To answer this, we need to see the polynomial. Descending order is in a way that the first term of the polynomial will be three, the second (in descending order, two....and so on).
420t+20t3-210t2
In descending order is:
20t^3 - 210t^2 + 420t
So, the option is number two.
Determine whether each sequence is arithmetic. If so, identify the common difference. -34, -28, -22, -16
Answer:
Question:
Determine whether each sequence is arithmetic. If so, identify the common difference. -34, -28, -22, -16
The numbers are given below as
[tex]-34,-28,-22,-16[/tex]Concept:
Define an arithmetic sequence
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
The general form of an arithmetic sequence is given below as
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ a_1=first\text{ }term \\ n=number\text{ of terms} \\ d=common\text{ difference} \end{gathered}[/tex]To check if they have a common difference, we will use the formulas below
[tex]\begin{gathered} d=a_2-a_1=-28-(-34)=-28+34=6 \\ d=a_3-a_2=-22-(-28)=-22+28=6 \\ d=a_4-a_3=-16-(-22)=-16+22=6 \end{gathered}[/tex]Hence,
Since the sequence has a common difference,
It is therefore an ARITHMETIC SEQUENCE
Their common difference is
[tex]\Rightarrow6[/tex]Um Im in fith grade and i need help with some of my math questions if your able to help me with five or 10 questions that will be great
Solution
For this case we can do the following:
Then the solution would be:
21 6/24 = 21 1/4
For this case we can do the following for 21 1/4
[tex]21\cdot\frac{1}{4}=\frac{21\cdot4+1}{4}=\frac{85}{4}[/tex]For the second part we can do this:
[tex]\frac{1}{3}\cdot5=\frac{5}{3}[/tex]Then the answer is 5/3
please finish this super fastWhat is the median travel time, in minutes? 21 24 29 36
Given:
Required:
We need to find the median.
Explanation:
Recall that the vertical line that split the box in two is the median.
The vertical line that split the box in two is the median at 24 minutes.
The median is 24.
Final answer:
The median is 24.
15. WORK REQUIRED: Given : ZA = 2D and BA – ED. What congruent sides would allow us to use SAS to prove Triangle ABC is congruent to Triangle DEF? (write your answer in this form: WX=YZ with no spaces) NN TA Your answer This is a regulired question
Let's begin by listing out the information given to us:
Both triangles have Line BD equal
[tex]BD=BD[/tex]Line AB equals Line CD
[tex]AB=CD[/tex]Angle A equals Angle C
[tex]m\angle A=m\angle C[/tex]Hence, Triangle ABD is congruent to Triangle CDB
Enter your searchrmFind the compound interest and future value. Do not round intermediate steps. Round your answers to the nearest cent.Principal Rate Compounded Time$895Annually11 years2%The future value is $, and the compound interest is $ХS
Given:
Principal, P = $895
Time, t = 11 years
Rate, r = 2% compounded annually.
Let's find the compound interest and the future value.
To find the future value apply the formula:
[tex]A=P(1+r)^t[/tex]Where:
A is the future amount.
P is the principal = 895
r is the rate = 2% = 0.02
t is the time in years = 11
Hence, we have:
[tex]\begin{gathered} A=895(1+0.02)^{11} \\ \\ A=895(1.02)^{11} \\ \\ A=895(1.2433743) \\ \\ A=1112.82 \end{gathered}[/tex]Therefore, the future value is $1112.82
To find the compound interest, substitute the principlal (P) from the future value (A).
Compound interest = $1112.82 - $895
= $217.82
The compound interest is $217.82
A
The length of a rectangle is 5 times its width if the perimeter is at most 96 cm what is the greatest possible value for the width
The value of the width in the rectangle is 8cm.
How to calculate the width?Based on the information, let the width be represented as w.
Let the width be represented as 5 × w = 5w
Perimeter = 96cm
Perimeter of a rectangle = 2(length + width)
Perimeter = 2(5w + w)
96 = 12w
Divide
w = 96/12
w = 8
The value of the width is 8cm.
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Rational Expression and EquationsClassify each equation as direct inverse or joint variation then state the constant of variation
2. Given:
[tex]y=7z[/tex]To classify the equation as direct, inverse or joint variation then state the constant of variation:
It is of the form,
[tex]y=kz,\text{ whe}re\text{ }k\text{ is the constant}[/tex]If y increases then z increases and if y decreases then z decreases.
Therefore, it is direct variation.
We know that the ratio between two variables in a direct variation is a constant of variation.
Thus, the constant of variation is k = 7.
An empty shipping box weighs 250 grams. The box is then filled with t-shirts. Each tshirts weighs 132.5 grams. The equation W = 250 + 132.5T represents the relationship between the quantities in this solution where W is the weight in grams of the filled box and T the number of shirts in the box. Consider this equation 2900 = 250 + 132.5T. What does the solution to this equation tell us?
Given the next equation
2900 = 250 + 132.5T
its solution is:
2900 - 250 = 132.5T
2650 = 132.5T
2650/132.5 = T
T = 20
Given that W is weigth and T is t-shirts, the solution tell us that a box with 20 t-shirts weights 2900 grams
what is 7^3? Describe the strategy you used and explain why you used that approach
Given expression is
[tex]7^3[/tex]We can expand the given expression as follows.
[tex]7^3=7\times7\times7[/tex]Multiplying 7 and 7, we get
[tex]=49\times7[/tex]Multiplying 49 and 7, we get
[tex]=343[/tex]Hence 7^3 is 343.
We multiply the number twice by itself to find the cube of 7.
This strategy is easy and basic to find the cube of the number.
If ABCD is dilated by a factor of 3, thecoordinate of D' would be:4C3B21-5 -4 -3-2 -1 012345DA-1-2D-3D' = ([?],[ ]
Answer:
(6, -6)
Explanation:
The coordinate of D is the figure = (2, -2)
If ABCD is dilated by a factor of 3, then:
[tex]\begin{gathered} D(2,-2)\to D^{\prime}(2\times3,-2\times3) \\ =(6,-6) \end{gathered}[/tex]The coordinate of D' would be (6, -6).
The length of two sides of a triangle are 5 inches and 8 inches. Which of the following lengths could be the length of the third side of the triangle?
there are 2 possible triangles that can arranged one being the 8 the longest side, and another one being the 5 and 8 the sides of the triangle
use the pythagorean theorem to solve.
for the black triangle.
[tex]\begin{gathered} a^2+b^2=c^2 \\ (8^2+5^2)=c^2 \\ (89)=c^2 \\ \sqrt[]{89}=c \\ c=9.43 \end{gathered}[/tex]for the green triangle.
[tex]\begin{gathered} a^2+b^2=c^2 \\ 5^2+b^2=8^2 \\ b^2=(8^2-5^2) \\ b^2=39 \\ b=\sqrt[]{39} \\ b=6.25 \end{gathered}[/tex]slope = 2/5; y-intercept = -7
We want to find the equation of the line with given slope and y-intercept.
The slope-intercept form of a line is:
[tex]y=mx+b[/tex]Where
m is the slope
b is the y-intercept (y-axis cutting point)
We are given the slope and y-intercept, so we simply substitute it. Steps are shown below:
[tex]\begin{gathered} y=mx+b \\ y=\frac{2}{5}x+(-7) \\ y=\frac{2}{5}x-7 \end{gathered}[/tex]The equation of the line is:
[tex]y=\frac{2}{5}x-7[/tex]Directions: Drag each tile to the correct box.Put the recursive formulas below in order from least to greatest according to the value of their 10th terms.For all of the formulas, let n be equal to the whole numbers greater than or equal to one.
Solving for the 10th term for each of the recursive sequence
First sequence
[tex]\begin{gathered} a_1=32 \\ a_{n+1}=-5+a_n \\ \\ \text{This can be converted to} \\ a_n=a_1+(n-1)(-5) \\ \\ \text{Substitute }n=10 \\ a_{10}=32+(10-1)(-5) \\ a_{10}=32+(9)(-5) \\ a_{10}=32-45 \\ a_{10}=-13 \end{gathered}[/tex]Second sequence
[tex]\begin{gathered} a_1=2048 \\ a_{n+1}=-\frac{1}{2}a_n \\ \\ \text{This can be converted to} \\ a_n=a_1\cdot\Big(-\frac{1}{2}\Big)^{n-1} \\ \\ \text{Substitute }n=10 \\ a_{10}=2048\cdot\Big(-\frac{1}{2}\Big)^{10-1} \\ a_{10}=2048\cdot\Big(-\frac{1}{2}\Big)^9 \\ a_{10}=-4 \end{gathered}[/tex]Third sequence
[tex]\begin{gathered} a_1=0.125 \\ a_{n+1}=2a_n \\ \\ \text{This can be converted to} \\ a_n=a_1\cdot2^{n-1} \\ \\ \text{Substitute }n=10 \\ a_{10}=0.125\cdot2^{10-1} \\ a_{10}=0.125\cdot2^9 \\ a_{10}=64 \end{gathered}[/tex]Fourth sequence
[tex]\begin{gathered} a_1=-7\frac{2}{3} \\ a_{n+1}=a_n+1\frac{2}{3} \\ \\ \text{This can be converted to} \\ a_n=a_1+(n-1)\Big(1\frac{2}{3}\Big) \\ \\ \text{Substitute }n=10 \\ a_{10}=-7\frac{2}{3}+(10-1)\Big(1\frac{2}{3}\Big) \\ a_{10}=\frac{-23}{3}+(9)\Big(\frac{5}{3}\Big) \\ a_{10}=-\frac{23}{3}+\frac{45}{3} \\ a_{10}=\frac{22}{3} \\ a_{10}=7\frac{1}{3} \end{gathered}[/tex]Arranging the formulas from least to greatest according to their 10th terms, we have the following:
First Sequence → Second Sequence → Fourth Sequence → Third Sequence
Area of a cylinder: S = 2лr² + 2лrh; solve for h.
The given equation for the area of a cylinder is:
S = 2πr² + 2лrh
Subtract 2πr² from both sides
S - 2πr² = 2πr² - 2πr² + 2лrh
S - 2πr² = 2лrh
Divide both sides 2лr
[tex]\begin{gathered} \frac{S-2\pi r^2}{2\pi r}=\frac{2\pi rh}{2\pi r} \\ \\ h=\frac{S-2\pi r^{2}}{2\pi r} \end{gathered}[/tex]Please see attached photo for question
For the function g(x), the graph is shown and the domain of that function is set of all integer numbers.
Domain of a function is all possible input values for that function.
Here, the domain of g(x) is set of all integers numbers
The x intercept of g(x)
The x intercept is when the value of y is zero, analysing the graph the x intercept can be interpreted as -5 and 1
The y intercept is when the value of x is zero, analysing the graph the y intercept can be interpreted as 1
From the graph,
g(4) is 1
Therefore, For the function g(x), the graph is shown and the domain of that function is set of all integer numbers.
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1. An input-output table has constant differences. When the input is 3, the output is 10. When the input is 7, the output is 24. a. Find the constant difference. b. Find the output when the input is 0. C. Find the linear function that fits the table.
a)7,17
b)-25
c)
[tex]y=3.5x-25[/tex]Explanation
table
a) differences
10-3=7
24-7=17
Step 1
find the slope
[tex]\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]Let
P1(3,10)
p2(7,24)
replace,
[tex]\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{24-10}{7-3}=\frac{14}{4}=\frac{7}{2} \\ \text{slope}=\frac{7}{2} \end{gathered}[/tex]Step 2
find the equation
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-10=\frac{7}{2}(x-10) \\ y-10=\frac{7}{2}x-\frac{70}{2} \\ y=\frac{7}{2}x-\frac{70}{2}+10 \\ y=3.5x-25 \end{gathered}[/tex]Step 3
when x=0
[tex]\begin{gathered} y=3.5x-25 \\ y=3.5\cdot0-25 \\ y=-25 \end{gathered}[/tex]I hope this helps you
Sailor SheftalSimilar Figures / Proportion (Level 1)Aug 02, 10:17:02 AM?Triangle EFG is similar to triangle HIJ. Find the measure of side HI. Round youranswer to the nearest tenth if necessary.G94425Submit AnswerAnswer:attempt 1 out of 2
If we have two similar triangles, that ratio of the corresponding sides are all the same. This means that:
[tex]\frac{GF}{JI}=\frac{EF}{HI}[/tex]Substituting the lengths, we get:
[tex]\begin{gathered} \frac{44}{9}=\frac{25}{HI} \\ HI=25\cdot\frac{9}{44}=5.1136\ldots\approx5.1 \end{gathered}[/tex]») A box has a length of 6 centimeters, a width of 4 centimeters, and a height of 5 centimeters. Jen filled the bottom layer of the box with 24 cubes. What is the volume of the box? 120 cubic centimeters 24 cubic centimeters 5 cm 4 cm 96 cubic centimeters 6 cm = 1 cubic centimeter 144 cubic centimeters
We can find the volume of the box by multiplying the length, width and heigth.
We can write this as:
[tex]V=l\cdot w\cdot h=(6\operatorname{cm})\cdot(4\operatorname{cm})\cdot(5\operatorname{cm})=(24\operatorname{cm})(5\operatorname{cm})=120\operatorname{cm}^3[/tex]The base layer is 24 cm^3 (24 cubes of 1 cm^3) because its the volume of width 4 cm and length 6 cm, with a height of 1 cm (the height of the cube).
If we multiply the number of cubes, 24 of 1 cm^3, by the real height, that is 5 times 1 cm, we get: 24 cm^3 * 5 = 120 cm^3.
Answer: the box has a volume of 120 cm^3
I’m just starting writing these and I don’t understand it much
In geometry, formal definitions are formed using other defined words or terms. There are, however, three words in geometry that are not formally defined. These words are point, line, and plane, and are referred to as the "three undefined terms of geometry".
a. Defined terms can be combined with each other and with undefined terms to define still more terms. An angle, for example, is a combination of two different rays or line segments that share a single endpoint. Similarly, a triangle is composed of three noncollinear points and the line segments that lie between them.
b. Undefined terms can be combined to define other terms. Noncollinear points, for example, are points that do not lie on the same line. A line segment is the portion of a line that includes two particular points and all points that lie between them, while a ray is the portion of a line that includes a particular point, called the endpoint, and all points extending infinitely to one side of the endpoint.
SIMPLIFIED Uplift Summer Algebra 1 Final Assessment - Copy12 of 2012 of 20 ItemsQuestionColton solves -30=6(x-1) by dividing both sides by 6 first. Kaylee solves the same equation by using the Distributive Property first on the right side of the equation. Who is correct?
The method use by both students are correct. Hence the right answer to the question is OPTION D
John wishes to build a square fence with an area of 121 square yards. What is the perimeter of the fence in yards.
Solution:
Given that John wishes to build a square fence with an area of 121 square yards, as shown below:
The area of a square is expressed as
[tex]\begin{gathered} Area\text{ of square = L}^2 \\ where \\ L\Rightarrow length\text{ of a side of the square} \end{gathered}[/tex]Given that the area of the square fence is 121 square yards, this implies that
[tex]\begin{gathered} 121=L^2 \\ take\text{ the square root of both sides,} \\ \sqrt{121\text{ }}\text{ =}\sqrt{L^2} \\ \sqrt{11\times11}\text{ =}\sqrt{L\times L} \\ \Rightarrow L=11\text{ yards} \end{gathered}[/tex]The perimeter of a square is expressed as
[tex]\begin{gathered} Perimeter\text{ of square = 4}\times L \\ where \\ L\Rightarrow length\text{ of a side of the square} \end{gathered}[/tex]Thus, the perimeter of the fence is evaluated by substituting the value of 11 for L into the perimeter formula.
[tex]\begin{gathered} Perimeter\text{ of fence = 4}\times11 \\ \Rightarrow Perimeter\text{ of fence = 44 yards} \end{gathered}[/tex]Hence, the perimeter of the fence is 44 yards.
Assume that (a,b) is a point on the graph of f. What is the corresponding point on the graph of the following function?f(x-25)What is the point on the graph of f(x-25) that corresponds to the point (a,b) on the graph of f?
Given
There exist a point (a, b) on the original function f(x).
Two points are corresponding if they appear in the same place in two similar situations.
The new function f(x-25) is a function shifted right by 25 units.
Hence, the point on the graph of f(x-25) that corresponds to the point (a, b) on the graph of f is:
[tex](a+25,\text{ b)}[/tex]
A bowl has 4 green marbles 3 red marbles and 2yellow marbles what is the probability that you are going to select a red marble and a yellow marble. You replace the marble before another marble is selected
ANSWER
2/27
EXPLANATION
There are a total of 9 marbles in the bowl. The probability of drawing a red marble is,
[tex]P(red)=\frac{\#red.marbles}{\#total.marbles}=\frac{3}{9}=\frac{1}{3}[/tex]Then you draw another marble, but you put the first back in the bowl, so the total number of marbles is the same. The probability of drawing a yellow marble is,
[tex]P(yellow)=\frac{\#yellow.marbles}{\#total.marbles}=\frac{2}{9}[/tex]The probability of drawing a red marble and a yellow marble is,
[tex]P(red.and.yellow)=P(red)\cdot P(yellow)=\frac{1}{3}\cdot\frac{2}{9}=\frac{2}{27}[/tex]The graph of a function g is shown below.Find g (0) and find one value of x for which g(x) = 4,
From the graph provided,
a) For g(0), on the graph,
[tex]g(0)=-2[/tex]b) One value of x for which g(x) = 4 is given below as,
[tex]\begin{gathered} g(x)=4 \\ x=3\text{ where g(x) = 4} \end{gathered}[/tex]Hence, g(0) = -2 and one of the value of x for which g(x) = 4 is 3
Solve the following problems.a. After 6 points have been added to every score ina sample, the mean is found to be M=70 and thestandard deviation is s= 13. What were the valuesfor the mean and standard deviation for the originalsample?b. After every score in a sample is multiplied by 3, themean is found to be M=48 and the standard devia-tion is s=18. What were the values for the meanand standard deviation for the original sample?
Original mean = 64
standand deviation = 13
Explanations:Let the value of of the originalmean be X. If after 6 points have been added to every score in a sample, the mean is found to be M = 70, then;
X + 6 = 70
Subtract 6 from both sides
X + 6 - 6 = 70 - 6
X = 70 - 6
X = 64
Hence the mean of the original sample will be 64.
The standard deviation of the data will remain unchanged since the distance from the mean will remain the same no matter the change in mean. Therefore the standard deviation of the sample will be 13.
determine the degree of the polynomial -56a^2y^3+23a^2y-29a+17
The degree a polynomial is determine by the highest highest power of variable in the equation.
However, for a multivariable polynomial, the degree is the highest sum of powers of different variables in any of the terms in the expression.
For this polynomial,
[tex]-56a^2y^3+23a^2y\text{ - 29a + 17}[/tex]The degree of polynomial is 5 at the term -56^2y^3 which has 2 and 3 exponent at variable a and y respectively.
Yael used to have a square garage with 222 ft2 of floor space. She recently built an addition to it. The garage is still a square, but now it has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now
• The length of one side of the garage originally is approximately 14.9 ft
,• The length of one side of the garage now is approximately 18.3 ft
Explanation:Old garage = 222 sq. ft
New garage has 50% more floor space.
50% of 222 = 111
Therefore, the new garage is (222 + 111) sq. ft = 333 sq. ft
Since the garage is square,
one side of the old garage is:
[tex]\sqrt[]{222}=14.9\text{ ft}[/tex]One side of the new garage is:
[tex]\sqrt[]{333}=18.3\text{ ft}[/tex]Which of the following expressions is equivalent to the one shown below?71377OA. 791OB. 720O C. 76O D. 75
Given
[tex]\frac{7^{13}}{7^7}[/tex]Find
Equivalent expression
Explanation
Here , we use laws of exponents
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]so ,
[tex]\begin{gathered} =\frac{7^{13}}{7^7} \\ \\ =7^{13-7} \\ \\ =7^6 \end{gathered}[/tex]Final Answer
Therefore , the correct option is C
If.A = (e, x, a, m) and U = {a, b, c, d, e, f, g, h, I, J. K, 1. m. n. o. p. q. r, S, t. u, v. w.x.y.z} find A.
Given that the set A contains the letters e, x, a and m, the complement A' will be the set that does not include these letters, thus, A' can be written as:
[tex]A^{\prime}=\mleft\lbrace b,c,d,f,g,h,i,j,k,l,n,o,p,q,r,s,t,u,v,w,y,z\mright\rbrace[/tex]A parabola has a vertex at (2, -1) and a y- intercept at (0,3). Is this enough information to sketch a graph? Explain your answer. Henny Yoffe . 11:20 AM
It is given that the parabola has the vertex at (2,-1)and y intercept of 3,
Consider the general equation of the parabola with vertex (p,q),
[tex]y=a(x-p)^2+q[/tex]Sbstitute 2 for 'p' and -1 for 'q',
[tex]y=a(x-2)^2-1[/tex]Given that the y-intercept is 3, it means that the curve passess through (0,3),
So it must satisfy the equation,
[tex]3=a(0-2)^2-1\Rightarrow4a=4\Rightarrow a=1[/tex]Substitute the value of 'a', 'p', and 'q' in the standard equation,
[tex]y=1(x-2)^2-1\Rightarrow y=(x-2)^2-1[/tex]Thus, the equation of the parabola can be obtained using the given conditions.