Answer:
x=7
Step-by-step explanation:
an aircraft is climbing at 30° angle to the horizontal how fast is the aircraft gaining alitude if it’s speed is 500 mph
The speed rate at which the aircraft is gaining altitude is;
dx/dt = 250 miles per hour
Since the aircraft is climbing at 30° to the horizontal. it means there will be a vertical component which will be the altitude and also a horizontal component which will be the horizontal distance covered. while the hypotenuse will be how far it has climbed.
Let us call the vertical component x and the hypotenuse component z.
Thus, from trigonometric ratios, we can say that;
sin 30 = x/z
We are looking for how fast the aircraft is gaining altitude. Thus, using Liebniz notation, we can say this rate is; dx/dt. Thus;
sin 30 = (dx/dt)/(dz/dt)
0.5 = (dx/dt)/(dz/dt)
0.5 × (dz/dt) = dx/dt
Its' speed is 500 mph. This means dz/dt = 500
Thus;
dx/dt = 0.5 × 500
dx/dt = 250 mph
Hence, the speed rate at which the aircraft is gaining altitude is;
dx/dt = 250 miles per hour
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In a population where 25% of voters prefer Candidate A, an organization conducts a poll of 9 voters. Find the probability that 2 of the 9 voters will prefer Candidate A.
(Report answer accurate to 4 decimal places.That is, round to 4 decimal places.)
The probability that 2 of the 9 voters will prefer Candidate A is 0.30033
Given that 25 % of voters prefer candidate A
Total number of voters = 9
Do we have to calculate the probability that 2 of the 9 voters will prefer Candidate A =?
In this question, we used binomial distribution to find the probability that 2 of the 9 voters will prefer candidate A.
The binomial distribution follows the probability mass function of:
⁹C₂ * (0.25) ² * (0.75)⁷ =>
⁹C₂ = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)/ (7 * 6 * 5 * 4 * 3 * 2 * 1) (2 * 1) =>
⁹C₂ = 9 * 8/2 = 36
Now, 36 * (1/4)² * (3/4)⁷ = 0.30033
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Joe wants to purchase a new 4-wheeler that costs $18,550. He decides to get it in installments plants but needs to leave an 15.25% down payment. How much will the finance charge be if he has a monthly payment of $250 for 10 years? ROUND TO THE NEAREST CENT!
Rates, however, differ for specific customers depending on their credit score, loan term, and other factors.
How much is a finance charge?In conclusion, the finance charge formula is as follows:
Finance fee = Balance that is owed. Annual Percentage Rate (APR) / 365 Days in Billing Cycle.
The average cost of an ATV is between $5,000 and $15,000, with a down payment that is often between 10% and 20%.The typical deposit for recreational vehicles is in the range of 10% to 20%. You might need between $500 and $5,000 for the down payment for a UTV that ranges in price from $5,000 to $25,000.
Conventional ATV loans are provided by banks and credit unions for set terms that are typically between three and six years long. The yearly percentage rates are also fixed. Your credit score, the loan period, the cost of the ATV, and the company funding the loan will all have an impact on the APR.
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The charge-to tap time (m) for carbon steel in one type of open-hearth furnace is to be determined for each heat in a sample n. If the investigator believes that almost all times in the distribution are between 320 and 440, what sample size would be appropriate for estimating the true time to within 5 min confidence level of 95%
The sample size appropriate for estimating the true time to within 5 min confidence level of 95% is 139
How to solve for sample sizeWe have to get the range of the values in this distribution
The range is given as: 440 - 320
= 120
through the range rule, we would have to solve for the standard deviation
= 120 / 4
= 30
At the 95 percent level of confidence, the critical value of Z is solved as 1.96
To get the value of n which is the sample size, we would have to use the Margin of error formula
[tex]ME = z*\frac{sd}{\sqrt{n} }[/tex]
ME = 5
[tex]5 = 1.96 * \frac{30}{\sqrt{n} }[/tex]
n = 138.2976
n is approximately 139
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Which BEST describes the decimal form of a rational number?
Responses
A either terminates in 0's or repeats. either terminates in 0's or repeats.
B eventually repeats a non-zero digit eventually repeats a non-zero digit
C neither terminates nor repeat sn either terminates or repeats
D always terminates in 0's
Answer:
Step-by-step explanation:
A.) either terminates in 0's or repeats.
Some decimals repeat and some decimals don't.
At a local ice-cream store, 210 people were surveyed on whether they preferred eating ice cream from a cone or a cup. Of the 210 people surveyed, 70 were adults and 140 were children. Of the responses, 150 indicated the cone as the preferred method of eating ice cream. For those surveyed, there was no association between age and preferred method of eating ice cream. Which of the following tables show the distribution responses?
answer choices
Graph i
Graph ii
Graph iii
Graph iv
Graph v
Graph ii shows that 150 people preferred eating ice cream from a cone, while 60 people preferred eating ice cream from a cup. There was no association between age and preferred method of eating ice cream.
Graph ii is a table that shows the distribution of responses to the survey about preferred method of eating ice cream. The table shows that out of the 210 people surveyed, 70 were adults and 140 were children. Of the 210 people surveyed, 150 indicated the cone as the preferred method of eating ice cream, while 60 indicated the cup as the preferred method. This table indicates that there is no association between age and preferred method of eating ice cream, as the responses were evenly distributed between adults and children. This information can be used to determine the preferences of customers at the ice-cream store and can help inform decisions about how to serve the ice cream. For example, the store may choose to provide more cones than cups based on the survey results. Additionally, this table can be used to compare the preferences of different demographic groups, although in this case the survey showed that there was no association between age and preferred method of eating ice cream.
Adults: 70 people surveyed, 35 preferred cone, 35 preferred cup
Children: 140 people surveyed, 115 preferred cone, 25 preferred cup
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This is for my calculus class, please help.
The area bounded by y = x² + 5 and the x-axis from x = 3 to x = -2 is 110/3.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
y = x² + 5
The area bounded by y = x² + 5 from x = -2 to x = 3.
= [tex]\int\limits^{3}_{-2} {(x^2 + 5)} \, dx[/tex]
= [tex][x^3/3]^{3}_{-2}[/tex] + 5 [tex][x]^{3}_{-2}[/tex]
= 1/3 [tex][(3)^3 - (-2)^3][/tex] + 5 [3 + 2]
= 1/3 [27 + 8] + 5 x 5
= 1/3 x 35 + 25
= 35/3 + 25
= (35 + 75)/3
= 110/3
Thus,
The area bounded is 110/3.
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What is 99 to the power of 74?
Answer:
4.75340042E147
Step-by-step explanation:
How to Graph y-2=2/3(x+4)
Answer:
Step-by-step explanation:
To graph the equation y-2=2/3(x+4), you can follow these steps:
Begin by isolating the y term on one side of the equation. To do this, you can add 2 to both sides of the equation:
y-2+2=2/3(x+4)+2
y=2/3(x+4)+2
Next, you can simplify the right side of the equation by multiplying 2/3 by (x+4):
y=2/3(x+4)+2
y=(2/3)x+(2/3)4+2
y=(2/3)x+8/3+2
y=(2/3)x+14/3
This is the standard form of the equation y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is m=2/3 and the y-intercept is b=14/3.
To graph the equation, you can use the slope and y-intercept to plot the first point on the graph. The y-intercept is the point where the graph crosses the y-axis, so you can plot the point (0,14/3) on the graph.
From this point, you can use the slope to find the next point on the graph. The slope is the change in y over the change in x, so you can use the slope to find the change in y and the change in x between two points on the graph. For example, you could choose a point that is 1 unit to the right of the y-intercept, or (1,0). The change in y between these two points is (14/3)-0=14/3 and the change in x is 1-0=1. Using the slope, you can find the y-coordinate of the next point on the graph:
y2=y1+m(x2-x1)
y2=14/3+2/3(1-0)
y2=14/3+2/3
y2=20/3
You can repeat this process to plot additional points on the graph. For example, you could choose a point that is 2 units to the right of the y-intercept
write the ratio as a fraction in simplest form 35 to 112
Answer:
5 :16
Step-by-step explanation:
35:112 <===== divide both by '7 ' to get 5/16
A tree casts a shadow 21 m long. The angle of elevation of the sun is 51. What is the height of the tree?
13.2m
25.9 m
17m
16.3m
The height of the tree would be 25.9 meters.
Option (B) is correct.
What is the tangent ratio in trigonometry?
The ratio of the opposite side of a right triangle to the adjacent is called the tangent and is given the symbol tan.
tan = Opposite side/Adjacent side
A tree casts a shadow 21 m long. The angle of elevation of the sun is 51.
In the given figure, Apply the tangent ratio
tan51° = AB/BC
1.23 = h/21
h = 1.23 * 21
h = 25.9 m.
Hence, the height of the tree would be 25.9 meters.
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Find length, width, perimeter, and area
Answer:
length is 4 units
width is 2 units
Perimeter is 12 units
Area is 8 sq units
Step-by-step explanation:
Since you have a graph of the points, you can see the shape is a rectangle. Count to find the measure of the length and width.
Perimeter is the distance all the way around the shape.
length + width + length + width
Or 2(length)+2(width)
= 2 + 4 + 2 + 4
= 12
Area is
length × width
= 4 × 2
= 8 sq units.
NO LINKS!!!
Write an expression for the apparent nth term a_n of the sequence. (Assume that n begins with 1.)
a. 1, -1, 1, -1, 1, . . .
a_n =
b. -1, 2, 5, 8, 11, . . .
a_n =
a_n=
Answer:
[tex]\textsf{a)} \quad a_n=(-1)^{n-1}[/tex]
[tex]\textsf{b)} \quad a_n=3n-4[/tex]
Step-by-step explanation:
Sequence aGiven sequence:
1, -1, 1, -1, 1, ...
The given sequence is geometric since there is a common ratio of -1 between consecutive terms.
To find the common ratio of a geometric sequence, divide a term by the previous term:
[tex]\dfrac{a_5}{a_4}=\dfrac{1}{-1}=-1[/tex]
[tex]\dfrac{a_4}{a_3}=\dfrac{-1}{1}=-1[/tex]
[tex]\dfrac{a_3}{a_2}=\dfrac{1}{-1}=-1[/tex]
[tex]\dfrac{a_2}{a_1}=\dfrac{-1}{1}=-1[/tex]
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given:
a = 1r = -1Substitute the values of a and r into the formula to create an equation for the nth term:
[tex]\implies a_n=1 \cdot (-1)^{n-1}[/tex]
[tex]\implies a_n=(-1)^{n-1}[/tex]
Sequence bGiven sequence:
-1, 2, 5, 8, 11, ...
The given sequence is arithmetic since there is a common difference of 3 between consecutive terms.
To find the common difference of an arithmetic sequence, subtract consecutive terms:
[tex]a_2-a_1=2-(-1)=3[/tex]
[tex]a_3-a_2=5-2=3[/tex]
[tex]a_4-a_3=8-5=3[/tex]
[tex]a_5-a_4=11-8=3[/tex]
[tex]\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a_n$ is the nth term. \\ \phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given:
a = -1d = 3Substitute the values of a and d into the formula to create an equation for the nth term:
[tex]\implies a_n=-1+(n-1)3[/tex]
[tex]\implies a_n=-1+3n-3[/tex]
[tex]\implies a_n=3n-4[/tex]
Find f'(x) and simplify.
f(x)=x²+5/3x-2
Which of the following shows the correct application of the quotient rule?
A. (3x-2)(2 x)-(x²+5)(3)/(3 x-2)²
B. (3 x-2)(2 x)-(x²+5)(3)/(x²+5)²
C. (x²+5)(3)-(3 x-2)(2 x)/(x²+5)²
D. (x²+5)(3)-(3 x-2)(2 x)/(3 x-2)²
The correct application of the quotient rule is f'(x) = [(3x - 2)2x - (x²+5)(3)]/[(3x - 2)]²
What is the derivative of a function?The derivative of a function f'(x) is the rate of change of the function with respect to a variable.
How to find the correct application of the quotient rule?Since we have f(x) = (x²+5)/(3x-2), to find its derivative f'(x), we use the quotient rule.
What is the quotient rule?Given a function f(x) = u(x)/v(x) then the derivative of f(x) which is f'(x) = [v(x)du(x)/dx - u(x)dv(x)/dx]/[v(x)]²
So, with f(x) = (x²+5)/(3x-2)
u(x) = (x²+5) and v(x) = (3x-2)
So, du(x)/dx = d(x²+5)/dx
= d(x²+5)/d(x²+5) × d(x²+5)/dx
= 2x
and
dv(x)/dx = d(3x - 2)/dx
= d3x/dx - d2dx
= 3 - 0
= 3
Since f'(x) = [v(x)du(x)/dx - u(x)dv(x)/dx]/[v(x)]², substituting the values of the variables into the equation, we have that
f'(x) = [v(x)du(x)/dx - u(x)dv(x)/dx]/[v(x)]²
f'(x) = [(3x - 2)2x - (x²+5)(3)]/[(3x - 2)]²
So, the quotient rule is f'(x) = [(3x - 2)2x - (x²+5)(3)]/[(3x - 2)]²
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I’ll give BRAINLIEST if correct I need asap question is in the photo attached
The domain and range of the function will be Real number and [0, ∞). The parent function f(x) is get shifted down by 2 units.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
If the vertex of the absolute function is at (h, k). Then the absolute function is given as
f(x) = |x - h| + k
The function is given below.
g(x) = |x + 3|
The graph of the function g(x) is given below. From the graph, the domain and range of the function will be Real number and [0, ∞).
The parent function and translated function are given below.
f(x) |x| and h(x) = |x| - 2
The parent function f(x) is get shifted down by 2 units.
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Paul pays the newspaper company 70% of what he collects how much would he keep for himself in a month when he collected 450.00
Answer:
135.00
Step-by-step explanation:
since,he pays 70% then he keeps 30%.
and 30% of 450.00 is 135.00
Let f be a differentiable function, defined for all realnumbers x, with the following properties. Find f(x). Show yourwork.
i) f'(x)=ax2+bx
ii) f'(1)=6 and f"(1)=18
iii. =18
The differentiable function f with the given properties is [tex]f(x)=4x^3-3x^2+10[/tex].
What is a differentiable function:
A function with a differentiable value of one real variable is one whose domain contains a derivative. In other words, each interior point in the domain of a differentiable function's graph has a non-vertical tangent line.
The given properties for the differentiable function f are:
[tex](i) f'(x)=ax^2+bx\\ (ii) f'(1)=6, f''(1)=18\\ (iii) \int\limits^2_1 {f(x)} \, dx =18[/tex]
From (i) we can get [tex]f''(x)=2ax+b[/tex]
By substituting (ii) in (i) we will get:
a+b=6 and 2a+b=18. By solving these two equations we will get the following:
a=12, b=-6.
We will integrate (i) on both sides, we will get:
[tex]f(x)=\frac{ax^3}{3} +\frac{bx^2}{2} +c[/tex] where c is the integration constant.
In this equation, we will substitute a,b.
[tex]f(x)=\frac{12x^3}{3} +\frac{-6x^2}{2} +c\\ \\ f(x)= 4x^3-3x^2+c[/tex]...................(iv)
Now we will substitute (iv) in (iii), and we will get:
[tex]\int\limits^2_1 {( 4x^3-3x^2+c)} \, dx =18\\ \\ (2^4-2^3+2c)-(1^4-1^3+c)=18\\ \\c=10[/tex]
Therefore [tex]f(x)=4x^3-3x^2+10[/tex].
Complete question:
Let f be a differentiable function, defined for all real numbers x, with the following properties. Find f(x). Show your work.
[tex](i) f'(x)=ax^2+bx\\ (ii) f'(1)=6, f''(1)=18\\ (iii) \int\limits^2_1 {f(x)} \, dx =18[/tex]
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write and equivalent expression to 24x^2 +56x choose all that apply
Here is the step by step x
The equivalent expression to 24x^2 +56x is : 8x(3x+7)
What is an equivalent expression?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).Using the equality (=) symbol, equivalent phrases are represented. Because both expressions have the same value for any value of x, 3(x + 2) and 3x + 6 are identical expressions. 3x + 6 = 3 × 4 + 6 = 18.When two expressions can be reduced to a single third expression or when one of the expressions can be expressed in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.Given data :
= 24[tex]x^{2}[/tex] + 56
= 24 xx + 56
Rewrite 24 as 8 * 3
Rewrite 56 as 8 * 7
= 8 * 3xx + 8 * 7x
= 8x (3x+7)
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сделайте пожалуйста 5 заданий из этих
Answer:
Step-by-step explanation:
HELP PLEASE
Look at the picture below
Answer:
a) TPR
b) NM
c) x=6
Step-by-step explanation:
a) since the angle K is the middle letter on in the first triangle, the second triangle's middle letter will be P since they correspond
b) TR is congruent to NM because if you flipped TR upside down, it would match directly with NM
c) 4x-3=21
4x=24
x=6
this is because TR and NM are congruent, so 4x-3 is equal to 21
Select the correct answer.
Convert 3-3i to polar form.
A. 3√2cis π/4
B. 3√2cis 3π/4
C. 3√2cis 5π/4
D. 3√2cis 7π/4
(Please mark brainliest <3)
Correct option is D.
We have been given a complex number 3-3i we have to convert it in the polar form:
Polar form of a complex number: z=r(cosθ+isinθ)
Where, r=√x^2+ y^2
the general form of complex number is:
x+iy
•Here, x=3 and y=-3
•Hence, r=√3^2+(-3)^2}= √18
•And θ=tan −1 y/x
•θ=tan −1 -3/3
•θ=tan −1 (−1)
•θ=2π− π/4
•θ= 7π/4
•Hence, substituting all the values in polar form formula we get:
z= √18cos( 7π/4) + isin (7π/4)
Kylie reads about two popular cell phone apps one app uses 1/2 of a phones storage space the other app uses 5/12 of a phone storage space Explain how Kylie can find the difference in the two storage space of the two apps without drawing a visual model
Answer:
5/12 phone uses less storage space
Step-by-step explanation:
Find a common denominator so you can compare the fractions easily. Use 12.
1/2 = 6/12
5/12 < 6/12, so now you can see that the phone that uses 5/12 of storage space uses less than the one that uses 1/2
what are the coordinates of the centroid of ABC with vertices A (-3, 1), B (-2, 4), and C (5, -2)
Answer:
(0, 1/3)
Step-by-step explanation:
To find the centroid of a triangle with vertices A, B, and C, we can use the following formula:
centroid = (x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3
where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices A, B, and C, respectively.
In this case, we have A = (-3, 1), B = (-2, 4), and C = (5, -2), so the centroid of the triangle is:
centroid = ((-3) + (-2) + 5) / 3, (1 + 4 + (-2)) / 3 = (0, 1/3)
Therefore, the coordinates of the centroid of ABC are (0, 1/3).
write the equation of the line that crosses the y-axis at "-2" and has a slope of 2/3
The slope intercept form of equation of required line is
[tex]y = \frac{2}{3}x - 2[/tex]
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Slope of the required line = [tex]\frac{2}{3}[/tex]
The line passes through (0, -2)
Equation of the required line =
[tex]y - (-2) = \frac{2}{3}(x - 0)\\y + 2 = \frac{2}{3}x\\y = \frac{2}{3}x-2[/tex]
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Solve the system of equations graphed on
the coordinate axes below.
y=-3x - 5
y =4/3x-5
Placing a point at the graph's y-intercept offor the equation (0,-5).
How to solve the system of equations graphed?Placing a point at the graph's y-intercept of -4 for the equation y =3x - 5 (0,-5). From the point (0,-5) go one down, three to the right, and then add another point because the slope is -5The two points may be connected by drawing a line using a straightedge. Keep going after the two points. Past them, continue the line.same for y = 4/3x-5. Place a point at since the y-intercept is at 2, (0,-5). Since the slope is 4/3, go up 4and to the right 3 before drawing a second point from (0,-5). The two points may be connected by drawing a line using a straightedge. Don't, once more, end at the two points. Past them, continue the line.To learn more about graph's y-intercept refer to:
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assume that there is a party consisting of people between the ages of 18 and 24 inclusive. how many people would have to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year? note: assume the range of birth years include 2 leap years. (
The minimum number of people that would need to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year is Three (3).
To find the number of people that would need to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year, we need to consider the number of possible birthdays that exist within the given age range (18 to 24 inclusive).
There are 12 months in a year, and each month has between 28 and 31 days (depending on the month). Therefore, there are a total of 12 * 31 = 372 possible birthdays within a given year.
There are 7 possible birth years within the given age range (18 to 24 inclusive), which means there are a total of 7 * 372 = 2596 possible birthdays within the given age range.
Since we want to guarantee that at least three people share the same birthday, we need at least 3 people to be at the party.
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Complete Question:
Assume that there is a party consisting of people between the ages of 18 and 24 inclusive. How many people would have to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year? Note: assume the range of birth years include 2 leap years.
The scale of map is 4m = 18mi
map : 6.8m
actual : ____ mi
Answer:
30.6
Step-by-step explanation:
18/4 = 4.5
4.5 × 6.8 = 30.6
The sum of three numbers is 68. The first number is 8 more than the second. The third number is 2 times the second. What are the numbers?
The numbers are 23,15,30 if the sum of three numbers is 68.
What is an equation?When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions. For instance, an equation is defined as having one or more variables in French.
Determine which values of the variables result in the equality to be true in order to solve an equation with variables. The values of the variables that must fulfill the equality to constitute the answer are known as the unknowns, together with the variables for which the equation must be solved.
Let the first number be x
The second number is 8 Less than the x is x-8
The third number is 2 times the second is 2(x-8)
Sum of the three numbers is 68
x+x-8+2(x-8)=68
4x-24=68
4x=92
X=23
Therefore, the numbers are 23,15,30
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PLEASE HELP FAST WILL GE T BRAINLIEST!!
Answer:
Step-by-step explanation:
bro get some lighting in ur room and set it on a table,i cant even see what im lookking at ._.
pls help ill mark brainliest
Answer:
Step-by-step explanation:
since you are rotating the image it shows y k j and l so it would be 5.5