Answer:
C. [tex]\Rightarrow \bold{8x = 16}[/tex]
Step-by-step explanation:
Given the two equations:
[tex]y=2x ........ (1)\\ 2x+3y=16.......(2)[/tex]
To find:
The correct option when value of y is substituted to 2nd equation using the 1st equation.
Solution:
First of all, let us learn about the substitution method.
Substitution method is the method to provide solutions to two variables when we have two equations and two variables.
In substitution method, we find the value of one variable in terms of the other variable and put this value in the other equation.
Now, the other equation becomes only single variable and then we solve for the variable's value.
Here, we have two equations and value of one varible is:
[tex]y=2x[/tex]
Let us put value of y in 2nd equation:
[tex]2x+3y=16\\\Rightarrow 2x + 3(2x) = 16\\\Rightarrow 2x + 6x = 16\\\Rightarrow \bold{8x=16}[/tex]
So, the correct answer is option C. [tex]\Rightarrow \bold{8x = 16}[/tex]
Answer: 8x=16
Step-by-step explanation:a pex
At time, t=0, Billy puts 625 into an account paying 6% simple interest. At the end of year 2, George puts 400 into an account paying interest at a force of interest, δt=16+t for t≥2. If both accounts continue to earn interest indefinitely at the levels given above, the amounts in both accounts will be equal at the end of year n. Calculate n.
Answer:
26
Step-by-step explanation:
Given that:
At time, t=0, Billy puts 625 into an account paying 6% simple interest
At the end of year 2, George puts 400 into an account paying interest at a force of interest, 1/(6+t), for all t ≥ 2.
If both accounts continue to earn interest indefinitely at the levels given above, the amounts in both accounts will be equal at the end of year n. Calculate n.
In order to calculate n;
Let K constant to be the value of time for both accounts
At time, t=0, the value of time K when Billy puts 625 into an account paying 6% simple interest is:
[tex]K = 625 \times (1+ 0.06 K)[/tex]
[tex]K = 625 +37.5 K[/tex]
At year end 2; George amount of 400 will grow at a force interest, then the value of [tex]K = 400 \times e^{\int\limits^2_k {\dfrac{1}{6+t}} \, dx }[/tex]
[tex]K =400 \times \dfrac{6+K}{6+2}[/tex]
[tex]K =400 \times \dfrac{6+K}{8}[/tex]
[tex]K =50 \times ({6+K})[/tex]
[tex]K =300+50K[/tex]
Therefore:
If K = K
Then:
625 + 37.5 = 300 +50 K
625-300 = 50 K - 37.5 K
325 = 12.5K
K = 325/12.5
K = 26
the amounts in both accounts at the end of year n = K = 26
What does 0 = 0 mean regarding the solution to the system?
Answer:
It means the left side of the equation equals the right side of the equation regardless of the value of the variables. The solution is all real numbers for each variable
Step-by-step explanation:
Which of the following is a correct tangent ratio for the figure?
Answer:
C) tan(39°) = 11/15
Step-by-step explanation:
SohCahToa
tangent = opposite / adjacent
The given angle is 39°. The angle directly opposite of 39° is 11 and the angle adjacent to 39° is 15.
Answer:
tan(39°) = 11∕15
Step-by-step explanation:
Determine the values of \theta if sec\;\theta=-\frac{2}{\sqrt{3}}.
Answer:
See below.
Step-by-step explanation:
So, we have:
[tex]\sec(\theta)=-2/\sqrt{3}[/tex]
Recall that secant is simply the reciprocal of cosine. So we can:
[tex]\cos(\theta)=(\sec(\theta))^{-1}=(-2/\sqrt{3})^{-1}\\\cos(\theta)=-\sqrt{3}/2[/tex]
Now, recall the unit circle. Since cosine is negative, it must be in Quadrants II and/or III. The numerator is the square root of 3. The denominator is 2. The whole thing is negative. Therefore, this means that 150 or 5π/6 is a candidate. Therefore, due to reference angles, 180+30=210 or 7π/6 is also a candidate.
Therefore, the possible values for theta is
5π/6 +2nπ
and
7π/6 + 2nπ
PLS HELP!!!!ILL MARK YOU THE BRAINLISt
Translate into an algebraic expression and simplify if possible. C It would take Maya x minutes to rake the leaves and Carla y minutes, what portion of the leaves do they rake in one minute if they work together?
Answer:
(x+y)/xy or (1/x + 1/y) portion of the leaves
Step-by-step explanation:
Let the total work done to rake the leaves be a for representation.
Thus,
given Maya takes x minutes to rake the leaves
thus,
work done by may in x minutes = a
dividing both side by x
work done by maya in x/x = 1 minutes = a/x
similarly
given Calra takes y minutes to rake the leaves
thus,
work done by may in y minutes = a
dividing both side by y
work done by maya in y/y = 1 minutes = a/y
__________________________________
Total work done by both in 1 minutes = a/x + a/y = a(1/x+1/y) = a(x+y)/xy
Thus, if a is the total work , then they do (x+y)/xy of a work in one minute.
Thus, (x+y)/xy portion of leaves do they rake in one minute if they work together.
I NEED HELP ASAP PLEASE
Answer:
D. x^2 - 6x + 7.
Step-by-step explanation:
The roots are 3 plus or minus sqrt(2). That means the equation is...
(x - [3 + sqrt(2)]) * (x - [3 - sqrt(2)])
= [x - 3 - sqrt(2)] * [x - 3 + sqrt(2)]
= x^2 - 3x - xsqrt(2) - 3x + 9 + 3sqrt(2) + xsqrt(2) - 3sqrt(2) - (sqrt(2))^2
= x^2 - 3x - 3x + 9 - 2 - xsqrt(2) + xsqrt(2) + 3sqrt(2) - 3sqrt(2)
= x^2 - 6x + 7.
Hope this helps!
Help please!!!!!!! Thxxxxx
Answer:
x= 155°
straight line equals 180°
since you have a side that equals to 25°
you subtract
180°-25° = 155°
Mike can stitch 7 shirts in 42 hours
He can stitch 1 shirt in hours, and in 1 hour he can stitch of a shirt
Answer:
He stitched 1 shirt in 6 hours.
He can stitch 1/6 of a shirt in one hour
Step-by-step explanation:
Given Mike can stitch 7 shirts in 42 hours
No. of shirt stitch in one hour = total no of shirt stitch/total time taken
No. of shirt stitch in one hour = 7/42 = 1/6
Thus, he can stitch 1/6 of a shirt in one hour
Time taken to stitch 1 shirt = total time taken by him to stitch 7 shirts/ total no. of shirt stitch(i.e 7) = 42/6 = 6 hours.
Thus, he stitched 1 shirt in 6 hours.
Answer:
He can stitch 1/6 of a shirt in one hour
Step-by-step explanation:
Because he stitched 7 shirts in 42 hours
42/7 = 6
so 6 hours per shirt
In one hour:
1/6
Solve the system using multiplication for the linear combination method. 6x – 3y = 3 –2x + 6y = 14 What is the solution to the system
Answer:
work is shown and pictured
Correct Answer would be
D: (2,3)
Solve the given simultaneous equations : 2x + 3y = 17 ; 3x - 2y = 6
Answer:
x= 4, y=3
Step-by-step explanation:
2x + 3y = 17
3x - 2y = 6
----------
If we double the first and triple the second equation, and add up, we can get rid of y:
4x+6y= 34+9x - 6y= 18-----------------13x= 52x= 4Then it is easy to find the value of y:
2*4+3y= 173y= 9y= 3Answer is: x= 4, y=3
Imagine you have a data set with 9,987 names. The data set is sorted alphabetically. You want to find out if the name "David Joyner" is in the data set. Using a linear search, what is the minimum number of names we might have to check?
Answer:
1
Step-by-step explanation:
David Joyner might be the first name, so you may only have to check 1 name.
match the inequality, x²≥0, with it's equivalent interval notation
Answer:
[tex](-\infty, \infty)[/tex]
Step-by-step explanation:
Every number, when you raised to the second power is positive, therefore that inequality would be all real numbers.
[tex](-\infty, \infty)[/tex]
Solve for x in the equation x squared + 11 x + 121/4 = 125/4.
Step-by-step explanation:
x² + 11x + 121/4 = 125/4
x² + 11x + 121/4 - 125/4 = 0
x² + 11x - 1 = 0
after that apply quadratic formula
x = ( -b + or - √b² - 4ac ) ÷ 2a
x = (-11 + or - √11² - 4×1×-1 ) ÷ 2×1
+ = 0.090169....
- = -11.090168.....
x = 0.090 or x = -11.09
These two polygons are similar.
Find the value of z.
z = [?]
Answer:
Definitely 3 hmmm..
Step-by-step explanation:
6/2=3 so 9/z=3
tfo 9/3=3
The missing variables have values of 12, 5, 9, and 3, respectively, for x, y, w and z.
Given that there are two similar polygons with dimension:
Larger polygon = 9, 6, w, 15, x.
Smaller polygon = z, 2, 3, y, 4.
We need to find the missing value of the side length.
According to the definition of the similar polygons, the corresponding sides shows proportionality.
9/z = 6/2 = w/3 = 15/y = x/4
Solving for each variable =
i) Solve for z:
9/z = 6/2
Cross-multiplying:
6z = 9 × 2
6z = 18
Dividing both sides by 6:
z = 18/6
z = 3
ii) Solve for w:
6/2 = w/3
Cross-multiplying:
2w = 6 × 3
2w = 18
Dividing both sides by 2:
w = 18/2
w = 9
iii) Solve for y:
6/2 = 15/y
Cross-multiplying:
6y = 30
Dividing both sides by 6:
y = 5
iv) Solve for x:
6/2 = x/4
Cross-multiplying:
2x = 24
Dividing both sides by 2:
x = 12
Hence the values of the missing variables are x = 12, y = 5, w = 9 and z = 3.
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Four friends are on a basketball team. During a game, each friend kept track of how many shots they attempted and how many of those attempts they made. Henry made 0.45 of his shots. Allison made Arthur made of her shots. of his shots. Trevor missed 58% of his shots. Which friend had the best record for the number of shots made?
Answer:
Henry had the best record for the number of shots made
Step-by-step explanation:
From the given information.
Four friends are on a basketball team.
Henry
Allison
Arthur
Trevor
We are being told that Henry made 0.45 of his shots out of all his attempts
Allison made Arthur made of her shots of his shots.
i,e Arthur did the work for Allison , so out of Arthur's shot , we have to figured out Allison shots,
Trevor missed 58% of his shots.
i.e Trevor failed 0.58 of his shot, If he failed 0.58 shot
Then the attempts Trevor made is :
= 1 - 0.58
= 0.42
SO , Trevor made 0.42 shots out of all his attempt
N:B We are not given any information about Arthur's shots , so we can't determine Allison shot as well.
Therefore; we will focus on only Henry and Trevor shots
So ;
Henry made 0.45 of his shots
Trevor made 0.42 out of his shots
We can thereby conclude that :
Henry had the best record for the number of shots made
Solve the equation for X. 2(2x-4)=3(x+4) A -4 B 4 C 20 D 6
Answer:
X=20
Step-by-step explanation:
The answer is C
a parabola has an x-intercept at 2, its axis of symmetry is the line x=4, and the y-coordinate of its vertex is 6. Determine the equation of the parabola.
Answer:
The standard equation of the parabola is:
[tex]y=-\frac{3}{2}x^2+12x-18[/tex]
Step-by-step explanation:
An x intercept of 2 means that the point (2, 0) is in the graph of the parabola.
We can also write the general expression for the parabola in vertex form, since we can use the information on the coordinates of the vertex: (4, 6) - recall that the axis of symmetry of the parabola goes through the parabola's vertex, so the x-value of the vertex must be x=4.
[tex]y-y_{vertex}=a\,(x-x_{vertex})^2\\y-6=a\,(x-4)^2[/tex]
Now we can find the value of the parameter "a" by using the extra information about the point (2, 0) at which the parabola intercepts the x-axis:
[tex]y-6=a\,(x-4)^2\\0-6=a\,(2-4)^2\\-6=a\,4\\a=-\frac{6}{4} =-\frac{3}{2}[/tex]
Then the equation of the parabola becomes:
[tex]y-6=-\frac{3}{2} \,(x-4)^2\\y-6=-\frac{3}{2} (x^2-8x+16)\\y-6=-\frac{3}{2}x^2+12x-24\\y=-\frac{3}{2}x^2+12x-18[/tex]
A manufacturing company has an old machine which produces 25 components per hour. The company has recently installed a new machine which produces 35 components per hour. Yesterday, both machines were in operation for different periods of time. If 430 components were produced when the total number of hours of operation was 14 hours, determine for how many hours each machine was in operation
Answer: old machine 150, new machine 280
Step-by-step explanation:
given data:
Old machine = 25t
New machine = 35t
where t = hrs
we dont know the time for old machine so we assume it to be ( t ),
while that of the new machine is ( 14-t ) hours for new machine, and sum of 430 components.
therefore;
25t +490 - 35t = 430
-10t = -60
divide both sides by -10
t = 6 hours for the first machine.
6hrs * 25 components /hr
= 150 component parts For old machine.
for new machine
= 14 - t ........... eq1.
where ( t = 6 ), substitute t into the equation
= 14 - 6
= 8 hours for the second machine
= 8 * 35
= 280 components parts
find the slope of a line that is perpendicular to the line y= - 1/3x+7
the slope of the line is 3
Which ideas from the excerpt would be most appropriate to include in a summary? Select three options. Popular novels from the past often ask provocative questions that are important to consider today. Many Americans have given up and say that the nation is no longer great or a land of dreams. John Wayne, nicknamed Duke, was an iconic Hollywood actor and filmmaker. President Reagan believed that John Wayne would argue that he was not the last American hero, because there are many more. Duke Wayne died as a symbol of the Hollywood dream industry.
Answer:
Short answer A,B,D
Step-by-step explanation:
The ideas from the excerpt would be most appropriate to include in a summary are;
Popular novels from the past often ask provocative questions that are important to consider today. Many Americans have given up and say that the nation is no longer great or a land of dreams. President Reagan believed that John Wayne would argue that he was not the last American hero, because there are many more. What is a summary of a passage?Summary is known to be a form of quick or short review of what has happened in a specific passage.
The summary is regarded as a statement that present the main points of a passage as seen above.
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19] After increasing the price of an article by 20%. The price was GHC
3000.00. What was the original price?
Step-by-step explanation:
Let the original price be x
After increasing by 20% the price is 3000
Thus,
x + ( x × 20%) = 3000
x + 20x/100 = 3000
x + x/5 = 3000
(5x + x)/5 = 3000
6x/5 = 3000
x = 3000 * 5/6
x = 2500
Hope it helps :)
An important proportion that the ancient Greeks used was the
the ancient Greek used the golden ratio
Answer:
An important proportion that the Ancient Greeks used was the Golden Mean, the a0
Step-by-step explanation:
Also known as Golden Ratio, Divine Proportion, or Golden Section
How do i solve this? F (x)=x³-2x²+x+1, then f (-x)=
Step-by-step explanation:
F (x)=x³-2x²+x+1,
Then F (-x)= - x³ - 2x² - x + 1
Tell me if I'm right.
Hope this helps.
Have a great day!
A word is anything of seven letters of the alphabet(26 letters) (no space in between). Repeated lettersare allowed. How many words are there?
Answer:
26^7=8 031 810 176
Step-by-step explanation:
The word has 7 letters. So the word have 7 places where any of 26 letters can be placed.
Any of 26 letters can stay at 1st place
Any of 26 letters can stay at 2-nd place (because letters can be repeated)
Any of 26 letters can stay at 3rd place
Any of 26 letters can stay at 4th place
Any of 26 letters can stay at 5th place
Any of 26 letters can stay at 6th place
Any of 26 letters can stay at 7th place
So N= 26*26*26*26*26*26*26=26^7=8 031 810 176
46/100 46/1,000
which is greater
Answer:
46/100.
Step-by-step explanation:
46 / 100 = 0.46
46 / 1,000 = 0.046
0.046 < 0.46
So, 46/100 is greater than 46/1,000.
Hope this helps!
46/100 is greater because it equals 0.46 while 46/1000 would equal 0.046.
Choose the correct equation for the parabola based on the given information. Given: Focus:(4,-3) Vertex: (-2,-3) a. 24(y+3) = (x+2)^2 b. 24(x+2)=(y+3)^2 c. 6(x-4)= (y+3)^2 d. 6(y+3)=(x-4)^2
Answer: b. 24(x + 2) = (y + 3)²
Step-by-step explanation:
Vertex: (-2, -3)
Focus: (4, -3)
↓
same y-value so equation will be y²
Equation: a(x - h) = (y - k)²
a = 4p where p is the distance from Vertex to Focush is the x-coordinate of the Vertexk is the y-coordinate of the VertexGiven: h = -2, k = -3, a = 4[4 - (-2)] --> a = 24
Input those values into the equation: 24(x + 2) = (y + 3)²
PLEASE EXPLAIN IN DETAILS HOW TO SOLVE LINEAR INEQUALITIES. Heres an example problem. Please solve and show your steps/explain.
6(x+8) ≥ ‒43+4x
Answer:
[tex]x \geq -91/2[/tex]
Step-by-step explanation:
[tex]6(x+8) \geq -43 + 4x[/tex]
Resolving Parenthesis
[tex]6x+48 \geq -43 + 4x[/tex]
Collecting like terms
[tex]6x - 4 x \geq -43-48[/tex]
[tex]2x \geq -91[/tex]
Dividing both sides by 2
[tex]x \geq -91/2[/tex]
Answer:
x ≥ - 91 / 2
Step-by-step explanation:
In this sample problem, the first thing we want to do is expand the part in parenthesis through the distributive property. This will make the simplification process easier. Another approach would be to divide either side by x + 8, but let's try the first.
Approach 1 : [tex]6(x+8) = 6x + 6 8 = 6x + 48[/tex]
[tex]6x + 48 \geq - 43+4x[/tex] - so we have this simplified expression. We now want to isolate x, so let's combine common terms here. Start by subtracting 6x from either side,
[tex]48 \geq - 43-2x[/tex] - now add 43 to either side,
[tex]91\geq -2x[/tex] - remember that dividing or multiplying a negative value changed the inequality sign. Dividing - 2 on either side, the sign changes to greater than or equal to, with respect to x,
[tex]- 91 / 2 \leq x[/tex], or in other words [tex]x \geq - 91 / 2[/tex]. This is our solution.
need help fast APR is an ____?
When a fish is selected at random from a tank, the probability that it has a green tail is 0.54, the probability that it has red fins is 0.18, and the probability that it has both a green tail and red fins is 0.02. What is the probability that the selected fish will not have a red fin or a green tail? A) 28% B) 70% C) 2% D) 30%
Answer:
the answer is C
Step-by-step explanation:
hope this helps
The probability that the selected fish will not have a red fin or a green tail is 0.30.
To find the probability.
What is probability?probability is the ratio of the number of favorable outcomes and the total number of possible outcomes.
Given that:
G=fish has green tail
R=fish has red fin
G^R = fish has both a red fin and a green tail
P(G)=.54
P(R) = .18
P(G^R) = .02
P(GvR) = P(G) + P(R) - P(G^R) = .54 + .18 - .02 =
P(GvR) =.72 - .02 = .7
P(neither G nor R) = 1-.7 = .3 = 30%
So, the probability that the selected fish will not have a red fin or a green tail is 0.30.
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really really need help!!!! Which Venn diagram has a shaded region that represents X n Z????
The answer is Diagram 4 or D
Explanation:
A Venn diagram is a type of model that represents sets, and their relationships. Additionally, each set is usually named with a letter and symbols such as ∪ or ∩ are used to represent specific zones of the diagram. In the case of the symbol ∩, this is used to represent the intersection between two sets. This means X ∩ Z represents the intersection between X and Z. Therefore, the correct representation is the fourth diagram, which shows in red only the intersection between these two sets.
Answer:
See below.
Step-by-step explanation:
None of the choices represent the intersection of sets X and Z, so there is some mistake with this problem. The question is not correct for these choices.