by-step explanation:
By graphing the equation, it will form a vertical line. This is an undefined slope.
Linear Algebra.
Can anyone help with the 3rd task
Use determinants to decide if the set of vectors is linearly independent.
Answer:
Jajkmama
Step-by-step explanation:
Use iteration to find the solution to the equation 2x2 – 9x = 4, the answer is between 4 and 6.
HELP ME SOS THIS IS DUE IN 40 MIS HELP ME PLEASE
Step-by-step explanation:
Ordered candy canes:
30*49 = 1470This is 3 less than the number of students.
Mr. Kellenberger calculated the required packs wrongly.
He should have ordered one more pack.
Correct way of calculation:
1473/30 = 49.1, this number needs rounding up, so 50 packs requiredThe graph shows the relationship between the distance traveled by car and the amount of fuel used by the car. What is the constant of proportionality for this graph?
1
1/20
2
20
Answer:
20
Step-by-step explanation:
Find the intersection of the circle x^2+ y^2 = 29 and y = x - 3 algebraically
Answer:
Intersections: (-2, -5) and (5, 2)
Hope this helps!
[tex]x^{2} +y^{2} =29[/tex] circle and [tex]y=x-3[/tex]
[tex]y^{2} =29-x^{2}[/tex] [tex]\left ( y \right )^{2}=\left ( x-3 \right )^{2}[/tex]
[tex]y^{2}=x^{2}-6x+9[/tex]
[tex]\Rightarrow x^{2} -6x+9=29-x^{2}[/tex]
[tex]\Rightarrow 2x^{2} -6x-20=0[/tex] [tex]\Rightarrow 2x^{2} -3x-10=0[/tex]
[tex]x^{2} -5x+2x-10=0[/tex] [tex]\Rightarrow x\left ( x-5 \right ) +2\left ( x-5 \right )=0[/tex]
[tex]x=5, \ x=-2[/tex]
[tex]\Rightarrow y=29-25=4\pm 2[/tex] [tex]\Rightarrow y=29-4=25\pm 5[/tex]
The circle intersects the line at [tex]\left ( 5,2 \right )[/tex] and [tex]\left ( -2,-5 \right )[/tex].
What is 230−−√+1030−−√ in simplified radical form?
2030−−√
2060−−√
1230−−√
1260−−√
Answer: B
Step-by-step explanation: Hope this helps :)
What is the measure in each angle? A? B? C?
Answer:
∠A = 48°, ∠B = 48°, and ∠C = 84°
Step-by-step explanation:
AB = CB Given
m ∠A = m ∠C If opposite sides are =, then those opposite angles are =
6(x - 3) = 4(x + 1)
6x - 18 = 4x + 4
2x - 18 = 4
2x = 22
x = 11
m ∠A = 6(11 - 3) = 6(8) = 48°
m ∠C = 4(11+ 1) = 4(12) = 48°
The sum of the angles in a triangle = 180°
48° + 48° m ∠B = 180°
96°+ m ∠B = 180°
84° = m ∠B
) How many arrangements of the 26 different letters of the alphabet (with no repeats) are there in which all the consonants appear before all the vowels (a,e,i,o,u)
Answer:the answer is 21 with np repeats
Step-by-step explanation:
This graph represents −3x+y=−4. Which ordered pair is in the solution set of −3x+y≥−4?
Answer: When an inequality shows a multiple of -4 = -8 or -16 then we know it is a parallel line and therefore could be a straight line continuation - we see -3(1) -(5) = -8 and -3(5) -(1) = -16 therefore (1 -5) and (5 -1) are both ordered pairs
-3 (2) + 2 = -4 shows 2 and 2 are an ordered pair of system -3 (0) -4 = -4 shows 0 and -4 is an ordered pair of the system
Step-by-step explanation:
-3x + y = - 4 when we +3x both sides we get y = 3x - 4 so when y intercept starts in -4 we an assume if x is positive and as x is top heavy and not equal to 1 we have a fraction x = (y + 4) / 3 and the only thing we hanged to find this fraction value for x was to eliminate 3 and separate x through dividing by x to see other coordinates see attachment for ordered pairs by seeing each coordinate on the graph
A rectangular field has the area equal to that of a square field of side 60m.if the breadth of the rectangular field is 32m, find it's length
Given -
Area of rectangular field = Area of square field side of square = 60mbreadth of the rectangular field = 32mTo find -
length of the rectangular fieldSolution -
Area of square = side × side = (60 × 60)m² =
Area of square =3600m²
Hence,
Area of rectangular field = Area of square field = 3600m²
Area of rectangular field = l × b = 3600m²
=> l × 32m = 3600m²
=> l = [tex]\sf{\frac{3600}{32}\:m}[/tex]
=> l = 112.5m
so, the length = 112.5m
elp
37(37)
What is 37 to the 37th power
Answer:
1.0555135e+58
Step-by-step explanation:
How many lines of symmetry does a regular polygon with 10 sides and 10 congruent interior angles have?
Answer:
ten
Step-by-step explanation:
I hope this helps!!!!!!!!!
