Answer:
a = - 2, [tex]\frac{9}{4}[/tex] , b = 2, - [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
Since x = 1, y = 2 is a solution to the equations , then substitute these values into the 2 equations and solve for a and b
a + 2b = 2 → (1)
b + 2a² = 10 → (2)
In (1) subtract 2b from both sides
a = 2 - 2b → (3)
Substitute a = 2 - 2b into (2)
b + 2(2 - 2b)² = 10 ← expand parenthesis using FOIL
b + 2(4 - 8b + 4b²) = 10 ( simplify left side )
b + 8 - 16b + 8b² = 10 ( subtract 10 from both sides )
8b² - 15b - 2 = 0
Consider the factors of the product of the coefficient of the b² term and the constant term which sum to give the coefficient of the b- term
product = 8 × - 2 = - 16 and sum = - 15
The factors are - 16 and + 1
Use these factors to split the b- term
8b² - 16b + b - 2 = 0 ( factor first/second and third/fourth terms )
8b(b - 2) + 1(b - 2) = 0 ← factor out (b - 2) from each term
(b - 2)(8b + 1) = 0
Equate each factor to zero and solve for b
b - 2 = 0 ⇒ b = 2
8b + 1 = 0 ⇒ 8b = - 1 ⇒ b = - [tex]\frac{1}{8}[/tex]
Substitute these values into (3) and evaluate for a
b = 2 ⇒ a = 2 - 2(2) = 2 - 4 = - 2
b = - [tex]\frac{1}{8}[/tex] ⇒ a = 2 - 2(- [tex]\frac{1}{8}[/tex] ) = 2 + [tex]\frac{1}{4}[/tex] = 2 [tex]\frac{1}{4}[/tex] = [tex]\frac{9}{4}[/tex]
The possible values of a and b are 8, -3 or 9/4 , -1/8 respectively.
What is an equation ?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equations are,
ax + by = 2 (1)
and bx + a²y = 10 (2)
Also, x = 1 and y = 2 are the solution of the equation,
Substitute x = 1 and y = 2in equation (1),
a(1) + b(2) = 2
a + 2b = 2 (3)
Further substitute x = 1 and y = 2 in equation (2),
b(1) + a²(2) = 10
2a² + b = 10 (4)
By solving equation (3) and (4),
The possible values of a are 8 and 9/4.
And possible value of b are -3 and -1/8.
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PLSS HELP MEE WILL MARK BRAINLIEST
What would be the point in between the 700 and 800?
Answer:
750
Step-by-step explanation:
Order the expressions
Answer:
1. 3^4 x 3^3 < 3^12
2. 3^3 x 4^3 < 12^4
3. 3^4 x 4^3 > 12^3
Maria's monthly income is $1,250. She can afford to spend 25% of her income for rent. How much can she pay for rent each month?
Answer:
312.5
Step-by-step explanation: 25 percent of 1250 is 312.5(calculated)
to check your answer we multiply 312.5 by 4 as its (25%=1/4)
A cycle is marked at ₹ 4500 and sold for rupees ₹4185 padma said that the discount percentage is 7 % do you agree ? give reasons.
DON'T SPAM!JUST DON'T
Answer:
Yes
Step-by-step explanation:
Given:A cycle is marked at ₹4500 and sold for rupees ₹4185.
Now, To find discount
4500 × 7 ÷ 100 = ₹315
Now,
4500 - 315 = ₹4185
Thus, The answer is Yes Agreed!
-TheUnknownScientist 72
2) If it is 12° outside and the temperature is going to -7° drop 19º. What will the new temperature be?
Answer:
69 degrees
Step-by-step explanation:
yeah
Need help this please!
Answer:
My earlier answer was deleted, so I'm reposting. The only thing I can think happened is that I included a link to a free bar chart program, which I used for the attached chart.
Step-by-step explanation:
Make your own chart or find an online bar chart utility. I was unable to properly label the title and axes on my chart, so modify these properties.
Someone please help me solve the problem
========================================================
Explanation:
Check out the diagram below.
We have the following points
A = center of both the circle and the squareB = point on the circle directly to the left of point AP,Q,R,S = corner points of the squareE = intersection of segments AB and PSF = point on the square directly to the right of point AC and D = intersection of segment PS and the circleLet x be the length of segments DE and EC. Note how segment AB bisects segment DC. Whenever the radius is perpendicular to the chord like this, the radius will bisect the chord.
We're told that the chord length CD is the same as the radius AD, since CD = CE+ED = x+x = 2x, this means AD = 2x as well.
At this point, you probably can recognize we have a 30-60-90 triangle. One useful property of such triangles is that the hypotenuse is double the length of the short leg. The long leg is [tex]x\sqrt{3}[/tex] which is the length of segment EA. You can use the pythagorean theorem to confirm this.
----------------------------------
To summarize that last section, we formed triangle DAE and this triangle is a 30-60-90 triangle as shown in the diagram below.
Notice how the segments EA and FA span the entire width of the square. That width being [tex]EA+FA = x\sqrt{3}+x\sqrt{3} = 2x\sqrt{3} = EF[/tex]
The square has side lengths of [tex]2x\sqrt{3}[/tex] while the circle has radius 2x.
Use these two facts to find the area of each in terms of x.
[tex]A_1 = \text{area of square} = (\text{side})^2 = (2x\sqrt{3})^2 = 12x^2[/tex]
[tex]A_2 = \text{area of circle} = \pi*r^2 = \pi*(2x)^2 = 4\pi x^2[/tex]
-----------------------------------
The last step is to divide the two results. The x^2 terms cancel out.
We'll be left with...
[tex]\frac{A_1}{A_2} = \frac{12x^2}{4\pi x^2} = \frac{12}{4\pi} = \frac{3}{\pi} \approx 0.9549[/tex]
There are many ways to express this ratio. One way we could write it is to say 3:pi to indicate that if the area of the square is 3, then the circle has area of pi (approximately 3.14). No matter what the square's area is, the circle is always slightly larger in area.
The bearing of point Y from point X is 065°.
The bearing of point Z from point Y is 145º.
The bearing of point Z from point X is 105º.
Find the bearing of point X from point Z.
Answer:
285°
Step-by-step explanation:
You have probably learned bearing in geography and maybe even mathematics.
First off, skip the Y part since the answer you're looking for have nothing to do with it.
So, 180°+105°=285°
Those red-colored angles.. they have the same angle.
That's cause they're alternate angles and alternate angle are equal.
That arrow-like thing is to proove that they're parallel.
nin
1) What is the equation of the line that passes through the point (-2,1) and has a slope of
-5/2?
Answer:
y=(-5/2)x-4
Step-by-step explanation:
Step 1: Define the equation of a line.
Equation of a line is written in the form y=ax+b where a is the slope and b is the y-intercept.
Step 2: Write the given parameters
(x1,y1)=(-2,1)
m=-5/2
Using the formula y-y1=m(x-x1)
y-1=-5/2(x-(-2))
y-1=-5/2(x+2)
y-1=(-5x-10)/2
By cross multiplication,
2(y-1)=-5x-10
2y-2=-5x-10
2y=-5x-10+2
2y=-5x-8
y=(-5x-8)/2
y=(-5/2)x-4
A diver descends 3.2m in 5min. what was his average rate of descent in metres per minute?
Divide distance by time:
3.2 meters / 5 minutes = 0.64
The descent was -0.64 meters per minute
Answer:
.64
Step-by-step explanation:
Whenever you see x per y that means that you're looking at a ratio, which can be expressed as a fraction.
It would look like 3.2/5
The rate of descent may not be consistent, but on average it's reflected by the ratio and so you can just cut 3.2 meters into five equal parts to see, on average, how far the diver descended every minute.
HELP!!!
‐9z = ‐207
Please solve this with math explanations and NOT just the answer! Whoever explains first will get brainly!
Answer:
23
Step-by-step explanation:
this is because
the equation is saying -9time something = -207
so
you would -207 divided by -9
which gives you 23
so
z=23
The corner store sells pairs at a rate of $2.50 for per pair if Fiona has $15 how many pairs can if you fiona buy?
Answer: Fiona can buy six pairs.
15/2.5 = 6
Answer:
Fiona can buy 6 pairs
Step-by-step explanation:
2.50x 6
Help me with my math work please! Whoever helps gets 50 points! Thnx!
Answer:
6) y=-2
7) w=15
8) x=1
Area codes are the first three digits of a 10-digit telephone number. The first digit of an area code cannot be 0 or 1.
a. How many area codes can be created if digits are allowed to be repeated?
b. How many area codes can be created if digits are not allowed to be repeated?
Answer:A
Step-by-step explanation:because the numbers can be allowed to be repeated
What is the difference (how far apart on a number line are the solutions) between the sum of roots versus the product of the roots of the equation:
(x-5)(x+2)=0?
answer should be a number only
Answer:
7
Step-by-step explanation:
(x - 5)(x + 2) = 0
x = 5 & -2
Now,
given
r > s
r = 5, s = -2
Now,
=> r - s
=> 5 - (-2)
=> 5 + 2
=> 7
if the discriminant is negative how many solutions are there
Answer:
Two solutions.
Step-by-step explanation:
Question is in picture please help will mark brainliest
Answer:
4+2(n-1)+5(n-1)
Step-by-step explanation:
We know the pattern always has a +5 to the previous term then plus the lowest unrepeatded even number, such as +0, +2, +4, +6, and so on. The next erm will be 36+5+8, which is 49. The nth then will be the first term+2(n-1)+5(n-1).
That will result in
4+2(n-1)+5(n-1)
Please give brainliest! Thank you!
a cafe sells a regular cup of coffee for $1 and a large sup for $1.50. melissa and her friend buy 5 cups of coffee and spend a total of $6. find the number of large cups.
Answer:
65
Step-by-step explanation:
it is the largest cup so it is 65
The x and y axis are negative what's the quadrant or axis
Answer:
Need more information
If you want put a graph or explain more your question
A map is drawn using a scale of 1 centimeter to 25 kilometers.
What actual distance is represented by a map length of 3.2 centimeters?
The Hayes family and the Cook family each used their sprinklers last summer. The water output rate for the Hayes family's sprinkler was 30L per hour. The water output rate for the Cook family's sprinkler was 20L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1450L. How long was each sprinkler used?
Answer:
30 hours of use by Washington family
35 hours of use by Choi family
Step-by-step explanation:
Help help help math math
Answer:
Step-by-step explanation:
Answer:
volume of sphere is 4000cubic ft..... when
[tex]\pi = 3 \: and \: r = \frac{1}{2} d[/tex]
i will give you brainliest or whatever it’s called just pls answer within 45 minutes !!
Answer:
x = y1 x x1/ y2 x2
Step-by-step explanation:
how do I do this, what is the answer?
Answer:
g=2-X/-3
Step-by-step explanation:
X=3g+2
To make g the subject, make it stand alone
While transferring 3g to the other side of the equation, the sign changes i.e + changes to -
The equation will then be written as: -3g = -X + 2 or -3g = 2 - x
Divide both sides by -3
g= (2-x)/-3
if it's 11:24 what time will it be in 49 minutes
Hi,
if it's 11:24, it wil be 12:13
✅(◠‿◕)
Find the perimeter of the shape below:
Answer:
8m
Step-by-step explanation:
!!!HELP!!!
1) Which transformation can be used to map ABCD onto EFGH and to confirm that the figures are congruent?
A) ABCD can be mapped to EFGH with a translation right 4 units and down 4 units.
B) ABCD can be mapped to EFGH with a translation left 4 units and down 4 units.
C) ABCD can be mapped to EFGH with a translation left 4 units and up 4 units.
D) ABCD can be mapped to EFGH with a translation right 4 units and up 4 units.
2) Which sequence of transformations will only produce a figure similar to but not congruent to the figure ABCD?
A) ABCD is translated 2 units to the right and then reflected across the x-axis.
B) ABCD is translated 4 units left, 2 units up, and then reflected across the y-axis.
C) ABCD is rotated 180° clockwise about the origin and the translated 3 units right.
D) ABCD is dilated by a scale factor 3 and then rotated 90° clockwise about the origin.
Answer:
itsb a
Step-by-step explanation:
sorry
Why does it take 30 years to pay $150.000 lan, even though you pay $100 a month
Answer:
because you have to multiply the 100x12= 1200 than multiply that by another 1200
Step-by-step explanation:
are these lines perpendicular explain
Answer:
Yes because the slopes are negative reciprocals of each other.
Step-by-step explanation:
The slope of line B is: 1/3
(-2, -4) and (1, -3)
(-3+4)/(1+2) = 1/3
The slope of line A is: 3
(-3, 0) and (-2, -3)
(-3-0)/(-2+3) = -3
basic help :(
its math
Answer:
the slope or rate of change is 8 over 6 or 4 over 3 4/3
Answer:
the slope or rate of change is 8 over 6 or 4 over 3 4/3
Step-by-step explanation: