Answer:
The polynomial in standard form is [tex]y = 14 + 6\cdot x - 8\cdot x^{2}+4\cdot x^{3}[/tex].
Step-by-step explanation:
A polynomial in standard fulfills the following condition:
[tex]y = \Sigma_{i=0}^{m}\,c_{i}\cdot x^{i}[/tex], [tex]\forall\,i\in \mathbb{N}[/tex], [tex]0 \leq i \leq m[/tex]
Let be [tex]y = (4\cdot x^{3}-2\cdot x^{2}+9)-(6\cdot x^{2}-6\cdot x + 5)[/tex], which is now handled algebraically:
1) [tex](4\cdot x^{3}-2\cdot x^{2}+9)-(6\cdot x^{2}-6\cdot x + 5)[/tex] Given
2) [tex](4\cdot x^{3}-2\cdot x^{2}+9) +(-1)\cdot (6\cdot x^{2}-6\cdot x + 5)[/tex] [tex](-1)\cdot a = -a[/tex]
3) [tex](4\cdot x^{3}-2\cdot x^{2}+9) +[(-1)\cdot (6\cdot x^{2})+(-6\cdot x)\cdot (-1)+5][/tex] Definition of substraction/Distributive property
4) [tex](4\cdot x^{3}-2\cdot x^{2}+9)+(-6\cdot x^{2}+6\cdot x + 5)[/tex] [tex](-1)\cdot a = -a[/tex]/ [tex](-a)\cdot (-b) = a\cdot b[/tex]
5) [tex]4\cdot x^{3}+ (-2\cdot x^{2}-6\cdot x^{2})+6\cdot x + (9+5)[/tex] Associative and commutative properties
6) [tex]4\cdot x^{3}-8\cdot x^{2}+6\cdot x + 14[/tex] Distributive property/Definition of addition
7) [tex]14 + 6\cdot x -8\cdot x^{2}+4\cdot x^{3}[/tex] Commutative property/Result
The polynomial in standard form is [tex]y = 14 + 6\cdot x - 8\cdot x^{2}+4\cdot x^{3}[/tex].
3^2 • 3^-8 • 3^0
i need help with this asap
Steps to solve:
3^2 • 3^-8 • 3^0
~Apple exponent rule [ a^b * a^c = a^b+c ]
3^2-8+0
~Simplify
3^-6
~Use exponent rule [ a^-b = 1/a^b ]
1/3^6
~Simplify
1/729
Best of Luck!
Answer:
3^-6 which equals 1/3^6
Step-by-step explanation:
all you do is add the exponents.
3^0 is equal to 0 so that one doesn't matter, you just cross it out.
now you're left with 3^2x3^-8
so add 2+(-8) which is -6 so the answer is: 3^-6
since the exponent is negative, you put a 1 above the problem, making it a fraction: 1/3^-6
The balance of your savings account is 208$ more than it was 4 years ago. The current balance is $4709. What was the balance 4 years ago?
Answer:
$4501
Step-by-step explanation:
Since we are already given the amount gained in 4 years, we simply need to subtract the same amount to find the balance 4 years ago.
4709-208=4501
$4501
Which of the diagrams below represents the statement "If it is an triangle,
then it has three vertices”?
A. Figure A
B. Figure B
Answer:
Figure A i don't know
Step-by-step explanation:
Answer:
the answer is A. Figure A
Samantha Ice creamy sold 67 sundaes with nuts and 15 sundaes without nuts what is the ratio of the number of sundaes without nuts to the total number of sundaes
Answer:
its 15 to 82
Step-by-step explanation:
add 67 and 15 to get 77 add 5
Answer:
15:82
Step-by-step explanation:
15:(67+15) [Because ratio of the number of sundaes without nuts to the total number of sundaes]
=>15:82
What is the correct classification for JML?
Answer:
Option (2)
Step-by-step explanation:
From the picture attached,
m∠JKL = m∠JMK + m∠KML
Since, m∠KML + m∠HML = 180° [Linear pair of the angles]
m∠HML = 180° - m∠KML
= 180° - 132°
= 48°
Therefore, m∠JML = 41° + 48°
= 89°
Since measure of angle JML is less than 90°, by definition of an acute angle it will be an acute angle.
Option (2) will be the answer.
Answer:
The answer is acute bru
Step-by-step explanation:
It's a Yes or No question
Answer:
its a yes i think
Step-by-step explanation:
the value is probably
Is 80 a rational number
Answer:
Yes
Step-by-step explanation:
Yes, 80 can be written in the form a / b where a and b are integers. In this case, a = 80 and b = 1. Plus, 80 itself is an integer and all integers are rational numbers.
please help, ASAP!!
Answer:
The answer should be x ≤ 5
STUGO sells hot chocolate and coffee at the high school football games.
At the last game, they had sales of $200. They need to keep track of how
many of each type of drink was sold so that they can make predictions for
future sales. Mrs. Mendoza knows that they used 275 cups that night. If
the hot chocolate sells for 75 cents and coffee sells for 50 cents, how
much of each type of drink were sold?
Answer:
Number of hot chocolate = 250
Number of coffee = 25
Step-by-step explanation:
Given:
Total income = $200 = 20,000 cents
Number of total item sell = 275
Amount of each hot chocolate = 75 cents
Amount of each coffee = 50 cents
Find:
Number of each drink sold
Computation:
Assume
Number of hot chocolate = x
Number of coffee = 275 - x
So,
Total income = [Number of hot chocolate][Amount of each hot chocolate] + [Number of coffee][Amount of each coffee]
20,000 = [x][75] + [275-x][50]
20,000 = 75x + 13,750 - 50x
x = 250
Number of hot chocolate = 250
Number of coffee = 275 - 250
Number of coffee = 25
Answer: 250 Hot chocolates 25 Coffee
Step-by-step explanation:
6). The mean salary of 5 employees is $42100. The median is $40200. The lowest paid
employee's salary is $30000. If the lowest paid employee gets a $4100 raise, then ...
Hint: It will help to write down what salaries you know of the five and think about how you
normally calculate mean and median.
a) What is the new mean?
New Mean = $
b) What is the new median?
New Median = $
Answer,
The answer should be
B
The radius of a circle is 4 inches. What is the circle's area?
p=4 in
Use 3.14 for T.
Answer:
50.27
Step-by-step explanation:
Answer:
50.24
Step-by-step explanation:
[tex]r = 4 \\ \pi = 3.14 \\ area = \pi {r}^{2} [/tex]
Input the values into the equation
[tex]3.14 \times {4}^{2} \\ = 3.14 \times 16 \\ = 50.24[/tex]
what would be an example of a plane
Answer:
A plane extends infinitely in two dimensions. It has no thickness. An example of a plane is a coordinate plane. A plane is named by three points in the plane that are not on the same line.
Step-by-step explanation:
[tex]\bf Step-by-step~explanation:[/tex]
Remember: In math, a plane is a flat, two-dimensional surface that stretches infinitely far in all directions.
An example of a plane would be the photo below.
The purple rectangle is one plane, and the brown one is another one. If there are points there, then they would be on both planes if the points lie exactly on the intersection between the two planes.
We label planes when they have a letter (K, M, etc.), or if there are three non - collinear points on one plane, we take those letters and make them into the plane's name. (ex: Plane AGE, QDE, etc.)
HELP ASAP PLEASE
List the numbers from LEAST to GREATEST
22/25, 8/9, and 0.8888
Answer:
I think its 22/25 , 0.8888, and then 8/9
Step-by-step explanation:
first convert them to decimals
can i get brainliest
what is r to the power of 5 times r to the power of 9
Answer:
r^14
multiply r^5xr^9 by adding the exponents
7 = 3t - 3 - 2+ + 6.
Justification: ? property
Answer:
7 = 3t + 1
t = 6
....................
7 = 3t - 2t + 3
t = 4
What is the slope-intercept form equation of the line that passes through (5.7) and (8, 22)?
A) y=-5x+18
B) y=5x+18
C) y=5x-18
D) y=-5x-18
Answer:
C . y= 5x -18
Step-by-step explanation:
[tex](5,7) = (x_1 ,y_1) \\ (8,22)=(x_2,y_2)[/tex]
Plug in the values into the following equation
[tex] \frac{y - y _1}{x - x_1} = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex] \frac{y - 7}{x - 5} = \frac{22 - 7}{8 - 5} \\ \frac{y - 7}{x - 5} = \frac{15}{3} [/tex]
Cross Multiply
[tex]3(y - 7) = 15(x - 15) \\ 3y - 21 = 15x - 75[/tex]
Collect like terms and simplify
[tex]3y = 15x - 75 + 21 \\ 3y = 15x - 54[/tex]
Divide through by 3
[tex] \frac{3y}{3} = \frac{15x}{ 3 } - \frac{54}{3} \\ y = 5x - 18[/tex]
If f(x)=3x^2+10, what is f(-7)?
Answer:
157
Step-by-step explanation:
Solve for x (5x-17)+(3x-11)=180
Answer:
Step-by-step explanation:
5x - 17 + 3x - 11 = 180
8x - 28 = 180
8x = 208
x = 26
Answer:
The answer would be x=26
Step-by-step explanation:
There is a triangular parking lot at the local mall. The second angle of the triangular parking lot is six more than twice as large as the first angle. The third angle is equal to the sum of the other two angles. What are the measures of the three angles?
Answer:
The measure of the three angles are;
The first angle is 62°
The second angle is 28°
The third angle is 90°
Step-by-step explanation:
The given information are;
The shape of the parking lot = Triangular
Let the angles of the triangle be given as follows
First angle = A
Second angle = B
Third angle = C
The given triangle interior angle dimensions are;
A = 6 + 2× B
C = A + B
However, we have;
A + B + C = 180° (Angle sum property for a triangle)
Therefore;
A + B + C = 180° gives;
C + C = 180° (Transitive property)
2·C = 180°
C = 180°/2 = 90°
C = 90°
However, C = A + B therefore;
90° = A + B and, A = 6 + 2 × B, we get;
A + B = 90° (Symmetric property)
6 + 2× B + B = 90° (Substitution property)
6 + 3·B = 90°
3·B = 90° - 6° = 84°
B = 84°/3 = 28°
B = 28°
From, A = 6 + 2 × B, we have;
A = 6 + 2 × 28° = 62°
A = 62°
First angle = A = 62°
Second angle = B = 28°
Third angle = C = 90°
The measure of the three angles are;
First angle is 62°
Second angle is 28°
Third angle is 90°.
F(x)=(x-2)2
X=8
Need answers ASAP
Answer:
substitute 8 into x =(8-2)2
(6)2=12
Please help me I’ll mark brainliest for whoever answers
Step two is wrong, the answer would have been 9 instead of 8.
Answer:
Step 2 is incorrect
Step-by-step explanation:
8d = 72
Divide each side by 8
8d/8 = 72/8
d = 9
Step 2 is incorrect
Question 3
A sequence of numbers follows the rule: multiply the previous number by-2 and add 3. The fourth term in the sequence is -7.
a. What are the next 3 terms in the sequence? Select Choice
b. What are the 3 terms that came before-7 in the sequence? Select Choice v
Answer:
(a) The next 3 terms in the sequence are 17, -31, and 65
(b) The 3 terms that came before -7 are 2, -1, and 5
Step-by-step explanation:
a. To determine the next 3 terms in the sequence after -7,
From the question, the sequence follows the rule: multiply the previous number by-2 and add 3.
Then, for the next number after -7, we will get
-7 × -2 = 14; 14 + 3 = 17
For the second number after -7, we will get
17 × -2 = -34; -34 + 3 = -31
For the third number after -7, we will get
-31 × -2 = 62; 62 + 3 = 65
Hence, the next 3 terms are 17, -31, and 65
(b) For the 3 terms that came before -7 in the sequence, the rule will be reversed, that is: subtract 3 from the immediate number and divide by -2
Hence, the previous number to -7 (that is, the third term in the sequence)
-7 -3 = -10; -10 ÷ -2 = 5
Then, the second term will be
5 - 3 = 2; 2 ÷ -2 = -1
and the first term will be
-1 -3 = -4; -4 ÷ -2 = 2
Hence, the 3 terms that came before -7 are 2, -1, and 5
Order of operations
(6+5) +9 =
Answer:
(6+5)+9=20
Step-by-step explanation:
Write (-infinity, -3) as an inequality.
X <-3
X > -3
x <_ -3
X >_ -3
Answer:
x < - 3
Step-by-step explanation:
Given the interval (- ∞, - 3 )
The parenthesis on both ends indicates that x cannot equal the end values.
Thus
x < - 3 represents the interval
Find a pattern for each sequence. Use the pattern to show the next two terms.
2, 6, 7, 21, 22, 66, 67, ..., ...
*urgent*
En un colegio hay 627 alumnos y sabemos que hay el doble de chicas que de chicos. De las chicas, a todas menos a 15, les gustan mucho las matemáticas. ¿Cuántas chicas disfrutan con las matemáticas en este colegio?
Answer:
Hay 403 chicas que disfrutan las matemáticas en este colegio.
Step-by-step explanation:
Podemos obtener las siguientes pistas tras una lectura cuidadosa del enunciado:
1) Existen 627 alumnos entre hombres y mujeres en el colegio.
2) La cantidad de chicas es el duplo de la cantidad de chicos.
3) Solo a 15 chicas les disgusta las matemáticas.
Matemáticamente hablando, podemos construir las siguientes tres fórmulas:
[tex]x+y = 627[/tex] (1)
[tex]y = 2\cdot x[/tex] (2)
[tex]m = y - 15[/tex] (3)
Donde:
[tex]x[/tex] - Cantidad de chicos en el colegio, adimensional.
[tex]y[/tex] - Cantidad de chicas en el colegio, adimensional.
[tex]m[/tex] - Cantidad de chicas que disfrutan de las matemáticas en el colegio, adimensional.
Al eliminarse [tex]y[/tex] en (1), se puede hallar la cantidad de chicos en el colegio:
[tex]x + 2\cdot x = 627[/tex]
[tex]3\cdot x = 627[/tex]
[tex]x = 209[/tex]
Hay 209 chicos en el colegio.
Por (2) podemos determinar la cantidad de chicas:
[tex]y = 2\cdot (209)[/tex]
[tex]y = 418[/tex]
Hay 418 chicas en el colegio.
Finalmente, se calcula la cantidad de chicas del colegio que disfrutan las matemáticas por (3):
[tex]m = 418-15[/tex]
[tex]m = 403[/tex]
Hay 403 chicas que disfrutan las matemáticas en este colegio.
Which of these represent a whole number? Select all that apply. (There should only be two answers) A. 4 b. 3.2 C. 4/7 D. 8/4
Answer:
A and D.
Step-by-step explanation:
4 is an integer which is a whole number.
3.2 is a decimal, so it is not a whole number.
4/7 is a fraction that cannot be simplified.
8/4 is a fraction that can be simplified to give 2, a whole number.
How can you find the product of four polynomials
.Answer: When we find the product of any two polynomials, we just multiply each term of the first polynomial by each term of the second polynomial then simplify. When we find the product of two binomials, we can use a technique known as the FOIL method. FOIL is an acronym which stands for First, Outside, Inside and Last.
Step-by-step explanation:
can you simplify a chain of if then statements? if so what do we call it?
A conditional statement (also called an If-Then Statement) is a statement with a hypothesis followed by a conclusion. ... The hypothesis is the first, or “if,” part of a conditional statement. The conclusion is the second, or “then,” part of a conditional statement.
A ball is thrown into the air with a velocity of 34 ft/s. It's height in feet after t seconds is given by y=34t-26(t)^2. Find the avg velocity for the time period beginning when t(0)= 3 seconds and lasting for the given time t= .01 seconds: ???
Answer:
The average velocity of the ball at the given time interval is -122.3 ft/s
Step-by-step explanation:
Given;
velocity of the ball, v = 34 ft/s
height of the ball, y = 34t - 26t²
initial time, t₀ = 3 seconds
final time, t = 3 + 0.01 = 3.01 seconds
At t = 3 s
y(3) = 34(3) - 26(3)² = -132
The average velocity of the ball in ft/s is given as;
[tex]V_{avg} = \frac{y(3.01)-y(3)}{3.01 -3}\\\\V_{avg} = \frac{34(3.01)-26(3.01)^2-y(3)}{3.01 -3}\\\\V_{avg} = \frac{-133.223-y(3)}{0.01}\\\\V_{avg} = \frac{-133.223-(-132)}{0.01}\\\\V_{avg} =\frac{-1.223}{0.01}\\\\V_{avg} = -122.3 \ ft/s[/tex]
Therefore, the average velocity of the ball at the given time interval is -122.3 ft/s