Step-by-step explanation:
If two lines have the same slope and the same y-intercept, there are infinite solutions.
If two lines have the same slope and different y-intercepts, there are zero solutions.
Otherwise, if the two lines have different slopes, then there is one solution.
The slope of the first line is 3/8. The slope of the second line is 16/32 = 1/2. The slopes are different, so there is only one solution.
The solution of the given system of equations is (x, y) = (8.75, 2).
What is a Linear equation of two variables?These are the system of equations with two variables having a no solution, unique solution or infinitely many solutions.The highest order of the equation for this systems is one.Given: System of equations
3x - 8y = 10 …(1)
16x - 32y = 75 …(2)
Consider equation (2).
⇒ 16x - 32y = 75
Dividing both sides by 16, we get:
⇒ x - 2y = 75/16
⇒ x = 2y + 75/16 …(3)
Now, substitute the value of x = 2y + 75/16 in equation (1), we get:
⇒ 3(2y + 75/16) - 8y = 10
⇒ 6y + 225/16 - 8y = 10
⇒ 2y = 225/16 - 10
⇒ 2y = (225 - 160)/16
⇒ 2y = 65/16
⇒ y = 65/32
⇒ y ≈ 2
Now, put the value of y = 65/32 in equation (3), we get:
⇒ x = 2(65/32) + 75/16
⇒ x = (65/16) + (75/16)
⇒ x = 140/16
⇒ x = 8.75
Therefore, the solution for the given simultaneous equation is;
(x, y) = (8.75, 2)
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What would 489,000,000,000,000,000 in scientific notation
A rectangle that is 4 inches by 6 inches has been scaled by a factor of 7 . What are the side lengths of the scaled copy ?
Step-by-step explanation:
step one:
The question is incomplete it did not specify weather the scale was a reduction or an increase in the dimension of the rectangle.
step two:
let us assume it was to be an increase i.e 7x
the length would be 4*7= 28 inches
the width would be 6*7= 42 inches
step three:
Also, we assume it was to a decrease i.e 7x
the length would be 4/7= 0.57 inches
the width would be 6/7= 0.85 inches
By what number should 1 1/2 be divided to get 2/3 ? *
Answer:
1
Step-by-step explanation:
1) The equation is 1 1/2 ÷ x = 2/3
2) You can multiply 2/3 with 1 1/2 to get your answer
3) 2/3 × 1 1/2 = 1
Hope this helps!
While on vacation in Canada, you notice that temperatures are reported in degrees Celsius. You know there is a linear
relationship between Fahrenheit and Celsius, but you forget the formula. you remember the freezing point of water is 0°C
or 32°F and its boiling point is 100°C or 212°F
a Write an equation that represents degrees Fahrenheit in terms of degrees Celsius. Let x represent the temperature in degrees Celsius and
let y represent the temperature in degrees Fahrenheit
Since , the relation is linear .
Let equation is y = mx + c .
Putting , x = 0 and y = 32 .
32 = c .......( 1 )
Also , putting x = 100 and y = 212 .
We get :
212 = 100m + c .......( 2 )
Comparing equation 1 and 2 .
100m = 212 - 32
x = 1.8
Therefore , y = 1.8x + 32 .
Hence , this is the required solution .
[tex]y=\dfrac{9}{5}x+32[/tex] represents degrees Fahrenheit in terms of degrees Celsius. where x represent the temperature in degrees Celsius and y represents the temperature in degrees Fahrenheit.
Temperature can be expressed in different units like degrees Celsius and degrees Fahrenheit.
Let us consider two variables x and y as following:
x represent the temperature in degrees Celsius
y represent the temperature in degrees Fahrenheit
Equation depicting relation between variable x and y is
[tex]y-y_1=m(x-x_1)[/tex]...........................1
where, [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Using the given conditions:
[tex](x_1,y_1)=(0,32) \text{\ and\ }(x_2,y_2)=(100,212)[/tex]
Substituting to calculate the value of m,
[tex]m=\dfrac{212-32}{100-0}\\\\m=\dfrac{180}{100}\\\\m=9/5[/tex]
From equation 1
[tex]y-32=\dfrac{9}{5}(x-0)\\y-32=\dfrac{9}{5}x\\y=\dfrac{9}{5}x+32[/tex]
Thus, an equation that representing degrees Fahrenheit in terms of degrees Celsius is [tex]y=\dfrac{9}{5}x+32[/tex].
Learn more about unit conversion, here:
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What is the next two items in the row?
-1
2
5
8
Box 1
Box 2
Select the correct answer from each dropdown menu.
Box 1
[ Select ]
Box 2 [Select]
20 pts
Answer:
12, 15 would be the next two in that order
Please help on number 9 and 10. Will mark brainliest.
Answer:
9. 1.24 mL
10. $5.93
Step-by-step explanation:
Question 9:
If the dosage of medicine is 0.01 mL per pound of weight of the patient, and the patient's weight is 124 pounds, we can set up an equation to solve for how much medicine the patient would need to take:
Dosage of medicine per pound of body weight x Total body weight = Total medicine required
OR
0.01 * w = m,
where w is total body weight and m is total medicine required.
To solve for the dosage the patient needs, just plug the numbers into the right places (124 for w and leave m as it is):
0.01 * 124 = m
1.24 = m
Therefore, a patient with a body weight of 124 pounds would need a 1.24 mL dosage.
Question 10:
To make the multiplication easier, we could rewrite 15% as 0.15 ( because 15% = 15/100):
0.15 * Total bill = Total tax payed for bill (Also can be written as [tex]\frac{15}{100} * 39.51[/tex])
OR
0.15*39.51 = Total tax
5.9265 = Total tax
5.93 = Total tax <-------- (rounded)
Find the axis of symmetry f(x) = 2x2 - 4x.
Answer:
x=1
Step-by-step explanation:
The function graph is a parabola (branches pointing up). Vertex (1; -2). The graph is symmetrical about the x axis = 1
[tex]f(x)=2x^{2} -4x \\x_{0} =-b/2a=-(-4)/(2*2)=1\\f(1)=-2\\[/tex]
4+10=-2(8x-7) this dosent make any sence to me. can someone help me out
Answer: x=0
Step-by-step explanation:
(you are trying to find x)
4+10=-2(8x-7)
2+5=(8x+7)
7=(8x+7)
0=8x
x=0
Pls rate this brainliest
pls help i need help
Answer:
4.69, hope this helps, Thank you
What is 8.325 rounded to the nearest hundredth?
Answer:
8.3
Step-by-step explanation:
hope it helps
f f(x) = 0, what is x?
0 only
–6 only
–2, 1, or 3 only
–6, –2, 1, or 3 only
At Nancy's Newsstand, 3 magazines cost $15.00. How many magazines could you buy with $45.00?
Answer:
9
Step-by-step explanation:
If three magazines cost $15 then that means that each magazine costs $5. So we do 5 divided by 45 which equals 9. SO the answer is 9!
If you are happy with my answer I would like branliest:)
Suppose S is between R and T. Use the Segment Addition Postulate to solve for the variable. Round to three decimal places. RS = 9y − 2 ST = y + 7 RT = 26
Answer:
The variable y = 2.100
Step-by-step explanation:
Here, we are told to solve for the variable y.
We are asked to use the segment addition postulate. In summary, the postulate is of the opinion that given 3 points X,Y and Z, we can only say that these 3 points are collinear(lie on the same line) if they obey the formula below;
XZ = XY + YZ
Now, we have that S is between R and T.
Mathematically that means;
RT = RS + ST
from the question, we are told that RT = 26, RS = 9y-2 and ST = y + 7
Now, insert these values into the alphabetical equation;
26 = (9y-2) + (y + 7)
26 = 9y-2 + y + 7
26 = 9y+y -2 + 7
26 = 10y + 5
26-5 = 10y
10y = 21
y = 21/10
y = 2.1
Which is y = 2.100 to three decimal places
find the distance between (-6,4) and (-2,1)
Answer:
[tex]d=2.65[/tex]
Step-by-step explanation:
Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2-(y_2-y_1)^2}[/tex]
Simply plug in your 2 coordinates into the formula to find distance d:
[tex]d=\sqrt{(-2-(-6))^2-(1-4)^2}[/tex]
[tex]d=\sqrt{(-2+6))^2-(-3)^2}[/tex]
[tex]d=\sqrt{(4)^2-9}[/tex]
[tex]d=\sqrt{16-9}[/tex]
[tex]d=\sqrt{7}[/tex]
[tex]d=2.65[/tex]
Mario and his family are discussing how to pay for his college
education. The cost of tuition at the college that Mario wants to attend is
$7,500 per year. Mario's parents will pay 60% of the tuition cost every
year, and Mario will pay the rest. Mario has two years to save enough
money to attend his first two years of college. What is the minimum
amount of money he should save every month in order to reach his goal?
Answer:
$250 per month for 2 years
Step-by-step explanation:
evaluate the expression -8 + (-15)
Hey there!
ANSWER: [tex]-23[/tex]EXPLANATION:[tex]-8+(-15)[/tex]
To easily solve this, try removing the negative and add 8 + 15.
[tex]8+(15)=23[/tex]
Now add back the negative.
[tex]-8+(-15)=-23\\-23(ANSWER)[/tex]
Hope this helps and have a great weekend!
[tex]\text {-TestedHyperr}[/tex]
Use the order of
operations to evaluate
the expression
(-8X14)-(-2X-10)
Answer:
the order of operations is .called BODMAS rule
B.brackets
O.of
D.division
M.multiplication
A.addition
S.subtraction
Step-by-step explanation:
= (-112)-(20)
= -132
Find the slope of the line that passes through point (2,8) and point (9,7).
Answer:
m = -1/7
Step-by-step explanation:
7 - 8 = -1
9 - 2 = 7
m = -1/7
Which letter represents the first number in an ordered pair?
Step-by-step explanation:
Example: (5,2)
On a graph, the 5 goes on the x-axis and the 2 goes on the y-axis.
Also, in the world of variables, and the alphabet, x is before y.
So x represents the first number in an ordered pair.
hope it helps!
-7k + 5(6k + 5) < 209
Answer:
k < 8
Step-by-step explanation:
-7k + 30k + 25 < 209
23k < 209 - 25
23k < 184 /: 23
k < 8
If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ÷)
A hockey game had 2,058 fans Friday night. The baseball game has 1,300 fans that night. How many more fans were at the hockey game?
Subtract the number at the baseball game from the hockey game:
2058 - 1300 = 758
There was 758 more people at the hockey game.
Answer:
758 more fans were there
Step-by-step explanation:
Difference = Hockey fans - Baseball fans
= 2058 - 1300
= 758
(-1,0) (-10,-1) find coordinates
Answer:
Use a graph calculator
Step-by-step explanation:
Omar is playing a computer game. He starts with 0 points, wins 8 points, loses 6 points 4 times, and then wins 2 points. Which integer represents Omar’s score? –30 –14 16 34
The answer is -14. 0+8 =8 8 - (6x4) = - (-16 + 2 = -14
Answer:
-14
Step-by-step explanation:
QUICK NEED HELP FAST 60 POINTS TWO WHOEVER ASNWERS FIRST
State the domain and range of the given relation
(-4,3), (-1,-4), (0, -4), (2, 3), (3, -3) (4, 7)
Answer:
work is shown and pictured
y=2x+3 help please ...
Answer:
x=-3/2
y=3
Step-by-step explanation:
i hope this helps
Answer:
x=2x+3 Improper question not enough details The only answer can be found right now is 3x+3
Step-by-step explanation:
Combine like terms and give me brainliest please
find the area of the isosceles triangle.
Answer:
60 cm
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
Which is greater?
[tex]4 \sqrt{20} [/tex]
or
[tex] \sqrt{40} [/tex]
Answer:
4√20
Step-by-step explanation:
√40 = √4 * √10 = 2√10
4√20 > 2√10
then:
the greater is:
4√20
Polygon ABCD is a przimage of an enlargement with a scale factor of 3 and a
total area of 4. What is the total area of the enlarged image?
i dont think you have a whole question down and we need examples of the triangles so please shw examples
Answer:
hi not sure you need this still but its 36
Step-by-step explanation
a Number m plus 4 is greater than or equal to seven
Answer:
m ≥ 3
m is greather or equal to 3
Step-by-step explanation:
m + 4 ≥ 7
m ≥ 7 - 4
m ≥ 3