Polynomials are mathematical expressions made up of many terms.
To simplify a polynomial as much as possible, you must group all the like terms and rearrange them from higher to lower power.
3x³ - 12x² - 2x-8The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of any constant term is 0. The derivative of axⁿ it's naxⁿ⁻¹.
3 × 3x³⁻¹ + 2(-12)x²⁻¹ - 2x¹⁻¹Multiply 3 x 3.
9x³⁻¹ + 2(-12)x²⁻¹ - 2x¹⁻¹Subtract 1 from 3.
9x² + 2(-12)x²⁻¹ - 2x¹⁻¹Multiply 2 by −12.
9x² - 24x²⁻¹ - 2x¹⁻¹Subtract 1 from 2 and subtract 1 from 1.
9x² - 24x¹ - 2x⁰For any term t, t¹ = t.
9x² - 24x - 2x⁰For any term t except 0, t⁰=1.
9x² - 24x - 2Answer: The solution of the polynomial 3x³ - 12x² - 2x-8 is 9x² - 24x - 2.
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Standard six-sided dice have their dots arranged so that the opposite faces add up to 7.
If 27 standard dice are arranged in a 3×3×3 cube on a solid table what is the maximum number of dots that can be seen from one position?
Answer: 153
Step-by-step explanation:
The maximum number of dots that can be seen from one position is 153 dots.
Thanom has a roll of paper consisting of a very long sheet of thin paper tightly rolled around a cylindrical tube, forming the shape indicated in the diagram.
Initially, the diameter of the roll is 12cm and the diameter of the tube is 4cm.
After Thanom uses half of the paper, the diameter of the remaining roll is closest to
Answer:
8 if including the tube and 4 if just counting the roll of toilet paper itself.
Step-by-step explanation:
Well like the question says the diameter of the toilet paper is 12 cm full both including the toilet paper and the tube. But we are also told the tube has a Diameter of 4. Taking this into consideration we both know that the tube will never get smaller but we do know the roll will decrease in size by half so while keeping the diameter of the tube at 4 we evenly remove half of the other 2 and we are left with a diameter of 2 / 4 / 2 in which giving us a total diameter of 8 therefore the diameter now being 8. (pls let me know if im wrong though i doubt i am)
How many significant digits are there in the number obtained by dividing 10.24 by 16 using significant digits?
A. 1
B. 2
C. 3
D. 4
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:▪ [tex]\longrightarrow \sf{10.24}[/tex]
▪ [tex]\longrightarrow \sf{16}[/tex]
We start by obtaining it:
[tex]\longrightarrow \sf{\dfrac{10.24}{16} = 0.64}[/tex]
Therefore, we are asked how many significant figures 0.64 has. The answer is 2. In this case, the significant digits are 6 & 4.
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex]\large \bm{B. \: 2}[/tex]
In a group of 200 students, the ratio of students who like Nepali and Social studies is 2:3. If 45 students like both the subjects and 20 students like none of the subjects:
A. Illustrate the given information in a venn diagram.
B. How many students like Nepali?
C. How many students like Social study only?
Please give right answer don't give any thing wrong to get 50 points .
Answer:B. 80 students like Nepali
C. 75 students like Social Studies only
Step-by-step explanation: The total of the ratio = the total number of students
2 + 3 = 5
5 parts = 200 students
1 part = 200 ÷ 5 = 40 students
Therefore,the students who liked Nepali(2 parts) = 2 × 40 = 80
The students who liked Social Studies(3 parts) = 3 × 40 = 120
But since 45 students liked both subjects,then those who liked Social Studies only:
120 - 45 = 75
The answers are a) attached b) 80 and c) 75
What is a Venn diagram?A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.
Given that, In a group of 200 students, the ratio of students who like Nepali and Social studies is 2:3. If 45 students like both the subjects and 20 students like none of the subjects,
The total of the ratio = the total number of students
2 + 3 = 5
5 parts = 200 students
1 part = 200 / 5 = 40 students
b) Therefore, the students who liked Nepali(2 parts) = 2 × 40 = 80
c) The students who liked Social Studies(3 parts) = 3 × 40 = 120
Since, 45 students liked both subjects, then those who liked Social Studies only:
120 - 45 = 75
Hence, The answers are a) attached b) 80 and c) 75
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Ariana was looking at rent costs for 555 apartments. Each rent was a different amount between \$1{,}000$1,000dollar sign, 1, comma, 000 and \$1{,}400$1,400dollar sign, 1, comma, 400 per month, except for one apartment whose rent was \$4{,}800$4,800dollar sign, 4, comma, 800 per month. [Show data]
Ariana looked at the mean and median of the rents. Then, she decided to remove the \$4{,}800$4,800dollar sign, 4, comma, 800 rent from the set and recalculate the mean and median.
How will removing this rent affect the mean and median?
The way that this action is going to affect the mean and the mean and the median value would be decreased than what it was supposed to be.
What is the mean?In a frequency distribution, the mean is the number that is used to represent the average of a group of data. To get the mean, you have to add up the numbers in the data set and divide by the total number in the data set.
The formula is fx/n
When the average of $4800 is removed from the data set, the mean is going to decrease by the number and the value of fx would also decrease. Hence we can conclude that it would cause the value to reduce.
The median is the middle value, it would also cause the median in the data set to be smaller than it was.
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Marita spent $13.0 at the grocery store. She bought pears, kiwis and pineaples. Pears cost $0.50 each, pineapples cost $1.50 each, and kiwis are $0.30 each. how many of each kind of fruit did she buy if she bought 9 more pears than pineapples and 2 fewer kiwis than pears?
Answer:
◘ 12 pears
◘ 3 pineapples
◘ 10 kiwis
Step-by-step explanation:
Let [tex]x[/tex] be the number of pears bought.
Therefore:
• number of pears = [tex]x[/tex]
• number of pineapples = [tex]x - 9[/tex]
• number of kiwis = [tex]x - 2[/tex]
We know that the total cost was $13.50.
This means if she bought [tex]x[/tex] pears at $0.50 each, [tex](x - 9)[/tex] pineapples at $1.50 each, and [tex](x -2)[/tex] kiwis at $0.30 each, the total would be $13.50.
∴ [tex][x \times 0.50] + [(x-9) \times 1.5] + [(x-2) \times 0.3] = 13.50[/tex]
Expanding and multiplying:
⇒ [tex]0.5 x + 1.5x - 13.5 + 0.3x - 0.6 = 13.5[/tex]
Collect like terms:
⇒ [tex]2.3x -14.1 = 13.5[/tex]
Solve for [tex]x[/tex]:
⇒ [tex]2.3x = 13.5 + 14.1[/tex]
⇒ [tex]2.3 x = 27.6[/tex]
⇒ [tex]x = 27.6 \div 2.3[/tex]
⇒ [tex]x = \bf 12[/tex]
Therefore, she bought:
• 12 pears
• [tex]x - 9[/tex] = 12 - 9 = 3 pineapples
• [tex]x - 2[/tex] = 12 - 2 = 10 kiwis
Marita bought 12 pears, 3 pineapples and 10 kiwis.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
Let x the number of pears bought,
y the number of pineapples bought,
z the number of kiwis bought,
Given that, Marita bought 9 more pears than pineapples and 2 fewer kiwis than pears,
y + 9 = x
y = x -9 and
z + 2 = x
z = x - 2
We know that the total cost was $13.50.
This means if she bought pears at $0.50 each, pineapples at $1.50 each, and kiwis at $0.30 each, the total would be $13.50.
∴ 0.50x + 1.50y+ 0.30z = 13.50
Substitute the values of y and z in equation,
⇒ 0.50x + 1.50(x -9)+ 0.30(x - 2) = 13.50
Expanding and multiplying terms in equation,
⇒ 0.50x + 1.50x -13.50+ 0.30x - 0.60 = 13.50
Rearrange the like terms and apply the arithmetic operation
⇒ 2.3x - 14.1 = 13.50
⇒ 2.3x = 13.50 + 14.1
⇒ 2.3x = 27.6
⇒ x = 27.6/2.3
⇒ x = 12
Therefore, the number of pears bought = 12
So, the number of pineapples bought = 12 - 9 = 3
And the number of kiwis bought = = 12 - 2 = 10
Hence, Marita bought 12 pears, 3 pineapples and 10 kiwis.
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Which of the following is a line segment as shown in the drawing?
Answers:
- DH is correct because a line is connecting the two points D and H as shown in the image, forming a line segment.
- ED is correct because a line is connecting the two points D and E, forming another line segment, as shown in the drawing.
- EH is incorrect because in the drawing shown, there is no line connecting the two points E and H, so there would be no line segment formed between these two points.
- CD is correct because there is another line connecting the two points C and D, forming another line segment in the drawing.
Therefore, lines DH, ED, and CD are all line segments.
PLEASE HELP ME!!! I NEED THIS ASAP!!!!!
Answer:
It is proved because line segment AC and line segment BD are parallel.
Step-by-step explanation:
I am also trying my best. Please let me know if it’s wrong or you need more help. Have a great day!
Manu borrowed Rupees 8500 at the rate of 5% interest per annum for 150 days. Find the interest and amount he paid
Answer:
See below
Step-by-step explanation:
5% interest = .05 :
8500 x .05 x 150days /365 days/year = R 174 .66 = interest......
then amount to be paid = 8500+ 174.66 = R 8674.66
Pls assistance
What is X?
x =x=x, equals
^\circ
∘
Answer:
x = 60°
Step-by-step explanation:
A straight angle is bascially a line with a point marked in it. That is 180°. Supplementary angles add up to 180°. Like the two right angles on the top part of the image are supplementary, as well as the two angles on the bottom part of the image.
120° + x = 180°
x = 60°
please explain your answer :)
and don’t answer if you won’t provide an explanation please :”D
Question: Explain why 200 people with email addresses may not be a random sample. When might it be a random sample?
Answer:
Explained Below
Step-by-step explanation:
200 people with those email addys might be people you know. While collecting addys randomly is a random sample.
its straight forward
Q1 Write the number in expanded form for the significant digits ( as fractions)
117.000
20.018
13.265
3.4000
0.8100
Q2 - Write the difference in place value of the underlined digits
ex . 12.352 - 2 in the ones place is 1000x bigger than the 2 in the thousandths place
1568.156 ( both of the 5s are underlined)
03.3000 ( both of the 3s are underlined)
5164.66 ( both of the 6s are underlined
9.09 ( the 9s r underlined)
To write in expanded form is to simply mean writing each number into its place value.
help
Is Figure BBB a scale copy of Figure AAA?
The ratios of corresponding side lengths are not equal.
Therefore, Figure B is not a scale copy of Figure A.
Here, we have to determine if Figure B is a scale copy of Figure A, we need to compare the corresponding sides of the two triangles and check if the ratios of their side lengths are equal.
Figure A has side lengths: 3.6, 2, and 5.
Figure B has side lengths: 8.9, 4, and 11.3.
Let's check if the ratios of corresponding side lengths are equal:
Ratio of corresponding side lengths of A and B:
3.6 / 8.9 ≈ 0.4045
2 / 4 = 0.5
5 / 11.3 ≈ 0.4425
The ratios of corresponding side lengths are not equal.
Therefore, Figure B is not a scale copy of Figure A.
In order for two triangles to be scale copies of each other, all corresponding side lengths must have the same ratio.
Since the ratios of side lengths in Figure A and Figure B are not equal, they are not scale copies of each other.
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in a survey of 3,100 people who owned a certain type of car, 2,015 said they would buy that type of car again. What percent of people of the people surveyed were satisfied with the car?
The percent of people of the people surveyed were satisfied with the car is the percent of people of the people would buy that type of car again, so we have: 2015 ÷ 3100 × 100% = 65%
ANSWER: 65%
Ok done. Thank to me :3
Answer:
2015 / 3100%= 65%
Step-by-step explanation:
You could never tell how many people there are in this world. So that is why the 3100 should have a percentage which is divided by 2015, equals 65%.
PLEASE I REALLY NEED THIS RN!!! PLEASE HELP ME!!!
1) [tex]\overline{UP}[/tex]
2) [tex]\overline{UP} \cong \overline{UP}[/tex]
3) [tex]\overline{UR}[/tex]
4) [tex]\overline{PR}[/tex]
5) [tex]\triangle OUP \cong \triangle RUP[/tex] by SSS
6) CPCTC
Answer:
Medunno got the first pic, now i help with the second pic.
Step-by-step explanation:
Draw segment PU (don't forget the line above)
PU ≅ PU reflexive property
UO≅ UR given
PO≅ PR given
△OUP ≅ △RUP by SSS congruence postulate
∠O ≅ ∠R corresponding parts of congruent triangles are congruent.
Sara has 845 beads to put on the bracelets she is making. It takes 13 beads to make each bracelet. How many bracelets can Sara make?
Answer:
65
Step-by-step explanation:
845 beads divided by 13 beads is 65. You can make 65 bracelets.
Use a table to identify three equivalent ratios of 2/5.
Answer: The simplest form of ratio 6:15=2×3:5×3=2:5
Step-by-step explanation: So, 2:5 is equivalent to 6:15.
Please help with this qn :)
The sum of the length of a side of two squares is 18cm and the sum of their areas is 212 cm^2. find the length of a side of the smaller square
Answer:
4 is the length
Step-by-step explanation:
14 and 4
14 x 14 + 4 x 4 = 212
14 + 4 = 18
which symbol will make the number sentence |-12|?12 true
A =
B with a line going through it
C<
d>
Answer:
A
Step-by-step explanation:
|-12| = 12
distance from 0 to -12 is 12
and 12 = 12
PLEASE HURRY!!!!! Which statement describes the situation shown in the graph?
Answer:
Sales increase with a decrease in the price.
Step-by-step explanation:
PLEASE PLEASE PLEASE HELP ME ASAP!!!
The table completing the proof is:
Statements Reasons
Draw segments UT Construction.
[tex]\overline {UT}[/tex] ≅ [tex]\overline {UT}[/tex] This is reflexive property.
[tex]\overline{BT}[/tex] ≅ [tex]\overline {EU}[/tex] Given
[tex]\overline {BU}[/tex] ≅ [tex]\overline {ET}[/tex] Given
ΔUBT ≅ ΔUET SAS congruency
∠B ≅ ∠E Proof
We have,
From the figure,
Step 1:
Draw segments UT.
Construction.
Step 2:
UT ≅ UT
This is reflexive property.
Step 3:
BT ≅ EU
Given
Step 4:
BU ≅ ET
Given
Step 5:
ΔUBT ≅ ΔUET
This is due to SAS.
Side-Angle-Side (SAS) Congruence.
The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
Step 6:
∠B ≅ ∠E
Thus,
Statements Reasons
Draw segments UT Construction.
[tex]\overline {UT}[/tex] ≅ [tex]\overline {UT}[/tex] This is reflexive property.
[tex]\overline{BT}[/tex] ≅ [tex]\overline {EU}[/tex] Given
[tex]\overline {BU}[/tex] ≅ [tex]\overline {ET}[/tex] Given
ΔUBT ≅ ΔUET SAS congruency
∠B ≅ ∠E Proof
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PLS HELP BEST OF YOUR ABILITY
Figure B is a scaled copy of Figure A.
What is the scale factor from Figure A to Figure B?
Answer: x = 60°
Step-by-step explanation:
We know a circle is equal to 360°, so we can subtract from 360° to find x using vertical angles and other given details.
Vertical (opposite) angles are equal to each other. This is why, for example, we know AGE and FGC are both 30°.
See attached for a breakdown of the angles.
360° - 30° - 30° - 90° - 90° = 2x
120° = 2x
60° = x
Answer:
x = 60°
Step-by-step explanation:
Hello!
The sum of angles on a line is 180°.
Given that Angle G is 90°, the other measure on Line DB would also be 90°. The missing angle next to x can be called y.
x° + y° = 90°Angle YThe Angle y can be calculated by using the Vertical Angles Theorem. The theorem states that if two non-adjacent angles are formed by the intersection of two lines, the measures of the angles are congruent.
This means that the measure of Angle y is 30°, as the 30° angle and y are non-adjacent and are formed by the intersection of lines AC and EF.
Angle XWe can now solve for x by plugging in 30° for y in the equation.
x° + y° = 90°x° + 30° = 90°x° = 60°The value of x is 60°.
HEEEELLLLLLLPPPPPPPP
The hexagon PQRSTU is plotted on a coordinate plane with vertices P(–1, 0), Q(–1, 3), R(1, 4), S(2, 5), T(4, 4), and U(4, 0). What is the hexagon's perimeter?
15.8 units
14.4 units
17.8 units
12.0 units
PLEASE HELP ME ASAP!!!! PLEASE!!!
1) [tex]\overline{UT}[/tex]
2) [tex]\overline{UT} \cong \overline{UT}[/tex]
3) [tex]\overline{BT} \cong \overline{EU}[/tex]
4) [tex]\overline{BU} \cong \overline{ET}[/tex]
5) [tex]\triangle UBT \cong \triangle TEU[/tex] by SSS
6) CPCTC
HELP PLS
Figure AAA is a scale image of figure BBB.
Figure AAA maps to figure BBB with a scale factor of \dfrac{2}{3}
3
2
start fraction, 2, divided by, 3, end fraction.
What is the value of xxx?
20 POINTS+BRAINLIEST: 8TH GRADE MATH PART 3: Word problem with fractions - please list out the steps and explain how you came to the answer
Answer: H. 12
Step-by-step explanation:
Add all cost of each price of the each fabric once to get $925 (150+275+500). Then, divide 5,550/925 to get 6. Then multiply 1/3 by 6 to get 2. Then multiply 2/3 by 6 to get 4. Then add 2+4+6 to get 12.
Michael is baking cookies. His cookie recipe calls for 3/4 cups sugar and makes 24 cookies. If he wants to scale the recipe to make exactly 18 cookies, how many cups of sugar will he need? Express your answer as a mixed number.
[tex]\begin{array}{ccll} \stackrel{cups}{sugar}&cookies\\ \cline{1-2} \frac{3}{4}&24\\[1em] x&18 \end{array}\implies \cfrac{ ~~ \frac{3}{4} ~~ }{x}~~ = ~~\cfrac{24}{18}\implies \cfrac{ ~~ \frac{3}{4} ~~ }{\frac{x}{1}}~~ = ~~\cfrac{4}{3}\implies \cfrac{3}{4}\cdot \cfrac{1}{x}=\cfrac{4}{3} \\\\\\ \cfrac{3}{4x}=\cfrac{4}{3}\implies 9=16x\implies \cfrac{9}{16}=x[/tex]
now, the fraction is not an improper one, thus we can't quite put it in a mixed format, unless you count 0 as its whole, then I guess we can say is [tex]0\frac{9}{16}=x[/tex]
Answer:
9/16
Step-by-step explanation:
24/6=4
18/6=3
(3/4)x(3/4)=9/16
Please Help!
Below are the data collected from two random samples of 500 American adults on the number of hours they work per day (rounded to the nearest hour):
Number of hours of work per day 6 7 8 9 10
Sample A: Number of adults 60 90 145 150 55
Sample B: Number of adults 70 80 140 145 65
Ryan concludes that adults spend a mean of 8 hours working each day. Malia thinks the mean is 9 hours. Who is correct—Ryan or Malia?
Make Sure You Do Tis Because I Will Report You If You Don't
Explain your answer in two or three sentences. Make sure to use facts to support your answer.
Answer:
8 or Ryan
Step-by-step explanation:
mean = sum of terms / number of terms so,
6+7+8+9+10/5=8
Please Helpppp!!!!! I Have no clue I forgot how to find the slope.
NEED HELP
rouund each number to the nearest TEN
# 1
82.14
#2
38.5
#3
41.3
Answer:
80, 40, 40
Step-by-step explanation:
The rule is if the number before the tens place is 5 or more round up and if it is 4 or less round down.
I like to look at it without the rule and what makes sense.
82.14: my choices are 80 or 90. What number is 82.14 closer to on the number line? 80.
38.5 The choices are 30 and 40. This number on a number line would be closer to 40
41.3 The choices are 40 and 50. On a number line this number would be closer to 40.
