The solution is x = 7 and y= 3
Solution:
Given pairs of equation are:
x = 1 + 2y ------- eqn 1
2x + y = 17 ------- eqn 2
We have to use algebraic method
Algebraic method involves substitution and elimination method
Let us use the substitution method
From equation 1, we can see that x is equal to 1 + 2y. If we substitute this for y in equation 2, we have:
2(1 + 2y) + y = 17
Solve for brackets
2 + 4y + y = 17
Combine the like terms which has same variable
2 + 5y = 17
5y = 17 - 2
5y = 15
Divide both sides of equation by 5
y = 3
So the value of y is 3. This value of y can be substituted into either equation 1 or 2 to find the value of x
Substitute y = 3 in eqn 1
x = 1 + 2(3)
x = 1 + 6
x = 7
So the solution is x = 7 and y = 3
An apartment building currently has rented x apartments with two occupants and 16 apartments with one occupant. The apartment building has 92 total occupants.
2× + 16 = 92
How many double-occupancy apartments are currently rented?
38 double-occupancy apartments are currently rented
Solution:
Given that, apartment building currently has rented x apartments with two occupants and 16 apartments with one occupant
Number of apartments with one occupant = 16
Number of apartments with two occupants = x
The apartment building has 92 total occupants
Therefore, we frame a equation as,
Number of apartments with one occupant + 2 x Number of apartments with two occupants = 92
[tex]16 + 2 \times x = 92[/tex]
16 + 2x = 92
Solve the above equation for "x"
2x = 92 - 16
2x = 76
x = 38
Thus 38 double-occupancy apartments are currently rented
Final answer:
To determine the number of double-occupancy apartments that are currently rented, we solve the equation: 2x + 16 = 92. After simplifying, we find that there are 38 double-occupancy apartments rented.
Explanation:
To determine the number of double-occupancy apartments that are currently rented, we need to solve the equation: 2x + 16 = 92.
First, we subtract 16 from both sides of the equation: 2x = 76.
Next, we divide both sides of the equation by 2 to isolate x: x = 38.
Therefore, there are 38 double-occupancy apartments currently rented.
The number of seahorses is 4 times the number of sea urchins.There are 16 seahorses write and solve and equation to find how many seahorses are there.
Answer:
[tex]4\ sea\ urchins[/tex]
Step-by-step explanation:
The correct question is
The number of seahorses is 4 times the number of sea urchins.There are 16 seahorses write and solve and equation to find how many sea urchins are there.
Let
x ----> the number of seahorses
y ----> the number of sea urchins
we know that
The number of seahorses is 4 times the number of sea urchins
so
[tex]x=4y[/tex] -----> equation A
There are 16 seahorses
so
[tex]x=16[/tex] ----> equation B
Solve the system by substitution
substitute equation B in equation A
[tex]16=4y[/tex]
solve for y
divide by 4 both sides
[tex]y=16/4\\y=4\ sea\ urchins[/tex]
Answer:
4.
Step-by-step explanation:
if 4 is the number of Urchins 4*4 is 16 which is how many seahorses there are.
PROBABILITY DISTRIBUTIONS?? Do anyone know how to find probabilities??
Probability of more than 3 = 0.25
Solution:
Given table shows the pitches, frequency and probability of pitches.
P(x = 1) = 0.15, P(x = 2) = 0.2, P(x = 3) = 0.4, P(x = 4) = 0.15, P(x = 5) = 0.1
To find the probability that the pitcher will throw more than 3 pitches.
Probability of more than 3 pitches = P(x > 3)
= P(x = 4) + P(x = 5)
= 0.15 + 0.1
= 0.25
P(x > 3) = 0.25
Hence the probability that the pitcher will throw more than 3 pitches to a batter is 0.25.
Final answer:
Probability distributions are used to assess the likelihood of different outcomes in a given set of data. To find probabilities, you need to determine the type of probability distribution and use the appropriate formulas or tables.
Explanation:
Probability distributions are used to assess the likelihood of different outcomes in a given set of data. They can take different shapes depending on the nature of the population. One common type of probability distribution is the normal distribution, which represents a bell curve.
To find probabilities using a probability distribution, you can follow these steps:
Determine the type of probability distribution you are dealing with, such as binomial or normal.Identify the values or events for which you want to find probabilities.Use the appropriate formulas or tables to calculate the probabilities, considering factors such as mean and standard deviation.mon Core Algebra I A-CR
The graph of f(x) = (x - h\ + k contains the points (-6, -2)
and (0, -2). The graph has a vertex at (h, -5). Describe
how to find the value of h. Then, explain how this value
translates the graph of the parent function.
Answer:
h = -3
The value h = -3 translates the graph of the parent function [tex]y=x^2[/tex] 3 units to the left.
Step-by-step explanation:
The graph of [tex]f(x)=(x-h)^2+k[/tex] contains the points (-6, -2) and (0, -2).
This is the equation of parabola in vertex form, where [tex](h,k)[/tex] are the coordinates of the vertex.
If the graph has a vertex at [tex](h,-5),[/tex] then [tex]k=-5.[/tex]
So, the equation of the parabola is
[tex]f(x)=(x-h)^2-5[/tex]
If the graph passes through the points (0,-2) and (-6,-2) (these two points lie on the same horizontal line y = -2), then the parabola vertical line of symmetry divides the segment between these points into two congruent segments. Hence, the equation of the line of symmetry is
[tex]x=\dfrac{0+(-6)}{2}=-3[/tex]
The vertex lies on the line of symmetry, so its x-coordinate is -3. Thus, (-3,-5) is the vertex.
The value h = -3 translates the graph of the parent function [tex]y=x^2[/tex] 3 units to the left.
Answer:
Sample Response: The absolute value function is symmetric. Since the points (–6, –2) and (0, –2) have the same output, the points are the same distance from the line of symmetry. Between –6 and 0 is the value of –3. So, the vertex must have an x-coordinate of –3, which is the value of h. This would translate the graph of the parent function 3 units to the left.
I will mark brainliest
Answer:
A) 2x+50
Step-by-step explanation:
First, let's make a variable for each person
Sam = x
Hector = h
Ted = t
Gina = g
We know that Hector has twice the amount hat Sam has so his equation is
h = 2x
We know that Ted has 100 more than Hector so his equation is
t = h + 100
Gina has 50 less than Ted to she has
g = t - 50
Since we need to find out how much Gina has using units of Sam the equation will be
g = 2x + 100 - 50 or simplified g = 2x + 50
The measure of an angle is 135 degrees. What is the measure of its supplementary angle ?
Remember that if two angles are supplementary, then the sum of their measures is 180°. So if the measure of an angle is 135 degrees. What is the measure of its supplement?
If the measure of an angle is 135°,
then the measure of its supplement is 45°.
We can find the measure of its supplement by taking 180 minus the measure of the original angle which in this case is 180 - 135 or 45°.
Final answer:
The measure of the supplementary angle to a 135-degree angle is 45 degrees, calculated by subtracting 135 degrees from 180 degrees.
Explanation:
The measure of an angle is 135 degrees. Supplementary angles are two angles whose measures add up to 180 degrees. To find the measure of the supplementary angle, we subtract the given angle's measure from 180 degrees. Here's the calculation:
Identify the measure of the given angle (135 degrees).Subtract the measure of the given angle from 180 degrees: 180 degrees - 135 degrees = 45 degrees.The measure of the supplementary angle is therefore 45 degrees.An equation for the depreciation of a car is given by y = A(1-r), where y = current value of the car, A = original cost, r = rate
of depreciation, and t = time, in years. The current value of a car is $12,282.50. The car originally cost $20,000 and
depreciates at a rate of 15% per year. How old is the car?
Answer:
Step-by-step explanation:
y = A(1 - r)^t......y = value of car after t years.....A = original cost....r = rate of depreciation.....t = time in years
y = 12,282.50
A = 20,000
r = 15% = 0.15
12,282.50 = 20,000(1 - 0.15)^t
12,282.50 / 20,000 = 0.85^t
0.614125 = 0.85^t
log 0.614125 = t * (log(0.85))
t = (log 0.614125) / (log 0.85)
t = 3 <=== 3 years old
Answer:
C. 3 years
Step-by-step explanation:
I can confirm that the answer to your question is C.
Please help I will mark brainliest
Answer:
10
Step-by-step explanation:
The square length of hypotenuse is equal to two sides' length square added together
C = 10^2 + 7.5^2 = √156 approximately 12.5
The answer is 10 if needed to round to nearest tenth.
just 3 math problem show step by step
1 5x+y=-12
5x-7y=4
2. -5x+4y=-3
-9x-y=-30
3. -9x+6y=27
-x+3y=10
please help me out
Answer:
see attached picture please
Which situation is best represented by the following equation?
40w + 12.50 = 492.50
A) Nicole paid $40 for self-defense classes. She paid a $12.50 registration fee and $492.50 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
B) Nicole paid $12.50 for self-defense classes. She paid a $492.50 registration fee and $40 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
C) Nicole paid $492.50 for self-defense classes. She paid a $40 registration fee and $12.50 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
D) Nicole paid $492.50 for self-defense classes. She paid a $12.50 registration fee and $40 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
Eliminate
Final answer:
The equation 40w + 12.50 = 492.50 best represents Nicole paying $40 per week for self-defense classes, plus a one-time registration fee of $12.50, totaling $492.50.
Explanation:
The situation best represented by the equation 40w + 12.50 = 492.50 is option A) Nicole paid $40 for self-defense classes. She paid a $12.50 registration fee and $492.50 for each week she was enrolled in the classes. Here, w represents the number of weeks Nicole was enrolled in self-defense classes. The equation can be understood as follows: $40 is multiplied by the number of weeks (w), and $12.50 is added for the registration fee, summing to a total of $492.50.
PLEASE HELP ME PLEASE HELP PLEASE IF YOU HAVE A HEART! What do you know about yourself as a learner?
How can you use this information to help you succeed in math?
Answer:
Hope this helps!
Step-by-step explanation:
1. Do all of the homework. ...
2. Fight not to miss class. ...
3. Find a friend to be your study partner. ...
4. Establish a good relationship with the teacher. ...
5. Analyze and understand every mistake. ...
6. Get help fast. ...
7. Don't swallow your questions. ...
8. Basic skills are essential.
Simplify. (x^4)^3
Write your answer without parentheses.
Answer:
x^12
Step-by-step explanation:
The system of equations is graphed on the coordinate plane.
y=−12x−1y=14x−4
Enter the coordinates of the solution to the system of equations in the boxes.
(
,
)
A graph with a blue line passing through coordinates (0, -4) and (4, -3) and a red line passing through coordinates (0, -1) and (4, -3).
Answer:
Step-by-step explanation:
y = -12x - 1
y = 14x - 4
-12x - 1 = 14x - 4
-1 + 4 = 14x + 12x
3 = 26x
3/26 = x
y = 14x - 4
y = 14(3/26) - 4
y = 42/26 - 4
y = 42/26 - 104/26
y = - 62/26 reduces to - 31/13
solution : x = 3/26 and y = -31/13 or (3/26,-31/13)
Which expression are equivalent 10
Answer:
I believe the answer to this question is: B.
Answer: The first part is the 2nd & 4th.
The second part is the 1st & 3rd.
Step-by-step explanation:
Edge 2021
There is a bag with 7 blue marbles and 4 orange marbles. You pull a marble out of the bag three times, without replacing the marble each time. What is the probability that you will pull out 3 blue marbles?
a. 0.64
b. 0.56
c. 0.27
d. 0.21.
Answer:
Answer D
Step-by-step explanation:
Answer:Option D
Step-by-step explanation:
Savanah solved the equation 3 + 4|3 plus 4 StartAbsoluteValue StartFraction x Over 2 EndFraction plus 3 EndAbsoluteValue equals 11. + 3| = 11 for one solution. Her work is shown below:
Answer:
x=-2 OR x=-10 i.e.
Solution Set = {-2,-10}
Step-by-step explanation:
The equation described in words is typed and solved below:
[tex]3+4|\frac{x}{2}+3|=11 \\4|\frac{x}{2}+3|=11-3\\4|\frac{x}{2}+3|=8\\|\frac{x}{2}+3|=\frac{8}{4} \\|\frac{x}{2}+3|=2\\\frac{x}{2}+3=2 OR \frac{x}{2}+3=-2\\\frac{x}{2}=2-3 OR \frac{x}{2}=-2-3\\\frac{x}{2}=-1 OR \frac{x}{2}=-5\\x=-2ORx=-10\\[/tex]
Answer:
it is -10
Step-by-step explanation:
What is 6/6 equivalent to
Answer:
1 whole
Step-by-step explanation:
Answer:1
Step-by-step explanation:You have 6 sixths. That means it is a whole number
Identify the x-intercept and y-intercept of a line with the equation -3x+6y=12 and use these points to graph the line below.
Answer:
x-intercept: -4
y-intercept: 2
Step-by-step explanation:
ax+by=c
divide c by a and then c by b
-3x+6y=12
X-intercept: 12/-3= -4
Y-intercept: 12/6=2
Answer:
Step-by-step explanation:
if ur gonna graph it, u should put it in y = mx + b form
-3x + 6y = 12
6y = 3x + 12
y = 3/6x + 12/6
y = 1/2x + 2
in y = mx + b form, the slope is in the m position, and the y int is in the b position.
y = mx + b
y = 1/2x + 2.....so ur slope (which will help u in graphing) is 1/2, and ur y intercept is 2 or (0,2) <===
u could also find ur y intercept by subbing in 0 for x and solving for y...in ur original equation.
to find ur x intercept, sub in 0 for y and solving for x
-3x + 6y = 12
-3x + 6(0) = 12
-3x = 12
x = -12/3
x = -4...so ur x int is -4 or (-4,0) <=====
What is the simplified expression of 8 times y times 9
Answer:
72y
Step-by-step explanation:
Multiplication can be done in any order
8x9=72
72 times y is 72y
What value of x is in the solution set of 2(3x - 1) = 4x - 6?
Answer:
x=-2
Step-by-step explanation:
[tex]2(3x - 1) = 6x - 2 = 4x - 6 \\ 2x = - 4 \\ x = - 2[/tex]
95-a (b+c) when a=9, b= 3, and c = 7.4
Step-by-step explanation:
95-a (b+c)
95-9 (3+7.4)
95-9×10.4
95-93.6
=1.4
Answer: 894.4
Step-by-step explanation:
95-9(3+7.4)
⬇️
95-9 (10.4)
⬇️
86(10.4)
⬇️
894.4
What is the answer to -2(3x+2)=2x+6
Answer:
x=-5/4
Step-by-step explanation:
-2(3x+2)=2x+6
-6x-4=2x+6
-6x-2x-4=6
-8x-4=6
-8x=6+4
-8x=10
x=10/-8
x=-10/8
simplify
x=-5/4
Jared made 12 3/4 cups of snack mix for cups of snack mix for a party. His guests are 2/3 of the mic. How much snack mix did his guests eat.
a. 4 5/12
b. 4 1/2
c. 8 1/2
d 12 5/7
Answer:
8 1 /2
For this we need to determine what
2 /3 of 12 3/4 is, so we multiply the fractions together.
The Johnsons need to put up a fence, as shown in the picture. They have already measured two of the sides. Find the length of the missing side of the farmyard (round to two decimal places). A) 17.00 feet B) 27.00 feet C) 32.15 feet D) 46.77 feet
Answer:
D
Step-by-step explanation:
its D for sure
Answer:
d
Step-by-step explanation:
46.77 feet Use the Pythagorean theorem.
Find the equation of the line normal to the curve of y=cos1/3x, where x=pi
Answer:
The equation of the line normal to the curve of y=cos1/3x, where x=pi is y= 2√3 x - 10.38
Step-by-step explanation:
The equation of the normal to the curve is
Y- y1 = - 1/m (x- x1)
Where m is the gradient.
See attached picture for the complete solution.
The equation of the line normal to the curve of y=cos(1/3)x, where x=pi, can be found by taking the negative reciprocal of the derivative of the curve at that point and using the point-slope form of a line.
Explanation:The equation of the line normal to the curve of y=cos(1/3)x at x=pi can be found by taking the negative reciprocal of the derivative of the curve at that point.
The derivative of cos(1/3)x is -sin(1/3)x*(1/3).
At x=pi, the derivative is -sin(pi/3). Taking the negative reciprocal of this gives the slope of the line normal to the curve
So the slope is 1/ tan(pi/3).
Now, we can use the point-slope form of a line to find the equation of the line.
The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope.
Plugging in the values, we get y - cos(pi/3) = (1/tan(pi/3))(x - pi).
Simplifying further will give us the equation of the line normal to the curve at x=pi.
A playground is in the shape of a square. If the perimeter of the playground is 40 feet, find the diagonal distance across the park. Leave your answer in radical form
The length of diagonal of park is √200 feet.
Step-by-step explanation:
Given,
Perimeter of square playground = 40 feet
Let,
a be the length of one side.
Perimeter = 4a
[tex]4a=40\\\\a=\frac{40}{4}\\\\a=10[/tex]
Length of one side of square is 10 feet.
A diagonal will form a right triangle, where,
Diagonal = c
a = 10
b = 10
Using pythagoras theorem
[tex]a^2+b^2=c^2\\(10)^2+(10)^2=c^2\\100+100=c^2\\200=c^2\\c^2=200[/tex]
Taking square root on both sides
[tex]\sqrt{c^2}=\sqrt{200}\\c=\sqrt{200}[/tex] feet
The length of diagonal of park is √200 feet.
Keywords: perimeter, square
Learn more about perimeter at:
brainly.com/question/9045597brainly.com/question/8955867#LearnwithBrainly
Answer:
10√2 (Simplest Radical Form)
Step-by-step explanation:
While Absor201 got √200, it is still not in simplest radical form. If you got this question from MathNation, then 10√2
Can someone show me how to do this please?
⦁ A sculptor is planning to make two triangular prisms out of steel. The sculptor will use for the bases of one prism and for the bases of the other prism.
⦁ Is similar to ? Explain.
⦁ Suppose the sculptor makes both prisms with the same height. Which prism will have a greater volume? How many times greater? Show your work.
Answer:
Answer:
they are similar as the enlargement has a scale factor divide it then woke it out
The United States Postal Service charges a
"nonmachinable surcharge" for first-class mail
If the length of the envelope (parallel to the
address) divided by the height of the envelope
is less than 1.3 or more than 2.5. Charlene has
an envelope with a height of 3.5 inches. Write
a compound inequality to show the lengths in
inches for which Charlene will have to pay the
surcharge.
Graph the solutions.
Answer:
Step-by-step explanation:
1.3 < Length/3.5 < 2.5
4.55 < Length < 8.75
Graph:
|-----------------|
| |
| |
| |
| |
| |
| |
| 4.55 -------- 8.75 |
| |
| |
| |
| |
| |
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|-----------------|
Expression for the calculation the sum of the product of 4 and 3 and 1 and 1
Answer:
(4 × 3) + (1 × 1)
Step-by-step explanation:
Sum means adding, so you are adding the product of 4 and 3 to the product of 1 and 1.
Product means multiplying, so you are multiplying 4 and 3 together, and since you just want an expression, this is expressed as 4 × 3.
You are also multiplying 1 and 1 together, so that can be expressed by 1 × 1.
Since you are adding these together, you just put a plus sign in between the two terms. That gives you (4 × 3) + (1 × 1).
12. Noah raised $54 to support the animal shelter, which is 60% of his fundraising goal.
a. Write an algebraic equation to represent the situation.
b. What is Noah's fundraising goal?
To represent the situation algebraically, we use the equation 54 = 0.60G, and solving it gives us Noah's fundraising goal of $90.
Let's represent Noah's fundraising goal as G. According to the problem, Noah has raised $54, which is 60% of his goal. This situation can be translated into the algebraic equation:
54 = 0.60GTo find Noah's fundraising goal (G), we can divide both sides of the equation by 0.60:
G = 54 ÷ 0.60G = $90Therefore, Noah's fundraising goal is $90.