Answers
The solution of the system of equation of the matrix is as follows:
x = - 8
y = 3
How to find the solution of matrix?3x + 10y = 6
x + 3y = 1
multiply equation(ii) by 3
3x + 10y = 6
3x + 9y = 3
Therefore,
y = 3
Hence,
x + 3y = 1
x + 3(3) = 1
x + 9 = 1
x = 1 - 9
x = -8
learn more on matrix here: https://brainly.com/question/9967572
#SPJ1
Related Questions
Can anyone tell me what 9/2 simplified completely is??
Answers
Answer:
You can't simplify 9/2, but 9/2 as a mixed number is 4 1/2
hope this helped
Step-by-step explanation:
Answer:
You can't simplify 9/2, but 9/2 as a mixed number is 4 1/2
Step-by-step explanation:
Which ordered pair is a solution of the inequality?
y > 4x - 5
Answers
Answer:
(1,1)
Step-by-step explanation:
Which of the following is The function f(x)=2x2−1 is/has
A. order 2 rotational 2 symmetry about the origin
B. symmetry about the y-axis
C. neither symmetric about the y-axis nor has order 2 rotational symmetry about the origin
D. odds a good way to get someone to participate in a group?
Answers
The given function has symmetry about the y - axis.
Symmetry of the Function
If we reflect a function's graph about the y-axis, we will get the same graph since if the function is symmetrical about the y-axis. We can reflect a function about the x- and y-axis and obtain the same graph. These two symmetry kinds are known as the even function and odd function.
The given function is,
f(x) = 2x² - 1
It is an even function since the function remains same for both x and -x.
Putting f(x) = 0, we get,
2x² - 1 = 0
2x² = 1
x² = 1/2
x = ±1/2
⇒ Axis of symmetry is, x=0
Hence, the function f(x) is symmetric about y-axis.
Learn more about a function here:
https://brainly.com/question/12431044
#SPJ1
A ball is thrown from an initial height of 5 feet with an initial upward velocity of 31 ft/s. The ball's height (in feet) after t seconds is given by the following.
h=5+31t-16t^2
Find all values of t for which the ball's height is 19 feet.
t= _ seconds
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Answers
Solving a quadratic function, it is found that the ball has a height of 19 feet at t = 0.72 seconds and t = 1.22 seconds.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
In this problem, the function is:
h(t) = -16t² + 31t + 5
The height is of 19 feet when h(t) = 19, hence:
19 = -16t² + 31t + 5
16t² - 31t + 14 = 0.
Then:
[tex]\Delta = (-31)^2 - 4(16)(14) = 65[/tex][tex]x_1 = \frac{31 + \sqrt{65}}{32} = 1.22[/tex][tex]x_2 = \frac{31 - \sqrt{65}}{32} = 0.72[/tex]More can be learned about quadratic functions at https://brainly.com/question/24737967
#SPJ1
Select the correct answer from each drop-down menu .
Answers
Answer:
Fountain= 147.65 square yards
path= 28.28 square yards
Step-by-step explanation:
pi*47 <---square root cancels out the square
=147.65
pi*56=175.93
175.93-147.65=28.28
A genetic experiment with peas resulted in one sample of offspring that consisted of 427 green peas and 161 yellow peas.
a. Construct a 90% confidence interval to estimate of the percentage of yellow peas.
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
No, the confidence interval includes 0.25, so the true percentage could easily equal 25%
O Yes, the confidence interval does not include 0.25, so the true percentage could not equal 25%
a. Construct a 90% confidence interval. Express the percentages in decimal form.
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
Sub
Answers
Using the z-distribution, we have that:
a) The confidence interval is: (24.33%, 30.37%).
b) The correct option is: No, the confidence interval includes 0.25, so the true percentage could easily equal 25%.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
The other parameters are given as follows:
[tex]n = 427 + 161 = 588, \pi = \frac{161}{588} = 0.2735[/tex]
Then the bounds of the interval are:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2735 - 1.645\sqrt{\frac{0.2735(0.7265)}{588}} = 0.2433[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2735 + 1.645\sqrt{\frac{0.2735(0.7265)}{588}} = 0.3037[/tex]
As a percentage, the interval is: (24.33%, 30.37%).
25% is part of the interval, hence the correct statement is:
No, the confidence interval includes 0.25, so the true percentage could easily equal 25%.
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 316 people entered the park, and the admission fees collected totaled 924.00 dollars. How many children and how many adults were admitted
Answers
Answer: pretty sure
There were 108 children and 175 adults.
NEEEEEEEDDDD HELPPPPPPP ASAPPPPPPPPP
Answers
The true statement about the diagram is (a) IJ ≅ JG
How to determine the true statement?From the question, we understand that:
KH bisects line IG at point J
This means that:
Line segment IG is divided into two equal parts, and point J is the middle
So, we have:
IJ ≅ JG
Hence, the true statement about the diagram is (a) IJ ≅ JG
Read more about perpendicular bisector at:
https://brainly.com/question/24753075
#SPJ1
Which of the following is the constant in the equation below:
16x + 42 = 78
16x
16
42
78
Answers
Find the Simple Intrest on
#60,000.00 for 3 years at
5% per annum
Answers
Answer:
the ans is 9000
Step-by-step explanation:
simple interest= 60000*3*5/100
There are 8 marbles in a bag, all of different colors. In how many orders can 4 marbles be chosen? In other words, what is the
number of permutations of picking 4 marbles from the bag?
A
1680
B
70
С
40320
Answers
I got 70
Combination=n!/((n-r)!r!)
=8!/((8-4)!*4!)
=8*7*6*5*4!/(4!*4!)
=8*7*6*5/(4*3*2)
=70 ways
What is the correct classification for each given angle?
Drag and drop the answer into the box to match each angle.
Answers
Answer:
∠AFB = Acute
∠DFB = Obtuse
∠CFD = Right
Step-by-step explanation:
∠AFB is acute b/c its less than 90°
∠DFB is obtuse b/c it more than 90°
∠CFD is right b/c it's exactly 90°
An artist is making a sketch based on a 12 inch by 30 inch poster. She divides the poster into grid squares. What are the greatest size grid squares she can make?
Answers
The greatest size grid squares she can make is; 12 inch by 12 inch.
What are the greatest size grid squares she can make?Since, it follows from the task content that the poster at the artist's disposal is 12 inch by 30 inch, it follows that the smaller dimension of the poster is; 12inch.
It is the limiting dimension and hence, the greatest size grid squares she can make is; 12in by 12 inch.
Read more on grid squares;
https://brainly.com/question/27892243
#SPJ1
Your friend is helping to raise money for a local charity by participating in a cartwheel-a-thon. Your
friend is 70 inches tall with your friend's arms raised in the air. Your friend is able to complete a
cartwheel in 15 seconds. The charity sponsor supplies a wristband to each participant to assist in
counting the number of cartwheels completed. The wristband is 4 inches from the end of your friend's
arm. Write a model for the height h (in inches) of the wristband as a function of the time (in minutes)
given that the wristband is at the highest point when ; = 0.
Answers
The equation for the height exists h = 31 sin((8π)t + π/2) + 35.
How can the height of the wristband be modeled?The model for the height can be emanated from the general formula of the sine function, then
y = A sin(Bt - C) + D
Maximum point = 70 - 4 = 66 at t = 0
Minimum point = 4
Amplitude, A = (66 - 4) ÷ 2 = 31
D = 4 + 31 = 35
At t = 0, we have;
66 = 31 × sin(B × 0 - C) + 35
31 = 31 × sin(- C)
sin(- C) = 1
C = -π/2
1 minute = 60 seconds
1 second = 1 minute/60
15 seconds = (15/60) minutes
Period = 15 seconds = 15/60 minutes
Period = 2π/B
Therefore, 15/60 = 2π/B
1/4 = 2π/B
B = 2π/(1/4) = 8π
y = Height of the function
Let h denote the height of the wristband.
The equation for the height exists h = 31 sin((8π)t + π/2) + 35.
To learn more about sine function refer to:
brainly.com/question/12102275
#SPJ9
Name a pair of complementary angles in this figure.
a protractor, with segment DEF along the bottom, EH point to the 55 degree on the left, EJ to 90 degrees, EK to the 30 degrees on the right
angles DEH and HEJ
angles DEH and DEJ
angles DEH and DEK
angles DEF and DEH
Answers
The answer choice which represents a pair of complementary angles in the task content is; angles DEH and DEJ.
Which pair of angles represent complementary angles?It follows from the concept of angle geometry that two or more angles are said to be complementary when the sum of their measures is 90°.
It follows from the task content therefore that since, DEJ = 90° and the sum of the measures of angles DEH and DEJ amounts to 90°.
Hence, the pair of angles are complementary.
Read more on complementary angles;
https://brainly.com/question/16281260
#SPJ1
(1 point)
Carlos measured the rainfall amounts, in inches, in his town for one week. The amounts were
0.1, 0.5, 0, 0.32, 0, 0, 1.5, and 0. What is the outlier in this set of data?
Oo
00.1
O 0.32
O 1.5
Answers
:
Knowing the average monthly rainfall for a location is helpful when you're packing for a ... Add together all of the monthly rainfall totals in your sample data. ... in inches because rainfall is generally measured in inches in the United States. ... is to maintain the linear relationship of the formula, since there is no 0 BC or 0 AD
If (x, 68, 85) form a Pythagorean Triple, what is the value of x?
Answers
Answer:
x = 51Step-by-step explanation:
If (x, 68, 85) form a Pythagorean Triple, what is the value of x?
to solve we again use Pythagoras, x is the smallest number, so 68 is a cathetus and 85 the hypotenuse
x = √(85²- 68²)
x = (7225 - 4624)
x = √2601
x = 51
Answer:
x = 51
Step-by-step explanation:
The missing value of the Pythagorean triple can be found using the Pythagorean theorem, or it can be found by comparing the values in the triple to known triples.
What are Pythagorean triples?A Pythagorean triple is a set of integers {a, b, c} that satisfy the equation of the Pythagorean theorem:
a² +b² = c²
The smallest such triple is {3, 4, 5}. It is also the only triple that is an arithmetic sequence. Other triples of small integers are ...
{5, 12, 13}, {7, 24, 25}, {8, 15, 17}
There are an infinite number of "primitive" Pythagorean triples, ones that are not multiples of another triple.
What is this triple?The given values of the triple have the ratio ...
68/85 = (4·17)/(5·17) = 4/5
Only the values in the {3, 4, 5} triple and its multiples will have this ratio.
The value of x is 3·17 = 51, so the triple is {51, 68, 85}.
x = 51
__
Additional comments
Any primitive triple will have two odd numbers.
The ratios of numbers in a primitive triple are unique to that triple. That is, the numbers are mutually prime.
For any pair of positive integers m > n, there is a Pythagorean triple {2mn, m²-n², m²+n²}. Such triples will not be primitive if m and n have the same parity.
__
The above triple can be verified using the Pythagorean theorem:
51² +68² = 2601 +4624 = 7225 = 85²
Which equation has no solution?
O 1-x-31=5
O 12x-11=0
O15-3x = -8
O|-x+91=0
Answers
Since the four choices have solution, there is no choice that have no solutions. (Correct choice: E)
What linear equation has no solution?
Herein we must check each choice to find if a solution exists or not by algebra properties. Now we proceed to check each case:
Choice A
1/(x - 31) = 5
1 = 5 · (x - 31)
1 = 5 · x - 155
5 · x = 156
x = 31.2
Choice B
12 · x - 11 = 0
12 · x = 11
x = 11/12
Choice C
15 - 3 · x = - 8
3 · x = 23
x = 23/3
Choice D
- x + 91 = 0
x = 91
Since the four choices have solution, there is no choice that have no solutions. (Correct choice: E)
RemarkThe statement presents typing mistakes and is incomplete. Correct form is shown below:
Which equation has no solution?
A. 1/(x- 31) = 5
B. 12 · x - 11 = 0
C. 15 - 3 · x = - 8
D. - x + 91 = 0
E. Neither of all
To learn more on linear functions: https://brainly.com/question/21107621
#SPJ1
Which of these is equal to ⅔ × ¾ × ⅗?
Answers
Answer:
3/10
Step-by-step explanation:
Just multiply all of the numerators (top numbers) and then multiple all of the denominators (bottom numbers)
2/3x3/4x3/5 would be 18/60 Then take any number that is a factor to both 18 and 60 and divide both numbers by that factor. I could use 2 or 3 or 6 because both 18 and 60 is divisible by any of these numbers. I will choose 3. I will divide the top and bottom of 18/60 by 3 to get 6/20, now I will divide the top and bottom of that number by 2 to get 3/10
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{3}{5}}[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{3}{5}}[/tex]
[tex]\mathsf{= \dfrac{2\times3\times3}{3\times4\times5}}[/tex]
[tex]\mathsf{= \dfrac{6\times3}{12\times5}}[/tex]
[tex]\mathsf{= \dfrac{18}{60}}[/tex]
[tex]\mathsf{= \dfrac{18\div3}{60\div 3}}[/tex]
[tex]\mathsf{= \dfrac{6}{20}}[/tex]
[tex]\mathsf{= \dfrac{6\div2}{20\div2}}[/tex]
[tex]\mathsf{= \dfrac{3}{10}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\dfrac{3}{10}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Take a two digit number represented by ab, such that neither a nor b is zero and a is not equal to b. Reverse the digits and add the result to the original number. Divide this sum by a+b. What is the quotient?
Answers
Answer:
11
Step-by-step explanation:
We can have any. two numbers that represent a and b
It CANT BE THIS FOLLOWING
A AND B CANT BE ZERO SO WE CAN USE MULTIPLES OF 10
A CANT BE EQUAL TO B SO WE CANT USE MULTIPLES OF 11( ALL THE WAY UP TO 99 BUT WE CANT USE ANY NUMBER AFTER THAT SINCE NUMBERS THAT COME AFTER 99 ARE THREE DIGIT NUMBER)
Let use 5 and 6.
56
Reverse the digits
65
add 56 to 65
121
Divide this by 6+5=11
The answer is 11 This vary for all answers let use 1,7
17 then reverse
71 then add 71 and 17
88 then divide by 1+7=8
11
The quotient is 11.
Step-by-step explanation:
Given:
A two-digit number,'ab'.
Where a and b are non-zero and are unequal to each other.
To find:
Quotient after dividing the sum of the given digit and its reverse with(a+b).
Solution:
The given digit = [tex]ab = (10a+b)[/tex]
[tex]Where:\\a \neq b, a\neq 0,b\neq 0[/tex]
On reversing the given digit =[tex]ba = (10b +a)[/tex]
Now adding the given digit and its reverse:
[tex]= ab +ba = (10a+b)+(10b+a)\\=(11a+11b)=11(a+b)[/tex]
Diving the sum with (a+b):
[tex]=\frac{11(a+b)}{(a+b)}=11[/tex]
The quotient is 11.
Learn more about algebra here:
brainly.com/question/953809?referrer=searchResults
https://brainly.com/question/21261790?referrer=searchResults
car travels 22 miles for every gallon of gasoline used. The table below represents this relationship.
Gas Mileage
Distance Traveled
(miles)
Gasoline Used
(gallons)
22
1
44
2
x
3
88
4
Answers
The equation that shows a pair of equivalent ratios that can be used to find the unknown is [tex]\frac{22}{1} =\frac{x}{3}[/tex]
Writing an EquationFrom the question, we are to determine which equation shows a pair of equivalent ratios that can be used to find the unknown
In the given table, the unknown is x
Consider the given values in the table,
The equation that shows a pair of equivalent ratios that can be used to find the unknown is
[tex]\frac{22}{1} =\frac{x}{3}[/tex]
Hence, the equation that shows a pair of equivalent ratios that can be used to find the unknown is [tex]\frac{22}{1} =\frac{x}{3}[/tex]
Here is the complete question:
A car travels 22 miles for every gallon of gasoline used. The table below represents this relationship. Gas Mileage Distance Traveled (miles) Gasoline Used (gallons) 22 1 44 2 x 3 88 4. Which equation correctly shows a pair of equivalent ratios that can be used to find the unknown.
Learn more on Writing an equation here: https://brainly.com/question/18815248
#SPJ1
Can you solve question 6 and 8 i need it for my math homework
Answers
Explain the difference between using area and volume with 2-D and 3-D figures.
Answers
The difference between using Area and Volume with 2D and 3D figures is that Area is a measure of square units while Volume is a measure of cubic units.
What is the difference between Area and Volume?The area of an object is the measure of space occupied by the two-dimensional object (flat) in a plane. Volume on the other hand is the quantity of space occupied by the object, 3-dimensional object in this case. The unit of area is in square units. The unit of volume is in cubic units.
Read more on Area and Volume;
https://brainly.com/question/15612720
#SPJ1
In AABC, m/A = 15°, a = 9, and b = 12. Find c to the nearest tenth.
A. 20.0 B. 17.4 C. 8.4 D. 11.5
Answers
Answer:
Step-by-step explanation:
This is a Law of Sines problem. The expanded formula is
[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex] where the capital letters are the angles and the lowercase letters are the side lengths. We only use 2 of these ratios at a time. And in order to do that, we can only have one unknown per set of ratios. I have angle A and side a, so I'll use that ratio, but I don't have angle C to help me find side c. I also don't have angle B. But I do have side b, so I'll use the A and B sin stuff and then solve for C indirectly.
[tex]\frac{sin15}{9} =\frac{sinB}{12}[/tex] to solve for angle B. Cross multiply:
[tex]sinB=\frac{12sin15}{9}[/tex]
[tex]sinB=.3450926061[/tex] Use the inverse and sin keys on your calculator (in degree mode) to get that
B = 20.2°. Now that we have that, we can find the measure of angle C:
180 - 15 - 20.2 = 144.8°
Now we can use the sin ratio involving the angle C, side c (our unknown), and angle A and side a:
[tex]\frac{sin144.8}{c}=\frac{sin15}{9}[/tex] and cross multiply to solve for c:
[tex]c=\frac{9sin144.8}{sin15}[/tex] gives us that
c = 20.0
The eccentricity of the conic section shown is
Answers
Answer:
1
Step-by-step explanation:
This is a U shaped graph, so the shape is a parabola
Eccentricity of any parabola is 1.
Answer:
Step-by-step explanation:
Just for some extra confrontation indeed the correct answer is 1.
I need help with b and c please and thank you!!
Answers
Answer:
rjdjdj shiejd shsuisis shusisos
A catering service offers 11 appetizers, 7 main courses, and 4 desserts. A customer is to select 9 appetizers, 5 main courses, and 2 desserts for a banquet. In how many ways can this be done?
Answers
Based on the various meals offered by the catering service, the ways that the order can be done is 6,930 ways..
How many ways can the food be served?This can be found as:
= (11! / (9!2!)) x (7! / (5!2!)) x (4! / (2!2!)
= 55 x 21 x 6
= 6,930 ways
In conclusion, the order can be made in 6,930 ways.
Find out more on permutations at https://brainly.com/question/1216161.
#SPJ1
1.The time taken to complete a motorcycle race is normally distributed, with an average time (µ) of 2.5 hours and a standard deviation (sigma) of 0.5 hours.
What is the probability that a randomly selected cyclist will take between 2.35 and 2.45 hours to complete the race?
Answers
Using the normal distribution, there is a 0.0781 = 7.81% probability that a randomly selected cyclist will take between 2.35 and 2.45 hours to complete the race.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 2.5, \sigma = 0.5[/tex].
The probability that a randomly selected cyclist will take between 2.35 and 2.45 hours is the p-value of Z when X = 2.45 subtracted by the p-value of Z when X = 2.35, hence:
X = 2.45:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.45 - 2.5}{0.5}[/tex]
Z = -0.1
Z = -0.1 has a p-value of 0.4602.
X = 2.35:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.35 - 2.5}{0.5}[/tex]
Z = -0.3
Z = -0.3 has a p-value of 0.3821.
0.4602 - 0.3821 = 0.0781.
0.0781 = 7.81% probability that a randomly selected cyclist will take between 2.35 and 2.45 hours to complete the race.
More can be learned about the normal distribution at https://brainly.com/question/4079902
#SPJ1
Help!!!
d - ⅔d = -⅚n
Answers
Answer:
n = -5/2d or d = -5n/2
Step-by-step explanation:
What is the simplest form of the expression?
✓4502 +502 + 425
Assume all variables are positive.
Answers
Answer:
A. [tex] 8x\sqrt{5} [/tex]
Step-by-step explanation:
Given:
[tex] \sqrt{45x^2} + \sqrt{5x^2} + 4x\sqrt{5} [/tex]
Required:
Simplify
[tex] \sqrt{9*5*x^2} + \sqrt{5*x^2} + 4x\sqrt{5} [/tex]
[tex] 3x\sqrt{5} + x\sqrt{5} + 4x\sqrt{5} [/tex]
Add like terms
[tex] 8x\sqrt{5} [/tex]