The correct classification of the expression 5x + 3x⁴ - 7x³ + 10, is that it is the fourth-degree polynomial.
The degree of a polynomial is the highest power of the variable in the expression.
In the expression 5x + 3x⁴ - 7x³ + 10, there are 4 terms, and the term 3x⁴ involves the highest power = 4.
Therefore, the degree of the polynomial is 4.
Hence, we can say that the correct classification of the expression 5x + 3x⁴ - 7x³ + 10, is that it is the fourth-degree polynomial.
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While driving, Carl notices that his odometer reads 25,952 miles, which happens to be a palindrome. He thought this was pretty rare, but 2.5 hours later, his odometer reads as 36,563 miles, anoher palindrome. What was Carl's average speed during those 2.5 hours
Carl's average speed was 4244 miles/hr during those 2.5 hours
First, the odometer showed palindromic no. 25952 miles
after 2.5 hours odometer showed the next palindromic no. is 36563.
hence the distance covered in 2.5 hours = 36563 - 25952 = 110611 miles.
Now, we have to find the average speed with the distance covered 110611 miles in a particular time of 2.5 hours.
Using formula,
average speed = total distance / total time
[tex]\frac{10611}{2.5}[/tex] =4244 miles/hour is the average speed
Hence, Carl's average speed was 4244 miles/hr during those 2.5 hours
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2. Find four consecutive integers such that six times the sum of the first and third is 12
greater than 9 times the fourth.
Answer:
9
Step-by-step explanation:
a,a+1,a+2,a+3,...
6(a+(a+2))=12+9(a+3)
6(2a+2)=12+9a+27
12a+12=12+9a+27
12a-9a=27
3a=27
a=9
Identify each of the following as rational or irrational.
Answer:A rational number can be written as a fraction of two integers. √23 is irrational because we do not know what the square root of 23 is in terms of integers in a fraction. 104.42 is rational because it can be expressed as 10442/100 . We can express it as this because.
Step-by-step explanation:
find the values of x work 10% of my grade
Answer:
x = 35
Step-by-step explanation:
1. Add all angles
[tex]115+(x+36)+24+(2x+10)+2x[/tex]
= [tex]5x+185[/tex]
2. Match 360 and fix
[tex]5x+185=360[/tex]
[tex]5x=360-185[/tex]
[tex]5x=175[/tex]
[tex]x=175/5[/tex]
[tex]x=35[/tex]
Hope this helps
Answer:
[tex]\boxed{\sf x = 35^o}[/tex]
Step-by-step explanation:
Let's find the value of x :-
[tex]\sf 115 + x + 36 + 24 + 2x + 10 + 2x = 360^o[/tex]
Add the numbers.
[tex]\sf 185 + x + 2x + 2x = 360[/tex]Combine like terms.
[tex]\sf 5x + 185 = 360[/tex]Subtract 185 from both sides.
[tex]\sf 5x = 175[/tex]Divide both sides by 5.
[tex]\sf x = 35^o[/tex]--------------------------------------
I need to find the restrictions for this equation:
Answer:
Simplify 2x^2-5x-3/x^2-9
The answer is 2x+1 / x+3
Step-by-step explanation:
Simplify the expression.
You enter a room. 2 dogs, 4 horses, one giraffe, and a duck are laying on a bed. 3 chicken are flying over a chair. How many legs are on the ground?.
Answer: the answer is 28
Step-by-step explanation:
PLEASE HELP ASAP. I WILL MARK AS BRAINLIEST
You must go 45 miles per hour to reach the longest distance.
Number of hours the car can runThe given parameters are:
Speed = 60 miles per hourTime = 5 hoursWhen the speed increases by 1 mile per hour, the time reduces by 10 minutes.
This means that:
When
Speed = (60 + x) miles per hour
The time is:
Time = 5 hours - 10 minutes * x
Convert minutes to hour
Time = 5 hours - 1/6 * x hour
This gives
Time = 5 - x/6 hour
Hence, the car can run for (5 - x/6) hours
The distance for 1 tank of gasWe have:
Speed = (60 + x) miles per hour Time = (5 - x/6) hoursThe distance is calculated using
Distance = Speed * Time
This gives
Distance = (60 + x)(5 - x/6)
Expand
Distance = 300 - 10x + 5x - x^2/6
Evaluate the like terms
Distance = 300 - 5x - x^2/6
Hence, the distance for 1 tank of gas is 300 - 5x - x^2/6 miles
The longest distanceWe have:
D = 300 - 5x - x^2/6
Differentiate
D' = -5 - x/3
Set to 0
-x/3 = 5
Solve for x
x = -15
Substitute x = -15 in D = 300 - 5x - x^2/6
D = 300 - 5(-15) - (-15)^2/6
Evaluate
D = 337.5
Hence, the longest distance is 337.5 miles
The speed for the longest distanceWe have:
x = -15
Substitute x = -15 in Time = (5 - x/6) hours
Time = (5 + 15/6) hours
Evaluate
Time = 7.5 hours
The speed is calculated as:
Speed = Distance/Time
This gives
Speed = 337.5/7.5
Evaluate
Speed = 45
Hence, you must go 45 miles per hour to reach the longest distance.
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A fence is to be built to enclose a rectangular area of 200 square feet. The fence along three sides is to be made of material that costs 3 dollars per foot, and the material for the fourth side costs 12 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.
y = 220/ ((10/3) * √22)
It is given that area is 200 square feet. Cost is 3 dollar per foot. Fourth side costs 12 dollars per foot.
This f(x,y) needs to represent the cost of the fence so we can look at each side's price. We can choose the fourth side to be along the x axis and be represented by 13x. The other sides therefore must be represented by 5y, 5y, and 5x.
So, our cost, f(x,y) = 13x + 5x + 5y + 5y = 18x + 10y
Our constraint is xy = 220 as defined by the area of a rectangle.
We can then take our constraint to be put in terms of exclusively x, giving us y = 220/x
Plugging this into our cost, the thing we are minimizing, we get f(x) = 18x + 2200/x
In order to find the minimum we use the first derivative test, taking f'(x) and finding the critical points.
f'(x) = 18 - 2200/x2
Setting this equation to be equal to 0 we find that x = ±√2200/18 . But the negative answer doesn't make sense because distance cannot be negative so we throw it out.
x = (10/3) * √22
We must verify that this is a minimum by confirming the following:
If x < (10/3) * √22, f'(x) < 0. So, f(x) is decreasing when x < (10/3) * √22.
If x > (10/3) * √22, f'(x) > 0. So, f(x) is increasing when x > (10/3) * √22.
Thus, we have guaranteed that (10/3) * √22 is the x dimension. Now we plug in this value in our original equation to find y and that is our y dimension. So, y = 220/ ((10/3) * √22)
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How many sandwiches do
you think would be supplied by this
market if the price were $3.50?
=========================================================
Explanation:
Start at $3.50 on the vertical y axis. Draw a horizontal line until you reach the supply curve. Then drop straight down to land somewhere between 650 and 700 units supplied per day. Check out the diagram below.
A good estimate may be to use the midpoint. Add up those values and divide in half.
(650+700)/2 = 1350/2 = 675
Therefore, we estimate that 675 sandwiches per day would be supplied if the price was $3.50 per sandwich.
PLEASE HELP URGENT
B Pick the inequality that matches the graph shown. Show all of your work to explain the
choice you selected. (See Ex. 1)
Answer:
B. y > 3x -7
Step-by-step explanation:
We can choose the correct inequality based on the y-intercept and the shading.
Y-interceptThe dashed line crosses the y-axis at approximately y=-7. This is the value of y when x=0. This observation eliminates choices D, E, F.
ShadingThe shading on the graph is seen to be above and to the left of the line. This means the variables in relation to the inequality symbol must be ...
y > ( ) . . . . eliminates choice A
and
x < ( ) or ( ) > x . . . . eliminates choice C, confirms choice B
The inequality that matches the graph is y > 3x -7.
__
Additional comment
For looking at shading, we are interested in the relation of the inequality symbol to a variable term with a positive coefficient. If the coefficient is negative, you can do either of ...
add the opposite of that variable term to both sides of the equationreverse the inequality symbolThat is, if you have -3x < ( ), when considering shading, you can consider the relation x > ( ) with the inequality reversed, or you can consider ( ) < x, which has x on the other side of the inequality. Both of these tell you shading is right of the line, where x-values are greater than those on the line.
The endpoints of FG are F(3.75,9) and G (2,-12).
If point E divides FG in the ratio 3:4, the coordinates of point E are what?
If point H divides FE in the ratio 2:3, the coordinates of point H are what?
Using proportions, it is found that:
The coordinates of point E are (3,0).The coordinates of point H are (3.45, 5.4).What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Point E divides FG in the ratio 3:4, hence:
[tex]E - F = \frac{3}{7}(G - F)[/tex]
This is used to find both the x and y coordinates.
For the x-coordinate, we have that:
[tex]E - F = \frac{3}{7}(G - F)[/tex]
[tex]x - 3.75 = \frac{3}{7}(2 - 3.75)[/tex]
x - 3.75 = -0.75.
x = 3.
For the y-coordinate:
[tex]E - F = \frac{3}{7}(G - F)[/tex]
[tex]y - 9 = \frac{3}{7}(-12 - 9)[/tex]
y - 9 = -9
y = 0.
The coordinates of point E are (3,0).
Point H divides FE in the ratio 2:3, hence:
[tex]H - F = \frac{2}{5}(E - F)[/tex]
This is used to find both the x and y coordinates.
For the x-coordinate, we have that:
[tex]H - F = \frac{2}{5}(E - F)[/tex]
[tex]x - 3.75 = \frac{2}{5}(3 - 3.75)[/tex]
x - 3.75 = -0.3.
x = 3.45.
For the y-coordinate, we have that:
[tex]H - F = \frac{2}{5}(E - F)[/tex]
[tex]y - 9 = \frac{2}{5}(0 - 9)[/tex]
y - 9 = -3.6
y = 5.4.
The coordinates of point H are (3.45,5.4).
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Answer:
The coordinates of point E are (3,0).
The coordinates of point H are (3.45, 5.4).
Step-by-step explanation:
I just got it right on the test
An inequality is shown below:
−np − 3 ≥ 7(c − 4)
Which of the following solves for n?
The solution of n is [tex]n \le -\frac 1p(7(c - 4) + 3)[/tex]
How to solve for n?The inequality is given as:
−np − 3 ≥ 7(c − 4)
Add 3 to both sides
−np ≥ 7(c − 4) + 3
Divide through by -p;
This changes the inequality sign.
So, we have:
[tex]n \le -\frac 1p(7(c - 4) + 3)[/tex]
Hence, the solution of n is [tex]n \le -\frac 1p(7(c - 4) + 3)[/tex]
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Y=
Help me please thank u
Answer:
Y≈4.6
Step-by-step explanation:
Because the hypotenuse is 9rad2 and the angle opposite of it is a 90. You can deduce it is a 90-45-45. From this you can tell the legs are 9. You then do 9 tan 26 to get about 4.4, and after this you subtract it from 9.
what is 2,104.50 divided by 122
2104.50 ÷ 122 = 17.25
...
Which expressions are equivalent to 12r-5
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
6(2r+(-1))+1
(Choice B)
B
-4(2+(-3r))+3
(Choice C)
C
None of the above
The expression 12r - 5 are equivalent to 6(2r+(-1))+1 and -4(2+(-3r))+3 option (A) and (B) are correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
= 12r - 5
A) 6(2r+(-1))+1
= 12r + 6(-1) + 1
= 12r -5
B) -4(2+(-3r))+3
= -8 -4(-3r) + 3
= -5 + 12r
or
= 12r - 5
Thus, the expression 12r - 5 are equivalent to 6(2r+(-1))+1 and -4(2+(-3r))+3 option (A) and (B) are correct.
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A sum of Rs. 500 is in the form of denominations of Rs. 10 and Rs. 20. If total number of notes are 35, find the number of notes of each denomination.
Answer: 20 of banknotes, denomination of Rs. 10 and 15 of banknotes, denomination of Rs. 20.
Step-by-step explanation:
Let the number of banknotes, denomination of Rs. 10 will be equal to x,
and the number of banknotes, denomination of Rs. 20 will be equal to y.
Hence; [tex]\left \{ {{x+y=35\ \ \ \ } \atop {10*x+20*y=500\ |:10 \ \ }} \right. \ \ \ \ \left \{ {{x+y=35\ \ (1)} \atop {x+2y=50\ \ (2)}} \right. \\[/tex]
From (2) subtract (1):
[tex]y=15\ \ \ \ \ \Rightarrow\\x+15=35\\x=20.[/tex]
The interior angle of a regular polygon is twice the exterior angle how many sides has the polygon
Answer:
6 sides
Step-by-step explanation:
the interior angle + the exterior angle = 180°
let x be the exterior angle then 2x is the interior angle and
x + 2x = 180
3x = 180 ( divide both sides by 3 )
x = 60
the exterior angle = 60°
the sum of the exterior angles of a polygon = 360°
since the polygon is regular the the exterior angles are congruent, then
number of sides = 360° ÷ 60° = 6
PLEASE HELP!!!!
Use the following set of data:
78, 78, 83, 85, 89, 91, 95, 98
What is the median for the set of data?
(A) 85
(B) 89
(C) 87
(D) 98
Answer:
87
Step-by-step explanation:
The median of a data set is the value that is exactly in the middle of all other values.
To find the median of a data set, we typically list the values in order of greatest to least, and we look for the number in the middle.
Here, the list-maker has already provided the list in this order!
78, 78, 83, 85, 89, 91, 95, 98
we can see two numbers exactly in the middle here--when this happens, we take the mean/average of the two:
85 + 89 = 174
174 / 2 = 87
So, the median of this data set is 87
hope this helps! have a lovely day :)
-2x
10. What is the least common denominator of 21+2+³=1?
+3
O(x - 1)(x+1)
Ox(x - 1)2(x + 1)
O(x-1)2(x + 1)
Ox(x - 1)(x + 1)
Answer:
O(x-1)2(x + 1)
Step-by-step explanation:
Solve for t 16−2t=t+9+4t
Answer:
Step-by-step explanation:
16-2t=t+9+4t
7=7t
t=1
Miss Goh bought 6 blouses, 2 skirts and 2 dresses for $560. A blouse and a skirt cost $107. A blouse and a dress cost $134. What was the cost of a dress?
Answer:
$95 FOR A DRESS
Step-by-step explanation:
Let's rearrange the given:
She bought a blouse and skirt for two, a blouse and a dress for two, and a blouse for two.
A blouse and a skirt cost $107
A blouse and a dress cost $134
blouse cost x dollars
The equation:
2($107) + 2($134) + 2x = $560
SOLUTION:
$214 + $268 + 2x = $560
2x = $560 - $214 - $268
2x = $78
x = $39 for a single blouse
FIND THE COST OF DRESS:
A blouse and a dress cost $134 - $39 for a single blouse
$134 - $39 = $95
$95 IS THE COST OF DRESS
60 POINTS PLEASEEEEEEEEEEEE
Answer:
A.) Two
Step-by-step explanation:
You can determine the amount of solutions the functions have by counting the number of intersections they have. Since the functions cross each other at two different points, there are two solutions.
find the area of a circle whose radius is 'x', unit.
3.14 x² units
Step-by-step explanation:
Radius = x units. ----(given)
π = 3.14
Area of cirlce = πr²
= 3.14 * x²
= 3.14 x² units.
Hope it helps you!!Answer:
area = πx² square units
Step-by-step explanation:
Formula for the area of a circle:
area = πr²,
where r = radius.
In this problem, the radius is x, so we substitute r in the formula with x.
area = πx² square units
The French army stayed behind in Egypt—and so did the scholars. In late August, shortly after Napoleon's departure, a large, heavy package arrived at the scholars' palace in Cairo. When they opened it, they found it contained a black stone slab covered with writing in three different scripts.
A note from a French army officer accompanied the package. He told the scholars that the stone had been unearthed in an old fort near the town of Rosetta, thirty-five miles north of Alexandria. French soldiers were tearing down a ruined wall in the fort when they came upon the slab.
Which statement accurately describes a cause-and-effect relationship described in this excerpt?
Because Napoleon departs for France, the French army and scholars decide to stay in Egypt.
Because the French army and scholars decide to stay in Egypt, Napoleon decides to depart for France.
Because the French soldiers are tearing down a ruined wall in a fort, they discover the Rosetta Stone.
Because the French soldiers are searching for the Rosetta Stone, they tear down a ruined wall in a fort.
The statement that accurately describes a cause-and-effect relationship described in this excerpt is C. Because the French soldiers are tearing down a ruined wall in a fort, they discover the Rosetta Stone.
What is a cause-and-effect relationship?A cause-and-effect relationship occurs when:
Two events occur at the same time and in the same place.One event immediately precedes the other.The second event appears unlikely to have happened without the first event occurring.Thus, the statement that accurately describes a cause-and-effect relationship described in this excerpt is C. Because the French soldiers are tearing down a ruined wall in a fort, they discover the Rosetta Stone.
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Simplify 4a - 2a + a
Answer:
=> 3a
Step-by-step explanation:
=> 4a - 2a + a
=> 2a + a
=> 3a
Answer:
[tex]\boxed{\bf 3a}[/tex]
Step-by-step explanation:
[tex]\bf 4a - 2a + a[/tex]
Combine 4a and -2a = 2a.
[tex]\bf 2a+a[/tex]Combine 2a and a = 3a
[tex]\bf 3a[/tex]---------------------------------------
Which is the graph of f(x) = 4( 1 /2)x
Answer:
I don't see any option to choose from.
Step-by-step explanation:
See attached graph.
f(x) = 4( 1 /2)x can be rewritten as y = 2x. This is a straight line with slope 2 and a y-intercept of 0.
Thirty-three college freshmen were randomly selected for an on-campus survey at their university. The participants' mean GPA was 2.5, and the standard deviation was 0.5. What is the margin of error, assuming a 95% confidence level
The margin of error is ±0.1706
What is the margin of error?The margin of error is a statistical solution for the amount of random sampling error in the survey results.
What is 95% of a confidence level?The 95% confidence interval means from 100 different samples computing a 95% of confidence for each sample. From this, we get the approximate value 95 of the 100 confidence intervals will contain the true mean value.
We have a sample size of n=33
The critical value of the significance level is [tex]\alpha =0.05\\z_{\frac{\alpha }{2} }=1.96[/tex]
Then our sample mean will be 2.5
then the standard deviation is 0.5
from this, we can assume that this is a normal distribution.
then our margin of error will be
[tex]E=[/tex]±[tex]z_{\frac{\alpha }{2} }\frac{deviation}{\sqrt{n} }[/tex]
⇒[tex]E=[/tex]±[tex](1.96)\frac{0.5}{\sqrt{33} }\\[/tex]
≅±0.1706 is the margin of error.
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35. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
35. Passes through (-2, 8) and (4, 6)
Answer:
The linear equation for the line which passes through the points given as (-2,8) and $(4,6), is written in the point-slope form as [tex]$y=-\frac{1}{3} x-\frac{26}{3}$[/tex].
Step-by-step explanation:
A condition is given that a line passes through the points whose coordinates are (-2,8) and (4,6).
It is asked to find the linear equation which satisfies the given condition.
Step 1 of 3
Determine the slope of the line.
The points through which the line passes are given as (-2,8) and (4,6). Next, the formula for the slope is given as,
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute [tex]$6 \& 8$[/tex] for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and 4&-2 for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows, [tex]$m=\frac{6-8}{4-(-2)}$[/tex]
[tex]$$\begin{aligned}&m=\frac{-2}{6} \\&m=-\frac{1}{3}\end{aligned}$$[/tex]
Step 2 of 3
Write the linear equation in point-slope form.
A linear equation in point slope form is given as,
[tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]
Substitute [tex]$-\frac{1}{3}$[/tex] for m,-2 for [tex]$x_{1}$[/tex], and 8 for [tex]$y_{1}$[/tex] in the above equation and simplify using the distributive property as follows, [tex]y-8=-\frac{1}{3}(x-(-2))$\\ $y-8=-\frac{1}{3}(x+2)$\\ $y-8=-\frac{1}{3} x-\frac{2}{3}$[/tex]
Step 3 of 3
Simplify the equation further.
Add 8 on each side of the equation [tex]$y-8=-\frac{1}{3} x-\frac{2}{3}$[/tex], and simplify as follows, [tex]$y-8+8=-\frac{1}{3} x-\frac{2}{3}+8$[/tex]
[tex]$y=-\frac{1}{3} x-\frac{2+24}{3}$$\\ $$y=-\frac{1}{3} x-\frac{26}{3}$$[/tex]
This is the required linear equation.
Trini rode her bike 12 miles on Friday. She rode 14 miles on Saturday and 15 miles on Sunday. How many miles did she ride in all?
Answer: 41
Step-by-step explanation:
12+14+15= 41
The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, sold by the company:
Graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 6, 0. The vertex is at 3, 120.
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)
Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent? (3 points)
Part C: Describe the constraints of the domain. (3 points)
The answers to the various part as well as its reasons are given below
Part A:The x-intercepts shows a zero profit.The maximum value of the graph tells or depict the maximum profit.The function is one that goes up or increases upward until it reach the vertex and then it falls or decreases after it.This implies that the profit goes up as it reaches the peak at the vertex and it goes down after the vertex up until it gets to zero.The profits are negative as seen on the left of the first zero and on the right of the second zero.Part B:An approximate average rate of change of the graph from x = 3 to x = 5, shows the reduction in profit from 3 to 5.
Part C:Based on the above, the domain is one that is held back or constrained by x = 0 .
We are compelled at x = 6 due to the fact that we have to maneuver a negative profit.
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