Answer:
4x-2y=2
Step-by-step explanation:
Line R is represented by the following equation:
x+y=2
We need to choose another system of equation of x+y=2
whose solution is (1,1)
The equation must be satisfy the point (1,1)
Option 1: 2x+y = 2
Put x=1 and y=1
2(1)+1 = 3
3 ≠ 2
False
Option 2: 4x-2y=2
Put x=1 and y=1
4(1) - 2(1) = 2
2 = 2
True
Option 3: 2x-2y=2
Put x=1 and y=1
2(1) - 2(1) = 0
0 ≠ 2
False
Option 4: x+y=4
Put x=1 and y=1
1+1 = 2
2 ≠ 4
False
Hence, The system of equation is 4x-2y=2
Sarah rolls a fair dice 54 times.
How many times would Sarah expect to roll a four?
Answer:
9
Step-by-step explanation:
The dice will have 6 sides so divide 54 by 6
Answer:
9
Step-by-step explanation:
The dice will have 6 sides so divide 54 by 6
HOPE THIS HELPS!!!!
A geometric sequence is given by the recursive rule $a_1=\frac{2}{3},\ a_n=3a_{n-1}$ . Give an explicit rule for the nth term of the sequence $b_1,\ b_2,\ b_3,\ \dots\ ,$ given that $b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots$ .
Answer:
[tex]b_n = \frac{2}{27} (9^n)[/tex]
Step-by-step explanation:
Given
[tex]a_1=\frac{2}{3},\ a_n=3a_{n-1}.[/tex]
Required
An explicit rule for [tex]b_1,\ b_2,\ b_3,\ \dots[/tex]
Where [tex]b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots[/tex]
We have:
[tex]a_1=\frac{2}{3},\ a_n=3a_{n-1}.[/tex]
Calculate a2
[tex]a_2 = 3a_{2-1}[/tex]
[tex]a_2 = 3a_1[/tex]
[tex]a_2 = 3 * \frac{2}{3}[/tex]
[tex]a_2 = 2[/tex]
Calculate a3
[tex]a_3 = 3a_{3-1}[/tex]
[tex]a_3 = 3a_2[/tex]
[tex]a_3 = 3 *2[/tex]
[tex]a_3 = 6[/tex]
Calculate a4
[tex]a_4 = 3a_{4-1}[/tex]
[tex]a_4 = 3a_3[/tex]
[tex]a_4 = 3*6[/tex]
[tex]a_4 = 18[/tex]
Calculate a5
[tex]a_5 = 3a_{5-1}[/tex]
[tex]a_5 = 3a_4[/tex]
[tex]a_5 = 3*18[/tex]
[tex]a_5 = 54[/tex]
So:
[tex]b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots[/tex]
[tex]a_1=\frac{2}{3}[/tex] [tex]a_3 = 6[/tex] [tex]a_5 = 54[/tex]
The above sequence form a geometric sequence.
Calculate common ratio (r)
[tex]r = \frac{b_3}{b_2}[/tex]
[tex]r = \frac{a_5}{a_3}[/tex]
[tex]r = \frac{54}{6}[/tex]
[tex]r = 9[/tex]
So, the explicit formula is:
[tex]b_n = b_1 * r^{n-1[/tex]
[tex]b_1=a_1[/tex], so:
[tex]b_n = a_1 * r^{n-1[/tex]
[tex]a_1=\frac{2}{3}[/tex], so:
[tex]b_n = \frac{2}{3} * 9^{n-1[/tex]
Split:
[tex]b_n = \frac{2}{3} * \frac{9^n}{9}[/tex]
[tex]b_n = \frac{2}{3*9} (9^n)[/tex]
[tex]b_n = \frac{2}{27} (9^n)[/tex]
The explicit rule is: [tex]b_n = \frac{2}{27} (9^n)[/tex]
Blank minus 1/10 equals 1/2
Z+k, when z=1 and k = 7
Answer:
8
Step-by-step explanation:
Replace the variables with numbers.
1+7=8
Answer:
8
Step-by-step explanation:
Since z equals 1 and k equals 7, we do 1 + 7 which is equal to 8. Therefore, the answer would be 8.
Simplify by combining like terms and then FACTOR the expression -3+5y+5+3y
Answer:
7y+2
Step-by-step explanation:
3y+5y=7y
5-3=2
11x + 4y = 32
x = -2y - 2
PLEASE HELP ASAP PRE ALG. 20 POINTS!!!!!
Answer:
0.5/3 or 16.67
Step-by-step explanation:
Slope is y 2 minus y 1 / x 2 minus x 1.
1-0.5/6-3
0.5/3
Two trains on opposite tracks leave the same station at the same time. One train travels at an average speed of 80 kilometres per hour and the other travels at an average speed of 70 kilometres per hour. How long after they leave the station will they be 50 km apart?
Answer:
1/3 hr or 20 min.
Step-by-step explanation:
Call the trains A and B
Remember d = rt
Distance train A travels is 80t
Distance train B travels is 70t
Now, 80t + 70t = 50
150t = 50
t = 50/150 = 1/3 hr or 20 min.
HELP NO WRONG ANSWER PLS
it's π 11²-π 3²
π(121-9)
3.14(112)
=351.68cm²
round off yourself (╥﹏╥)
In 2011 a sweatshirt cost $20 and in 2012 the price increase to 25 what is the percent change
PLEASE HELP ASAP PLEASE WILL GIVE BEST RATE AND BRAINLEST PLEASE
Answer:
I think it's 145.225 sq in.
Step-by-step explanation:
2.5 x 2 x 3.14 = 15.7
15.7 x 9.25 = 145.225
Answer:
its the second one
Step-by-step explanation:
2.5 x 2 x 3.14 = 15.7 because 3.14 is pi
and then do
15.7 x 9.25 = 145.225 so there you go
What is the perimeter of a rectangle with a length of 6cm and a width of
5cm?
Answer:
perimeter = 22 cm
Step-by-step explanation:
perimeter = 2(L + W) = 2(6 + 5) = 22 cm
Answer:
22cm
Step-by-step explanation:
P=2(l+b)
so length (l)=6cm
width (b)=5 cm
The measure of angle R is 129 degrees,
What is the measure of angle S?
Answer:51
Step-by-step explanation:
Can you guys help me with this please it suppose to use the synthetic substitution or the remainder theorem.
9514 1404 393
Answer:
(b) -36
Step-by-step explanation:
Synthetic division is often performed using a table of the kind shown in the attachment. The coefficients of f(x) are placed across the top, and the x-value to be evaluated is placed at the left. The rule for finding table entries is shown. (The first (left-most) number at the bottom is the leading coefficient of the polynomial.)
This table shows the remainder, which is f(-2), is -36.
__
The equation itself can be rewritten in "Horner form" to facilitate evaluation.
f(x) = (((-x +2)x -1)x +4)x +8
In this form, substituting for x and doing the evaluation is easier for mental arithmetic. You will notice that the contents of parentheses at each level match the bottom line of the synthetic division table.
f(-2) = (((-(-2) +2)(-2) -1)(-2) +4)(-2) +8
= (((4)(-2) -1)(-2) +4)(-2) +8
= ((-9)(-2) +4)(-2) +8
= (22)(-2) +8
= -36
f(-2) = -36 . . . . remainder from synthetic substitution
Cups are sold in packages of 8. Napkins are sold in packages of 12.
What is the fewest number of packages of cups and the fewest number of packages of napkins that can be purchased so there will be the same number of cups as napkins?
Answer:
2 Packages of Napkins, 3 Packages of Cups
Step-by-step explanation:
12 * 2 = 24
8 * 3 = 24
Answer:
3 packages of cups and 2 packages of napkins
Matteo spends a total of 38 min exercising. He walks for 6 min to warm up and then runs at a constant rate of 8 min per mile for the rest of the time. Matteo says that he ran 4.75 mi. Is he correct?
Answer:
No, he not correct because he only ran 4 mi
Step-by-step explanation:
If he walks for 6 min out of the 38 min, then he ran for 32 min.
d = rt 1 mi = 8r
r = 1/8 = 1 mi/8 min Since he ran 32 min we have
d = 1/8(32) = 4 mi.
No, he not correct because he only ran 4 mi
Which triangle is similar to triangle T
Answer:
2nd one from the left.
Step-by-step explanation:
it has the same angle measures.
What is the difference between a wheel and a roller?
The store brought a pair of shoes for 40$ and sold it for 50$. What percentage was the markup?
Answer:
20%
Step-by-step explanation:
You would do 40/50 and then 40/50 is also 80/100. Then you'd take the remainder and that'd be the mark up price.
PLLLEASEEE HELLPPP I WILL GIVE BRAINLIEST!!!!
Answer:
Step-by-step explanation:
to make it quick
2*110 = arc FI
220° = arc FI
arc LI = 97°
arc FL = x
360 = 220 + 97 + x
43 = X
arc FL = 43°
:)
19.87 but there’s a 20% discount what’s the answer now?
19.87 = 100%
If you divide both sides by ten, you would get what ten percent is.
1.987 = 10%
Multiply this by two to get 20%.
3.974 = 20%
Minus twenty percent from the original amount.
18.87 minus 3.974 = 15.886 after the discount.
Which of the following situations are equal to 40%? Select all that apply.
A) 5 out of 20
B) 6 out of 15
C) 10 out of 25
D) 45 out of 90
E) 32 out of 80
can someone give me the answer to this !
Answer:
9
Step-by-step explanation:
Answer:
there are nine teachers
Step-by-step explanation:
please help!!!! find the value of x
Answer:
The answer is x+2=7,
Step-by-step explanation:
because x is a variable
4/6-3/8 zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Answer:
The answer is 7/24 ~hope this helps~
btw, sick pic B-)
Step-by-step explanation:
Which equation, when graphed, has x-intercepts at (8,0) and (-2, 0) and a y-intercept at (0, -48)?
f(x) = -3(x – 8)(x + 2)
f(x) = -3(X + 8)(x - 2)
f(x) = 3(x-8)(x + 2)
O f(x) = 3(X + 8)(- 2)
Answer:
f(x)=-3(x-8)(x+2)
Step-by-step explanation:
f(8)=-3(8-8)(8+2)=-3×0×10=0
f(-2)=-3(-2-8)(-2+2)=-3×(-10)×0=0
f(0)=-3×(0+8)×(0+2)=-3×8×2=-48
Find the approximate radius of a circle with a circumference of 198 centimeters. Use 3.14
for it Round to the nearest hundredth.
A. 63.06
B. 31.53
C. 621.72
D. 310.86
The radius of the circle is around 31.65 cm. Choice B
The formula C = 2πr , where C is the circle's circumference and r is its radius, yields the circumference of a circle. In this illustration, the circle's circumference is given as 198 cm
C = 2πr
The formula to calculate the radius can be revised as follows:
r = C / (2π)
r = 198 / (2 * 3.14)
To perform the calculation, divide the numbers:
r ≈ 198 / 6.28
r ≈ 31.65
The circle's estimated radius is 31.65 centimetres as a result.
So, rounded to the closest hundredth, the estimated radius of the circle with a circumference of 198 centimetres is 31.65 centimetres.
The closest option to 31.65 in the list of possible answers is B. 31.53. It's crucial to keep in mind that choosing 3.14 as an approximation for involves some mistake and that the precise radius number might change slightly.
When rounded to the next hundredth, the radius is 31.65. This result can be compared to the other solutions to show that:
B. 31.53.
For more such questions on radius visit;
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What is an equation of the line that passes through the points (-6,-5) and (-3,0)?put your answer in fully reduced form
Step-by-step explanation:
The equation is y = -3x + 6.
Answer:
3y = 5x + 15
Step-by-step explanation:
Slope = Change in y-cordinates
---------------------------------
Change in x-cordinates
= 0 - (-5)/-3 - (-6)
= 5/3
Using point (-3,0)
y - y1 = m(x - x1)
y - 0 = 5/3 (x - (-3))
y = 5/3 (x + 3)
Expand the bracket
y = 5x/3 + 15/3
Multiply through by 3
3y = 5x + 15
Write the fraction 3248 in simplest form.
Answer:
Step-by-step explanation:
ok so im not sure what the fraction is.... so i'll put all the choices
3/248= simplified
32/48= 2/3
324/8= 81/2
3248/1= 3248
plz besties can you help me
a) show that k lies between - 8 and 1 in the following inequality
[tex] {k}^{2} + 7k \leqslant 8[/tex]
Answer:
-8≤k≤1
Step-by-step explanation:
k²+7k-8≤0
(k+8)x(k-1)≤0
k1= -8
k2= 1
-8≤k≤1