if 2x+y=7 and y=2x-5 what is the value of x. solve using substitution or elimination
The value of x is found as 3 using the method of substitution.
What is the method of substitution?The substitution method is a straightforward method for algebraically solving a system of linear equations and determining variable solutions. It entails determining the value of x-variable in aspects of y-variable using the first equation and afterwards substituting or fixing the value of x-variable with in second equation, as the name implies.For the given expression, use substitution method to solve.
2x + y = 7 ........eq 1
y = 2x - 5 ........eq 2
Substitute the value of y from eq 2 in eq 1.
2x + 2x - 5 = 7
Solving;
4x = 7 + 5
4x = 12
x = 3
Thus, the value of x is found as 3.
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Please help me with this maths question thanks!
Answer:
x = 2
Step-by-step explanation:
x + 3 + 1/2 x + 3 +x + 1 = 12 Combine like terms
21/2 x + 7 = 12 Subtract 7 from both sides of the equation
2 1/2 x = 5
Another name for 2 1/2 is [tex]\frac{5}{2}[/tex] ([tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{1}{2}[/tex])
[tex]\frac{5}{2}[/tex] x = 5 Multiply both sides of the equation by [tex]\frac{2}{5}[/tex]
[tex](\frac{2}{5})[/tex][tex](\frac{5}{2})[/tex]x = [tex]\frac{2}{5}[/tex][tex](\frac{5}{1})[/tex]
x = 2
Which recursive formula can be used to determine the total amount of money earned in any year based on the amount earned in the previous year? f(n 1) = f(n) 5 f(n 1) = 5f(n) f(n 1) = 1.05f(n) f(n 1) = 0.05f(n)
Answer: y = f (n 1)
Step-by-step explanation:
If we count interest rate = 5%
then if he earned 'y' amount in 1st year then in 2nd year he must earned
= y + 5% of y
== 1.05 y
here, y = f(n 1)
Find the equation of the line shown.
Answer:
y = mx + b
y = 1/4x + 2
Step-by-step explanation:
m(slope) = rise/run = 1/4
b(y intercept) = 2
The lowest point in Denmark is 7
meters below sea level. The highest point is 173 meters above sea level. What is the range of elevations in
Denmark?
The range of elevations is 166 meters.
What is range?
Find the biggest observed value of a variable (the maximum) and subtract the smallest observed value to determine the range (the minimum). The data points between the distribution's two extremes are not taken into account by the range; just these two values are.
So as mentioned above, given to us are the lowest and highest values
So as the lowest value is 7 meters and the highest value is 173 .
Thus range is equal to 173-7
which is equal to 166.
Thus range is 166 meters.
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Find the distance from a point (4, 6) to the line y = 2x - 5.
Answer:
1.34 units.
Step-by-step explanation:
The line y = 2x - 5 has a slope of 2 so the line passing through the given point will be perpendicular to y= 2x - 5 and will have a slope of -1/2.
Let this line be y = -1/2x + c.
Its passes through (4, 6) so:
6 = -1/2*4 + c
6 = -2 + c
c = 6 + 2 = 8
So, equation of this line is y = -1/2x + 8.
Now we find the point where the 2 lines intersect:
y = 2x - 5
y = -1/2x + 8
2x - 5 = -1/2x + 8
2x + 1/2 x = 5 + 8
(5/2)x = 13
x = 26/5
= 5.2.
and y = 2(5.2) - 5
= 5.4.
So, the point of intersection is (5.2, 5.4)
and the distance between the point (4,6) and the line y = 2x - 5
= √((6 - 5.4)^2 + (4-5.2)^2)
= √(0.36 + 1.44)
= √1.8
= 1.34
There is a formula you can use directly to solve this.
Vicky makes 8 purses and 9 key rings to sell for charity.
The price of a purse will be twice as much as the price of a key ring.
Vicky wants to get a total of exactly £40 when she sells all the purses and all the key rings.
Work out the price Vicky needs to charge for each purse and for each key ring
Price of key ring = £1.6
Price of purse = £3.2
What is unitary method?The unitary approach is a strategy for problem-solving that involves first identifying the value of a single unit, then multiplying that value to figure out the required value.
Given Data
Vicky makes 8 purses and 9 key rings to sell for charity.
Vicky wants to get a total of exactly £40
Suppose the price of key ring be v
and the price of purses be 2v
£40 = £8(2v) + £9(v)
40 = 16v + 9v
40 = 25v
v = [tex]\frac{40}{25}[/tex]
v = 1.6
Price of key ring = £1.6
Price of purse = £3.2
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9 Evaluate the expression 3[a(4bc)] for a = 2, b = 3, and c = 2.8.
8
7
୨)|୨)
Answer:
3(2(4)(3)(2.8))
3(24(2.8))
3(67.2)
2016
Write an Algebraic proof for the following
To prove this, we need to show that 2 is equal to x.
Given:
2(x + 5) - 3x = 7x - 6
Distribute:
2x + 10 - 3x = 7x - 6
Combine like terms:
-1x + 10 = 7x - 6
Add 1x to both sides of the equation:
10 = 8x - 6
Add 6 to both sides of the equation:
16 = 8x
Divide both sides of the equation by 8:
2 = x
Reflexive property:
x = 2
✓
2(x + 5) - 3x = 7x - 6
x = 2
Find the value of x.
(3x + 3) (5x + 1)
Please help me:)
Answer:
x=22
Step-by-step explanation:
Since a straight line is equal to 180 degrees,
(3x+3)+(5x+1) = 180
(3x+3)+(5x+1)-180=0
8x+4-180=0
8x-176=0
8x=176
x=176/8
x=22
Which also means that the first angle is (3(22)+3)=69 degrees
the second angle is (5(22)+1) = 111 degrees
111 + 69 = 180
Help math
How am i suppose to do this ?
Answer:
16/5
Step-by-step explanation:
The direct variation equation (where k is the constant variation):
z = kw
First, we must solve for k:
k = w/z
Plug in -5 and 2:
k = 2/-5 = -2/5
Now plug k into the formula with 8 to solve for z:
z = -2/5 x 8 = 16/5
s=1/2pl+b solve for l
Approximately 3 out of every 25 Amerloans live in California. About 3 out of every 50
Americane live in New York and about 2 out of every 25 Americans live in Texas.
Which state has the largest population?
10. Which state hos the smallest population?
11. About what percentage of Americans do nar live in Colifornia, New York, or Texas?
California is the most populated state, New York is the least populated, and 26% of Americans live in California, New York, and Texas.
Convert all statistics to percentages:
CA: 3 25 = 0.12 or 12%, 0.12 100 to calculate percentages.
NY: 3 50 = 0.06, or 6%, and 0.06 100 to get the percentage.
TX: 2 25 = 0.08 = 8%, 0.08 100 = percent
(A) California has the largest population of the three states.
(B) New York has the smallest population of the three states.
(C) USA = 100%, CA + NY + TX = 26%, so 74% of Americans do not live in these three states.
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A rectangular sandbox has a width represented by the polynomial (x-1) and a length represented by (6x-5). What is the total area of the sandbox?
The total area of the sandbox is given by 6x^2-11x+5
Width of the sandbox = (x-1)
Length of the sandbox = (6x-5)
Rectangle area in geometry refers to the area that a rectangle occupies on a two-dimensional plane. A quadrilateral, a form of a two-dimensional object with four sides and four vertices, is what a rectangle is. The rectangle's four angles are all right angles or exactly 90 degrees. The rectangle's opposing sides are equal and parallel to one another.
The formula for the area of a rectangle:
Area of rectangle = Length*Width
Substituting the value in the formula we get:
Area of rectangle = (x-1)*(6x-5)
= 6x^2-5x-6x+5
= 6x^2-11x+5
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PLEASE HELP ASAP
State whether the point is on the x-axis or the y-axis. If the point is not on an axis, state which quadrant it is in.
(10,–7)
Choose the correct answer from the drop-down menu.
Point (10,–7) is
in:
On the x axis
On the y axis
Quadrant l
Quadrant ll
Quadrant lll
Quadrant lV
The given coordinate pair, (10, -7) is not on the x–axis or the y–axis, but it is in Quadrant IV
What is a coordinate pair?
A coordinate pair specifies a point on the coordinate plane.
The coordinates of points on the x–axis have a y–coordinate of 0
Therefore, the coordinates of a point that is on the x–axis can be expressed as (x, 0)
Points that are on the y–axis have a x–coordinate of 0, which gives the coordinates of the points located on the y–axis as (0, y)
The coordinates of the given point is (10, -7), therefore, the point is neither on the x or y–axis, but in one of the four quadrants.
The coordinate of points in the first quadrant can be represented generally as (x, y)
Points in the second quadrant have the general form of (-x, y)
The points in the third quadrant can be expressed generally in the form (-x, -y)
The coordinates of points on the fourth quadrant are of the form, (x, -y)
The given point is (10, -7), therefore it is in the fourth quadrant or Quadrant IV
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If the lower legs of the ironing board are equal in length, what is the measure of n?
Point G is on line segment \overline{FH}
FH
. Given FH=4x+8,FH=4x+8, FG=x,FG=x, and GH=5x,GH=5x, determine the numerical length of \overline{GH}.
GH
.
The numerical length of GH = 20 units
FH is a line segment.
G is a point on the line segment.
Then G divides the line segment FH into two line segments FG and GH.
We are given the lengths of FH, FG and GH in terms of x.
That is, FH=4x+8, FG=x and GH=5x
We need to find the numerical length of the line segment GH. We first need to find the x for this.
As G cuts the line segment FH into two parts, the length of the line segment FH is the sum of the lengths of the line segments FG and GH.
That is, FH = FG + GH
⇒ 4x+8 = x +5x
⇒ 4x+8 = 6x
⇒ 2x = 8
⇒ x = 4
So the numerical length of GH = 5x = 5 x 4 = 20 units
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Please answer the two questions in the photo ( will mark brainliest if correct )
Answer:
2; 6
Step-by-step explanation:
for the first shape there are 2 lines of symmetry
TWO
for the hexagon or the regular polygon there are 6 lines of symmetry
SIX
you can find lines of symmetry by drying a line down and seeing if when you fold them they will be exactly the same
Write the equation of line perpendicular to y = 4 that passes through (5, 2)
one may note that y = 4 is a horizontal line, and a line perpendicular to a horizontal line will be a vertical one, Check the picture below.
i need help with this Solve this equation.
13(y+7)=3(y−1)
Answer: y=-47/5
Step-by-step explanation:
Yw
The customers at the bank would like to withdraw money from the automated teller machine. Help them enter their personal ID numbers by completing the numeric patterns. 2, 13, 24, 35,
To withdraw money from the automated teller machine the numeric pattern required to complete the personal ID numbers is 2, 13, 24, 35,46,57,68.
As given in the question,
Using automated teller machine customers at the bank withdraw money
Numeric pattern given for the personal ID numbers is
2, 13, 24, 35
First term 'a'= 2
Common difference between consecutive terms are same
'd'=13 -2
=11
It is an arithmetic progression series
nth term = a+ (n-1)d
5th term = 2 +(5-1)11
=46
6th term =2+(6 -1)11
=57
7th term= 2+ (7-1)11
= 68
Therefore, to withdraw money from the automated teller machine the numeric pattern required to complete the personal ID numbers is 2, 13, 24, 35,46,57,68.
The complete question is:
The customers at the bank would like to withdraw money from the automated teller machine. Help them enter their personal ID numbers by completing the numeric patterns. 2, 13, 24, 35, ___, ___, ____.
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What is the special angle pair relationship between the two
Answer: Alternate exterior angles
Step-by-step explanation:
Find the X and Y values.
The answer should be written as a coordinate point (x,y)
(reward 70 points)
Answer:
(x,y)=(10,11)
Step-by-step explanation:
Drew actually has almost finished the equation. So I'm starting with the left part
[tex]2.5x+ 6= 31[/tex]
Cancel out 6 from both sides and divide both sides 2.5 which leaves us with
[tex]x=\boxed{10}[/tex]
Plug in the value of x into the second equation and simplify
y=-2.10+ 31
[tex]y=\boxed{ 11}[/tex]
There are 24 total customers seated at 4 tables in a restaurant Each table has the same number of customers. At that rate, what is the maximum number of costumers who could sit at 6 tables
Answer:
36
Step-by-step explanation:
24 customers dividend into 4 tables
so 24/4 = 6
then 6 customers can sit in 1 table
in case of 6 tables 6×6 =36
36 customers would sit in 6 tables
How can this expression be written another way?
105 + 35m
Factor using the distributive property and the greatest common factor to write an equivalent expression.
Enter your answer by filling in the boxes.
An equivalent expression to given expression is 35(3 + m)
In this question, we have been given an expression 105 + 35m
We need to write an equivalent expression of given expression.
To find an equivalent expression we factorize given expression using the distributive property and the greatest common factor.
A common number for 35 and 105 is 35.
105 = 35 × 3
So, we can write given expression as,
105 + 35m
= (35 × 3) + 35m
= 35(3 + m)
Therefore, an equivalent expression to given expression is 35(3 + m)
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Please hep me solve picture below thank uou
Answer:
x= -1, -13
Step-by-step explanation:
Answer: x=-13 x=-1
Step-by-step explanation:
[tex]x^2+14x=-13\\x^2+2(x)(7)+7^2-7^2=-13\\(x^2+2(x)(7)+7^2)-49=-13\\(x+7)^2-49=-13\\(x+7)^2-49+49=-13+49\\(x+7)^2=36[/tex]
[tex](x+7)^2-36=36-36\\(x+7)^2-36=0\\(x+7)^2-6^2=0\\(x+7+6)(x+7-6)=0\\(x+13)(x+1)=0\\x+13=0\\x+13-13=0-13\\x=-13\\x+1=0\\x+1-1=0+(-1)\\x=-1[/tex]
I need help pleaseeee
Answer: 60 inches in 5 feet
Step-by-step explanation:
5X12=60
Solve the given right triangle for its missing angle and side measures.
An Image of a Right triangle FED With E being the right angle and FE being the base with 12units. The acute angle is F at 35degree.
Note: Figure not drawn to scale
A.
m∠D = 35°, DE ≈ 8.40 units, DF ≈ 13.65 units
B.
m∠D = 35°, DE ≈ 8.40 units, DF ≈ 14.65 units
C.
m∠D = 55°, DE ≈ 4.40 units, DF ≈ 13.65 units
D.
m∠D = 55°, DE ≈ 8.40 units, DF ≈ 14.65 units
Answer:
D
Step-by-step explanation:
the sum of the 3 angles in Δ DEF = 180° , that is
∠ D + 90° + 35° = 180°
∠ D + 125° = 180° ( subtract 125° from both sides )
∠ D = 55°
------------------------
using the tangent and cosine ratios in the right triangle
tan35° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{DE}{EF}[/tex] = [tex]\frac{DE}{12}[/tex] ( multiply both sides by 12 )
12 × tan35° = DE , then
DE ≈ 8.40 ( to 2 dec. places )
--------------------------
cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{EF}{DF}[/tex] = [tex]\frac{12}{DF}[/tex] ( multiply both sides by DF )
DF × cos35° = 12 ( divide both sides by cos35° )
DF = [tex]\frac{12}{cos35}[/tex] ≈ 14.65 ( to 2 dec. places )
x+4y+32
Terms:
Variable:
Constant:
Coefficients:
Answer:
Terms: x, 4y, 32
variables: x, y
constant: 32
coefficients: 4, 1
Step-by-step explanation:
Hope this helps!
Kristen goes on a cave tour with her family. They climb down to 8 meters below ground level.
Then they climb the opposite of –8 meters to return to ground level.
How many meters did they climb in all? Enter your answer in the box.
meters
The total distance climbed by Kristen and her family is 16 meters.
It is given in the question that Kirsten and family climb down to 8 meters below ground level. Then they climb the opposite of 8 meters to return to ground level.
We have to find the total distance climbed by Kristen and her family.
We know that,
Total distance climbed by Kristen and her family = Distance climbed down the cave + distance climbed up the cave to reach ground level
Hence, we can write that,
Total distance climbed by Kristen and her family = 8+8 = 16 meters.
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