Answers
Next, lets convert those decimals into fractions by adding a denominator 1 to each decimal and multiply both its numerator and denominator by a power 10 that lets us get rid of the decimal point:
[tex]( \frac{-2.5}{1} )( \frac{10}{10} )= \frac{-25}{10} =- \frac{5}{2} [/tex]
[tex]( \frac{0.5}{1} )( \frac{10}{10} )= \frac{5}{10} = \frac{1}{2} [/tex]
[tex]( \frac{1.5}{1} )( \frac{10}{10} )= \frac{15}{10} = \frac{3}{2} [/tex]
Since we know that each one of those points is a zero of the function ([tex]x=0[/tex]), we can replace each value into our [tex]x=0[/tex], and work backwards to get our binomials:
[tex]x=- \frac{5}{2} [/tex]
[tex]2x=-5[/tex]
[tex]2x+5=0[/tex]
So, our first binomial is [tex](2x+5)[/tex]
[tex]x= \frac{1}{2} [/tex]
[tex]2x=1[/tex]
[tex]2x-1=0[/tex]
So, our second binomial is [tex](2x-1)[/tex]
[tex]x= \frac{3}{2} [/tex]
[tex]2x=3[/tex]
[tex]2x-3=0[/tex]
So, our next binomial is [tex](2x-3)[/tex]
Now lets put all together to find the equation of our function:
[tex]y=(2x+5)(2x-1)(2x-3)[/tex]
And of course, we can rewrite it in a different order:
[tex]y=(2x-1)(2x-3)(2x+5)[/tex]
We can conclude that the equation that most likely represents the graph of the function is [tex]y=(2x-1)(2x-3)(2x+5)[/tex]
The subject of this question is Mathematics, specifically Algebra 2.
Explanation:The subject of this question is Mathematics, specifically Algebra 2.
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Related Questions
The volume of a cone is 180 in3. find a function that models the height h of the cone in terms of its radius r.
Answers
Final answer:
The function modeling the height of the cone in terms of its radius, given the volume of 180 in³, is h(r) = 540 / (πr²).
Explanation:
The volume V of a cone with radius r and height h is given by the formula V = (1/3)πr²h, where π is Pi (approximately 3.14159). Given that the volume of the cone is 180 in³, we can solve for the height h in terms of the radius r.
Starting with the formula:
V = (1/3)πr²h
We plug in the volume:
180 = (1/3)πr²h
To solve for h, we rearrange the equation:
h = 3*180 / (πr²)
h = 540 / (πr²)
So the function modeling the height h of the cone in terms of its radius r is:
h(r) = 540 / (πr²)
To covert 180 seconds to minutes, which proportion should you use?
Answers
there are 60 seconds in 1 minute, how many minutes in 180 seconds?
[tex]\bf \begin{array}{ccll} seconds&minutes\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 60&1\\ 180&x \end{array}\implies \cfrac{60}{180}=\cfrac{1}{x}\implies x=\cfrac{180\cdot 1}{60}[/tex]
but usually, the proportion wil be a fraction, so usually you'd put the unit you need cancelled at the bottom or the denominator.
60s/m or m/60s , in this case we need to cancel the seconds, so 180 s * m/60s.
Peter is making an "X marks the spot" flag for a treasure hunt. The flag is made of a square white flag with sides of 121212 inches. He will make the "X" by stretching red ribbon diagonally from corner to corner.
How many inches of ribbon will Peter need to make the "X"?
Answers
The length of diagonal of square with side 12 inches will be:
[tex] \sqrt{ 12^{2}+ 12^{2} }= \sqrt{288} =16.97[/tex]
The length of one diagonal is 16.97 inches. The length of 2 diagonals will be 33.94 inches or approximately 34 inches.
Therefore, 34 inches of ribbon will be needed to make the mark X on a square shaped flag having a side length of 12 inches.
find the average rate of change for the equation [1,6] f(x)=-ln(x)
Answers
[tex] \frac{f( x_{2})-f( x_{1})}{ x_{2} - x_{1} } [/tex]
We are to find the find the average rate of change of given function over the range [1,6], so,
[tex] x_{1}=1 \\ x_{2}=6 [/tex]
Using the values in above formula, we get:
[tex] \frac{f(6)-f(1)}{6-1} \\ \\ = \frac{-ln(6)-(-ln(1))}{5} = \frac{-ln(6)-0}{5} \\ \\ = \frac{-ln(6)}{5} [/tex]
Thus the average rate of change for f(x) = -ln(x) for the interval [1,6] is given by the above expression
What is the missing reason in Step 8? Pythagorean theorem definition of cosine substitution properties of multiplication
8.a2 = b2 – 2bccos(A) + c2 8.?
Answers
Pythagorean theorem is used only for the right angled triangles.
For ΔABC,
Cosine rule is
[tex] a^2=b^2 + c^2-2bc$ cosA $ [/tex]
[tex] b^2=a^2 + c^2-2ac$ cosB $ [/tex]
[tex] c^2=a^2 + b^2-2ab$ cosC $ [/tex]
Here we have used one of these formulae
Hence definition of cosine or Cosine rule is the right answer
Option 2) is the right answer
The missing reason in Step 8 is substitution of a² = b² – 2bc·cosA + c²
What is the law of cosines?The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.
Given is a proof using triangles property and rule,
In △ ABC, BD ⊥ AC
Prove: the formula for the law of cosines, a² = b² + c² – 2bccos
Statements Reasons
1. In △ ABC, BD ⊥ AC 1. given
2. In △ ADB, c² = x² + h² 2. Pythagorean thm.
3. In △ BDC, a² = (b – x)² + h² 3. Pythagorean thm.
4. a² = b² – 2bx + x² + h² 4. prop. of multiplication
5. a² = b² – 2bx + c² 5. substitution
6. In △ ADB, cos(A) = x/6 6. def. cosine
7. ccos(A) = x 7. mult. prop. of equality
8. a² = b² – 2bccos(A) + c² 8. ?
9. a² = b² + c² – 2bccos(A) 9. commutative property
We are asked to find the reason used in step 8,
From step 5) we have, a² = b² – 2bx + c².......(i)
From step 7) we have, ccos(A) = x
So, by substituting ccosA for x in eq(i), we get the equation for step 8)
a² = b² – 2bc·cosA + c²
Hence, the missing reason in Step 8 is substitution of a² = b² – 2bc·cosA + c²
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Choose the correct classification of 4x4 ??? 4x3 + 10x6.
4th degree trinomial
12th degree trinomial
3rd degree trinomial
6th degree trinomial
Answers
we have that
4x^4 - 4x^3 + 10x^6---------> is a 6th degree trinomial
because
a) Having three terms
b) highest degree is 6
therefore
the answer is the option 6th degree trinomial
The polynomial [tex]\( 4x^4 - 4x^3 + 10x^6 \)[/tex] is classified as a 6th degree trinomial. The correct option is d) 6th degree trinomial.
To classify the polynomial [tex]\( 4x^4 - 4x^3 + 10x^6 \)[/tex]:
Identify the degree of each term:
- [tex]\( 4x^4 \)[/tex] has a degree of 4.
- [tex]\( 4x^3 \)[/tex] has a degree of 3.
- [tex]\( 10x^6 \)[/tex] has a degree of 6.
Determine the degree of the polynomial:
The degree of the polynomial is the highest degree of its terms, which is 6.
Count the number of terms: The polynomial has three terms.
Thus, the polynomial has 6th degree and number of terms trinomial.
The complete question is:
Choose the correct classification of [tex]4x^4-4x^3+10x^6.[/tex]
a) 4th degree trinomial
b) 12th degree trinomial
c) 3rd degree trinomial
d) 6th degree trinomial
A salesperson earns a weekly base salary plus a commission of 20% of all sales over the first $500. This situation can be represented by the expression 750+0.2(x-500). Which of the following describes the meaning of 0.2(x-500) for this situation?
a. total amount of sales
b. total amount of salary earned
c. total amount of sales after the first $500
d. total amount of commission earned
and example why it is the answer
Answers
Answer:
d. total amount of commission earned
Step-by-step explanation:
A salesperson earns a weekly base salary plus a commission of 20% of all sales over the first $500.
This situation can be represented by the expression [tex]750+0.2(x-500)[/tex]
0.2(x-500) means total amount of commission earned.
This is because firstly its given that 20% is commission so we have 0.2.
The x-500 represents the sales over $500, where x is total sales. Like the person sold $800 worth of items so he will get 20% commission on $300.
Henry plots triangle UVW on a coordinate grid. The coordinates of U are (4, 3). After the triangle is translated 3 units to the left, what are the new coordinates of U ?
(7, 3)
(1, 3)
(4, 6)
(4, 0)
Answers
(x, y) -----> (x-3, y)
Applying the rule for point U we have:
(4, 3) -----> (4-3, 3) ----> (1, 3)
Answer:
the new coordinates of U are:
(1, 3)
What is the arc length of an angle of 7π 6 radians formed on the unit circle? A) π 6 B) 5π 6 C) 7π 6 D) 5π 6
Answers
y=sint
so x^2+y^2=1
could be represented parametrically
and you would take
Integral
sqrt (1-(dx/dt)^2+(dy/dt)^2) from 0 to 7pi/6
Note, I'm note sure if this is the correct integration formula
Answer:
C
Step-by-step explanation:
C'MON, PLS HELP, I WILL GIVE BRAINLIEST-A farmer has 300 ft of fencing with which to enclose a rectangular pen next to a barn. The barn itself will be used as one of the sides of the enclosed area.
What is the maximum area that can be enclosed by the fencing?
Enter your answer in the box.
ft²
Answers
width: 15, length: 30
Also, the max area of the garden is 450 square feet.
Hope this helps,
Master Yoda
Match the trinomials with their factors.
Answers
(a-10)(a-2) goes with d
(a-4)(a+5) goes with a
(a-10)(a+2) goes with c
e is not used.
if you want to check take the pairs and foil or box them out.
8. On a map, Jenia draws a segment from her home to her school. She measures
this segment and finds it is 3 cm. She knows her home is 0.5 mi from school.
What is the scale of her map in cm/mi?
A.6
B.3
C.13
D.16
Answers
3/.5 so we turn that into a division problem and divide 3 b .5
and our final answer is 6
April is randomly choosing five CDs to bring in her car from the following: 6 pop CDs, 8 rock CDs, and 10 R&B CDs. What is the complement of April choosing five pop CDs? choosing five CDs where none of them are pop choosing five CDs where not all of them are pop choosing five CDs where at least one of them is pop choosing five CDs where all of them are pop
Answers
Answer:
choosing five CDs where not all of them are pop
Step-by-step explanation:
The complement of an event is everything possible except that event. It is found by subtracting the probability of an event from 1.
The event we have listed is April choosing 5 pop CDs. The complement would literally be read as "not choosing 5 pop CDs." This means she would choose 5 CDs, where some could possibly be pop, but others would not.
Using the concept of complementary events, it is found that the complement of April choosing five pop CDs is given by:
choosing five CDs where not all of them are pop.
What are complementary events?Two events are complementary if the sum of their probabilities is of 1.
For example, either you choose five pop CDs, or you do not choose five pop CDs.
Hence the complement of this event is given by not choosing five pop CDs, that is:
choosing five CDs where not all of them are pop.
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Is it possible to place 158 books on three shelves so that the first shelf has 8 fewer books than the second and 5 more books than the third shelf?
plz halp
Answers
We are given 158 books to place them on three different shelves like A, B, and C.
It says that shelf A has eight fewer books than shelf B and five more books than shelf C.
Mathematically, it can be written as (A = B - 8) and (A = C + 5).
Or we can write it as (B = A + 8) and (C = A - 5).
If we consider there are 'x' books in shelf A, then shelf B would have 'x+8' books and shelf C would have 'x-5' books.
We know that Total books are 158, so its sum must be equal to total books.
A + B + C = 158
x + (x+8) + (x-5) = 158
3x + 3 = 158
3x + 3 - 3 = 158 - 3
3x = 155
[tex] \frac{3x}{3} =\frac{155}{3} [/tex]
x = 51.667 books
But 'x' must be an integer value because number of books can not be a decimal form.
Hence, this arrangement is "NOT possible" for this question.
Answer:
it is NOT possible
Step-by-step explanation:
Javier has 4 juice boxes. Three are grape flavored. Write two equivalent fractions that describe the part of the juice boxes that is grape
Answers
—
4
And
6
—
8
They are two equivalent fractions that can describe the last of the juice boxes that is grape.
If you need me to explain, comment something
Final answer:
Javier has 4 juice boxes, 3 of which are grape flavored. The fraction representing grape juice boxes is 3/4, with equivalent fractions being 6/8 and 9/12.
Explanation:
Javier has 4 juice boxes and three are grape flavored. To describe the part of the juice boxes that is grape in the form of a fraction, we would use the total number of juice boxes as the denominator and the number of grape juice boxes as the numerator. So, the fraction representing the grape juice boxes is 3/4 (three out of four).
To write two equivalent fractions, we can multiply the numerator and the denominator by the same number. If we multiply both by 2, we get 6/8, which is equivalent to 3/4. Similarly, multiplying both by 3 gives us 9/12, which is also equivalent to 3/4.
A set of data points has a line of best fit of y=-0.2x+1.8. What is the residual for the point (5,1)?
Answers
The residual for the point (5,1) is
To calculate residuals, we need to calculate the value of the line of best fit in the same x coordinate as the point we want to study to know the Predicted-y-value. To do so, we make the substitution of 5 into the equation:
[tex]y=-0,2x+1,8 \\ y=-0,2*(5)+1,8=0,8[/tex]
Now we determine the residual with the following equation:
[tex]Residual=yobs-ypred=1-0,8=0,2[/tex]
Have a nice day!
Answer:
0.2
Step-by-step explanation:
Prism A is similar to Prism B. The volume of Prism A is 2720 cm³.
What is the volume of Prism B?
Answers
[ (side length of A)/(side length of B) ]^3 = (volume of A)/(volume of B)
(8/4)^3 = 2720/x
2^3 = 2720/x
8 = 2720/x
8x = 2720
x = 2720/8
x = 340
The volume of Prism B is 340 cubic cm
can u find the volume of a cone?
Answers

The volume of a 33 -dimensional solid is the amount of space it occupies. Volume is measured in cubic units ( in3,ft3,cm3,m3,in3,ft3,cm3,m3, et cetera). Be sure that all of the measurements are in the same unit before computing the volume.
The volume VV of a cone with radius rr is one-third the area of the base BB times the height hh .
V=13Bh or V=13πr2h, where B=πr2V=13Bh or V=13πr2h, where B=πr2
Note : The formula for the volume of an oblique cone is the same as that of a right one.
The volumes of a cone and a cylinder are related in the same way as the volumes of a pyramid and a prism are related. If the heights of a cone and a cylinder are equal, then the volume of the cylinder is three times as much as the volume of a cone.
The formula v =bh means that the volume of a prism is equal to its base area times its height. Solve v= bh for b
Answers
Answer:
[tex]b = \frac{v}{h}[/tex]
Step-by-step explanation:
The formula v =bh means that the volume of a prism is equal to its base area times its height.
WE need to solve for b, we need to get 'b' alone
v=bh
to get 'b' alone we need to eliminate 'h'
To eliminate any variable we always do opposite operation.'
bh mean b times h
the opposite of multiplication is division
so to eliminate 'h' we divide by 'h' on both sides
[tex]\frac{v}{h} = \frac{bh}{h}[/tex]
[tex]b = \frac{v}{h}[/tex]
The formula for the base area (b) of a prism is b = v/h.
To solve the formula v = bh for b (the base area), to isolate b on one side of the equation. Follow these steps:
Divide both sides of the equation by h:
v/h = b
The base area (b) is now isolated on one side of the equation.
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y=f (x)=-4^x solve for f (x) when x = 3
Answers
Answer:
-64
Step-by-step explanation:
Plato/Edmentum users -64 is correct.
PLSSSS HELP WILL MARK BRAINLIEST 20PTS
Answers
.. tan(52°) = "opposite"/"adjacent"
.. tan(52°) = height/(41 m)
.. height = (41 m)*tan(52°) ≈ 52 m . . . . . . . 3rd selection
1B) Same deal.
.. tan(52°) = height/(side/2) = 2*height/side
.. side = 2*147 m/tan(52°) ≈ 230 m . . . . . . 4th selection
2) The sine is the ratio of opposite to hypotenuse. Side BC is opposite angle A, and side AB is the hypotenuse
.. sin(A) = (8√3)/16 = (√3)/2
Subtract. (5z−3)−(3z−8) Enter your answer, in simplified form, in the box.
Answers
= 5z − 3 − 3z + 8
= 2z + 5
In order to solve this problem, we must first distribute the -1 into the (3z - 8)
5z - 3 - 3z + 8
Next, we can combine like terms. We can combine everything that has a "z" in it together and anything that doesn't have a "z" together.
5z - 3z = 2z and -3 + 8 = 5
So your simplified answer is 2z + 5
Hope this helped!
WORTH 20 POINTS AND BRAINLIEST!!!
Some steps to rewrite the expression x3 − 9x + x2 − 9 as a product of three factors are shown below:
Step 1: x3 − 9x + x2 − 9
Step 2: x3 + x2 − 9x − 9
Step 3: x2(x + 1) − 9(x + 1)
Which of the following best shows the next two steps to rewrite the expression?
Step 4: (x2 + 9)(x + 1); Step 5: (x + 3)(x + 3)(x + 1)
Step 4: (x2 − 9)(x + 1); Step 5: (x + 3)(x + 3)(x + 1)
Step 4: (x2 + 9)(x + 1); Step 5: (x − 3)(x + 3)(x + 1)
Step 4: (x2 − 9)(x + 1); Step 5: (x − 3)(x + 3)(x + 1)
Answers
Answer:
[tex](x+1)\cdot(x^2-9)[/tex]
[tex](x+1)\cdot(x-3)\cdot(x+3)[/tex]
Step-by-step explanation:
We can simplify the expression as follows:
[tex]x^3-9\cdot(x)+x^2-9[/tex]
[tex]x^3+x^2-9\cdot(x)-9[/tex]
we have a write the expression with a common factor of (x+1)
[tex]x^2\cdot(x+1)-9\cdot(x+1)[/tex]
[tex](x+1)\cdot(x^2-9)[/tex]
We can simplify (x²-9) as:
[tex](x-3)\cdot(x+3)=x^3-3\cdot(x)+3\cdot(x)-9[/tex]
Therefore the final form of the expression is:
[tex](x+1)\cdot(x-3)\cdot(x+3)[/tex]
The fourth option is the best option.
A) –6m + 38
B) –6m + 76
C) –6m + 19
D) –24m + 19
Answers
In order to find the answer to this particular problem. you would have to do the [tex]Distributive [/tex] [tex]Property[/tex]
So, [tex] \frac{1}{2} (-12m + 38)[/tex]
[tex] \frac{1}{2} (-12m) = -6m \\ \\ \\ \frac{1}{2} (36) = 19 [/tex]
Your answer: [tex]-6m + 19 [/tex] (option C,)
Good luck on your assignment and enjoy your day
~[tex]LoveYourselfFirst:)[/tex]
The table of values represents a quadratic function. What is the average rate of change for f(x) from x = 0 to x = 10 ? Enter your answer in the box.
Answers
AVR = (f (x2) - f (x1)) / (x2 - x1)
Substituting the values we have:
AVR = (204 - (-6)) / (10 - 0)
Rewriting we have:
AVR = (204 + 6) / (10 - 0)
AVR = 210/10
AVR = 21
Answer:
the average rate of change for f (x) from x = 0 to x = 10 is:
AVR = 21
n a right triangle, the sum of the squares of the leg lengths is equal to the square of the hypotenuse length.
Answers
CAN SOMEONE HELP ME PLZ!!
Answers
Hey !!
Check the attachment.
Hope it helps you :)
The salesperson earn $172 in COMMISSION last week. How much money, in dollars, did he have in SALES last week?
The correct answer is $3,640 ($3,640 is really the answer). Explain step-by-step how to come to that answer or show your work.
Answers
[tex] \frac{3640---\ \textgreater \ 100}{172---\ \textgreater \ x} [/tex]
[tex] \frac{100}{172} = \frac{100}{x} [/tex]
Now we just solve for [tex]x[/tex]:
[tex]x= \frac{(172)(100)}{3640} [/tex]
[tex]x=4.73[/tex]
We can conclude that our sales person has a commission of 4.73% over the total amount of sells per week. Since the commission of the last week was $172, the total sales was $3640 because the 4.73% of $3640 is $172.
Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 1 or a 6, nothing otherwise. What is your expected value?
Answers
Final answer:
The expected value of the game where you pay $3.00 to roll a die and win $5.00 for rolling a 1 or a 6 is -$0.33 per roll, indicating a loss over time.
Explanation:
The problem is asking us to calculate the expected value of the game in which you pay $3.00 to roll a fair die with the potential of winning $5.00 for rolling a 1 or a 6. To find the expected value, we need to multiply the outcomes by their respective probabilities and then sum these products.
The probability of rolling a 1 or a 6 is 1/6 for each number, so the combined probability for these winning rolls is 1/6 + 1/6 = 1/3. The probability of rolling a 2, 3, 4, or 5 is therefore 2/3 since these are the non-winning rolls.
Let's calculate the expected value (EV):
Winning: (1/3) * $5.00 = $1.67
Losing: (2/3) * -$3.00 = -$2.00
Now we add the two values:
EV = $1.67 - $2.00 = -$0.33
Therefore, the expected value of playing the game is a loss of $0.33 per roll. This means that in the long run, you can expect to lose an average of $0.33 for each time you play this game.
The sum of two numbers is 37. Their difference is 7. What are the numbers?
Answers:
17 and 24
16 and 21
15 and 22
18 and 25
Answers
Answer:
15 and 22
Step-by-step explanation:
15+22=37 and 22-15=7