The given linear system is:
[tex]\displaystyle \left \{ {{5x+7y=33} \atop {11x+7y=39}} \right.[/tex]
The question is asking to solve using elimination. When eliminating, you can either eliminate x or y. In this system, y is much easier to eliminate. The y variable in both equations are 7y. To eliminate, one of them has to be negative, so multiply one of the equations by -1.
I will be multiplying the second equation by -1.
[tex]\displaystyle (11x + 7y = 39) \times -1 = -11x-7y=-39[/tex]
Rewrite the system:
[tex]\displaystyle \left \{ {{5x+7y=33} \atop {-11x-7y=-39}} \right.[/tex]
Subtract:
[tex]5x+7y=33\\-11x-7y=-39[/tex]
[tex]5x-11x=33-39\\-6x=-6[/tex]
Lastly, you need to leave the variable x alone. The variable is currently -6x or -6 times x. To remove it, you need to do the opposite of it, which is dividing by -6.
[tex]\displaystyle \frac{-6x}{-6} =\frac{-6}{-6}[/tex]
[tex]\displaystyle x=1[/tex]
Now that you have the value of x, substitute it into one of the equations to find y. I will be substituting it into the first equation.
[tex]5x+7y=33 \rightarrow 5(1)+7y=33[/tex]
Open the parentheses and multiply:
[tex]5+7y=33[/tex]
Move 5 to the other side to leave the variable alone:
[tex]5+7y-5=33-5[/tex]
You will be subtracting since you're "removing" it by doing the opposite of it.
[tex]7y=28[/tex]
Lastly, divide both sides by 7 to leave y alone.
[tex]\displaystyle \frac{7y}{7} =\frac{28}{7}[/tex]
[tex]y=4[/tex]
[tex]\displaystyle (x,y) \rightarrow (1, 4)[/tex]
The answer is (1, 4).
Answer:
(1, 4)
Tbh this question was a bit of a challenge for me but hopefully it helps ya.
Step-by-step explanation:
First, let's solve for y. So we have to eliminate the x values.
(5x + 7y = 33 ) *11
(11x + 7y = 39) *-5
___________
55x + 77y = 363
-55x -35y = -195 This eliminates the x value.
42y = 168 Divide both sides by 42 to isolate y: 168/42= y = 4
Now let's solve for x.
(11x + 7y = 39) *7
(5x + 7y = 33 ) *-7
___________
77x + 49y = 273
-35x -49y = -231 This cancels out the y values, which leaves 42x = 42
x = 1 and y = 4, so the answer is (1, 4)
A certain stock has grown continuously from 1980 to 2015. A $10,000 investment in the stock in 1980 would be worth $3,500,000 in 2015. Find the stock's average annual growth rate during this period. Round to the nearest percent.
If a certain stock has grown continuously from 1980 to 2015, for this period of time its average annual growth rate is 18%.
It is given that A certain stock has grown continuously from 1980 to 2015.
Stock's initial value in 1980 (I) = $10,000
Stock's final value in 2015 (F) = $3,500,000
time period t = 2015-1980 = 35 years.
Since, the stock has grown continuously, it should have grown compounded annually.
Stock's average annual growth rate (r) is calculated as:
[tex]\text{r} = {(\dfrac{F}{I})^{\frac{1}{t}}-1[/tex]
Substitute all the given values in the above formula:
[tex]\text{r} ={ (\dfrac{3500000}{10000})^{\frac{1}{35}}-1[/tex]
[tex]\text{r} = {(350})^{\frac{1}{35}}-1[/tex]
[tex]r = (350)^{0.02857142857}-1[/tex]
[tex]r=1.18219102629-1[/tex]
[tex]r=0.18219102629[/tex]
[tex]r=0.18[/tex]
[tex]r\approx 18\%[/tex]
Hence, stock's average annual growth rate during the period of 35 years is 18%.
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Two factors of –48 have a difference of 19. The factor with a greater absolute value is positive.
What is the sum of the factors?
–19
–13
13
16
Answer with no step-by-step explanation:
13
what is a tanslation in math
Answer:
A translation moves a shape up, down or from side to side but it does not change its appearance in any other way. Translation is an example of a transformation. A transformation is a way of changing the size or position of a shape. Every point in the shape is translated the same distance in the same direction
Step-by-step explanation:
Grayson biked 45 miles in 3 hours.Maya bikes 26 miles in 2 hours.If they both kept a constant speed,how much faster did Grason Bike than Maya
Write your answer as a decimal or a whole number
Answer:
2
Step-by-step explanation:
Divide 45 and 3, then divide 26 and 2. subtract those answers and u get 2. (the dude that said your mom has no life and got his mom raped)
Grason's Bike is 2 miles/hour faster than Maya's if Grayson biked 45 miles in 3 hours. Maya bikes 26 miles in 2 hours.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
It is given that:
Grayson biked 45 miles in 3 hours. Maya bikes 26 miles in 2 hours.
As we know,
The speed = distance/time
Plug the respective values in the above formula:
For Grayson:
speed = 45/3 = 15 miles/hour
For Maya:
speed = 26/2 = 13 miles/hour
Difference in speed = 15 - 13 = 2 miles/hour
Thus, Grason's Bike is 2 miles/hour faster than Maya's if Grayson biked 45 miles in 3 hours. Maya bikes 26 miles in 2 hours.
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A librarian sorts 450 books at a constant rate. After 4 days, the librarian still has 150 books to sort. How much time does it take to sort the books from start to finish?
Answer:
6 days
Step-by-step explanation:
hope this helps
A librarian sorts 450 books at a constant rate. After 4 days, the librarian still has 150 books to sort. Then 6 days time does it take to sort the books from start to finish
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The librarian sorted at a constant rate, then they sorted the same amount of books all 4 days.
450-150=300
If they still have 150 books left to sort, then they sorted 300 books over 4 days.
300/4=75
This means that they sorted 75 books per day.
150 divided by 75 is 2
So it will take 2 more days to finish sorting all the books.
So altogether, it will take 6 days to sort all of the books.
Hence 6 days time does it take to sort the books from start to finish
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What is the slope of the linear function shown in the table below:
Answer:
It's 2
Step-by-step explanation:
Positive 2.
(not -1/2)
23 kg of potatoes cost $138. How much would 7 kg cost? lol i haven't done this in a while and there just now telling us to do it
Answer:
$42
Step-by-step explanation:
138/23 = $6 per kg
6*7 = 42
Work out value x 4x 5x angles
Answer:
x=20
Step-by-step explanation:
5x+4x=180
9x=180
/9 on both sides
x=20
The value of 4x and 5x is 80° and 100° respectively .
What is the same-side interior angle theorem?The same-side interior angle theorem states that when two lines that are parallel are intersected by a transversal line, the same-side interior angles that are formed are supplementary, or add up to 180 degrees.
According to the question
4x , 5x are angles given
As,
They are angles between parallel line and same side of transversal line
according to same-side interior angle theorem that are formed are supplementary .
i.e there sum = 180°
4x + 5x= 180°
9x = 180°
x = 180°/9
x = 20°
So,
4x = 20 * 4 = 80°
5x = 20 * 5 = 100°
Hence, The value of 4x and 5x is 80° and 100° respectively .
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What is the slope and y-intercept of 8x – 2y = -16?
Answer:
4x+8=y
Step-by-step explanation: This is because you take everything and isolate the y you take the 8x and subtract it from the other side then after that you divide everything by -2 to get your answer
Add the following using horizontal method
i.)abc,-2abc,4abc
ii.)8xz,-2xz,-6xz
Answer:
i - 3abc
ii - 0
Step-by-step explanation:
i- abc,-2abc= -abc (think of it as 1-2)
-abc,+4abc=3abc (-1+4)
ii- 8xz,-2xz=6xz (8-2)
6xz,-6xz=0 (6-6)
What the other guy said :D
What is the slope of the linear relationship shown in this table of values? x y -4 11 2 -1 5 -7
Answer:
2
Step-by-step explanation:
-1-11/-4-2 = -12/-6 = 2
The required slope for the linear relationship is -2.
Slope to be determine for table x = -4 2 5, y = 1 -1 -7 showing linear relationship.
Slope of function is defined as the rate at which function is increasing.
Here, slope
[tex]=\frac{y_2-y_1}{x_2-x_1} \\=\frac{-1-11}{2+4}\\= -2[/tex]
Thus, the required slope for the linear relationship is -2.
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At a school, 60% of the sixth-grade students said that pizza is their favorite kind food. If 210 sixth-grade students prefer pizza, how many sixth-grade students are at the school?
Answer:
350
Step-by-step explanation:
Let [tex]s=[/tex] total number of sixth-grade students.
It is given that 60% of sixth-grade students prefer pizza which is equivalent to 210 sixth-grade students. With this, the following can be written:
[tex]60\%s = 210[/tex]
[tex]0.6s=210[/tex] ([tex]60\%[/tex] can be converted into the decimal form [tex]0.6[/tex])
[tex]s = 210\div 0.6[/tex]
[tex]=350[/tex]
∴ There is a total of 350 sixth-grade students in the school.
Hope this helps :)
Solve each equation. Check your solution.
Answer:
y = 15
Step-by-step explanation:
-1/3 y -6 = -11
Add 6 to each side
-1/3 y -6+6 = -11+6
-1/3 y = -5
Multiply each side by -3
-1/3 y * -3 = -5*-3
y = 15
Check
-1/3 *15 -6 = -11
-5 -6 = -11
-11=-11
4,914÷7=
4
,
914
÷
7
=
Four pounds of bananas cost $2.60
What the cost per pound?
Answer:
$0.65 per pound
Step-by-step explanation:
Divide the total cost by the number of pounds to find price per pound.
$2.60 ÷ 4 = $0.65 per pound
y-intercept. y = -3/2x
Answer:
i hope you find the answer but unfortunaatly im not sure
Step-by-step explanation: thankyou for the points though :)
If a 5 and b=4, then 2a +b=
An expression is defined as a set of numbers, variables, and mathematical operations. The value of the expression 2a+b when the value of a is 5 and b is 4 is equal to 14.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given the expression 2a+b, whose values are needed to be calculated when the value of a is 5 and the value of b is 4. Therefore, the value of the given expression 2a+b can be written as,
2a + b
Substitute the value of a and b,
= 2(5) + 4
= 10 + 4
= 14
Hence, the value of the expression 2a+b when the value of a is 5 and b is 4 is equal to 14.
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if 1/2=-3/7q, then q= -1 1/6 true or false
Answer:
false
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
[tex]\frac{1}{2}=\frac{-3}{7}q[/tex]
1/2*7/-3= -7/6
q = -7/6 NOT -11/6 so the statement is false
Increase £120 by 25%
Find the slope pls help !!!
Determine and state an equation of the line perpendicular to the line 4x – 5y = 10 and passing through the point (-4, -2).
What is the equation for the parabola that
has a focus at (-7, 6) and a directrix of x
1?
Answer:
Step-by-step explanation:
Parabola's equation is
y
=
1
16
(
x
−
7
)
2
+
1
and vertex is
(
7
,
1
)
.
Explanation:
Parabola is locus of a point which moves so that its distance from a given point calld focus and a given line ccalled directrix is always constant.
Let the point be
(
x
,
y
)
. Here focus is
(
7
,
5
)
and distance from focus is
√
(
x
−
7
)
2
+
(
y
−
5
)
2
. Its distance from directrix
y
=
−
3
i.e.
y
+
3
=
0
is
|
y
+
3
|
.
Hence equaion of parabola is
(
x
−
7
)
2
+
(
y
−
5
)
2
)
=
|
y
+
3
|
2
or
x
2
−
14
x
+
49
+
y
2
−
10
y
+
25
=
y
2
+
6
y
+
9
or
x
2
−
14
x
+
65
=
16
y
i.e.
y
=
1
16
(
x
2
−
14
x
+
49
−
49
)
+
65
16
or
y
=
1
16
(
x
−
7
)
2
+
65
−
49
16
or
y
=
1
16
(
x
−
7
)
2
+
1
Hence parabola's equation is
y
=
1
16
(
x
−
7
)
2
+
1
and vertex is
(
7
,
1
)
.
graph{(1/16(x-7)^2+1-y)((x-7)^2+(y-1)^2-0.15)((x-7)^2+(y-5)^2-0.15)(y+3)=0 [-12.08, 27.92, -7.36, 12.64]}
BRAINLY. what is the equation of the line in slope intercept form
What is the definition of a relation?
An association between two sets of data
Ordered pairs where each x-value is paired with only one y-value
The rules applied to a number
A set of data with a defined rule
Answer:
i did not understant your question
i think u want the definition of relation
A relation between two sets is a collection of ordered pairs containing one object from each set. If the object x is from the first set and the object y is from the second set, then the objects are said to be related if the ordered pair (x,y) is in the relation. A function is a type of relation.
Step-by-step explanation:
plssssssssssss markkkk meee brainlist
A relation is a collection of Ordered pairs where each x-value is paired with only one y-value.
What do you mean by domain and range of a function?
For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of x for which [y] exists.
Given is the graph of a equation
A relation between two sets is a collection of ordered pairs containing one object from each set. If the object x is from the first set and the object y is from the second set, then the objects are said to be related if the ordered pair (x, y) is in the relation.
Therefore, a relation is a collection of Ordered pairs where each x-value is paired with only one y-value.
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Which equation is not true?
Answer:
the answer is B
David's bowling score is 6 less than 3 times Aaron's score. The sum of their scores is 214. Find the score of each student. Use the variable a for Aaron's score.
plz help
Step-by-step explanation:
Let aron's variable be = a
Let davids variable be( 6 less tan 3 times aron) = 3×a-6
Thier sum is =214
So,
3×a-6 + a = 214
3a -6 +a = 214
(transpose)
3a + a = 214 + 6
4a = 220
a = 220/4
a= 55
Thus,aron's score is = 55
And davids score is (3×a-6) = 3×55-6 = 159
Checking,
Aron score + david score = 214
55 + 159 = 214
SO, ITS CORRECT
HOPE IT HELPS :)
Don’t mind the question at the bottom but I need to know if this is right or not please help!
Answer:
the answer is d.
Answer:
no its not correct, the answer is d
Step-by-step explanation:
too long to explain, just trust me man
Is it possible for two numbers to have a difference of 5, and a sum of 12?
Answer:
yes, 8.5 and 3.5
Step-by-step explanation:
8.5 + 3.5 = 12
8.5 - 3.5 = 5
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The two numbers are 8.5 and 3.5.
Yes, it is possible to have two numbers that have a difference of 5 and a sum of 12.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 4 is an equation.
3x = 4 + 3 is an equation.
We have,
Let the two numbers be M and N.
Now,
Two numbers have a difference of 5.
This can be written as,
M - N = 5 _____(1)
Two numbers sum is 12.
This can be written as,
M + N = 12 _____(2)
From (1) and (2) we get,
M - N = 5
M = 5 + N _____(3)
Putting (3) in (2)
M + N = 12
5 + N + N = 12
5 + 2N = 12
2N = 12 - 5
2N = 7
N = 7/2
N = 3.5
Putting in (3) we get,
M = 5 + 3.5
M = 8.5
We can cross-check.
M - N = 5
8.5 - 3.5 = 5 (PROVED)
M + N = 12
8.5 + 3.5 = 12 (PROVED)
Thus,
The two numbers are 8.5 and 3.5.
Yes, it is possible to have two numbers that have a difference of 5 and a sum of 12.
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For every 60 students there's 3 teachers so for every 15 teachers how many students would there be?
Answer:
300 students
Step-by-step explanation:
divide 60 by 3 to find how many students there are per teacher: 60/3 = 20
multiply 20 by 15 to find how many students there are for 15 teachers:
20 x 15 = 300
Which of the following capital letters results in the same letter over again when reflected about a
horizontal line? (1 point)
Ο:Α
O:Y
O:S
O:D
Answer: D
Step-by-step explanation:
When D is reflected over a horizontal line (think of it as a mirror on the ground with D on top of it), the reflection will show the letter D in the same way all over again.
I have attached a picture to show it. It's a tad unclear but I believe gets the point across.