Given:
The system of equations is:
[tex]x+3y=5[/tex]
[tex]x-3y=-1[/tex]
The given matrices are [tex]\left[\begin{array}{cc}5&3\\-1&-3\end{array}\right] [/tex], [tex]\left[\begin{array}{cc}1&5\\1&-1\end{array}\right][/tex], [tex]\left[\begin{array}{cc}1&3\\1&-3\end{array}\right][/tex].
To find:
The correct names for the given matrices.
Solution:
We have,
[tex]x+3y=5[/tex]
[tex]x-3y=-1[/tex]
Here, coefficients of x are 1 and 1 respectively, the coefficients of y are 3 and -3 respectively and constant terms are 5 and -1 respectively.
In the x-determinant, the coefficients of x are in the first column and the constant terms are in the second column. So, the x-determinant is:
[tex]\left[\begin{array}{cc}1&5\\1&-1\end{array}\right][/tex]
In the y-determinant, the constant terms are in the first column and the coefficients of y are in the second column. So, the y-determinant is:
[tex]\left[\begin{array}{cc}5&3\\-1&-3\end{array}\right] [/tex]
In the system determinant, the coefficients of x are in the first column and the coefficients of y are in the second column. So, the system determinant is:
[tex]\left[\begin{array}{cc}1&3\\1&-3\end{array}\right][/tex]
Therefore, the first matrix is y-determinant, second matrix is x-determinant and the third matrix is the system determinant.
Plsssss ans I am suffering
Find the Length of ST
Step-by-step explanation:
Consider Similarity and enlargement
To get the enlargement factor,
Take the ratio result of any two similar sides. i.e
PQ/AB = 3.6/2 = 1.8
The enlargement factor is 1.8
To get ST, consider ED then multiply it by the enlargement factor. i.e
= 5 x 1.8
= 9
Find the value of PR if Q is between P and R
when PQ=25, PQ=2x+1, and QR=x.
X
ат
X=8
Answer:
[tex]PR = 37[/tex]
Step-by-step explanation:
Given
[tex]PQ = 25[/tex]
[tex]PQ = 2x +1[/tex]
[tex]QR = x[/tex]
Required
PQ
Since Q is between the given points, then:
[tex]PR = PQ + QR[/tex]
This gives:
[tex]PR = 2x + 1 + x[/tex]
Collect like terms
[tex]PR = 2x + x+ 1[/tex]
[tex]PR = 3x + 1[/tex]
Next, solve for x
We have:
[tex]PQ = 25[/tex]
[tex]PQ = 2x +1[/tex]
This gives:
[tex]2x + 1 = 25[/tex]
Collect like terms
[tex]2x = 25 -1[/tex]
[tex]2x = 24[/tex]
Divide by 2
[tex]x = 12[/tex]
So:
[tex]PR = 3x + 1[/tex]
[tex]PR = 3 * 12 + 1[/tex]
[tex]PR = 37[/tex]
a solid wooden cube has 4.35cm long.calculate the volume of the cube
Answer:
82.31
Step-by-step explanation:
I believe this is correct, if it isn't feel free to let me know and I will fix it. I'm sorry in advance if this is incorrect.
Graph the equation. Let x3, 2, 1, 0, 1, 2, and 3. y=3x-1
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The attachment shows the table of point values and the graph.
Ahmed can 8 1/3 km in one hour. how much distance will he cover in 2 2/5
Answer:
In 2 2/5 hours, he will cover 20 km.
Step-by-step explanation:
Given that,
Ahmed can 8 1/3 km in one hour.
We need to find the distance he cover in 2 2/5 h.
In 1 hour = 8 1/3 km = 25/3 km
2 2/5 hour means 12/5 hour
In 12/5 hour = 12/5 × 25/3 km
= 20 km
So, in 2 2/5 hours, he will cover 20 km.
I 0 ×I 1× I 2 ×I 3×I 4
Answer:
the answer is twelve by multiplying them all.
Answer:
2 , 40,420
Step-by-step explanation:
10 × 11 × 12 × 13 × 14
1,320 × 182
2,40,240
Which statement correctly compares the centers of the distributions?
A. The median penguin height is greater at Park Zoo than at Cityview Zoo.
B. The median penguin heights are the same.
C. The median penguin height is greater at Cityview Zoo than at Park
Zoo.
D. The range of penguin heights is greater at Cityview Zoo than at
Park Zoo.
The median penguin height is greater at Cityview Zoo than at Park
Zoo, Option C is correct.
Mode is the most occuring number.
The range is the difference of the highest value and the lowest value.
The median is the middle value in a set of data
After finding the range and medians of the given data.
The median penguin at Cityview Zoo is 42 cm tall,
The median penguin at Park Zoo is barely 41 cm tall.
Cityview Zoo's median penguin height is higher than that of Park Zoo.
Hence, the median penguin height is greater at Cityview Zoo than at Park Zoo.
To learn more on Statistics click:
https://brainly.com/question/30218856
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Use elimination to solve the system of equations.
10x + 5y = 55
y - 2x = -9
A. (1,1)
B. (1,5)
C. (5, 1)
D. (4,5)
Answer:
C. (5,1)
Step-by-step explanation:
10x+5y=55 equation 1
y-2x=-9 equation 2
y=-9+2x isolate y in equation 2
10x+5(-9+2x)=55 substitute value of y from equation 2 into equation 1
10x-45+10x=55
20x=100
x=5
solve for y by using x value (5) in either equation
y-2x=-9
y-2(5)=-9
y-10=-9
y=1
Solve the equation by completing the square. Round to the nearest hundredth x^2 + 2x = 15
Answer:
x = 3, x = -5
Step-by-step explanation:
A perfect square trinomial is represented in the form a^2 + 2ab + b^2. We are already given the a^2 term, x^2, and the 2ab term, 2x. From this we can say:
a^2 = x^2
a = x
Now, we can substitute x for a in the other expression to create the equation:
2ab = 2x
2(x)b=2x
b = 1
From this, b^2 is one, so, to get our trinomial all on one side, we add 1 to both sides:
x^2 + 2x = 15
x^2 + 2x + 1 = 16
Now, we can factor. The perfect square trinomial factors into (a + b)^2. In this case, a is x, and b is one. We can factor and get:
(x + 1)^2 = 16
Now, we take the square root of both sides:
x + 1 = ± 4
We can separate this into two equations and solve:
x + 1 = 4
x = 3
x + 1 = -4
x = -5
Answer:
Step-by-step explanation:
x^2 + 2x = 15
x^2 + 2x + [1/2(2)]^2 = 15 + [1/2(2)]^2
(x + 1/2(2) )^2 = 15 + [(1/2)(2)]^2
(x + 1)^2 = 15 + 1^2
(x + 1)^2 = 15 + 1
(x+1)^2 = 16 Take the square root of both sides.
sqrt( (x + 1)^2 ) = sqrt(16)
x + 1 = +/- 4
x + 1 = 4
x = 4 - 1 = 3
x + 1 = -4
x = -4 - 1
x = - 5
So the roots are 3 and - 5
anna opened a bank account she adds the same amount of money to it
Answer:
What’s the numbers? Or the question?
Step-by-step explanation:
Help me with this answer I don’t it
Answer:
f(-2) = g(-2) this is the answer
Workers employed in a large service industry have an average wage of $9.00 per hour with a standard deviation of $0.50. The industry has 64 workers of a certain ethnic group. These workers have an average wage of $8.85 per hour. Calculate the probability of obtaining a sample mean less than or equal to $8.85 per hour. (Round your answer to four decimal places.)
Answer:
The probability of obtaining a sample mean less than or equal to $8.85 per hour=0.0082
Step-by-step explanation:
We are given that
Average wage, [tex]\mu=[/tex]$9.00/hour
Standard deviation,[tex]\sigma=[/tex]$0.50
n=64
We have to find the probability of obtaining a sample mean less than or equal to $8.85 per hour.
[tex]P(\bar{x} \leq 8.85)=P(Z\leq \frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}})[/tex]
Using the values
[tex]P(\bar{x}\leq 8.85)=P(Z\leq \frac{8.85-9}{\frac{0.50}{\sqrt{64}}})[/tex]
[tex]P(\bar{x}\leq 8.85)=P(Z\leq \frac{-0.15}{\frac{0.50}{8}})[/tex]
[tex]P(\bar{x}\leq 8.85)=P(Z\leq -2.4)[/tex]
[tex]P(\bar{x}\leq 8.85)=0.0082[/tex]
Hence, the probability of obtaining a sample mean less than or equal to $8.85 per hour=0.0082
Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.
y = 5x
20x - 4y = 0
Answer:
Dependent Equations
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsCoordinates (x, y)Solving systems of equations by substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = 5x
20x - 4y = 0
Step 2: Solve for x
Substitution
Substitute in y [2nd Equation]: 20x - 4(5x) = 0Multiply: 20x - 20x = 0Combine like terms: 0 = 0Here we see 0 does indeed equal 0.
∴ our systems has an infinite amount of solutions.
Answer:
0
Step-by-step explanation:
y = 5x
20 x - 4 y = 0substitute the value of y in equation
= 20x - 4 ( 5x ) = 0multiply to get 20x
= 20x - 20x = 0collect like terms
= 0we can see here that 0 indeed equal 0.
so, system has an infinite solutions.
B
These triangles
are congruent by
the triangle
congruence
postulate [?].
D
E
A. SSS
B. SAS
C. Neither, they are not congruent
Answer:
SAS
Step-by-step explanation:
AC ≅ EC (Given), ∠ACB ≅∠ECD ( Vertical Angles), and BC ≅ DC
cort
Here are ten numbers:
3 7 2 4 7 5 7 1 8 8
Write down the mode.
b)
Work out the median.
c)
Calculate the mean.
What is the range?
Answer:
The mode is 7 and 8
The mean is 5.2
The range is 7
A landscaper buys 1 gallon of plant fertilizer. He uses 1/5 of the fertilizer, and then divides the rest into 3 smaller bottles. How much does he put in each bottle?
Answer:
[tex]\frac{4}{15}[/tex] of a gallon per bottle
Step-by-step explanation:
1 - [tex]\frac{1}{5}[/tex] = [tex]\frac{4}{5}[/tex]
[tex]\frac{4}{5}[/tex] / 3 = [tex]\frac{4}{5}[/tex] x [tex]\frac{1}{3}[/tex] = [tex]\frac{4}{15}[/tex]
consider a triangle ABC. Suppose that a=16, b=30, and c=35. Solve the triangle. Carry your intermediate computations to at least four decimal places and round your answers to the nearest tenth
9514 1404 393
Answer:
A = 27.1°B = 58.8°C = 94.1°Step-by-step explanation:
An angle can be found using the Law of Cosines.
c² = a² +b² -2ab·cos(C)
C = arccos((a² +b² -c²)/(2ab)) = arccos((16² +30² -35²)/(2·16·30))
C = arccos(-69/960) ≈ 94.1217°
Then another angle can be found using the Law of Sines:
sin(B)/b = sin(C)/c
B = arcsin(b/c·sin(C)) ≈ 57.7516°
The third angle can be found from the sum of angles of a triangle.
A = 180° -94.1217° -58.7516° = 27.1267°
The angles of the triangle are about (A, B, C) = (27.1°, 57.8°, 94.1°).
what is 1.0185 rounded to the nearest thousandth???
Answer:
1.019 is the answer
it cost $246 to turf a lawn of 43m ² . how much will it cost to turf a lawn of 61m square 2 .
Answer:
$348.96
Step-by-step explanation:
246÷43=5.72
61-43=18
18×5.72=102.96
102.96+246=348.96
Find the slope of each line (each block is one unit):
Answer:
-2
Step-by-step explanation:
Slope formula for any given two points
(y2 - y1 / x2 - x1)
The points chosen may vary but the points I chose were (0,1) and (2,-3)
Our next step is to identify the variables
y2 = -3
y1 = 1
x2 = 2
x1 = 0
We then plug in the values into the slope formula
slope = ( -3 - 1 ) / ( 2 - 0 )
Simply
Slope = -4 / 2
Simply even further
Slope = -2
the slope of each line is -2.
Answer:
Solution Given:
let's find out the given points.
1st point[tex] (x_1,y_1)=(0,1)[/tex]
another point is:
[tex](x_2,y_2)=(2,-3)[/tex]
now
By using slope formula
[tex] \green{\boxed{m=\frac{y_2-y_1}{x_2-x_1}}}[/tex]
now
substituting value
we get
m=[tex]\frac{-3-1}{2-0}=\frac{-4}{2}=-2[/tex]
the line below are parallel. If green line has a slope of 2/5 what is the slope of the red line? enter your answer as an integer or fraction in lowest terms
Answer:
if they are parallel it would almost be opposite but they would be negative instead of positive
by selling 33m of cloth ,prabha gained the selling price 11 m.what is the gain percent
Answer:
The gain percent is 33.3 %
Step-by-step explanation:
Let the selling price of 1 m cloth is p.
Cost of 33 m = 33 p
gain = cost of 11 m = 11 p
The gain percentage is given by
[tex]\frac{11 p}{33 p}\times 100\\\\= 33.3 %[/tex]
The gain percent is 33.3 %.
Simplify log2 20-log2 30.
Answer:
[tex] log_{2}(20) - log_{2}(30) \\ log_{2}(20 \div 30) \\ log_{2}(0.667) [/tex]
hope this helps you
Brainliest appreciated
log1(20)-log2(30)
log2 (20÷30)
log2=0.667
the pizza Question i cant do and need desperate help
Answer:
the answer is c
Step-by-step explanation:
A meeting on an unpopular topic has been announced. The number of attendees may be modeled by X where What is the probability that at least 5 people attend the meeting given that at least 2 attend
Answer:
The probability that at least 5 people attend the meeting given that at least 2 attend is 12.50%.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
A meeting on an unpopular topic has been announced. The number of attendees may be modeled by X where:
P(X = x) = 1 / 2^(x+1), for x = 0,1,2,...
What is the probability that at least 5 people attend the meeting given that at least 2 attend?
The explanation of the answer is now provided as follows:
Given:
P(X = x) = 1 / 2^(x+1), for x = 0,1,2,... (1)
Since it is given that at least 2 attend, it implies that we need to calculate P(x) at x = 2.
Substituting x = 2 into equation (1), we have:
P(X = 2) = 1 / 2^(2 + 1)
P(X = 2) = 1 / 2^3
P(X = 2) = 1 / 8
P(X = 2) = 0.1250, or 12.50%
Therefore, is the probability that at least 5 people attend the meeting given that at least 2 attend is 12.50%.
hello how are you today. Question 2(×+-5)+×=×+(-6)
Answer:
x = 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
2(x + -5) + x = x + (-6)
Step 2: Solve for x
[Distributive Property] Distribute 2: 2x - 10 + x = x - 6[Addition] Combine like terms (x): 3x - 10 = x - 6[Subtraction Property of Equality] Subtract x on both sides: 2x - 10 = -6[Addition Property of Equality] Add 10 on both sides: 2x = 4[Division Property of Equality] Divide 2 on both sides: x = 2Answer:
x=2 ( see Image below)
Step-by-step explanation:
cancel equal terms on both sides of the equation
2(x-5)=-6
move the constant to the right -hand side and change its sign
2x= -6 +10
Calculate the sum
2x=4
divide both sides of the equation by 2
x=2
how to solve letters and numbers in a box
Write the formulae of area and volume of different solid shapes. Find out the variables and constants in them.
Answer:
Step-by-step explanation:
1 . Sphere :
[tex]Surface \ Area = 4\pi r^2\\\\ Volume = \frac{4}{3} \pi r^3[/tex]
Variable is ' r '
Others Constants.
2. Cone :
[tex]Surface \ Area = \p r^2 + \pi rs[/tex] [tex][ \ s = \sqrt { r^2 + h^2 } \ , r = base \ radius, h = height \ ][/tex]
[tex]Volume = \frac{1}{3} \pi r^2 h[/tex]
Variables are ' r ' and ' h '
Others constants.
3. Cuboid ( Rectangular Prism )
[tex]Surface \ Area = 2 ((l\times b) + ( b \times h) + ( l \times h)) \\\\Volume = l \times \ b \times \ h[/tex]
Variables : l , b , h
Constant is 2
4. Cylinder
[tex]Surface \ Area = 2 \pi r h + 2 \pi r^2 \\\\Volume = \pi r^2 h[/tex]
Variables : ' r ' and ' h '
Others constants..
Answer:
shapes. cuboid. cube. cylinder. prism. sphere. pyramid. rightcircularcone. volumeformula. l×w×h. v=a . 3. v=πr . 2. h. v=b×h. v=( 3. 4)πr . 3. v=( 3. 1)×h×b. v=( 3. 1)πr . 2. h. variables. l=length,w=width,h=height. a=side. r=radius,h=height. b=base,h=height. r=radiusofthesphere. b=areaofthebase,h=heightofthepyramid. r=radiusofthecircularbase,h=height
Step-by-step explanation:
What's the surface area of this shape???
Answer:
197 in^2
Step-by-step explanation:
Add the areas of each face:
2 trapezoid faces:
(5+9) ÷ 2 x 5 = 35
2(35) = 70 in^2
2 squares:
5 x 5 = 25
2(25) = 50 in^2
Rectangular base:
5 x 9 = 45 in^2
Area of slanted rectangle:
6.4 x 5 = 32 in^2
Add:
32 + 45 + 50 + 70 = 197