Answer:
x= -3 and y= 0
Step-by-step explanation:
5x+2y=-15
2x-2y=-6
7x =-21
x= -3
Putting value of x in equation 1
5(-3) +2y=-15
-15+2y= -15
2y= 0
y= 0
This can be solved with the help of matrices
In matrix form the above equations can be written in the form
[tex]\left[\begin{array}{ccc}5&2\\2&-2\/\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-15\\-6\\\end{array}\right][/tex]
Let
[tex]\left[\begin{array}{ccc}5&2\\2&-2\/\end{array}\right][/tex] = A [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] = X and [tex]\left[\begin{array}{ccc}-15\\-6\\\end{array}\right][/tex]= B
Then AX= B
or X= A⁻¹ B
where A⁻¹= adj A/ ║A║ where mod A≠ 0
adj A= [tex]\left[\begin{array}{ccc}-2&-2\\-2&5\/\end{array}\right][/tex]
║A║= ( 5*-2- 2*2)= -10-4= -14≠0
X= A⁻¹ B
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] =- 1/14 [tex]\left[\begin{array}{ccc}-2&-2\\-2&5\/\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}-15\\-6\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] =- 1/14 [tex]\left[\begin{array}{ccc}-2*-15&+ -2*-6\\-2*-15&+ 5*-6\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] =- 1/14 [tex]\left[\begin{array}{ccc} 30&+12\\30&+-30\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] =- 1/14 [tex]\left[\begin{array}{ccc}42\\0\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-42/14\\0/-14\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-3\\0\\\end{array}\right][/tex]
From here x= -3 and y= 0
Solution Set = [(-3,0)]
please help asap I will make you brainliest and please don't put a link The area of the base of a triangular pyramid is 90 meters squared, and its height is 6 meters. The volume of a pyramid can be found using the formula V = one-third B h. Which expressions can be used to find the volume of the pyramid? Select three choices.
Answer:
I think It is the third and fifth.
Step-by-step explanation:
i do not know for sure though.
The area of a rectangular park is 300 sq.M. If the length of the park is 25 m, find the breadth. *
Answer:
Breadth = 12 m
Step-by-step explanation:
Area of a rectangle is given by the formula,
Area = Length × Width
Value of area and length of the rectangular park has been given in this question.
Therefore, by substituting these values in the formula,
300 = 25 × Width
Width = [tex]\frac{300}{25}[/tex]
= 12 m
Therefore, width or breadth of the rectangular park will be 12 m.
PLEASEE help I’m stuck on this
Answer:
x = √149
Step-by-step explanation:
Compartmentalize the odd figure into a rectangle (with sides 3 and 7) and a triangle (with sides 10 and x). Now, that you have a triangle, you can use the rectangle underneath to find the bottom side of the triangle--it is 7. The triangle that has been formed is a right triangle, so we can use the Pythagorean Theorem to find x, which is the hypotenuse.
10² + 7² = x²
100 + 49 = x²
149 = x²
√149 = x
Answer:
7√2
Step-by-step explanation:
Remark
Draw another line parallel to 7.
Move to the other end of 3
that makes the vertical leg on the left 10 - 3 = 7
You now have a smaller right triangle.
Equation
a = 7
b = 7
c = x
Solution
x^2 = 7^2 + 7^2
x^2 = 49 + 49
x^2 = 98
x^2 = 7 * 7 *2
sqrt(x^2) = sqrt(7 * 7 * 2)
The rule about square roots is for every pair of factors you can take one out of the square root sign and throw the other one away.
x = 7 sqrt(2)
Explain Jan’s error
Answer:
Please check explanations
Step-by-step explanation:
To find the volume of the surface area of a cone, we need to use the height and not the slant height of the cone
The slant height, the height and the base radius forms a right triangle with the slant height being the hypotenuse of this triangle
By Pythagoras’ theorem, the square of the hypotenuse (slant height) equals the sum of the squares of the two other sides
6.5^2 = 2.5^2 + h^2
h^2 = 36
h = √36
h = 6 cm
So we have the volume as;
V = 1/3 * pi * r^2 * h
where r in this case is base radius of 2.5 cm
V = 1/3 * pi * 2.5^2 * 6 = 39.3 cm^3
Please help i know this is kind of easy but I am having a hard time with it unfortunately
Answer:
x=2
Step-by-step explanation:
Answer:
x=2
Step-by-step explanation:
if x^3 is = 8, then
x= ∛8
∛8 = 2
x=2
to check
2*2*2= 8
Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 68 miles. If the two airplanes are 85 miles apart, how far has the eastbound airplane traveled?
Answer:
17 miles
Step-by-step explanation:
85 - 68
17
The front view of the top of a house is in the shape of a triangle whose
height is 10 inches less than the length of its base and its area is 75 in2. If b
represents the length of the base, which of the following equations can be
used to find the value of b?
Answer:
uiptyftyfkghfcytfghvchjcghcfgcjvbcfg
Step-by-step explanation:
Answer:
2nd option
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here A = 75, b = b , h = b - 10, then
[tex]\frac{1}{2}[/tex] b(b - 10) = 75 ( multiply both sides by 2 to clear the fraction )
b(b - h) = 150 ← option 2
Micheal is using the table below to find the value of 128 x 72 .
Thank you to anyone who answers .
Answer:
it's 128 x 72 =9,216
Step-by-step explanation:
N = 560
Which of the following could be true if y ≤ -75?
Hello!
Lets go through each choice, and determine if it is correct.
So, the symbol ≤, means less than or equal to. So our answer must be less than -75 or -75 on the dot.
A: y = 75
Okay, so we can tell this one is wrong off the bat. 75 is much more than -75. (Make sure you notice the symbol!) So it cannot be equal to said answer. A is wrong.
B: y =-74
Another trick question! When you are in the negatives, less is more! So -74 is actually greater than -75. This is also incorrect!
C: y > -75
This one is straight forward. Our equation up top strictly says less than or equal too, while C says greater than. Incorrect!
D: y = -75
The last answer! We see that the symbol in our equation up top says less than or equal too, and y = -75 is equal. This is the correct answer.
Our correct answer is D: y = -75
waffletowne
A teacher is making worksheets for the next unit. He can create 3 worksheets in an hour and has 10 worksheets already created from the previous year. Which of the following lengths of time worked will not be long enough for the teacher to have created 27 worksheets. * Check All That Are True*
6 hours, 10 hours, 8 hours, 2 hours, 4 hours
Answer:
2 hours, 4 hours
Step-by-step explanation:
So lets go over what we know.
There are already 10 worksheets created.
Every 1 hour 3 more are made.
27 worksheets need to be made.
Ok, the first thing we can do is subtract the amount of worksheets needed by the amount we laready have:
27-10
=
17
Now, lets divide the amount of worksheets we still need, by how many we make each hour:
17/3
=
Well, 3 goes into 15, 5 times. Then 2 is left. So we know it takes 5 2/3 hours to create all 27 worksheets.
Looking at the answers, 6 hours, 8 hours, and 10 hours would work. However 2 hours and 4 hours would not work.
Hope this helps! ;)
4. Ann bought four pens and three exercise books for a total of sh 17 while peter bought five
similar pens and two exercise books for a total of sh.16 find the cost of a pen and an exercise
book.
Answer:
pen = 2 book = 3
Step-by-step explanation:
p= pens
b=books
4p +3b =17
5p+2b=16
Multiply the first by 5
Multiply the second by -4
Add both (p variable will ce cancelled)
20p +15b = 85
-20p -8b = -64
7b = 21
b=3 (book =3)
Lets plug this in one of the equations
4p + 3x3 = 17
4p +9 0 19
4p = 8
p= 2 (pencil = 2)
Find the indicated measure. Round answers to the nearest hundredth.
What is the volume of the rectangular prism?
I need a lot of help bro
3x^5 + 2x^2 What is the degree of this polynomial?
A. 1
B. 3
C. 5
D. 6
option ( C )
5
...........
Answer:
C. 5
Step-by-step explanation:
The degree is the highest exponent in the polynomial and in the polynomial given, 3x^5 has the highest exponent, being 5, so that would be the degree.
Hope this helps :)
Jamya is making a rectangular blanket. The length of the blanket is 10inches greater than it's worth, W, in inches. Write the function, f(w), that describes the area, in square inches, of Jamya's blanket as a function of the width, w.
Answer: (w² + 10)inches²
Step-by-step explanation:
Since the width of the rectangular blanket is given as w and the length of the blanket is 10inches greater than it's width, therefore the length will be:
= 10 + w.
Therefore,
length = 10 + w
width = w
Area = length × width
Area = (10 + w) × w
Area = 10w + w²
Therefore, the area of the blanket will be (w² + 10)inches².
Mark is six years older than his brother Sam. The sum of their ages is 30. Let 'a' be Sam's age.
Answer:
a = 12 years
Step-by-step explanation:
Mark is 6 years older than his brother Sam. Now, we are asked to represent Sam’s age by a. This means that if Sam is a years old, Mark is (a + 6) years old.
The sum of their ages is 30, this means that when we add their ages together, we get the sum of thirty.
Mathematically this means a + a + 6 = 30
2a + 6 = 30
This is the equation needed to get a. To get a , we proceed to solve the equation to completion.
2a = 30 - 6
2a = 24
a = 24/2
a = 12
How many four letter words can be made from the letters X, B, O, M, T?
Answer:
tombexplanation:
thats it
The amount of sprinkles needed for a cookie recipe is proportional to the number of
cookies. A batch of 26 cookies calls for 2 tablespoons of sprinkles. What is the
constant of proportionality between the number of cookies and the number of
tablespoons of sprinkles?
Can someone please help me? And explain and show work.?
Answer:
C. 13
Step-by-step explanation:
26 ÷ 2 = 13
Let me know if that helped!
Thanks for letting me answer!
PLEASE HELP WAITING 3 HOURS NOW
NO NONSENSE WILL REPORT
How much time does it take for a bird flying at a speed of 45km/h to travel a distance of 1800km?
Answer:
40 hours
Step-by-step explanation:
Time=Distance/Speed
Time=1800/45
Time=40 hrs
Answer:
[tex]40h[/tex]
Step-by-step explanation:
[tex]speed = \frac{distance}{time} \\ time = \frac{d}{s} \\ = \frac{1800km}{45kmh ^{ - 1} } \\ = 40h[/tex]
hope this helps you.
Can I have the brainliest please?
Have a nice day!
Which two integers is √31 between?
Answer:
5 & 6
Step-by-step explanation:
The nearest two perfect squares are √25 and √36 which are 5 and 6
At a point 70 feet from a tree, a forester measures the angle of elevation to the top of the tree to be 62°. How tall is the tree to the nearest foot?
Answer:
The tree is about 62ft tall
Step-by-step explanation:
sin(62)=x/70
70sin(62)=x
61.8=x
Find the perimeter of a rectangle with length (x-5) and width (3x+1).
Answer:
8x-8
Step-by-step explanation:
P=s+s+s+s or in this case P= 2l+2w
P= 2(x-5)+2(3x+1)
P=(2x-10)+(6x+2)
P=8x-8
8x-8 will be the perimeter of a rectangle with length (x-5) and width (3x+1).
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Given that,
Length of rectangle = x - 5
Width of rectangle = 3x + 1
Now,
Perimeter of rectangle = 2(width + length)
Perimeter of rectangle = 2(3x + 1 + x - 5)
The perimeter of the rectangle = 8x - 8
Hence "8x-8 will be the perimeter of a rectangle with length (x-5) and width (3x+1)".
For more about rectangles,
https://brainly.com/question/15019502
#SPJ2
04/17: Average: Mean
Alex has grades of 87, 75 and 86 on three math tests. What grade must he obtain on the next test to have an avera
tests?
Answer:
dam
Step-by-step explanation:
Amy plotted these four points on a coordinate grid.
• Point A: (-2,-9)
•Point B: (-2,9)
•Point C: (2,-9)
•Point D: (2,9)
Which point is the first quadrant?
Answer:
Point D: (2, 9)
Step-by-step explanation:
The first quadrant includes points that have a positive x coordinate and a positive y coordinate. The only point that meets these conditions is point D, (2, 9).
help, thank youu
A: 75
B: 61
C: 48
D: 80
Answer:
The answer is C, 48
Step-by-step explanation:
Its the only answer that makes sense
Answer:
75
Step-by-step explanation:
1. Eliminate wrong answers
a. (boys 5 & girls 4) meaning the boys should have a higher number than girls (which is 60) this meaning that 48 and 61 can not be the correct answer.
5/4=x/60
x=(5/4)*60
x=75
Math rocks
Leaving it to the obvious chose(The answer is 75)
Hope this helps
What is the answer to this problem
Answer:
791.68
Step-by-step explanation:
have a nice day! :)
After a company celebrated its ten year anniversary, the president of the company wanted to know how long employees have been with the company. Human resources provided the president with the box plot below.
Using the box plot, determine the best measures of the data.
The best measure of center is the (blank)
, and the best measure of variability is the (blank)
.
The number that best summarizes the data is (blank)
years of service.
The number that best describes how the data varies is (blank)
years of service.
Step-by-step explanation:
the center=3 bc it is in the middle of the box
variability is 2
the number that best summarizes the data is 4.5
the number that describes how the data varies is 9-0=9
Hope that helps :)
Answer:
what's the answer?
Step-by-step explanation:
There is a hot market at school for used graduation gowns, in fact the price is growing exponentially! Last week I could have gotten one for $25, but today, one week later, the price is $37.50. What would the price be if I decide to wait to buy my graduation gown at graduation, six weeks from now?
Answer:
$100
Step-by-step explanation:
the equation to solve this is:
[tex]y=12.5x+25[/tex]
[tex]y=12.5x+25\\ =(12.5*6)+25\\ =75+25\\ =100[/tex]
(Assuming, of course, that this is a homework assignment and not you actually buying it cuz' in real life the numbers would be different from month to month)
Please help, I need this answer ASAP
Answer: x= (2/3,0) y=(0,2)
X=(4,0) y=(0,8)
X=(-3,0) y=(0,-3)
Step-by-step explanation:
