Answer:
y = (2x/9) + 1
Step-by-step explanation:
Solving for y we get 3(-2y+x) = 5(-3y+x)+9
Expand the above we get -6y+3x=5(-3y+x)+9
which is -6y+3x = -15y+5x+9
then 9y = 2x+9
which y = (2x/9) + 1
A number cube with faces labeled from 1 to 6 will be rolled once.
The number rolled will be recorded as the outcome.
Give the sample space describing all possible outcomes.
Then give all of the outcomes for the event of rolling the number 2.
If there is more than one element in the set, separate them with commas.
The sample space S = {1, 2, 3, 4, 5, 6} describing all possible outcomes and outcomes for the event of rolling the number 2 is E = {2}
What is sample space?It is defined as the space in which all possible outcomes are represented in a list form for a particular event.
We have:
A number cube with faces labeled from 1 to 6 will be rolled once.
Let S is the sample space:
As we know, the sample space is the set of all possible outcomes:
S = {1, 2, 3, 4, 5, 6}
The total number of outcomes:
n(S) = 6
The outcomes for the event of rolling the number 2.
E = {2}
n(E) = 1
Thus, the sample space S = {1, 2, 3, 4, 5, 6} describing all possible outcomes and outcomes for the event of rolling the number 2 is E = {2}
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How do you solve this?
[tex]\text{L.H.S}\\\\=\begin{vmatrix} 1 & bc& b+c\\ 1 & ca& c+a\\ 1 &ab&a+b\end{vmatrix}\\\\\\=\begin{vmatrix} 1 & bc& b+c-(a+b+c)\\ 1 & ca& c+a-(a+b+c)\\ 1 &ab&a+b-(a+b+c)\end{vmatrix}~~~~~~~~~~~~~~~;c_3\rightarrow c_3 -(a+b+c)c_1\\\\\\=\begin{vmatrix} 1 & bc& -a\\ 1 & ca& -b\\ 1 &ab&-c\end{vmatrix}\\\\\\=\dfrac 1{abc}\begin{vmatrix} a & abc& -a^2\\ b & abc& -b^2\\ c &abc&-c^2\end{vmatrix}\\\\\\=-\dfrac {abc}{abc}\begin{vmatrix} a & 1& a^2\\ b & 1& b^2\\ c &1&c^2\end{vmatrix}\\[/tex]
[tex]=-1\begin{vmatrix} a & 1& a^2\\ b & 1& b^2\\ c &1&c^2\end{vmatrix}\\\\\\=-1 \times -1 \begin{vmatrix} 1 & a& a^2\\ 1 & b& b^2\\ 1 &c&c^2\end{vmatrix}\\\\\\=\begin{vmatrix} 1 & a& a^2\\ 1 & b& b^2\\ 1 &c&c^2\end{vmatrix}\\\\\\=\text{R.H.S}\\\\\text{Showed.}[/tex]
A bank converts U.S. dollars to European euros at a rate of $1 for 0.88 euros. Kelsey wants 100 euros for her trip to Europe.
How much money, in dollars, does Kelsey need to give the bank
Answer:
$113.64
Step-by-step explanation:
0.88 x $113.636364 = 100 euros
= $113.64
(Hope this helps ^-^)
An amusement park charges $5 as an admittance fee and $1.50 per ride. Jason has $20 to spend, but used $3 to buy a
drink and hot dog.
A. Write an inequality that represents the situation,
B. What is the maximum number of rides Jason can go on.
Answer:
a=
b=8
Step-by-step explanation:
20-5=15 (admittance fee)
15-3=12 (food and drink)
12÷1.5=8 rides because 1.50 is price for every ride
need help as soon as possible
5. If the longer side of the rectangle is 25.5 in., what are its width, perimeter, and area?
Step-by-step explanation:
1) The width of the rectangle is 10.2 in.
2) The perimeter of the rectangle is 71.4 in.
3) The area of the rectangle is 260.1 sq.in
Find the inequality represented in the graph.
Answer: y > -1/2x + 2
Step-by-step explanation: first, in order to find the inequalities you should find the gradient by choosing two points from the line and you should you the formula m=y2-y1/x2-x1 to find the gradient.
Next, you should find the y-intercept in order to complete the inequality it can be easily found as the y-intercept is the place where the line crosses the y axis
Then you create your equation { y = -1/2x + 2 } and then if above the line is shaded then it is {> greater than} and if below the line is shaded then it should be {< less than}
(so you should replace the equation with the lesser or greater sign according to the way the graph is shaded)
Without simplifying, find:
a) the 6th term of (2x+5)^15
b) the 4th term of (x^2+5/x)^9
Answer:
Part A)
[tex]\displaystyle z_6 = 9609600000x^{10}[/tex]
Part B)
[tex]z_4 = 10500 x^9[/tex]
Step-by-step explanation:
Recall the binomial expansion theorem:
[tex]\displaystyle (x+y)^n = \sum_{k=0}^{n}{n \choose k} x^{n-k} y^k[/tex]
Part A)
Our expression is equivalent to:
[tex]\displaystyle (2x+5)^{15} = \sum_{k = 0}^{15} {15 \choose k} (2x)^{15-k}\cdot 5^k[/tex]
To find the sixth term, let k = 5. Therefore, the sixth term is:
[tex]\displaystyle \begin{aligned} z_6 &= {15\choose 5} (2x)^{15-5}\cdot 5^5 \\ \\ & = {15\choose 5}x^{10} \cdot (2)^{10}\cdot 5^5 \\ \\ &= 9609600000x^{10}\end{aligned}[/tex]
Part B)
Likewise:
[tex]\displaystyle \begin{aligned} \left(x^2 + \frac{5}{x}\right)^9 = \sum_{k=0}^9 {9\choose k}(x^2)^{9-k}\left(\frac{5}{x}\right)^{k}\end{aligned}[/tex]
To find the fourth term, let k = 3. Therefore, the fourth term is:
[tex]\displaystyle \begin{aligned} z_4 & = {9\choose 3}\left(x^2\right)^{9-3} \left(\frac{5}{x}\right)^{3} \\ \\ & = {9\choose 3}x^{12} \cdot \frac{5^3}{x^3} \\ \\ & = 10500x^9\end{aligned}[/tex]
Solve for x. Calculate the area
Answer:
32 sq inches
Step-by-step explanation:
Hope that given shape is a rectangle.Measures of the opposite sides of a rectangle are equal-> x/2 = 8->x = 8*2-> x = 16 inches-> x/4 = 16/4 = 4 inchesA (rectangle) = 8*4 = 32 sq inchesA model plane weighs 150 grams, rounded to the
nearest ten grams.
How much could the plane weigh?
Answer:
its 150
Step-by-step explanation:
the "ten" is 5 to round it it will have to be the number to the right, which is 0 if its below 4 its changed to 0 and nothing happens to the ten
It's always a good idea to check your solutions to any equation in the original equation. When solving an absolute value equation, when must you check for extraneous solutions?
A. Sometimes, when u only get one solution
B. Never
C. Always
D. Sometimes, when the variable appears both inside and outside the absolute value expression
You should must check for an extraneous solution when the variable appears both inside and outside the absolute value expression
What is an extraneous solution?
An extraneous solution is a solution that in obtained after completely solving an equation but it does not work in the original given equation.
You should must check for an extraneous solution when the variable appears both inside and outside the absolute value expression (Option D).
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What is value of x in the equation 6x+7-2x=3+5x-9
Answer: x = 13
Step-by-step explanation: First, we simplify the equation to get 4x + 7 = 5x - 6. Then, from there, we subtract 7 on both sides to get 4x = 5x - 13. Then we subtract 5x from both sides, which would give us -x = -13. Finally, we can divide both sides by -1 (because remember, x = 1) to get that x = 13. Hope this helps!
Find the solution to each system please show your work!
Answer:
infinite number of solutions
Step-by-step explanation:
x + y = 1 → (1)
3y = - 3x + 3 ( add 3x to both sides )
3x + 3y = 3 ( divide through by 3 )
x + y = 1 → (2)
since the 2 equations are the same, this indicates the system has an infinite number of solutions
PLease HELP!!! 20 POINTS!!! WILL GIVE BRAINLIEST!!!
Which of the following is the equation of the quadratic function below?
10
-10
10
O A. y = x² +9x-18
OB. y=x²-2x+1
C. y=x²-9x+18
OD. y=x²+2x-1
-10
Answer:
ehhhh probably C cuz it makes more sense
Karen purchased a used vehicle that depreciates under a straight line method the initial value if the car is 4400 and the salvage value is 800 if the car is expected to have a useful life of another six years how much will it depreciate each year?
Answer:
Karen expects the vehicle to depreciate by 600 each year.
Step-by-step explanation:
Given:
- initial value: 4400
- salvage value: 800
- another six years
It is expected to depreciate from 4400 to 800 in 6 years.
The depreciation per year is the ratio
depreciation per year = (total depreciation) / (number of years)
Total depreciation is the change in value, so the depreciation per year is
(4400 - 800)/6 = 600
B Christian installed an electric pump to pump water from a borehole into a 30 000 litre cement dam. If the water is pumped at a rate of 75 litres per minute. How long does it take to fill the dam?
A.4 h
B.6 h 40 min
C.6 h 20 min
D.3h 40 min
Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.
Option B)6h 40min is the correct answer.
How long does it take to fill the dam?Given that;
Amount of water needed to fill the dam A = 30000 litresPump rate r = 75 litres per minuteTime needed to fill the dam T = ?To determine how long it take to fill the dam, we say;
Time need = Amount of water needed ÷ Pump rate
T = A ÷ r
T = 30000 litres ÷ 75 litres/minute
T = 400 minutes
Note that; 60min = 1hrs
Hence,
T = 6hours 40minutes
Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.
Option B)6h 40min is the correct answer.
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A plane has a speed of 840 km/h in still air. It can travel 3120 km with the wind in the same time it would take to travel 1920 km against the wind. Find the speed of the wind.
Answer:
200 KM/H
Step-by-step explanation:
A plane has a speed of 840 km/h in still air. It can travel 3120 km with the wind in the same time it would take to travel 1920 km against the wind. Find the speed of the wind.
let x=speed of wind
(840+x)=speed of plane with wind
(840-x)=speed of plane against wind
Travel time = distance/speed (same with and against the wind)
3120/(840+x)=1920/(840-x)
cross-multiply
3120*840-3120x=1920*840+1920x
3120*840-1920*840=1920x+3120x
5040x=1008000
x=200 km/hr
answer
Speed of wind=200 km/hr
Find the measure of side b
Answer:
230??
Step-by-step explanation:
If C =270°
And b=40°
270-40= 230
Actually belive the one on top
please, I really need this answer the soon as possible. I'm going to be so thankful if anyone could help me with this...
Answer:
5/6
Step-by-step explanation:
i'm not rly confident,, but i used a calculator and solved it,,
so im sry if im wrong. Good luck!!
Find the 5th term of the sequence which has a first term of 1 and has a common ratio of 2.3. Round your answer to the nearest hundredth if necessary.
The 5th term of the sequence is 27.98
How to determine the 5th term?The given parameters are:
First term, a = 1Common ratio, r = 2.3The nth term of a geometric sequence is calculated using:
[tex]T_n = ar^{n-1[/tex]
So, we have:
[tex]T_5 = 1 * 2.3^{5-1[/tex]
Evaluate the difference
[tex]T_5 = 1 * 2.3^4[/tex]
Evaluate the product
[tex]T_5 = 27.98[/tex]
Hence, the 5th term of the sequence is 27.98
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Write the ratio 6 mm: 180 cm in the form 1:n
The ratio in the form of 1 :n is 1:300.
What is a ratio ?Ratio of two number A and B is the comparison of A with respect to B and when two ratios are equal they are said to be in proportion.
It is given that a ratio is
6mm : 180cm
It has to be simplified in the form of
1:n
1 cm = 10mm
therefore
180 cm = 1800 mm
6mm:180cm = 6/ 1800
= 1/300
Therefore the ratio in the form of 1 :n is 1:300.
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if f(x) = 4x²-2 then f(-2) is
3(2x-9) - 4(3x + 4) = 2(x − 12) + 7/3
pls answer the question
Answer:
[tex]\normalsize \textsf{$x = -\dfrac{8}{3}$}[/tex]
Step-by-step explanation:
Given: [tex]\normalsize \textsf{$3(2x - 9) - 4(3x + 4) = 2(x - 12) + \dfrac{7}{3}$}[/tex]
1. Distribute
For 3:
[tex]\normalsize \textsf{$3(2x - 9)$}\\\normalsize \textsf{$3(2x) + 3(- 9)$}\\\normalsize \boxed{\textsf{$6x -27$}}\\[/tex]
For -4:
[tex]\normalsize \textsf{$-4(3x + 4)$}\\\normalsize \textsf{$-4(3x) + -4(4)$}\\\normalsize \boxed{\textsf{$-12x -16$}}\\[/tex]
For 2:
[tex]\normalsize \textsf{$2(x - 12)$}\\\normalsize \textsf{$2(x) + 2(-12)$}\\\normalsize \boxed{\textsf{$2x -24$}}\\[/tex]
Now we have: [tex]\normalsize \textsf{$6x - 27 - 12x -16 = 2x-24 + \dfrac{7}{3}$}[/tex]
2. Combine like terms:
[tex]\normalsize \textsf{$-6x -43 = 2x -\dfrac{72}{3} + \dfrac{7}{3}$}\\\\\normalsize \textsf{$-6x -43 = 2x -\dfrac{65}{3}$}\\\\[/tex]
3. Subtract 2x from both sides:
[tex]\normalsize \textsf{$-6x-2x -43 = 2x -2x -\dfrac{65}{3}$}\\\\\normalsize \textsf{$-8x -43 = -\dfrac{65}{3}$}\\\\[/tex]
4. Add 43 to both sides:
[tex]\normalsize \textsf{$-8x -43 +43 = -\dfrac{65}{3} + 43$}\\\\\normalsize \textsf{$-8x = -\dfrac{65}{3} + \dfrac{129}{3}$}\\\\\normalsize \textsf{$-8x = \dfrac{64}{3}$}[/tex]
5. Divide both sides by -8
[tex]\normalsize \textsf{$-8x = \dfrac{64}{3}$}\\\\\normalsize \textsf{$-8x \div 8 = \dfrac{64}{3} \div -\dfrac{8}{1}$}\\\\\normalsize \boxed{\textsf{$x = -\dfrac{8}{3}$}}[/tex]
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brainly.com/question/27543580brainly.com/question/27759148The financial planner for a beauty products manufacturer develops the system of equations below to determine how many combs must be sold to generate a profit. the linear equation models the income, in dollars, from selling x plastic combs; the quadratic equation models the cost, in dollars, to produce x plastic combs. according to the model, for what price is each comb being sold?
The income that's made based on the equation when 1 comb is sold is $0.5.
How to calculate the price?From the information given, the equation is given as y = x/2. In this case, it was illustrated that the income is depicted based on the combs sold.
Therefore, the income by selling 1 comb will be:
y = 1/2
y = $0.5
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2.5. For his homework Thulani defined a factor as: "Factors of a number are formed when the number is multiplied by 1; 2; 3; 4". You realise that Thulani has a misconception when it comes to factors and multiples. (5)
Answer:
yes of course it was a question about the same as you can use it for a while now I am with you forever
NEED ASAP
What is the rule for the function that is graphed?
Answer:
C
Step-by-step explanation:
The y-intercept if the graph is 2 and the slope is 2 so the rule is y=2x+2
What is the perimeter of triangle JKL (same triangle as question #1)?
Answer:
x=30
Step-by-step explanation:
You have to use intercept theorem, also known as Thales's theorem to slvoe this.
Solve 7p+ 13 = 30 Give your answer as a fraction in its simplest form.
Answer: p = 2 3/7
Step-by-step explanation:
7p+13 = 30
7p = 17
p = 17/7
p = 2 3/7
A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
The value of p as a fraction in its simplest form is 17/7
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
Example:
1/2, 1/3 is a fraction.
2/4 is a fraction but we can simplify further since there is a common factor of 2 with 2 and 4.
2/4 = 1/2 is a fraction.
4/16 = 4/(4x4) = 1/4 is a fraction.
We have,
7p + 13 = 30
Solve for p.
Subtract 13 on both sides.
7p + 13 - 13 = 30 -13
7p = 17
Divide both sides by 7.
p = 17/7
We can not further simplify the fraction as there are no common factors between 17 and 7.
Thus,
The value of p as a fraction in its simplest form is 17/7
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If y varies directly as x and y = 8 when x = 4, what is the value of y when x = 16? a. 32 b. 16 c. 64 d. 28
By finding the proportional relation between x and y, we will see that when x = 16, we have y = 32.
How to get the value of y when x = 16?If y varies directly with x, then we can write the relation as:
y = k*x
Where k is the constant of proportionality.
First, we know that when x = 4, we have y = 8, replacing that we get:
8 = k*4
Solving for k, we get:
k = 8/4 = 2.
Then the relation between x and y is:
y = 2*x
When x = 16, we have:
y = 2*16 = 32
Then the correct option is a.
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