Degree of polynomials:
[tex]6x^2 = 2\\\\18x^3+5ab-6y = 3\\\\4x^3y +3x^2-xy-4 = 4\\[/tex]
Least to greatest based on degree:
[tex]6x^2[/tex]
[tex]18x^3+5ab-6y[/tex]
[tex]4x^3y +3x^2-xy-4[/tex]
Solution:
The degree of the polynomial is the highest degree of any of the terms
Know that the degree of a constant is zero
Option I
[tex]6x^2[/tex]
Here the highest degree is 2 ( x power 2)
In this case, degree of polynomial is 2
Option II
[tex]18x^3+5ab-6y[/tex]
To find the degree of the polynomial, add up the exponents of each term and select the highest sum.
[tex]Degree\ of\ 18x^3 = 3[/tex]
[tex]Degree\ of\ 5ab = 5a^1b^1 = 1+1 = 2[/tex]
[tex]Degree\ of\ 6y = 6y^1 = 1[/tex]
Thus the highest degree is 3
Option III
[tex]8a^{-5}[/tex]
This is not a polynomial
A polynomial does not contain variables raised to negative
Option IV
[tex]4x^3y +3x^2-xy-4[/tex]
To find the degree of the polynomial, add up the exponents of each term and select the highest sum.
[tex]Degree\ of\ 4x^3y = 4x^3y^1=3+1 = 4\\\\Degree\ of\ 3x^2 = 2\\\\Degree\ of\ xy = x^1y^1 = 1+1 = 2\\\\Degree\ of\ 4 = 0[/tex]
Thus highest degree is 4
Then organize the expressions from least to greatest based on their degree
Least to greatest based on degree:
[tex]6x^2[/tex]
[tex]18x^3+5ab-6y[/tex]
[tex]4x^3y +3x^2-xy-4[/tex]
Which expression is equivalent to (x2 +9x – 1)(-4x + 3)?
-4x3- 33x2+31x – 3
4x3 +39x2-23x + 3
4x3+33x2-31x + 3
-4x3 -39x2+23x – 3
Answer:
- 4x³ - 33x² + 31x - 3------------------------------------------------------------------------------------------
Plot the points (–4, –3), (–3, –5), (0, –4), (0, 3), and (–2, 3) and connect them to form a polygon. What is the length of the vertical side? 2 units 3 units 6 units 7 units
Answer:
7 units
Step-by-step explanation:
I plotted your points to form the polygon in the diagram below.
The vertical side joins the points (0 ,3) and (0, -4).
The vertical distance between them is
3 - (-4) = 3 + 4 = 7
The length of the vertical side is 7 units.
Answer:
7 units
Step-by-step explanation:
I’m a given rectangle the shorter side is 2 units less than the longer side. If we let the longer side be represented as the variable x create an expression that represents the perimeter of the rectangle.
Answer:
4(x-1)units
Step-by-step explanation:
In a given rectangle, the length of the rectangle is the shorter side while its breadth is the longer side.
Since we have 2 lengths and 2 breadths in a rectangle, the perimeter of the rectangle will be 2L+2x where
L is the length(shorter side) and x is the breadth (longer side).
According to the question, the shorter side(L) is 2 units less than the longer side(x). Mathematically,
L = x-2
Substituting L = x-2 into the formula of perimeter of a rectangle we have,
P = 2(x-2) + 2x
P = 2x-4+2x
P = 4x-4
P = 4(x-1)
The perimeter of the rectangle will be 4(x-1)units
Where do you add the parentheses in this equation?
3 + 6 × 5 + 4÷2 - 7
Answer: to get to what answer
Step-by-step explanation:
You open a bank account with $100 and deposit 15 every week. Create an equation to model the total amount of money,y, in dollars, you will need to save after x months. How many weeks will it take to have $250?
Answer:
[tex]Y = 15x+ 100[/tex]
x = 10 months
Step-by-step explanation:
Given:
Initial deposit = $100
Weakly deposit = $15
Solution:
We need to create an equation where total amount is y is equal to initial deposit plus multiplication of weakly deposit and month x, so the equation is written as.
[tex]Y = 15x+ 100[/tex] ---------(1)
Where:
Y = Total amount
x = Number of months.
Second thing we need to find the month for y = $250
Now, we substitute y = 250 in equation 1.
[tex]250 = 15x+ 100[/tex]
[tex]15x=250-100[/tex]
[tex]15x =150[/tex]
[tex]x=\frac{150}{15}[/tex]
x = 10 months
Therefore, we need to required 10 months for $250.
Find the equation of the line.
y=__x+__
PLEASE HELP THIS IS DUE TODAY!! D:
Answer:
aaf ducks chicks h.c Khan ffc blackjack wUtah's hands perches yachts
A website charges $3 for each movie you
download. They also charge a one-time sign-up
fee of $14.99
What is the input variable?
DONE
Answer: A. M, the number of movies.
Step-by-step explanation: I put A, and it was the right answer.
We have an upcoming test on Logorithms and my teacher forgot to go over how to solve logorithms with different bases. How would you solve them? for example,
3log[tex]_{4}[/tex] 2 +log[tex]_{5}[/tex] 512
The value of [tex]3log_{4}(2)+log_{5}(512)[/tex] is about 5.376
Step-by-step explanation:
Let us revise some rules of logarithm
[tex]log(a)^{n}=n.log(a)[/tex] [tex]log_{b}(a)=\frac{log(a)}{log(b)}[/tex]∵ The expression is [tex]3log_{4}(2)+log_{5}(512)[/tex]
- By using the 1st rule in the first term
∵ [tex]3log_{4}(2)=log_{4}(2)^{3}[/tex]
∵ 2³ = 8
∴ [tex]log_{4}(2)^{3}=log_{4}(8)[/tex]
- By using the second rule
∵ [tex]log_{4}(8)=\frac{log(8)}{log(4)}=1.5[/tex]
∵ [tex]log_{5}(512)=\frac{log(512)}{log(5)}=3.876[/tex]
- Add the two answers
∴ [tex]3log_{4}(2)+log_{5}(512)[/tex] = 1.5 + 3.876
∴ [tex]3log_{4}(2)+log_{5}(512)[/tex] = 5.376
The value of [tex]3log_{4}(2)+log_{5}(512)[/tex] is about 5.376
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A metalworker has a metal alloy that is 15% copper and another alloy that is 75% copper. How many kilograms of each alloy should the metalworker combine to create 120 kg of a 51% copper alloy?
48 kilograms of 15 % copper is combined with 72 kilograms of 75 % copper to create 120 kg of a 51% copper alloy
Solution:
Let "x" be the kilograms of 15 % copper
Then, (120 - x) be the kilograms of 75 % copper
Then, according to question,
"x" kilograms of 15 % copper is combined with (120 - x) kilograms of 75 % copper to create 120 kg of a 51% copper alloy
Thus we frame a equation as:
15 % of x + 75 % of (120 - x) = 51 % of 120
Solve the equation for "x"
[tex]15 \% \times x + 75 \% \times (120-x) = 51 \% \times 120\\\\\frac{15}{100} \times x + \frac{75}{100} \times (120-x) = \frac{51}{100} \times 120\\\\0.15x + 0.75(120-x) = 0.51 \times 120\\\\0.15x + 90 - 0.75x = 61.2\\\\0.6x = 90 - 61.2\\\\0.6x = 28.8\\\\Divide\ both\ sides\ by\ 0.6\\\\x = 48[/tex]
Thus 48 kilograms of 15 % copper used
Then, (120 - x) = (120 - 48) = 72
Thus, 72 kilograms of 75 % copper is used
If you invested $500 at 5% simple interest for 2 years, how much interest do you earn? Show work and answer in complete sentences to earn full credit.
If you invest $500 at 3% compounded monthly for 2 years, how much interest you do earn? Show work and answer in complete sentences to earn full credit.
Which would you rather do?
Therefore I earn $50 interest
Therefore I earn $30.88 interest.
I would do the first one.
Step-by-step explanation:
A.
Given , I invested $500 at 5% simple interest for 2 years.
P=$500, r =5% and t = 2 years
[tex]Interest (I) =\frac{P \times r \times t}{100}[/tex]
[tex]=\$\frac{500 \times 5 \times 2}{100}[/tex]
=$50
Therefore I earn $50 interest.
B.
Given , I invested $500 at 3% compounded monthly for 2 years.
P=$500, r =3% = 0.03 and t = 2 years
[tex]Amount (A) =P(1+\frac{r}{n})^{nt}[/tex]
[tex]=\$500(1+\frac{0.03}{12})^{ 2\times 12}[/tex]
=$530.88
Interest = $(530.88-530) = $30.88
I would do the first one.
mass of a spherical grape is 8.4 grams and
The volume of an object is equal to the ratio of its mass to density,
its density is 2 grams per cubic centimeter.
What is the radius of the grape? Round to the nearest tenth of a centimeter.
O 1.0 cm
O 1.5 cm
O 1.9 cm
O 21 cm
The radius of grape is 1 cm
Solution:
Given that,
The volume of an object is equal to the ratio of its mass to density
[tex]Volume = \frac{mass}{density}[/tex]
From given,
Mass = 8.4 grams
Density = 2 grams per cubic centimeter
Substituting in above formula,
[tex]Volume = \frac{8.4}{2} = 4.2\ cm^3[/tex]
Given is a spherical grape
The formula for volume of sphere is given as:
[tex]Volume = \frac{4}{3} \pi r^3[/tex]
Where, "r" is the radius of sphere
[tex]4.2 = \frac{4}{3} \times 3.14 \times r^3\\\\4.2 = 4.187 \times r^3\\\\r^3 = \frac{4.2}{4.187}\\\\r^3 = 1.003\\\\\text{Take cube root on both sides}\\\\r = 1.000999 \approx 1[/tex]
Thus the radius of grape is 1 cm
Answer:
1.0 cm
Step-by-step explanation:
What is the approximate area of a circle with a diameter of 14 inches
Given the system of equations, what is the solution?
3x - 2y + 10 = 0
5y = 4x + 8
{(-34/7, -16/7)}
{(-34/7, 16/7)}
{(34/7, -16/7)}
Answer:
{(-34/7, -16/7)}
Step-by-step explanation:
Rearrange values, multiply to solve for x.
(5) 2y = 3x + 10
(-2) 5y = 4x + 8
Solve for x.
10y = 15x + 50 ↓
-10y = -8x -16
Combine and evaluate.
0 = 7x + 34
Subtract 34 from both sides.
7x = -34
Divide both sides by 7.
x = [tex]\frac{-34}{7}[/tex]
Plugin x value into either equation to solve for y.
2y = (3 × [tex]\frac{-34}{7}[/tex]) + 10
2y = [tex]\frac{-106}{7}[/tex] + 10
2y = [tex]\frac{-32}{7}[/tex]
y = [tex]\frac{-16}{7}[/tex]
Final answer:
By rewriting one equation to isolate y and substituting it into the other, the solution to the system of equations is determined to be {(-34/7, 16/7)}.
Explanation:
The solution to the system of equations provided is found by solving the equations simultaneously. We begin by expressing the second equation in terms of y:
Rewrite the second equation:
5y = 4x + 8
y = (4/5)x + 8/5.
Substitute y in the first equation:
3x - 2((4/5)x + 8/5) + 10 = 0.
Simplify and solve for x:
(3 - 8/5)x + (10 - 16/5) = 0
which gives us-
x = -34/7
Substitute x back into y = (4/5)x + 8/5 to find
y = 16/7
Thus, the solution to the system of equations is {(-34/7, 16/7)}.
hellppp 70 pointsss
what is the equation of the quadratic function shown in the graph ?
f(x)=___ (x + ___) (x-___)
y=a.(X-x1)(X-x2)
x1 and x2 are x-intercepts
x1=-3
x2=1
other points: (-1,8) and (0,5)
y=a.(x+3).(x-1)
a=-2
f(x)= -2.(x+3)(x-1)
The equation is [tex]\[f(x) = -2 \cdot (x + 3)(x - 1)\][/tex]
How to get the equationGiven the quadratic equation in the form \(y =[tex]a \cdot (X - x_1)(X - x_2)\), where \(x_1\) and \(x_2\)[/tex]represent the x-intercepts, and the given x-intercepts are[tex]\(x_1 = -3\) and \(x_2 = 1\).[/tex]
Using the given x-intercepts [tex]\(x_1 = -3\) and \(x_2 = 1\)[/tex], the equation becomes [tex]\(y = a \cdot (x + 3)(x - 1)\).[/tex]
We are also provided with two other points: (-1, 8) and (0, 5).
We can substitute the point (-1, 8) into the equation to solve for \(a\):
[tex]When \(x = -1\) and \(y = 8\):\[8 = a \cdot ((-1) + 3)((-1) - 1)\]\[8 = a \cdot (2)(-2)\]\[8 = -4a\]\[a = -2\][/tex]
Therefore, the value of \(a\) is -2.
Substituting [tex]\(a = -2\) into the equation \(y = a \cdot (x + 3)(x - 1)\), we get:\[y = -2 \cdot (x + 3)(x - 1)\][/tex]
[tex]\[f(x) = -2 \cdot (x + 3)(x - 1)\][/tex]
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Can someone do question 13 please
Answer:
A = 4/7
B = 2/3
C = 2/5
Step-by-step explanation:
It's Easy.
Answer:
A is 4/7
B is 2/3
C is 2/5
Step-by-step explanation:
8r + 12p - 7 - 3p = ?
Answer:
9p+8r-7
Step-by-step explanation:
1) subtract like terms: 12p-3p=9p
2) add unlike terms: 8r+9p -7
The given algebraic expression can be simplified as 8r+9p-7.
The given expression is 8r+12p-7-3p.
To simplify algebraic expression, simplify like terms in it.
In the given expression group the like terms, that is
8r+12p-3p-7
=8r+9p-7
Therefore, the given algebraic expression can be simplified as 8r+9p-7.
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Find the sum of (3x2 + 16x + 9) and (−16x − 12)
Answer:
3
Step-by-step explanation:
(3*2 + 16x +9) + (-16x -12)
6 + 16x + 9 -16x -12
3
Here’s another one I don’t understand, please give me the answer and explain how you got it
Answer:
39 degrees
Step-by-step explanation:
The angle of a straight line is 180 degrees. This is constant and will never change. You will add 57 and 84 to get 141 degrees for <LMP. Take 180-141 to get 39 degrees for <PMN
If RSU~VST, then the triangles are similar by:
show work for brainlist
Step-by-step explanation:
[tex] \because \triangle \: RSU \sim \: \triangle VST \\ \\ \therefore \: \frac{RS}{VS} = \frac{7}{14} = \frac{1}{2} ....(1) \\ \\ \angle RSU \cong \: \angle VST ....(2) \\ (vertically \: opposite \: angles) \\ \\ \frac{US}{TS} = \frac{4}{8} = \frac{1}{2} ....(3) \\ \\ from \: equations \: (1) \: (2) \: and \: (3) \\ it \: is \: clear \: that: \\ \triangle \: RSU \sim \: \triangle VST\\ ..(by \:SAS\:similarity\:postulate) [/tex]
Thus, given triangles are similar by SAS similarity postulate.
When the triangles RSU and VST are said to be similar, it means the corresponding sides and angles are proportional and equal respectively, which is known as the Angle-Angle criterion for similarity.
Explanation:If the triangles RSU and VST are similar (RSU ~ VST), it means the corresponding sides and angles of the two triangles are proportional, and the corresponding angles are equal. This is also known as the Angle-Angle (AA) criterion for similarity. The order of the letters signifies the corresponding parts of the triangles. R corresponds to V, S to S, and U to T. So, the angles R and V are congruent, as are the angles U and T. Because we have two pairs of congruent angles, we can say that the triangles are similar by the AA criterion.
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Given: Angle T S R and Angle Q R S are right angles; Angle T Is-congruent-to Angle Q
Prove: Triangle T S R Is-congruent-to Triangle Q R S
Triangles T S R and Q R S share side S R. Angles T S R and S R Q are right angles. Angles S T R and S Q R are congruent.
Step 1: We know that Angle T S R Is-congruent-to Angle Q R S because all right angles are congruent.
Step 2: We know that Angle T Is-congruent-to Angle Q because it is given.
Step 3: We know that Line segment S R is-congruent-to line segment R S because of the reflexive property.
Step 4: Triangle T S R Is-congruent-to Triangle Q R S because
of the ASA congruence theorem.
of the AAS congruence theorem.
of the third angle theorem.
all right triangles are congruent.
Answer:
B. of the AAS congruence theorem.
Step-by-step explanation:
Triangles TSR and QRS share side SR
SR=RS
Angle TSR and Angle QRS are right angles, so
∠S= ∠R
Angle T Is-congruent-to Angle Q, so
∠T= ∠Q
From these data, we have one congruent side and two congruent angles. The possible congruence theorem that we can apply will be either ASA or AAS. In the ASA theorem, the congruence side must be between the two congruent angles.
The congruence side required for the ASA theorem for this triangle is ST = RQ. It is wrong because the congruent side we have is SR=RS. The correct option is the AAS theorem.
An algebraic equation is an equation that includes:
a no variables
b. only one variable
С.
one or more variables
just numbers
Please select the best answer from the choices provided
Answer:
ç
Step-by-step explanation:
fufujphgfhjunkksbkbbdkdbkdldbdjdbdkdjjdkdmdljdbdivdjbdkd
Explain how you can use a table or graph to find the slope. What does the slope
represent in the problem?
if A's income is 25% less than that of B, then how much percent is B's income more than that of A ?
Answer:
125%
Step-by-step explanation:
this is because the difference is 25% so b is 125% more than a
which function has a simplified base of 4^3√4?
Answer:
The function is [tex]f(x) = 4(\sqrt[3]{16} )^{2x}[/tex].
Step-by-step explanation:
We have to choose from options the exponential function which has a simplified base of 4∛4 i.e. ∛(256).
Now, the exponential function in the option III will be the answer.
The function is [tex]f(x) = 4(\sqrt[3]{16} )^{2x}[/tex].
So, the base is [tex](\sqrt[3]{16} )^{2}[/tex] = [tex]\sqrt[3]{16^{2}} = \sqrt[3]{256} = 4\sqrt[3]{4}[/tex]. (Answer)
The general formula of an exponential function is [tex]f(x) = a(b)^{x}[/tex] , where b is called the base of the function.
The function that has a simplified base of (4∛4) is;
Option C; 4(∛16)^(2x)
From the general formula of an exponential function, we know that;
f(x) = a(b)^(x)
Now, we have;
f(x) = (4∛4)^(x)
Thus, looking at the options, option C is correct because;
In 4(∛16)^(2x), the base is (∛16)² and when we simplify it, we will get 4³(√4) because;
(∛16)² = √(16^(⅔))
>> 256^(⅓)
>> 4∛4
This is the same as our initial value.
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The leas been $31 on a movie ticket for two adults and three children the Smiths Station $26 on a movie ticket for two adults and two children what are the prices for an adult and child movie ticket
Answer:
Adults: $8
Children: $5
Step-by-step explanation:
First Step:
Let's represent The leas by: 2A + 3C = 31
Let's represent The Smiths Station by: 2A+2C=26
Second step:
Solve The leas expression for A → 2A + 3C = 31
[tex]A =\frac{31-3C}{2}[/tex]
Third step:
Replace A on The Smiths Station and solve for C:
2([tex]\frac{31-3c}{2}[/tex]) + 2C = 26
31-3C+2C = 26
31-C=26
31-26 = C
C= 5
Fourth step:
Replace C=5 in expression [tex]A =\frac{31-3C}{2}[/tex]
A = [tex]\frac{31-3*5}{2}[/tex] →→ A=[tex]\frac{31-15}{2}[/tex] →→ A=[tex]\frac{16}{2}[/tex] →→ A= 8
Greatest common factor of 16k - 24
Answer:
8
Step-by-step explanation:
The greatest common factor of 16k - 24 is 8.
Explanation:The first step to find the greatest common factor (GCF) of 16k - 24 is to factor out any common terms. In this case, both 16k and 24 are divisible by 8, so we can factor out an 8: 8(2k - 3). Now, we need to look at the expression inside the parentheses, 2k - 3, and try to factor out any common terms. However, since 2k - 3 does not have any common factors, the GCF of 16k - 24 is simply 8.
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How can you solve the equation 4x= 2X-2 graphically?
Lines a and b are parallel. What is the measure of angle 3 if angle 6 measures 84
Answer:
angle 3 is 84 degree
Step-by-step explanation:
because angle 3 and angle 6 are equal
Which number is greater?
a) 1.204×10^24
b)3.01×10^23
I need the answer ASAP
The answer will be number (a).
Yo sup??
This question can only be solved when the power of 10 in both the numbers is same.
therefore we can express the two numbers as
12.04*10^23 and 3.01*10^23
Clearly we can now say that a>b
Hence a is greater
Hope this helps.
what is the solution to this problem
x+5y=4
3x-7y=-10
To solve the given system of linear equations, we use the elimination method to find the solution, which is (x, y) = (-1, 1).
The student is asking how to find the solution to a system of linear equations:
x + 5y = 4
3x - 7y = -10
To solve this system, one can use the method of elimination.
Multiply the first equation by 3 and the second equation by 1 to align the coefficients of x.
The resulting equations are:
3x + 15y = 12
3x - 7y = -10
Subtract the second equation from the first to eliminate x:
22y = 22
Divide by 22 to find y:
y = 1
Substitute y = 1 into the original first equation:
x + 5(1) = 4
Solve for x:
x = -1
The solution to the system is (x, y) = (-1, 1).