We need to find the multiples of 4 using the next given set:
The multiples of 4 are given by
4*1 =4
4*2 = 8
4*3= 12
4*4=16
4 *5 =20
Then:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20.
x³=yis this a linear or nonlinear equation
ANSWER:
No, it is not a linear equation
Explanation:
Given:
x³=y
Equations are categorized base on the highest exponent of their variables.
An equation with an exponent less rthan equal to 1 is a linear equation, am equation with an exponent of 3 is a cubic equation
This equation x³=y is a non linear equation. It can also be called a cubic equation because x has an exponent of 3.
Also the satndard form of a linear equation is:
y = mx + b
In this case, x³=y is not in that form, so it is not a linear equatio.
y = x³
Michael annual salary is 39,110 and has a budget of 26%of annual salary for housing what is the most that Michael may spend on monthly rent
Since each year has 12 months, divide the annual salary by 12 to find the monthly salary. Then, multiply it by 26/100 to find the amount of money that Michael may spend.
[tex]\frac{39,110}{12}\times\frac{26}{100}=847.38333\ldots[/tex]Therefore, the most that Michael ay spend on monthly rent, is approximately:
[tex]847.38[/tex]Can you help me with #7? X^3-2x^2+3x-6 = 0Please follow prompt b
Given:
The polynomial is given as,
[tex]x^3-2x^2+3x-6=0[/tex]The objective is to factor the polynomial completely.
Explanation:
Consider x = 2 in the given equation.
[tex]\begin{gathered} f(2)=2^3-2(2)^2+3(2)-6 \\ =8-8+6-6 \\ =0 \end{gathered}[/tex]Thus, (x -2) is a factor of the polynomial.
Now, using synthetic division,
Thus, the polynomial equation will be,
[tex]x^2+3=0\text{ . . . . .(1)}[/tex]On factorizing the equation (1),
[tex]\begin{gathered} x^2=-3 \\ x=\pm\sqrt[]{-3} \\ x=\pm i\sqrt[]{3} \\ x=i\sqrt[]{3},-i\sqrt[]{3} \end{gathered}[/tex]Hence, the factors of the polynomial are (x-2), (x+i√3), (x-i√3).
TASK 2: Awards DinnerTran is in charge of the school's Awards Dinner. She set up the multi-purpose room with a stage in front and round tables for parents, students, and family membersto sit around for dinner. Below is the floor plan that she drew for the event.StageCLUE Illuminate EducationIncSign out11US 01:09hp
According to the image each table has an amount of 8 seats, and there are
yki10.87-2110-9--2-6-10Which system of equations is best represented by this graph?А3x – y = 240 +9y = 36B3. - y = 64x + 9y = 42- 3y = -18
System 2x2
Find slopes of k1 and k2
k1 slope = (10--2)/(4-0) = 12/4 = 3
k2 slope= (-9 -9)/ (8-0) = 8/-18 = -4/9
Now find k1, and k2 interceptions with y
k1 , interception= -2
k2 ,interception = 4
Then now, form the 2 equations
y = 3x - 2
and
y = (-4/9)x + 4
Now rewrite equations
3x - y = 2
and
9y + 4x = 36
Then now looking at options ,we find that
ANSWER IS
OPTION A)
3x - y = 2
Describe the situation and why you think analytical or Euclidean geometry is more applicable need helps with this homework question
EXPLANATION
Since the Euclidean Geometry is the Geometry of the Flat Space, we can affirm that it's in two dimensions, where rotation and similarity make sense.
Although it may be expanded to three-dimensional space and beyond, it is still referred to as flat space. The concept is that all dimensions are equal and that they are equal everywhere in space.
The area of a square created on the diagonal of a rectangle, rectangular parallelepiped, or higher dimensional hyperrectangle is equal to the sum of the areas of the squares built on the mutually perpendicular sides of the rectangle, according to the Pythagorean Theorem.
This is known as Euclidean Geometry. Non-Euclidean Geometry, such as spherical, elliptic, hyperbolic, or relativistic geometry, is distinguished by the fact that the same Pythagorean theorem does not apply (though variations do).
So the true dilemma is when to utilize synthetic geometry instead of analytic geometry. Whenever possible, we could say. The challenge with synthetic geometry is that proofs and constructions frequently need some ingenuity on the prover's side.
Find the common difference of the arithmetic sequence 5,14,23
The Solution.
The given sequence is
[tex]5,14,23[/tex]The common difference of the arithmetic sequence is given by the formula below:
[tex]\text{common difference(d)=T}_2-T_1=T_3-T_2[/tex]In this case,
[tex]T_1=5,T_2=14,T_3=23[/tex]Substituting these values in the formula above, we get
[tex]\begin{gathered} \text{common difference = 14-5=23-14}=9 \\ \text{common difference}=9 \end{gathered}[/tex]So,the correct answer is 9.
Find the horizontal and vertical components for a vector round to the nearest tenth
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The horizontal component of a vector having:
[tex]\text{ a magnitude of v and a direction of }\theta\text{ = v cos }\theta[/tex]The vertical component of a vector having:
[tex]a\text{ magnitude of v and direction of }\theta\text{ = v sin}\theta[/tex]
Then, with the information above, the horizontal component of a vector having a magnitude of 15 and a direction of 210 degrees:
[tex]\begin{gathered} \text{Horizontal component = 15 x cos 210}^{\text{ 0}}=\text{ 15 x -0.8860 = -12.99}\approx\text{ -13.0 } \\ \text{Taking the absolute value, we have } \\ \text{Horizontal component = 13.0 units ( to the nearest tenth)} \end{gathered}[/tex]The vertical component of a vector having a magnitude of 15 and a direction of 210 degrees:
[tex]\begin{gathered} vertical\text{ component = 15 x sin 210}^{\text{ 0}}=\text{ 15 x -0.5 = -7.5 } \\ \text{Taking the absolute value, we have } \\ Vertical\text{component = 7.5 units ( to the nearest tenth)} \\ \\ \text{Hence the horizontal and vertical component of the vector =} \\ (\text{ 13. 0 , 7. 5 ) ( to the nearest tenth)} \end{gathered}[/tex]Shopping: Discounts Situation: You want to buy three books that are on sale at 20% off. The original prices of the books are $2.50, $4.95, and $6.00. How much will you save? Calculation With Distribution Calculation Without Distribution (Show all steps.) (Show all steps.) I think it is easier: to distribute. to not distribute. Why I Think it is Easier
Let's begin by listing out the information given to us:
Discount = 20%
Book prices: $2.50, $4.95, and $6.00
Taking discount with distribution, we have:
[tex]\begin{gathered} discount=0.2(2.50+4.95+6.00) \\ discount=0.5+0.99+1.2 \\ discount=\text{\$}2.69 \end{gathered}[/tex]Taking discount without distribution, we have:
[tex]\begin{gathered} \text{Sum of books = 2.50 + 4.95 + 6.00 =13.45} \\ discount=0.2(13.45)=2.69 \\ discount=\text{\$}2.69 \end{gathered}[/tex]I think it is easier to not distribute. This is because it reduces significantly the chances of numerical error in computing
Coach De Leon purchases sports equipment. Basketballs cost $20.00 each and soccer balls cost $18.00 each. He has a budget of $150.00. The graph shown below represents the number of basketballs and soccer balls he can buy given his budget constraint.
Solution:
Cost of a basketball = $20.00
Cost of a soccer ball = $18.00
Budget of Coach De Leon = $150.00
Check the given combinations can be purchased within the budget.
3 soccer balls, basket
how to calculate the amount compounded to 6 years not only one year1) $3000 deposit that earns 6% annual interest compounded quarterly for 6 years
Step 1
State the compound interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where;
[tex]\begin{gathered} A=\text{ amount} \\ P=Prin\text{cipal}=\text{\$3000} \\ r=\text{ rate= }\frac{\text{6}}{100}=0.06 \\ n=\text{ number of periods of compounding= 4} \\ t=\text{ time = 6 years} \end{gathered}[/tex]Step 2
Find the amount as required
[tex]\begin{gathered} A=3000(1+\frac{0.06}{4})^{6\times4} \\ A=3000(1+0.015)^{24} \\ A=3000(1.015)^{24} \\ A=\text{\$}4288.508436 \\ A\approx\text{ \$}4288.51 \end{gathered}[/tex]Hence the amount compounded quarterly for 6 years based on a principal of $3000 and a 6% annual interest rate = $4288.51
Here’s the question. Just let me know when you have the answer. Just apart of a homework practice
By using the given zeros, we will see that the simplest polynomial is:
p(x) = x^3 - 7x - 6
So the correct option is the second one.
How to write the equation for the polynomial?Remember that the first simplest polynomial with the zeros x₁, x₂, x₃, ..., xₙ, is written as:
p(x) = (x - x₁)*(x - x₂)*...*(x - xₙ)
Here we have only 3 zeros, which are -1, -2, and 3, then we can write:
p(x) = (x - (-1))*(x - (-2))*(x - 3) = (x + 1)*(x + 2)*(x - 3)
Expanding the polynomial we get:
p(x) = (x + 1)*(x + 2)*(x - 3)
p(x) = (x^2 + x + 2x + 2)*(x - 3)
p(x) = (x^2 + 3x + 2)*(x - 3)
p(x) = x^3 + 3x^2 + 2x - 3x^2 - 9x - 6
p(x) = x^3 - 7x - 6
Then the correct option is the second one.
Learn more about polynomials.
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two factor of 2=2²two factor of 3=3²
Exponents indicate how many times a number is multiplied by itself
Two factor two= 2*2= 2²=4
Two factor of three is 3*3=3²=9
Determine the shaded area. This figure is not drawn to scale.
To find:
The area of the shaded region.
Solution:
From the figure, it is clear that the length and width of the rectangle inside the circle are 75m and 40m. The diameter of the circle is 85m. The radius of the circle is 85/2m.
The shaded region is equals (area of the circle - area of the rectangle).
So, the area of the shaded region is:
[tex]\begin{gathered} A=\pi r^2-l\times w \\ A=\pi(\frac{85}{2})^2-75\times40 \\ A=\frac{22}{7}\times\frac{7225}{4}-3000 \\ A=\frac{158950}{28}-3000 \\ A=5676.79-3000 \\ A=2676.79m^2 \end{gathered}[/tex]Thus, the area of the shaded region is 2676.79 m^2.
x - 2/5 = 7 what is the value of x?write answer in simplest form.
Explanation:
x - 2/5 = 7
Collect like terms:
[tex]\begin{gathered} x\text{ = 7 + }\frac{2}{5}=\text{ }\frac{7}{1}+\frac{2}{5} \\ \text{LCM = 5} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{35\text{ + 2}}{5}\text{ = }\frac{37}{5} \\ x=\text{ 7}\frac{2}{5} \end{gathered}[/tex]Find the perimeter of with vertices A(1, –3), B(7, –3), and C(1, 5).
This is a triangle with 3 vertices given.
A population of 2000 is decreasing by 4% each year. In how many years the population will be reduced in half?
the initial amount is 2000
the rate of change is 4%
t=time in years
Therefore we have the next exponential decay function
[tex]\begin{gathered} y=2000(1-0.04)^t \\ y=2000(0.96)t \end{gathered}[/tex]Half of the population is y=1000 so we need to find find the value of t
[tex]1000=2000(0.96)^t[/tex]we need to isolate the t
[tex]\frac{1000}{2000}=0.96^t[/tex][tex]\frac{1}{2}=0.96^t[/tex]Using logarithms
[tex]\begin{gathered} \ln (\frac{1}{2})=\ln (0.96^t) \\ \ln (\frac{1}{2})=t\ln (0.96^t) \end{gathered}[/tex][tex]t=\frac{\ln (\frac{1}{2})}{\ln (0.96^{})}=16.98\approx17[/tex]ANSWER
in 17 years the population will be reduced in half
Which of these numbers is irrational?
✍️Record your work/explanation on your document or paper
Which of these numbers is irrational?
✍️Record your work/explanation on your document or paper
\sqrt{5}
5
\frac{3}{5}
5
3
-3.5
3.\overline{5}3.
5
Identify the explicit formula for the sequence given by the following recursive formula: A) f(n) = –2 + 4(n – 1)B) f(n) = –4 + 2(n – 1)C) f(n) = 4 – 2(n – 1)D) f(n) = 2 – 4(n – 1)
Given the recurssive formula;
[tex]f(n)=\begin{cases}f(1)=-2 \\ f(n)=f(n-1)+4\text{ if n>1}\end{cases}[/tex]Let's find the sequence using the recurssive formula, we have;
[tex]\begin{gathered} f(2)=f(2-1)+4 \\ f(2)=f(1)+4 \\ f(2)=-2+4 \\ f(2)=2 \\ f(3)=f(3-1)+4 \\ f(3)=f(2)+4 \\ f(3)=2+4 \\ f(3)=6 \\ f(4)=f(4-1)+4 \\ f(4)=f(3)+4 \\ f(4)=6+4 \\ f(4)=10 \end{gathered}[/tex]Thus, we have the sequence as;
[tex]-2,2,6,10,\ldots[/tex]We observed that the sequence is an arithmetic sequence with a common difference of 4 and first term of -2.
So, the recursive formula is;
[tex]\begin{gathered} f(n)=f(1)+d(n-1)_{} \\ f(n)=-2+4(n-1) \\ f(n)=-2+4n-4_{} \\ f(n)=4n-6 \end{gathered}[/tex]CORRECT OPTION: A
I am trying to create a study guide and I need step by step explanation on this question please
Answer:
[tex]-5a^3[/tex]Explanation:
We are given the expression:
[tex]\begin{gathered} \frac{10a^6}{-2a^3} \\ We\text{ can simplify the expression further to become:} \\ =\frac{10}{-2}\times\frac{a^6}{a^3} \\ =-5\times a^3 \\ =-5a^3 \\ \\ \therefore\frac{10a^6}{-2a^3}\Rightarrow-5a^3 \end{gathered}[/tex]Having simplified the expression, the answer obtained is: -5a^3
Which statements are true about the result of simplifying this polynomial?
To answer the question, we must simplify the following expression:
[tex]t^3(8+9t)-(t^2+4)(t^2-3t)[/tex]We expand the terms in the polynomial using the distributive property for the multiplication:
[tex]8t^3+9t^4-(t^4-3t^3+4t^2-12t)[/tex]Simplifying the last expression we have:
[tex]^{}^{}8t^4+11t^3-4t^2+12t[/tex]We see that the simplified expression:
• is quartic,
,• doesn't have a constant term,
,• has four terms,
,• is a polynomial,
,• it is not a trinomial.
Answer
The correct answers are:
• The simplified expression has four terms.
,• The simplified expression is a polynomial.
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 6 36 1, 5' 25 . Find the 10th term
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary)
1, 6/5, 36/25, Find the 10th term
__________________________________________________________________
1, 6/5, 36/25
(6/5)^(n-1)
n= 1
(6/5)^(1-1) = (6/5)^0 = 1
n= 2
(6/5)^(2-1) = (6/5)^1 = 6/5
n= 3
(6/5)^(3-1) = (6/5)^2 = 36/25
_______________________
n= 10
(6/5)^(10-1) = (6/5)^9 = 5. 1598
_______________________
Answer
Round to the nearest thousandth
The 10th term is 5.160
9=3(x+2) simplified
x=1
Explanation
Step 1
[tex]9=3(x+2)[/tex]apply distributive property
[tex]\begin{gathered} 9=3(x+2) \\ 9=3x+6 \end{gathered}[/tex]Step 2
[tex]\begin{gathered} 9=3x+6 \\ \text{subtract 6 in both sides} \\ 9-6=3x+6-6 \\ 3=3x \end{gathered}[/tex]Step 3
finally, divide both sides by 3
[tex]\begin{gathered} 3=3x \\ \frac{3}{3}=\frac{3x}{3} \\ 1=x \end{gathered}[/tex]so, the answer is x=1
I hope this helps you
need two column proof I'm not understanding how the process with a midpoint and difference with a bisect
we have that
GJ=JL -------> given
so
1) HJ=JK ------> by GL bisects HK
2) m by vertical angles
3) triangle GJH is congruent with triangle LJK ------> by SAS theorem
Xandro's Lighting Company purchased a dozen light bulbs for 900 pesos each. This purchased was subject to a trade discount of 25%. What was the total net price?
Total price of one dozen light bulbs will be equal to
[tex]12\times900=10800[/tex]Total trade discount is equal to (list price x trade discount rate)
[tex]\text{Discount }=10800\times0.25=2700[/tex]So, the net price will be (List price - discount)
[tex]\text{Net price = 10800-2700=}8100[/tex]Therefore, the total net price is 8100 pesos.
1. Mother bought 13.5 kg of sugar and then she repacked the sugar in several bags. If she put 1.5 kg in each bag, how many bags of sugar did she have? only numbers
I need help figuring out which of the following statements is false
EXPLANATION
We can first array the sets in order to match the terms:
X= {15, 22, 33, 44, 89, 165, 1025}
Y= {-5, 15, 33, 88, 99, 150, 160, 1025}
We can see that the common terms are {15,33,1025}, thus the third statement is true.
Now, we can check if the second statement is true or false.
If we put both sets together from smaller to greater and using just one common term, we get the following expression:
X U Y = {-5, 15, 22, 33, 44, 89, 99, 150, 160, 165, 1025}
In conclusion, the second statement is also true.
Find the volume of the cylinder and round to the nearest hundreth. Use 3.14 for pi
Volume of a cylinder: pi * r^2 * h
Where:
pi = 3.14
r= radius = 8km
h= heigth = 7km
Replacing:
V = 3.14 * (8)^2 * 7 = 1,406.72 km3
Plot ( 0 -5/8) on the coordinate axes. Where is it located? State the axis or the quadrant.
We need to plot the coordinate (0, -5/8).
An ordered pair (x, y) represents the location of the point in the coordinate plane. Based on the given, we have x = 0 and y = -5/8. No movement will happen around the x-axis since we have x = 0. Since y is a negative number, we will go down on the y axis from the origin depending on the value of y.
We see that our y value is equal to -5/8. What we can do first is to represent each grid to be equal to 2/8. There are 4 grids that we will encounter before going to -1. At the second grid, the value is (2/8)*2 = 4/8. At the third grid, we have (2/8)*3 = 6/8. The middle term for these two fractions is equal to 5/8, hence, the plot of (0, -5/8) will be around:
Based on the plot above, the coo
Find the volume of the composite figure.First, find the volume of the cylinder.Use 3.14 for it.CylinderVolume = [?] cm9 cm9 cmCube6 cmVolume = [ ]cm4 cmTotal Volume ofComposite Figure = [] cm3=9 cm
Solution
- The question gives us a composite figure made up of a cylinder and a cube.
- We are required to find the volume of the cylinder and the cube and then use the results to find the volume of the composite figure.
- The formulas needed for this calculation are:
[tex]\begin{gathered} Volume\text{ of Cylinder}=\pi\times r^2\times h \\ where, \\ r=radius\text{ of the cylinder} \\ h=height\text{ of the cylinder} \\ \\ Volume\text{ of Cube}=l^3 \\ where, \\ l=dimension\text{ of the cube} \\ \\ Volume\text{ of Composite figure}=Volume\text{ of Cylinder }+Volume\text{ of Cube} \\ \end{gathered}[/tex]- With the information above, we can proceed to solve the question
Volume of the Cylinder:
[tex]\begin{gathered} V=\pi\times r^2\times h \\ r=\frac{6}{2}=3\text{ \lparen Since 6cm is the diameter of the cylinder\rparen} \\ h=4 \\ \\ \therefore V=\pi\times3^2\times4 \\ \\ V=36\pi cm^3 \end{gathered}[/tex]Volume of Cube:
[tex]\begin{gathered} V=l^3 \\ l=9 \\ \therefore V=9^3=729cm^3 \end{gathered}[/tex]Volume of Composite Figure:
[tex]\begin{gathered} V=36\pi+729 \\ use\text{ }\pi=3.14 \\ \\ V=36\left(3.14\right)+729 \\ \\ V=842.04cm^3 \end{gathered}[/tex]Final Answer
The volume of the composite shape is 842.04 cm³