Answers
Answer:
Step-by-step explanation:
2x + 3y = 2
x = 2 - 3y /2
x + y = 0
substitute the value of x
[tex]\frac{2 \\- 3y}{2}[/tex] + y = 0
2 - 3y + 2y = 0
2 = y
again,substitute the value of y
x = 2 - 3y / 2
=2 - 3*2 / 2
=2 - 6 / 2
=-2
Answer:
x = 2, y = -2
Step-by-step explanation:
This is an alternate way. You can also solve simultaneous equations using matrices. First, rewrite the simultaneous equations in matrix form.
[tex]\displaystyle \large{\left[\begin{array}{ccc}2&3\\1&1\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}2\\0\end{array}\right]}[/tex]
Let:
[tex]\displaystyle \large{A= \left[\begin{array}{ccc}2&3\\1&1\end{array}\right]}\\\displaystyle \large{X = \left[\begin{array}{ccc}x\\y\end{array}\right]}\\\displaystyle \large{B =\left[\begin{array}{ccc}2\\0\end{array}\right]}[/tex]
So now we have [tex]\displaystyle \large{AX = B}[/tex] and we have to solve for X which:
[tex]\displaystyle \large{A^{-1}AX = A^{-1}B}\\\displaystyle \large{X = A^{-1} B}[/tex]
Where:
[tex]\displaystyle \large{A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right]}[/tex]
**ad-bc is determinant of 2*2 matrices and shortened as det(var) or |var|**
Therefore, from A:
a = 2b = 3c = 1d = 1Find detA:
[tex]\displaystyle \large{\det A = |A| = ad-bc = 2(1)-3(1) = 2-3 = -1}[/tex]
Therefore, detA = -1. Hence:
[tex]\displaystyle \large{A^{-1}=-1\left[\begin{array}{ccc}1&-3\\-1&2\end{array}\right]}[/tex]
And [tex]\displaystyle \large{X = A^{-1}B}[/tex]:
[tex]\displaystyle \large{X = -1\left[\begin{array}{ccc}1&-3\\-1&2\end{array}\right] \left[\begin{array}{ccc}2\\0\end{array}\right] }[/tex]
Evaluate the matrices:
[tex]\displaystyle \large{X = -1\left[\begin{array}{ccc}1 \cdot 2-3 \cdot 0\\-1 \cdot 2+2\cdot 0\end{array}\right] }\\\displaystyle \large{X = -1\left[\begin{array}{ccc}2-0\\-2+0\end{array}\right] }\\\displaystyle \large{X = -1\left[\begin{array}{ccc}2\\-2\end{array}\right] }\\\displaystyle \large{X = \left[\begin{array}{ccc}-2\\2\end{array}\right] }\\\displaystyle \large{\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}-2\\2\end{array}\right] }[/tex]
Therefore, x = -2 and y = 2.
Related Questions
The measure of an angle is 116.3°. What is the measure of its supplementary angle?
Answers
Answer:
63.7°
Step-by-step explanation:
supplementary_interier angle 180_116.3=63.7
Which of the rulers are similar in shape? Explain.
Answers
Crystal earns $5.50 per hour mowing lawns.how much does crystal earn if she works 3 hours and 45 minutes
Answers
Work:
You have to multiply 5.50 to 3.75 because 45 is 75 percent of 60
I need help with all these 5 questions please please help me with these questions
Answers
Answer:
1. (4,5) 2. D 3. J 4.D 5. 64.8 oz
Step-by-step explanation:
math
what is 3x +5+4 (x+2) +2
Answers
Answer:
4x+13
Step-by-step explanation:
Answer:
7x+15
Step-by-step explanation:
3 ln x = ln 16 + ln 4. Solve for x.
Please walk me through which log rule to use once you get to the point:
ln x = (ln 16 + ln 4)/3
Answers
Answer:
4
Step-by-step explanation:
[tex] ln(x) = ln(16) + ln(4) [/tex]
Use the Produxt Rule
[tex] ln(a) + ln(b) = ln(a + b) [/tex]
Remeber that Ln is a log function with base e,
so know we have
[tex]3 ln(x) = ln(64) [/tex]
[tex] ln(a) = ln(b) [/tex]
Only if a=b So we have
x^3=64
x=4
[tex]x = 64[/tex]
Step-by-step explanation:
See the picture for steps
609,982 + -17,237 - 415
Answers
Answer: 592330
Step-by-step explanation:
-17237-415=. -17652-17652 + 609,982= 592,330Your answer is. 592,33O.
12. (5+4 -2)* (-2) = ?
O A.-22
O B. 14
O C.22
O D.-14
Answers
Answer:
D : -14
Step-by-step explanation:
(5+4-2)(-2) = x
7(-2) = x
-14 = x
x = -14
need help with math problem if do 5 star and brain point
Answers
Find all values of y such that the distance between (1. y) and (-3. - 6) is 5 units. Express numbers as integers, simplified fractions, or radicals.
Answers
Answer:
Step-by-step explanation:
Distance = d
d² = [1 - (-3)]² + [y - (-6)]²
5² = 16 + (y + 6)²
25 = 16 + (y + 6)²
(y + 6)² = 25 - 16 = 9
y + 6 = ±3
y = -6 ±3
so
y = -3 or -9
Find the circumference of the
circle. Use 3.14 for T.
1.5 cm
The circumference of the circle is cm.
(Round to the nearest hundredth as needed.)
Answers
C= 9.42 cm
PLEASE ANSWER FAST
How much power is required to lift a 240 N table up 3 m in 20 seconds?
A. 1600 W
B. 0 W
C. 36 W
D. 720 W
Answers
Answer:
I am not sure but the answer may be 36 w
Answer:
A.1600
Step-by-step explanation:
I hope its help keep safe
Mrs. Thomas made 60 cupcakes for the Valentine's Day party. She put chocolate icing on 2/3 of them. She put vanilla icing on 1/2 of the remaining cupcakes. She put strawberry icing on what was left. How many cupcakes did she put strawberry icing on?
Answers
!Answer:
Mrs. Thomas put 1/4 icing on the remaining cupcakes
Step-by-step explanation
Terry is making 3 hat and scarf sets. Each scarf requires 2 yards of material and each hat requires 30 inches
of material.
How many feet of material does he need for all 3 hat and scarf sets?
He will need
feet of material for all 3 hat and scarf sets.
Answers
Answer: 25.5 feet
Step-by-step explanation:
if each hat requires 30 inches of material, then 3 hats will require 3(30) = 90 inches.
if each scarf requires 2 yds of material, then 3 scarfs will need 3(2) = 6 yds.
The question wants us to give our answer in feet, so we will be converting:
Using 12in = 1ft:
90 in = 90/12 feet = 7.5 feet
Using 1 yd = 3 ft:
6 yds = 6(3) = 18 feet.
Now that the units are the same, we can add them up to get our answer:
7.5 + 18 = 25.5 feet
So Terry will need 25.5 feet of material to make 3 sets of hat and scarves.
A real life scenario could be like earning 15 dollars.
need written response
Answers
Answer:
Step-by-step explanation:
first of all you need to do is make a lemonade stand and make the lemonade taiste good then you can sell it for 15 dollars which is a good price to get you started with your life
Which line has a slope of -1/2?
Line A
Line B
Line C
Line D
Answers
Answer:
Line D
Step-by-step explanation:
Two points that passes through line D : (0,-2) & ( -4 , 0)
[tex]Slope =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\\=\dfrac{0-[-2]}{-4-0}\\\\\\=\dfrac{0+2}{-4}\\\\\\=\dfrac{2}{-4}\\\\\\=\dfrac{-1}{2}[/tex]
. Solve: - 5x² + 5 = - 2x The solution contains a reduced fraction another reduced
fraction with a radical numerator. What is this fraction with a radical numerator?
a
Answers
Consider the given quadratic equation that we have :
[tex]{:\implies \quad \sf -5x^{2}+5=-2x}[/tex]
Multiplying both sides by -1 will yield ;
[tex]{:\implies \quad \sf 5x^{2}-5=2x}[/tex]
Write the above quadratic equation in the form of standard quadratic equation ax² + bx + c = 0 ,
[tex]{:\implies \quad \sf 5x^{2}-2x-5=0}[/tex]
Now , comparing this with the standard form of quadratic equation we will get a = 5 , b = -2 , c = -5 . So now , Discriminant (D) = (-2)² - 4 × 5 × -5 = 4 + 100 = 104
Now , by the quadratic formula ;
[tex]{:\implies \quad \sf x=\dfrac{-(-2)\pm \sqrt{104}}{2\times 5}}[/tex]
[tex]{:\implies \quad \sf x=\dfrac{2\pm 2\sqrt{26}}{2\times 5}}[/tex]
[tex]{:\implies \quad \sf x=\dfrac{\cancel{2}(1\pm \sqrt{26})}{\cancel{2}\times 5}}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{x=\dfrac{1\pm \sqrt{26}}{5}}}}[/tex]
Used Concepts :-For any quadratic equation of the form ax² + bx + c , the Discriminant (D) is given by D = b² - 4ac , and the root [tex]\bf x[/tex] of the quadratic equation is given by the quadratic formula as
[tex]{\boxed{\bf{x=\dfrac{-b\pm \sqrt{D}}{2a}}}}[/tex]How long would it take an investment to double at 18% compounded daily?
Answers
Answer:
The rule says that to find the number of years required to double your money at a given interest rate, you just divide the interest rate into 72. For example, if you want to know how long it will take to double your money at eight percent interest, divide 8 into 72 and get 9 years
A farmer needs to enclose three sides of a plot with a fence (the fourth side is a river). The farmer has 54 yards of fence and wants the plot to have an area of 360 sq-yards. What should the dimensions of the plot be? (For the purpose of this problem, the width will be the smaller dimension (needing two sides); the length with be the longer dimension (needing one side). Additionally, the length should be as long as possible.)
length = yards
width = yards
Enter your answers as numbers. If necessary, round to the nearest hundredths.
Answers
Answer:
The length of the field = 24.5 yards
The width of the field = 12 yards.
Step-by-step explanation:
If "w" is the width, then the length is 49 - 2w.
The area of the rectangle field = length × width
= w(49 - 2w)
Area =
This a quadratic equation, the vertex of x coordinate is w
w =
Here a = -2 and b = 49
w = .
So width of the field is 12.25 yards.
The length of the filed = 49 - 2(12.25) = 24.5
Area = 12.25 × 24.5 = 300.125 square yards.
The field has an area of 294.
Therefore, the length must be 24.5 yards and width must be 12 yards.
24.5 × 12 =294 square yards.
Therefore, the length of the field = 24.5 yards
the width of the field = 12 yards.
help someone please sjsj
Answers
Answer:
17
Step-by-step explanation:
Seeing that traingle ABC is = to triangle DEF.
It means that the angles are equal too.
So you would equate them to each other.
Hence 5X+2=87
5X=87-2
5X=85 (divide by 5)
X=17
Hope that helps :)
Correct answers only and answer all of them please
Put number by answer ex:(1:A, 2:B, 3:C,.....etc)
I'll mark brainliest!!
Answers
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
[tex]u\cdot v=\langle4,-7\rangle\cdot\langle-6,9\rangle=(4*-6)+(-7*9)=-24-63=-87[/tex], so A is correct. Remember to multiply the horizontal components with each other and then add that to the product of the vertical components to get the dot product.
Problem 2
Two vectors are orthogonal if their dot product is 0, which also means that they must be perpendicular to each other, so we can check this:
[tex]u\cdot v=(6*-24)+(-9*36)=-144-324=-468[/tex]
Since the dot product of the two vectors is 0, they aren't orthogonal. Therefore, they are parallel since [tex]v=4u[/tex], making A the best choice.
Problem 3
Recall that the angle between two vectors is [tex]\theta=cos^{-1}(\frac{u\cdot v}{||u||*||v||})[/tex] where [tex]u\cdot v[/tex] is the dot product of vectors [tex]u[/tex] and [tex]v[/tex] while [tex]||u||[/tex] and [tex]||v||[/tex] are the magnitudes of vectors [tex]u[/tex] and [tex]v[/tex] respectively. If we let [tex]F_1=u[/tex] and [tex]F_2=v[/tex], we can then continue on:
[tex]u\cdot v=(190*128)+(160*-121)=24320+(-19360)=4960[/tex]
[tex]||u||=\sqrt{190^2+160^2}=\sqrt{61700}=10\sqrt{617}[/tex]
[tex]||v||=\sqrt{128^2+(-121)^2}=\sqrt{31025}=5\sqrt{1241}[/tex]
[tex]\theta=cos^{-1}(\frac{u\cdot v}{||u||*||v||})\\\\\theta=cos^{-1}(\frac{4960}{10\sqrt{617}*5\sqrt{1241}})\\\\\theta\approx83.49^\circ\approx83^\circ[/tex]
Therefore, B is the correct answer
Problem 4
We observe that [tex]u=\langle-8,-9\rangle[/tex] and [tex]v=\langle3,7\rangle[/tex], so [tex]-3(u\cdot v)=-3[(-8*3)+(-9*7)]=-3[-24+(-63)]=-3(-87)=261[/tex]. This means that B is the correct answer.
Problem 5
Recall that the projection of a vector [tex]u[/tex] onto [tex]v[/tex] is [tex]proj_vu=(\frac{u\cdot v}{||v||^2})v[/tex], thus:
[tex]proj_vu=(\frac{u\cdot v}{||v||^2})v\\\\proj_vu=(\frac{(-10*4)+(-3*8)}{\sqrt{4^2+8^2}^2})\langle4,8\rangle\\\\proj_vu=(\frac{-40+(-24)}{\sqrt{80}^2})\langle4,8\rangle\\\\proj_vu=(\frac{-64}{80})\langle4,8\rangle\\\\proj_vu=(-\frac{4}{5})\langle4,8\rangle\\\\proj_vu=\langle-\frac{16}{5},-\frac{32}{5}\rangle[/tex]
Therefore, D is the correct answer
You want to find out the height of a tree, so you hold a square cardboard so that the edges line up with the top and bottom of the tree, as shown in the diagram below. Your friend measures the horizontal distance from you to the tree, and the vertical distance from the ground to your eye. What is the height of the tree to the nearest tenth of a foot? 9.2 ft 5.8 ft
Answers
The vertical distance from the ground to your eye is 10.9 feet and the height of the tree is 20.5 feet.
What is Pythagoras theoremPythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given by:
Hypotenuse² = Adjacent² + Opposite²
From the diagram, let d represent the horizontal distance, hence:
d² = 9.2² + 4.8²
d = 10.9 feet
Let h represent the height of the tree, hence:
h / 10.9 = 10.9 / 5.8
h = 20.5 feet
The vertical distance from the ground to your eye is 10.9 feet and the height of the tree is 20.5 feet.
Find out more on Pythagoras theorem at: https://brainly.com/question/343682
9 Yuki and Roman are photographers for the yearbook. Yuki starts with 20 photos.
She then takes 60 photos each week. Roman starts with 110 photos. He then takes
35 photos each week. After how many weeks will Yuki and Roman have taken the
same number of photos? Write a system of equations that can be used to solve the
problem. Write your answers in the blanks.
P=
W +
p=
W +
Answers
Yuki
y = 60x + 20
(total = 60 photos a week * x weeks + 20 starting photos)
Roman
y = 35x + 110
(total = 35 photos a week * x weeks + 110 starting photos)
So the system of equations for this problem is:
y = 60x + 20
y = 35x + 110
A function contains the 5 ordered pairs below (x,y). Four of the points as given below
(1,3) (2,5), (6, 13), (9,27)
Question:
Identify a 5th point that would maintain the function.
*Provide an ordered pair
*Explain why this maintains the function
Answers
A 5th point that would maintain the function is (11, 31)
Coordinate pairs of a functionGiven the following pairs of coordinates
Four of the points are given as (1,3) (2,5), (6, 13), (9,27)
Using the coordinates (1,3) (2,5), to determine the slope
[tex]Slope=\frac{5-3}{2-1} = \frac{13-5}{6-2}=2\\[/tex]
Let the required coordinate be (x, y) to have:
[tex]2 = \frac{y - 27}{x - 9} \\[/tex]
Since the x coordinate of (9, 27) is greater than 8, hence the best x-coordinate will be 11. Substitute to get the y-coordinate
[tex]2 = \frac{y - 27}{11- 9}\\2(2) = y - 27 \\4 = y - 27\\y=27 + 4\\y=31[/tex]
Hence a 5th point that would maintain the function is (11, 31)
Learn more on functions here; https://brainly.com/question/25638609
Ms. Williams asked her class if they prefer doing their homework before school to students who prefer doing homework after school is 7:15 what does the ratio 7/22
Answers
Answer:
The number of students that prefer to do homework from the group of all students
Step-by-step explanation:
The question says that the ratio between the student who prefer doing homework before school and the students who prefer doing homework after school is 7:15.
That means 7 students prefer doing homework before school and 15 students prefer doing after school.
In this scenario, the total number of students is 7 + 15 i.e. 22
So the percentage 7/22 is the number of students that prefer to do homework before school from the group of all students
Solve 3x+12+7= -5x -5 for x
Answers
[tex]\fbox{Answer ~}[/tex]
Here ,
[tex]\bold\purple{3x + 12 + 7 = - 5x - 5} \\\\\bold{3x + 19 = - 5x - 5}[/tex]
gather and solve the like terms together ,
[tex]\bold{3x + 5x = - 5 - 19} \\\\ \bold{8x = - 24} \\\\\bold{ x = \cancel{ \frac{ - 24}{8} }} \\ \\\bold\red{ x = - 3}[/tex]
hope helpful~
The first train leaves the station at 6:15 A.M The second train leaves at 6:55A.M How much later does the second train leave the station?
Answers
Answer:
40 minutes later
Step-by-step explanation:
6:15 + 40 minutes = 6:55
Step by step pls••••••••••••••••••••
Answers
Answer:
[tex]\frac{20r^5}{c}[/tex]
Step-by-step explanation:
[tex]4c^{4}[/tex]·[tex]5c^{-5} r^{5}[/tex]
=[tex]4c^{4}[/tex]·[tex]\frac{5 r^{5}}{c^{5} }[/tex]
=[tex]\frac{20c^{4}r^{5} }{c^5}[/tex]
=[tex]\frac{c^4}{c^4} \frac{20r^5}{c}[/tex]
=[tex]\frac{20r^5}{c}[/tex] or =[tex]20c^{-1}r^5[/tex]
Help me to answer this please
Thankyou!
Answers
Answer:
131
Step-by-step explanation:
When we attempt to find the square root of 5607, we get a remainder of 131. (5607=74^2 + 131) That means 5607-131 is a perfect square. (Which is 5476=74^2)
What is this problem?
Answers
Answer:
That its a problem there u go
Step-by-step explanation: