Solve this system of linear equations. -14x + 11y = 23 7x - 3y = 37
x=? y=?
To solve the linear system given by -14x + 11y = 23 and 7x - 3y = 37, we used the elimination method, which resulted in finding the solution x = 13.6 and y = 19.4.
Explanation:To solve the system of linear equations given by -14x + 11y = 23 and 7x - 3y = 37, you can use the method of substitution or elimination. Here, I'll demonstrate the elimination method:
Multiply the second equation by 2 to make the coefficients of x in both equations equal in magnitude but opposite in sign:Therefore, the solution to the system of equations is x = 13.6 and y = 19.4.
First four terms of f(n)=3n-1
The first four terms of the function f(x) = 3n - 1 are 2, 5, 8, and 11.
Given,
f(n) = 3n - 1
We need to find the first four terms.
What is a function?A function has an input and an output.
Example:
f(x) = x + 1
x = 1,2,3 are inputs.
f(1) = 1 + 4 = 5
f(2) = 2 + 4 = 6
f(3) = 3 + 4 = 7
5, 6, and 7 are the outputs.
We have,
f(n) = 3n - 1
We can assume that the first four terms can be found with n= 1,2,3,4.
f(1) = 3 x 1 - 1 = 3 - 1 = 2
f(2) = 3 x 2 - 1 = 6 - 1 = 5
f(3) = 3 x 3 - 1 = 9 - 1 = 8
f(4) = 3 x 4 - 1 = 12 - 1 = 11
Thus the first four terms of the function f(x) = 3n - 1 are 2, 5, 8, and 11.
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[2/(n+2)] - (3/n+2) = 5
Solve by u-substitution
(6v^3+42v)/(2v^2+26v+84)
4. Making financial decisions is fairly rare; most people make only a few during their lifetime. True False
A fair coin is tossed four times. what is the probability that the sequence of tosses is hhtt?
A hummingbird can travel up to 15 meters per second. What is the hummingbird's speed in miles per hour? 1 mile ≈ 1609 meters Enter your answer, as a decimal to the nearest tenth, in the box.
there are 3600 seconds per hour
15 * 3600 = 54000 meters per hour
54000/ 1609 = 33.56
round to 33.6 miles per hour
The speed of Hummingbird's in miles per hour is 8,153.6463 mph.
What is speed-distance formula?Speed = Distance/Time – This tells us how slow or fast an object moves. It describes the distance travelled divided by the time taken to cover the distance. Speed is directly Proportional to Distance and Inversely proportional to Time. Hence,Distance = Speed X Time, and
Time = Distance / Speed, as the speed increases the time taken will decrease and vice versa.Given:
A hummingbird can travel up to 15 meters per second.
As,
1 m/s= 2.23694 mph
So, 15 m/s= 15 * 2.23694
= 8,153.6463 mph
Hence, the speed in mph is 8,153.6463.
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What’s he hypotenuse, x, if ( 20, 21,x) is a Pythagorean triple?
Answer:
B) - 29
Step-by-step explanation:
Over a 8 week period, the price of an MP3 player dropped steadily, from $82 to $26. What is the average weekly change in the price of the MP3 player over this period?
4(2x - 5) + 15 = 11 Write the steps you will use to solve the equation and explain each step.
The table shows the pricing for four different types of gasoline. Type Cost A $20.20 for 10 gal B $26.04 for 12 gal C $28.14 for 14 gal D $30.45 for 15 gal Which type costs the least per gallon?
The bottom answer is incorrect
The answer is C.$28.14 for 14 gal
Given a standard deck of cards, what is the probability of drawing a face card, given that it is a red card?
Help pleeeeease
Theo deposited $1,250 in a savings account that pays 6% interest, compound quarterly. What was his balance at the end of the second quarter after the interest had been added?
A. $1,270.31
B. $1,270.65
C. $1,290.62
D. $1,287,78
Please explain your answer clearly! and explain how you got it!
On an uphill hike, Ted climbs at a rate of 3 miles an hour. Going down, he runs at a rate of 5 miles an hour. If it takes him 40 minutes longer to climb up than run down, what is the total length of Ted's hike?
So the other guy has the right work but at the end he messed up. The real answer is 10 miles.
By establishing the relationship between Ted's uphill and downhill travel times, we can set up an equation to solve for the one-way distance D of the hike. We find that the one-way distance D is 5 miles, making the total length of the hike 10 miles.
Explanation:On an uphill hike, Ted climbs at a rate of 3 miles an hour. Going down, he runs at a rate of 5 miles an hour. If it takes him 40 minutes longer to climb up than run-down, we need to figure out the total length of Ted's hike.
First, let's establish the relationship between the times it takes Ted to hike up and run down the hill. If T is the time it takes to run down, then the time to hike up is T + 40/60 hours (since 40 minutes is two-thirds of an hour).
Let D be the distance of the hike one way. As Ted climbs up at a rate of 3 miles per hour, the uphill time is D/3. Running down at a rate of 5 miles per hour, the downhill time is D/5. We can set up the following equation:
D/3 = D/5 + 40/60
Multiplying through by 15 to eliminate fractions, we get:
5D = 3D + 10
This simplifies to:
2D = 10
Dividing by 2:
D = 5 miles
Since the total hike involves going up and then down the same distance, the total length of the hike is:
Total Length = 5 miles + 5 miles = 10 miles.
Write the first 4 terms in the sequence defined by the explicit rule f(n)=n^2 - 5 *n^2 means n squared
Problem page two trains leave stations 390 miles apart at the same time and travel toward each other. one train travels at 65 miles per hour while the other travels at 85 miles per hour. how long will it take for the two trains to meet
Teds needs a average of at least 70 on his three history test. he has already scored 85 and 60 on two test. what is the minimum grade ted needs on his third test
What is the greatest common factor for 96, 72 48?
the height of a triangle is 4 times its base. if he are of a triangle is 200cm, what is the height
The sum of two numbers is 39 . the smaller number is 13 less than the larger number. what are the numbers
The required numbers are given as 26 and 13.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
here,
let the number be x and y,
According to the question,
x + y = 39 - - - - (1)
x = y + 13 - - - - - (2)
Put value from equation 2, in equation 1
y + y + 13 = 39
2y = 39 - 13
y = 26/y
y = 13
Now,
x = 13 + 13
x = 26
Thus, the required numbers are given as 26 and 13.
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You are playing a video game. For each diamond you collect, you earn 80 points. You also earn 100 bonus points by completing the level in less than 2 minutes. You need to earn more than 1220 points to continue on to the next level. Write and solve an inequality that represents the numbers dd of diamonds you must collect in less than 2 minutes to advance to the next level.
Given
For each diamond you collect, you earn 80 point
earn 100 bonus points by completing the level in less than 2 minutes.
earn more than 1220 points to continue on to the next level
Find the inequality that represents the numbers dd of diamonds you must collect in less than 2 minutes to advance to the next level.
To proof
As given in the question
For each diamond earn point = 80
bonus points by completing the level in less than 2 minutes = 100
earn more than 1220 points to continue on to the next level
Let us assume that the number of diamond = d
The inequality written in the form
we get
[tex]80d + 100 \geq 1220[/tex]
now solving the above equation
[tex]80d \geq1120[/tex]
[tex]d \geq14[/tex]
Thus the numbers of diamonds you must collect in less than 2 minutes to advance to the next level be 14.
Hence proved
Using the figure below A) What is the length of A'B'? B) Show your work/ explain how you got your answer. Question 10 options:
Which statement is true about regular exercise? 1.It decreases your resting heart rate.
2.It decreases your lung capacity.
3.It decreases your intelligence.
4.It increases your blood pressure.
Answer:
got correct on edmentum mastery test, hope this helps
A bakery sells packages of 6 cupcakes for $10. If the bakery starts selling the cupcakes in packages of 12, how much would you expect a packet of 12 to cost?
How to find the slope intercept form of the equation using another line in slope intercept form and a point for the line?
Answer:
IF the other line is parallel you use the same slope (m) as the line given then find the y intercept (b) by plugging in the (x,y) and m into y = mx + b
Step-by-step explanation:
if angle A has a measurement of 42 degree and is complementary to angle B whats the measurement of angle B
solve 7d + d - 4d - 7 - 5d
Which statement is true? @jimthompson5910
An isosceles triangle has a perimeter of 82 cm. The lengths of the legs of the triangle are represented by (3x +2) and (5x-14). Find the length of the base of the triangle.
The triangle's base measures 82 in length.
What is the Permeter of a traingle?
The perimeter of any polygon is equal to the sum of its side lengths. Considering a triangleSum of the three sides equals the perimeter.Units are always a part of the ultimate response. The final solution should be given in centimeters if the triangle's sides are in that unit.According to our question,
IF (3X+2) & (5X-14) ARE THE EQUAL SIDES THEN
3X+2=5X-14
-2X=-16
X=-16/-2
X=8
THUS THE EQUAL SIDES ARE
3*8+2=24+2=26
5*8-14=40-14=26
SO
82=BASE+26+26
BASE=82-52
B=30 CM.
30+26+26=82
82=82
Hence we can say that the triangle's base measures 82 in length.
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Final answer:
The lengths of the two legs of the isosceles triangle are equal, and by setting the expressions for these lengths equal to each other and solving for 'x', we find that the length of the base of the triangle is 30 cm.
Explanation:
The perimeter of an isosceles triangle is given as 82 cm. The two legs are represented by the expressions (3x + 2) and (5x - 14). Since it is isosceles, these two expressions must be equal because the lengths of the legs are equal, as stated by the theorem.
First, set the expressions equal to each other to find the value of 'x':
3x + 2 = 5x - 14
We then solve for 'x' by subtracting 3x from both sides and adding 14 to both sides:
16 = 2x
x = 8
After finding 'x', we can determine the length of one of the equal sides by substituting 'x' back into either of the original expressions:
Length of one side = 3x + 2 = 3(8) + 2 = 26 cm
Since we have two sides of the same length, we multiply by 2 to find the total length of the two legs:
Total length of two legs = 26 cm imes 2 = 52 cm
To find the length of the base, subtract the total length of the two legs from the perimeter:
Length of the base = 82 cm - 52 cm = 30 cm.
Therefore, the length of the base of the isosceles triangle is 30 cm.
The function f(x) = ax^3 -x^2 + bx -24 has three factors. Two of these factors are x-2 and x+4. Determine the values of a and b, then determine the other factor. (My Nelson Advanced Functions Grade 12 book chapter 3)
Please help :)
The roots of any equation, always satisfies that equation.
Values of , a = - 2 and b = 22
Other factor of given function is (x - 3/2)
The given function [tex]f(x) = ax^3 -x^2 + bx -24[/tex]
Since, (x - 2) and (x + 4) are factors of given function
Therefore, x = 2 and x = -4 satisfies the given function.
[tex]f(2)=8a-4+2b-24=0\\8a+2b=28\\\\f(-4)=-64a-16-4b-24=0\\-64a-4b=40\\-16a-b=10[/tex]
Now , solving above two equation by elimination method
We get, a = -2 and b = 22
So, [tex]f(x) = -2x^3 -x^2 + 22x -24[/tex]
To find other factors , we divide above function by multiplication of (x - 2)(x+4).
So we get other factors, (x - 3/2)
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