The solution to given equation 5x - 12 - 6x = -10x + 7 - 1 is x = 2.
In this question,
we have been given an equation 5x - 12 - 6x = -10x + 7 - 1
We need to solve above equation using given steps.
5x - 12 - 6x = -10x + 7 - 1 .................(Given equation)
Step 1. Collect like terms
⇒ (5x - 6x) - 12 = -10x + (7 - 1)
⇒ -x - 12 = -10x + 6
Step 2.Move variables to one side of the equation (addition/subtraction property of equalities)
⇒ -x + 10x -12 = 6
Step 3. Move constant to the other side of equation (Addition/subtraction property of equalities)
⇒ 9x = 6 + 12
⇒ 9x = 18
Step 4.(multiplication/division property of equalities)
⇒ x = 18 ÷ 9
⇒ x = 2
Therefore, the solution to given equation 5x - 12 - 6x = -10x + 7 - 1 is x = 2.
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ASAP PLEASE HELP IF RIGHT ANSWER WILL GIVE BRAINLIEST, 15 POINTS, AND 5 STAR OVERALL!!!! IF WRONG ANSWER OR INVALID WILL REPORT, PLEASE, PLEASE, PLEASE!!
Answer:
The answer is 7
Step-by-step explanation:
The formula is y=mx+b so m=10 and b=7
Answer:
Hope this helps :)
The y-intercept is 7.
Step-by-step explanation:
This is because the in the slope-intercept form, y = mx + b, so the b in this case is 7.
There are two identical figures with all sides of equal length the combined perimeter of the figure is 80centimeters what shape are the figures what is the length of one side
Two identical figures with all sides of equal length = Both are square
Solution :
The perimeter of a square is defined as the total length that its boundary covers. The perimeter of any closed geometrical shape is calculated by finding the distance around that shape. For a square, the perimeter can be calculated by finding the sum of all the sides. Since all four sides are equal, it is four times the length of each side of a square. Let us learn about perimeter of square in detail in this article.
Derivation of Perimeter of Square Formula
The perimeter of the square is defined as the total length of the boundary of a square. In order to calculate the perimeter of the square, we will find the sum of all of its sides. Since all sides of a square are equal for a square, with each side measuring "s" units, perimeter will thus be given as,
Perimeter of square = s + s + s + s
⇒ Perimeter of square = 4s, where "s" is the side length of the square.
Squares :
A square is a special kind of rectangle (an equilateral one) and a special kind of parallelogram (an equilateral and equiangular one). A square has four axes of symmetry, and its two finite diagonals (as with any rectangle) are equal. Bisection of a square by diagonal results in two right triangles.
The formula for the perimeter of a square is,
P = Side + Side + Side + Side. Or,
P = 4 × Side.
two identical figures with all sides of equal length the combined perimeter of the figure is 80centimeters
2(4*side ) = 80
8*side = 80
side = 10
length of one side =10
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The figure below is a rectangular prism. One edge that is perpendicular to line segment BG
is line segment ___.
Answer:
GD.
Step-by-step explanation:
The mccarthy family is installing a rectangular patio in their backyard that will be 18 3 4 feet by 12 feet. what will be the area of the patio in square fe
The area of a rectangular patio with the dimensions of 18-3/4 feet and 12 feet will be determined by using the formula for the area of rectangle.
Area of rectangle is calculated by multiplying the length of the rectangle to the width of the rectangle. i.e.,
Area of rectangle= Length*Width
In the given situation,
Length= 18-3/4feet
Width=12 feet.
1. Convert the value of length to improper fraction:
18-3/4=75/4
2. Multiply the length and width to find the area:
Area=(75/4)x12
Solving the expression:
3. Area=75x3=225 sq. feet
The area of a 18-3/4 feet and 12 feet rectangular patio is 225 sq. feet.
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simplify the expression: 3a+4a
Answer: 7a
Step-by-step explanation:
Step-by-step explanation:
do sum of 3a and 4a your answer will be 7a
Write an equation in slope intercept form with the given information. Slope = -1 and goes through point (0,-6)
Answer:
y = x − 6
Step-by-step explanation:
Find slope: (y2-y1)/(x2-x1)
(6-3)/(1-0) = 3/1 = 3
Y = 3x + b, plug in point
3 = 3(0) + b, b = 3
Equation: y = 3x + 3
The slope intercept form of the equation of a line is:
y
=
m
x
+
b
where m is the slope and b is the value of y when x is 0.
We are given that the slope is 1 and the given point shows us that y is -6 when x is 0. Therefore, the equation of the line is:
y = x - 6
Divide. Write your answer in scientific notation.
5 x 10⁹
5 x 10¹
Answer:
= 4.875 × 105
(scientific notation)
= 4.875e5
(scientific e notation)
= 487.5 × 103
(engineering notation)
(thousand; prefix kilo- (k))
Step-by-step explanation:
hope this helps
Lee bought a T-Shirt originally priced at $55 that was reduced in price by 40%. What was the reduced price?
$45
$43
$35
$33
Answer: $33
Step-by-step explanation: I've done it before Have a nice day <3
From a standard deck of 52 playing cards what are the ODDS IN FAVOR of selecting an ace then a face card WITH REPLACEMENT.
Enter your answer as a simplified ratio.
Odds in Favor:
The odds in favor of selecting an ace then a face card is 3/52.
What is the probability?
Probability is used to determine the odds in favor of an event happening. The odds in favor of an event happening lies between 0 and 1. The greater the odds in favor of the event happening, the closer to one, the probability value would be. In a deck of cards, there are 13 aces and there are 12 face cards
The odds in favor of selecting an ace then a face card = (number of ace cards / total number of cards) x (number of face cards / total number of cards)
(13 / 52) x (12 / 52)
1/4 x 3/13 = 3/52
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Find the x and y intercepts from the graph. Be sure to include parenthesis in your answer.
The x-intercept will be 5 , y-intercept will be 4 and the coordinate will be (x , y) = (5 , 4).
What is an intercept ?
An intercept is a location on the y-axis where the line's slope passes. It is the y-coordinate of the location where a line or curve crosses the y-axis.
It is given that we have to find out the x and y intercepts from the given graph.
We know that , a function's x-intercept is the value of x at the point where the graph crosses the horizontal axis, or when y = 0. As a result, while examining the function's graph, we find out that the x-intercept is equal to 5.
Similarly , The value of y when the graph crosses the vertical axis, or the value of y when x = 0, is the y-intercept of a function. As a result, while examining the function's graph, we find out that the y-intercept is equal to 4.
So , the coordinate will be (x , y) = (5 , 4).
Therefore , the x-intercept will be 5 , y-intercept will be 4 and the coordinate will be (x , y) = (5 , 4).
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M (4,6) is the midpoint of AB. If B is (5,7), find the
coordinates of A.
The coordinates of A are (3, 5).
According to the section formula-
If a point (x , y) divides a line in the ratio of m : n, where the two endpoints of the line are (x1, y1) and (x2, y2), then-
x = (nx1 + mx2)/ (m + n)
and y = (ny1 + my2)/ (m + n)
Here, M (4,6) is the midpoint of AB and B is (5,7)
Let the coordinates of A be (x2, y2)
Therefore,
x1 = 5, y1 = 7
x = 4, y = 6
Since, midpoint divides a line segment into two equal halves, m : n = 1 : 1
Now, substituting the values in the section formula we get-
4 = (5 + x2)/2
4 × 2 = 5 + x2
8 = 5 + x2
5 + x2 = 8
x2 = 8 - 5
x2 = 3
and 6 = (7 + y2)/2
6 × 2 = 7 + y2
12 = 7 + y2
7 + y2 = 12
y2 = 12 - 7
y2 = 5
Thus, the coordinates of A are (3, 5).
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After following her exercise program from Problem 4 for a month, your friend plans to increase the calories she burns with each session. She still wants to exercise for 40 min every other day, but now she wants to burn 460 calories during each session. If she only runs and jogs, how many minutes of each exercise type should she do now?
The following system of equations is solved to find how many minutes of each exercise type she should do now:
x + y = 40.ax + by = 460.In which a is the amount of calories lost per minute running, and b is the amount of calories lost per minute jogging.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: number of minutes running.Variable y: number of minutes jogging.She still wants to exercise for 40 min every other day, hence:
x + y = 40.
She wants to burn 460 calories during each session, hence:
ax + by = 460.
In which a is the amount of calories lost per minute running, and b is the amount of calories lost per minute jogging. (the problem is incomplete and I couldn't find it anywhere, hence I am speaking into general terms).
Then the following system of equations is solved to find how many minutes of each exercise type she should do now:
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Please help me please
Step-by-step explanation:
I can't draw here, but I can tell and explain to you what happens to the points (incl. N).
remember the slope of lines, and what happens when we have to create a perpendicular slope (90°) ?
x and y in the slope ratio y/x go upside down and the sign flips (that means it flips for one of them).
a rotation by 90° follows the same principles.
x and y trade places, and for one of them the sign flips.
the only "difficult" trick is to determine, if the sign of x or of y flips.
let's look at N first.
N = (-5, -4)
the rotation counterclockwise takes it over into the 4th (bottom right) quadrant, where x values are positive.
aha, so the sign of x flips after x and y trade places, and we get
N' = (4, -5)
now for the other points
X = (-3, -2)
the same principle as for N
X' = (2, -3)
B = (-4, 1)
this is now moving from the 2nd (where y values are positive) to the 3rd quadrant (where x and y are negative).
so, again the sign of x flips after x and y trade places
B' = (-1, -4)
with the new coordinates of the points you can now easily draw the new triangle'.
Which statements about square roots are true? Check all that apply.
1.) The square root of a positive number cannot be negative.
2.) All positive numbers have two square roots.
3.) 18 9 because 9(2) = 18.
4.) √49 7 because 7(7) = 49.
5.) 25=5 because 5²= 25.
Statements 2, 4 and 5 are true.
Let us check each statement one by one-
1. The square root of a positive number cannot be negative-
This statement is false. Let us take an example. If we take a number, say 4, 4 has 2 square roots- 2 and -2. This is because 2 × 2 = -2 × -2 = 4. Thus, the square root of a positive number can be negative.
2. All positive numbers have two square roots.
This statement is true. It follows from the example in 1 that any positive number has 2 square roots- one negative and one positive.
3. √18 = 9 because 9(2) = 18
The given statement is false. √18 ≠ 9. If √18 was equal to 9, then 9 × 9 must be 18. But 9 × 9 is 81. Hence, false.
4. √49 = 7 because 7(7) = 49
The given statement is true. √49 = 7 as 7 × 7 = 49
5. √25 = 5 because 5²= 25
The given statement is true. √25 = 5 as 5 × 5 = 25
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Enter the range of values for x:
A
15
B
18
2x-10
[?] << <[ ]
48°
C
A triangle is congruent, and Range of values for x is 5 < x < 29
According to the figure, if L(AB) is less than L(AD), the ∠ACB must be less than the ∠ACD. Take note of how these angles are opposite to the sides stated.
∴ ∠ACB < ∠ACD
⇒2x-10 < 48
At the same time, 2x-10 > 0.
∴ 0< 2x-10 < 48
0+10 < 2x < 48+10 , add 10 to both sides
10 < 2x < 58
10/2 < x < 58/2 , divide 2 by both the side
∴ 5 < x < 29
Range of values for x is 5 < x < 29
Complete question is
Enter the range of values for x:
AB =15, ∠BCA =( 2X-10)°, and AD=18 have angle ∠DCA= 48°
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write the equation of the parabola that passes through the point (1,5) and has x-intercepts 2 and 6
Answer:
[tex]x^2-8x+12[/tex]
Step-by-step explanation:
Knowing both intercepts we can write the equation in factored form:
[tex](x-2)(x-6)[/tex]
Now use distributive property to find the equation in standard form:
[tex](x-2)(x-6)\\x^2-6x-2x+12\\x^2-8x+12[/tex]
-8
8
-4
ty
-8
4
8
00
x
What is the x-coordinate of the y-intercept?
05
Step-by-step explanation:
the X is always O when we talk about the y intercept and the Y id always O when we talk about the x intercept
x³=729 solve the equation
Answer:
x = 9
Step-by-step explanation:
Rearrange
[tex]\sf \rightarrow x^3 - 729 = 0[/tex]
Factor using (a-b) × (a^2 +ab +b^2)
a^3 + a^2b + ab^2 - ba^2 - b^2a - b^3 =
a^3 + (a^2b-ba^2) + (ab^2-b^2a) - b^3 =
a^3 + 0 + 0 - b^3 =
a^3 - b^3
x^3 = x^1
Rearrange(Using polynomial/cube roots)
(x - 9) × (x2 + 9x + 81) = 0
Subtract/Add
x - 9 = 0 = 9
x^2 + 9x = -81
-81 + 81/4
-243/4
x^2 + 9x + (81/4) = -243/4
(x + (9/2)) × (x + (9/2)) = (x + (9/2)) × 2
(x + (9/2))2 = -243/4
x^2 + 9x + 81 = 0
√243 = 3 × 3 × 3 × 3 × 3 = 3 × 3 × √3 = ±9 × √3
= ±9x = (-9 ± 9 × 1.732(i)) / 2
= ±9x
Divide by 9 (Absolute value: positive)
|9/9| = x
Reverse, re-arranging x (Assuming x = 1)
x = |9/x|
Thus,
x = 9
Hope this helped, let me know if anything confuses you, and I will try my best to address that. Have a good day!
Problem (Please HELP!!!)
Kyra, Tai, and Rodney all measure sections of a tree that fell over during the last thunderstorm. They have different measurement tools, so Kyra measures 4 feet, Tai measures 3.5 yards, and Rodney measures 50 centimeters. There are 12 inches per foot, 3 feet per yard, and 2.54 centimeters per inch. If Kyra wants the total length of the tree to the nearest inch, how long is the tree?
Why was it necessary to add the three separate measurements together?
Why couldn't you add the feet, yards, and centimeters together? Use at least 1 complete sentence.
Kyra wants the total length of the tree to the nearest inch it will be 193.68 inches.
The measurement couldn't have been added earlier because they're in different units
How to illustrate the information?Kyra measures 4 feet. This in centimeters will be:
= 4 × 30.48 = 121.92 cm
Tai measures 3.5 yards. This in centimeters will be:
= 91.44 × 3.5
= 320.04 cm
Rodney measures 50 centimeters.
Therefore, the addition will be:
= 121.92 cm + 320.04 cm + 50cm
= 491.96 cm
The total length in inches will be:
1 inch = 24 cm
= 491.96 / 2.54
= 193.68 inches.
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A rectangular swimming pool is 8 ft deep. One side of the pool is 4.5 times longer than the other. The amount of water needed to fill the swimming pool is 5184
cubic feet. Find the dimensions of the pool.
Answer: The dimensions are 8 and 28
PLEASE I NEED HELP ASAP!!! 50 POINTS!
Expand each logarithm.
log₄5 x
If the expression is log₄5 x,then the expansion of this will look like
(log 5+ log x)/log 4.
Given that the expression is log₄5 x.
We are required to find the expansion of the expression.
Base change theorem says that [tex]log_{a}b[/tex]=[tex]log_{x}b/log_{x}a[/tex]. We use the change of base formula to re-write a logarithm operation as a fraction of logarithms with a new base.
The expression is log₄5 x.
log₄5 x=(log 5+log x)/log 4
(We know that [tex]log_{a}b[/tex]= log b/ log a and log mn =log m +log n)
Hence if the expression is log₄5 x then the expansion of this will look like (log 5+ log x)/log 4.
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Interest Suppose you deposit $ 2000 in a savings account that pays interest at an annual rate of 4 % . If no money is added or withdrawn from the account, answer the following questions.
b. How much will be in the account after 18 years?
$4051.63 will be in the account after 18 years.
The formula to be used is given as follows :
A(t) = a ( 1 + r )^t (1)
where, A(t) = future value
a = principal amount or amount initially deposited.
r = annual interest rate
t = time
According to the question we have been given that
a = $2000
r = 0.04
t = 18 years
putting the required values in equation (1) we get
A(t) = 2000 (1+0.04)^18
A(t) = 2000 (1.04)^18
A(t) = 2000*2.03
A(t) = $4051.63
Thus $4051.63 will be in the account after 18 years.
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Two cities have the same longitude. the latitude of the city a is 6 degree north and the latitude of city b is 30 degree north. assume the radius of earth is 3960 miles. find the distance between two cities.
Two cities have the same longitude .The latitude of the city a is 6 degree north and the latitude of city b is 30 degree north. Then the distance between two cities is 1658.844 miles
Two cities have the same longitude. the latitude of the city a is 6 degree north
and the latitude of city b is 30 degree north.
assume the radius of earth is 3960 miles.
find the distance between two cities.
City A = 6° = 6°× π/180 = 0.1047 rad
City B = 30° = 30° × π /180= 0.5236 rad
multiply by π/180 to convert the degree to radian
radius of Earth = 3960 miles
to find out
distance between City A and City B
solution
we first get here central angle between A and B city is
central angle between A and B city = 0.5236rad - 0.1047 rad
and
now by arc length so we get distance
distance = 3960 miles × (0.5236 rad - 0.1047rad ) as radius given 3960
distance = 1658.844 miles
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Use v=-0.0098 t+c ln R , where v is the velocity of the rocket, t is the firing time, c is the velocity of the exhaust, and R is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. A rocket has a mass ratio of 24 and an exhaust velocity of 2.5km/s . Determine the minimum firing time for a stable orbit 300km above Earth.
The minimum firing time for a stable orbit 300km above Earth is 25 seconds.
What is an orbit?An orbit, in the context of celestial mechanics, is the curved path taken by an object, such as the trajectory of a planet around a star, a natural satellite around a planet, or an artificial satellite around an object or place in space, such as a planet, moon, asteroid, or Lagrange point.
Ordinarily, the term "orbit" denotes a trajectory that repeats itself on a regular basis, though it can also denote a non-repeating trajectory. Kepler's rules of planetary motion roughly describe the elliptic orbits that planets and satellites take, with the center of mass orbiting at a focal point of the ellipse.
We know that to achieve stable orbit 300 km above earth, the velocity must be ≈ 7.7 km/s
We will use the given formula
v = -0.0098 t+c ln R
Here given that c = 2.5 km/s
R = 24
Apply the information in the equation we get,
7.7 = -0.0098t + 2.5 In 24
we can also write
t = [tex]\frac{7.7 - 2.5 In 24}{-0.0098}[/tex]
= [tex]\frac{7.7 - 7.945}{-0.0098}[/tex]
= 25s
Hence, the minimum firing time for a stable orbit 300km above Earth is 25 seconds
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A water park has pools, slides, and rides that, in total, make use of 6.1 x 107 gallons
of water. They plan to add a ride that would make use of an additional 6.3 × 104
gallons of water. Use scientific notation to express the total gallons of water made use
of in the park after the new ride is installed.
as i said i would go with 93-51=42
Step-by-step explanation:
8.7*10.6=92.22 and 8.7*10+6=93
4.8*10.3=49.44 and 4.8*10+3=51
so i am thinking that you would add 93+51 which equals 144...
or you could try 93*51 but your gunna get 4,743
or try 93-51 which is 42
or try 93 diveded by 51 which is 1.8235294117647058
I would go with 93-51=42!
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hope this helped :)
please help me!!!!!!!!!!!!
Answer: 38 and 24
Step-by-step explanation:
38 and 24
Sam has only quarters and dimes in his pocket. He has a total of 12 coins, totaling 1.95 . How many of each coin does Sam have?
Answer: Sam has 7 quarters and 2 dimes
Step-by-step explanation: If you have 7 quarters you would have $1.75 and with the 2 dimes which make 20 cents more give you $1.95 in total! and every quarter is worth 25 cents multiplied by 7 gave me 175 but in decimal form would 1.75
Hope this helps! :D
What is the inverse of f if f(x)=√√x-5
The inverse function of f(x) is; f-¹(x) = x³ + 5
To find the inverse of the function;
We should represent f(x) as y.
Now we have;
By taking the cube of both sides;
y³ = x - 5
By solving for x;
x = y³ + 5
By swapping x and y; we have;
y = x³ + 5
f-¹(x) = x³ + 5.
The inverse function of f(x) is; f-¹(x) = x³ + 5.
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what is 0.378937382 in surds
Answer:
2√2 -√6
Step-by-step explanation:
You want to know the surd representation of the irrational number that rounds to 0.378937382.
Trial and errorThe plural "surds" suggests this is the difference of two irrational roots. Looking at √(n+1) -√n, we find that √3 -√2 is the nearest, but does not match.
Looking at √(n+2) -√n, we find that √8 -√6 matches all 9 digits when rounded to the 9th decimal place. 20 digits of that value are ...
0.37893738196301199941
The given number approximately matches the irrational value ...
2√2 -√6
__
Additional comment
We programmed a calculator to find the values of √(n+2) -√n for n = 1..10. The result is attached. The 6th value matches, and corresponds to n=6.
In general, finding a surd representation of an arbitrary value seems to be a matter of trial and error. Perhaps your curriculum materials offer an algorithm.