Given:
The system of equations is
[tex]3x-2y=7[/tex]
[tex]6x-4y=14[/tex]
To find:
The correct statement for the given system of equations.
Solution:
On comparing the given equations and general form of linear equation, i.e., [tex]ax+by+c=0[/tex], we get
[tex]a_1=3,b_1=-2,c_1=-7[/tex]
[tex]a_2=6,b_2=-4,c_2=-14[/tex]
Here,
[tex]\dfrac{a_1}{a_2}=\dfrac{3}{6}=\dfrac{1}{2}[/tex]
[tex]\dfrac{b_1}{b_2}=\dfrac{-2}{-4}=\dfrac{1}{2}[/tex]
[tex]\dfrac{c_1}{c_2}=\dfrac{-7}{-14}=\dfrac{1}{2}[/tex]
Since, [tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}[/tex], therefore, the two equations are equivalent and the system has infinitely many solutions.
Hence, the correct option is b.
twice the greater of two integers odd integers is 13 less than 3 times the lesser number. find the integers. what are the integers to this riddle?
Answer:
17 and 19
Step-by-step explanation:
n= lesser integer n+2= greater integer
2(n+2) = 3n -13
2n +4 = 3n-13
n= 17
lesser number =17
The other greater number = 19 (they are odd,so skipping 18)
19 x 2 = 38
17x3 - 13 =51-13 = 38
Given the sum of the interior angles of a polygon, tell the number of sides of the polygon.
If the interior angle sum is 360°, the polygon has _
sides.
If the interior angle sum is 540°, the polygon has _
sides.
If the interior angle sum is 900°, the polygon has _
sides.
If the interior angle sum is 1260°, the polygon has _
sides.
Answer:
[tex] \underline{the \: sides \: are} \: \to \\ \underline{ \boxed{ n= 4}} \\ \: \underline{ \boxed{ n= 5}} \\ \:\underline{ \boxed{ n= 7}} \\ \: \underline{ \boxed{ n= 9}} \\ \: [/tex]
Step-by-step explanation:
[tex] \\ the \: sum \:o f \: the\: interior \: angles \: of \: aregular \: polygon \: \\ is \: generaly \: given \: by \to \: 180(n - 2)\\ \underline{ \boxed {case \:( 1) \to}} \\ If \: the \: interior \: angle \: sum \: is \: 360°, \\ then : \: the \: polygon \: has \to \: \\ 180(n - 2) = 360 \\ n - 2 = 2 \\ \underline{ \boxed{ n= 4}} \\ \: \underline{ \boxed {case \:( 2) \to}} \\ If \: the \: interior \: angle \: sum \: is \: 540°, \\ then : \: the \: polygon \: has \to \: \\ 180(n - 2) = 540 \\ n - 2 = 3 \\ \underline{ \boxed{ n= 5}} \\ \: \underline{ \boxed {case \:( 3) \to}} \\ If \: the \: interior \: angle \: sum \: is \: 900°, \\ then : \: the \: polygon \: has \to \: \\ 180(n - 2) = 900 \\ n - 2 = 5 \\ \underline{ \boxed{ n= 7}} \\ \: \underline{ \boxed {case \:(final ) \to}} \\ If \: the \: interior \: angle \: sum \: is \: 1260°, \\ then : \: the \: polygon \: has \to \: \\ 180(n - 2) = 1260 \\ n - 2 = 7\\ \underline{ \boxed{ n= 9}} \\ \: [/tex]
♨Rage♨
Answer:
4,5,7,9
Step-by-step explanation:
Got it right on edge
solve each system of equations using substitution. x=y+1 x=3y+2
Answer:
x=1/2
y=-1/2
Step-by-step explanation:
x = y+1
x = 3y+2
Substitution means that you solve one equation for a variable by plugging it into the other equation. In this case, the first part is already done for you, and all you have to do is plugging in.
As you're given the value of the x in both equations, it does not matter which equation you plug into. You can plug either equation into one another.
For this, I will show you by plugging in the bottom equation for the top equation.
x = y+1
x = 3y+2
As we know x=3y+2, you must SUBSTITUTE that for the "x" in the top equation.
3y+2 = y+1
From there, you must solve it for the "y" value. In order to solve for the "y" value, you must get the "y" by itself onto one side.
So, subtract y from both sides.
(3y-y)+2 = (y-y)+1
Rewrite the equation.
2y+2 = 1
Remember, the goal is to get the "y" BY ITSELF.
There's a "+2" on the side of the y, so that has to be cancelled out. You can cancel it out by doing the OPPOSITE of adding, which is subtracting. So subtract both sides by 2.
2y+(2-2)=(1-2)
When subtracting a bigger number from a smaller number. The pattern is: Keep it, flip it, flip it.
Keep the 1.
Flip the - to a +
Flip the 2 into a -2.
So you get 1+(-2) which is -1. Now, rewrite the equation.
2y=-1
You want the y by itself. Right now, the y is being multiplied by 2, so you have to do the OPPOSITE, which is division. Divide both sides by 2.
y=-1/2
Now, use this value to plug into your ORIGINAL equations (you can pick either)
x = y+1 OR x = 3y+2
x= -1/2 + 1
x=1/2
(1/2, -1/2)
HELP WILL GIVE BRAINLIEST
Answer:
A. 2000 square inches
B. 53.1 square inches
help
i dunno it
please please
Answer:
it takes 24 days
A construction crew has repaired 1.37 miles of a highway. The total length of the highway to be repaired is 7.9. How many miles are left to be repaired?
Answer:
Part A: m+1.37=7.9
Part B: 6.53 miles are left to be repaired.
Step-by-step explanation:
Given,
Length of repaired part = 1.37 miles
Total length to be repaired = 7.9 miles
Miles left to be repaired = m
Part A:
Create an equation to show the relationship between the number of miles repaired and the number of miles left to be repaired, m.
Miles left to be repaired + Length of repaired part = Total length to be repaired
m+1.37=7.9
Part B
How many miles are left to be repaired?
Subtracting 1.37 from both sides
6.53 miles are left to be repaired.
Keywords: length, subtraction
Step-by-step explanation:
Find the product. Write your answer as a mixed number in simplest form. 5 2/9 x 2 3/7
Answer:
12, 43/63
Step-by-step explanation:
Answer: 12 43/63
Step-by-step explanation: it was correct on my test
4y - 9 - 6y = 2(y + 5) - 3 solve for y
Answer:
[tex] \huge{ \boxed{ \bold{ \tt{y = - 4}}}}[/tex]
Step-by-step explanation:
[tex] \sf{4y - 9 - 6y = 2(y + 5) - 3}[/tex]
Subtract like terms : 6y from 4y
[tex] \longrightarrow{ \sf{ - 2y - 9 = 2(y + 5) - 3}}[/tex]
Distribute 2 through the parentheses
[tex] \longrightarrow{ \sf{ - 2y - 9 = 2 *y + 2 *5 \: - 3}}[/tex]
[tex] \longrightarrow{ \sf{ - 2y - 9 = 2y + 10 - 3}}[/tex]
Subtract 3 from 10
[tex] \longrightarrow{ \sf{ - 2y - 9 = 2y + 7}}[/tex]
Move 2y to left hand side and change it's sign
[tex] \longrightarrow{ \sf{ - 2y - 2y - 9 = 7}}[/tex]
Move 9 to right hand side and change it's sign
[tex] \longrightarrow{ \sf{ - 2y - 2y = 7 + 9}}[/tex]
Combine like terms
[tex] \longrightarrow{ \sf{ - 4y =7 + 9}}[/tex]
Add the numbers : 7 and 9
[tex] \longrightarrow{ \sf{ - 4y = 16}}[/tex]
Divide both sides by -4
[tex] \longrightarrow{ \sf{ \frac{ - 4y}{ - 4} = \frac{16}{ - 4}}} [/tex]
Remember : Dividing a positive integer by any negative integer gives a negative integer.
[tex] \longrightarrow{ \boxed{ \sf{y = - 4}}}[/tex]
------------------------------------------------------------
Let's check whether the value of y is -4 or not.
VerificationL.H.S : [tex] \sf{4y - 9 - 6y}[/tex]
plug the value of y and simplify
[tex] \dashrightarrow{ \sf{4 * (- 4 )- 9 - 6 * (- 4)}}[/tex]
[tex] \dashrightarrow{ \sf{ - 16 - 9 - ( - 24)}}[/tex]
[tex] \dashrightarrow{ \sf{ - 16 - 9 + 24}}[/tex]
[tex] \dashrightarrow{ \sf{ - 16 + 15}}[/tex]
[tex] \dashrightarrow{ \sf{ - 1}}[/tex]
R.H.S :[tex] \sf{2(y + 5) - 3}[/tex]
plug the value of y and simplify
[tex] \dashrightarrow{ \sf{2( - 4 + 5) - 3}}[/tex]
[tex] \dashrightarrow{ \sf{2 *1 - 3}}[/tex]
[tex] \dashrightarrow{ \sf{2 - 3 }}[/tex]
[tex] \dashrightarrow{ \sf{ - 1}}[/tex]
∴ L.H.S = R.H.S
The value of y is -4
And we're done!
------------------------------------------------------------
Rules for solving an equationIf any equation contains fractions , multiply each term by the LCM of denominators.Remove the brackets , if any.Collect the terms with the variable to left hand side and constant terms to the right side by changing their signs ' + ' into ' - ' and ' - ' into ' + '.Simplify and get the single term on each side.Divide each side by the coefficient of variable and then get the value of variable.Hope I helped!
Best regards! :D
~TheAnimeGirl
I will brainlist HELP
Answer:
x = 7
y = 10
Step-by-step explanation:
<K and <NLK are marked as being equal.
That means that KN and LN are equal.
So LN = 6
y - 4 = 6
y = 4 + 6 = 10
For the same reason LN = LM
That means that x + 3 = 10
x = 10 - 3
x = 7
1.15÷0.23=? pls answer guys
Answer:
5
Step-by-step explanation: I used a calculator
Carlos is making party favors. Every bag has exactly the same treats in it. Carlos has 96 granola bars and 64 popcorn balls. What is the greatest number of party favors Carlos can make?
Answer:
32
Step-by-step explanation:
Given that:
Number of granola bars = 96
Number of popcorn balls = 64
Greatest number of party favors that can be made from granola bars and popcorn balls ;
Obtain the greatest common factor of both 96 and 64
Factors of :
96 : 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
64 : 2, 4, 8, 16,32
greatest common factor is 32,
Hence, greatest number of party favors that can be made is 32
Make t the subject of the formula
t = (3m -1) / (m - 1)
What is subject of formula?The subject of a formula is the variable that is being worked out. It can be recognized as the letter on its own on one side of the equals sign.
In order to change the subject of a formula, or rearrange a formula, items in the formula need to be rearranged so a different variable is the subject. Knowledge of solving equations and inverse operations is very useful.
Given formula.
m = t + 1 / t - 3
m ( t - 3) = t - 1
mt - 3m = t - 1
mt - t = 3m - 1
t(m - 1) = (3m - 1)
t = (3m -1) / (m - 1)
Hence, the formula becomes t = (3m -1) / (m - 1).
Learn more about subject of formula here:
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LAST QUESTION PLS HELP idk if you can see it all
Answer:
C is the right answer
Step-by-step explanation:
Your making chocolate chip cookies. The recipe calls for 1/8 teaspoon salt to 1/4 teaspoon baking soda. How much salt is needed for one teaspoon of baking soda
Answer:
1/2 teaspoon salt
Step-by-step explanation:
We can make this into a ratio of salt:baking soda
1/8:1/4
now, how many 1/4 will we need to make 1?
If we multiply 1/4 by 4, we get one. So, we should do the same to 1/8!
1/8*2=4/8, or 1/2 teaspoon
What is the slope of the line that passes through the points (-6, -10) and (3,-13)? Write your answer in simplest form.
We must use slope formula* to solve this.
[tex]\frac{-13 - (-10)}{3 - (-6)}\\\\\frac{-3}{9} = -\frac{1}{3}[/tex]
m** = [tex]-\frac{1}{3}[/tex]
*Slope Formula: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
**m is the symbol for slope.
again i need some help with this :D
Answer:
v + u - 4
Step-by-step explanation:
what is the slope of the line ? please
Answer:
1/3
Step-by-step explanation:
Answer:
1/3
Step-by-step explanation:
HELPPPP.
Suppose a bird is 500 feet above the ground. It descends at a steady rate. After 10 seconds, it is 250 feet above the ground.
a) Write an equation that gives the height of the bird as a function of time. Be sure to define your variables!
b) After how many seconds will the bird land on the ground?
Answer:
500-10x=250
x=how much the bird descended in a second
the bird will land on the ground in another 10 seconds.
Step-by-step explanation:
the bird will land on the ground in 10 seconds since it descended 250 ft in 10 seconds so that is 25 ft per second. then do 250/25 and you get 10. that is how you know the bird will land on the ground in 10 seconds.
Answer:
a) [tex]h(t)=500-25t[/tex]
b) [tex]t=20[/tex]
Step-by-step explanation:
a)
Let [tex]h[/tex] = height above ground
Let [tex]t[/tex] = time
Because the bird descended down to 250 feet in 10 seconds with a steady rate, that means it descends 25 feet per second.
∴ [tex]h(t) = 500-25t[/tex]
b)
To find the time it takes until the bird reaches the ground, [tex]h[/tex] must equal [tex]0[/tex]:
[tex]0=500-25t[/tex]
[tex]25t=500[/tex]
[tex]t=20[/tex]
∴ It takes 20 seconds for the bird to reach the ground.
Please help me with this :((
Answer:x=5 or F
Step-by-step explanation:(8x+6)/(5x-2)=2, because it is the midsegment, cross multiply, and you get 2x=10, so x=5
answer the question for good boy stars
Answer:
its-5.5°C
explanation
combine it
Answer:
the answer is br-br
Step-by-step explanation:
that is answer bro
Cuáles son los métodos de integración
Answer:
Spanish:
Los diferentes métodos de integración incluyen:
Integración por sustitución.
Integración por partes.
Integración mediante identidades trigonométricas.
Integración de alguna función particular.
Integración por fracción parcial
Step-by-step explanation:
English:
The different methods of integration include:
Integration by Substitution.
Integration by Parts.
Integration Using Trigonometric Identities.
Integration of Some particular function.
Integration by Partial Fraction.
A satellite travels 12 miles in 15 minutes at a constant speed. What is the satellite’s speed in mile per hour?
Answer: 46 mph
Step-by-step explanation: 15*4=60 so 12*4=46
I hope this helps!
What is the slope of the line (-3,0) and (0,-4)
What is the measure of Zx in the diagram shown below?
A
23°
B
33°
С
113°
157°
Answer:
Since that is a right angle it is going to equal 90 degrees. Since you know that the first angle is 67 degrees subtract 67 from 90 and get 23 degrees.
Step-by-step explanation:
In the diagram below, find the value of x to the nearest hundredth
Answer:
x = √324 = 18
Step-by-step explanation:
x shows up only in the second problem, so I'll focus on that problem.
This is a right triangle because one of the three angles is 90 degrees.
Thus, the Pythagorean Theorem applies: x^2 + 24^2 = 30^2, or
x^2 = 900 - 576 = 324
Then x = √324 = 18
Given m∥n, find the value of x and y.
Answer:
x=15
y=63
Step-by-step explanation:
jess makes salad dressing by mixing lemon juice and olive oil in the ratio 2:5 by volumr.me. shes uses 0.5 litres of lemon juice. work out how much olive oil she uses to make the salad dressing.
Answer:
its 2.5 liters of olive oil because .5 times 5 equals 2.5 needed to satisfy ratio.
If you subtract 16 from my number and multiply the difference by -3, the result is -39 what is my number
Answer:
29
Step-by-step explanation:
Start with -39. We need to do inverse operations to figure out the solution. -39 divided by -3 is 13, and 13 plus 16 is 29.
Answer:
29
Step-by-step explanation:
-39=-3(n-16)
13=n-16
29=n
What is the value of the expression 5y² + 4x when x = 2.5 and y = 3?
Answer:
55
Step-by-step explanation:
the value of the expression 5y² + 4x when x = 2.5 and y = 3 will be 55.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given an expression 5y² + 4x
To calculate the value of expression at x = 2.5 and y = 3
Substitute the value of x and y in the expression:
=> 5y² + 4x
=> 5* 9 + 4 * 2.5
=> 45 + 10
=> 55
therefore, 55 is the value of the expression 5y² + 4x when x = 2.5 and y = 3.
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There are 20 students. Two-fifths of the students are girls. How many students are girls?
Answer:
There are 8 girls.
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
20 divided by 5 = 4.
4x2=8