Answer:
[tex]\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right][/tex]
Step-by-step explanation:
The matrix system for the linear equations: x + 2y = 8, 2x + 6y = 9
[tex]\left[\begin{array}{ccc}1&2&\\2&6\\\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}8\\9\end{array}\right][/tex]
To get the coefficient of x and y, the inverse of the first matrix (let the first matrix be A) must be known.
[tex]A^{-1}[/tex] = (1 / determinant of A) x Adjoint of A
the determinant of A = (1 x 6) - (2 x 2) = 6 - 4 = 2
Adjoint of A = [tex]\left[\begin{array}{ccc}6&-2&\\-2&1\\\end{array}\right][/tex]
[tex]A^{-1}[/tex]= [tex]\frac{1}{2} \left[\begin{array}{ccc}6&-2\\-2&1\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right][/tex]
The table below shows the coordinates of a figure that was transformed.
Pre-Image Image
A(5,2) A'(-5,-2)
B(6,1) B'(-4,-3)
C(4,5) C'(-6, 1)
Which is the correct description of the transformation?
A rotation 180° clockwise
b
Reflection over the x-axis
c
Translation 5 units left and 2 units down
d
Translation 10 units left and 4 units down
Answer: You're answer to you question would be D
Step-by-step explanation:
The correct description of the transformation translation 10 units left and 4 units down. The correct option is D.
What is transformation?The transformation can be defined as the introduction of a new set of mathematical coordinates that are declared to be different functions of the original coordinates.
Given the per-image and image of different points. Now, if we look at the coordinates of the A and A', then it can be observed that if 10 units is deducted from the x-coordinate of A, then the x-coordinate of A' will be the result.
Similarly, if 4 units is deducted from the y-coordinate of A, then the y-coordinate of A' will be the result.
Further, it is known that reducing n units from x-coordinate means that the point is shifted left by n units. Also, if p units are deducted form the y-coordinate then the point is shifted p units down.
Hence, the correct description of the transformation translation 10 units left and 4 units down.
Learn more about Transformation here:
https://brainly.com/question/11709244
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The radius of the cone is 7 in and y = 25 in. What is the volume of the cone in terms of π? A cone with a right triangle formed from its dimensions; the value of the height is h, and the value of the slant height is y; the height x and the radius form a right angle at the center of the cone.
Answer:
142.1π in³
Step-by-step explanation:
Given that:
The radius (r) = 7 in
The slant height (y) = 25 in
Then the height (x) can be determined by using the Pythagoras rule:
y² = x² + r²
25² = x² + 7²
125 = x² + 49
125 - 49 = x²
x² = 76
x = √76
x = 8.7
The formula for the volume of a cone is;
= 1/3 πr²h
where;
height(h) is calculated as "x" from above = 8.7
Then;
= 1/3 × π × (7 in)² × 8.7 in
= 142.1π in³
Answer:
its A. 392
Step-by-step explanation:
took the test. hope this helps
Liz is using the distributive property to evaluate the expression 27 (36) by using friendlier numbers. Her work is shown below.
Liz’s Work
27(36)
Step 1
27 (3 + 12)
Step 2
27 (3) + 27 (12)
Step 3
81 + 324
Step 4
405
What was the first error that Liz made?
Step 1 should have been 27(6 + 30).
Step 2 should have been 27(3) + 12.
Step 3 should have been 27(30)(12).
Step 4 should have been 16,244.
Answer:
in step one
Step-by-step explanation:
it looks wrong
Answer:
step 1
Step-by-step explanation:
i took the test
Jack bought 5 pairs of socks for $12.50. At this rate, how much would 12 pairs of socks cost?
Answer: $30
Step-by-step explanation:
5 pairs of socks cost 12.50 you divide 12.50 by 5 and you how much each pair of socks cost which is 2.5 which is 2.50 each pair of socks is 2.50 so now you multiply 2.50 by 12 and you get $30
What is the cost of each item? What is the subtotal? What is the tax? What is the total paid? Shoes: $49.99 (normally) they are on sale for 25% off Jacket: $137.99 (normally) it is on sale for 33% off Pack of Cookies: $4.49 7.3% Sales Tax What is the cost of each item? What is the subtotal? What is the tax? What is the total paid?
Answer:
Cost of shoes = $37.4925
Cost of jacket = $92.4533
Tax = $9.81
Total paid = $144.2458
Step-by-step explanation:
Normal price of shoes = $49.99
Discount = 25%
Discounted price:
[tex]\$49.99 - \$49.99\times \dfrac{25}{100} = \$37.4925[/tex]
Normal price of jacket = $137.99
Discount = 33%
Discounted price:
[tex]\$137.99 - \$137.99\times \dfrac{33}{100} = \$92.4533[/tex]
Price of pack of cookies = $4.49
No discount on cookies as per question statement.
Total amount without tax = $37.4925 + $92.4533 + $4.49 = $134.4358
Sales Tax = 7.3% of total amount without tax = 7.3% [tex]\times[/tex] $134.4358 = $9.81
Total paid = $134.4358 + $9.81 = $144.2458
Lamar ordered some books online and spent a total of $133.each book cost $8 and he paid a total of $5 for shipping. How many books did he buy
Answer:
16 books
Step-by-step explanation:
133-5=128
128/8=16
Answer:
He bought sixteen books
Step-by-step explanation:
Take away the five dollars spent on shipping, get 128 and divide it by 8.
Use the distance formula to find the distance, to the nearest tenth, from S(5,-4) to W(-3,7)
Answer:
Distance (d) =13.6
Step-by-step explanation:
[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\\\(5,-4)=(x_1,y_1)\\(-3,7)=(x_2,y_2)\\\\d=\sqrt{\left(-3-5\right)^2+\left(7-\left(-4\right)\right)^2}\\\\d=\sqrt{(-3-5)^2+(7+4)^2}\\\\d=\sqrt{(-8)^2+(11)^2}\\\\d=\sqrt{64+121}\\\\d=\sqrt{185} \\\\d = 13.60147\dots \\\\\\d =13.6[/tex]
Please help!!
Find x and CB
Answer:
x is -9
CB is 10
Step-by-step explanation:
In order to solve this question we need to figure out what x is first
First we do
2(x+19)=x+29
Then we get 2x+28=x+29
subtract and divide to get
x=-9
Plug in the x to get CB
-9+19=10
5≤3y+8<17 solve and graph
20 points for best answer to my test
Answer:
A,C,D,E
Step-by-step explanation:
HOPE THIS HELPED :)
3) Monica is listening to Spotify. She noticed that during one hour, 15 songs were played and 3 of them were country. What is the ratio of country songs to the number of songs played? *
A:5/1
B:1/15
C:1/3
D:1/5
Answer:
D. 1/5
Step-by-step explanation:
The ratio would be 3/15 and when it's reduced it is 1/5
I hope this helps
hector and alex traded video games. alex gave hector one fourth of his video games in exchange for 6 video games. then he sold 3 video games and gave 2 video games to gis brother. alex enbed up with 16 video games. how many video games did alex have when he started?
Answer:
20 games
Step-by-step explanation:
Lets work backwards; *Adding what he gave away or lost*
-Alex started with 16 video games
-Add the games gave to his brother (+2)
-Add the games he sold (+3)
-The number is 3/4 of his games
-Subtract the games he traded with hector (-1/4)
Equation: 16+2+3-6= 3/4 X (variable) *You can choose other than X*
21-6 = 15
15 = 3/4
Take the reciprical of 3/4 which is 4/3 and multiply it by both sides
4/3 x 15 = 3/4 x 4/3
4/3 X 15 = 20!
ALEX STARTED WITH 20 GAMES!
At the local dairy farm, Kareem buys a 32-oz container of yogurt for $0.48. Are the cost, y, in dollars and the amount of yogurt, x, proportional?
Answer:
The formula should be y=0.015x
Step-by-step explanation:
Each oz of yogurt costs $0.015.
Not sure if this helps, but i hope it does :)
Which function is increasing and has a constant slope?
O A.
B.
y = 10(0.2)
4x + 3y = 14
6.1 5y 10
C.
OD.
y
www
2+ + 1
Find the mean of 11, – 7, – 14, 10, and -5.
Answer:
-1
Step-by-step explanation:
What percent of 40 is 20?
Answer:
8
Step-by-step explanation:
When doing these types of problems, we convert the percent to a decimal. In this case,
40%=0.4
0.4*20=8
Answer:
200%
Step-by-step explanation:
20 = 100% (in this case)
40 = 200% (because you multiply both sides to get 40)
Therefore, 40 is 200% of 20.
what are the six regions of the united states
Answer:
New England.
Mid-Atlantic.
The South.
Mid-West.
The Southwest.
The West.
Step-by-step explanation:
If C=24, what values of A and B complete Ax+By=C for each graph? Write the standard form for each equation.
For the graph in part a, the value for A is =
and the value for B is =
Answer:
Step-by-step explanation:
For graph (a),
Let the equation of the line is,
Ax + By = C
For the line passing through (4, 0) and C = 24,
4A + B(0) = 24
4A = 24
A = 6
For a point (0, -3) lying on this line,
A(0) + B(-3) = 24
-3B = 24
B = -8
Therefore, equation of the line will be,
6A - 8B = 24
3A - 4B = 12
b). If the equation of the given line is,
Ax + By = 24
For a point (3, 0) lying on the line,
3A + B(0) = 24
A = 8
For a point (0, 2) lying on the line,
A(0) + 2B = 24
2B = 24
B = 12
Therefore, equation of the given line will be,
8A + 12B = 24
2A + 3B = 6
Solve the equation-4=2y+4x for y
Answer:
y=-2−2x
hope this helps!
plz mark me brainliest if u can
Have a GREAT DAYY!!!
:D
Find the area of this sector.
19cm length on side 118degree angle in centre
Answer:
87.68 cm²Step-by-step explanation:
Arc length:
118*2πr/360 = 19 cm118*3.14r/180 = 19r = 19*180/118*3.14r = 9.23 cmArea of sector:
A = πr²*118/360 A = 3.14*9.23²*118/360A = 87.68 cm²I NEED THIS LITERALLY RIGHT NOW PLSSS HELP
Answer:
its C 10/9
Step-by-step explanation:
What is the value of x in the equation 1.5(x + 4) – 3 = 4.5(x – 2)?
Answer:
open the brackets of two sides
ie; 1.5x+6-3=4.5x-9
1.5x+3=4.5x-9
4.5x-1.5x=3+9
3x=12
X=4
What is the equation of the line that goes through (-3,-1) and (3,3)
Answer:
3
Step-by-step explanation:
What is the simplified value of the expression below?
Negative 2.6 + 5.8
Answer:
3.2
Step-by-step explanation:
Given that you have 2 parallel lines cut by a transversal, what is the measure of angle 2?
Step-by-step explanation:
angle 2 = 2x + 10 deg (corresponding angles) or 180 - 4x + 46 deg (angles on a straight line are supplementary)
therefore,
2x + 10 = 226 - 4x
6x = 216
x = 36
hence,
angle 2 = 2(36) + 10 = 82deg
Topic: Angles
If you like to venture further, do check out my insta (learntionary) where I regularly post useful math tips! Thank you!
Please help me out!! :c
Nerissa paid a total of $8 for 4 packs of pencils she purchased from the convenience store. Let p represent the cost of one pack of pencils.
Which equation shows an equality between two different ways of expressing the cost for all the pencils?
A. 8 = 4p
B. 8 = 4/p
C. 8 = 4 + p
D. 8 = 4 – p
==================================================
Explanation:
p is a placeholder for a number. Think of it like a box where a number goes inside.
In this case, p is the price of one pack of pencils.
We can use a proportion to help set up an equation
(4 packs)/(8 dollars) = (1 pack)/(p dollars)
4p = 8*1 ... cross multiply
4p = 8
8 = 4p which points to choice A as the answer.
---------------------------
Alternative method:
4 packs = 8 dollars
1 pack = p dollars
Multiply both sides of the second equation by 4 and you'll get
4 packs = 4p dollars
Then replace the "4 packs" on the left hand side with "8 dollars"
8 dollars = 4p dollars
that turns into
8 = 4p
--------------------------
Yet another method:
We know it's $8 for 4 packs. This must mean it is 8/4 = 2 dollars per pack.
If p is the cost of one pack, then p = 2.
Now plug p = 2 into each of the four answer choices. You should find that only 8 = 4p results in a true equation.
Choice B is false because 8 = 4/p turns into 8 = 4/2 and that becomes 8 = 2, which is a false equation. Choices C and D are similar stories.
Answer:
The answer is A
Step-by-step explanation:
Help me please.. :)
(favorite song?)
Answer:
(3,7)
Step-by-step explanation: My favorite song rn is like I want you by giveon
a line through the point (5,-2) and parallel to the line 4x+6y=10
Answer: y = mx + b
4x - 6y = 10
-6y = -4x + 10
y = (-4/-6)x + 10/-6
y = (2/3)x - 5/3
m = 2/3
b = -5/3
Step-by-step explanation:
Sam ran 3 1/2 miles in 25 minutes. If he continues running at this pace how far will he run in 1 hour
Answer: 8.4 or 8 2/5
Step-by-step explanation:
3 1/2 for 25 minutes and 0.14 miles per minute so 0.14 * 60 since there are 60 minutews in a hour and you get ur answer.
Use the distributive property to remove the parentheses.
(w+11)8
Answer:
Done!
Step-by-step explanation:
8(w + 11)
8w + 88
9514 1404 393
Answer:
8w +88
Step-by-step explanation:
Each of the terms inside parentheses multiplies the factor outside:
(w + 11)8 = w·8 +11·8 = 8w +88