What is the value of a?
Enter your answer in the box. Enter your answer as a simplified fraction.
Answers
==========================================
Work Shown:
The scalar (2/5a+6) multiplies with the matrix on the left side to get the matrix on the right side
So this is what your steps could look like
[tex](\frac{2}{5}a+6)\begin{bmatrix}3 \\ -2 \\ 7\end{bmatrix}=\begin{bmatrix}15 \\ -10 \\ 35\end{bmatrix}\\\\\\\begin{bmatrix}(\frac{2}{5}a+6)*3 \\ (\frac{2}{5}a+6)*(-2) \\ (\frac{2}{5}a+6)*7\end{bmatrix}=\begin{bmatrix}15 \\ -10 \\ 35\end{bmatrix}\\\\\\[/tex]
[tex]\begin{bmatrix}\frac{2}{5}a*3+6*3 \\ \frac{2}{5}a*(-2)+6*(-2) \\ \frac{2}{5}a*7+6*7\end{bmatrix}=\begin{bmatrix}15 \\ -10 \\ 35\end{bmatrix}\\\\\\\begin{bmatrix}\frac{6}{5}a+18 \\ -\frac{4}{5}a-12 \\ \frac{14}{5}a+42\end{bmatrix}=\begin{bmatrix}15 \\ -10 \\ 35\end{bmatrix}\\\\\\[/tex]
The last matrix equation leads to this system of equations
[tex]\begin{cases}\frac{6}{5}a+18=15 \\ -\frac{4}{5}a-12=-10 \\ \frac{14}{5}a+42=35\end{cases}\\\\\\[/tex]
If we pick any of those equations, and solve for 'a', then we'll get our answer.
---------------------
Let's say we pick the first equation
(6/5)a+18 = 15
(6/5)a = 15-18
(6/5)a = -3
a = -3(5/6)
a = -15/6
a = -5/2
--------------------
If we pick on the second equation, then,
(-4/5)a-12 = -10
(-4/5)a = -10+12
(-4/5)a = 2
a = 2(-5/4)
a = -10/4
a = -5/2
--------------------
Or we could solve the third equation for 'a'
(14/5)a+42 = 35
(14/5)a = 35-42
(14/5)a = -7
a = -7*(5/14)
a = -35/14
a = -5/2
-------------------
You only need to solve one equation to find 'a', though it's good practice to solve all three to see all three rows agreeing with one another.
The multiplication of the matrix by a constant will multiply for each term in the matrix value of the "a" given system of the matrix will be -2.5.
What is a matrix?A matrix is a collection of numbers lined up in rows and columns to produce a rectangular array.
In computer graphics, where they have been used to describe picture transformations and other alterations, matrices have vital applications as well in many sectors.
As per the given system of the matrix.
When we multiply anything in a matrix then it will multiply to each and every term of the matrix.
Therefore the (2/5)a + 6 will be multiplied by 3,-2, and 7 each.
So the first term of the left-hand side matrix becomes,[(2/5)a + 6]3
If we compare two matrices then each corresponding term will be the same.
Therefore, the first term of the left-hand matrix = first term of the right-hand matrix
[(2/5)a + 6]3 = 15
6a/5 + 18 = 15
6a/5 = -3
6a = -15
a = -15/6 = -2.5
Hence "The value of the "a" given system of the matrix will be -2.5".
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Related Questions
Can someone help me please!!
Answers
Answer:
y = (-3x/5) +1
Step-by-step explanation:
We know that the line passes through the point (-5 , 4)
AND
the slope is given to be -3/5
let's look at the slope a bit more
we know that the formula for slope of a line is Rise / Run
Which means that the rise of this line is -3 after spanning 5 units to the right
Hence, the line goes down 3 units after moving 5 units to the right
We know that to find the equation of a line through the point-slope equation, we need the slope as well as the y-intercept of the line
since we are already given the slope, we need to find the point where the line intersects the y-axis
Now, back to the given point the line passes through
this point has a x - coordinate of -5 and we know that after moving 5 units to the right, the line moves 3 units downwards
So, if the line moves 5 units to the right from the given point, it will reach the y- axis and we know that it's y-coordinate will decrease by 3
Hence, the y-intercept will be 3 units below the given y -coordinate
y - intercept = (4 - 3) = 1 = y-intercept
Now, using the slope-intercept formula to get the equation:
y = (slope)*x + (y-intercept )
y = (-3/5)x + (1)
y = (-3x/5) + 1
Write a word phrase for each expression. 2(n+1)
Answers
Answer:
A number increased by one multiplied by two.
Two distributed into a number and one.
Step-by-step explanation:
First one is way more likely.
What are the measures of each interior and exterior angles of regular quadrilateral MNOP?
Answers
Answer:
A regular polygon is a polygon that is equilateral and equiangular.
The only regular quadrilateral is the square.
We know that all the interior angles of a square are 90° each, so we are fine with that.
Now, for the exterior angles.
If we fix our position in the vertex, we can do from one side, to the same side, a full rotation of 360°.
Now, if we only do an external rotation, this means, from one side to other side, we will do a rotation of 360° minus the interior angle:
this is:
360° - 90° = 270°
Below is an image as a guide of this.
PLEASE HELP DUE IN LESS THAN 10 MINUTES. Thank you
Answers
Answer:
answer is B all the best for your exam
Step-by-step explanation:
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What additional information is needed to prove the triangles are congruent by ASA?
Answers
Answer:
The additional information that needed is m∠ABD = m∠CDB ⇒ C
Step-by-step explanation:
In the given figure
Triangles ADB and CBD are congruent by ASA under these conditions
m∠ADB = m∠CBDDB = BD ⇒ the side joining the congruent anglesm∠ABD = m∠CDBLet us see the given to find the correct answer
∵ ∠ADB and ∠CBD have the same mark
∴ m∠ADB = m∠CBD ⇒ (1) given
∵ Side DB is a common side in the two triangles
∴ DB = BD ⇒ (2) given
∵ ∠ABD and ∠CDB are the angles at the end of BD
∴ m∠ABD must equal m∠CDB ⇒ (3) to prove the congruency using ASA
∴ The additional information that needed is m∠ABD = m∠CDB
Answer:
To prove that two triangles with three congruent, corresponding angles are congruent, you would need to have at least one set of corresponding sides that are also congruent. You could then use ASA or AAS congruence theorems or rigid transformations to prove congruence.
Step-by-step explanation:
PLEASE HURRY!
Evaluate the following expression.
Your answer must be exact.
Answers
Answer:
1Step-by-step explanation:
= [tex](-\frac{\sqrt{3}}{2} - \frac{1}{2}i)^1^2[/tex]
= [tex](-\frac{\sqrt{3}}{2} - \frac{i}{2})^1^2[/tex]
= [tex](\frac{\sqrt{3} -i}{2})^1^2[/tex]
apply the exponential rule:
([tex]-\sqrt{3}-i[/tex])¹²
= --------------
2¹²
note: ([tex]-\sqrt{3}-i[/tex])¹² = 4096
= 4096
4096
= 1
Olivia buys 4 masks that each cost the same amount and a scarecrow. She spent a total of $176.75. If the scarecrow costs $56.75, write an equation she can use to find the cost of each mask. * 10 points 4m + 56.75 = 176.75 5m + 56.75 = 176.75 4m - 56.75 = 176.75 5m - 56.75 = 176.75
Answers
4m+56.75=176.75
Solve the equation to find the cost of each mask.
What is the expanded form of 894?
Answers
Answer:
Hope this helps! <3
( Pic Below )
Answer:
800+90+4
Step-by-step explanation:
800+90=890 and 890+4=894
HOPE THIS HELPS
Doreen Schmidt is a chemist. She needs to prepare 32 ounces of a 12% hydrochloric acid solutionFind the amount of 16% solution and the amount of 8% solution she should mix to get this solution
Answers
Explanation: Let x be the number of ounces of the 14% solution and 28 - x be the number of ounces of the 7% solution.
The equation you must set up shows the number of ounces of acid added from each solution equals the number of ounces in the 11% solution.
The key thing to remember is that the number of ounces of acid is the amount of solution times the concentration of acid it contains.
Thus,
.11x + .07(28-x) = .11(28).
You can solve this in the usual way, but it helps to clear the decimals by multiplying both sides by a suitable number.
So here goes,
.14x + 1.96 - .07x = 3.08
Multiply both sides by 100:
14x + 196 - 7x = 308.
Now finish solving:
7x = 308 - 196 = 112
x = 112/7 = 16
Then 28-x = 28 - 16 = 12.
Solve: 2x-3 = 5(x + 6) O A. x=33/7 A. X = 7 O B. x=-11 O C. x= -9 O D. x= -3
Answers
Answer:
B -11
Step-by-step explanation:
2x-3=5x+30
or,2x-5x=30+3
or,-3x=33
x=-11
Identify the number of decimal places in each factor.
0.47
× 3.2
The number of decimal places in 0.47 is .
The number of decimal places in 3.2 is .
The number of decimal places in the product will be the sum of the factors’ decimal places. So the product will have decimal places.
Answers
Answer:
Step-by-step explanation:
Identify the number of decimal places in each factor.
0.47
× 3.2
The number of decimal places in 0.47 is
✔ 2
.
The number of decimal places in 3.2 is
✔ 1
.
The number of decimal places in the product will be the sum of the factors’ decimal places. So the product will have
✔ 3
decimal places.
What is the quotient for 3 and 3/4 divided by 5 and 5/8
Answers
Answer:
It's 9 3/8! :)
Step-by-step explanation:
Solve the system of equations by the substitution method.
5x + 10y = 25
2x + 12y = 18
Answers
Answer
5x + 10y = 25 x=1 y=2
2x + 12y = 18 x=3 y=1
plz mark brainliest
also plz try to answer this question
Write the expression as a power of 2, then find its value.
a) 2^4·2
Answers
Step-by-step explanation:
((2^2)^2)*2
=(4^2)*2=16*2=32
At an amusement park, 25 riders ride the race cars every 30 minutes and 20 riders ride the spinning swings every 20 minutes. Which ride will have more Riders each hour and how much more?
Answers
Answer:
The spinning swings would have 10 more an hour.
Answer:
5
Step-by-step explanation:
35 more
-5 + 10m + -2m^2 simplify
Answers
Answer:
−2m2+10m−5
Step-by-step explanation:
−5+10m−2m2
=−5+10m+−2m2
Find the slope of the line that passes through the pair of points (-1,-9) and (-3,10)
Answers
Answer:
-9.5
Step-by-step explanation:
The slope (m) is the ratio of the change in y to the change in x:
m = (y2 -y1)/(x2 -x1)
m = (10-(-9))/(-3-(-1)) = 19/-2
m = -9.5
The slope of that line is -9.5.
__
The graph shows the line through those points, written in point-slope form.
what is cardinality of A={1,4,9}
Answers
Answer:
3
Step-by-step explanation:
The cardinality of a set a measure of the number of elements in a set.
A set is a group of objects that have a well defined relationship between them.
In the given set, A={1,4,9}
The set of A has 3 elements which are 1, 4 and 9
So, the cardinality of this set is 3.
Please help me solve for angle B!!
Answers
I believe it is 50 degrees
Explanation:
180-115 = 65 degrees
Since the base angles of of an isosceles triangle are equal,
Angle C =angle A= 65 degrees
65 times 2 = 130
180-130=50
50 degrees=measure of angle B
Hope this helps
Young Professional magazine was developed for a target audience of recent college graduates who are in their first 10 years of a business or other professional career. The magazine has been fairly successful and the publisher is interested in expanding the publication's advertising base. As a recent hire into the marketing department at the magazine, you have been asked to help develop a survey asking readers demographic information and questions about their interests. Your survey results will be used to help the magazine choose articles of interest and provide advertisers with a profile of subscribers.The culmination of your work will be a presentation of your findings to management. Therefore, you not only have to present summary data, but must also be able to explain the results in a manner that is accurate and easy to understand.After running your analysis, the software returns the following information about the age of the respondents:Which statement should you use to explain the 95% confidence interval to management?a. We are 95% confident that the interval 29.7215 to 30.5029 includes the population mean age of all respondents.b. We are confident that 95% of our readers have ages between 29.7215 to 30.5029.c. There is a 95% probability that the population mean age of all respondents lies within the interval 29.7215 to 30.5029.d. We are 95% confident that the interval 29.7215 to 30.5029 includes the sample mean age of all respondents.
Answers
information about the age of the respondents is missing, so i have attached it.
Answer:
Option A: We are 95% confident that the interval 29.7215 to 30.5029 includes the population mean age of all respondents.
Step-by-step explanation:
From the attached information given, we see that under the 95% Confidence interval column, that the corresponding mean age of all respondents is the interval 29.7215 to 30.5029.
Now, the mean is population mean because it's the mean of all the respondents in the population.
Thus, the correct answer is;
We are 95% confident that the interval 29.7215 to 30.5029 includes the population mean age of all respondents.
What is the equation of a line passing through the point (4,-1) and parallel to the line whose equation is 2y-x=8
Answers
9514 1404 393
Answer:
2y -x = -6
Step-by-step explanation:
You can use the same x- and y-coefficients. You just have to change the constant on the right. Put the point values into the left expression to see the new constant.
2y -x = 2(-1)-(4) = -6
The parallel line is ...
2y -x = -6
1. In the multiplication problem shown below, label
each factor and the product.
5•10• 50
Answers
Answer:
2,500
Step-by-step explanation:
Ramona believes that plants exposed to radio waves will become extra tall. She decides to plant two
seeds in 20 separate pots. She placed 10 pots near a radio for 5 days and the other 10 pots in a room
without a radio. Each plant had the same size pot and the same amount of soil and water She
compared the height of the exposed plants to those not exposed. The average height of the plants
exposed to the radio waves was 6.5 cm. The average height of the plants unexposed was 70 cm
Answers
Answer:I have this same problem but if you’re asking for the independent and other questions here’s the answer. Independent variable is the radio since that’s the only change happening to the 10 other pots. Dependent variable is the height of the plant since that’s what Ramona wants to see change as the output. Control group is the 5 pots without the radio i’m pretty sure. The constants are the amount of seeds, pots, soil, and water.
Step-by-step explanation:
There are 3 different cheeses at the deli. Yasuko buys Three-fourths of a pound of each. There are also 4 different meats. She buys One-half of a pound of each. How much total meat and cheese did Yasuko buy at the deli?
Answers
Answer:
Yasuko buys 2.25 pound of cheeses and 6 pound of meats at the deli
Step-by-step explanation:
3 x 3/4 = 2.25 pound cheese
4 x 1.5 = 6 pound of meat
Answer:
4 1/4
Step-by-step explanation:
I did the test
Factor (5x − 6)2 − (4x − 3)2.
Answers
Answer:
9( x-3) (x-1)
Step-by-step explanation:
(5x − 6)^2 − (4x − 3)^2
This is the difference of squares a^2 - b^2 = ( a-b) (a+b)
(5x − 6)^2 − (4x − 3)^2 where a = 5x-6 and b = 4x-3
( 5x-6 - (4x-3)) ( 5x-6 +(4x-3)
Distribute
( 5x-6 -4x+3) ( 5x-6 +4x-3)
Combine like terms
(x-3) ( 9x-9)
Factor out the 9
9( x-3) (x-1)
The value of an ambulance depreciated by 17.5% from the purchase price of $35,400 a
year ago. What is its current value?
Answers
Answer:
29,205
Step-by-step explanation:
100% - 17.5% = 82.5%
82.5% * 35,400 = answer
make percent a decimal
.825 * 35,400 = 29,205
29,205 is answer
The required current value of the ambulance is given as $29,205.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
The value of an ambulance depreciated by 17.5% from the purchase price of $35,400 a year ago.
Current price = 35400[1 - 0.175]
Current price = $29,205
Thus, the required current value of the ambulance is given as $29,205.
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A survey found that 12 out of every 15 people like eating at restaurants. If 500 people surveyed like eating at restaurants, how many people took the survey?
if the answers are 600 | 625 | 15 | 500
[URGENT]
Answers
Answer:
625
Step-by-step explanation:
625
i just need x and y please
Answers
Answer:
Step-by-step explanation:
Since you know both triangles are congruent, you can say that the corresponding sides are equal. For example, you can say:
17x+3 = 57
because they are corresponding sides of both triangles. To further solve the equation:
17x = 54 --> x = 54/17 --> 3 3/17
Same thing for Y. lines PX and FD are congruent, so, you can say:
4y-3 = 54
4y=57
y= 14.25
PLEASE HELP IM BEING TIMED!!!
WILL MARK BRAINLIEST FOR CORRECT!
100 PTS!!!
Which graph shows h(x) = (f(x))(g(x))?
Answers
Hi! I'd be happy to help you. However, there is not enough information here for us to help, as there is no way to tell which graph is correct without the equations of f(x) and g(x). They'd look something like:
"f(x) = x-2," or "g(x) = 7x+3."
Are you able to provide the equations of of f(x) and g(x)? I would be more than happy to help.
----------------------------------------------------------------------------------------------------------------
UPDATE: I did not realize that you could solve this problem without the original equations. Please refer to the other user's response for an amazing and detailed explanation of this problem! :)
Answer:
The first graph.
Step-by-step explanation:
We want to find the graph that shows:
[tex]h(x)=f(x)g(x)[/tex]
Notice that g(x) is a line and f(x) is a quadratic.
So, their product must be a cubic.
Also, g(x) and f(x) is the same across all four graphs. The only difference is h(x).
Notice that our quadratic f(x) is curving upwards. Therefore, the leading coefficient of f(x) is positive.
Notice that the line g(x) is sloping downwards. Therefore, the leading coefficient of g(x) is negative.
So, this means that the leading coefficient of our cubic h(x) must be negative since a positive times a negative yields a negative.
Remember that the parent cubic function has a positive leading coefficient and it rises from left to right.
So, if our leading coefficient is negative, the cubic will fall from left to right.
Therefore, we can eliminate the 2nd and 3rd graphs since in those two, h(x) has a positive leading coefficient.
Now, we can just pick a test point and determine whether our graph is the first or the fourth.
Let's let x = -2. So, we have the equation:
[tex]h(x)=f(x)g(x)[/tex]
Substitute all Xs for -2s:
[tex]h(-2)=f(-2)g(-2)[/tex]
Looking at the graphs, we can see that f(-2) is 8. g(-2) is 0.5. Substituting this back, we get:
[tex]h(-2)=8(.5)=4[/tex]
So, h(-2) should be 4.
For the first graph, h(-2) is indeed 4.
For the second graph, h(-2) is 6.
So, the correct graph that represents f(x)g(x) is the first graph.
And we're done!
Which statement can be concluded using the true statements?
If a quadrilateral has 4 equal sides and 4 equal angles, then it is a square.
If a figure is a square, then each of its angles must measure 90 degrees.
If a quadrilaterál has 4 equal sides and 4 equal angles, then each of its angles must measure 90 degrees.
If a quadrilateral has 4 equal sides and 4 equal angles, then none of its angles measures 90 degrees.
If all four angles in a quadriateral measure 90 degrees, the quadrilateral is a square.
If all four angles in a quadriateral measure 90 degrees, the quadrilateral cannot be a square.
Answers
Answer:
A) If a quadrilateral has 4 equal sides and 4 equal angles, then each of its angles must measure 90 degrees.
Step-by-step explanation:
just did the unit review on edgenutiy 2020
hope this helps :)
Answer:
A) If a quadrilateral has 4 equal sides and 4 equal angles, then each of its angles must measure 90 degrees.
Hope it helps!! :)