here is an inequality 2x + 5 > 50 explain the steps you would use to solve the equation for x what would the graph look like
Answers
Answer:
[tex]x>22.5[/tex]
Step-by-step explanation:
Given linear inequality:
[tex]2x+5>50[/tex]
Solving for [tex]x[/tex]
Subtracting both sides by 5.
[tex]2x+5-5>50-5[/tex]
[tex]2x>45[/tex]
Dividing both sides by 2.
[tex]\frac{2x}{2}>\frac{45}{2}[/tex]
∴ [tex]x>22.5[/tex]
The graph of the inequality is shown below.
The line is represented by dotted line because the inequality sign is only greater than which means 22.5 is not included in the solution.
Related Questions
Please help! Thanks in advance!
Answers
Answer:
The are certain things that need to be carefully observed when you add or combine the polynomials. Here is the list of certain rules for adding/combining polynomials.
Step-by-step explanation:
The are certain things that need to be carefully observed when you add or combine the polynomials - especially the polynomials with more than one variable.
Here are some of the rules for adding polynomials:
First we must identify like terms in the given polynomials, and then combine them based on the correct integer operations.When there is a plus sign, we add polynomials. It must be noted that, within polynomials, we need to add or subtract like terms. For example, when we combine like terms, such as 4x and 5x, we tend to add their coefficients i.e. 4x + 5x = 9xPlease remember we can not add polynomials if they have different exponents. For example, x²+ x can not be added.Lets add and simplify the following polynomials.
(4x + 7y) + (5x – 3y)
First clear the parenthesis.4x + 7y + 5x – 3y
Then make sue to group the like terms in accordance to their variables - try to keep them in alphabetically order, and ultimately just simplify.4x + 5x + 7y - 3y
9x + 4y
So, 9x + 4y is the answer.
Note: I can not further combine or add 9x + 4y as they are un-like. The reason is simple; un-like polynomials have different variables.
The polynomials can be add vertically too.
Just put each variable in its own columnFirst column can be termed as x-column and second column can be termed as y-columnChoosing the horizontal or vertical method is just a matter of taste.Here is the vertical method of adding (4x + 7y) and (5x – 3y) .
4x +7y
5x -3y
________
9x + 4y
________
Keywords: add, combine, polynomials
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Find the equation of a line that has the same slope ask why equals 10-4x and the same Y intercept is why equals -9x-8
Answers
Answer:
[tex]y=-4x-8[/tex]
Step-by-step explanation:
we know that
The equation of the line in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
so
1) Find the slope of the given line [tex]y=10-4x[/tex]
The slope is [tex]m=-4[/tex]
2) Find the y-intercept of the given line [tex]y=-9x-8[/tex]
The y-intercept is [tex]b=-8[/tex]
therefore
The equation of the line with
[tex]m=-4[/tex]
[tex]b=-8[/tex]
is equal to
[tex]y=-4x-8[/tex]
the ratio of the corresponding linear measures of two similar cans of cat food is 4:3. the larger can has a SA of 100 inches. find the surface area of the smaller can. round to the nearest tenth.
Answers
Answer:
56.3 in²
Step-by-step explanation:
Given 2 similar figures with linear ratio = a : b, then
area ratio = a² : b²
Here linear ratio = 4 : 3, thus
area ratio = 4² : 3² = 16 : 9
Let x be the surface area of the smaller can then by proportion
[tex]\frac{16}{100}[/tex] = [tex]\frac{9}{x}[/tex] ( cross- multiply )
16x = 900 ( divide both sides by 16 )
x ≈ 56.3 in² ( to the nearest tenth )
The surface area of the smaller can is approximately 56.3 square inches.
The student's question involves finding the surface area of a smaller can based on its similarity ratio to a larger can. Given that the ratio of the corresponding linear measures of two similar cans is 4:3 and the larger can has a surface area of 100 square inches, we can determine the surface area of the smaller can by using the square of the ratio between their sizes. Since the ratio of their surface areas is the square of their linear dimensions ratio, we can set up the calculation as follows:
[tex](3/4)^2 = x/100,[/tex]
where x represents the surface area of the smaller can. Solving for x:
[tex](3/4)^2 = (9/16) = x/100,[/tex]
x = (9/16) * 100,
x = 56.25.
Therefore, the surface area of the smaller can is approximately 56.3 square inches when rounded to the nearest tenth.
can someone help me with this problem
[tex]4b + 3 = - 9[/tex]
we have to find what b is
Answers
Answer: b= -3
Step-by-step explanation:
what does a midpoint of a line segment create? Choose All The Apply.
(in pic below)
Answers
Answer: Two lines of equal length
A point equidistant from two end points
Step-by-step explanation:
The mid - point of a line segment is the point on the segment that is equidistant from the endpoints.
It is not equidistant to all point on the segment , it is only equidistant from the endpoints.
With this , the first option is out.
The midpoint of a line divides the line into two equal part , so the second option holds and the third option holds too.
10 POINTS!!!!
2.Point p is chosen at random on CF. Find the probability that p is on DE .
Answers
Answer:
[tex]\frac{8}{17}[/tex]
Step-by-step explanation:
The total length of CF is 17 units and the length of DE is 8 units, so the probability of p being on DE is [tex]\frac{8}{17}[/tex]
Answer:
8/17 is correct.
Step-by-step explanation:
if a rectangle is 95 meters long and 65 meters wide what is the diagonal
Answers
Answer:
115.1
Step-by-step explanation:
Nadia spent 1/4 of her money on a shirt and 2/5 of her money on new shoes. What fraction of Nadias money was spent?
Answers
Answer:
13/20 of her money was spent.
Step-by-step explanation:
To find the answer you have to add these two fractions together, and to do that you must find a common denominator.
For this problem I chose to use 20 for the denominator since it is the smallest number that both 4 and 5 have in common.
Keep in mind that, whatever you do to the denominator, you must also do to the numerator, so if you multiply 5 by 4, you must also multiply 2 by 4.
5/20 + 8/20 = 13/20
Find ∫sin²x cos3x dx
Answers
Answer:
[tex]-\frac{1}{4} sin(x)+\frac{1}{6} sin(3x)-\frac{1}{20} sin(5x)+C[/tex]
Step-by-step explanation:
We begin with the integral [tex]\int{sin^2(x)cos(3x)} \, dx[/tex]
First, we can apply the power reducing formula to [tex]sin^2(x)[/tex]
This formula states: [tex]sin^2(x)=\frac{1}{2} -\frac{1}{2} cos(2x)[/tex]
This gives us
[tex]\int{(\frac{1}{2} -\frac{1}{2} cos(2x))(cos(3x)} \, dx \\\\\int{(\frac{1}{2}cos(3x) -(\frac{1}{2} cos(2x)cos(3x)} \, dx \\\\\frac{1}{2} \int{cos(3x)} \, dx -\frac{1}{2} \int{cos(2x)cos(3x)} \, dx[/tex]
Now, we can use integrate the first integral
[tex]\frac{1}{2} \int{cos(3x)} \, dx\\u=3x\\du=3dx\\\\\frac{1}{6} \int{3cos(u)} \, du\\\\\frac{1}{6} sin(u)+C\\\\\frac{1}{6} sin(3x)+C[/tex]
And now we can begin to integrate the second
[tex]-\frac{1}{2} \int{cos(2x)cos(3x)} \, dx[/tex]
To integrate this, we need to use the Product-to-sum formula, which states
[tex]cos(\alpha )cos(\beta )=\frac{1}{2} [cos(\alpha +\beta )+cos(\alpha -\beta )[/tex] . For this formula, we will use [tex]\alpha =3x\\\beta =2x[/tex]
This gives us
[tex]-\frac{1}{2} \int{\frac{1}{2}[cos(5x)+cos(x)] } \, dx \\\\-\frac{1}{4} \int{[cos(5x)+cos(x)] } \, dx\\\\-\frac{1}{4}\int{cos(5x)} \, dx -\frac{1}{4}\int{cos(x)} \, dx[/tex]
We can then use the same process of u-substitution as the previous to get the answer of [tex]-\frac{1}{20} sin(5x)-\frac{1}{4} sin(x)+C[/tex]
Lastly, we can add the values of the two integrals together to give us the final solution of
[tex]-\frac{1}{4} sin(x)+\frac{1}{6} sin(3x)-\frac{1}{20} sin(5x)+C[/tex]
What is 3/4 divided by 1/2
Answers
Answer:
3/2
Step-by-step explanation:
(3/4)/(1/2)=(3/4)(2/1)=6/4=3/2
Answer: in decimal form it is 0.375
Step-by-step explanation:
100 points and brainiest
Which of the following is true?
|−6| < 5
|−6| < |5|
|−5| < |−6|
|−5| < −6
Answers
Answer:
l-5l < l-6l
Step-by-step explanation:
the absolute will remove the negative of both numbers
Answer: |−5| < |−6|
Step-by-step explanation:
The function of the absolute symbol is to cancel out negative , considering the values one after the other.
/ - 6/ < 5 is the same as 6 < 5 ....... this is not true
(ii) /-6/ < /5/ is the same as 6 < 5 ..... this is not true
(iii) /-5/ < / -6/ is the same as 5 < 6 ...... this is true
(iv) /-5/ < -6 is the same as 5 < -6 ..... this is not true
What is the equation of the line that has a slope of -1/3 and a y intercept of 5/2
Answers
Answer:
y=-1/3x+5/2
Step-by-step explanation:
Slope intercept form makes this a breeze. Essentially, just plug these values into the following formula:
y = [SLOPE]x + [Y-INTERCEPT]
Answer:
y=-1/3x+5/2
Hope this helps
According to the theorem, which statement, about Parallelogram ABCD is true?
Answers
bisect = to cut into two equal halves.
so from that theorem Juan used we can derive that once both diagonals bisect each other, the halves of AO = OC and DO = OB.
Can someone solve this quick plz
Answers
Answer:
length = x + 5
Step-by-step explanation:
Given
area = x² + 8x + 15 and area = length × width
We require to factorise x² + 8x + 15
Consider the factors of the constant term (+ 15) which sum to give the coefficient of the x- term (+ 8)
The factors are + 5 and + 3, since
5 × 3 = 15 and 5 + 3 = 8, thus
x² + 8x + 15 = (x + 5)(x + 3)
x + 3 is the width, thus x + 5 is the length
2 cars raced at a track. the faster car traveled 20mph faster than the slower car. in the time that the slower car traveled 165 miles, the faster car traveled 225 miles. if the speeds of the cars remained constant, how fast did the slower car travel during the race.
Answers
Answer:
The speed of slower car is 55 miles per hour.
Step-by-step explanation:
Given as :
The speed of slower car = [tex]s_2[/tex] = s mph
The speed of faster car = [tex]s_1[/tex] = ( s + 20 ) mph
The distance cover by slower car = [tex]d_2[/tex] = 165 miles
The distance cover by faster car = [tex]d_1[/tex] = 225 miles
The time taken by both cars for travelling = t hours
The speed of the cars remains constant
Now, According to question
∵ Time = [tex]\dfrac{\textrm Distance}{\textrm Speed}[/tex]
So, For slower car
t = [tex]\dfrac{d_2}{s_2}[/tex]
Or, t = [tex]\dfrac{165}{s}[/tex] ............1
So, For faster car
t = [tex]\dfrac{d_1}{s_1}[/tex]
Or, t = [tex]\dfrac{225}{s+20}[/tex] ............2
Now, equating both the equations
I.e [tex]\dfrac{225}{s+20}[/tex] = [tex]\dfrac{165}{s}[/tex]
By cross multiplying
Or, 225 × s = 165 × (s + 20)
Or, 225 s = 165 s + 3300
Or, 225 s - 165 s = 3300
Or, 60 s = 3300
∴ s = [tex]\dfrac{3300}{60}[/tex]
I.e s = 55 miles per hour
So , The speed of slower car = [tex]s_2[/tex] = s = 55 miles per hour
Hence , The speed of slower car is 55 miles per hour. Answer
What is the slope, m, and the y-intercept of the line that is graphed below?
NO
-5
4-3-2-1, 1
1
2
3
4
5
x
Answers
This looks confusing. Can you try reposting this to make it look clear?
How do I solve 42÷227
Answers
Answer:
42÷227=42/227
Step-by-step explanation:
Answer:
0.185
Step-by-step explanation:
Do the long division.
In a figure, OB is the radius of a big semicircle and XB is the radius of the small semicircle. Given that OX = 14 cm, Calculate the area and the perimeter of the shaded region in the figure.
(Take π = 22/7).
Answers
Answer:
perimeter of the shaded region = 88 +44+28 =160 cm
Step-by-step explanation:
perimeter of shaded region = length AO + arc OB + arc AB
length AO = radius of bigger circle
radius of bigger circle = OX + OB = 2×radius of smaller circle = 2×14 cm = 28 cm
therefore AO = 28 cm
length of arc oB= half of circumference of smaller circle = [tex]\pi[/tex]×14 = 44 cm
length of arc ab = half of circumference of bigger circle = [tex]\pi[/tex]×28 =[tex]\frac{22}{7}[/tex]×28= 88
therefore perimeter of the shaded region = 88 +44+28 =160 cm
area of the shaded region = half of area of bigger circle - half of area of smaller circle
=[tex]\frac{1}{2} \pi 28^{2} -\frac{1}{2} \pi 14^{2}[/tex]
=[tex]\frac{\pi }{2} (28^{2} -14^{2} )[/tex]
solving we gen area of shaded region = 924
the zeros of f(x) algebraically
Answers
Answer:
The zeros are 4, -6, and 1.
Step-by-step explanation:
Given f(x) = x³ + x² - 26x + 24
(x - 4) is a factor of f(x). That means it is a zero of f(x).
To find the remaining factors algebraically, we take out the factor (x - 4) from f(x).
That is, [tex]$ f(x) = x^3 + x^2 - 26x + 24 $[/tex]
[tex]$ \implies x^3 - 4x^2 + 5x^2 - 20x - 6x + 24 $[/tex]
Taking [tex]$ x^2 $[/tex] out, we have:
[tex]$ = x^2(x^2 - 4) + 5x(x - 4) - 6(x - 4) $[/tex]
Taking (x - 4) common out, we have:
[tex]$ = (x - 4) \{x^2 + 5x - 6\} $[/tex]
[tex]$ = (x - 4)(x^2 + 6x - x - 6) $[/tex]
[tex]$ = (x - 4)\{x(x + 6) -1(x + 6)\} $[/tex]
[tex]$ = (x - 4)(x + 6)(x - 1) $[/tex]
This means the zeros are 4, -6, & 1.
How many solutions are there to the system of equations?
StartLayout enlarged left-brace 1st row 4 x minus 5 y = 5 2nd row negative 0.08 x + 0.10 y = 0.10 EndLayout
no solutions
one solution
two solutions
an infinite number of solutions
Answers
Answer:
The system has no solutions
Step-by-step explanation:
we have
[tex]4x-5y=5[/tex] -----> equation A
[tex]-0.08x+0.10y=0.10[/tex] ----> equation B
Isolate the variable y in the equation A
[tex]5y=4x-5[/tex]
[tex]y=\frac{4}{5}x-1[/tex]
[tex]y=0.8x-1[/tex] -----> equation A'
Isolate the variable y in equation B
[tex]0.10y=0.08x+0.10[/tex]
[tex]y=\frac{0.08}{0.10}x+1[/tex]
[tex]y=0.8x+1[/tex] ------> equation B'
Compare the equations A' and B'
The lines have the same slope but different y-intercept
Are parallel lines
therefore
The system has no solutions
Answer:
A. no solutions
Step-by-step explanation:
100% on edge
Which ordered pair is a solution of the equation?
y=-3x-4y=
Answers
To find the solution to the given equation y = -3x - 4 from the provided pairs, substitute the values and solve, giving the solution as (0,-2).
The given equation is y = -3x - 4.
To find which ordered pair is a solution, substitute the given pairs into the equation and check:
(1,0): y = -3(1) - 4 = -3 - 4 = -7
(0,-2): y = -3(0) - 4 = -4
(13,-3): y = -3(13) - 4 = -39 - 4 = -43
Therefore, the ordered pair that is a solution of the equation is (0,-2).
F(x)= x^3-9x
What is the average rate of change of f over the interval [1,6]?
Answers
Answer: 34
Step-by-step explanation:
The average rate of change of f(x)= x³-9x in interval [1,6] is 34.
Average rate of changeIf f(x) is a function the [a,b] is interval then the average rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]
How to find the average rate of change of f?Given the function is f(x)= x³-9x and the interval is [1,6].
then first we have to find the value of f(1) and f(6).
So
f(1) = (1)³-9(1)
= 1-9
= -8
and
f(6) = (6)³-9(6)
= 216- 54
= 162
therefore average rate of change of f is
[tex]\frac{f(6)-f(1)}{6-1}= \frac{162+8}{6-1}[/tex]
= 170/5
= 34
Hence the average rate of change of f is 34.
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a pancake recipe asks for one and one half times ad much milk as flour. if two and one quarter cups of milk is used what quantity of flour would then be needed
Answers
Answer:
x = 4/3
Step-by-step explanation:
x = amount of flour
x = amount of milk / 2.5
x =(3 1/3) / 2.5
change both to improper fractions
x = 10/3 / (5/2)
invert and mutiply
x = 10/3 * 2/5
Length: 32 in
Width: 9 in
Height: 9 in
Which is the best estimate of the lateral area of a cube with edges that are 2.1 inches long?
Answers
Answer:
The lateral Area of a cube [tex]= 17.64in^{2}[/tex]
Step-by-step explanation:
In Mathematics Geometry, the lateral surface of a solid object like cube would be the face of the sold on its side, excluding base. Meaning, any surface, apart from base, would be included to determine the lateral surface of the solid.
A cube has six sides - also called faces.
A cube has a base i.e. the bottom side of the cube, and an ant-bottom base i.e. the top side of the cube.
So, lateral area of a cube would exclude both bottom side base and anti-bottom side base. In other words, it is the area of all the sides of the object, excluding the area of its base and top.
Hence, lateral area of a cube is the square of all the remaining four sides of the object, excluding the area of its base and top.
Hence, the lateral area of a cube can be calculated by the formula:
Lateral Area of a cube [tex]= 4s^{2}[/tex], where s is the length of one edge.
So,
As the given length of edge = s = 2.1
So,
lateral Area of a cube [tex]= 4s^{2}[/tex]
[tex]= 4(2.1)^{2}[/tex]
[tex]= 17.64in^{2}[/tex]
Keywords: cube, lateral area
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please help me!! what's the expression in simplest form?
Answers
Answer:
2a² - 2b - 1
Step-by-step explanation:
Given
- 5 + b + 2a² - 3b + 4 ← collect like terms
= 2a² + (b - 3b) + (- 5 + 4)
= 2a² + (- 2b) + (- 1)
= 2a² - 2b - 1
An airplane takes 3 hours to travel a distance of 2250 miles with the wind. The return trip takes 5 hours against the wind. Find the speed of the plane in still air and the speed of the wind.
Answers
Answer:
Speed of Plane = 600 miles per hour
Speed of Wind = 150 miles per hour
Step-by-step explanation:
The distance equation is D = RT
Where
D is the distance
R is the rate
T is the time
Let rate of airplane be "x" and rate of wind be "c"
Also, note: rate with wind is airplane's and wind's, so that would be "x + c"
and rate against the wind is airplane's minus the wind's, so that would be "x - c"
Now,
2250 miles with wind takes 3 hours, so we can write:
D = RT
2250 = (x + c)(3)
and
2250 miles against the wind takes 5 hours, we can write:
D = RT
2250 = (x - c)(5)
Simplifying 1st equation:
[tex]2250 = (x + c)(3)\\3x+3c=2250[/tex]
Simplifying 2nd equation:
[tex]2250 = (x - c)(5)\\5x -5c=2250[/tex]
Multiplying the 1st equation by 5, gives us:
[tex]5*[3x+3c]=2250\\15x+15c=11250[/tex]
Multiplying the 2nd equation by 3 gives us:
[tex]3*[5x -5c=2250]\\15x-15c=6750[/tex]
Adding up these 2 equations, we solve for x. Shown below:
[tex]15x+15c=11250\\15x-15c=6750\\---------\\30x=18000\\x=600[/tex]
Now putting this value of x into original 1st equation, we solve for c:
[tex]3x+3c=2250\\3(600)+3c=2250\\1800+3c=2250\\3c=450\\c=150[/tex]
Speed of Plane = 600 miles per hour
Speed of Wind = 150 miles per hour
2x + 7 = 4 + x solve equation using tables
Answers
Answer:
x=-3
Step-by-step explanation:
2x+7=4+x
2x-x+7=4
x+7=4
x=4-7
x=-3
HELP/ANSWER PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
Answers
Answer:
Step-by-step explanation:
in six years rose will be two times as old as anne. Four years ago, anne was one third the age of rose. how old are they now
Answers
Answer:
Rose is 34.
Anne is 14.
Step-by-step explanation:
Let rose be x years age now and anne be y years old now. Then:
x + 6 = 2 (y + 6)
x - 4 = 3(y - 4)
Subtracting:
6 - -4 = 2y + 12 - (3y - 12)
10 = - y + 24
-y = -14
y = 14
Substituting for y:
x + 6 = 2(14+6)
x = 40 - 6 = 34.
An artist is making a mural by reproducing a painting at a different scale. The original painting is 12 1/2 inches long and 5 inches wide. The mural will cover an entire wall that is 52.5 feet long and 20 feet wide. What will be the scale that relates the original painting to the mural?
Answers
Answer:
The scale is [tex]\frac{1}{60}[/tex]
Step-by-step explanation:
The correct question is
An artist is making a mural by reproducing a painting at a different scale. the original painting is 10 1/2 inches long and 4 inches wide. the mural will cover an entire wall that is 52.5 feet long and 20 feet wide. what will be the scale that relates to the original painting to the mural?
we know that
To find out the scale divide the measure of the original painting by the measure of the mural
so
Long
[tex]\frac{10.5}{52.5}\ \frac{in}{ft}[/tex]
Remember that
[tex]1\ ft=12\ in[/tex]
Convert feet to inches
[tex]\frac{10.5}{52.5*12}=\frac{10.5}{630}\ \frac{in}{in}=\frac{10.5}{630}[/tex]
simplify
[tex]\frac{1}{60}[/tex]
That means ----> 1 unit in the original painting represent 60 units in the mural
Verify the scale with the wide (both scale must be equals)
wide
[tex]\frac{4}{20}\ \frac{in}{ft}[/tex]
Remember that
[tex]1\ ft=12\ in[/tex]
Convert feet to inches
[tex]\frac{4}{20*12}=\frac{4}{240}\ \frac{in}{in}=\frac{4}{240}[/tex]
simplify
[tex]\frac{1}{60}[/tex]
That means ----> 1 unit in the original painting represent 60 units in the mural