Answer: y = 2 and x = 2
Step-by-step explanation:
[tex]9x^2+4(y-2)^2=36\\x^2=2y[/tex]
First, get the entire thing in terms of y, because you cant solve for two variables at the same time. They gave us the fact that x^2 = 2y
[tex]9(2y)+4(y-2)^2=36\\18y+4(y^2-4y+4)=36\\18y+4y^2-16y+16=36\\4y^2+2y-20=0[/tex]
What two numbers multiply to equal -80 but add to equal 2? That is +10 and -8.
[tex]4y^2+2y-20=0\\(4y^2-8y)+(10y-20)=0\\4y(y-2)+10(y-2=0)\\(4y+10)(y-2)=0\\y=-5/2\\y=2[/tex]
Now solve for x by plugging in y to the easier equation
[tex]x^2=2(-5/2)\\x\neq \sqrt{-5}[/tex]
If I didn't make a mistake, this should be the only answer. In the case of y = -5/2, you would get an imaginary x-value. Therefore y cannot equal -5/2
[tex]x^2=2(2)\\x=2[/tex]
The solution of the expression are,
x = 2.28 , y = 2.62
Or, x = 3.9i , y = - 7.62
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The system of equations are,
9x² + 4 (y - 2)² = 36 .. (i)
x² = 2y .. (ii)
Substitute the value of x² from (ii) in (i);
9x² + 4 (y - 2)² = 36
9 × 2y + 4 (y - 2)² = 36
18y + 4 (y - 2)² = 36
9y + 2 (y - 2)² = 18
9y + 2 (y² + 4 - 2y) = 18
9y + 2y² + 8 - 4y = 18
2y² + 5y + 8 - 18 = 0
2y² + 5y - 10 = 0
y = - 5 ± √5² - 4×2×- 10 / 2×2
y = - 5 ± √ 25 + 80 / 2
y = - 5 ± √ 105 / 2
y = - 5 ± 10.24 / 2
y = - 5 + 10.24 / 2
y = 5.24/2
y = 2.62
y = - 5 - 10.24 / 2
y = - 15.24 / 2
y = - 7.62
From (ii);
x² = 2y
x² = 2 × 2.62
x² = 5.24
x = 2.28
x² = 2y
x² = 2 × - 7.62
x² = - 15.24
x = 3.9i
Thus, The solution of the expression are,
x = 2.28 , y = 2.62
Or, x = 3.9i , y = - 7.62
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ5
20. Mr. Reed bought tickets for 7 teachers
to attend a concert. He paid a total of
$245 for the tickets. If each ticket
cost the same amount, how much
did Mr. Reed pay for each ticket?
A $24.50
B $25.00
C $32.00
D $35.00
Which of the following could be the side measures of a right triangle?
Answer:
c
Step-by-step explanation:
if you use the Pythagorean Theorem and take the sum of the square of the legs, it will equal the square of the hypotenuse in answer (c)
8² + 6² = 10²
64 + 36 = 100
100 = 100
Answer:
Step-by-step explanation:
C
x^2 + 9x + 14 I need help !
Answer:
x² + 9x + 14 can be factored as (x+2)(x+7)
Step-by-step explanation:
The general form is ax² + bx + c. If a=1, then you can start looking for two numbers that multiplied give c and added give b.
14 = 2*7
and
9 = 2+7
hence the easy factorization
(x+2)(x+7)
Keep in mind that it only works if a=1.
Answer:
( + 2 ) (x+7 )
Step-by-step explanation:
Use the sum-product pattern 2 + 9 + 1 4 2 + 7 + 2 + 1 4 2
Common factor from the two pairs 2 + 7 + 2 + 1 4 ( + 7 ) + 2 ( + 7 ) 3
Rewrite in factored form ( + 7 ) + 2 ( + 7 ) ( + 2 ) ( + 7 )
I NEED HELP ASAP!!!!!
Solve the equation and show your work.
Here's the problem: 4x + 3x - 3(4x - 8) = 14
Step 1.) Eliminate parentheses by distributing the -3.
Step 2.) Collect any like terms on the left side of the equation.
Step 3.) Subtract 24 from both sides of the equation.
Step 4.) Divide both sides of the equation by -5.
Answer:
Step-by-step explanation:
x=2
Solve this problem, please!
Answer:
B
Step-by-step explanation:
Please help me. Thank you
Answer:
AE - 3, EB - 2, EC - 5
Step-by-step explanation:
Use the Pythagorean theorem and you'll find that these are the answers.
I'll answer problem 19
=======================================================
Part (a)
The tickmarks on segments DE and DC indicate they are the same length. We're also told that |DC| = |DE| = 5.
So DE is also 5 cm long. Triangle DAE is a right triangle with the 90 degree angle at angle A. Let x be the length of segment AE.
We'll use the pythagorean theorem to find x
a^2 + b^2 = c^2
(AE)^2 + (AD)^2 = (DE)^2
x^2 + 4^2 = 5^2
x^2 + 16 = 25
x^2 = 25-16
x^2 = 9
x = sqrt(9)
x = 3
Segment AE is 3 cm long
=======================================================
Part (b)
For any rectangle, the opposite sides are parallel and the same length. This means AB = DC = 5 cm.
We found earlier that AE = 3 cm, so,
AE+EB = AB
3+EB = 5
EB = 5-3
EB = 2
Segment EB is 2 cm long
=======================================================
Part (c)
We know that AD = BC = 4 cm, because the opposite sides are the same length.
Earlier in part (b), we found that segment EB was 2 cm long.
Triangle EBC is a right triangle with legs EB = 2 and BC = 4. Let's apply the pythagorean theorem to find EC. Let y = EC.
a^2 + b^2 = c^2
(EB)^2 + (BC)^2 = (EC)^2
2^2 + 4^2 = y^2
4 + 16 = y^2
20 = y^2
y^2 = 20
y = sqrt(20)
y = sqrt(4*5)
y = sqrt(4)*sqrt(5)
y = 2*sqrt(5)
y = 4.4721359
As an exact value, EC is sqrt(20) or 2*sqrt(5) cm long.
As an approximate value, EC is roughly 4.4721359 cm long.
I would ask your teacher if you should use the exact or approximate value.
The measure of the second angle is 15 degrees more then the measure of the 1st angle. The measure of the 3rd angle is 45 degrees more than the measure of the 1st angle. Find the measures of the interior angles in the triangle.
Let the first angle be x
So, second angle = (x+15)°
and third angle= (x+ 45)°
Now,
x+ (x+15) + (x+45)= 180°. ( Triangle sum property)
x+x+x+15°+45° = 180°
3x+ 60° = 180°
3x= 180°-60°
3x= 120°
x= 120°/3
x= 40°
Now,
first angle=x= 40°
second angle = (x+15)°= 40°+15° = 55°
third angle= (x+45)° = 40°+45° = 85°
Hope it helps you. Please mark as brainliest if it does.
4(6-5x)^2+11=20
quadratic equations
Answer:
(x-114.5), (x-14.05)
Step-by-step explanation:
Answer attached
write an expression equivalent to 2(2x + 2y).
Answer:
4x+4y
Step-by-step explanation:
You can write an equivalent expression by simply simplifying the expression. In order to simplify this expression, distribute the numbers.
You'll get:
(2*2x)+(2*2y) = 4x + 4y
4x + 4y is an equivalent expression.
Christopher is going to use a computer at an internet cafe. The cafe charges
$0.20 for every minute using a computer on top of an initial charge of $7.
Make a table of values and then write an equation for C, in terms oft,
representing the total cost of using a computer for t minutes at the internet
cafe.
Answer:
0 7
1 7.20
2 7.40
3 7.60
Step-by-step explanation:
Choose all the fractions that are in simplest form. 4/26 8/21 6/19 9/10 10/22
Answer:
8/12, 6/19 and 9/10!
Step-by-step explanation:
All of them cannot be simplified.
but the rest can like
4/26 can be simplified by 2
and 10.22 can be simplified by 2
simpliyfy (-3/7)^3 * (-3/7)^4
Answer:
Step-by-step explanation:
(-3/7)³ × (-3/7)⁴ = (-3/7)³⁺⁴ = (-3/7)⁷
Answer:
the answer to this question is (-3/7)^7
Rosie has £m in her pocket she is given £4 pocket money write an expression for how much money she has now
Answer:
m+4
Step-by-step explanation:
She currently has a variable "m" in her pocket which we don't know, BUT we know how much she is getting, which is 4.
Enter the ordered pair for the vertices for 180°,0)(QRST).
Q
o
S
IR
O Q' = (-1,-3) R' = (-3,3 ) S'= (0,2)T' =(2, -1)
OQ' = (-1,3) R' = (-3,-3) S'=(0, -2)T' =(2, 1)
Q' = (1, -3) R' =(3,3) S' = (0,2)T' = (-2,-1)
Answer:
The ordered pair for the vertices for r₍₁₈₀ ₀₎(QRST), is given as follows;
Q' = (-1, -3) R' = (-3, 3) S' = (0, 2) T' = (2, -1)
Step-by-step explanation:
The coordinates of he vertices of the triangle QRST are;
Q(1, 3), R(3, -3), S(0, -2), T(-2, 1)
A rotation of a point with coordinates (x, y) 180° about the origin gives;
The coordinate of the point of the preimage before the rotation = (x, y)
The coordinate of the point of the image after the rotation = (-x, -y)
Therefore we have;
The image of point Q(1, 3) after 180° rotation = Q'(-1, -3)
The image of point R(3, -3) after 180° rotation = R'(-3, 3)
The image of point S(0, -2) after 180° rotation = S'(0, 2)
The image of point T(-2, 1) after 180° rotation = T'(2, -1)
The ordered pair for the vertices for r₍₁₈₀ ₀₎(QRST), is therefore, Q'(-1, -3), R'(-3, 3), S'(0, 2), and T'(2, -1);
Q' = (-1, -3) R' = (-3, 3) S' = (0, 2) T' = (2, -1).
*PLEASE ANSWER!!! THANK YOU*
Greg is a pharmaceutical sales rep who works on commission. He needs to sell his product to at least 5 doctors each month. What is the term that represents needing to sell a certain amount before getting paid?
a.) Quota
b.) Salary
c.) Gross pay
Answer:
A
Step-by-step explanation:
What is the smaller angle formed by the minute and hour hands at 3:30pm?
[asy]
unitsize(50);
draw(Circle((0,0),1),black+1);
dot((0,0));
for(real i=0;i<360;i+=6){
draw(0.96*(cos(i*pi/180),sin(i*pi/180))--(cos(i*pi/180),sin(i*pi/180)),black+0.5);
};
for(real i=30;i<390;i+=30){
draw(0.93*(cos(i*pi/180),sin(i*pi/180))--(cos(i*pi/180),sin(i*pi/180)),black+0.5);
label(string(i/30),0.83*(sin(i*pi/180),cos(i*pi/180)));
};
real h=3.5; real m=30;
draw(0.65*(sin(pi/6*(h)),cos(pi/6*(h)))--(0,0)--0.9*(sin(pi/30*m),cos(pi/30*m)),black+1,Arrows(TeXHead));
draw(anglemark(dir(-90),origin,dir(-15),5));
[/asy]
Answer:
75 degrees
Step-by-step explanation:
At 3:30, the hour hand is halfway between the 3 and the 4. The minute hand is exactly on the 6.
There are 360/12 = 30 degrees between each of the marked hours. The angle between the hands covers 2.5 of these gaps, so the angle between the hands is 2.5(30) = 75 degrees.
Hope this helps!
The angle between the hands at 3:30 pm is 90°.
What is the angle between the hands of a clock at 3:30 pm?
At that time, one hand points at the 3, and the other hand points at the 6.
Now, there is a rule to transform time into angles.
We know that a clock has 12 hours in a full revolution, and a circle has 360° in a complete revolution.
Then we know that:
12 hours = 360°
Then:
1 hour = (360°/12) = 30°
So each between each number in the clock we have an angle of 30°.
Then, between 3 and 6 (3 hours) we have:
3*30° = 90°
The angle between the hands at 3:30 pm is 90°.
If you want to learn more about angles, you can read:
https://brainly.com/question/17972372
HELP!!!!
Given that x=6 and y=-4, evaluate each of the following expressions:
A. 5x/3y+x
B. 2x (square) - y (cube)
Answer:
A. 5x/3y+x=5×6/(3×-4)=30/-12=-10/4=-5/2
B. 2x (square) - y (cube)=2×6²-(-4)³=72--64=72+64=136
LeBron bought a 8-pack of Powerade for $7.68. What is the unit rate for one bottle of Powerade?
Washington Middle School is painting a circle on their playground with a radius of 12 feet. What will be the total area of the circle, in square feet?
Answer: circle
A=452.39ft2
R radius 12
A=πr 2=π. 12 ‘2=452.38934ft’2
Question Help
3.3 PS-14
A salesperson at a jewelry store earns 4% commission each week. Last week, Jarrod sold $750
worth of jewelry. How much did he make in commission? How much did the jewelry store make
from his sales?
Me Help ASAP or when everrr
Answer:
Base = 3√5
Step-by-step explanation:
Given:
Hypotenuse = 9
Perpendicular = 6
Find:
Base(x)
Computation:
Using Pythagorean theorem
Base = √Hypotenuse² - Perpendicular²
Base = √9² - 6²
Base = √81 - 36
Base = √45
Base = 3√5
Which function matches the graph?
-2
a. f(x) = -2(x - 3)2 + 1
b. f(x) - 2(x+3)2 - 1
c. f(x) = (x+3)²+2
d.
A(x) = 1/(x - 3)² - 1
Answer:
Its a or c sorry if im wrong
(hope this helps :D hehe)
Step-by-step explanation:
Answer:
Please insert a graph.
Step-by-step explanation:
If you submit a picture of the graph on here, I will see how how I can help.
6.37x10^-2
Thanks to anyone who answers this.
Answer:
6.37 x 10^-2 =0.0637
brainliest give an explanation to
Answer:
70 caps, 72 hotdogs, 50 paintings, 8 scouts
Step-by-step explanation:
the table below shows the speed of a falling object that every second within the first 5 seconds of its downward motion based on the relationship between speed and time that the same will suggest which equation can be used to find the speed of the object at t seconds A. 8=t/32 B. S=32t C. S=32-t D. s=t+32
Answer:
B. s = 32t
Step-by-step explanation:
The equation would be in the form of s = mt.
Where, m = rate of change
Find rate of change using any two values given in the table, say (1, 32) and (2, 64)
Rate of change (m) = ∆s/∆m = (64 - 32)/(2 - 1) = 32/1 = 32
✔️To write the equation, substite m = 32 into s = mt
s = 32t
Kaylin buys a greeting card for $3.79. She then buys 4 postcards that all cost the same amount. The total cost is $5.11. How much is each postcard?
Answer:
$0.33
Step-by-step explanation:
5.11-3.79=1.32 1.32/4
Hope this helps :)
Answer:
each postcard cost .33 or 33 cent
Step-by-step explanation:
5.11(total cost)-3.79(greeting card)= 1.32
1.32(cost of all postcards)/4= .33
Alvin is 15 years younger than Elga. The sum of their ages is 49. What is Elga's age?
Answer:
32
Step-by-step explanation:
Suppose Alvin is x years old. Then Elga is x+15 years old.
x+x+15=49
2x=34
x=17
17+15=32
Simplify the following.
Answer:
[tex]m^{4}n^{5}[/tex]
Step-by-step explanation: ( I'm a student, I'm not really good at explaining maths )
When dividing variables with exponents, you subtract the exponents that has the same variables, like this:
[tex]m^{16-12}n^{10-5}[/tex]
Simplifying this becomes:
[tex]m^{4}n^{5}[/tex]
math su.cks......................................................................................................................................................................................................................... on suc.kers! i like bad jokes.
Answer:
Step-by-step explanation:
Ok
Answer:
what
Step-by-step explanation:
:(
The function f(x) = {}]" is reflected across the y-axis to create the function g(x). Which ordered pair is on g(x)?
0 (-3.375)
o(-22
O (3)
10 (2-23
Answer:
I think your problem didn't copy correctly because you didn't provide a function. if you could provide it to me I would be glad to help and give you the answer.
I also do exams and quizzes if your interested