Answer:
y = -2 and x = 4
Step-by-step explanation:
8x + 14y = 4
-6x - 7y = -10
First, find the lowest common multiple of 8 and 6 (which is 24). Multiply the first equation by 3:
8x + 14y = 4
3(8x + 14y) = 3(4)
24x + 42y = 12
Multiply the second equation by 4:
-6x - 7y = -10
4(-6x - 7y) = 4(-10)
-24x - 28y = -40
Now, add the two equations together:
24x + 42y = 12
-24x - 28y = -40
24x + -24x = 0
42y + -28y = 14y
12 + -40 = -28
14y = -28
Divide both sides by 14:
14y ÷ 14 = -28 ÷ 14
y = -2
Plug this known variable back into the first equation:
8x + 14(-2) = 4
8x + (-28) = 4
8x - 28 = 4
Add 28 to both sides:
8x - 28 + 28 = 4 + 28
8x = 32
Divide both sides by 8:
8x ÷ 8 = 32 ÷ 8
x = 4
So y = -2 and x = 4.
Hope this helps!
A mass oscillating up and down on the bottom of a spring (assuming perfect elasticity and no friction or air resistance) can be modeled as harmonic motion. If the weight is displaced a maximum of 6 cm, find the modeling equation if it takes 4 seconds to complete one cycle. Be to show, illustrate and explain your work.
The motion of the mass as it moves on the bottom of the spring is a
repetitive motion.
[tex]\mathrm{The \ motion \ of \ the \ mass \ attached \ to \ the \ spring \ is \ }\displaystyle d = 6 \cdot sin\left(\frac{\pi}{2} \cdot t \right)[/tex]Reasons:
The general form of the equation of the simple harmonic motion of the
mass is d = a·sin(ω·t)
Where;
d = The distance of the mass from the rest position
a = The maximum displacement of the mass from the equilibrium position = 6 cm
ω = The frequency of rotation
t = The time of motion
ω = The frequency of rotation
[tex]\displaystyle \omega = \mathbf{\frac{2 \cdot \pi}{T}}[/tex]
Where;
T = The time to complete one cycle (the period of oscillation) = 4 seconds
[tex]\displaystyle \omega = \frac{2 \cdot \pi}{4} = \frac{\pi}{2}[/tex]
Combining the above values gives the modelling equation as follows;
[tex]\displaystyle d = 6 \cdot sin\left(\frac{\pi}{2} \cdot t \right)[/tex]
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what is the equation of line that passes through(-6,-3) and is parrelel to the line 5x-3y=9
Answer:
y+3=5/3(x+6)
Step-by-step explanation:
Since it is parallel to 5x-3y=9, you need to find the slope of that line because then you would find the slope to your line.
5x-3y=9
5x=9+3y
5x-9=3y
y=5/3x-3, and the slope would be 5/3.
Now you can apply point slope form [tex]y-y_{1}=m(x-x_{1} )[/tex] to get an equation.
y+3=5/3(x+6)
Answer: [tex]\frac{5}{3}[/tex]x + 7
Step-by-step explanation:
Marsha watched 1 4 of a movie in the morning, and she watched some more at night. By the end of the day, she still had 1 3 of the movie left to watch. How much of the movie did Marsha watch at night?
A company sells three types of gift baskets. The basic basket has two movie passes and one package of microwave popcorn, and costs $15.50. The medium basket has two movie passes, two packages of microwave popcorn, and one DVD, and costs $37. The super basket has four movie passes, three packages of microwave popcorn, and two DVDs, and costs $72.50.
Create a system of equations and solve using matrices to find the price of each basket item.
The price of each movie is $7, the price of each microwave popcorn is $1.50 and the price of each DVD is $20.
Let x represent the cost of each movie, y represent the cost each microwave and z represent the cost of each DVD.
For the basic:
2x + y = 15.50 (1)
For medium:
2x + 2y + z = 37 (2)
For super:
4x + 3y + 2z = 72.50 (3)
[tex]\left[\begin{array}{ccc}2&1&0\\2&2&1\\4&3&2\end{array}\right] \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}15.5&37&72.5\end{array}\right] \\\\\\ \left[\begin{array}{c}x&y&z\end{array}\right] =\left[\begin{array}{ccc}2&1&0\\2&2&1\\4&3&2\end{array}\right]^{-1}\left[\begin{array}{c}15.5&37&72.5\end{array}\right]\\\\\\ \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}7&1.5&20\end{array}\right] =[/tex]
The price of each movie is $7, the price of each microwave popcorn is $1.50 and the price of each DVD is $20.
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4(x+6)=3x-7 please could you help me
Hello!
Let's use the Distiributive property:
4(x+6)
4x+24
4x+24=3x-7
Move all the variables to the left:
4x-3x=-7-24
x=-31
Hope this helps!
~Just a determined gal
#CarryOnLearning
[tex]MysteriousNature[/tex]
The table shows a set of points on a line. What is the slope of the line?
Answer:
-3
Step-by-step explanation:
take a set of points (2,3) (3,-6)
[tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{-6-(-3)}{3-2}[/tex]
[tex]\frac{-3}{3-2}[/tex]
[tex]\frac{-3}{1}[/tex]
-3
Which equation has the solution x = 5?
Select each correct answer.
18−2x=9
x/5+5=6
32−4x=12
11 + 6x = 22
3x + 1 = 9
25/x+4=9
FOR A BRAINLST PLS BE ACCURATE
Answer:
the answer is the third
hope it help
the maximum speed of a car is 252 km/h change this speed into meters per second
Answer:
70.0000000001 meters per second
Step-by-step explanation:
The formula is to multiply by the factor 0.27777777777817.
252 km/h * 0.27777777777817 = 70.0000000001
How to solve quadratic inequalities.
Find all the zeros of the polynomial, and arrange the zeros in increasing order. ...
Plot those numbers on the number line as open or closed points based upon the original inequality symbol.
Choose a test value in each interval to see if the interval satisfies the inequality or not.
Solve for q
a-q=a+sx
Answer: q = -sx
Step-by-step explanation:
Round 0.817446 to the ten-thousandths place. Please I need this fast!!!!
Describe the signs (positive/negative) of the coordinate in each of the regions shown below. Then give one point contained within each region.
Answer:
A = positive
B = positive, negative
C = negative
D = positive, negative
Answer:
A Positive coordinates (5,5) B Negative and Positive coordinates (-5,5) C Negative coordinates (-5,-5) D Negative and Positive coordinates (5,-5)
Step-by-step explanation:
Pls mark brianlist hope this helps .
Determine whether 5^25m^2 • 5^25m is equivalent to each of the following expressions.
I’ll give brainliest
Answer:
None of the listed expressions
Step-by-step explanation:
Using the Product Law of Exponents, we can simplify 5^25m^2 • 5^25m into 5^(25m^2 + 25m).
Simplify:
5^25m(m + 1)
In this case, none of the following responses are equivalent. The first two are incorrect because you can't add variables that are set to different powers and the last one is incorrect because if you wanted to change the base from 5 to 25, you would divide the exponent by 2 instead of take the square root.
Answer:
Step-by-step explanation:
A graph representing a proportional relationship goes through the origin:
Question 2 options:
Always
Sometimes
Never
When it feels like it
The graph representing a proportional relationship ALWAYS goes through the origin (0, 0).
Recall:
A proportional relationship graph represents a relation between two variables that are directly proportional to each other.In a proportional graph, the constant of proportionality, k, remains the same.The graph attached below shows a proportional graph between time and water used.In the proportional relationship graph, the line goes through the origin (0, 0) as shown in the image attached below.
Therefore, the graph representing a proportional relationship ALWAYS goes through the origin (0, 0).Learn more about proportional relationship on:
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Answer these question
c = 1 > 7 =
According to very reliable sources.
Which expression uses the associative property to make it easier to evaluate
6.)?
O A. (6)
O B. (6-3);
OC. 6(3)
OD D. 3(5.5)
9514 1404 393
Answer:
B
Step-by-step explanation:
The associative property just moves parentheses, without changing the values or order of the operands. The only expression for which that is true is ...
B. (6·1/3)·7/5
In a parallelogram ABCd, angle a + angle b = ?
Answer:
180
Step-by-step explanation:
Easy way: they're conjugate angles relative to the two parallel sides and the trasversal joining them, their sum is 180.
Longer(??) way: In a parallelogram two opposite angles are congruent. Since the sum of the internal angles is 360, a pair of two different angles must sum to 180.
Step-by-step explanation:
In a Parallelogram ABCD , ∠ A + ∠B = 180°
Since , The Adjacent angles in a Parallelogram are Supplementary.
Additional comment:
• In a Parallelogram, Opposite angles are equal
•The sum of two adjacent angles is 180° called Linear pair.
HELP!!
Formula
Y=___x +___
Answer:
look at the slope rise of 2 run of -1 or other way around so slope is
[tex] y = - \frac{2}{1}x + 5[/tex]
Point C has a _____ abscissa and a _____ ordinate.
positive, negative
positive, positive
negative, positive
negative, negative
Answer:
i think its b but im not that sure
Step-by-step explanation:
you plan to purchase a plane ticket $299.00and you are going to use a discount code to receive 15% off
Answer: The answer is $254.15
The temperature at 1 AM is "-10F." The temperature drops 3 degrees per hour for 4 hours. What is the temperature at 5AM?
Answer:
-13
Step-by-step explanation:
Answer:
-22 F
Step-by-step explanation:
basically since iy drops 3 degrees for 4 hours multiply -3 times 4 to get -12. Once you get that add to the original temperature to get your answer :) hope this helped be sure to mark me brainliest and rate :)
You can buy a seat cushion at the College Softball World Series for $4. They
paid $2.50 to have them made, and they make a profit of $300 when sold out.
How many seat cushions did they have made?
Answer:
$118.40
2.50x Plus 4 Equal 300
2.50x Equal 296
2.50x/2.50 Equal $118.40
PLEASE TELL ME IF I AM WRONG!The bookstore sold coloring books for $4. They are on sale for $1. Find the percent decrease.
Step-by-step explanation:
4 -1=3 so 4divided by 3= 1.33 so 1.33 as a percent is 133%
(-5)^-2
Please help me
Answer:
0.04
Step-by-step explanation:
Answer:
0.05
Step-by-step explanation:
don't want to write it
what is the answer ?????
Q. 1 [tex] \frac{19}{20} \times 100 = 19 \times 5 = 95\% \\ [/tex]
Q. 2). 30 - 24 = 6
[tex] \frac{6}{30} \times 100 = \frac{1}{5} \times 100 = 20 \\ [/tex]
Xavier wants to order CDs online. Each CD costs $17.50 and shipping is $4. He only has $90 to spend.
If 2/15 is 40 then 1/15 is?
(Sorry I know this is a easy question but my brain isn't processing the question right now so I need help)
Answer:
20
Step-by-step explanation:
[tex]\frac{2}{15}[/tex] = 40
[tex]\frac{2}{15}[/tex] ÷ [tex]\frac{2}{1}[/tex] = [tex]\frac{1}{15}[/tex]
40 ÷ [tex]\frac{2}{1}[/tex] = 20
For every 1000 veiws a tv showgets it makes £2 from ad revenue.
How many veiws are required to make £21?
Answer:
10500 views.
Step-by-step explanation:
If 1000 views is £2 then 500 views would be £1 so 2 x 10 = 20 so 10,000 views and 500 more to make it £21 pounds.
1D. The least prime that is the sum of four different prime numbers is 17 because 17 = 2 + 3 + 5 + 7. What is the least prime greater than 17 that is the sum of four different prime numbers?
The least prime greater than 17 that is the sum of four different prime numbers is 23
The least prime that is the sum of four different prime numbers is 17
That is, 17 = 2 + 3 + 5 + 7
Prime numbers greater than 17 are 23, 29, 31. 37, 41,........
Prime numbers less than 17 are 2, 3, 5, 7, 11, 13
How can we combine the prime numbers 2, 3, 5, 7, 11, and 13 to give the least prime number greater than 17
The only possible combination is:
2 + 3 + 7 + 11 = 23
Therefore, the least prime greater than 17 that is the sum of four different prime numbers is 23
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