The factored expression of x^3 - 5x^2 + 3x - 15 is (x^2 + 3)(x- 5)
How to factor the polynomial?The polynomial is given as:
x^3 - 5x^2 + 3x - 15
Group the terms
(x^3 - 5x^2) + (3x - 15)
Factorize each group
x^2(x - 5) + 3(x - 5)
Factor out x - 5
(x^2 + 3)(x- 5)
Hence, the factored expression of x^3 - 5x^2 + 3x - 15 is (x^2 + 3)(x- 5)
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9+10=21
Yes, my calculation says , it is possible.
But only in other number base.
Let me explain.
9 + 10 = 21
or, 19 = 21
Assume that , 19 is a decimal number.
and 21 is a n base number.
As 19 is equivalent to 21,
So 10 base 19 is equivalent to n base 21.
So with the help of math I can get that,
19 = 1 × 10^1 + 9× 10^0
21 = 2 ×n^1 + 1×n^0 = 2n + 1
So , 2n + 1 = 19
or, 2n = 18
or, n = 9
So finally, we can say that,
10 base 19 = 9 base 21
Thus 9+10=21 is possible
The reason why people sometimes assume that the calculation 9 + 10 = 21 is as explained below.
How to calculate in number bases?We want to find out the reason why people say that; 9 + 10 = 21
Now, the way you have explained it is one way to look at it by utilizing number bases to play around with the figures to arrive at 21.
However, another way is to use algebra trick pattern which is;
9 can be expressed as 3 * 3
Also, 10 can be expressed as 5 * 2. Thus, we now have;
(3 * 3) + (5 * 2)
The applying properties of algebra to cross multiply gives;
(3 * 2) + (5 * 3)
= 6 + 15
= 21
Now, though your explanation arrived at 21 and mine also 21, but those are not correct mathematical methods as 9 + 10 must be equal to 19 and not 21.
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One fifth of r is 15 how would I write that in an equation
Answe1/5 of r = 15
Step-by-step explanation:
1/5 r=
Which expression is equivalent to [tex]10\sqrt{5}[/tex] ?
Giving 20 points
A)√500 is the correct answer.
What is an equivalent expression?It is an expression that has the same value but does not look the same. If you simplify an expression, you're trying to write it in the simplest way possible.
According to the question,
The given expression is 10√5.
By computing the number out of the square root,
So,
[tex]=10 \sqrt{5} \\=\sqrt{10^2(5)} \\=\sqrt{100 (5)} \\=\sqrt{500}[/tex]
Therefore,
The equivalent expression for 10√5 is √500.
Complete question is attached below.
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Patrons (P) Revenue (R)
32
480
500
550
750
33
40
60
81
1,215
Find a linear model for the data.
The linear model for the data is expressed as: R = 20p - 160.
How to Write a Linear Model?Using two pairs of values from the table values, say, (32, 480) and (33, 500), find the unit rate (m).
Unit rate (m) = (500 - 480)/(33 - 32) = 20/1
Unit rate (m) = 20.
Substitute (p, R) = (32, 480) and m = 20 into R = mp + b to find b
480 = 20(32) + b
480 = 640 + b
480 - 640 = b
b = -160
To write the linear model, substitute m = 20 and b = -160 into R = mp + b:
R = 20p - 160
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f(x) = 3x+2
What is f(5)?
Answer:
f(5)=17
Step-by-step explanation:
if,f(x)=3x+2
Then,f(5)=3*5+2
f(5)=17
AC and BD bisect eachother prove AB || CD and BC ll AD
1) [tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex] bisect each other (given)
2) [tex]\overline{AE} \cong \overline{EC}[/tex] (a bisector splits a segment into two congruent parts)
3) [tex]\overline{BE} \cong \overline{ED}[/tex] (a bisector splits a segment into two congruent parts)
4) [tex]\angle BEA \cong \angle CED[/tex] (vertical angles are congruent)
5) [tex]\triangle BEA \cong \triangle DEC[/tex] (SAS)
6) [tex]\angle EBA \cong \angle EDC[/tex] (CPCTC)
7) [tex]\overline{AB} \parallel \overline{CD}[/tex] (converse of alternate interior angles theorem)
8) [tex]\angle DEA \cong \angle BEC[/tex] (vertical angles are congruent)
9) [tex]\triangle AED \cong \triangle BEC[/tex] (SAS)
10) [tex]\angle BCE \cong \angle EAD[/tex] (CPCTC)
11) [tex]\overline{BC} \parallel \overline{AD}[/tex] (converse of alternate interior angles theorem)
PLEASE HELP I HAVE 45 min to SUBMIT WILL GIVE BRAINL
The average rate of change from x=1 to x= 4 is -0.7
How to solve for the rate of changeWe have f(1) to be 3
while we have f(4) as 1
The average rate of change can be solved as
f(4) - (f(1) / 4 - 1
This is solved as
1 - 3 / 4 - 1
= -2 / 3
= -0.7
Hence the average rate of change for the graph that we have above is -0.7
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The table shows certain values of a cubic function
Use the table to complete the statements.
The function has a relative maximum when x is near... -1, 3,-3, 7, or -7
As x approaches positive infinity, the value of the function approaches... negative infinity, positive infinity or zero.
Considering the given table, we have that:
The function has a relative maximum when x is near 3.As x approaches positive infinity, the value of the function approaches negative infinity.When a function has a relative maximum?A function has a relative maximum when it changes from increasing to decreasing.
Looking at the given table, it happens when x is near 3.
Also, looking at the table, for x > 3 the function is decreasing, hence as x approaches positive infinity, the value of the function approaches negative infinity.
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Jen and marcus got 15 miles up river before they ran out of gas they floated 9 miles back down river before they reached the shore how far did they get
Answer:
they reached the shore they get 135 miles
please help me im in a rush 25 points
Answer:
74 yards squared
Step-by-step explanation:
Divide the shape up into 2 3x5 rectangles and one 11x4 rectangle
2(3x5)+11x4=30+44=74
74 yards squared
Audrey has a ribbon that measures yards long. She cuts the ribbon into pieces that are each
Audrey has a ribbon that measures 6 yards long. She cuts the ribbon into pieces that are each 1/3 yard long. yard long. Then she cuts each of these pieces in half. How many pieces of ribbon does Audrey have now?
Answer:
36 pieces of ribbon
Step-by-step explanation:
When Audrey cuts the ribbon into pieces that are each 1/3 yards long, she has 18 pieces (1/3 * 18 is 6, or the other way to think about it would be, 6 / (1/3) = 18). If she were to cut each of the pieces in half one more time, she would have 18 * 2 or 36 pieces of ribbon
If the machine can produce 280 inches of ribbon in 30 minutes, approximately
how many feet can it produce in an 8 hour work day?
O 328 feet
O 358 feet
O 373 feet
O 309 feet
Answer:
373 feet
Step-by-step explanation:
Since the rate of the machine producing ribbon is proportional to time, we can determine the number of inches of ribbon in 8 hours by some quick operations.
There are 16 1/2 hours in 8 hours, so we can multiply 280 by 16.
[tex]280 *16=4480[/tex]
Now, we have the number of inches it can produce in an 8-hour work day. However, we must convert to feet since that is the form of measurement the question is asking for. We can do so by dividing by 12.
[tex]4480/12=373.33[/tex]
Therefore, the number of feet the machine can produce in an 8-hour work day is 373.
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Step-by-step explanation:
the other answer is correct.
a few add-ons :
1 ft = 12 in
30 minutes = 1/2 hour (as every hour has 60 minutes)
every hour has therefore 2 half hours.
1 hour = 2 × 1/2 hour
8 hours = 8 × 2 × 1/2 hours = 16 × 1/2 hour
so, in 16 times the amount of time (8 hours) the machine can produce 16 times the amount of ribbon (16 × 280 in).
16 × 280 = 4480 in
and because every 12 in is 1 ft, this is then
4480/12 = 373.3333333... ft
therefore, 373 is the right answer (rounded).
For the following exercises, determine whether each of the following relations is a function.
2. {(2, 1), (3, 2), (−1, 1), (0, −2)}
Answer:
The relation {(2,1),(3,2),(-1,1),(0,-2)} is a function because the domain {2,3,-1,0} and range {1,2,1,-2} of the relation is paired exactly only once.
Step-by-step explanation:
The given relation is {(2,1),(3,2),(-1,1),(0,-2)}.
It is required to determine the relation is a function.
Step 1 of 1
The given relation is {(2,1),(3,2),(-1,1),(0,-2)}.
This relation shows that the domain of the relation {2,3,-1,0} is paired with one element of the range {1,2,1,-2}.
Hence, the relation is a function.
Tracy invests $1,000 into a mutual fund which
earns 12% per year. In 15 years, how much will
Tracy's investment be worth if interest is
compounded monthly? Round to the nearest
dollar.
Omar is playing a computer game. He starts with 0 points wins 8 points loses 6 points 4 times and the wins 2 points. Which integer represents Omar’s score
The integer that represents Omar's score is -14.
What is the integer represents Omar’s score?Integers are whole numbers. It is a number without a fraction or decimal component. Integers can either be positive, negative or zero.
When Omar wins, the points are added and when he losses, the points are subtracted.
0 + 8 - (6 x 4) + 2
0 + 8 - 24 + 2 = -14
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Peaches are being sold for $2 per pound.The customer created a model to represent the total cost of peaches bought. If x represents the number of pounds of peaches bought and y represents the total cost of the peaches, which best describes the values of x and y?
The values of both x and y can be any real number.
The values of both x and y will be real numbers greater than or equal to 0.
The value of x and y will always be zero
The value of x can be any real number greater than or equal to 0, but the value of y must be an integer greater than or equal to 0.
Mark this and return
The thing that best describes the values of x and y is option B; they will be real numbers greater than or equal to 0.
What is a Real Number?The real number refers to the union of both rational and irrational numbers that can have negative or positive values.
From the given information:
Peaches are being bought and sold for $2 per pound.
There is no negative value used here if x represents the number of pounds of peaches bought and y represents the total cost of the peaches.
Thus, a conclusion that can be reached as to the values of x and y is that they contain real numbers greater than or equal to 0.
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Answer:
im pretty sure its d
Step-by-step explanation:
----- ______------
What is the volume of the composite figure? 6 cm 6 cm 18 cm 6 cm 6 cm 10 cm 8 cm V = [?]cm³ 6 cm What is the volume of the composite figure ? 6 cm 6 cm 18 cm 6 cm 6 cm 10 cm 8 cm V = [ ? ] cm
Answer:
2304 cm³
Step-by-step explanation:
To find the volume of a composite figure, it is easiest to break it down into smaller, more recognizable shapes.
here, we can break our shape into two sections: the green section and the blue section
then, we will add the volumes of these shapes together
green section's volume:
note: you could also calculate this as four separate cubes
to find the volume of a rectangle, we need to multiply
length × width × height
here, our length is 12 (6 + 6); our height is 12 (6 + 6); and our width is 6
let's multiply these together: (12)(12)(6) = 864
so, the volume of the green section is 864 cm³
now, let's work with the blue section:
once again, the volume for a rectangle is length × width × height
here, our length is 18, our height is 10, and our width is 8
let's multiply these together: (18)(10)(8) = 1440
so, the volume of the blue section is 1440cm³
now, we can add our sections together:
1440 + 864 = 2304
meaning that the volume of the composite figure is 2304 cm³
hope this helps!! have a lovely day :)
A golf club manufacturer measures the impact elasticity of a new material. This is done by randomly selecting a driver head made from the new material, firing a golf ball at it from an air cannon (under carefully controlled conditions), and making certain measurements of the ball's motion. These measurements are used to calculate a number called the coefficient of restitution of the driver head. Engineers use this procedure 30 times. The sample mean coefficient of restitution is 0.835. Calculate a 99% confidence interval for the true mean coefficient of restitution, assuming the population standard deviation of such coefficients is 0.019. Round your answers to the fourth decimal digit.
The confidence interval for the true mean coefficient of restitution is (29.9911,30.0089).
Given sample mean coefficient of restitution 0.835,population standard deviation of 0.019 and the confidence level of 0.835.
We have to find the confidence interval for the true mean coefficient of restitution.
We can easily find the confidence interval through the formula of margin of error.
Margin of error is the difference between the calculated values and the real values.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where z is the z value of p value,
σ is population mean or sample mean,
n is the sample size.
In our problem the sample size is 30.
z value for the p value of 0.99 is 2.576.
Margin of error=2.576*0.019/[tex]\sqrt{30}[/tex]
=0.048944/5.4772
=0.0089
Upper level=mean +margin of error
=30+0.0089
=30.0089
Lower level=Mean-margin of error
=30-0.0089
=29.9911.
Hence the confidence interval for the true mean coefficient of restitution is (29.9911,30.0089).
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what is the solution to the system of equations: 4x-y=10 and x-4=y
Answer:
(2, - 2 )
Step-by-step explanation:
4x - y = 10 → (1)
x - 4 = y → (2)
substitute x - 4 = y into (1)
4x - (x - 4) = 10 ← distribute parenthesis on left side by - 1
4x - x + 4 = 10
3x + 4 = 10 ( subtract 4 from both sides )
3x = 6 ( divide both sides by 3 )
x = 2
substitute x = 2 into either of the 2 equations and solve for y
substituting into (2)
2 - 4 = y
- 2 = y
solution is (2, - 2 )
Answer:
x = 2 , y = -2
Step-by-step explanation:
I will use the elimination method :
4x-y = 10 - Equation Number 1
x-4 = y - Equation Number 2
For the second equation we add 4 to both sides and subtract y from both sides :
x = y + 4
x - y = 4 - Let's call this equation number 3 :
Now we can subtract the equation 1 with 3 to eliminate y :
3x = 6
x = 2
Now we substitute this value into equation 2 to solve for y :
(2)-4 = y
y = -2
Substitute these values into equation 1 to verify :
4(2) - (-2) = 10
8 + 2 = 10
10 = 10
So these values must be correct
Hope this helped and have a good day
3(-3x-3)+2x+4= -33
solve for X
Answer:
x = 4
Step-by-step explanation:
3(-3x -3) + 2x + 4 = -33
(3*-3x + 3*-3) + 2x + 4 = -33
(-9x - 9) - 2x + 4 = -33
-9x + 2x - 9 + 4 = -33
-7x -5 = -33
-7x = -33 + 5
-7x = -28
x = -28/-7
x = 4
Check:
3((-3*4)-3) + 2*4 + 4 = -33
3(-12-3) + 8 + 4 = -33
3(-15) + 12 = -33
-45 + 12 = -33
A step function h(x) is represented by y = -2[x]. Which phrase best describes the range of the function h(x)
O all real numbers
O all rational numbers
O all negative integers
all even integers
Mark this and return
Save and Exit
lext
Subm
The range of the step function is all negative integers, thus, the correct option is A.
What are domain and range of a function ?Domain is the set of values for which the given function is defined.
Range is the set of all values which the given function can output.
For the given function h(x)=-2|x|, any value of x will return a negative value, therefore, the range of the function is all negative numbers. This can be observed in the graph given below.
Hence, the range of the step function is all negative integers, thus, the correct option is A.
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There are 5 trees with 6 birds in each tree. 4 birds fly away. How many birds are left?
Angela has 108 pieces of candy. If she gives each person 4 pieces, how many people can she give candy to?
At lincoln high school, the probability that a student takes both art and music is 9%. the probability that a student takes music is 12%. what is the probability that a student takes art, given that the student takes music?
The probability that a student takes art, given that the student takes music is 10.8%
In probability, we say two events are independent if knowing one event occurred doesn't change the probability of the other event.
For example, the probability that a fair coin shows "heads" after being flipped is 1/21/21, slash, 2. What if we knew the day was Tuesday? Does this change the probability of getting "heads?" Of course not. The probability of getting "heads," given that it's a Tuesday, is still 1/21/21, slash, 2. So the result of a coin flip and the day being Tuesday are independent events; knowing it was a Tuesday didn't change the probability of getting "heads."
Two events, A and B, are independent if
P(A ∣ B)=P(A)
P(A).P(B) = P(A ∩ B)
In the given question there are independent events.
Given:-
P(A) = Student takes both art and music = 0.9
P(B) = Student takes music = 0.12
P(A ∩ B) = student takes art, given that the student takes music
Thus by using the formula we get,
P(A ∩ B) = 0.9 x 0.12 = 0.108 = 10.8%
The probability that a student takes art, given that the student takes music is 10.8%
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abcd is a trapizium calculate the area of the area of abcd 10 9 7 15
The area of the trapezoid is 87.5 square cm if the parallel side lengths are 10 and 15 cm, the height is 7 cm.
What is a trapezoid?It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a trapezoid ABCD shown in the picture.
As we know the area of the trapezoid is given by:
= (a+b)h/2
= (10+15)(7/2)
= 87.5 square cm
Thus, the area of the trapezoid is 87.5 square cm if the parallel side lengths are 10 and 15 cm, the height is 7 cm.
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The total cost of 2 novels and 4 fiction books is $84. Each novel costs $6 more than each fiction book. What is the total cost of a novel and a fiction book?
Answer:
$30
Step-by-step explanation:
Let,
x - fiction book
x + $6 - novel
EQUATION:
4(x) + 2(x + $6) = $84
6x + $12 = $84
6x = $84 - $12
6x = $72
x = $12
SUBSTITUTE:
novel = $12
fiction = $18
TOTAL COST OF NOVEL AND FICTION
$18 + $12 = $30
What is the measure of this line?
80 mm
840mm
84mm
80.4 mm
Answer:
84 mm (C)
Step-by-step explanation:
We are given the centimeter/millimeter side of the ruler. It is probably easier to first look at the centimeters since the lines are much bigger. We can see that the line goes from 0cm to around 8.4cm. Now, we can convert centimeters to millimeters because we know that there are 10 millimeters in one centimeter. 8.4cm * 10 gives us 84 millimeters (C)
Select the correct answer. Find the inverse of the given function. f(x) = (x+3)^3-1
The inverse function of f(x) is [tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]
How to determine the inverse function?The function is given as:
f(x) = (x + 3)^3 - 1
Rewrite as:
y = (x + 3)^3 - 1
Swap x and y
x = (y + 3)^3 - 1
Add 1 to both sides
(y + 3)^3 = x + 1
Take the cube root of both sides
[tex]y + 3 = \sqrt[3]{x + 1}[/tex]
Subtract 3 from both sides
[tex]y = \sqrt[3]{x + 1} - 3[/tex]
Rewrite as:
[tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]
Hence, the inverse function of f(x) is [tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]
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PLEASE ANYONE HELP !!!!
Answer:
28 should do it
Step-by-step explanation:
35+35+82= 152
180-152=28
Please help me with this linear inequalities as graphs question!
I'd really appreciate if you added workings out and explained it a bit, as I'm terribly stuck.
The system of linear inequalities which satisfy the region R in the graph above are:
y ≤ 2x + 3y ≥ -x + 4y ≤ x + 4How to find the inequalities?Mathematically, the general equation of a straight line is given by y = mx + b.
In order to determine the system of linear inequalities that satisfy the region R, we would identify the points through which these straight lines passes through.
For the left line, we have:
y-intercept = 3.
x-intercept = -3/2.
Points (x, y) = (0, 3) and (-3/2, 0).
Thus, the inequality is given by:
(x/-3/2) + y/3 ≤ 1.
-2x + y ≤ 3
y ≤ 2x + 3
For the right line, we have:
y-intercept = 4.
x-intercept = 4.
Points (x, y) = (0, 4) and (4, 0).
Thus, the inequality is given by y ≥ -x + 4
For the lower line, we have:
y-intercept = 0.
x-intercept = 4.
Points (x, y) = (4, 0)
Thus, the inequality is given by y ≤ x + 4
In conclusion, the system of linear inequalities which satisfy the region R in the graph above are:
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A regular quadrilateral has what type of symmetry?
A Line symmetry only
B Both point and line symmetry
C Neither point nor line symmetry
D Point symmetry only
Answer:
B
Step-by-step explanation:
It has both point and line symmetry