Answer:
x = 3
y = -2
Step-by-step explanation:
x + 2y + 1 = 0
2x - 3y - 12 = 0
Multiply first equation by -2.
-2x + -4y + -2 = 0
2x - 3y - 12 = 0
Add equations.
0x + -7y - 14 = 0
Solve for y.
-7y = 14
y =-2
Put y as -2 in the first equation and solve for x.
x+2(-2)+1=0
x + -4 + 1 = 0
x = 0 + 4 - 1
x = 3
Answer:
[tex]\boxed{x = 3, y = -2}[/tex]
Step-by-step explanation:
[tex]x+2y +1 = 0[/tex]
=> [tex]x+2y = -1[/tex] -------------------(1)
[tex]2x-3y-12 = 0[/tex]
=> [tex]2x-3y = 12[/tex] -------------------(2)
Multiplying (1) by 2
=> [tex]2(x+2y) = 2(-1)[/tex]
=> [tex]2x+4y = -2[/tex] ------------------(3)
Subtracting (3) from (2)
=> [tex]2x-3y+2x-4y = 12+2[/tex]
=> -3y-4y = 14
=> -7y = 14
Dividing both sides by -7
=> y = -2
Now, Put y = -2 in Eq (1)
=> x+2(-2)+1 = 0
=> x -4+1 = 0
=> x - 3= 0
Adding 1 to both sides
=> x = 3
What equation represents the slope intercept from the line below y intercept ( 0, 2) slope -3/7 ( PLEASE HELP FAST TOP ANSWER GETS BRAINLIEST!!)
Answer:
[tex]\boxed{Option \ A}[/tex]
Step-by-step explanation:
y-intercept = b = 2 [y-intercept is when x = 0]
Slope = m = -3/7
Putting this in slope-intercept equation
=> [tex]y = mx+b[/tex]
=> [tex]y = -\frac{3}{7}x + 2[/tex]
Answer:
a
Step-by-step explanation:
A school librarian can buy books at a 20% discount from the list price. One month she spent $72 for books. What was the list price value of the books? Is the answer $90?
Answer:
[tex]\boxed{\sf \ \ YES \ \ }[/tex]
Step-by-step explanation:
Hello
let's say that the price of the book was x
the price after a 20% discount is x - 20%*x = x*(1-20%)=x*(1-.20)=0.8*x
and this is $72 so we can write that
0.8*x=72
and then divide by 0.8 both parts
x = 72/0.8=90
So the list price value of the book is $90
and we can verify as 90 - 20%*90 = 90 - 18 = 72
Hope this helps
Drag each tile to the correct box.
Three geometric sequences are given below.
Sequence A: 160, 40, 10, 2.5,
Sequence B: -21, 63, -189, 567, ...
Sequence C: 8, 12, 18, 27,
Order the sequences from least common ratio to greatest common ratio.
Sequence A
Sequence C
Sequence B
Answer:
Sequence B, Sequence A, Sequence C
Step-by-step explanation:
Data obtained from the question include the following:
Sequence A: 160, 40, 10, 2.5,
Sequence B: -21, 63, -189, 567, ...
Sequence C: 8, 12, 18, 27
Next, we shall determine the common ratio of each sequence. This is illustrated below:
Common ratio (r) is simply obtained by dividing the 2nd term (T2) by the 1st term (T1) or by dividing the 3rd term (T3) by the 2nd term (T2). Mathematically, it is expressed as:
r = T2/T1 = T3/T2
For sequence A:
160, 40, 10, 2.5
2nd term (T2) = 40
Ist term (T1) = 160
Common ratio (r) =..?
r = T2/T1
r = 40/160
r = 1/4
r = 0.25
Therefore, the common ratio is 0.25.
For sequence B:
-21, 63, -189, 567
2nd term (T2) = 63
Ist term (T1) = -21
Common ratio (r) =..?
r = T2/T1
r = 63/-21
r = - 3
Therefore, the common ratio is - 3.
For Sequence C:
8, 12, 18, 27
2nd term (T2) = 12
Ist term (T1) = 8
Common ratio (r) =..?
r = T2/T1
r = 12/8
r = 3/2
r = 1.5
Therefore, the common ratio is 1.5.
Summary:
Sequence >>>>> Common ratio
A >>>>>>>>>>>>> 0.25
B >>>>>>>>>>>>> - 3
C >>>>>>>>>>>>> 1.5
From the above illustration,
Ordering the sequence from least to greatest common ratio, we have:
Sequence B, Sequence A, Sequence C.
15 points are placed on a circle. How many triangles is it possible to form, such that their vertices will be the given points?
Answer: 445 triangles can be form with 15 dots of a circle (I hope good luck)
Step-by-step explanation:
Answer:
455
Step-by-step explanation:
There are 15 points on a circle.
We need three points to form a triangle
Therefore the number of triangles = 15 choose 3 = 15!/(3!x12!) = (15x14x13)/(3x2x1) = 5x7x13 = 455
Hence the number of triangles formed is 455
An electronics company designed a cardboard box for its new line of air purifiers. The figure shows the dimensions of the box.
The amount of cardboard required to make one box is___square inches.
a)130
b)111
c)109
d)84
Answer:
130
Step-by-step explanation:
just did test on plato/edmentum..it was correct
84 (the answer above) is incorrect
Answer:
Hi sorry for late respond but the answer in 130!!
Step-by-step explanation:
A standard deck of of 52 playing cards contains 13 cards in each of four suits : diamonds, hearts , clubs and spades. Two cards are chosen from the deck at random.
Answer:
Probability of (one club and one heart) = 0.1275 (Approx)
Step-by-step explanation:
Given:
Total number of cards = 52
Each suits = 13
FInd:
Probability of (one club and one heart)
Computation:
Probability of one club = 13 / 52
Probability of one heart = 13 / 51
Probability of (one club and one heart) = 2 [(13/52)(13/51)]
Probability of (one club and one heart) = 0.1275 (Approx)
Answer:
D. 0.1275
Step-by-step explanation:
Justo took the Pre-Test on Edg (2020-2021)!!
22.
Makes s the subject
[tex] \sqrt{p} \: is \: equals \: to \: \sqrt[r]{w \: - as ^{2}}[/tex]
Step-by-step explanation:
[tex] \sqrt{p} = \sqrt[r]{w - {as}^{2} } [/tex]
Find raise each side of the expression to the power of r
That's
[tex]( \sqrt{p} )^{r} = (\sqrt[r]{w - {as}^{2} } ) ^{r} [/tex]we have
[tex]( \sqrt{p} )^{r} = w - {as}^{2} [/tex]Send w to the left of the equation
[tex]( \sqrt{p} )^{r} - w = -{as}^{2} [/tex]Divide both sides by - a
We have
[tex] {s}^{2} = -\frac{( \sqrt{p} )^{r} - w}{a} [/tex]Find the square root of both sides
We have the final answer as
[tex]s = \sqrt{ -\frac{( \sqrt{p} )^{r} - w }{a} } [/tex]Hope this helps you
Suppose the probability that a randomly selected man, aged 55 - 59, will die of cancer during the course of the year is StartFraction 300 Over 100 comma 000 EndFraction . How would you find the probability that a man in this age category does NOT die of cancer during the course of the year?
Answer:
The probability that a man in this age category does NOT die of cancer during the course of the year is 0.997.
Step-by-step explanation:
Suppose the probability of an event occurring is [tex]P_{i}[/tex].
The probability of the given event not taking place is known as the complement of that event.
The probability of the complement of the given event will be,
[tex]1 - P_{i}[/tex]
In this case an events X is defined as a man, aged 55 - 59, will die of cancer during the course of the year.
The probability of the random variable X is:
[tex]P (X) = \frac{300}{100000}=0.003[/tex]
Then the event of a man in this age category not dying of cancer during the course of the year will be complement of event X, denoted by X'.
The probability of the complement of event X will be:
[tex]P(X')=1-P(X)[/tex]
[tex]=1-0.003\\=0.997[/tex]
Thus, the probability that a man in this age category does NOT die of cancer during the course of the year is 0.997.
A plot of land is represented on a map whose scale is 1:10000.On the map perimeter of the plot is 24.8cm.Calculate,in km ,the actual perimeter of the plot
Answer:
24.8 km
Step-by-step explanation
To do this we would just multiply 24.8 by 10,000 which is 248000 and if we divide that by 10000 (to get km) we would get 24.8km
On August 8, 1981, American Savings offered an insured tax-free account paying 23.24% compounded monthly. If you had invested $90,000 at that time, how much would you have on August 8, 2014, assuming that you could have locked the interest rate at the time of deposit? Someone please help me!!
Answer:
$181,432,754
Step-by-step explanation:
We use the formula for compound interest here, to determine the amount
Mathematically, that would be;
A =I (1 + r/n)^nt
where A is the amount which we want to calculate
I is the initial amount which is $90,000
r is the rate = 23.24% = 23.24/100 = 0.2324
n is the number of times per year the interest is compounded = 12 (compounded monthly)
t is the number of years = 2014 - 1981 = 33
Substituting these values, we have;
A = 90,000(1 + 0.2324/12)^(33 * 12)
A = 90,000(1 + 0.0194)^396
A = 90,000(1.0194)^396
A = 181,432,754.27210504
Which is approximately $181,432,754 to the nearest whole dollars
How many minutes are in 324 hours?
Answer: 19440 minutes
Step-by-step explanation:
Hi there! Hopefully this helps!
--------------------------------------------------------------------------------------------------
Answer: There are 19440 minutes in 324 hours.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Since there are 60 minutes in each hour, we need to multiply the time value by 60. Like this:
324 x 60 = 19440.
Given the sequence 38, 32, 26, 20, 14, ..., find the explicit formula.
Answer:
The explicit formula for the sequence is
44 - 6nStep-by-step explanation:
The above sequence is an arithmetic sequence
For an nth term in an arithmetic sequence
A(n) = a + ( n - 1)d
where a is the first term
n is the number of terms
d is the common difference
From the question
a = 38
d = 32 - 38 = - 6 or 20 - 26 = - 6 or
14 - 20 = - 6
So the formula for the sequence is
A(n) = 38 + ( n - 1)-6
= 38 - 6n + 6
We have the final answer as
A(n) = 44 - 6nHope this helps you
Answer:
[tex]\huge\boxed{a_n=-6n+44}[/tex]
Step-by-step explanation:
This is an arithmetic sequence:
32 - 38 = -6
26 - 32 = -6
20 - 26 = -6
14 - 20 = -6
The common difference d = -6.
The explicit formula of an arithmetic formula:
[tex]a_n=a_1+(n-1)(d)[/tex]
Substitute:
[tex]a_1=38;\ d=-6[/tex]
[tex]a_n=38+(n-1)(-6)[/tex] use the distributive property
[tex]a_n=38+(n)(-6)+(-1)(-6)\\\\a_n=38-6n+6\\\\a_n=-6n+(38+6)\\\\a_n=-6n+44[/tex]
The sum of ages Afful and Naomi is 34. In 5 years time , Afful will be 2 times the age on Naomi now. How old are they now.
Answer:
Afful is 21 and Naomi is 13.
Step-by-step explanation:
Let [tex]A[/tex] represent the age of Afful and [tex]N[/tex] represent the age of Naomi.
The sum of their ages is 34. In other words:
[tex]A+N=34[/tex]
In 5 years time, Afful will be two times the age of Naomi now. In other words:
[tex]A+5=2N[/tex]
Solve for the system. Substitute.
[tex]A+N=34\\A=34-N\\34-N+5=2N\\39=3N\\N=13\\\\A=34-N\\A=34-(13)\\A=21[/tex]
Afful is currently 21 and Noami is currently 13.
Answer:
Naomi=x
Afful=2x
In 5 years time= +5
So Naomi=x+5
and and Afful=2x+5
=x+5+2x+5=34
=3x+10=34
Subtract 10 on both sides
3x=24
Divide 3 on both sides
X=8
Check:
X=8
Naomi=16
In 5 years
=16+5=21
Naomi=8+5=13
13+21=34
Hope this helps
Step-by-step explanation:
I need this done help!!
Answer:
Because the triangle is isosceles, the base angles are congruent, meaning that the angles that are not right angles are x and x. Since the sum of angles in a triangle is 180°, we can write:
90 + x + x = 180
x + x = 90
2x = 90
x = 45°
Answer:
45 degrees
Step-by-step explanation:
This triangle is "isosceles..." two legs are equal. Thus, the triangle has two 45 degree angles. The indicated angle is 45 degreees.
Find the slope and y-intercept of the following graph.
Answer: y = -5*x + b
Step-by-step explanation:
A line is written as:
y = a*x + b
where a is the slope and b is the y-intercept.
IIf we have a line that passes through the points (x1, y1) and (x2, y2) then the slope of the line is:
a = (y2 - y1)/(x2 - x1)
In this case we can see that the line passes through the points:
(0, 2) and (1, - 3)
Then the slope is:
a = (-3 - 2)/(1 - 0) = -5
Then our line is:
y = -5*x + b
And when x = 0, y = 2 then:
y = 2 = -5*0 + b
2 = b
Our line is:
y = -5*x + b
4) Flying to Tahiti with a tailwind a plane averaged 259 km/h. On the return trip the plane only
averaged 211 km/h while flying back into the same wind. Find the speed of the wind and the
speed of the plane in still air.
A) Plane: 348 km/h, Wind: 37 km/h B) Plane: 243 km/h, Wind: 30 km/h
C) Plane: 235 km/h, Wind: 24 km/h D) Plane: 226 km/h, Wind: 13 km/h
fundraiser Customers can buy annle nies and
Answer: C) Plane: 235 km/h, Wind: 24 km/h
Step-by-step explanation:
Given that :
Average Speed while flying with a tailwind = 259km/hr
Return trip = 211km/hr
Let the speed of airplane = a, and wind speed = w
Therefore ;
Average Speed while flying with a tailwind = 259km/hr
a + w = 259 - - - (1)
Return trip = 211km/hr
a - w = 211 - - - (2)
From (2)
a = 211 + w
Substitute the value of a into (1)
a + w = 259
211 + w + w = 259
211 + 2w = 259
2w = 259 - 211
2w = 48
w = 48/2
w = 24km = windspeed
Substituting w = 24 into (2)
a - 24 = 211
a = 211 + 24
a = 235km = speed of airplane
If you had a cube with a side length of 4, how can your write the calculations in exponential form? What are 2 other ways to read the exponent verbally?
Answer: 4^3
(Four cubed or Four to the power of 3)
Step-by-step explanation:
These box plots show the prices for two different brands of shoes.
Answer: I’m pretty sure is letter A
Wolfrich lived in Portugal and Brazil for a total period of 141414 months in order to learn Portuguese. He learned an average of 130130130 new words per month when he lived in Portugal and an average of 150 new words per month when he lived in Brazil. In total, he learned 1920 new words. How long did Wolfrich live in Portugal, and how long did he live in Brazil
Answer:
Wolfrich lived in Brazil for 5 months and 9 months in Portugal
Step-by-step explanation:
Given;
Total Months = 14
Total Words = 1920
Required
Find the time spent in Portugal and time spent in Brazil
Let P represent Portugal and B represent Brazil; This implies that
[tex]P + B = 14[/tex] ---- Equation 1
Considering that he learnt 130 words per month in Portugal and 150 per month in Brazil; This implies that
[tex]130P + 150B = 1920[/tex] --- Equation 2
Make P the subject of formula in equation 1
[tex]P = 14 - B[/tex]
Substitute 14 - B for P in equation 2
[tex]130(14 - B) + 150B = 1920[/tex]
Open Bracket
[tex]1820 - 130B + 150B = 1920[/tex]
[tex]1820 + 20B = 1920[/tex]
Subtract 1820 from both sides
[tex]1820 - 1820 + 20B = 1920 - 1820[/tex]
[tex]20B = 100[/tex]
Divide both sides by 20
[tex]\frac{20B}{20} = \frac{100}{20}[/tex]
[tex]B = 5[/tex]
Substitute 5 for B in [tex]P = 14 - B[/tex]
[tex]P = 14 - 5[/tex]
[tex]P = 9[/tex]
Wolfrich lived in Brazil for 5 months and 9 months in Portugal
Enter the coordinates of the vertex of the graph of y=2(x+5)^2
Answer:
The vertex is ( -5,0)
Step-by-step explanation:
The vertex form of a parabola is
y = a( x-h) ^2 +k
where ( h,k) is the vertex
y=2(x+5)^2
y=2(x - -5)^2 +0
The vertex is ( -5,0)
Answer:
vertex = (- 5, 0 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
y = 2(x + 5)² , that is y = 2(x + 5)² + 0 ← is in vertex form
with (h, k) = (- 5, 0 )
4/6, 5/6, 2/6 how do you put it least to greatest?
Answer:
2/6 < 4/6 < 5/6
Step-by-step explanation:
2 < 4 => 2/6 < 4/6
4 < 5 => 4/6 < 5/6
=> 2/6 < 4/6 < 5/6
Answer:
2/6, 4/6 5/6
Step-by-step explanation:
convert 1000110binary into decimal number system
Answer:
70₁₀Step-by-step explanation:
In order to convert a binary number into a decimal, it is expanded in the power of 2. Then, by simplifying the expanded form of the binary number, we obtain a decimal number.
Let's solve:
[tex]1000110[/tex]
[tex] = 1 \times {2}^{6} + 0 \times {2}^{5} + 0 \times {2}^{4} + 0 \times {2}^{3} + 1 \times {2}^{2} + 1 \times {2}^{1} + 0 \times {2}^{0} [/tex]
[tex] = 1 \times 64 + 0 \times 32 + 0 \times 16 + 0 \times 8 + 1 \times 4 + 1 \times 2 \times 0 \times 1[/tex]
[tex] = 64 + 0 + 0 + 0 + 4 + 2 + 0[/tex]
[tex] = 70[/tex]₁₀
Hope I helped!
Best regards!!
Please answer question now what the answer
Answer:
100 degrees
Step-by-step explanation:
360-260=100
Answer:
x=100
Step-by-step explanation:
130+130+x=360
260+x=360
x=100
Have a great and magnificent day
A rectangular sheet of paper was folded in half 6 times. In the middle of this folded sheet, two holes were drilled. Then, the sheet of paper was unfolded back to its original shape. How many holes are there?
Answer:
There will be 128 holes
Step-by-step explanation:
Simply think of each fold as doubling the number of holes. So since we have 6 folds, that will be 2^6 and then we have 2 holes in those folds, which makes 2*2^6 == 2^7 == 128 holes. Cheers.
Folding of the paper is an illustration of a geometric sequence
The number of holes in the rectangular paper is 128
The given parameters are:
[tex]\mathbf{h = 2}[/tex] --- holes
[tex]\mathbf{t = 6}[/tex] --- number of times
The sheet was folded in halves i.e. in 2's.
So, the amount of each time is:
[tex]\mathbf{f(t) = 2 \times h^t}[/tex]
Substitute values for h and t
[tex]\mathbf{f(6) = 2 \times 2^6}[/tex]
Evaluate the exponent
[tex]\mathbf{f(6) = 2 \times 64}[/tex]
Multiply
[tex]\mathbf{f(6) = 128}[/tex]
Hence, the number of holes in the rectangular paper is 128
Read more geometric sequence at:
https://brainly.com/question/10564422
Ahmed wants to get a loan from his credit union for $20,000 to buy a new car. He can get an interest rate of 5% and can pay off the loan in 5 years. How much will Ahmed pay each month?, How much will Ahmed pay in interest?
Answer:
Step-by-step explanation:
The cost of the new car is $20,000.
We would apply the periodic interest rate formula which is expressed as
P = a/[{(1+r)^n]-1}/{r(1+r)^n}]
Where
P represents the monthly payments.
a represents the amount of the loan
r represents the annual rate.
n represents number of monthly payments. Therefore
a = $20000
r = 0.05/12 = 0.0042
n = 12 × 5 = 60
Therefore,
P = 20000/[{(1+0.0042)^60]-1}/{0.0042(1+0.0042)^60}]
20000/[{(1.0042)^60]-1}/{0.0042(1.0042)^60}]
P = 20000/{1.286 -1}/[0.0042(1.286)]
P = 20000/(0.286/0.0054012)
P = 20000/52.95
P = $378
Ahmed will pay $378 each month
The total payment is
378 × 60 = $22680
The amount that Ahmed will pay in interest is
22680 - 20000 = $2680
In △ABC, m∠A=45°, c=17, and m∠B=25°. Find a to the nearest tenth.
Answer:
12.8
Step-by-step explanation:
you have to use the law of sines to calculate it. the measure of angle c is 110 and you have to do
Sin(110)x=17sin(45)
and then it turns into 17sin(45)/sin(110)
then put it into desmos with it being in degrees mode
CAN ANYONE HELP IM VERY CLUELESS
Answer:
51°
Step-by-step explanation:
A circle has a total of 360 degrees. So,
360 = 62 + 66 + x + 73 + x + 57
Next, combine like terms:
360 = 2x + 258
Next, isolate your variable by subtracting 258 from both sides:
102 = 2x
Finally, divide both sides by 2 to get x:
x = 51
Answer:
x = 51
Step-by-step explanation:
x + 73 + x + 57 + 62 + 66 = 360
2x + 258 = 360
2x = 360 - 258
2x = 102
[tex]\frac{x}{2} =\frac{102}{2}[/tex]
x = 51
whats the equation for this
Answer:
[tex]x^2 + y^2 + 4x + 4y = -119/16[/tex]
Step-by-step explanation:
The axes x and y are calibrated in 0.25
If the circle is carefully considered, the radius r of the circle is:
r = -1.25 - (-2)
r = 0.75 units
The equation of a circle is given by:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
The center of the circle (a, b) = (-2, -2)
Substituting (a, b) = (-2, -2) and r = 0.75 into the given equation:
[tex](x - (-2))^2 + (y - (-2))^2 = (3/4)^2\\\\(x + 2)^2 + (y + 2)^2 = (3/4)^2\\\\x^2 + 4x + 4 + y^2 + 4y + 4 = 9/16\\\\x^2 + y^2 + 4x + 4y + 8 = 9/16\\\\16x^2 + 16y^2 + 64x + 64y + 128 = 9\\\\16x^2 + 16y^2 + 64x + 64y = -119\\\\x^2 + y^2 + 4x + 4y = -119/16\\[/tex]
PLEASE HELP ME! Please do not comment nonsense, and actually comment the answer and the solution.
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Explanation:
For choice C, the x values are out of order, so it might be tricky at first. I recommend sorting the x values from smallest to largest to get -2, -1, 0, 1, 2. Do the same for the y values as well. Make sure the correct y values stay with their x value pairs. You should get the list of y values to be 4, 2, 1, 1/2, 1/4
Check out the attached image below for the sorted table I'm referring to
We can see the list of y values is going down as x increases. This is a good sign we have decay. Further proof is that we multiply each term by 1/2 to get the next one
4 times 1/2 = 2
2 times 1/2 = 1
1 times 1/2 = 1/2
1/2 times 1/2 = 1/4
and so on. Effectively we can say the decay rate is 50%
3. Callum rolled a single six sided die 12 times and it landed on a six, three of the times. The probability that it will land on a six on the 13th roll is?
Answer:
1/6
Step-by-step explanation:
Each roll is independent. So the probability of rolling a six is 1/6, regardless of the previous rolls.