Like term's coefficient are added in addition of algebraic terms. The simplified form of the given expression is [tex]x^3 + 8x^2 + 13[/tex]
What are like terms?Those terms which have same variables raised with same power.
For example, [tex]5t^3[/tex] and [tex]6t^3[/tex] are like terms since variable is same, and it is raised to same power 3.
For example [tex]x^3[/tex] and [tex]3x^4[/tex] are not like terms as the variables are same but powers aren't same.
What are coefficients?Constants who are in multiplication with variables are called coefficients of those variables.
When can we add or subtract terms of polynomial by their coefficient's addition or subtraction?Suppose we have
[tex]5x^2 + 6y[/tex]
Since those terms are not like terms, their coefficient won't be add and the expression we've got right now, is its simplest form and cannot be reduced more.
If we have, suppose,
[tex]4x + 5x^2 + 2x[/tex]
then we see that [tex]4x[/tex] and [tex]2x[/tex] are like terms, their coefficient can be added and thus, the simplified form would be
[tex](4+2)x + 5x^2 = 6x + 5x^2[/tex]
For the given case, the considered expression is simplified as:
[tex]= > (6x^2 - 3 + 5x^3) - (4x^3 - 2x^2 - 16)\\= 6x^2 - 3 + 5x^3 -4x^3 + 2x^2 + 16\\ = 5x^3 - 4x^3 + 6x^2 + 2x^2 - 3 + 16\\= (5-4)x^3 + (6+2)x^2 + 13\\= 1.x^3 + 8x^2 + 13 \\= x^3 + 8x^2 + 13[/tex]
(variables with 1 as coefficient is not written explicitly as 1 is factor of all measurements).
Sign multiply by
[tex]-ve \times (+ve) = -ve\\(-ve) \times (-ve) = +ve\\(+ve) \times (+ve) = +ve\\(+ve) \times (-ve) = -ve[/tex]
where -ve, +ve are sign of operands and result.
Thus, the simplified form of the given expression is [tex]x^3 + 8x^2 + 13[/tex]
Learn more about simplification of expressions here:
https://brainly.com/question/26437497
what is the area of the triangle
Answer:
16 square units
Step-by-step explanation:
The area of a triangle is given by the formula ...
A = 1/2bh
Here, it is convenient to choose the base as the vertical segment between y=-5 and y=3. Its length is 3 -(-5) = 8 units.
The height of the triangle is the difference in x-coordinates between that segment and the opposite vertex: 6 -2 = 4.
Then the area is ...
A = 1/2(8)(4) = 16 . . . square units
5 ² - 11 × 2
Show all steps! Thanks!
Use the order of operations!
Answer:
Ok
Step-by-step explanation:
Question: 5²-11 x 2
Answer: 5x5 -11 x 2
25-22
3
Hope this helps you
have a great day :)
2+22+22+22+22+22+22+22+22+22+22+22+2
Answer:
246
Step-by-step explanation:
What question makes you do this much but what ever
How many solutions to this
Answer:
one
Step-by-step explanation:
one equation
tanks Please brianlist
Can anyone help me with this problem
8
Find the volume of the prism.
6 m
7 m
8 m
V=
m
Solution:
Given:
L = 7 mB = 8 mH = 6 mVolume of rectangular prism: L x H x B
Use the formula to find the volume.
Finding the volume:
Volume of rectangular prism = L x H x B=> Volume of rectangular prism = 7 x 6 x 8=> Volume of rectangular prism = 336 m³The volume of the rectangular prism is 336 m³.
Answer:
336 meters^3
Step-by-step explanation:
336 meters^3
volume = length x width x height
in this case it would be
6 x 7 x 8 = 336
if there are 1200 tickets sold for a raffle and you bought 300, what is the probability you will not win..
Answer:
fraction form 3/4
decimal form 0.75
percentage form 75%
Step-by-step explanation:
Does anyone know the answer?
Supplementary angles are two angles whose measures add up to 180° . The two angles of a linear pair , like ∠1 and ∠2 in the figure below, are always supplementary. But, two angles need not be adjacent to be supplementary. In the next figure, ∠3 and ∠4 are supplementary, because their measures add to 180° so
angle ∠ABC 90° therefore subtract the 90 to 180 to get the final answer
180-90=90
Final Answer is ∠QRS 90
A pen costs twice as much as a pencil. 7 pens and 12 pencils cost a total of $6.50. What is the price of one pencil?
- Please show your work, I know the answer, but I just don’t know HOW to get the answer.
Answer:
$ 2.167
Step-by-step explanation:Let the cost of a pencil be x and that of a pen be y.
A pen costs twice as much as a pencil.
==> cost of a pen = 2 × cost of a pencil
==> y = 2x
Their total cost is $6.50
==> x + y = $6.50
since y = 2x, substituting y for 2x
==> x + 2x = 6.50
==> 3x = 6.50
dividing both sides by 3
==> x = 2.16
As per our assumption, x is the cost of one pencil.
Therefore, the cost of a pencil is $2.167
Members of a junior high basketball team want to brag about how tall they are. First, they measured each player’s height in inches. Now they have to decide whether the mean or the median is better. Which measure of center should the team use? Basketball team’s height (in inches) 64, 67, 83, 65, 66, 62, 69 The team’s mean height is. The team’s median height is. If the team members wants to brag about how tall they are, they should use their height.
If the team members want to brag about how tall they are, they should use the mean height of approximately 65.14 inches.
The basketball team should use the mean height as the measure of center to brag about how tall they are.
The team’s mean height is calculated by summing up all the heights and dividing by the total number of players. In this case, the sum of the heights is 64 + 67 + 83 + 65 + 66 + 62 + 69 = 456. Dividing 456 by the total number of players (7) gives us a mean height of approximately 65.14 inches.
The team’s median height is the middle value when the heights are arranged in ascending order. In this case, the heights arranged in ascending order are 62, 64, 65, 66, 67, 69, 83. The middle value is 66 inches.
If the team members want to brag about how tall they are, they should use the mean height of approximately 65.14 inches. The mean takes into account all the heights and provides an overall average, whereas the median only represents the middle value and may not accurately reflect the heights of all the players.
For more such answers on median
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Simplify 3 y − 2 y + 3 − y + 5
Answer:
8
Step-by-step explanation:
3y - 2y + 3 - y + 5
y + 3 - y + 5
3 + 5
8
hope this helps :]
Answer:
8
Step-by-step explanation:
3y - 2y + 3 - y + 5
(3y - 2y - y) + (3 + 5)
0 + 8
8
Hope this helps!
please help me with this work
Answer:
about 243.9 cm³35828 4/7 cm² = 3 102/175 m²Step-by-step explanation:
1.The 8-cm diameter sphere has a radius of 4 cm. The volume of it is given by ...
V = 4/3πr³ = 4/3π(4 cm)³ = 256/3π cm³
The 8-cm cube has a volume of ...
V = s³
V = (8 cm)³ = 512 cm³
The volume of the empty space is the difference of these volumes:
space = 512 cm³ -256/3π cm³ = 256(6 -π)/3 cm³
space ≈ 243.9 cm³
__
2.The area of a hemisphere is twice the area of a circle with the same radius. Then the area of the top and bottom of the birdbath will be 2+1 = 3 times the area of a circle with radius 30 cm.
top+bottom area = 3 × πr² = 3 × 22/7(30 cm)² = 8485 5/7 cm²
The lateral area of the cylinder is ...
LA = 2πrh
= 2(22/7)(30 cm)(145 cm) = 27342 6/7 cm²
Then the total surface area of the birdbath is ...
total area = top+bottom area + lateral area
total area = 8485 5/7 cm² +27342 6/7 cm² = 35828 4/7 cm²
= 3 102/175 m²
Help with this question.
What is cos 45*?
Answer:
0.7071.Step-by-step explanation:
Now, this can be tricky.
But, we can use a calculator.
cos 45*= 0.7071.According to the calculator, the answer was 0.7071.
That means 0.7071 is the answer.
This image is optional. Use it for hints.
a farm loan officer has a four-drawer cabinet. one drawer is 3/5 full, one drawer is 1/2 full, one drawer is 2/3 full, and one drawer is 3/4 full. can the contents be combined into three drawers? explain.
Answer:
Yes
Step-by-step explanation:
3/5, 1/2, 2/3, and 3/4 must be 3 or lower if added together.
We need to find the LCM of the denominators. The LCM, or lowest common multiple, of the denominators is 60. So we have to multiply the fractions by the LCM and add them up.
36 + 30 + 40 + 45 = 151.
60 x 3 = 180.
151 isn't up to 180, so yes. And also, if you divide 151 by 60, you would get 2.52 approximately.
Lisa charges $28 for 2 hours of swimming lessons, Tara charges $75 for 5 hours of swimming lessons. Who offers a better deal?
Answer:
Lisa
Step-by-step explanation:
Find the amount of money Lisa and Tara charge every hour.
Lisa's ratio is 28 : 2 hours
Divide both sides of the ratio by 2
Lisa charges 14 dollars per hour
Tara's ratio is 75:5 hours
Divide both sides of the ratio by 5
Tara charges 15 dollars per hour
Lisa charges 1 dollar less each hour, so Lisa offers a better deal.
Hope this helps :)
Have an awesome day!
Please help me with number 1 and 3!!!?!???? Pleaseee
PLEASE HELP!! I am so confused
Answer: 1.5 ft
Step-by-step explanation:
You can set up a proportion since the triangle are similar:
3 / 12 = x / 6
meaning x=1.5 ft
I need help please! I've been stuck on this for a week and its really stressful lol
Answer:
[tex]y=0.2*4^{x}[/tex]
Step-by-step explanation:
Notice when x increases 1, y is 4 times the previous one, so
the function is like [tex]y=C*4^{x}[/tex]
To determine the constant C, put any pair of (x, y)
Use x = 0, y = 0.2, so
0.2 = [tex]C*4^{0}[/tex] = C * 1 = C
then [tex]y=0.2*4^{x}[/tex]
Answer:
[tex]y=(0.2)4^x[/tex]
Step-by-step explanation:
General form of the exponential function: [tex]y=ab^x[/tex]
Substituting the first point (0, 0.2) into the function:
[tex]\implies 0.2=ab^0[/tex]
As any number to the zero power always gives one, [tex]b^0=1[/tex]
[tex]\implies0.2=a \times 1[/tex]
[tex]\implies a=0.2[/tex]
Therefore, [tex]y=(0.2)b^x[/tex]
Substituting the second point (1, 1.8) into the function:
[tex]\implies0.8=(0.2)b^1[/tex]
[tex]\implies0.8=(0.2)b[/tex]
[tex]\implies b=\frac{0.8}{0.2}[/tex]
[tex]\implies b=4[/tex]
So the final exponential equation is:
[tex]y=(0.2)4^x[/tex]
Checking the equation with the remaining two points:
[tex]x=2 \implies (0.2)4^2=3.2 \ \ \ \checkmark[/tex]
[tex]x=3 \implies (0.2)4^3=12.8 \ \ \ \checkmark[/tex]
if 45% of a number is 54,what is 65% of the number?
Answer:
78
Step-by-step explanation:
Let the number be y
45/100 * y = 54
y = 120
The number is therefore 120
Hence, 65% of 120 is 78
Find the vertex of the quadratic function
f(x) = 2x^2 - 6x + 7
A.) (0, 7)
B.) (1, 2)
C.) (-1.5, 2.5)
D.) (1.5, 2.5)
Answer:
(1.5,2.5)
Step-by-step explanation:
f(x) = 2x^2 - 6x + 7
Take the first derivative and set it equal to 0 (the slope is 0 at the vertex)
f'(x) = 4x -6
0 = 4x - 6
4x = 6
x = 3/2 or 1.5
If x = (3/2), then y = 2(3/2)^2 - 6(3/2) + 7
y = 2(9/4) - 18/2 + 7
y = (9/2) - 2
y = 2.5
See attached graph.
Please find x I really need help.
Answer:
x = 20°
explanation:
Both the pair sides are parallel to each other.The whole sums up to total 360°Steps:
2(7x + x + 20°) = 360°8x + 20° = 180°8x = 160°x = 20°[tex]\qquad\huge\underline{\sf Answer}[/tex]
x = 20 Explanation :- 7x + ( x + 20 ) = 180 8x + 20 = 180now , subtract 20 from both sides which will give you, 160
8x = 180 - 20 8x = 160divide both sides by 8
x = 20Hope it helps ~
You are making 20 fleece jackets for a craft fair. For each jacket, you need 1 7/8 yards of fleece. If fleece costs $9 per yard, how much money will you spend?
Answer:
$7.88
Step-by-step explanation:
Help me with this pleae
Answer:
0
x
Step-by-step explanation:
I need help and i need to solve for x
Please help me with this question
Answer:
76
because if you get 51-31 = 20, 31- 16= 15, 16-6= 10 and 6- 1= 5. they add each number by using a multiplication of 5
Number of 5 digit multiples of 13
What is the measure of XYZ?
x
A. 136
B. 34°
C. 68°
D. 22°
Angles can be measured in degrees and radians
The measure of angle XYZ is 34 degrees
How to determine the measure of XYZFrom the question, the measure of arc XY is 68 degrees
The measure of angle XYZ is then calculated as:
Angle XYZ = 0.5 * Arc XY
This gives
Angle XYZ = 0.5 * 68
Evaluate the product
Angle XYZ = 34
Hence, the measure of angle XYZ is 34 degrees
Read more about angles at:
https://brainly.com/question/14362353
9 + 6 to the 2 pwer - 2 times 8
SOLUTION:
=) 9 + 6² - 2 × 8
=) 9 + 36 - 16
=) 45 - 16
=) 29
The price of a certain item changes over time. The equation y=−3.42x^2+173.64x−983.48 models the total y dollars of profit a company makes in one day on the item the when the price of the item that day is x dollars.
What is the approximate profit the company makes on the item on a day when the item price is $12?
$492.48
$607.72
$1592.68
$2574.68
Answer:$607.72
Step-by-step explanation: it’s a lot simpler than it looks. Since x represents the price of the item, you’ll have to substitute 12 dollars for x.
Making the equation, -3.42(12)^2+173.64(12)-983.48
help i give 5 stars and a crown
Answer:
A. 82°
B. 144°
C. 75°
D. 150°
E. 241°
F. 80°
Step-by-step explanation:
A circle is 360°
A. 360 - 278 = 82 °
B. 360 - (124 + 92) = 144 °
C. 360 - (255 + 30) = 75 °
D. 360 - (118 + 30 +62) = 150 °
E. 360 - (21 +41 + 57) = 241 °
F. 360 - (30 + 60 + 80 + 110) = 80°
Also, the 80° is congruent so it's the same on both sides.