Answers
Answer:
k = -1/2 or 2
Step-by-step explanation:
For equations ...
ax +by +c = 0
dx +ey +g = 0
Cramer's Rule tells you the solutions are ...
x = (-ce +gb)/(ae -db)
y = (-ga +dc)/(ae -db)
In order for these equations to be consistent, the solution for any pair of them must be the same. It is sufficient for us to find 'k' such that the values of x are the same.
__
first and third equations
x = (-1·7 +1·(k+1))/(1·7 -3·(k+1)) = (k -6)/(4-3k)
second and third equations
x = (3·7 +1·5)/(2k·7 -3·5) = 26/(14k -15)
__
For these values to be the same, we must have ...
(k -6)/(4-3k) = x = 26/(14k -15)
(k -6)(14k -15) = (4 -3k)(26) . . . . . cross multiply
14k² -99k +90 = -78k +104 . . . . . simplify
14k² -21k -14 = 0 . . . . . . . . . . . . . put in standard form
7(2k +1)(k -2) = 0 . . . . . . . . factor
The solutions are the values of k that make the factors zero: k=2, k=-1/2.
These equations will be consistent if k = -1/2 or k = 2.
_____
Additional comment
Using our above expression for x, we can find the value of x for the solution x = -1/2 to be ...
x = 26/(14(-1/2) -15) = 26/(-22) = -13/11
The first equation tells us the corresponding value of y will be ...
x +(-1/2 +1)y +1 = 0
y = -2(x+1) = -2(-13/11 +11/11) = 4/11
For k = -1/2, (x, y) = (-13/11, 4/11).
The attached graph shows the solution for k=2.
For k = 2, (x, y) = (2, -1).
Related Questions
George and Carla are going on a road trip together, but they have a limited budget. They consider several different routes and then calculate
the cost of gas for each route. The longer the route, the greater the cost of gas. What is the independent variable?
A. the amount of money they have bugeted
B. the number of routes
C. the cost of gas
D. the length of the route
Answers
Independent: r- the length of the route
a plumber had 2 plastic pipes that were each 9 ft long. he used all of the 2 pipes and cut them into sections that were each 1/10 foot long. how many sections of pipe did he have in all
Answers
Answer:
180
Step-by-step explanation:
so 1 section is 0.1 feet long, that is 10 sections per foot(since 0.1*10 = 1)if you have 9 feet, imagine how many 0.1 feet can fit in ityou can fit 90 sections in 9 feet, since 9 / 0.1 = 90since you have 2 pipes, multiply 90 by 2, which is 180so you would have 180 sectionsThree friends earned more than $200 washing cars. They paid their parents $28 for supplies and divided the rest of the money equally. Write an inequality to find possible amounts each friend earned. Identify what your variable represents.
Answers
Answer: 3x + 28 > 200
Step-by-step explanation:
[tex]$$Let $x$ be the amount each friend received. Since there are 3 friends, then $3 x$ is the amount of money they split evenly. The amount of money they split evenly was the amount left over after paying their parent's $\$ 28$. Therefore $3 x+28$ is the total amount they earned.[/tex]
The sum of the Squares of three consecutive number is 110.
Then determine the Three Numbers.
Answers
[tex]\large\bold{{Question :-}}[/tex]The sum of the Squares of three consecutive number is 110. Then determine the Three Numbers.
[tex]\large\bold\red{\underline{Answer :-}}[/tex]
So, First of all The Question is to find out three consecutive Numbers .
First of all let's learn a little about Consecutive Numbers. So, Consecutive Numbers are the Numbers which follows each other. For example :- 1,2,3,4 are consecutive Numbers.
Let's start with Our Question :-
Let The First consecutive number be = xand second number be = x + 1Third number be = x + 2So,
[tex]:\pink\implies[/tex] [tex]\bold{{(x)^{2}}}[/tex] + [tex]\bold{{(x + 1)^{2}}}[/tex] + [tex]\bold{{(x + 2)^{2}}}[/tex] = [tex]\bold{{110}}[/tex]
[tex]:\pink\implies[/tex] [tex]\bold{{(x)^{2}}}[/tex] + [tex]\bold{{(x)^{2}}}[/tex] + [tex]\bold{{(1)^{2}}}[/tex]+ [tex]\bold{{2x}}[/tex] +[tex]\bold{{(x)^{2}}}[/tex] + [tex]\bold{{(4)}}[/tex]+ [tex]\bold{{(4x)}}[/tex] = [tex]\bold{{110}}[/tex]
[tex]:\pink\implies[/tex] [tex]\bold{{3x^{2}}}[/tex] + [tex]\large\bold{{6x}}[/tex] + [tex]\bold{{5}}[/tex] - [tex]\large\bold{{110}}[/tex] = [tex]\bold{{0}}[/tex]
[tex]:\pink\implies[/tex] [tex]\bold{{3x^{2}}}[/tex] + [tex]\bold{{6x}}[/tex] - [tex]\bold{{105}}[/tex] = [tex]\bold{{0}}[/tex]
By taking 3 Out as Common, we are left with the Quadratic Equation :—
[tex]:\pink\implies[/tex] [tex]\large\bold{{1x^{2}}}[/tex]+ [tex]\large\bold{{2x}}[/tex] - [tex]\large\bold{{35}}[/tex] = [tex]\large\bold{{0}}[/tex]
By Using Quadratic Formula,
x = -b ± √(b)^2— 4 × a × c / 2a
x = -2 ± √(2)^2— 4 × 1 × -35 / 2×1
x = -2 ± √144/2
[ As we know that "144" is square of 12 ]
x = -2 ± 12/2
Taking Positivex = -2+12/2x = 5Hence, x = +5
x +1 = 5+1 = +6
x+2 = 5+2 = +7
Taking Negative signx = -2-12/2x = -7Hence, x = -7
x+1 = -7+1 = -6
x+2 = -7+2 = -5
Hence, The Three consecutive Numbers are ±5,±6,±7.Answer:
± (5, 6, 7)Step-by-step explanation:
Let the three consecutive numbers be denoted as :
xx + 1x + 2Identity
(x + a)² = x² + 2ax + a²It is given that the sum of the squares of these numbers add up to 110.
(x)² + (x + 1)² + (x + 2)² = 110x² + x² + 2x + 1 + x² + 4x + 4 = 1103x² + 6x + 5 = 1103x² + 6x - 105 = 0x² + 2x - 35 = 0x² + 7x - 5x - 35 = 0x(x + 7) - 5(x + 7) = 0(x - 5)(x + 7) = 0x = 5 or x = -7Taking x = 5
x² = 5² = 25(x + 1)² = 6² = 36(x + 2)² = 7² = 49⇒ 25 + 36 + 49 = 110Taking x = -7
x² = (-7)² = 49(x + 1)² = (-6)² = 36(x + 1)² = (-5)² = 25⇒ 49 + 36 + 25 = 110Solution
5, 6, 7 ⇔ -7, -6, -5⇒ ± (5, 6, 7)A $10 book is 50% off. What is the cost?
Answers
Answer:
$5.00
Step-by-step explanation:
10 × 50/100
Discount = 10 x 0.5
You save = $5.00
13. The diameter of a merry-go-round at the playground is 12 feet. Elijah stands on the edge and his sister pushes him
around.
ST
a) How far does Elijah travel if he moves through an angle of 4 radians?
b) Through what angle does Elijah move if he travels a distance of 80 feet around the circumference?
Answers
Answer:
a.) 23.6
b.) 40/3
Step-by-step explanation:
Question 1 (1 point)
1.01011011101111...
Answers
Answer:
E: since irrational is non-terminating and the ... means it goes on forever which cannot be represented by a fraction
A picture is 10 inches by 14inches. The frame measures 2 inches longer and wider than the painting. What is the area of the frame?
Answers
Answer:
52
Step-by-step explanation:
so first you do 10x14=140
next you have to do 12x16=192
then u have to do 192-140=52in squared
Solve for an angle in right triangles. Round to the nearest hundredth
Answers
Answer:
6.53
Step-by-step explanation:
cos(theta)= adjacent/hypotenuse
cos(40)= 5/h
H= 5/cos(40)
=6.527
Rounded to the nearest hundredth will be 6.53
A triangle has a perimeter of 51 cm. If the three sides of the triangle are n, 4n-4, and 4n-8, what is the length of each side?
Answers
Answer:
see below
Step-by-step explanation:
The three sides add to 51
n + 4n-4 + 4n-8 = 51
9n -12 = 51
9n = 63
n = 7 4n-4 = 24 4n-8 = 20
Anyone have Inscribed angles practice answers ?
Unit 7 lesson 3
Answers
Applying the inscribed angle theorem, since x and 31° are subtended by the same arc in the given circle, then x = 31°.
What is the Inscribed Angle Thoerem?The inscribed angle theorem states that if two inscribed angles are subtended by the same arc, the measure of both inscribed angles are equal.
Inscribed angle = 1/2(measure of intercepted arc)
Based on the inscribed angle theorem, x = 31° because they are both subtended by the same arc.
Learn more about inscribed angle theorem on:
https://brainly.com/question/3538263
25-44 Differentiate.
28. [tex]J(v)=\left(v^{3}-2 v\right)\left(v^{-4}+v^{-2}\right)[/tex]
Answers
Make things easier by expanding J(v) first:
[tex]J(v) = (v^3-2v) \left(\dfrac1{v^4}+\dfrac1{v^2}\right) = \dfrac1v - \dfrac2{v^3} - \dfrac2v + v = v - \dfrac1v - \dfrac2{v^3}[/tex]
Now differentiate term-by-term (power rule):
[tex]J'(v) = \boxed{1 - \dfrac1{v^2} + \dfrac6{v^4}}[/tex]
In case you're supposed to use the product rule first, we have
[tex]J'(v) = (3v^2 - 2) \left(\dfrac1{v^4} + \dfrac1{v^2}\right) + (v^3-2v) \left(-\dfrac4{v^5} - \dfrac2{v^3}\right)[/tex]
Expanding and simplifying will yield the same result as before.
Cory is a bird-watcher. He estimates that 30% of the birds he sees are American robins, 20% are dark-eyed juncos, and 20% are song sparrows. He designs a simulation. Let 0, 1, and 2 represent American robins Let 3 and 4 represent dark-eyed juncos. Let 5 and 6 represent song sparrows. Let 7, 8, and 9 represent other birds The table shows the simulation results. According to the simulation, what is the probability that at least one of the next five birds he sees is a song sparrow?
A.)0.35
B.)0.2
C0.65
D.)0.5
Answers
Answer: 0.65
Step-by-step explanation:
the probability is high
The probability that at least one of the next five birds sees is a song sparrow will be 0.65
ProbabilityProbability is chance that a given event will occur
How to solve this problem?The steps are as follows:
Given, 5 and 6 represent song sparrowsUsing the above representations, the numbers that represent an occurrence of seeing at least one song sparrow in the next 5 birds are:05716 16803 96568 33855 76635 88864 05943 77510 74051 97895 86481 94036 24005
The number of occurrence is 13The number of simulation is 20Therefore probability of seeing at least one song sparrow will be:P=(number of occurrence/number of simulation)
∴ P=13/20
∴ P=0.65
There is 0.65 probability that at least one of the next five birds Cory sees is a song sparrow
Learn more about probability here:
https://brainly.com/question/25870256
#SPJ2
An object travels 43 miles. Given 1 mile 5280 feet, enter the distance the object travels in feet.
Answers
Answer:
43 x 5280= 227040
Step-by-step explanation:
Solve x2 = −49 by using square roots.
A. The solution is 7.
B. There are no real solutions.
C. The solution is −7.
D. The solutions are 7 and −7.
Answers
X=7i, -7i
Answer:
Option B, There are no real solutions
Step-by-step explanation:
Step 1: Square root both sides
[tex]x^2 = -49[/tex]
[tex]\sqrt{x^2} = \sqrt{-49}[/tex]
Since we are trying to square root a negative it would cause imaginary solutions so in conclusion we have no real solutions.
Answer: Option B, There are no real solutions
The gardeners at Bailey's Market planted 48
onions in each of 12 rows. How many onions
.
were planted?
Pls help
Answers
Answer:
576
Step-by-step explanation: multiply 48 by 12 and you should get 576
Use the given figure to solve the remaining parts of the triangle AIR.
Answers
Answer:
1. 15.49 cm
2. 14.39 cm
3. 17.32 cm
4. 11.53 cm
5. 5 cm
Step-by-step explanation:
In the given problem, you can solve the unknown side of the triangle using either Pythagorean Theorem or SOA CAH TOA method. In Trigo, you can use the Pythagorean Theorem if the triangle has 90 degrees, or it is a right triangle.
In the given problem, the angle of the triangles are unknown, therefore to solve the unknown side of triangles, we will you use the SOA CAH TOA.
In this case, since the given side are b and c, we can use CAH (Cos Teta equals Adjacent over Hypotenuse), and TOA ( Tan Teta equals Opposite over Adjacent)
Lets provide the solution for the number, and the rest have the same solutions and process.
b= 17, c= 3, let u is the angle
Cosu= 17/23, to get the angle, use inverse cosine.
The result will be 42.34°, and to get the unknown side, use TOA
Tanu=a/17, a=17Tanu
It will give you 15.49 cm
In the number 2 and 5, it will be the same when you rotate the triangle.
Read more about the concept of SOA CAH TOA at
https://brainly.com/question/22767551
#BrainlyFast
Question 9
Which measurement is closest to the distance between point p and point q in units?
14
13
P
12
11
10
9
R
Q
1 2 3 4 5 6 7 8 9 10 11 12 13 14
43
87654321
7
3
0
Answer
A 17 units
B) 13 units
(C) 11 units
D 2.4 units
Answers
Answer:
that means the answer is c
Which polygon has an interior angle sum of 1080°? Edge
Answers
Answer:
8
Step-by-step explanation:
(n−2) × 180°= 1080
=> n = 1080 / 180 + 2
Answer:
The first one with 8 points.
Step-by-step explanation:
It's an octagon.
You must select a team from a group of 6 boys and 10 girls. How many ways can you select 2 boys and 5 girls?
Answers
Using the combination formula, it is found that you can select 2 boys and 5 girls in 2,520 ways.
In this problem, Joao and Elisa would be the same team as Elisa and Joao, hence the order is not important and the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem:
2 boys are selected from a set of 6.5 girls are selected from a set of 10.Hence:
[tex]T = C_{5,2}C_{10,5} = \frac{5!}{3!2!} \times \frac{10!}{5!5!} = 2520[/tex]
You can select 2 boys and 5 girls in 2,520 ways.
More can be learned about the combination formula at https://brainly.com/question/25821700
#SPJ1
How many years of math do high schools require you to complete for
graduation?
O A. 2 to 3
O B. 1 to 2
O c. 3 to 4
O D. 0 to 1
ما
Answers
I want to know answer to Negative 3 minus positive 1?
Answers
you already have negative amount, so subtracting from that negative amount you go lower.
Step-by-step explanation:
-3-1 You want to factor out the negative sign.Add the numbersThe answer is four.Solve: x^2+4x-15
you don’t need to show steps
Answers
Answer:
-2 ± √19
Explanation:
Quadratic formula
Hope this helps!
What is the difference between 711 and 114?
Answers
Answer:
597
Step-by-step explanation:
711-114=597
Hope it helps you
Maddi plays a game in which she spends the spinner over and over again the spinner has four equally sized section labeled a, B, C, and D spinning a C7 times means the game is over Maddi uses a uniform probability model to predict the number of times the spinner will be spun before the letter C appears seven times what is Maddi’s prediction for the number of total spent before the letter C appears 7 times ? 12 spins 16 spins 21 spins 28 spins
Answers
The spinner of Maddi's game is an illustration of probability, and it is expected that the number of spins is 28
How to determine the expected number of vowels?The number of sections in the spinner is given as:
Sections = 4
The letter C is given as:
Letter C = 1
The expected appearance of letter C is given as:
Expected appearance = 7
The expected number of letter C is calculated using
Expected = Letter C/Sections * Number of spins (n)
So, we have:
7 = 1/4 * (n)
Multiply both sides by 4
n = 28
Hence, it is expected that the number of spins is 28
#SPJ1
Read more about expected values at:
brainly.com/question/15858152
The half-life of Radium-226 is 1590 years. If a sample contains 200 mg, how many mg will remain after 1000 years?
Answers
Answer: 129.33 g
Step-by-step explanation:
[tex]$$Let $p=A \cdot e^{n t}$ \\$(p=$ present amount, $A=$ initial amount, $n=$ decay rate, $t=$ time)[/tex]
[tex]\begin{aligned}&\Rightarrow \text { Given } p=\frac{A}{2} \ a t \ t=1590 \\&\Rightarrow \frac{1}{2}=e^{1590n} \Rightarrow n=\frac{\ln (1 / 2)}{1590}=-0.00043594162\end{aligned}[/tex]
[tex]$$If $A=200 \mathrm{mg}$ and $t=1000$ then,$$\begin{aligned}P &=200 e^{\left(\frac{\ln \left(1/2\right)}{1590}\right) \cdot 1000} \text \\\\&=129.33 \text { grams}\end{aligned}$$[/tex]
11/12-5/6 is it closer to 0/1/2
Answers
Answer:
0
Step-by-step explanation:
The answer is 1/12
Not sure what to do here can someone please help
Answers
Answer:
x = 2
Step-by-step explanation:
These equations are solved easily using a graphing calculator. The attachment shows the one solution is x=2.
__
SquaringThe usual way to solve these algebraically is to isolate radicals and square the equation until the radicals go away. Then solve the resulting polynomial. Here, that results in a quadratic with two solutions. One of those is extraneous, as is often the case when this solution method is used.
[tex]\sqrt{x+2}+1=\sqrt{3x+3}\qquad\text{given}\\\\(x+2)+2\sqrt{x+2}+1=3x+3\qquad\text{square both sides}\\\\2\sqrt{x+2}=(3x+3)-(x+3)=2x\qquad\text{isolate the root term}\\\\x+2=x^2\qquad\text{divide by 2, square both sides}\\\\x^2-x-2=0\qquad\text{write in standard form}\\\\(x-2)(x+1)=0\qquad\text{factor}[/tex]
The solutions to this equation are the values of x that make the factors zero: x=2 and x=-1. When we check these in the original equation, we find that x=-1 does not work. It is an extraneous solution.
x = -1: √(-1+2) +1 = √(3(-1)+3) ⇒ 1+1 = 0 . . . . not true
x = 2: √(2+2) +1 = √(3(2) +3) ⇒ 2 +1 = 3 . . . . true . . . x = 2 is the solution
__
SubstitutionAnother way to solve this is using substitution for one of the radicals. We choose ...
[tex]u=\sqrt{x+2}\qquad\text{requires $u\ge0$}\\\\u^2-2=x\qquad\text{solve for x}\\\\u+1=\sqrt{3(u^2-2)+3}\qquad\text{substitute for x in the original equation}\\\\(u+1)^2=3u^2-3\qquad\text{square both sides, simplify a little}\\\\2u^2-2u-4=0\qquad\text{subtract $(u+1)^2$}\\\\2(u-2)(u+1)=0\qquad\text{factor}[/tex]
Solutions to this equation are ...
u = 2, u = -1 . . . . . . the above restriction on u mean u=-1 is not a solution
The value of x is ...
x = u² -2 = 2² -2
x = 2 . . . . the solution to the equation
_____
Additional comment
Using substitution may be a little more work, as you have to solve for x in terms of the substituted variable. It still requires two squarings: one to find the value of x in terms of u, and another to eliminate the remaining radical. The advantage seems to be that the extraneous solution is made more obvious by the restriction on the value of u.
(this is probability) I'm confused..
Answers
Answer:
1/3
Step-by-step explanation:
probability = favorable events / total num of events
here total num of events is 3 and favorable is 1 since there is only one odd number.
therefore, p(odd) = 1/3
Answer:
[tex]\huge\boxed{\bf\:\frac{1}{3}=0.33}[/tex]
Step-by-step explanation:
Odd numbers are numbers that end with the digits [tex]\rightarrow 1,3,5,7,9[/tex], whereas even numbers are numbers that end with the digits [tex]\rightarrow 0,2,4,6,8[/tex].
Here, we can see that,
2 & 4 = even numbers = 2 even number cards3 = odd number = 1 odd number card3 = Total number of cards.Therefore,
Probability of getting an odd number (3) card
= Number of odd number cards / Total number of cards
= ⅓ = 0.33
[tex]\rule{150pt}{2pt}[/tex]
choose an appropriate metric unit for the mass of concrete in a section of sidewalk
kilogram
milligram
gram
meter
why dont you delete this question also brainly
Answers
Answer:
It should be a kilogram.
Gram = too small
milligram = too small
meter = distance