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
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URGENT I need help.
Plzzzzzzzzzzzzzzzzzzzzzz Its Attached
Answer:
what is you belling? yesterday y monday
Leticia and Carmen were each given 120 math questions for the month. After 3 weeks,
Leticia completed 75% of the problems and Carmen completed 60% of the problems
How many more questions did Leticia complete thon Carmen?
What's 9 + 10 ? give me the right answer
Answer:
19
Step-by-step explanation:
Add 9 to 10
16. What probability expression is equivalent to P( / z / > 1.96)?
Answer:
Please check the explanation.
Step-by-step explanation:
Given
[tex]P(Z > 1.96)[/tex]
To determine
What probability expression is equivalent to [tex]P(Z > 1.96)[/tex].
Suppose Z is a standard normal variable.
Therefore,
P(Z > 1.96) = 1 - P(Z ≤ 1.96)
solving
= 1 - Ф(1.96)
[tex]= 1 - 0.9750[/tex]
[tex]= 0.0250[/tex]
Azil runs 6 times four-fifths laps on Monday. Which fraction represents the number of laps that Azil runs on Monday?
Answer:
24 / 5 laps
Step-by-step explanation:
Fraction of laps run = 4/5 laps
Number of times lap was run = 6
Fraction representing total laps run :
6 * (4/5)
= 24 / 5
Or
24 /5 = 4 4/5 laps
Emir flew home from vacation with a heavy bag. With the first airline he flew, Emir had to pay $20 to check his bag, plus $10 for every pound that his bag was over the weight limit. The next flight was with another airline that had the same weight limit. Emir had to pay $5 per pound that his bag was over the weight limit, in addition to the checked bag fee of $30. By coincidence, the fees ended up being the same with both airlines. How large was each airline's fee?
Answer:
$27.5
Step-by-step explanation:
Let
x = pound over weight limit
Airline 1 = 20 + 10x
Airline 2 = 5 + 30x
Equate the fees
20 + 10x = 5 + 30x
20 - 5 = 30x - 10x
15 = 20x
x = 15/20
x = 0.75 pounds
How large was each airline's fee?
Airline 1 = 20 + 10x
= 20 + 10(0.75)
= 20 + 7.5
= $27.5
Airline 2 = 5 + 30x
= 5 + 30(0.75)
= 5 + 22.5
= $27.5
Simplify the following:
a) 3^2x3^2
b) 7x7^4
c) 10^9/10^7
d) 5^8/5
Answer:
see attached
Step-by-step explanation:
pleass see attached
write an equation of the line that passes through the two given points: (-5, -5) and (1,-3)
Answer:
slope-intercept formula -----> Y2-Y1/X2-X1
Step-by-step explanation:
X1= -5 X2= 1
Y1= -5 Y2= -3
-3+5/1+5=1/3
Page No.
Date :
33
2
4 Cosin 4 Go + eces4 300 3 citan
60 - tan245) + 5 ecos? 45.
A directed line segment begins at F(-8, -2), ends at H(8, 6), and is divided in the ratio 8 to 2 by G. What are the coordinates of G?
Given:
A directed line segment begins at F(-8, -2), ends at H(8, 6), and is divided in the ratio 8 to 2 by G.
To find:
The coordinates of point G.
Solution:
Section formula: If a point divide a line segment with end points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in m:n, then the coordinates of that point are
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Point G divide the line segment FH in 8:2. Using section formula, we get
[tex]G=\left(\dfrac{8(8)+2(-8)}{8+2},\dfrac{8(6)+2(-2)}{8+2}\right)[/tex]
[tex]G=\left(\dfrac{64-16}{10},\dfrac{48-4}{10}\right)[/tex]
[tex]G=\left(\dfrac{48}{10},\dfrac{44}{10}\right)[/tex]
[tex]G=\left(4.8,4.4\right)[/tex]
Therefore, the coordinates of point G are (4.8, 4.4).
6 A pair of adjacent angles is formed by lines
AD and CE.
What is the measure of angle ABC?
F 145°
G 217
H 85°
J Not here
Answer:
x° = 145°
Step-by-step explanation:
x° + (2x - 255)° = 180°
3x = 180 + 255
3x = 435
x° = 145°
Someone plz help me I will give brainliest
Answer:
Step-by-step explanation:
3/4 + 3/4 + 3/4 + 3/4 + 3/4 + 3/4 = (6 x 3)/4 = 18/4 = 4 1/2
I will give brainiest. There is 1/ 3 gallon of water in a 3-gallon container. What fraction of the container is filled?
GEOMETRY Identify the segment bisector of (FG) . Then find (FG)
Answer:
The segment bisector of FG is HI because it splits it into two equal parts. Since point F to the bisector equals 33 and the bisector to point G is the same, that would also be 33. 33+33=66=FG
Step-by-step explanation:
The measurement of the line segment FG is 66 units.
We need to identify the segment bisector of FG and then find FG.
What is the bisector of the line segment?A segment bisector is a line, a ray, a line segment, or a point that cuts a line segment at the centre dividing the line into two equal parts. The word segment can also be referred to as line segment which means a segment is a part of the line that has fixed endpoints. The word bisect means cutting any object or line into two equal halves. Hence, a segment bisector is referred to as when two line segments bisect or cut each other at a point dividing the lines into equal halves.
From the given figure, HI is the bisector of the line segment FG.
Given that, 1/2 (FG)=33 units
⇒FG=66 units
Therefore, the measurement of the line segment FG is 66 units.
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Please help will give brainliestw
Answer:
6 square units
Step-by-step explanation:
In oder to do this, you need graph paper to make it easier and then mark your graph paper with the quadrants.
I got 3 unites for the height and 4 units for the base
4 x 3 = 12 square units
however the formula for a triangle is Ab/2
so divide 12/2 = 6
So its 6 square units
plss helpppppppppp w,jvkwsvkjbw,vj effvdefv
Answer:180
Step-by-step explanation:
Can someone tell me if my answer is correct (and correct it if it's not)?
What is the area of an EQUALATERAL triangle with a side length of 6? I'm getting 5.19615242, is this right?
Answer:
15.59.
Step-by-step explanation:
The altitude of equilateral triangle bisects the base
So 1/2 base = 3.
Altitude of the triangle is found from Pythagoras theorem:
= sqrt(6^2 - 3^2)
= sqrt27
Area = 1/2 base * altitude
= 3 * sqrt27
= 15.59
a total of 11℅ students at a large high school are left-handed. A statistics teacher selects a random sample of 100 students and records L = the number of left-handed students in the sample.
a. Explain why L can be modeled by a binomial distribution even though the sample was selected without replacement.
b. use a binomial distribution to estimate the probability that 15 or more students in the sample are left-handed handed.
The probability that 15 or more students in the sample are left-handed handed is 0.0752
(a) Why L can be a binomial distribution
From the question, we understand that 11% of the students are left-handed; this means that 89% are not left-handed
This, in other words means that:
For each observation, the student is either left-handed or not left-handed
Hence, the distribution can be represented by a binomial distribution
(b) The probability that 15 or more are left-handed
The sample size is given as:
[tex]\mathbf{n = 100}[/tex]
And the proportion is
[tex]\mathbf{p = 11\%}[/tex]
The mean of the dataset is:
[tex]\mathbf{\mu = np}[/tex]
[tex]\mathbf{\mu = 100 \times 11\%}[/tex]
[tex]\mathbf{\mu = 11}[/tex]
The standard deviation of the dataset is:
[tex]\mathbf{\sigma = \sqrt{\mu(1- p)}}[/tex]
So, we have:
[tex]\mathbf{\sigma = \sqrt{11 \times (1- 11\%)}}[/tex]
[tex]\mathbf{\sigma = \sqrt{11 \times 89\%}}[/tex]
[tex]\mathbf{\sigma = \sqrt{9.79}}[/tex]
[tex]\mathbf{\sigma = 3.13}[/tex]
So, the probability is represented as:
[tex]\mathbf{P(x \ge 15)}[/tex]
Using continuity correction, we have:
[tex]\mathbf{P(x \ge 15) = P(x \ge 15.5)}[/tex]
Calculate the z-score for x = 15.5
[tex]\mathbf{z =\frac{x - \mu}{\sigma}}[/tex]
So, we have:
[tex]\mathbf{z =\frac{15.5 - 11}{3.13}}[/tex]
[tex]\mathbf{z =\frac{4.5}{3.13}}[/tex]
[tex]\mathbf{z =1.438}[/tex]
The probability is then calculated as:
[tex]\mathbf{P(x \ge 15) = P(z \ge 1.438)}[/tex]
Using z-tables of probabilities, we have:
[tex]\mathbf{P(x \ge 15) = 0.075217}[/tex]
Approximate
[tex]\mathbf{P(x \ge 15) = 0.0752}[/tex]
Hence, the probability is 0.0752
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Sam opens a savings account with $800. He saves $50 per month. Assume that he does not withdraw money or make any additional deposits.
Answer:
wheres the end of the question
Step-by-step explanation:
Sam opens a savings account with $800. He saves $50 per month. Assume that he does not withdraw money or make any additional deposits.
The rectangles are similar. What is the value of x?
Answer:
80
Step-by-step explanation:
30 ÷ 6 = 5
16 × 5 = 80
I hope this helped!
Find x
Geometry angles question
Answer:
5
Step-by-step explanation:
When the angles are vertical you set up your equation to 180
3x-35+130=180 and solve
Enter a range of values for x.
a
a
3x-90 930
26
27
[? ]
Answer:
the answer to your question is 3 and 34
Help me please......
Answer:
[tex] \huge \: 19[/tex]Step-by-step explanation:
to understand thisyou need to know about:equationtriangles congruencyPEMDASTIPS AND FORMULAS:when two triangles are congruent the included angles and sides of the triangles are equallet's solve:[tex]step - 1 : define[/tex]
[tex]2x - 9 = x + 5[/tex]
[tex]step - 2 :solve[/tex][tex]2x = x + 5+ 9[/tex]
[tex]2x = x + 14[/tex]
[tex]2x - x = 14[/tex]
[tex]x = 14[/tex]
given:KL=2x-9
=2.14-9
=28-9
=19
Learning Task 1
4/625
11.
796
A. Simplify the radical expressions
1. V63
6. V24
2. 48
7. 781
3. 775
8. V128
4. 99
9. 340
5. 92
12. 128
13. 4/243
14.
V3000
10. V135
15.
NO
Answer:
Step-by-step874747634734634347
How many three-digit numbers are divisible by 2,3 or 5? plEASe helP I aM DeSpeRatE
GIVE ME THE RIGHT ANSWER
Answer:
30
Step-by-step explanation:
- A number is divisible by 2 if its last digit is 2, 4, 6, 8 or 0
- A number is divisible by 3 if ist sum of digits is divisible by 3.
- A number is divisible by 5 if its last digit is a 5 or a 0.
_
The least 3 digit number divisible by 30 is 120 and the greatest is 990.
Answer: 30
Step-by-step explanation:
Divisible by 2,3 and 5 means divisible by 2*3*5=30
So we require to calculate number of multiples of 30 in the range 100 to 999.
The least 3 digit number divisible by 30 is 120 and greatest is 990.
This is an AP series with common difference 30.
First number is 120 and n'th number is 990.
We need to find n.
Using the AP series formula
120 + (n-1)*30= 990
or n= 30
There are 30 3-digit numbers divisible by 2,3 and 5.
Jada measured the height of a plant in a science experiment and finds that, to the nearest 1/4 of an inch, it is 4 3/4 inches.
a. What is the largest the actual height of the plant could be? Express your answer in decimal form.
Answer:
I dont know
Step-by-step explanation:
sorrryy
explain why the miniscus of water is bent downwards
Answer:
A concave meniscus, which is what you normally will see, occurs when the molecules of the liquid are attracted to those of the container. This occurs with water and a glass tube. A convex meniscus occurs when the molecules have a stronger attraction to each other than to the container, as with mercury and glass.
I really need help. ( Intro to limits )
PLS PLS PLS HELPPP please...
Answer: x=12
Step-by-step explanation: 10(x−3)=90
(10)(x)+(10)(−3)=90 (Distribute)
10x+−30=90
10x−30=90
Step 2: Add 30 to both sides.
10x−30+30=90+30
10x=120
Step 3: Divide both sides by 10.
x=12
plz help me solve this
Answer:
[tex]=2x^{5} y^{5} \sqrt{7}[/tex]
Step-by-step explanation: