x² + y² = 34
=
y = x+2
Show your working.
Answers
Answer:
[tex]\left \{ {{y=5} \atop {x=3}} \right.[/tex] or [tex]\left \{ {{y=-3} \atop {x=-5}} \right.[/tex]
Step-by-step explanation:
Answer:
(- 5, - 3 ) , (3, 5 )
Step-by-step explanation:
x² + y² = 34 → (1)
y = x + 2 → (2)
substitute y = x + 2 into (1)
x² + (x + 2)² = 34
x² + x² + 4x + 4 = 34
2x² + 4x + 4 = 34 ( subtract 34 from both sides )
2x² + 4x - 30 = 0 ( divide through by 2 )
x² + 2x - 15 = 0 ← in standard form
(x + 5)(x - 3) = 0 ← in factored form
equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x - 3 = 0 ⇒ x = 3
substitute these values into (2) for corresponding values of y
x = - 5 : y = - 5 + 2 = - 3 ⇒ (- 5, - 3 )
x = 3 : y = 3 + 2 = 5 ⇒ (3, 5 )
Related Questions
list all the possible order you can have
Answers
wala ako pake sau
Step-by-step explanation:
wala ako pake sau
The quotient of 7 and the difference of a number and 8.
Answers
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[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]
➪ What is the quotient of 7 and the difference of a number and 8?
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\diamond[/tex]
➪ First, the word "quotient" indicates that we divide.
✳︎ Here, we are asked to divide 7 by the difference of a number and 8.
➪ The word "difference" indicates that we subtract.
✳︎ Here, we are asked to subtract a number minus 8.
Let the number be x.
Since the difference of x and 8 means we subtract x minus 8, this expression looks as follows:-
[tex]\texttt{x-8}[/tex]
◈ Now, we are also asked to find the quotient of 7 and the difference of a number and 8, which equals [tex]\bold{x-8}[/tex].
As I said earlier, the "quotient" means we divide, so we divide 7 by [tex]\bold{x-8}[/tex].
So we conclude that the expression is:-
7÷(x-8)
Good luck.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
It takes Imani seven hours to dig a 10 ft by 10 ft hole. Stefan can dig the same hole in five hours. If they worked together how long would it take them
Answers
Answer:
2 hours and 44 min. or 2.7273 hours
Step-by-step explanation:
Ryan: 1 hole per 5 hours
Castel: 1 hole per 6 hours
x = time if working together then
x(1/5 + 1/6) = 1
x(6 + 5) = 30
11x = 30
x = 30/11
x = 2.7273 hours
or
x = 2 hours and 44 minutes
What multiplies to 4 and adds to 6
Answers
Step-by-step equation: 2 x 2= 4
2 + 4= 6
What is the product? startfraction x squared minus 16 over 2 x 8 endfraction times startfraction x cubed minus 2 x squared x over x squared 3 x minus 4 endfraction
Answers
The product of the given expression is [tex]\frac{x(x-1)(x-4)}{2(x+4)}[/tex] OR [tex]\frac{x(x^{2} -5x+4)}{2x+8}[/tex] OR [tex]\frac{x^{3} -5x^{2} +4x}{2x+8}[/tex]
Simplifying fractionsFrom the question, we are to determine the product of the given expressions
The given expressions are
[tex]\frac{x^{2} - 16}{2x+8}\times \frac{x^{3}-2x^{2} +x}{x^{2} +3x-4}[/tex]
[tex]\frac{(x+4)(x-4)}{2(x+4)}\times \frac{(x^{2} -x)(x-1)}{(x-1)(x+4)}[/tex]
[tex]\frac{(x-4)}{2}\times \frac{(x^{2} -x)}{(x+4)}[/tex]
[tex]\frac{(x-4)}{2}\times \frac{x(x-1)}{(x+4)}[/tex]
[tex]\frac{x(x-1)(x-4)}{2(x+4)}[/tex]
OR
[tex]\frac{x(x^{2} -5x+4)}{2x+8}[/tex]
OR
[tex]\frac{x^{3} -5x^{2} +4x}{2x+8}[/tex]
Hence, the product of the given expression is [tex]\frac{x(x-1)(x-4)}{2(x+4)}[/tex] OR [tex]\frac{x(x^{2} -5x+4)}{2x+8}[/tex] OR [tex]\frac{x^{3} -5x^{2} +4x}{2x+8}[/tex]
Learn more on Simplifying fractions here: https://brainly.com/question/27038950
Here is the complete and correct question:
What is the product? StartFraction x squared minus 16 Over 2 x + 8 EndFraction times StartFraction x cubed minus 2 x squared + x Over x squared + 3 x minus 4 EndFraction
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Answer:
A. StartFraction x (x minus 4) (x minus 1) Over 2 (x + 4) EndFraction
Step-by-step explanation:
correct on edge :)
If you get a $50.00 raise in pay per month and your taxes also increase about $50.00 per month, how would you probably feel?
appreciated because you are getting rewarded for your hard work
satisfied because you broke even
proud because the government needs your money more than you do
resentful because it seems unfair
Answers
Answer:
i would say satisfied because you broke even. Because then you still work the same as you did, because before that you were breaking even every month. So you are not getting paid any extra
Step-by-step explanation:
I need this solved now
Answers
Detailed Explanation:
If both pairs of Opposite sides of a Quadrilateral are equal, then it is a Parallelogram. These are the basic properties of a Parallelogram.
HEY GUYS THIS IS MY FINAL MATH ASSIGNMENT OF THE YEAR... PLS JUST HELP ME FIND THE DOMAIN AND RANGE THANK YOU
Answers
Answer:
domain: all real numbers (-∞,∞)
range: y ≤ 64
Step-by-step explanation:
since the domain is arn,
and range is the coordinates
coordniate (top or bottom-most point)
downward facing so the top
(2, 64)
since it is downward facing we use ≤ instead of ≥
y value is 64 (just as x is 2)
your answer is y ≤ 64
hope this helps:)
Answer:
[tex]D=[x E R | {x = \infty} ][/tex]
[tex]R = [yER| y\leq 64][/tex]
Step-by-step explanation:
1) Identify whether the [tex]x[/tex] and [tex]y[/tex] values are continuous
2) Since [tex]x[/tex] will continue below the [tex]x[/tex]-axis, it will approach infinity.
Therefore [tex]D=[x E R | {x = \infty} ][/tex]
3) Since [tex]y[/tex] ONLY continues below 64, [tex]R = [yER| y\leq 64][/tex]
The sum of three consecutive integers is 90. Find the integers. If the smallest integer is x, the equation will be. I NEED HELP PLS SOLVE THIS QUICKLY I BEG YOU.
Answers
Answer:
x = 29
Step-by-step explanation:
Take the smallest integer as x. The next one as (x+1) and the last one as (x+2)
x + (x+1) + (x+2) = 90
x + x + x + 3 = 90
3x = 87
x = 29
Hence, x = 29
Hope this helps out. Feel free to mark me as brainliest! :)
Russ walks 710 mile to school. How far has he walked when he has covered 58 of the distance to school?\
Answers
Answer: [tex]\frac{7}{16}[/tex]
Step-by-step explanation: Distance to school = [tex]\frac{7}{10}[/tex] mile
Distance covered = [tex]\frac{5}{8}[/tex] of [tex]\frac{7}{10}[/tex]
= [tex]\frac{5}{8}[/tex] x [tex]\frac{7}{10}[/tex]
= [tex]\frac{35}{80}[/tex]
= [tex]\frac{7}{16}[/tex]
Order the following integers from least to greatest: -32, -43, -28, -22 and 13
Answers
Answer:
-22, -28, -32, -43, 13
Step-by-step explanation:
If it is after the digit 0 it will be less than any number above itself.
A tire company wants to determine if tires made with a new type of tread will last longer than tires made with the original type of tread. The company has access to 24 different vehicles. Each vehicle will receive four tires with the new tread and four with the original tread. The position, front or back, will be randomly determined for a pair of each type of tread. For example, a vehicle will have the new type of tread on the front tires and the original tread on the back tires. After six months, the pairs of unused tires will be used with the position switched on the car. The vehicles will be driven for six more months. At the end of one year, the depths of the remaining tread will be measured for each tire and the average differences between the new and original tread types will be determined. The average differences will then be used to determine if the new tread does last longer.
Is this a matched pairs design for this experiment?
Yes, the company used 24 different vehicles.
Yes, both types of tread were randomly assigned to each vehicle.
No, the vehicles were not put into groups of two.
No, the tires with the different types of tread were not randomly assigned to each vehicle.
Answers
This is a matched pairs design because both types of tread were randomly assigned to each vehicle.
What is matched pairs design?The term matched pairs design has to do with the situation in which participants are randomly assigned to an experiment or a control group. For each participant assigned to an experimental group, another is assigned to the control group.
Thus, this is a matched pairs design because both types of tread were randomly assigned to each vehicle.
Learn more about matched pairs design:https://brainly.com/question/17144039
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Pls help will give brainilist
Answers
Answer:
$16.37
Step-by-step explanation:
They want to raise $463.72 and they already have $218.22 so if we subtract it
$463.72-$218.22=$245.50
we get $245.50 left to raise.
We have 15 teachers so we do
$245.50/15
we get 16.36 but we round it so we get $16.37.
short answer: Write an equation in the form y=ax2+bx+c for a parabola that intersects the x-axis at -6 and 2 and passes through the point (1,-14) (2 points). Show you work.
Answers
Answer:
y = 2x^2 + 8x - 24
Step-by-step explanation:
This is a "working backwards" kind of a problem. You know the solution (the x-intercepts) and work backwards to find the equation. See image.
Which values complete the function? f(x)=_(x-_)(x+_)
Answers
Answer:
the answer is b
Step-by-step explanation:
just took the test
Answer:
Step-by-step explanation:
-1
3
4
Can someone try to help me I’m trying to get to a 91
Answers
What is the value of z, rounded to the nearest tenth? use the law of sines to find the answer. 2.7 units 3.2 units 4.5 units 5.3 units
Answers
The triangle is a shape with 3 sides and angles. The value of z from the given figure to the nearest tenth is 3.2
Sine rule of triangleThe triangle is a shape with 3 sides and angles
From the given triangle, we will use the expression below to determine the value of z
2.6/sin51= z/sin76
simplify
z = 2.6sin76/sin51
z = 2.5227/0.7771
z = 3.246
Hence the value of z from the given figure to the nearest tenth is 3.2
Learn more on sine rule here: https://brainly.com/question/27174058
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ignore the numbers on top of the fruits but can someone help solve this?
Answers
Step-by-step explanation:
I don't know what the 3rd fruit is. let's call it an apple.
so,
1 apple + 3 cherries = 3 bananas
1 apple = 3 bananas - 3 cherries
1 banana + 2 cherries = 1 apple = 3 bananas - 3 cherries
5 cherries = 2 bananas
1 apple + 1 banana = (1 banana + 2 cherries) + 1 banana =
= 2 bananas + 2 cherries =
= 5 cherries + 2 cherries =
= 7 cherries
the numbers did not help, as they were wrong.
e.g. if you assume the apple = 5, a cherry = 1 and a banana = 2, you would get 8 = 6 on the first scale.
if you change the apple to a 3, that would make the first scale true (6 = 6), but the second scale wrong (4 = 3).
funny enough, the other answer got 7 nevertheless (but the wrong way - actually 2 mistakes balanced each other out).
it is 7 cherries, though !
the actual numbers would be e.g.
a cherry = 1
then
1 banana = 5/2 = 2.5
1 apple = 3×5/2 - 3 = 15/2 - 6/2 = 9/2 = 4.5
to get whole numbers, we could multiply all by 2 :
cherry = 2
banana = 5
apple = 9
and then the first balance :
9 + 3×2 = 3×5
9 + 6 = 15
15 = 15 correct
the second balance
5 + 2×2 = 9
9 = 9 correct.
I ALWAYS GIVE BRAINLIEST!!!!!!COME AND GET IT IF YOU WANT IT! ~20 POINTS AT STAKE!
Answers
3rd answer
Step-by-step explanation:
because for the width of the first rectangle (27 cm) it is just 3 times larger for the width of the second rectangle (9 cm)
same for the length, 33cm is 3 timer larger
also sorry if its the other way around, i just call the ones that are like "______" length
Answer: C
Step-by-step explanation:
QUESTION
Find 45% of 240.
Answers
Answer:
108
Step-by-step explanation:
Calculator
Answer:
108
Step-by-step explanation:
(45 * 240) / 100
(10,800) / 100
108
PLEASEEEEE
Match the expressions with their simplified versions.
Answers
Answer:
1. [tex]\normalsize \boxed{\textsf{$4\sqrt{2}\cdot\sqrt{2}$}} \implies \boxed{8}[/tex]
2. [tex]\normalsize \boxed{\textsf{$3\sqrt{7}-2\sqrt{7}$}} \implies \normalsize \boxed{\textsf{$\sqrt{7}$}}[/tex]
3. [tex]\normalsize \boxed{\textsf{$\dfrac{\sqrt{7}}{2\sqrt{7}}$}} \implies \normalsize \boxed{\textsf{$\dfrac{1}{2}$}}[/tex]
4. [tex]\normalsize \boxed{\textsf{$2\sqrt{5}\cdot 2\sqrt{5}$}} \implies \boxed{20}[/tex]
Step-by-step explanation:
The Radical Rules by Lial et al. (2017) state that:
Product rule: [tex]\large \textsf{$\sqrt[n]{a}\cdot\sqrt[n]{b}=\sqrt[n]{ab}$}[/tex]
"The product of two roots is the root of the product."Quotient rule: [tex]\large \textsf{$\sqrt[n]{\dfrac{a}{b}}=\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}$}\ \ \textsf{$(b \neq 0)$}[/tex]
"The root of a quotient is the quotient of the roots."1.
[tex]\implies \normalsize \textsf{$4\sqrt{2}\cdot\sqrt{2}$}\\\\\normalsize \implies \textsf{$4\sqrt{2\cdot2}$}\\\\ \implies \normalsize \textsf{$4\sqrt{4}$}\\\\ \implies\normalsize \textsf{$4\cdot 2 = 8$}[/tex]
[tex]\normalsize \boxed{\textsf{$4\sqrt{2}\cdot\sqrt{2}$}} \implies \boxed{8}[/tex]
2.
[tex]\implies \normalsize \textsf{$3\sqrt{7}-2\sqrt{7}$}\\\\ \implies\normalsize \textsf{$(3-2)\sqrt{7}$}\\\\ \implies\normalsize \textsf{$1\sqrt{7}$}\\\\ \implies\normalsize \textsf{$\sqrt{7}$}[/tex]
[tex]\normalsize \boxed{\textsf{$3\sqrt{7}-2\sqrt{7}$}} \implies \normalsize \boxed{\textsf{$\sqrt{7}$}}[/tex]
3.
[tex]\implies \normalsize \textsf{$\dfrac{\sqrt{7}}{2\sqrt{7}}$}\\\\\\ \implies\normalsize \textsf{$\dfrac{1\sqrt{7}}{2\sqrt{7}}$}\\\\\\ \implies\normalsize \textsf{$\dfrac{1}{2}$}\\\\[/tex]
[tex]\normalsize \boxed{\textsf{$\dfrac{\sqrt{7}}{2\sqrt{7}}$}} \implies \normalsize \boxed{\textsf{$\dfrac{1}{2}$}}[/tex]
4.
[tex]\implies \normalsize \textsf{$2\sqrt{5}\cdot 2\sqrt{5}$}\\\\ \implies\normalsize \textsf{$2\cdot2\sqrt{5\cdot5}$}\\\\ \implies \normalsize \textsf{$4\sqrt{25}$}\\\\ \implies \normalsize \textsf{$4\cdot5=20$}\\\\[/tex]
[tex]\normalsize \boxed{\textsf{$2\sqrt{5}\cdot 2\sqrt{5}$}} \implies \boxed{20}[/tex]
Reference:
Lial, M., Hornsby, J., Schneider, D., & Daniels, C. (2017). College Algebra and Trigonometry, Global Edition (6th ed., p. 94).
In a right triangle, a and b are the lengths of the legs and c is the length
of the hypotenuse. If a = 2 feet and b = 1 foot, what is c? If necessary,
round to the nearest tenth.
c =
feet
Answers
c=2.2feet
The solution in the attached file
Which function is represented by the graph?
Answers
Answer:
cos(x-[tex]\frac{pi}{4}[/tex])-2
Step-by-step explanation:
The function is cos(x).
The horizontal shift is caused by (x- pi/4) so it would go to the right a distance of pi/4. If it was positive the entire thing would go left (x + pi/4).
The vertical shift is caused by the negative 2. Unlike horizontal shifts, negative moves it down and positive moves it up.
The x-axis is in radians. Desmos has option to change it to radian.
Identify coordinate point A.
(0, 2)
(6, 7)
(1, 5)
(7, 3)
Answers
Answer:
(0, 2)
Step-by-step explanation:
it right I got 100% on my quiz
And… here are others that are right in the quiz
Identify coordinate point B.
(1, 5)
Identify coordinate point D.
(7, 3)
Identify coordinate point C.
(6, 7)
Hope it helps! :)
How many combinations without repetition are possible if n = 6 and r = 3? 56 20 27 18
Answers
Answer:18
Step-by-step explanation:
n+r=9
n×r=27
r²=9
n²=36
n+n=12
r+n=9
r+r=6
Which line is the best model for the data in the scatter plot?
Answers
Answer:
the top right (2) answer is probably what you'll want to go for, if this is incorrect then you have my deepest apologies
Step-by-step explanation:
1.Judy put 50 cents and 1 quarter into a vending machine to buy a bottle of fruit juice. She got 2 dimes and 1 nickel back from the vending machine. How much did the bottle of fruit juice cost
Answers
Nickel - 5 cents
Dime - 10 cents
Quarter - 25 cents
Judy put in: 50 + 25 = 75 cents
The machine gave back: 10 + 10 + 5 = 25
Subtract the two numbers to find the difference (what the fruit juice cost): 75 - 25 = 50 cents
Answer:
Nickel - 5 cents
Dime - 10 cents
Quarter - 25 cents
Judy put in: 50 + 25 = 75 cents
The machine gave back: 10 + 10 + 5 = 25
Subtract the two numbers to find the difference (what the fruit juice cost): 75 - 25 = 50 cents
Step-by-step explanation:
Help pleasseeeee!!!!
Which of the following statements is TRUE about using a quadrilateral to construct a parallelogram?
A. All sides of the quadrilateral must be congruent and all angles must be congruent?
B. Opposite sides of the quadrilateral must be parallel and opposite angles must be congruent.
C. The sides of the quadrilateral can be any length and the angles can be any measure.
D. Adjacent sides of the quadrilateral must be perpendicular and adjacent angles must be congruent.
Answers
Answer:
B. B. Opposite sides of the quadrilateral must be parallel and opposite angles must be congruent.
Answer: Opposite sides of the quadrilateral must be parallel and opposite angles must be congruent.
Step-by-step explanation:
If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
2,994 divided by 128 i need help
Answers
That is your answer
Answer:
Divide 320 by 128 to get 2
23.39062
128| 2994.00000
256
____
434
384
_____
500
384
_____
1160
1152
____
80
0
___
800
768
_____
320
256
_____
64
Stopping at 5 decimal places
The solution for Long Division of 2994/128 is 23.39062
23.39062
A rectangular pyramid has a volume of 492 cubic yards. if the base has a length of 18 yards and a width of 4 yards, what is the height of the pyramid?
Answers
Answer:
h = 20.5 yards
Step-by-step explanation:
Volume of Rectangular Pyramid: lwh/3
492 = (18) * (4) (h) /3
Multiply 3 on both sides
1476 = (18) (4) (h)
1476 = 72h
Flip the equation.
72h = 1476
h = 41/2 or 20.5 yards