Answer:
[tex]\boxed{(3,-1)}[/tex]
Step-by-step explanation:
Hey there!
Well to find the solution the the given system,
3y - 2x = -9
y = -2x + 5
So to find x lets plug in -2x + 5 for y in 3y - 2x = -9.
3(-2x + 5) - 2x = -9
Distribute
-6x + 15 - 2x = -9
-8x + 15 = -9
-15 to both sides
-8x = -24
Divide -8 to both sides
x = 3
Now that we have x which is 3, we can plug in 3 for x in y = -2x + 5.
y = -2(3) + 5
y = -6 + 5
y = -1
So the solution is (3,-1).
Hope this helps :)
Factorise the following using the Difference of Two Squares or Perfect Squares rule: a) (2x-2)^2 - (x+4)^2 b) (3x+4) (3x-4)
Answer:
Step-by-step explanation:
Hello, please consider the following.
a)
[tex](2x-2)^2 - (x+4)^2 \\\\=(2x-2-(x+4))(2x-2+x+4)\\\\=(2x-2-x-4)(3x+2)\\\\=\boxed{(x-6)(3x+2)}[/tex]
b)
[tex](3x+4) (3x-4)\\\\=(3x)^2-4^2\\\\=\boxed{9x^2-16}[/tex]
Thank you.
You flip two coins. What is the probability
that you flip at least one head?
Answer:
[tex]\boxed{Probability=\frac{1}{2} }[/tex]
Step-by-step explanation:
The probability of flipping at least 1 head from flipping 2 coins is:
=> Total sides of the coins = 4
=> Sides which are head = 2
=> Probability = 2/4 = 1/2
Graphs are everywhere in the news, but just because a graph is in print does not mean that it is trustworthy. Review the graph and determine why it is misleading or inaccurate.
Answer:
Kindly check explanation
Step-by-step explanation:
Taking a careful look at the graph above, the graph depicts that there is sizeable growth or increase in the rate of interest between 2008 to 2012. However, the actual increase in the rate of interest between 2008 - 2012 is (3.152% - 3.141%) = 0.011%. This change is very small compared to what is portrayed by the pictorial representation of the bar graph. This could be due to the scaling of the vertical axis which didn't start from 0, thereby exaggerating the increase in the actual rate of interest. It will thus mislead observers into thinking the increase is huge.
An equation for the depreciation of a car is given by y=A(1-r)t where y=current value of the car.A=original cost r=rate of depreciation and t=time in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately how old is the car?
The more accurate value is 6.57881347896059, which you can round however you need. I picked two decimal places.
==================================================
Explanation:
Let's pick a starting value of the car. It doesn't matter what the starting value, but it might help make the problem easier. Let's say A = 1000. Half of that is 1000/2 = 500.
So we want to find out how long it takes for the car's value to go from $1000 to $500 if it depreciates 10% per year.
The value of r is r = 0.10 as its the decimal form of 10%
t is the unknown number of years we want to solve for
---------------------------
y = A(1 - r)^t
500 = 1000(1 - 0.1)^t
500 = 1000(0.9)^t
1000(0.9)^t = 500
0.9^t = 500/1000
0.9^t = 0.5
log( 0.9^t ) = log( 0.5 )
t*log( 0.9 ) = log( 0.5 )
t = log( 0.5 )/log( 0.9 )
t = 6.57881347896059
Note the use of logs to help us isolate the exponent.
PLEASE HELP QUICK!!!Suppose the bill for dinner is $16.70, if you want to give a 10% tip what will be the total?
Answer:
$18.37
Step-by-step explanation:
$16.70 × 1.10 = $18.37
or
$16.70 × 0.10 = $1.67
$16.70 + 1.67 = $18.37
what does this answer 23498731345 times 36 over 2
Answer:422977164210 or it could be [tex]4.2297716421(10) ^{11}[/tex]
Step-by-step explanation:
Find the number of distinguished arrangements of the letters of the word. MILLION
Answer:
1260
Step-by-step explanation:
(7!)/ (2!times 2!)
7 factorial divided by 2factorial times 2 facotiral
The number of distinguishable ways the letters of the following word can be arranged 'MILLION' is 1260.
What are permutations?The different arrangements which can be made out of a given number of objects by taking out some or all at a time are called permutations.
The number of different permutations of n objects with m₁ repeated items, m₂ repeated items,...,mₙ repeated items can be calculated as;
m!/(m₁!)(m₂!)...(mₙ!)
Here, the letter of the word 'MILLION' is a total of 7 letters.
So, the number of possible arrangements will be
(7!)/ (2!times 2!)
= 1260
Therefore the number of distinguishable ways the letters of the following word can be arranged 'MILLION' is 1260.
Learn more about permutations here -
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Please answer this correctly without making mistakes
Answer: 7 mi
Step-by-step explanation: since the distance from bluepoint to Manchester is 12 9/10 mi and you know that bluepoint to Silverstone is 5 9/10 subtract that and you get 7 mi as your answer
Answer:
7 miles
Step-by-step explanation:
Hey there!
Well given BM and BS, we need to subtract them.
12 9 /10 - 5 9/10
9/10 - 9/10 = 0
12 - 5 = 7
Silvergrove to Manchester is 7 miles.
Hope this helps :)
Translate the expression from algebra to words: 6+r
Answer:
a number, r, added to 6
Step-by-step explanation:
a number, r, added to 6
Answer:
a number, r, added to 6
Step-by-step explanation:
a number, r, added to 6
3. A ladder is leaning against a wall. The ladder is 5 meters long. The top of the
ladder is 3 meters above the ground. The top of the ladder is sliding down at 8 meters/second.
a) How far is the bottom of the ladder from the wall?
b) How fast is the bottom of the ladder sliding away from the wall?
Answer:
1. The bottom of the ladder is 4 meters away from the wall
2. I'm not sure about this one, someone else answer please :D
Step-by-step explanation:
We can use the Pythagorean Theorem to find how far away the bottom of the ladder is.
The ladder is creating a triangle, with 5 as it's hypotenuse and 3 as one of the left.
[tex]a^2 + 3^2 = 5^2\\a^2 + 9 = 25\\a^2 = 25-9\\a^2 = 16\\a = 4[/tex]
I'm sorry I couldn't answer the second one, but I hope this helped!
Answer:
a. 4m
b. 6m/s
Step-by-step explanation:
wall height = y = 3m
ladder length = L = 5m
distance from bottom of ladder to the wall = x
a. y² + x² = L² -----------eq.(1)
3³ + x² = 5²
x = 4 m
b. How fast is the bottom of the ladder sliding away from the wall? = dx/dt
using eq.1 ---- y² + x² = L²
2y (dy/dt) + 2x (dx/dt) = 0
y (dy/dt) + 2 (dx/dt) = 0
we know that (dy/dt) = -8 m/s
3 (-8) + 4 (dx/dt) = 0
dx/dt = -24 / -4
dx/dt = 6 m/s
When trying to find the best deals for items, you should what?
Answer:
Try to find the unit rate for bulk items that you have for these and then compare all of the prices together.
Help please, I’m confused about this question.
Answer:
The order, least to greatest, is:
Lemon, Cherry, Grape.
Step-by-step explanation:
Adding all these values up, we get to 1. This means that the smallest values will be the least likely and the highest values will be the most likely.
With the numbers 0.2, 0.16, and 0.64, we can sort these by value.
0.16 is the smallest.
0.2 is the next biggest
and 0.64 is the largest number.
So, the order is Lemon, Cherry, Grape.
Hope this helped!
The area formula, A = tr2, would be used to find the area of a
A. square.
B. rectangle.
O circle.
D. triangle
E parallelogram.
Assuming you meant to write [tex]A = \pi r^2[/tex], then the answer is C) circle
On your keyboard, you can say A = pi*r^2 to mean the same thing as above.
Assume that we want to construct a confidence interval. Do one of the following, as appropriate:_________.
(a) find the critical value t Subscript alpha divided by 2 tα/2,
(b) find the critical value z Subscript alpha divided by 2 zα/2, or
(c) state that neither the normal distribution nor the t distribution applies. Here are summary statistics for randomly selected weights of newborn girls: n equals = 236, x overbar x equals = 30.3 hg, s equals = 7.2 hg. The confidence level is 95%.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. t Subscript alpha divided by 2 tα/2 equals = nothing (Round to two decimal places as needed.)
B. z Subscript alpha divided by 2 zα/2 equals = nothing (Round to two decimal places as needed.)
C. Neither the normal distribution nor the t distribution applies.
Answer:
B. z Subscript alpha divided by 2 zα/2 = 1.96.
Step-by-step explanation:
We are given that we want to construct a confidence interval. For this, the summary statistics for randomly selected weights of newborn girls:
n = 236, [tex]\bar x[/tex] = 30.3 hg, s = 7.2 hg. The confidence level is 95%.
As we can clearly see here that the population standard deviation is unknown and the sample size is also very large.
It has been stated that when the population standard deviation is unknown, we should use t-distribution but since the sample size is very large so we can use z distribution also as it is stated that at very large samples; the t-distribution corresponds to the z-distribution.
Here, [tex]\alpha[/tex] = level of significance = 1 - 0.95 = 0.05 or 5%
[tex]\frac{\alpha}{2}=\frac{0.05}{2}[/tex] = 0.025 or 2.5%
So, the value of [tex]Z_(_\frac{\alpha}{2} _)[/tex] in the z table is given as 1.96 with a 2.5% level of significance.
Apply the square root principle to solve (x-5)^2-40=0
Answer: {5 ± 2√10, 5 - 2√10}
Step-by-step explanation: First isolate the binomial squared by adding 40 to both sides to get (x - 5)² = 40.
Next, square root both sides to get x - 5 = ± √40.
Notice that root of 40 can be broken down to 2√10.
So we have x - 5 = ± 2√10.
To get x by itself, add 5 to both sides to get x = 5 ± 2√10.
So our answer is just {5 ± 2√10, 5 - 2√10}.
As a matter of form, the number will always come before the
radical term in your answer to these types of problems.
In other words, we use 5 ± 2√10 instead of ± 2√10 + 5.
Line A passes through the point (-1,2). Which of the
following CANNOT be the equation of line A?
A y=1 - 2
B
y = x +1
C
X = -1
D y=x+3
Answer:
b
Step-by-step explanation:
y = x + 1
The correct answer is (B). The slope-intercept form of a line is y = mx + b. Since the line passes through (−1,2), there are three possibilities: the line will have a slope (the "m" in front of the "x" variable), it will be vertical (x = −1), or it will be horizontal (y = 2). Plug x = −1 into all four equations to see which equation is not satisfied. The only answer choice that doesn't give us y = 2 is (B).
Option B is correct.
Given:
Line A passes through the point [tex](-1,2)[/tex].
To find:
Which of the given equations cannot be the equation of line A.
Solution:
If Line A passes through the point [tex](-1,2)[/tex], it means the equation of Line A must be satisfied by the point
In option A, consider the given equation is:
[tex]y=1-x[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=1-(-1)[/tex]
[tex]2=1+1[/tex]
[tex]2=2[/tex]
This statement is true. So, [tex]y=1-x[/tex] can be the equation of line A.
Similarly, check for the other options.
In option B,
[tex]y=x+1[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=-1+1[/tex]
[tex]2=0[/tex]
This statement is false. So, [tex]y=x+1[/tex] cannot be the equation of line A.
In option C,
[tex]x=-1[/tex]
It is a vertical line and it passes through the point [tex](-1,2)[/tex] because the x-coordinate is [tex]-1[/tex]. So, [tex]x=-1[/tex] can be the equation of line A.
In option D,
[tex]y=x+3[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=-1+3[/tex]
[tex]2=2[/tex]
This statement is true. So, [tex]y=x+3[/tex] can be the equation of line A.
Therefore, the correct option is B.
Learn more:
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On a coordinate plane, line K L goes through (negative 6, 8) and (6, 0). Point M is at (negative 4, negative 2). Which point could be on the line that is parallel to line KL and passes through point M? (–10, 0) (–6, 2) (0, –6) (8, –10)
Answer:
The point that lies on the line parallel to line KL would be ( 8, - 10 )
Step-by-step explanation:
Line KL passes through the points ( - 6, 8 ) and ( 6, 0 ) while it's respective parallel line passes through point M, ( - 4, - 2 ).
Our approach here is to first determine the slope of KL such that the slope of it's parallel line will be the same, and hence we can determine a second point on this line.
Slope of KL : ( y₂ - y₁ ) / ( x₂ - x₁ ),
( 0 - 8 ) / ( 6 - ( - 6 ) ) = - 8 / 6 + 6 = - 8 / 12 = - 2 / 3
Slope of respective Parallel line : - 2 / 3,
Another point on Parallel line : ( 8, - 10 )
How can we check if this point really belongs to the parallel line? Let's take the slope given the points ( - 4, - 2 ) and ( 8, - 10 ), and check if it is - 2 / 3.
( y₂ - y₁ ) / ( x₂ - x₁ ),
( - 10 - ( - 2 ) ) / ( 8 - ( - 4 ) ) = ( - 10 + 2 ) / ( 8 + 4 ) = - 8 / 12 = - 2 / 3
And therefore we can confirm that this point belongs to line KL's parallel line, that passes through point M.
Answer:
D
Step-by-step explanation:
Rosa is trying to copy an angle. She reads and understands all of the steps, but insists on drawing circles instead of arcs. Which of the following is the best response to tell Rosa?
A. It is acceptable to draw circles instead of arcs, but because they are bigger and take up more space, your drawing may become messy, increasing the chance for errors. <-- MY ANSWER
B. You have to use arcs because a compass cannot make a full circle.
C. You have to draw arcs because arcs and circles are not interchangeable.
D. She is right because it is better to draw circles than arcs. Circles are clearer and easier to draw than arcs so you are less likely to make a mistake.
Thanks!
You have the correct answer. It is choice A. Nice work.
I prefer using full circles because sometimes the arcs could be too small in measure to not go where you want them to. If you're worried about things getting too cluttered (a legitimate concern), then I recommend drawing everything in pencil and only doing the circles as faint lines you can erase later. Once the construction is complete, you would go over the stuff you want to keep with a darker pencil, pen or marker. You can also use the circle as a way to trace over an arc if needed.
Choice B is false as a full circle can be constructed with a compass. Simply rotate the compass a full 360 degrees. Any arc is a fractional portion of a circle.
Choice C is false for similar reasoning as choice B, and what I mentioned in the paragraph above.
Choice D contradicts choice A, so we can rule it out. Arcs are easier to draw since it takes less time/energy to rotate only a portion of 360 degrees. Also, as mentioned earlier, having many full circles tend to clutter things up.
Suppose you earn 2% cash back at grocery stores and 1% on all other purchases. If you spent $485.72 at the grocery store and $671.28 on all other purchases, how much would your cash back be?
Answer:
$16.43.
Step-by-step explanation:
At the grocery store, you spent $485.72. With 2% cashback, you would get 485.72 * 0.02 = 9.7144 dollars worth of cashback.
At other places, you spend $671.28. With 1% cashback, you would get 671.28 * 0.01 = 6.7128 dollars worth of cashback.
9.7144 + 6.7128 = 16.4272, which is about $16.43 of cashback.
Hope this helps!
The amount of cashback that you earned will be $16.42.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
Suppose you earn 2% cash back at grocery stores and 1% on all other purchases. If you spent $485.72 at the grocery store and $671.28 on all other purchases.
The total cashback is calculated as,
⇒ 0.02 x $485.72 + 0.01 x $671.28
⇒ $9.71 + $6.71
⇒ $16.42
More about the percentage link is given below.
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A shirt is on sale for 20% off. Sandy paid $8 for the shirt. What was the shirt's regular price?
Answer:16
Step-by-step explanation:
Find the area of the composite figure in terms of the figure (use 3.14 for pi)
Answer:
105.12 ft²
Step-by-step explanation:
Let's first find the area of the rectangle.
[tex]10\cdot8=80[/tex] ft², so the rectangle has an area of 80ft².
To find the area of the semi-circle, we find the area of a whole circle and divide by two.
The formula to find the area of a circle is [tex]\pi r^2[/tex]. The radius is 4, as the diameter is 8.
[tex]3.14\cdot4^2[/tex]
[tex]3.14\cdot16[/tex]
[tex]50.24\div2=25.12[/tex]
Add 80 and 25.12:
[tex]80+25.12=105.12[/tex]
Hope this helped!
If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation? 0.1 1 10
Answer:
1
Step-by-step explanation: diliation is like multiplilcation if you were to do 3*1 =3. simply congruent means all sides and angles are the same.
Given that the image and the preimage of the triangle are congruent, their
dimensions are the same.
The scale factor of dilation of an image of a triangle that is congruent to the pre-image is; 1Reasons:
Let ΔABC represent the preimage, and let ΔA'B'C' represent the image.
Given that the image and the preimage are congruent, we have;
AB ≅ A'B'
BC ≅ B'C'
AC ≅ A'C'
By definition of congruency, we have;
AB = A'B'
BC = B'C'
AC = A'C'
The scale factor of dilation is given as follows;
[tex]\displaystyle Scale \ factor = \mathbf{ \frac{A'B'}{AB}} = \frac{AB}{AB} = 1[/tex]Therefore;
If the image is congruent to the pre-image, the scale factor of dilation is; 1Learn more about dilation transformation here:
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Divide.round your answer to the nearest hundredth 1divide 3
Answer:
.33
Step-by-step explanation:
Hey there!
1 / 3
= .333333333
.33 rounded to the nearest hundredth
Hope this helps :)
Find the remainder in the Taylor series centered at the point a for the following function. Then show that limn→[infinity]Rn(x)=0 for all x in the interval of convergence.
f(x)=cos x, a= π/2
Answer:
[tex]|R_n (x)| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]
Step-by-step explanation:
From the given question; the objective is to show that :
[tex]\lim_{n \to \infty} R_n (x) = 0[/tex] for all x in the interval of convergence f(x)=cos x, a= π/2
Assuming for the convergence f the taylor's series , f happens to be the derivative on an open interval I with a . Then the Taylor series for the convergence of f , for all x in I , if and only if [tex]\lim_{n \to \infty} R_n (x) = 0[/tex]
where;
[tex]\mathtt{R_n (x) = \dfrac{f^{(n+1)} (c)}{n+1!}(x-a)^{n+1}}[/tex]
is a remainder at x and c happens to be between x and a.
Given that:
a= π/2
Then; the above equation can be written as:
[tex]\mathtt{R_n (x) = \dfrac{f^{(n+1)} (c)}{n+1!}(x-\dfrac{\pi}{2})^{n+1}}[/tex]
so c now happens to be the points between π/2 and x
If we recall; we know that:
[tex]f^{(n+1)}(c) = \pm \ sin \ c \ or \ cos \ c[/tex] (as a result of the value of n)
However, it is true that for all cases that [tex]|f ^{(n+1)} \ (c) | \leq 1[/tex]
Hence, the remainder terms is :
[tex]|R_n (x)| = | \dfrac{f^{(n+1)}(c)}{(n+1!)}(x-\dfrac{\pi}{2})^{n+1}| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]
If [tex]\lim_{n \to \infty} R_n (x) = 0[/tex] for all x and x is fixed, Then
[tex]|R_n (x)| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]
This person did something wrong and I do not know what it is :( Please help this is for points!
Answer:
It is, indeed, a reduction. But, the scale factor of the dilation should be a fraction instead of a whole number, since the shape has shrunk.
Instead of [tex]\frac{KN}{K'N'}[/tex], it should be [tex]\frac{K'N'}{KN}[/tex]. That would make it (4 - 2) / (8 - 4) = 2 / 4 = 1/2.
Hope this helps!
Simplify -5g + 10 + 7g - 3
Answer:
Hey there!
We can simplify this by combining like terms.
-5g+10+7g-3
-5g+7g+10-3
2g+7
Let me know if this helps :)
Answer: [tex]2g+7[/tex]
Combine Like Terms
[tex]-5g+10+7g+-3\\(-5g+7g)+(10+-3)\\2g+7[/tex]
Calculate: ㅤ [tex]\lim_{x \rightarrow +\infty}x(\sqrt{x^{2}-1}-x)[/tex]
Answer:
[tex]\displaystyle \large \boxed{ \lim_{x \rightarrow +\infty} {x\left(\sqrt{x^2-1}-x\right)}=-\dfrac{1}{2}}[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex]\sqrt{(x^2-1)}-x\\\\=\sqrt{x^2(1-\dfrac{1}{x^2})}-x\\\\=x\left( \sqrt{1-\frac{1}{x^2}}-1\right)[/tex]
For x close to 0, we can write
[tex]\sqrt{1+x}=1+\dfrac{1}{2}x-\dfrac{1}{8}x^2+o(x^2)\\\\\ \text{x tends to } +\infty \text{ means }\dfrac{1}{x} \text{ tends to 0}\\\\\text{So, when }\dfrac{1}{x}\text{ is close to 0, we can write.}\\\\\sqrt{1-\dfrac{1}{x^2}}=1-\dfrac{1}{2}\dfrac{1}{x^2}-\dfrac{1}{8}\dfrac{1}{x^4}+o(\dfrac{1}{x^4})[/tex]
So,
[tex]x\left( \sqrt{1-\frac{1}{x^2}}-1\right)\\\\=x(1-\dfrac{1}{2}\dfrac{1}{x^2}+o(\dfrac{1}{x^2})-1)\\\\=-\dfrac{1}{2x}+o(\dfrac{1}{x})[/tex]
It means that
[tex]\displaystyle \lim_{x \rightarrow +\infty} {x\left(\sqrt{x^2-1}-x\right)}\\\\=\lim_{x \rightarrow +\infty} {-\dfrac{x}{2x}}=-\dfrac{1}{2}[/tex]
Thank you
Rhombus J K L M is shown. The length of J K is 2 x + 4 and the length of J M is 3 x. What is the length of a side of rhombus JKLM? 4 units 8 units 12 units 16 units
Answer:
12 units
Step-by-step explanation:
Since all of the sides of a rhombus are congruent, JK = JM which means:
2x + 4 = 3x
-x = -4
x = 4 so 3x = 3 * 4 = 12
Change the polar coordinates (r, θ) to rectangular coordinates (x, y):(-2,sqrt2pi
Step-by-step explanation:
x=rcosθandy=rsinθ,. 7.7. r2=x2+y2andtanθ=yx. 7.8. These formulas can be used to convert from rectangular to polar or from polar to rectangular coordinates.
Please answer quick!!! Find the range of the data set represented by this box plot.
80
76
40
56
Answer:
highest value (H)= 80
lowest value (L)= 40
range (R)=?
now using formula,
Range (R)=H-L
=80-40
=40
therefore range (R)=40
