Answer:
2
Step-by-step explanation:
let the number be n then
[tex]\frac{n}{2}[/tex] = 2n - 3 ( myltiply both sides by 2 )
n = 4n - 6 ( subtract 4n from both sides )
- 3n = - 6 ( divide both sides by - 3 )
n = 2
check
[tex]\frac{2}{2}[/tex] = 1 and (2 × 2 ) - 3 = 4 - 3 =1
3q, –3p, 3pq, 13p
Question 4 options:
3 q and 3 pq
3q, –3p, and 3pq
–3p and 13p
–3p, 3pq, and 13p
which of the following are roots of the polynomial function below? F(x)=x^3-3x^2+2
The roots of the polynomial function F(x)=x^3-3x^2+2 can be found by reducing the function to zero and solving for x, likely by applying synthetic division or the Rational Root Theorem, as the polynomial is of third order.
Explanation:In Mathematics, especially in algebra, we often encounter the concept of finding the roots of polynomial functions. The roots of the function F(x)=x^3-3x^2+2 can be found by setting the function equal to zero and solving for the variable x:
Step 1: Set the equation to zero: x^3-3x^2+2 = 0.Step 2: Try to factor the polynomial or use a solving method such as the quadratic formula if it was a second-order polynomial. But in this case, the polynomial is of third order, and in such cases you typically apply synthetic division or the Rational Root Theorem to find the roots.Note: This explanation suggests general approaches. The actual solution would require longer calculations.
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The only root of the polynomial function F(x) = x³ - 3x² + x + 5 is 2 + i.
Explanation:Let's go through the possible roots of this polynomial function one by one and see which of them will make the function equal to zero. Recall that if a number p is a root of a polynomial, then when we substitute p into the polynomial, the resulting value will be zero.
A. First, let's consider 2+i as a possible root.
We would evaluate F(2+i) = (2+i)³ - 3(2+i)² +(2+i) + 5 = 0.
Upon evaluation, it turns out that F(2+i) does indeed equal 0.
B. Now let's see if -2+i is a root.
We evaluate F(-2+i) = ((-2+i)³ - 3(-2+i)² + (-2+i) + 5. This happens not to equal 0. Therefore, -2+i is not a root.
C. Then, we check if 1 is a root by computing
F(1) = 1³ - 3×1² +1 +5. Upon computing, we find that this doesn't result in 0 either. So, 1 is not a root
D. Finally, let's check if 2 is a root.
We compute F(2)= 2³ - 3×2² +2 +5. This computation also doesn't result in 0, therefore 2 is not a root of the polynomial function.
In conclusion, the only given number that is a root of the function is 2 + i.
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Question:Which of the following are roots of the polynomial function below?
F(x)=x³-3x²+x+5
A. 2+i
B. -2+i
C. 1
D. 2
Help me with these math questions........ WITH SCREENIES
Answer: 6.3093
Step-by-step explanation:
[tex]3^{\frac{x}{5}} = 4[/tex]
[tex]ln3^{\frac{x}{5}} = ln4[/tex]
[tex]\frac{x}{5} ln3 = ln4[/tex]
xln3 = 5ln4
[tex]x = \frac{5ln4}{ln3}[/tex]
x = 6.3093
************************************************************
Answer: 5, 3, [tex]\frac{1}{5}[/tex], D
Step-by-step explanation:
a) x ≤ 0 so, f(-5) = | -5 | = 5
x ≤ 0 so, f(-3) = | -3 | = 3
x > 0 so, f(5) = [tex]\frac{1}{5}[/tex]
b) graph D
************************************************************
Answer: [tex]\frac{\pi}{12}[/tex]
Step-by-step explanation:
[tex]\frac{25\pi}{12} - \frac{2\pi}{}[/tex]
= [tex]\frac{25\pi}{12} - \frac{24\pi}{12}[/tex]
= [tex]\frac{\pi}{12}[/tex]
Anumeha is mowing the lawns for a summer job. For every mowing job, she charges and initial fee of $10 plus a constant fee for each hour of work. Her fee for a 5-hour job, for instance is $35. Let F(t) denote Anumeha's for a single job F (measured in dollars) as a function of the number of hours t it took her to complete it. Write the functions formula
Answer:
F(t) = 10 +5t
Step-by-step explanation:
Income equals the initial fee plus the hours worked times the hourly rate
We know the initial fee = 10
hours = t
hourly rate =r
F(t) = 10 + r*t
We know a 5 hour job is 35 dollars
35 = 10 + r*5
Subtract 10 from each side
35-10 = 10-10 +5r
25 = 5r
Divide by 5
25/5 = 5r/5
5 =r
The hourly rate is 5
F(t) = 10 +5t
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y.)
midpoint (-18,-12) endpoint (-9,-11)
[tex]\text{The formula of a midpoint:}\\\\\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]
[tex]\text{We have}\\\\\text{endpoint}\ (-9,\ -11)\to x_1=-9,\ y_1=-11\\\\\text{midpoint}\ (-18,\ -12)\\\\\text{Therefore we have the equations:}\\\\\dfrac{-9+x_2}{2}=-18\qquad\text{multiply both sides by 2}\\\\-9+x_2=-36\qquad\text{add 9 to both sides}\\\\\boxed{x_2=-27}\\\\\dfrac{-11+y_2}{2}=-12\qquad\text{multiply both sides by 2}\\\\-11+y_2=-24\qquad\text{add 11 to both sides}\\\\\boxed{y_2=-13}\\\\Answer:\ \boxed{(-27,\ -13)}[/tex]
if f(x)=5x-7 then f^-1=__ _
Answer:
f^-1(x) = (x +7)/5
Step-by-step explanation:
Set x = f(y) and solve for y.
... x = 5y -7
... x+7 = 5y
... (x+7)/5 = y . . . . this is the inverse function
f^-1(x) = (x +7)/5
PLEASE NEED HELP ASAP WILL GIVE 50 POINTS
What is the value of x?
Enter your answer in the box.
x =
Answer:
x = 32
Step-by-step explanation:
This is an equilateral triangle, all three sides equal. Since all three sides are equal, all three angle are equal. 180/3 = 60. That means each angle is equal to 60 degrees.
2x-4 = 60
Add 4 to each side
2x-4+4 = 60+4
2x =64
Divide each side by 2.
2x/2 = 64/2
x = 32
how can we write 128 in exponent form?
Answer: 2⁷
Step-by-step explanation:
128
∧ 2 64 ∧ 2 32 ∧ 2 16 ∧ 2 8 ∧ 2 4 ∧ 2 2128 = 2 * 2 * 2 * 2 * 2 * 2 * 2
= 2⁷
Does anyone know how to do this?
[tex]2)\\\\6+5k+2=18\\\\(6+2)+5k=18\\\\8+5k=18\qquad\text{subtract 8 from both sides}\\\\5k=10\qquad\text{divide both sides by 5}\\\\\boxed{k=2}\\\\4)\\\\-8(a-8)=96\qquad\text{divide both sides by (-8)}\\\\a-8=-12\qquad\text{add 8 to both sides}\\\\\boxed{a=-4}[/tex]
[tex]6)\\7m+35=7(5m-3)\qquad\text{divide both sides by 7}\\\\m+5=5m-3\qquad\text{subtract 5 from both sides}\\\\m=5m-8\qquad\text{subtract 5m from both sides}\\\\-4m=-8\qquad\text{divide both sides by (-4)}\\\\\boxed{m=2}[/tex]
Beth and Carley are selling candy bars to raise money for new cheerleading uniforms. Beth has sold one less than twice the number of candy bars that Carley has sold. If they have sold 188 candy bars in all, how many has Beth sold?
Answer:
125 candy bars
Step-by-step explanation:
[tex]\text{Let the number of candy bars sold by Carley is }x\\\text{Then since Beth has sold one less than twice the number of candy bars}\\\text{that Carley has sold, so number of candy bars sold by Beth}=2x-1\\\\\text{also given that they have sold 188 candy bars in all, so we have}\\\\\text{Candy bars sold by Carley + Candy bars sold by Beth}=188\\\\\Rightarrow (x)+(2x-1)=188\\\\\Rightarrow 3x-1=188\\\\\Rightarrow 3x=189\\\\\Rightarrow x=\frac{189}{3}=63[/tex]
[tex]\text{Hence the candy bars sold by Beth are:}\\=2x-1\\\\=2(63)-1\\\\=126-1\\\\=125\\\\\text{Hence, Beth sold 125 candy bars.}[/tex]
Ralph sold brownies for ?$0.27 a piece in order to earn money to buy baseball cards. If the cards cost ?$0.81 per? pack, and if Ralph had no money left over after buying? them, what is the least number of brownies he must have? sold
Answer:
3 brownies
Step-by-step explanation:
To find this answer we need to divide the 0.81 by 0.27 to find out how many brownies total 0.81:
0.81 ÷ 0.27 = 3
So he needs to sell 3 brownies.
A seamstress uses 12 yards of fabric to make 3 costumes for students in the chorus. How many yards will she need to make costumes for all 25 students in chorus?
Answer:
100 yards
Step-by-step explanation:
It takes 4 yards of fabric to make a costume for one student. She needs to make costumes for every student in chorus, so you just multiply this number by 25 and get 100 yards.
Answer:
100 yards.
Step-by-step explanation:
We have been given that a seamstress uses 12 yards of fabric to make 3 costumes for students in the chorus.
We will use proportions to solve the given problem.
[tex]\frac{\text{Yards of fabric}}{\text{Costumes}}=\frac{12}{3}[/tex]
[tex]\frac{\text{Yards of fabric}}{25}=\frac{12}{3}[/tex]
[tex]\frac{\text{Yards of fabric}}{25}*25=\frac{12}{3}*25[/tex]
[tex]\text{Yards of fabric}=4*25[/tex]
[tex]\text{Yards of fabric}=100[/tex]
Therefore, 100 yards of fabric is needed to make costumes for 25 students.
The hospital shop buys cereal bars in packs of 4. In one day they sell 58 cereal bars. How many packets did they open tht day?
A polynomial function has a root of zero with multiplicity one, and root of two with multiplicity four. If the function has a negative leading coefficient, and is of odd degree, which of the following is true.
- the function is positive on (-infinity, 0)
-the function is negative on (0,2)
-the function is negative on (2,infinity)
-the function is positive on (0, infinity)
Answer: A, B, and C
Step-by-step explanation:
root of zero (x = 0) with multiplicity of 1 (x = 0)¹ means that the graph CROSSES the axis at x = 0
root of two (x = 2) with multiplicity of 4 (x = 2)⁴ means that the graph TOUCHES the axis at x = 2
WHY?
odd numbered multiplicity crosses the x-axiseven numbered multiplicity touches the x-axis (it is a turning point)Leading Coefficient (end behavior of right side):
If the leading coefficient is positive, then right side goes to +∞If the leading coefficient is negative, then right side goes to -∞Degree of polynomial (left side behavior):
If degree is even, then left side is the same as the right sideIf the degree is odd, then left side is opposite of right sideThe given polynomial has a negative leading coefficent and odd degree so the left side goes to +∞ and the right side goes to -∞
OBSERVE INTERVALS:
(-∞, 0) is above the x-axis so POSITIVE(0, 2) is below the x-axis so NEGATIVE(2, +∞) is also below the x-axis x=2 was a turning point so NEGATIVESee graph to confirm statements above
Answer:
A, B, and C
Step-by-step explanation:
Had the same question on Edge :)
Mallory has 535 e-mail messages in her inbox. She sorts them evenly among folders labeld family,work, school and recipes.How many messages does mallory put in each folder
Anwser could be 107 because 535/5=107
Find the length of the hypotenuse
We know that : In a Triangle, If Two Angles are Equal then Corresponding Sides with Respect to those Two Angles Should be Equal.
In the Given Right Angled Triangle, There are Two Angles which are Equal to 45°. It means The Lengths of the Sides Corresponding to those Equal 45° Angles should be Equal.
It Means The Given Right Angled Triangle is also an Isosceles Triangle
⇒ The Other Side of the Triangle is [tex]3\sqrt{2}[/tex]
As it is a Right Angled Triangle :
[tex]\mathsf{\implies (Hypotenuse)^2 = (3\sqrt{2})^2 + (3\sqrt{2})^2}[/tex]
[tex]\mathsf{\implies (Hypotenuse)^2 = 18 + 18}[/tex]
[tex]\mathsf{\implies (Hypotenuse)^2 = 36}[/tex]
[tex]\mathsf{\implies (Hypotenuse) = 6}[/tex]
The Length of Hypotenuse is 6
The graph of f(t) = 6 x 2^t shows the value of a rare coin in year t. What is the meaning of the y-intercept?
Answer: The meaning y-intercept is the initial value of a rare coin is 6.
Step-by-step explanation:
Given : The graph of [tex]f(t) = 6\times 2^t[/tex] shows the value of a rare coin in year t.
The y- intercept is the point on Cartesian plane when the graph intersects y axis. It given the initial value of the function by substituting the value of independent variable as zero.
i.e. , we need to put t=0, we get
[tex]f(0) = 6\times 2^0=6[/tex]
The meaning y-intercept is the initial value of a rare coin is 6.
A manufacturer of shipping boxes has a box shaped like a cube. The side length is (5a + 4b). What is the volume of the box in terms of A and b
The volume of the cube would be S^3, where S is the length of the side.
Volume = (5a + 4b)^3
Which becomes:
(5a+4b)(5a+4b)(5a+4b)
Multiply the first two sets of parenthesis by each other:
(25a^2+40ab+16b^2)(5a+4b)
Now multiply that by the 3rd set of parenthesis to get:
125a^3+300a^2b + 240ab^2 + b^3
Identify a pattern and sequence and fine the next number in the pattern. 54,52,26,24,_,_,_
Answer:
54, 52, 26, 24, 22, -6, -4
Step-by-step explanation:
a soccer team hopes to win at least 3 games for every 2 lost during the season. if there are 15 games scheduled, how many games can the team lose and still achieve its goal
Answer:
This team can lose 6 games and still achieve this goal.
Step-by-step explanation:
In order to find this, we can create a proportion and solve by cross multiplying. The proportion should compare amount of losses to total games.
Ratio = Total
2/5 = x/15
Now cross multiply
15*2 = 5x
30 = 5x
6 = x
This means the team can lose 6 games and still keep the necessary ratio.
Curtis traveled a distance of 12 miles in 2 hours from the park to his home. What was his average speed in miles per hour?
The average speed of an airplane is four times as fast as the average speed of a passenger train. To travel 1440 km, the train requires 12 h more than the airplane. Determine the average speeds of the train and the airplane.
Answer
Average speed of the train = 90 km/h and average speed of the airplane = 360 km/h.
Explanation:-
If speed of train = x then the speed of airplane = 4x km/h and we have the 2 equations
x = 1440 / (t + 12) (t = time taken by the train)
4x = 1440 / t................................(1) (t = time taken by train)
Multiply the first equation by 4:-
4x = 5760 / (t + 12).....................(2)
Combining equations (1) and (2):-
1440 / t = 5760 / (t + 12)
Cross multiplying:-
5760t = 1440t + 17,280
4320t = 17,280
t = 17280/4320
t = 4 hours
speed of train = 1440/ (4 + 12) = 90 km/h and speed of plane = 4*90 = 360 km/h.
Eva and Emily can clean the entire house in 4 hours. Eva can do it by herself in 6 hours. How long would it take Emily to do it by herself?
Answer:
12 hours would take emily
Step-by-step explanation:
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Lm is the midsegment of trapezoid ABCD ab=46 dc=125 what is lm
A. 103.5
B. 63
C. 79
D. 85.5
Answer: Choice D) 85.5
Work Shown:
To get the midsegment, we add up the sides parallel to this midsegment, then we divide by 2.
LM = (AB + DC)/2
LM = (46 + 125)/2
LM = 171/2
LM = 85.5
Answer: D is the answerb
Dean has 6 2/5 cups of yogurt. If it takes 4/5 cup of yogurt to make a fruit smoothie, how many smoothies can he make?
Answer:
8
Step-by-step explanation:
Change mixed number to decimal 6 2/5 = 6.4
Change needed fraction to decimal 4/5 = 0.8
Divide yogurt by yogurt needed 6.4 / 0.8 = 8
Working the problem like this will help you with any same type of problem.
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Answer: He can make 8 smoothies.
Step-by-step explanation:
Given : The total amount of yogurt Dean has = [tex]6\dfrac{2}{5}[/tex] cups
In Improper fraction , it will be :
[tex]6\dfrac{2}{5}=\dfrac{6\times5+2}{5}=\dfrac{32}{5}[/tex]
Also, the amount of yogurt required for a fruit smoothie = [tex]\dfrac{4}{5}[/tex]
Now , The number of smoothies he can make = (Total amount of yogurt Dean has) ÷ (amount of yogurt required for a fruit smoothie )
[tex]=\dfrac{32}{5}\div\dfrac{4}{5}\\\\=\dfrac{32}{5}\times\dfrac{5}{4}=8[/tex]
Hence, he can make 8 smoothies.
Find the measure of 1
A. 104
B.38
C.76
Answer:
a
Step-by-step explanation:
104 is the only number inside the box
The value of ∠1 is 38 degree , Option B is the correct answer.
What is a Parallelogram ?Parallelogram is a polygon with four sides , Opposite sides are parallel and equal.
From the figure given
One of the angle is 104 degree
when two lines are parallel and intersected by a transversal
then the sum of the consecutive interior angles is 180 degree
∠1 + ∠2 = 180 -104 = 76 degree
similarly the other two lines are parallel with each other
so ∠1 = ∠4
∠3 = ∠2
Therefore the diagonals are bisecting the angle and so
the value of ∠1 = 76 / 2 = 38 degree
Therefore , The value of ∠1 is 38 degree , Option B is the correct answer.
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You conduct an experiment where you roll a die and record the results. You roll the die 1,230 times, and the results are shown in the table below:
Result Frequency
1 245
2 172
3 219
4 201
5 137
6 256
What is the experimental probability of rolling a 1 on your next roll?
A.
0.1667
B.
0.1992
C.
0.245
D.
0.3275
Part B. What is the theoretical probability of rolling a 3 on your next roll?
A.
0.167
B.
0.178
C.
0.245
D.
0.333
The probability of an event is
2/7
What are the odds of the same event?
A. 7/9
B. 5/7
C. 2/9
D. 2/5
If I could get some help That'd Be Greattt
Answer: Other guy is right for 1 & 2 but is wrong for the last question.
I got a 100 on connections.
(1) 0.1992
(2)0.167
(3) 2/5
Step-by-step explanation:
The experimental probability of rolling a 1 on the next roll is 0.1992 (B). The theoretical probability of rolling a 3 on a six-sided die is 0.1667 (A). The odds of an event with a probability of 2/7 are 2 to 5 (D).
Explanation:The experimental probability of rolling a 1 in this experiment is calculated by dividing the frequency of rolling a 1 by the total number of rolls. There were 245 occurrences of rolling a 1 out of 1230 total rolls. To find the experimental probability, you divide 245 by 1230, which gives you 0.1992.
Part B: The theoretical probability of rolling any particular number on a fair six-sided die is 1/6, because there are 6 possible outcomes and each outcome is equally likely if the die is fair. Therefore, the theoretical probability of rolling a 3 on the next roll is 0.1667 (which is equivalent to 1/6 when rounded to four decimal places).
When the probability of an event is 2/7, the odds of the event are 2 to 5 (not 2/5). This is because odds are expressed as the ratio of the number of successful outcomes to the number of unsuccessful outcomes. Since there are 2 chances of success and 5 chances of failure (7-2=5), the odds are 2 to 5.
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Which value must be added to the expression x^2+16 to make it a perfect square trinomial
Adding the term 8x we will get:
x² + 8x + 4² = (x + 4)²
How to make a perfect square trinomial?
The perfect square trinomial is:
(a + b)² = a² + 2ab + b²
Here we start with:
x² + 16
We can rewrite this as:
x² + 4²
We can see that the term missing is the cross one, which will be:
2*(x)*4 = 8x
Then we will get:
x² + 8x + 4² = (x + 4)²
PLEASE ANSWER THIS QUESTION TOO !! FOR 30 POINTS AND BRAINLIEST!!
Answer:
3000 books
Step-by-step explanation:
We know the author receives a one time fee of $2500. On top of that, the author will receive $1.50 per book sold. This is a constant rate and is linear because of this. We can use y=mx+b. M is the slope or rate of change. M here is $1.50. B is the starting value which is $2500 here.
We write y=1.5x+2500.
This equation will give the amount of money the author earns for x number of books sold. If y=7000 for the author earning 7000. We will use inverse operations to isolate and find x.
7000=1.5x+2500
7000-2500=1.5x+2500-2500
4500=1.5x
4500/1.5=x
3000=x
Answer:
The author must sell 300 books.
Step-by-step explanation:
The total amount earned = advance + books sold * money per book
We know they want to make 7000
The advance is 2500
They earn 1.50 for each book sold
b= number of books sold
Substituting in
7000= 2500 + 1.5b
Subtract 2500 from each side
7000-2500 = 2500-2500 + 1.5 b
4500 = 1.5 b
Divide each side by 1.5
4500/1.5 = 1.5b/1.5
3000 = b
Montel sold 13 popcorn buckets and sold 13 fruit baskets for a fundraiser. The fruit baskets coast $20.75 each . If Montel raised a total of $469, how much did each popcorn buckets coast
Answer:
The popcorn buckets each cost around $15.34.
Step-by-step explanation: