Answers
y = 0.647
seems to be a good approximation of the solution.
Answer:
Solution of the system of the equations is (0.882, 0.647)
Step-by-step explanation:
As shown in the figure equations are [tex]y=-\frac{2}{5}x+1[/tex] and y = 3x - 2
Solution of the system of equations will be the common point or point of intersection of these lines.
To get the point of intersection we will solve these equations.
We will equate these equations to get the value of x.
[tex]-\frac{2}{5}x+1=3x-2[/tex]
[tex]-2x+5=15x-10[/tex]
15x + 2x = 10 + 5
17x = 15
[tex]x=\frac{15}{17}[/tex]
x = 0.882
By putting x = 0.882 in y = 3x - 2
y = 3(0.882) - 2
y = 0.647
So the solution of systems of equations is (0.882, 0.647)
Related Questions
A manufacturer of drinking glasses ships his delicate stock in speical boxes that can hold 32 glasses. if 1714 glasses are manufactured, how many full boxes are filled? are there any glasses left over?
Answers
53 boxes are filled and 18 glasses are left over.
Some one help me with this question!
One of the halves on the Hoover Dam releases 40,000 gallons of water per second. What is the rate, in gallons per minute?
Answers
40,000 gallons / second * 60 seconds / minute = 2,400,000 gallons / minute
This way, the seconds cancel out and we are left with 2,400,000 gallons / minute
after school, maurice walks 1/3 mile to the park and then walks 1/2 mile to his house. how far does maurice walk from school to his house?
Answers
x-----> distance school to the park
y-----> distance park to the house
we know that
x=1/3 mile
y=1/2 mile
[distance from school to the house]=x+y----> (1/3+1/2)
The common denominator is (3*2)---> 6
=(2*1+3*1)/(3*2)----> 5/6 mile
the answer is
5/6 miles
help please in eed answers asap
Answers
4.2 x 4.2 x 4.2 = 74.088 cm^3
Answer:
74,088 cm³
Step-by-step explanation:
[tex]whl = V \\ \\ [4,2]^{3} = 74,088[/tex]
I am joyous to assist you anytime.
New grass seeds grow rapidly. A grass seed has grown to 12 millimeters tall. tomorrow it will be 23 millimeters tall, the next day it will be 24 millimeters tall. and on the next day it will be 45 millimeters tall. write a rule to represent the height of the bean plant as an arithmetic sequence. how tall will the plant be in 15 days?
A) A(n) = 16 + (n-1) 11: 194 millimeters
B) A(n) = 12 + (n-1) 11: 166 millimeters
C) A(n) = 13n: 195 millimeters
D) A(n) = 12n; 180 millimeters
Answers
B) A(n) = 12 + (n-1) 11: 166 millimeters
solve the system of equations 6X + 5 y equals 55 + 6 x + 5 y equals 60
Answers
-5y. -5y
6x. =55+6x
-6x. -6x
0=55
no solution
A gardener crosses tall true-breeding pea plants with short true-breeding ones. Tall plants are dominant to short ones. He collects the seeds to grow F1 plants and then allows them to self-pollinate to form an F2 generation. Which of the following describes the traits of the offspring correctly?
Answers
a) Three–fourths of the F1 and one–half of the F2 plants will be tall.
b) All of the F1 and three–fourths of the F2 plants will be tall.
c) Three–fourths of the F1 and all of the F2 plants will be tall.
Let’s name tall as T and short as t
Since both are true breeding plants
Tall plants have the genotype TT and short plants have the genotype tt
Tall plants will make gametes of type T only
Short plants make gametes of type t only
After cross breeding the offspring would all be of genotype Tt as they’re made of T and t gametes
F1 generation formed have the genotype Tt
Since T is dominant all F1 plants are tall
When F1 self pollinates
F1 * F1
Tt *Tt
Gametes are
T t T t
F2 population offspring genotypes are as follows;
TT -1/4 tall
Tt -1/4 tall
Tt -1/4 tall
tt - 1/4 short
3/4 of the plants are tall
Remaining 1/4 is short
Therefore response b is correct
All f1 plants are tall and 3/4 of f2 plants are tall
Carlos’s hockey team has ten players, not counting the goalie.Five non goalie players need to be selected for a starting line-up.
A)How many different starting lineups are possible if positions are not assigned?
B)How many starting lineups are possible if positions are assigned?
Answers
Final answer:
There are 252 different starting lineups possible if positions are not assigned, and 30,240 starting lineups are possible if positions are assigned.
Explanation:
For part A of the question, where positions are not assigned, we can calculate the number of different starting lineup combinations by using the combination formula. Since we are choosing 5 players out of 10 without regard to order, we use:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of players to choose from, and k is the number of players we want to choose. Therefore, we have:
C(10, 5) = 10! / (5! (10-5)!) = 252
There are 252 different starting lineups possible if positions are not assigned.
For part B, where positions are assigned, we use the permutation formula because the order in which we select the players matters. This formula is:
P(n, k) = n! / (n-k)!
Since the order in which the players are chosen matters, we have:
P(10, 5) = 10! / (10-5)! = 30,240
There are 30,240 different starting lineups possible with positions assigned.
An after school club is building a clubhouse that has a rectangular floor that is 8 feet by 6 feet. What is the total floor area in square inches of the clubhouse?
Answers
Compute the area of the triangle ( express answer in cm2
Height =6 cm
Base= 12cm
Answers
1/2(12)(6)
1/2(72)
36cm2 is the answer.
Answer:
36 cm^2
Step-by-step explanation:
If the APY of a savings account is 5.3%, and if the principal in the savings account is $5100 for an entire year, what will be the balance of the savings account after all the interest is paid for the year?
A. $5300.00
B. $5127.03
C. $5100.00
D. $5370.30
Answers
Answer:
Option D - $5370.30
Step-by-step explanation:
Given : If the APY of a savings account is 5.3%, and if the principal in the savings account is $5100 for an entire year.
To find : What will be the balance of the savings account after all the interest is paid for the year?
Solution :
First we find the interest he paid.
The interest formula is [tex]I=P\times R\times T[/tex]
Where, P is the principal P=$5100
R is the rate of interest R=5.3%=0.053
T is the time T=1 year
Substituting the values,
[tex]I=5100\times 0.053\times 1[/tex]
[tex]I=\$270.3[/tex]
The balance of the saving account is the sum of interest paid and principal value.
Amount = Interest +Principal
Amount = $270.3 +$5100
Amount = $5370.3
Therefore, Option D is correct.
Help please !!!!!!! .......
Answers
A geometric sequence is a sequence of numbers, where the successive values after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. In this case the common ratio is 0.6.
5 * 0.6 = 3
3 * 0.6 = 1.8
1.8 * 0.6 = 1.08
If the side length of a square pyramid is triple and the slant height is divided by 5 what would be the formula to find the modified surface area
Answers
.. S = (base area) +(lateral area)
.. S = s² +(1/2)*(4s)*h
.. S = s(s +2h)
Now, if we make these replacements: s ⇒ 3s, h ⇒ h/5, we have
.. S' = (3s)(3s +2h/5)
.. S' = 9s² +(6/5)s*h . . . . . . . the formula for the modified area (in terms of original dimensions)
_____
Of course, in terms of the modified dimensions, the formula is the same:
.. S' = s'(s' +2h')
solve the system of equations by substitution y=5x-13 and 5x+2y=19
Answers
5x + 2y = 19 --------- (2)
Sub (1) into (2):
5x + 2(5x -13) = 19
5x + 10x - 26 = 19
15x = 19 + 26
15x = 45
x = 3 -------- sub back into (1)
y = 5(3) - 13
y = 15 - 13
y = 2
Ans: x = 3, y = 2
What number fills in the blank to complete the factorization of 3x + 24?
(x + 8)
Answers
Answer:
The factor form of given expression is 3(x+8) so the required number is 3.
Step-by-step explanation:
The given expression is
[tex]3x+24[/tex]
Write the factors of each term.
[tex]3x+24=3\times x+3\times 8[/tex]
In both terms, 3 is a common factor.
Take out the common factor 3.
[tex]3x+24=3(x+8)[/tex]
The factor form of given expression is 3(x+8). The factor (x+8) is given, therefore the required number is 3.
I need help on this one.
Answers
6-3+4x+1-----------> Group terms
(6-3+1)+4x
(3+1)+4x
4+4x
this is the equation of a line f(x)=4x+4
the domain is the interval (-∞,∞)
there are infinitely solutions for x---------> see the attached figure
Martin needs 60 meters of fence to go around a rectangular garden.
The length, l, of the garden is twice its width w.
Three of these equations give the correct value for w.
Which equation does NOT?
2 • w + 2 • 2w = 60
2 • (2w + w) = 60
w + 2w = 60
w + 2w + w + 2w = 60
Answers
Answer:
w + 2w = 60
Step-by-step explanation:
w + 2w = 60
This equation will not give you the correct value for W because W is the siez or represents the size of the smaller side, since you have 4 sides, 2 small and 2 big, the sum of this 4 sides will be the perimeter, or the total meters of fence needed, since the total meter of fence need is 60 and in the equation you just have 2 sides, the value for W will be double than the real.
There are four steps in solving one’s personal financial challenges:
1. considering opportunity costs
2. assessing risks and returns
3. setting short- and long-term goals
4. assessing needs and wants
Which of these is the correct order of these steps?
2, 3, 1, 4
1, 2, 3, 4
4, 1, 2, 3
3, 1, 4, 2
Answers
Answer: C. 4, 1, 2, 3.
I hope this helps :)
Answer: Third option is correct.
Step-by-step explanation:
Since there are four steps in solving one's personal financial challenges:
1) First he needs to assessing the needs and wants .
2) Then, he will consider opportunity costs, i.e. next best alternative.
3) Then, he will assessing the risks and returns associated with the opportunity costs.
4) Last, but not the least, he will be setting short and long term goals.
So, The correct order of these steps is 4,1,2,3.
Hence, Third option is correct.
What is the slope of the line on the graph. I need help I!!!
Answers
So using the Rise Over Run we can calculate the slope, from each point the slope rises 2 and runs -6 (-2/6) then simplify to -1/3
-1/3 is your slope
Angle A=11x-4, Angle B = 4x-11, and Angle C=63-4x. List the sides of triangle ABC in order from shortest to longest.
A. AB, AC, BC
B. AC, AB, BC
C. BC, AB, AC
D. AB, BC, AC
Answers
2. Keeping this on mind, you have:
A+B+C=180
A=11x-4
B = 4x-11
C=63-4x
3. When you substitute these values, you obtain:
A+B+C=180
11x-4+4x-11+63-4x=180
11x+48=180
11x=180-48
11x=132
x=132/11
x=12
3. Therefore:
A=11(12)-4
A=128°
B = 4(12)-11
B=37°
C=63-4(12)
C=15°
5. The answer is:
A. AB, AC, BC
The room measures 8 inches by 5 inches on the blueprint. If the scale on the blueprint is 1 inch by 4 feet, what is the actual area of the room
Answers
To solve this problem, we need to multiply each number by 4 ft.
8×4=32
5×4=20
Now, we films the area.
32×20 = 640
The area of the room is 640 feet squared.
Hope this helps!
A cardboard sheet is cut in the shape of a triangle, with vertices at (0,0), (20,0), and (3,4) units. the thickness of the sheet is uniform. what is the x-coordinate of its center of mass?
Answers
1. The long way
We know that the base of the triangle is along the x-axis, and the length of the base is 20.
The centre of mass is located at 2/3 of the distance from vertex (3,4) along the median, which cuts the base at (10,0).
Therefore the centre of mass is located at
x=3+(10-3)*2/3=23/3
y=4/3
2. The short way
It turns out that the centre of mass of a triangle sheet is located at the mean of the coordinates of the three vertices, i.e.
CG=((0+20+3)/3, (0+0+4)/3)=(23/3, 4/3) as before.
Will someone please find the value of x for these questions
Answers
12) for h=√(10²-6²)=8
then
[tex] \frac{x-6}{8} = \frac{8}{6}; \ =\ \textgreater \ \ x= \frac{50}{3} [/tex]
14) 6:11 as x:10. It means that
[tex] \frac{6}{11} = \frac{x}{10}; \ =\ \textgreater \ \ x=6*10/11= \frac{60}{11} [/tex]
Assume that the poisson distribution applies and that the mean number of hurricanes in a certain area is 5.55.5 per year.
a. find the probability that, in a year, there will be 44 hurricanes.
b. in a 5555-year period, how many years are expected to have 44 hurricanes?
c. how does the result from part (b) compare to a recent period of 5555 years in which 88 years had 44 hurricanes? does the poisson distribution work well here?
Answers
λ = mean = 5.5 hurricanes per year
and Poisson distribution applies.
P(k, λ ) = λ ^k * e^(- λ ) / k!
a) 4 hurricanes in a year
P(4,5.5)=5.5^(4)*e^(-5.5)/4!
=0.1558
b) In 55 years, the expected number of years with 4 hurricanes
= 55*0.1558 = 8.57, could be rounded to the nearest integer, 9.
c) Records show that in 55 years had 8 years had 4 hurricanes each year.
This compares very closely with the expected number 8.57.
A stained glass window is in the shape of an equilateral triangle. what is the measure of one interior angle of the triangle
Answers
60° x 3 (Angles) = 180°
Write the following decimal number in its equivalent fraction form. Show all work for full credit.
0.8(repeating)
Answers
x=0.8888 Start with the given equation
10x=8.8888 Multiply both sides by 10. The goal is to move the decimal point to the next repeating portion (which is just one spot to the right)
Now subtract the equation x=0.8888 from 10x=8.8888 to get
10x-x=8.8888-0.8888
9x=8 Combine like terms. Notice how the decimal portions cancel out.
x=8/9 Divide both sides by 9 to isolate x
So the answer is x=8/9 which means that 8/9=0.8888 (where the 8's repeat)
To write the decimal number 0.8(repeating) as a fraction, use the concept of an infinite geometric series and convert it to an equation. Multiply both sides of the equation by 10 to eliminate the decimal point and subtract the original equation to eliminate the repeating part. Finally, divide by 9 to get the equivalent fraction form.
Explanation:To write the decimal number 0.8(repeating) as a fraction, we can use the concept of an infinite geometric series. Let's assume the repeating decimal as x: x = 0.8(repeating). Now, multiply both sides of the equation by 10 to remove the decimal point: 10x = 8(repeating). Next, subtract the original equation from this new equation to eliminate the repeating part: 10x - x = 8(repeating) - 0.8(repeating). Simplifying these expressions gives us: 9x = 7.2. Finally, divide both sides of the equation by 9: x = 7.2/9. Therefore, the equivalent fraction form of 0.8(repeating) is 7.2/9.
How many 4-sequences on {0..9} do not begin with 0?
Answers
If that's the case, then for any 4-sequence, the first digits place (leftmost) has 9 possible choices (1-9). Once that number is used up, we have 9 numbers left in the pool of digits, from which we select a 3-sequence. The number of possible 3-sequences would be [tex]\dfrac{9!}{3!}=60,480[/tex]. Multiply this by 9 (to account for the first digit's possibilities) and we get a grand total of [tex]\dfrac{9\times9!}{3!}=544,320[/tex] possible 4-sequences on [tex]\{0,\ldots,9\}[/tex].
There are 9000 possible 4-sequences that do not begin with the digit 0.
The question asks how many 4-sequences on the set {0..9} do not begin with 0. To solve this, we need to consider the number of possible options for each of the four positions in the sequence, knowing that the first digit cannot be 0.
For the first position, there are 9 options (1-9), since 0 is not allowed. For the next three positions, each can be any of the 10 digits (0-9), since there are no restrictions. Thus, the total number of such sequences is the product of the number of options for each position.
9 options (1st position) x 10 options (2nd position) x 10 options (3rd position) x 10 options (4th position) = 9 x 10 x 10 x 10 = 9000.
So, to find how many 4-sequences do not begin with 0, multiply the number of choices for each position: 9 (first position, cannot be 0) x 10 (second position) x 10 (third position) x 10 (fourth position), resulting in 9000 such sequences.
Simplify (- 5/8) divided by (-3/4)
A: 20/24
B: -20/24
C: -15/32
D: 15/32
Answers
The answer is A (20/24)
Step 1: -5/8 · 4/-3
Step 2: -5 · (-4)
______
8 · 3
Step 3: 20/24
Answer: 5/6
Your answer is 5/6
Hope I helped!
Let me know if you need anything else!
~ Zoe (Rank:'Genius')
If A2 = I, where I is the identity matrix, which matrix correctly represents matrix A?
Answers
We know that [tex] \boldsymbol{A^2}=\boldsymbol{A\times A} [/tex]
We also know that [tex] \boldsymbol{I}=\begin{bmatrix}
1 &0 \\
0&1
\end{bmatrix} [/tex]
Now, it has been given to us that [tex] \boldsymbol{A^2}=\boldsymbol{I} [/tex]
Therefore, we will have to find the correct [tex] \boldsymbol{A} [/tex] from the given options and we find that when:
[tex] \boldsymbol{A}=\begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix} [/tex]
then [tex] \boldsymbol{A^2}=\boldsymbol{A\times A}=\begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix}\times \begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix}=\begin{bmatrix}
1 & 0\\
0 & 1
\end{bmatrix} [/tex]
Therefore, from the above given options, Option C is the correct option.
Therefore, [tex] \boldsymbol{A}=\begin{bmatrix}
3 & -2\\
4 & -3
\end{bmatrix} [/tex] is the correct answer.
Answer:
C. [3, -2]
[4, -3]
Step-by-step explanation:
PLATOOOO
Noel is playing a game where he draws one playing card each out of two stacks of 5 cards. The table below shows all possible sums for the two numbers on the cards.
Answers
Noel is more likely to draw two cards with a sum that is greater than 13.
To determine which outcome is more likely, let's count the number of combinations that meet each criterion.
1. **Sum that is a multiple of 3**:
- Possible sums: 3, 6, 9, 12
- Counting the combinations:
- 3: 1 combination
- 6: 2 combinations
- 9: 3 combinations
- 12: 4 combinations
- Total combinations: 1 + 2 + 3 + 4 = 10 combinations.
2. **Sum greater than 13**:
- Possible sums: 14, 15, 16, 17, 18, 19, 20, 21, 22, 23
- Counting the combinations:
- 14: 1 combination
- 15: 2 combinations
- 16: 2 combinations
- 17: 3 combinations
- 18: 2 combinations
- 19: 3 combinations
- 20: 2 combinations
- 21: 3 combinations
- 22: 1 combination
- 23: 1 combination
- Total combinations: 1 + 2 + 2 + 3 + 2 + 3 + 2 + 3 + 1 + 1 = 20 combinations.
Comparing the total combinations, we see that there are more combinations with a sum greater than 13 (20 combinations) than there are combinations with a sum that is a multiple of 3 (10 combinations). Therefore, Noel is more likely to draw two cards with a sum that is greater than 13.
The probable question may be:
Noel is playing a game where he draws one playing card each out of two stacks of 5 cards. The table below shows all possible sums for the two numbers on the cards.
3, 6, 7, 9, 1
1 = 4, 7, 8, 10, 12
4 = 7, 10, 11, 13, 15
6 = 9, 12, 13, 15, 17
8 = 11, 14, 15, 17, 19
12 = 15, 18, 19, 21, 23
Is Noel more likely to draw two cards with a sum that is a multiple of 3 or two cards with a sum that is greater than 13?
Noel is more likely to draw two cards with a sum greater than 13, as there are 37 combinations compared to 11 combinations for multiples of 3.
To determine whether Noel is more likely to draw two cards with a sum that is a multiple of 3 or two cards with a sum that is greater than 13, we can analyze the table provided.
1. Sum that is a multiple of 3:
- There are several combinations of card values that result in a sum that is a multiple of 3. We can count these combinations from the table:
- (3, 4), (3, 7), (3, 9), (3, 12)
- (6, 7), (6, 10), (6, 12)
- (7, 8), (7, 11)
- (9, 10), (9, 13)
- (11, 12)
2. Sum greater than 13:
- We need to count the combinations of card values that result in a sum greater than 13:
- (6, 8), (6, 10), (6, 11), (6, 12), (6, 13), (6, 15), (6, 17)
- (7, 8), (7, 9), (7, 10), (7, 11), (7, 12), (7, 13), (7, 15), (7, 17), (7, 19)
- (9, 10), (9, 11), (9, 12), (9, 13), (9, 15), (9, 17), (9, 19)
- (11, 12), (11, 13), (11, 15), (11, 17), (11, 19)
- (12, 13), (12, 15), (12, 17), (12, 19)
- (13, 15), (13, 17), (13, 19)
- (15, 17), (15, 19)
- (17, 19)
After counting the combinations, we can compare the number of combinations in each category:
1. Sum that is a multiple of 3:
- Total combinations: 11
2. Sum greater than 13:
- Total combinations: 37
Comparing the totals, we can see that Noel is more likely to draw two cards with a sum that is greater than 13, as there are more combinations resulting in this outcome.
Complete Question: