Answer: OPTION C
Step-by-step explanation:
To express a polynomial in Standard form, you need to see the exponent of each term of the polynomial and then order the polynomial from highest exponent to lowest exponent.
Therefore, for the polynomial [tex]5a^2 + 3a^3 + 1[/tex], you get:
[tex]3a^3 +5a^2 +1[/tex]
The highest exponent gives you the degree of the polynomial. In this case, the highest exponent is 3, then it is a polynomial of degree 3 or a cubic polynomial.
When a polynomial has three terms, is called "trinomial". Since this polynomial has three terms, it is a trinomial.
Therefore, the you can classify it as:
Cubic trinomial
Answer:
C
Step-by-step explanation:
Derek's collection: 1950, 1952, 1908, 1902, 1955, 1954, 1901, 1910
Paul's collection: 1929, 1935, 1928, 1930, 1925, 1932, 1933, 1920
Find the indicated measures of center and the measures of variation for each data set. Round your answer to the nearest hundredth, if necessary.
Find the mean, median, range, IQR, MAD for Derek's collection and Paul's collection.
Answer:
Derek:
Mean:1929
Median: 1930
range: 54
IQR: 48
MAD: 23.75
Paul:
Mean: 1929
Median: 1929.5
range: 15
IQR: 6
MAD: 3.5
Step-by-step explanation:
For the Derek's collection:
1. Mean = 1930.375
2. Median = 1930
For the Paul's collection:
1. Mean = 1929.75
2. Median = 1931
For Derek's collection:
Mean:
Add up all the numbers and divide by the total number of numbers:
Mean = (1950 + 1952 + 1908 + 1902 + 1955 + 1954 + 1901 + 1910) / 8
= 1930.375
Median:
The median is the middle value of the set, so we first need to put the numbers in order:
1901, 1902, 1908, 1910, 1950, 1952, 1954, 1955
The median is the average of the middle two numbers, which are 1910 and 1950:
Median = (1910 + 1950) / 2
= 1930
For Paul's collection:
Mean:
Add up all the numbers and divide by the total number of numbers:
Mean = (1929 + 1935 + 1928 + 1930 + 1925 + 1932 + 1933 + 1920) / 8
= 1929.75
Median:
The median is the middle value of the set, so we first need to put the numbers in order:
1920, 1925, 1928, 1929, 1930, 1932, 1933, 1935
The median is the average of the middle two numbers, which are 1930 and 1932:
Median = (1930 + 1932) / 2
= 1931
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A cake is shaped like a cylinder with a diameter of 9 in. The height of the cake is 6 in.
What is the exact volume of the cake?
Enter your answer in the box.
pi in^3
Answer: 121.5 pi in^3 or 381.7 in^3
Step-by-step explanation:
Volume of a cylinder = pi r^2(h)
Radius = 4.5 in, Height = 6 in
pi (4.5)^2(6)
pi(20.25)(6)
121.5 pi in^3 or 381.7 in^3
The exact volume of a cylindrical cake with a diameter of 9 inches and a height of 6 inches is 121.5π cubic inches.
The volume of a cylinder can be found using the formula V = πr^2h, where V stands for volume, r is the radius of the base of the cylinder, and h is the height of the cylinder. Given the diameter of the cake is 9 inches, the radius is half of that, which is 4.5 inches. Therefore, the exact volume of the cake is calculated as follows:
V = π × (4.5 )² ×2 × 6
Which simplifies to:
V = π × 20.25 ×2 × 6
So, the exact volume of the cake is:
V = 121.5π in^3
A gas at 89°C occupies a volume of 0.67 L. At what Celsius temperature will the volume increase to 1.12 L?
Answer:
V1 / T1 = V2 / T2
0.67 / (273 + 89) = 1.12 / (273 + t )
t = 332 °C
Given values:
Volume,
[tex]V_1 = 0.67 \ L[/tex][tex]V_2 = 1.12 \ L[/tex]Temperature,
[tex]T_1 = 89^{\circ} C \ or \ 362 \ K[/tex][tex]T_2 = \ ?[/tex]We know the relation,
→ [tex]\frac{V_1}{T_1} = \frac{V_2}{T_2}[/tex]
By substituting the values, we get
→ [tex]\frac{0.67}{362} = \frac{1.12}{T_2}[/tex]
→ [tex]T_2 = \frac{1.12\times 362}{0.67}[/tex]
[tex]= 332^{\circ} C[/tex]
Thus the answer above is right.
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Whats is the equation of the following line?
D. Y= - 4/3 x Rise over run
The equation of the line is:
C. [tex]y=\dfrac{-3}{4}x[/tex]
Step-by-step explanation:The line passes through the point (0,0) and (4,-3).
By using the two point formula to find the equation of the line.
i.e. any line passing through two points (a,b) and (c,d) is calculated by using the formula:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here (a,b)=(0,0) and (c,d)=(4,-3)
Hence, the equation of line is calculated as follows:
[tex]y-0=\dfrac{-3-0}{4-0}\times (x-0)\\\\i.e.\\\\y=\dfrac{-3}{4}\times x\\\\i.e.\\\\y=\dfrac{-3}{4}x[/tex]
Hence, the correct answer is: Option: C
can anyone help on these two questions show your work and explain please 5. the table below shows the temperature T(m) of a cup of hot chocolate that is allowed to chill over several minutes.) which expression best fit the data for T(m) ) A. 150(0.85)m B. 150(1.15)m C. 150(0.85)m-1 D. 150(1.15)m ) 7. the function f(x)=3x squared +12x+11 can be written as vertex form as what? and what is vertex form?
Answer:
(1), (3)
Step-by-step explanation:
5. If m starts at 1, a geometric series has the form a₁ (r)ᵐ⁻¹.
If m starts at 0, a geometric series has the form a₀ (r)ᵐ.
Here, m starts at 0. The first term, a₀, is 150. The temperature is decreasing, so we're looking for an r < 1. Therefore, the answer must be (1) 150 (0.85)ᵐ.
7. A quadratic written in vertex form is:
y = a(x - h)² + k
We can find the vertex of the parabola using x = -b/(2a).
x = -12 / (2*3)
x = -2
f(-2) = 3(-2)² + 12(-2) + 11
f(-2) = -1
So the vertex (h, k) is at (-2, -1).
Therefore, the answer must be f(x) = 3(x + 2)² - 1
We can also show this by completing the square.
f(x) = 3x² + 12x + 11
f(x) = 3(x² + 4x) + 11
f(x) = 3(x² + 4x + 4) - 3(4) + 11
f(x) = 3(x + 2)² - 1
How is 1.35 x 10 -5 written in standard notation
Hope this helps 1/2x(27)z
Answer:
The correct answer is B. 0.0000135
Step-by-step explanation:
I just did the assignment :D
have a nice day <33
In the diagram, rectangle ABCD is split in half by AC. What is the value of tan x?
A) 3/4
B) 4/5
C) 3/5
D) 5/4
E) 4/3
Random answers will be reported!
Answer:
Then tan(x) = 4/3
Step-by-step explanation:
Given that we have a rectangle ABCD, we can affirm the following:
AD = BC = 4
AB = DC = 3
Now, we now that tan = Opposite Side / Adjacent Side
Then the opposite side to the angle x is AB = 4, and the adjacent side to angle x is DC = 3.
Then tan(x) = Opposite Side / Adjacent Side = 4/3 = 1,3333.
Answer: E
Step-by-step explanation:
PLEASE ANSWERRRRRRR! THANKS!!!!!!!!!!!!!!!!!!!!!!
Solve for x.
57 = 3x + 12
57-12= 3x+12-12
45=3x
Divide by 3
x=15
Check answer
57= 3(15)+12
57=57
Answer is correct.
x= 15
In a bus there is, A pregnant lady 24 years old A security guard 37 years old A random woman 56 years old Driver 68 years old Who is the youngest?
Answer:
The baby
Step-by-step explanation:
If you count the baby inside the pregnant woman, then he is the youngest.
hahha funny the baby of course
You rent a bicycle for $20 plus $2 per hour
Answer:
It all depends on how long you have the bike for if you have it for only 1 hour it will be $22 dollars. If you have it for 2 hours it will be $24 dollars.
-1 3/5 ÷-2/3 as a mixed number
[tex]\text{Hey there!}[/tex]
[tex]-1\frac{3}{5}\div\frac{2}{3}[/tex]
[tex]-1\frac{3}{5}=-\frac{8}{5}[/tex]
[tex]\text{Problem becomes:}-\frac{8}{2}\div\frac{2}{3}[/tex]
[tex]\text{Solve that, and you will get:}\frac{-4}{5}\div{\frac{3}{1}}[/tex]
[tex]-4\times1=-4[/tex]
[tex]5\times3=15[/tex]
[tex]\rightarrow =\frac{-4}{15}[/tex]
[tex]\boxed{\boxed{\boxed{\bf{Answer:\frac{-4}{15}}}}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
I need help to solve this question.
Answer:
B
Step-by-step explanation:
The square of the sum of two consecutive positive even integers is 4048 more than the sum of the squares of these two numbers. Find the two numbers.
Answer:
The numbers are 44 and 46
Step-by-step explanation:
Let
x, x+2 ----> the two consecutive positive even integers
we know that
[tex](x+x+2)^{2} =4,048+x^{2} +(x+2)^{2} \\ \\(2x+2)^{2} =4,048+x^{2} +x^{2}+4x+4\\ \\4x^{2}+8x+4=2x^{2}+4x+4,052\\ \\2x^{2} +4x-4,048=0[/tex]
Solve the quadratic equation using a graphing calculator
The solution is x=44
see the attached figure
[tex]x+2=44+2=46[/tex]
therefore
The numbers are 44 and 46
Use the properties of logarithms to expand log(zy8).
(By 8, they mean the exponent of 8, or the eighth power.)
Each logarithm should involve only one variable and should not have any exponents. Assume that all variables are positive.
Answer:
log (y)+ 8 log (z)
Step-by-step explanation:
use the rules of logarithm
The expanded form of the given function is log (x)+ 8 log (y).
What is a logarithm?When you raise a number with an exponent, there comes a result.
Let's say you get
a^b = c
Then, you can write 'b' in terms of 'a' and 'c' using a logarithm as follows
[tex]b = \log_a(c)[/tex]
'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
Given;
[tex]log(xy^8)[/tex]
use the rules of the logarithm;
log (x)+ 8 log (y)
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$1250 is deposited in an account that pays 6.5% percent annual interest, compounded continuously. What is the balance after 8 years?
Answer:
$1441.90
Step-by-step explanation:
Formula-
A = P (1 + r/n)^(nt)
A= 1250(1 + 8/1)^(1*.065)
Answer:
2102.53
Step-by-step explanation:
1250e (0.065)8
A cube has an edge measuring 7 inches. What is the volume of the cube, in inches³?
Answer:
343 in^3
Step-by-step explanation:
The volume of a cube is found by V = s^3. Here s = 7. So the volume is 7*7*7 = 343 in^3.
Final answer:
The volume of a cube with an edge length of 7 inches is 343 cubic inches.
Explanation:
The volume of a cube is calculated by multiplying the length, width, and height of the cube. Since all sides of a cube are equal, we simply need to cube the length of one side.
In this case, the edge (length, width, and height) of the cube is 7 inches.
The volume of a cube with an edge length of 7 inches can be calculated as follows:
Volume = edge length³Volume = 7³Volume = 7 x 7 x 7 = 343 cubic inchesTherefore, the volume of the cube is 343 cubic inches.
Simplify 2x+x+x+2y x 3y x y
Answer:
3x+6y^3
Step-by-step explanation:
-First you add all the Xs
2x+x+x
-Then you multiply all the Ys
2y * 3y * y
* the Y has a 1 as an exponent by multiplying the Ys the exponents are added making the Y a Y^3
*the numbers are multiplied making it a 6
Together it forms 6y^3
-Ys and Xs cannot be added because they are different values so your answer would be 3x+ 6y^3
The simplification of the given algebraic expression 2x+x+x+(2y × 3y × y) is 4x + 6y³.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The simplification of 2x+x+x+(2y × 3y × y) can be done as,
2x + x + x + (2y × 3y × y)
= 4x + (2y × 3y × y)
= 4x + 6y³
Hence, the simplification of the given algebraic expression 2x+x+x+(2y × 3y × y) is 4x + 6y³.
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Solve for t.
-5 − 2t = 3t
First, we have to isolate the t, or keep it by itself, to solve. To do that, we need to move everything with t in it to on side.
-5 - 2t + 2t = 3t + 2t
The -2t and + 2t cross out, leaving us with t on one side, which is exactly what we want!
-5 = 5t
But t isn't alone yet. We need to get rid of its five. To do that, we need to use the same process: use the opposite symbol. In 5t, 5 is being multiplied by t. To get rid of, we need to divide 5. BUT the mega rule in algebra... what you do to one side you must do to the other, or else the equation would not be true anymore, so...
-5/5 = 5t/5
-1 = t
There's your answer! Hope this helps!
Bert is planning to open a savings account that earns 1.6% simple interest yearly. He wants to earn exactly $192 in interest after 2 years. How much money should be deposit?
Answers:
A: $6,000
B: $600
C: $60
D: $3,072
B is correct. Hope I helped yah.
I need help please.
Answer:
No
Step-by-step explanation:
No it is not the correct answer.
Lorena and Sebastian are both five years old. Every year they each get a cash present from their ncighbor.
Sebastian gets $1.50 for every year in his age, and Lorena gets $20. How old
will they be when Sebastian gets more money than Lorena
14, she will be 14 when she has more
Answer:
sebastian will be 14 when he gets more money than lorena
50 POINTS! HELP! A restaurant manager is planning a new layout for the tables in his store. He will be placing tables of 2, tables of 4, and tables of 6 throughout the dining room. To help him decide how many of each he needs, he decides to keep track of all table requests by customers during a 2-week period. Which measure of central tendency would BEST indicate the typical table size needed?
A) mean
B) median
C) mode
D) range
Answer:
The best possible answer for this would be: D. Mode.
This is because mode measures how many times each number appears.
Answer:
mine said c is the correct answer
Step-by-step explanation:
2y-9x= 14 what’s y??
Answer:
the answer is y= 9/2 x+7
Did you mean the interception or solve for? Anyway I'll do both.
Solve for y:
[tex]
2y-9x=14\Longrightarrow 2y=14+9x \\
2y=14+9x\Longrightarrow y=\frac{14+9x}{2} \\ \boxed{y=7+\frac{9x}{2}, x\in\mathbb{R}}
[/tex]
Intercept: [tex]2y-9x=14\Longrightarrow2y=14\Longrightarrow y=7[/tex]
Question 4
Use the figure below to find the value of x and y
Answer:
[tex]x=4, y=8[/tex]
Step-by-step explanation:
step 1
Find the value of y
we know that
In the right triangle of the figure
[tex]cos(30\°)=\frac{4\sqrt{3}}{y}[/tex]
Remember that
[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]
so
[tex]\frac{\sqrt{3}}{2}=\frac{4\sqrt{3}}{y}[/tex]
Simplify
[tex]y=8\ units[/tex]
step 2
Find the value of x
In the right triangle of the figure
[tex]sin(30\°)=\frac{x}{8}[/tex]
Remember that
[tex]sin(30\°)=\frac{1}{2}[/tex]
so
[tex]\frac{1}{2}=\frac{x}{8}[/tex]
[tex]x=4\ units[/tex]
A rectangular safe can hold 5184 cubic inches. Gold bars that are 3 inches by 6 inches by 2 inches fit to completely fill the safe. What is the maximum number of girl bars that will fit in the safe? 36 288 144 72
Answer:
144 gold bars
Step-by-step explanation:
first you fine the area gold bars take up in cubic inches by multiplying the 3, 2, and 6 to get 36
once you have the space 1 gold bar takes up you divide the total space by that the total space is 5184 so you divide 5184 by 36 to get 144
Answer:
c. 144
Step-by-step explanation:
:)
Graph the line with slope2/3 passing through the point(-2, 1)
Answer:
The graph in the attached figure
Step-by-step explanation:
step 1
Find the equation of the line into point slope form
The equation of the line is equal to
[tex]y-y1=m(x-x1)[/tex]
substitute the given values
[tex]y-1=(2/3)(x+2)[/tex]
step 2
To graph the line find the intercepts
Find the y-intercept
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
[tex]y-1=(2/3)(0+2)[/tex]
[tex]y=(4/3)+1[/tex]
[tex]y=(7/3)[/tex]
The y-intercept is the point (0,7/3)
Find the x-intercept
The x-intercept is the value of x when the value of y is equal to zero
so
For y=0
[tex]0-1=(2/3)(x+2)[/tex]
[tex]-1=(2/3)x+(4/3)[/tex]
[tex](2/3)x=-(4/3)-1[/tex]
[tex](2/3)x=-(7/3)[/tex]
[tex]2x=-7[/tex]
[tex]x=-7/2[/tex]
The x-intercept is the point (-7/2,0)
step 3
Plot the intercepts to graph the line
see the attached figure
4x+24=5x+1 what pus it really need answer
Subtract 4x from both sides
24 = 5x + 1 - 4x
Simplify 5x + 1 - 4x to x + 1
24 = x + 1
Subtract 1 from both sides
24 - 1 = x
Simplify 24 - 1 to 23
23 = x
Switch sides
x = 23
Answer:
Step-by-step explanation:
Subtract 4x from both sides
24 = 5x + 1 - 4x
Simplify 5x + 1 - 4x to x + 1
24 = x + 1
Subtract 1 from both sides
24 - 1 = x
Simplify 24 - 1 to 23
23 = x
Switch sides
x = 23
Solve for n. n + 1 = 4(n – 8) n = 1 n = 8 n = 11 n = 16
Answer:
The correct option is C) n= 11.
Step-by-step explanation:
Consider the provided equation.
[tex]n+1=4(n-8)[/tex]
Open the parentheses and apply the distributive property as shown:
Distributive property [tex]a(b+c)=ab+ac[/tex]
[tex]n+1=4n-32[/tex]
Now, isolate the variables by adding 32 and subtracting n on both the sides.
[tex]n+1-n+32=4n-32-n+32[/tex]
[tex]33=3n[/tex]
Now divide both the sides by 3.
[tex]\frac{33}{3}=\frac{3n}{3}[/tex]
[tex]11=n[/tex]
Hence the value of n is 11
Thus, the correct option is C) n= 11.
Answer: n=11 just took in on Engenuity
Step-by-step explanation:
What is 2% of 50??????
Answer:
1
Step-by-step explanation:
2%= 0.2
0.2*5= 1
When finding Percent of whole multiply.
To figure this out you must do a proportion. Typically you would do [tex]\frac{part}{whole}[/tex]
This means that you would set up your proportions like this:
[tex]\frac{x}{50} =\frac{2}{100}[/tex]
^^^you want to find 2% of 50, so 50 is the "whole" and x (what you are looking for) is the part. The reason there is the 100 is because % are always taken out of 100% , and therefore 100 is the "whole". 2 is on top of 100 because it is a "part" of 100
the next step is cross multiplication so you would get:
100x= (50*2) ---> 100x = 100
^^^you then solve this like a normal algebra equation to get x = 1
Hope this helped! Let me know if there is anything else I can do!
What is the measure of each angel of a rectangle ?
Answer:
All 4 four angles of the rectangle are 90°
Answer:
Opposite sides of a rectangle are the same length (congruent). The angles of a rectangle are all congruent (the same size and measure.) Remember that a 90 degree angle is called a "right angle." So, a rectangle has four right angles.
four- 90 degrees