Answer:
132 is the one to the right of it and next one going clockwise wold probably be 48 continueing clockwise the next would be 132 again
Step-by-step explanation:
1: solve the following pair of equations simultaneously using the method stated.
a) 2x-3y = 5 and 3x+4y = 6 (elimination method)
b) 4x-y = 9 and 3xy = -6 (substitution method)
c) y=x^2 - 2x and y = 2x -3 (substitution method)
Answer:
Your answers are below ↓
Step-by-step explanation:
Given ↓
A) 2x-3y = 5 and 3x+4y = 6 ( The method this has to be solved in is the elimination method. )
Now using these,
(1)×3 - (2)×2 = 6x + 9y - 6x - 8y = 15 - 12
therefore,
y = 3
putting the value of y in eqn. (1)
2x + 6 = 5
therefore,
x = -1/2
B) y=x^2 - 2x and y = 2x -3 ( The method this has to be solved in is the substitution method. )
Reduce the greatest common factor on both sides of the equation:
[tex]\left \{ {{4x-y=9} \atop {xy=-2}} \right.[/tex]
Rearrange like terms to the same side of the equation:
[tex]\left \{ {{-y=9-4x} \atop {xy=-2}} \right.[/tex]
Divide both sides of the equation by the coefficient of the variable:
[tex]\left \{ {{y=-9+4x} \atop {xy=-2}} \right.[/tex]
Substitute the unknown quantity into the elimination:
[tex]x(-9+4x)=-2[/tex]
Apply Multiplication Distribution Law:
[tex]-9x+4x^2=-2[/tex]
Reorder the equation:
[tex]4x^2-9x=-2[/tex]
Divide the equation by the coefficient of the quadratic term:
[tex]\frac{1}{4}(4x^2)+\frac{1}{4}(-9x)=\frac{1}{4}*(-2)\\[/tex]
Calculate:
[tex]x^2-\frac{9x}{4}=-\frac{1}{2}[/tex]
Add one term in order to complete the square:
[tex]x^2-\frac{9x}{4}+(\frac{9}{4}*\frac{1}{2})^2=-\frac{1}{2}+(\frac{9}{4}*\frac{1}{2})^2[/tex]
Calculate:
[tex]x^2-\frac{9x}{4}+(\frac{9}{8} )^2=-\frac{1}{2} +(\frac{9}{8} )^2[/tex]
Factor the expression using [tex]a^2$\pm$2ab+b^2=(a$\pm$b)^2[/tex]:
[tex](x-\frac{9}{8} )^2=-\frac{1}{2} +(\frac{9}{8} )^2[/tex]
Simplify using exponent rule with the same exponent rule: [tex](ab)^n=a^n*b^n[/tex]
[tex](x-\frac{9}{8} )^2=-\frac{1}{2} +\frac{9^2}{8^2}[/tex]
Calculate the power:
[tex](x-\frac{9}{8} )^2=-\frac{1}{2}+\frac{81}{64}[/tex]
Find common denominator and write the numerators above the denominator:
[tex](x-\frac{9}{8} )^2=\frac{-32+81}{64}[/tex]
Calculate the first two terms:
[tex](x-\frac{9}{8} )^2=\frac{49}{64}[/tex]
Rewrite as a system of equations:
[tex]x-\frac{9}{8} =\sqrt{\frac{49}{64} }[/tex] or [tex]x-\frac{9}{8} =-\sqrt{\frac{49}{64} }[/tex]
Rearrange unknown terms to the left side of the equation:
[tex]x=\sqrt{\frac{49}{64} } +\frac{9}{8}[/tex]
Rewrite the expression using [tex]\sqrt[n]{ab} =\sqrt[n]{a} *\sqrt[n]{b}[/tex]:
[tex]x=\frac{\sqrt{49} }{\sqrt{64} } +\frac{9}{8}[/tex]
Factor and rewrite the radicand in exponential form:
[tex]x=\frac{\sqrt{7^2} }{\sqrt{8^2} } +\frac{9}{8}[/tex]
Simplify the radical expression:
[tex]x=\frac{7}{8} +\frac{9}{8}[/tex]
Write the numerators over the common denominator:
[tex]x=\frac{7+9}{8}[/tex]
Calculate the first two terms:
[tex]x=\frac{16}{8}[/tex]
Reduce fraction to the lowest term by canceling the greatest common factor:
[tex]x=2[/tex]
Rearrange unknown terms to the left side of the equation:
[tex]x=-\sqrt{\frac{49}{64} } +\frac{9}{8}[/tex]
Rewrite the expression using [tex]\sqrt[n]{a} =\sqrt[n]{a} *\sqrt[n]{b}[/tex]:
[tex]x=-\frac{\sqrt{49} }{\sqrt{64} }+\frac{9}{8}[/tex]
Factor and rewrite the radicand in exponential form:
[tex]x=-\frac{\sqrt{7^2} }{\sqrt{8^2} } +\frac{9}{8}[/tex]
Simplify the radical expression:
[tex]x=-\frac{7}{8} +\frac{9}{8}[/tex]
Write the numerators over common denominator:
[tex]x=\frac{-7+9}{8}[/tex]
Calculate the first two terms:
[tex]x=\frac{2}{8}[/tex]
Reduce fraction to the lowest term by canceling the greatest common factor:
[tex]x=\frac{1}{4}[/tex]
Find the union of solutions:
[tex]x=2[/tex] or [tex]x=\frac{1}{4}[/tex]
Substitute the unknown quantity into the elimination:
[tex]y=-9+4*2[/tex]
Calculate the first two terms:
[tex]y=-9+8[/tex]
Calculate the first two terms:
[tex]y=-1[/tex]
Substitute the unknown quantity into the elimination:
[tex]y=-9+4*\frac{1}{4 }[/tex]
Reduce the expression to the lowest term:
[tex]y=-9+1[/tex]
Calculate the first two terms:
[tex]y=-8[/tex]
Write the solution set of equations:
[tex]\left \{ {{x=2} \atop {y=-1}} \right.[/tex] or [tex]\left \{ {{x=\frac{1}{4} } \atop {y=-8}} \right.[/tex] -------> Answer
C) y=x^2 - 2x and y = 2x -3 ( This method this has to be solved in is the substitution method. )
Step 1: We start off by Isolating y in y = 2x - 3
y=2x-3 ----------> ( Simplify )
y+(-y)=2x-3+(-y) ---- > ( Add (-y)on both sides)
0=-3+2x-y
y/1 = 2x-3/1 --------> (Divide through by 1)
y = 2x - 3
We substitute the resulting values of y = 2x - 3 and y = x^2 - 2x
(2 * x - 3) = x^2 - 2x ⇒ 2x -3 = x^2 - 2x ----> ↓
(Substituting 2x - 3 for y in y = x^2 -2x )
Next: Solve (2x - 3 = x^2 - 2x) for x using the quadratic formular method
2x - 3 = x^2 - 2x
x = -b±b^2-4ac/2a Step 1: We use the quadratic formula with ↓
a = -1,b=4,c= - 3
x = -4±(4)^2-4(-1)(-3)/2(-1) Step 2: Substitute the values into the Quadratic Formular
x = -4± 4/ - 2 x = 1 or x = 3 Step 3: Simplify the Expression & Separate Roots
x = 1 or x = 3 ------- ANSWER
Substitute 1 in for x in y = 2x - 3 then solve for y
y = 2x - 3
y = 2 · (1) - 3 (Substituting)
y = -1 (Simplify)
Substitute 3 for in y = 2x - 3 then solve for y
y = 2x - 3
y = 2 · (3) - 3 (Substituting)
y = 3 (Simplify)
Therefore, the final solutions for y = x^2 -2x; y = 2x - 3 are
x₁ = 1, y₁ = -1
x₂ = 3, y₂ = 3
need help I don’t know what to do please help !!
Answer:
Yes, because the monthly service fee is approximately the same each month.
Step-by-step explanation:
At one month, the service fee is around $50, then from month one to month two the service fee is around $50, and so on. Just focus on the line and the points it makes in respect to the month to cost ratio.
WILL GIVE BRAINLIEST, STARS, POINTS, AND THANK YOU FOR THE RIGHT ANSWER!!!
PLEASE. PLEASE HELP MEEE.
Computing Residuals
1/3
The table and scatter plot show the average monthly temperature, x, and a family's monthly heating cost, y, for 11 different months.
The equation of the line of best fit is y= -1.1x + 91.30
Use the equation of the line of best fit to fill in the blanks below.
Give exact answers, not rounded approximations.
Answer:
1st blank: $51.00. 3rd blank: 1.1 5th blank: 24.2
2nd blank: $67.00. 4th blank: 91.30. 6th blank: -57.4
Step-by-step explanation:
Which function has the same minimum value as ? f(x) = 3x 3 f(x) = |x| 3 f(x) = –x2 3
The function that has the same minimum value as fx= 3x³ is f(x) = x + 3.
What is a function?It should be noted that a function simply means a relation or expression that involves two or more variables.
In this case, the function that has the same minimum value as the expression of 3x³ is f = x + 3.
Learn more about functions on:
https://brainly.com/question/2833285
#SPJ4
Answer:b
Step-by-step explanation:
HELP PLS I NEED help this is to get my grade up
Answer: Around 10 days. The real answer is 10 2/3.
Answer:
10 and 2-third days.
Convert mixed number to improper fraction
Initial equation
[tex]\frac{176}{9} / \frac{11}{6}[/tex]
Next, multiply the numerators by the numerators, and do the same for the denominators. Flip the second number to 6/11
[tex]\frac{176 * 6}{9 * 11}[/tex]
[tex]= \frac{1056}{99}[/tex]
Simplify.
[tex]\frac{1056}{99} -- > 10\frac{2}{3}[/tex]
Answer this volume based Question. I will make uh brainliest + 50 points
Answer:
[tex]\huge{\purple {r= 2\times\sqrt[3]3}}[/tex]
[tex]\huge 2\times \sqrt [3]3 = 2.88[/tex]
Step-by-step explanation:
For solid iron sphere:radius (r) = 2 cm (Given)Formula for [tex]V_{sphere} [/tex] is given as:[tex]V_{sphere} =\frac{4}{3}\pi r^3[/tex][tex]\implies V_{sphere} =\frac{4}{3}\pi (2)^3[/tex][tex]\implies V_{sphere} =\frac{32}{3}\pi \:cm^3[/tex]For cone:r : h = 3 : 4 (Given)Let r = 3x & h = 4xFormula for [tex]V_{cone} [/tex] is given as:[tex]V_{cone} =\frac{1}{3}\pi r^2h[/tex][tex]\implies V_{cone} =\frac{1}{3}\pi (3x)^2(4x)[/tex][tex]\implies V_{cone} =\frac{1}{3}\pi (36x^3)[/tex][tex]\implies V_{cone} =12\pi x^3\: cm^3[/tex]It is given that: iron sphere is melted and recasted in a solid right circular cone of same volume[tex]\implies V_{cone} = V_{sphere}[/tex][tex]\implies 12\cancel{\pi} x^3= \frac{32}{3}\cancel{\pi}[/tex][tex]\implies 12x^3= \frac{32}{3}[/tex][tex]\implies x^3= \frac{32}{36}[/tex][tex]\implies x^3= \frac{8}{9}[/tex][tex]\implies x= \sqrt[3]{\frac{8}{3^2}}[/tex][tex]\implies x={\frac{2}{ \sqrt[3]{3^2}}}[/tex][tex]\because r = 3x [/tex][tex]\implies r=3\times {\frac{2}{ \sqrt[3]{3^2}}}[/tex][tex]\implies r=3\times 2(3)^{-\frac{2}{3}}[/tex][tex]\implies r= 2\times (3)^{1-\frac{2}{3}}[/tex][tex]\implies r= 2\times (3)^{\frac{1}{3}}[/tex][tex]\implies \huge{\purple {r= 2\times\sqrt[3]3}}[/tex]Assuming log on both sides, we find:[tex]log r = log (2\times \sqrt [3]3)[/tex][tex]log r = log (2\times 3^{\frac{1}{3}})[/tex][tex]log r = log 2+ log 3^{\frac{1}{3}}[/tex][tex]log r = log 2+ \frac{1}{3}log 3[/tex][tex]log r = 0.4600704139[/tex]Taking antilog on both sides, we find:[tex]antilog(log r )= antilog(0.4600704139)[/tex][tex]\implies r = 2.8844991406[/tex][tex]\implies \huge \red{r = 2.88\: cm}[/tex][tex]\implies 2\times \sqrt [3]3 = 2.88[/tex]Is substitutions the best method to use when one variable is already known
if n varies directly with m and m=-12 when n=4 what is the value when n=-3
Step-by-step explanation:
m and n are directly linked to each other by a factor.
m×k = n
-12×k = 4
k = 4/-12 = -1/3
m×-1/3 = -3
m = 9
Which statement best describes ratio
Find the measure of angle k
Answer:
30
Step-by-step explanation:
PLEASE I BEG OF YOU HELP ME
P is the point (2, 7) and Q is the point (6, -3).
What is the gradient of PQ?
The Gradient of the line PQ is -5/2.
What is Gradient?Gradient the basically the ratio between the change in vertical coordinate to change in horizontal coordinates.
Here, P (2, 7) and Q (6, -3)
Now, Gradient = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
m = [tex]\frac{-3 -7}{6 - 2}[/tex]
m = -10/4
m = -5/2
Thus, the Gradient of the line PQ is -5/2.
Learn more about Gradient from:
https://brainly.com/question/13050811
#SPJ1
For the function f(x) = x^1/3/3 find f^-1(x)
Answer:
To get f⁻¹(x), write f(x) = y = x^(1/3)/3, exchange x and y, so x = y^(1/3)/3, then y = (3x)³, this is just the f⁻¹(x) = (3x)³.
Step-by-step explanation:
What is the total number of different 13-letter arrangements that can be formed using the letters in the word ENLIGHTENMENT?
Answer:
86486400
Step-by-step explanation:
which set of measures could be the measures of the interior angles of a triangle?
a.30°, 90°, 30°
b.32°, 59°, 79°
c.35°, 65°, 75°
d.22°, 37°, 121°
Answer:
D
Step-by-step explanation:
Whatever angle you pick the three possibilities must add to 180.
a) adds to 150
b) 32 + 59 + 79 = 170. Close but not close enough
c) c has three 5s. The total will end in 5. Not the answer.
d) d does add to 180. It's the answer.
Which set of measures could be the measures of the interior angles of a triangle?
a.30°, 90°, 30°
b.32°, 59°, 79°
c.35°, 65°, 75°
d.22°, 37°, 121°
Explanation -:In this question we are asked to find out which one could be the measures of the interior angles of a triangle. Add the three measure angles given if you get 180° then those angles can be the interior angles of a triangle.
We know that,
[tex] \bull \: \small\boxed{ \rm{ Sum \: of \: all \: interior \: angles \: of \: a \: triangle = 180°}}[/tex]
a) 30°, 90°, 30°
→ 30° + 90° + 30° = 180°
→ 150° ≠ 180°
Option a) is not the correct answer.
b) 32° , 59° , 79°
→ 32° + 59° + 79° = 180°
→ 170° ≠ 180°
Option b) is not the correct answer.
c) 35° , 65° , 75°
→ 35° + 65° + 75° = 180°
→ 175° ≠ 180°
Option c) is not the correct answer.
d) 22° , 37° , 121°
→ 22° + 37° + 121° = 180°
→ 180° = 180°
Hence, opition d) is the correct answer
Kate's house exterior needs painting.
Disregarding windows and doors, find the surface area of the walls.
Explanation:
Perimeter of the base = 8+10+15+7+23+17 = 80 meters
The 23 is from 8+15 = 23 and it is the length along the back wall, while the 10+7 = 17 is the length along the left side wall. Both the sides of 23 and 17 are hidden from view. The height of 5 meters is not part of the perimeter of the base.
Multiply the perimeter of the base by the height of the building to find the lateral area, aka wall area.
80*5 = 400 square meters
In which data set does the range have the greatest spread?
A. 10, 11, 11, 14, 14
B. 10, 13, 13, 14, 15
C. 9, 11, 11, 13, 14, 15, 16
D. 8, 11, 13, 13, 17, 20, 23
Answer:
D (8, 11, 13, 13,17,20,23)
Step-by-step explanation:
I did this and got it correct.
Identify a pattern in the given list of numbers. Then use this pattern to find the next number. 17,7,-3,-13,-23
Answer:
-33
Step-by-step explanation:
The sequence is descending so the nth term would be -10n and the 0 term would be 27 so the nth term for the sequence would be -10n +27.
The question asks you to find the 6th term so (-10 x 6) + 27 = -60 + 27 = -33
A couple Invested $6100 in an account some of it went into a savings account paying 3% annual simple interest . The rest was invested in a riskier mini - mall development plan paying 11% annual simple interest . The combined interest earned for the first year was $503 . How much money was invested at each rate ?
Answer:
4387.63
Step-by-step explanation:
Simplify.
2
5x² - 7x + 3
-
10
+ 8x² + 9x
I need help
Answer:
621 i guess
Step-by-step explanation:
18x² + 2x² - 7
Tap on a clip to paste it in the text box.
Noel works as a driver for a transportation company. On average, he drives 152 hours to make 19 successful deliveries. Assume this rate is his constant rate for delivering goods. If you graph this relationship with time along the x-axis and number of deliveries along the y-axis, the slope of the line you get gives Noel's unit rate for a successful delivery. Which unit rate can be interpreted as the slope?
The unit rate can be interpreted as the slope will give [tex]\dfrac{1}{8}[/tex] of a delivery per hour
What is graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
Given: The total time for which Noel drives = 152 hours
The total number of successful deliveries = 19
Now, Noel's unit rate for successful delivery is given by:-
[tex]\rm =\dfrac{Total\ succesful\ deliveries}{Total\ hours}=\dfrac{19}{152}=\dfrac{1}{8}[/tex]
Hence, Noel's unit rate for the successful delivery 1/8 of a delivery per hour
To know more about graph follow
https://brainly.com/question/25020119
#SPJ1
Solve for X, will mark brainliest if right
Answer:
x = 8
Step-by-step explanation:
The sides are in proportion.
[tex]\frac{RG}{FG} =\frac{SH}{FH}[/tex]40 / 7x + 14 = 44 / 33 + 4440 / 7x + 14 = 44/77 = 4/740(7) = 4(7x + 14)280 = 28x + 5610 = x + 2x = 8Need help trying to find the answer
Answer:
3/20
Step-by-step explanation:
1. Multiply the numerators
2. Multiply the denominators
3. Your answer, in this case, will be 6/40
4. Simplify fraction to its simplest form* which gives you 3/20
*I halved both numbers as they are both even
Hope this helped :)
Find the simple interest charged for a loan of:
a $2000 for 3 months at 1.1% per month
Answer:
$5.50
Step-by-step explanation:
I = Prt
P = $2,000r = 1.1% = 0.011t = 3 months = 0.25 yearsSolving :
I = (2,000)(0.011)(0.25)I = (500)(0.011)I = $5.50PLEASE HELP ASAP
What is an
equation of the line that passes through the points (3,3) and (3, -3)
5
5.2
4
Find the area of the parallelogram.
square units
Answer:
20 square units
Step-by-step explanation:
Area of a parallelogram is calculated with the following formula:
b*h (b: base, h: height)
5*4 = 20 square units
15. A cone has a radius of 9 cm and slant height of 12 cm. Find its surface area.
A. 593.46 cm²
B. 693.46 cm²
C. 793.46 cm²
D. 893.46 cm²
Answer:
594
Step-by-step explanation:
A=πrl+πr²
(22/7×9×12)+(22/7×9²)
=594
If 27 out of 30 people passed a driving
test, what percent failed?
Answer:
10% failed the driving test
Step-by-step explanation:
27/30 = 90% and since 90% is what PASSED, 10% is what FAILED
this should be correct... if its not im sorry
Answer:
10% failed
27 / 30 is 90% so, 100% - 90% = 10%
Please mark Brainliest!!
In a class test containing 25 questions, 2 marks are given for every correct answer and 1 mark is deducted for every incorrect answer.
a. Aryan attempts only 22 questions and gets all of them correct. What is his total SCore?
b. Dhruv attempts all questions but gets 15 answers correct. What will be his Score?
Answer:
A. 44 (if unanswered questions do not deduct 1 point)
B. 40
Step-by-step explanation:
22 x 2 = 44
25 x 2 - 10 = 40
If function f : R --> R where f(X)=X³ - kX² + 12X - 7 is a one to one function, then k belongs to....
Since f(x) is a cubic polynomial, it has at most 3 distinct roots. If f(x) has 3 real roots, then f(x) = 0 for more than one instance of x.
But if f(x) is one-to-one, then there must be only one real root and the other two are non-real. Let a + bi and a - bi be these non-real roots and c the single real root; then we can factorize f(x) as
[tex]f(x) = x^3 - kx^2 + 12x + 7 = (x - (a + bi)) (x - (a - bi)) (x - c)[/tex]
Expand the right side to get
[tex]f(x) = x^3 - kx^2 + 12x + 7 = (x^2 - 2ax + a^2+b^2) (x - c)[/tex]
[tex]f(x) = x^3 - kx^2 + 12x + 7 = x^3 - (2a + c) x^2 + (a^2 + 2ac + b^2) x - (a^2c + b^2c)[/tex]
from which it follows that
[tex]\begin{cases}k = 2a + c \\ 12 = a^2+2ac+b^2 \\ 7 = -a^2c-b^2c\end{cases}[/tex]
Since f(x) has only one root, its graph will have no turning points/extrema. If f(x) has a critical point, it must be a saddle point. Differentiating f(x) yields
[tex]f'(x) = 3x^2 - 2kx + 12[/tex]
Solve for the critical point:
[tex]f'(x) = 3x^2 - 2kx + 12 = 0[/tex]
[tex]x^2 - \dfrac{2k}3 x = -4[/tex]
[tex]x^2 - \dfrac{2k}3 x + \dfrac{k^2}9 = \dfrac{k^2}9-4[/tex]
[tex]\left(x - \dfrac k3\right)^2 = \dfrac{k^2}9-4[/tex]
[tex]x = \dfrac k3 \pm \sqrt{\dfrac{k^2}9-4}[/tex]
There is at most one real critical point, so either the square root term vanishes or it produces a non-real number. This happens for
[tex]\dfrac{k^2}9 - 4 \le 0 \implies k^2 \le 36 \implies -6 \le k \le 6[/tex]
So, if f(x) is one-to-one, then
[tex]k \in \left\{\kappa \in \Bbb R \mid -6 \le \kappa \le 6\right\}[/tex]
