Answer:
(x, y) = (3/7, 1/7) or (3, 4)
Step-by-step explanation:
The second equation can be rearranged to ...
4x^2 +9y^2 = 15xy . . . . . . multiply by xy
4x^2 -15xy +9y^2 = 0 . . . subtract 15xy
(4x -3y)(x -3y) = 0 . . . . . . factor
This resolves to two linear equations:
4x -3y = 0
x -3y = 0
__
Combined with the first equation, we get two systems of equations. We can solve both of them at once by substituting for y and using a stand-in for the coefficient of x.
y = (3x -1)/2 . . . . first equation solved for y
Cx -3(3x -1)/2) = 0 . . . . substitute for y in the 2nd/3rd equations (C = 1 or 4)
2Cx -9x +3 = 0 . . . . . multiply by 2
x(2C -9) = -3 . . . . . . .subtract 3
x = -3/(2C -9) = 3/(9 -2C) . . . . . remembering that C = 1 or 4
__
For C=1, x = 3/(9 -2) = 3/7
y = (3(3/7) -1)/2 = 1/7
For C=4, x = 3/(9 -8) = 3
y = (3(3) -1)/2 = 4
The solutions are (x, y) = (3/7, 1/7) and (3, 4).
_____
Additional comment
We could have substituted for y in the quadratic form of the second equation. This would give a quadratic in x that could be solved in any of the usual ways.
A. Decide whether the given examples illustrate a constant or a variable.
1. Number of family members in each house
2. Amount of money in the bank every month
3. Number of seconds in a minute
4. Weekly expenses of groceries
5. Number of years in a millennium.
Asynchronous task on introduction to algebraic expressions
B. Make your own algebraic expressions based on the given conditions.
1. A variable
2. A combination of any number and any variable related by exponentiation.
3. A combination of any two variables related by subtraction.
4. A combination of any number and any three variables related by multiplication.
pls answer and help me..
Answer:
a constant is a data item whose value cannot change during the program execution just as its name implies that the value is constant a variable is a data item whose value can change during the program's execution . Thus as its name implies the the value can vary
What is the slope??
(The bottom one says : (1, 1)
Need help ASAP on #22 please!! Just #22. I couldn't take a proper picture of it because my hand was too shaky and I'm using P.C.
Giving Brainliest to a person who gets it right. I need an answer ASAP! This is my last question.
solve for c. 3c+2=-10 and thank you
Answer:
c= -4
Step-by-step explanation:
Given that:.3c+2 = -10
⇛ 3c = -10 - 2
⇛3c = -12
⇛c = -12:3 = -12/3
.°. c = -4 Ans .
BRANLIEST FOR CORRECT ANSWER
Complete the pairs of corresponding parts if △RST ≅ △TXY.
∠S =
∠ TXY
∠ XTY
∠ XYT
Complete the pairs of corresponding parts if △RST ≅ △TXY.
∠STR =
∠ XYT
∠ TXY
∠ XTY
Complete the pairs of corresponding parts if △RST ≅ △TXY.
RS =
TX
XY
TY
Complete the pairs of corresponding parts if △RST ≅ △TXY.
ST =
TY
XY
TX
Complete the pairs of corresponding parts if △RST ≅ △TXY.
RT =
TX
XY
TY
Complete the pairs of corresponding parts if △ABD ≅ △EFC.
∠A =
∠ FCE
∠ FEC
∠ EFC
Why is ▲MAE ≅ ▲TON?
HL
HA
LL
All of the following are ways to prove triangles congruent except
SAS
SSA
ASA
SSS
Answer:
Step-by-step explanation:
△ RST ≅ △ TXY
We are given ΔRST and ΔTXY are congruent to each other.
If two triangles are congruent to each other then their corresponding parts are equal.
Please see the attachment of two triangles.
∠R is corresponding to ∠T
∵ ∠R=∠T By CPCT
∠XYT is corresponding to ∠STR
∵ ∠XYT=∠STR By CPCT
∠XTY is corresponding to ∠SRT.
∵ ∠XTY=∠SRT By CPCT
∠TXY is corresponding to ∠RST
∵ ∠TXY=∠RST By CPCT
CPCT: Congruent part of congruence triangle.
Students who
ride the bus
65% of the 800 students at North High School ride the
bus. How many students ride the bus?
0 65
?
100 multiplied by
is equal to 800
H
65 multiplied by
vis equal to
0 100
800
out of
students ride the bus.
All
students
You have two different savings accounts. For account A, the interest earned after 18 months is $12. If the interest rate is 3.2% for account A, how much is the principal? Give the equation and solution you used to solve this problem.
Answer:
P = $250
Step-by-step explanation:
Interest (I) = Principal (P) x Interest Rate (r) x Time (t, in years)
I = Prt
12 = P(.032)(1.5)
12 = .048P
12/.048 = P
P = 250
Which statement is true
Shanice won 88 pieces of gum playing the bean bag toss at the county fair. At school she gave four to every student in her math class. She only has 8 remaining. How many students are in her class?
Equation:
Answer:
Steps to solve:
Answer:
20
Step-by-step explanation:
88 divided by 4 = 22, She gave 4 gums to each student, 8 divided by 4 = 2.
22 - 2 = 20
Solución
10x-3x=11+10
Answer: x=3
Step-by-step explanation:
Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (â€""3 i) (18 5i)? (â€""3 i) (18 5i) 0 â€""3 (i 18) 5i (â€""3 18) (i 5i) â€""(3 â€"" i) (18 5i).
The expression that demonstrates the use of the commutative property is
(-1 + 18) + (3i + 5i)
Give two integers A and B, according to the commutative law of addition;
A + B = B+ AThe arrangement of the integers does not affect the sum.Given the expression (-1+3i) + (18+5i)
The expression that demonstrates the use of the commutative property of addition in the first step of simplifying the expression is given as:
(-1+3i) + (18+5i)
-1 + 3i + 18 + 5i
(-1 + 18) + (3i + 5i)
We can see that the rearrangement does not affect the sum. Hence the expression that demonstrates the use of the commutative property is
(-1 + 18) + (3i + 5i)
Learn more on commutative property here: https://brainly.com/question/778086
Write an equation in slope-intercept form of the line that passes through (1,-9) and (3,-7)
Answer:
Y= x-10
Step-by-step explanation:
M= Y2-Y1/X2-X1
= -7-(-9)/3-1
= 2/2
= 1
sub x=1 and y=-9 into Y=MX + C
-9=1+C
-9-1=1+C-1
C=-10
what is the answer to the equation -7x-3x+2= -8x - 8
Answer:
x=5
Step-by-step explanation:
-7x-3x+2= -8x - 8
Add like terms
-7x-3x=-10x
-10x+2=-8x-8
+8x +8x
-2x+2=-8
-2 -2
-2x=-10
Divide by -2 to isolate the variable
x=5
Answer:
x = 5Step-by-step explanation:
what is the answer to the equation
-7x - 3x + 2= -8x - 8
-7x - 3x + 8x = -10
2x = -10
x = 5
----------------------
check
-7 * 5 - 3 * 5 + 2 = -8 * 5 - 8
-48 = -48
the answer is good
Question 16
What is the shortest distance between the line y = 2x+4 and the point at (0.0)? Round to the nearest tenth.
O A) 1.8
O B) 2.0
O C) 3.2
O D) 4.0
The shortest distance between the line y = 2x+4 and the point at (0.0) is 1.8 units option (A) is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that:
The equation of the line is:
y = 2x + 4
Or
2x - y + 4 = 0
The point is (0, 0)
As we know, the formula for the shortest distance between the line and a point:
D = |ax + bx + c|/√(a²+b²)
Plug x = 0 and y = 0
a = 2, b = -1, and c = 4
D = |2(0) + -1(0) + 4|/√(2²+(-1)²)
D = 4/√5
D = 1,78 ≈ 1.8 units
Thus, the shortest distance between the line y = 2x+4 and the point at (0.0) is 1.8 units option (A) is correct.
Learn more about the straight line here:
brainly.com/question/3493733
#SPJ2
Find the zeros of quadratic equation X^2 - 3x + 9 = 5x - 10
x^2 - 3x + 9 - 5x + 10 = 0
x^2 - 8x + 19 = 0
[tex]x^{2} -3x+9=5x-10 <=> x^{2} -3x-5x+9+10=0\\<=>x^{2} -8x+19=0 <=>x^{2} -2.4+16+3=0\\<=>(x-4)^2+3=0[/tex]
ok done. Thank to me :>
6. Find the average rate of change of Pete's height from 3 years
old to 5 years old.
Choices:
o 2 inches per year
o 4 inches per year
O 8 inches per year
Answer:
The Answer is "4 inches per year"
Step-by-step explanation:
To find the Average Rate of Change, you use:
[tex]\frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex]
So when you insert the numbers from the table, you get:
[tex]\frac{45-37}{5-3}[/tex]
After solving the answer you get is 4. So the avg rate of change is 4 inches per year.
a triangle with side 9,10and 11 has the same perimeter as a square with sides of length
Answer:
7.5.
Step-by-step explanation:
A square has 4 equal sides so:
4x = 9 + 10 + 11 where x is the length of one side of the square.
4x = 30
x = 7.5.
= 259.84 −168.789what is the answer
Answer:
91.051
Step-by-step explanation:
259.840
- 168.789
---------------
091.051
----------------
Suppose you have a box with 3 blue marbles, 2 red marbles, and 4 yellow marbles. You are going to pull out one marble, record its color, remove it from the box and draw another marble. What is the probability of pulling out a red marble followed by a blue marble? The multiplication rule says to use P(red) P(blue).
Question: Describe the process of finding the probability of finding a red marble followed by a blue marble if the first marble was permanently removed?
Answer:
that is dependent event when you are taking out first marble permanently
What is the sum of -6 and 9?
Answer:
3
Step-by-step explanation:
-6+9=3
Consider the equation below. Log Subscript 4 Baseline (x 3) = log Subscript 2 Baseline (2 x) Which system of equations can represent the equation? y 1 = StartFraction log (x 3) Over log 4 EndFraction, y 2 = StartFraction log (2 x) Over log 2 EndFraction y 1 = StartFraction log x 3 Over log 4 EndFraction, y 2 = StartFraction log 2 x Over log 2 EndFraction y 1 = StartFraction log 4 Over log 2 EndFraction, y 2 = StartFraction log (x 3) Over log (2 x) EndFraction y 1 = StartFraction log x 3 Over 4 EndFraction, y 2 = StartFraction log 2 x Over 2 EndFraction.
Equivalent equations are equations of equal values
The system of equations from the given equation are:
[tex]y= \log_2(2x)[/tex] and [tex]y=3\log_4(x)[/tex]
The logarithmic equation is given as:
[tex]\log_4(x^3) = \log_2(2x)[/tex]
Split the above equation as follows:
[tex]y = \log_4(x^3)[/tex]
[tex]y= \log_2(2x)[/tex]
Rewrite [tex]y = \log_4(x^3)[/tex] as:
[tex]y=3\log_4(x)[/tex]
Hence, the system of equations from the given equation are:
[tex]y= \log_2(2x)[/tex] and [tex]y=3\log_4(x)[/tex]
Read more about systems of equations at:
https://brainly.com/question/14265399
Brian had $40 in his savings account in January. He continued to add money to his account and by June, the value of the savings account had increased by 50%. How much money is in Brian's account in June?
Answer:
Well the answer is
Step-by-step explanation:
GET YO BUTT OFF THIS APP AND ACTUALLY READ A MATHS BOOK
Can someone help me with this problem plz
Answer:
mq - 12
ql - 36
Step-by-step explanation:
I am not for sure but this is what I think it is because the m-q is smaller than the q-l
The following diagram shows the side view of a roof and attic space of a newly constructed
home. Find m
A. 20°
B. 40°
C. 60°
D. 25°
Answer:
A 20
Step-by-step explanation:
yeah-ya....... right?
A square is cut diagonally into two equal parts. If each part has an area of 50cm^2, then what is the perimeter of each part?
50 points the answer isnt 30 so dont say it is because it isnt
Answer:
its 25.
Step-by-step explanation:because 50 divided by 2 is 25.
Answer:
40 units
Step-by-step explanation:
1) Find the side length of the square
Let the side be "s".
[tex]\rightarrow \frac{1}{2} \times s \times s = 50 \ \text{cm}^{2}[/tex]
[tex]\rightarrow s \times s = 50 \times 2[/tex]
[tex]\rightarrow s \times s = 100[/tex]
[tex]\rightarrow \sqrt{s \times s} = \sqrt{100}[/tex]
[tex]\rightarrow s = \±10[/tex]
[tex]\rightarrow s = 10 \ \text{units}[/tex] (Side lengths can never be negative)
2) Find the perimeter of the square
[tex]\text{Perimeter of square = 4(s) = 4(10) = 40 units}[/tex]
find the values of x and y ????
show step plz
Answer:
x= 90 degrees
y= 47 degrees
Step-by-step explanation:
Since the two sides of this triangle are equal in lengths, you know that it is an isosceles triangle.
So with this information, you know that the angle at the bottom left is also 47 degrees.
x would be equal to 90 degrees because it is perpendicular to the bottom of the triangle (assuming).
A triangle has 180 degrees, so add up the lengths we have to solve for the missing angle, y.
90+47+y=180
y= 43
[tex]{\huge{\boxed{\mathfrak{Answer\:With\:Explanation}}}[/tex]
First we can say [tex]x=90[/tex]°, since x is located at the right angle part.
Now we can make an equation
[tex]90+47+y=180[/tex]
subtract 137 from sides.
[tex]y=43[/tex]
_________________________________
[tex]{\huge{\boxed{\mathfrak{Answer}}}[/tex]
[tex]x=90[/tex]° [tex]y=43[/tex]°_________________________________
If f(x) = 14
then what does f(-3) equal?
Answer:
27 I do believe so sorry if im wrong
Step-by-step explanation:
) It took 2 pumps 6 hours to pump the water out of a pond. How long would it take if 3 pumps
were used?
Answer:
it would take 2 hours with 3 pumps
Step-by-step explanation:
hope this helps! :D
A donut shop made 50 donuts. They put frosting on 2 of the donuts. What is the ratio of the
number of donuts with frosting to the number of donuts without frosting?
50:48
2:48
50:2
2:4
Submit
Answer:
50-2
Step-by-step explanation:
there is 50 donuts and 2 that are frosted :)
Step-by-step explanation:
2 have frosting, therefore 50-2 = 48 don't.
so, the ratio is for frosting vs. non-frosting
2 : 48 (which would be also 1 : 24).
There are 30 kilograms of 10 percent apple juice how much more aplle juice does it need to get to 25 percent?
Answer:
45 kg of apple juice
Step-by-step explanation:
Divide 25% by 10%
The answer you get multiply it by 30
Take the answer you get subtract the 30 kg