Looking at the series, we have a geometric sequence, where the first term is a1 = 5 and the common ratio is q = -3/5.
(This ratio can be calculated by dividing one term by the term before)
To find the sum of an infinite geometric sequence, we can use the formula below:
[tex]S_{\infty}=\frac{a_1}{1-q}[/tex]Since a1 = 5 and q = -3/5, we have:
[tex]S_{\infty}=\frac{5}{1-(-\frac{3}{5})}=\frac{5}{1+\frac{3}{5}}=\frac{5}{\frac{8}{5}}=5\cdot\frac{5}{8}=\frac{25}{8}[/tex]Therefore the correct option is C.
A contractor bought 8.2 ft2 of sheet metal. He has used 3.7 ft² so far and has $90 worth of sheet metal remaining. The equation 8.2x-3.7x = 90 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
By solving the equation, we get the cost of sheet metal =$20 per sq. feet
What is an equation?
An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. Solving an equation with variables entails finding which variables' values make the equality true. The variables for which the equation must be solved are also known as unknowns, and the values of the unknowns that fulfill the equality are known as equation solutions. Identity equations and conditional equations are the two types of equations.
Given equation 8.2x-3.7x = 90
or, 4.5x = 90
or, x = 90/4.5 = 20
Hence, the cost of sheet metal is $20 per sq. feet
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The ratio of the area between a small square of land and a large squareof land is 3: 7. Given that the total area of the two squares of land is4,000 m2, find the area of each square of land.
Given:
The ratio of the area between a small square of land and a large square
of land is 3: 7.
Total area of the two squares of land (in sq. meter) is 4000.
Required:
The area of each square of land.
Answer:
We have the ratio of the area between a small square of land and a large square of land is 3: 7.
Let
[tex]x^[/tex]be the area of the square of land.
Then their ratio is given by,
[tex]3x^:7x^[/tex]Also given that the total area of the two squares of land (in sq.meter) is
4,000.
The area of
Therefore,
[tex]\begin{gathered} 3x^+7x^=4000 \\ \Rightarrow10x^=4000 \\ \Rightarrow x^=400 \\ \end{gathered}[/tex]Therefore,the area of small square (in sq. meter) is,
[tex]3x=3(400)=1200[/tex]and the area of large square (in sq. meter) is,
[tex]7x=7(400)=2800[/tex]Final Answer:
The area of small and large square respectively (in sq. meter) is,1200 and 2800.
who can solve this equation 4x-6=x+9 ??
Answer:
x = 5
Step-by-step explanation:
Hello!
According to the question, what's the value of 4x-6=x+9
4x-6=x+9
Collect like terms
x - 4x = -6 - 9
-3x = -15
Divide both sides by the coefficient of x which is -3
-3x/-3 = -15/-3
x = 5
When checking
4x-6=x+9
(4)(5)−6 = 5+9
14=14
True
A store sells juice in different sizes. Determine which size is the best buy and the unit price.8 oz $2.4024 oz $6.4864 oz $14.08
To determine which is the best buy, we need to first find the unit price of each
8 oz $2.40
Unit price
$2.40/8 = $0.3
1 oz = $0.3
24 oz $6.48
Unit price
$6.48/24 =$0.27
1 oz = $0.27
64 oz $14.08
Unit price
$14.08/64 =$0.22
From the above the best best buy is the one with the lowest price which is $0.22
The best buy is;
64 oz $14.08
and the unit rate is $0.22 per oz
The lines below are perpendicular. If the slope of the green line is ž, what isthe slope of the red line?maO A A. -O B.O c. - 3O D.1Nim
-3/2 (option A)
Explanation:The line of green and red are perpendicular.
For two lines to be perpendicular, the slope of one line will be the negative reciprocal of the second line.
slope of one line (green) = 2/3
slope of red line = negative reciprocal of green line
slope = 2/3
reciprocal of line = 3/2
negative reciprocal of the line = -3/2
The slope of the red line = -3/2 (option A)
SOmE ONE PLEASE PLEASE I BEG HELP on number 4.
The absolute value function as piecewise function of y = -3(x + 24)/4 and y = 3(x - 38)/4
The absolute value function is commonly understood as a function providing the distance the number is from zero on a number line.
y = 3/4|x-6|-8
y = 3/4(-(x-6))-8
y= 3/4( -x + 6) -8
y = 3(-x + 6 - 32)/4
4y = -3x - 24
y = -3(x + 24)/4
For another function of y
y = 3/4|x-6|-8
y= 3/4( x - 6) -8
y = 3(x - 6 - 32)/4
4y = 3(x - 38)
y = 3(x - 38)/4
The absolute value function as piecewise function of y = -3(x + 24)/4 and y = 3(x - 38)/4
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Given f(x) = 8(12 − x) — 5, what is the value of f(-2)?
Answer:
f(2)=8(12-x)-5
=8(12-2)-5
f(2)=8(10)-5
=75
Can you give me two examples of a absolute value parent function
SOLUTION:
Step 1:
In this question, we are given the following:
Can you give me two examples of an absolute value parent function?
Step 2:
What is the parent function for absolute value?
An absolute value function is a function that contains an algebraic expression within absolute value symbols. Recall that the absolute value of a number is its distance from 0 on the number line.
Examples include:
1. The absolute value parent function, written as: f(x)=| x |, is defined as:f(x)={x if x>00 if x=0−x if x<0.
[tex]f(x)\text{ =}\lvert x\rvert[/tex], is defined as:
[tex]f(x)\text{ =}\lvert x\rvert[/tex][tex]\begin{gathered} f(x)\text{ =}\lvert x\rvert \\ \text{if x > 0, then f(x) = x} \\ \text{if x < 0, then f(x) = x} \end{gathered}[/tex]2. The second example of absolute value function is:
[tex]f(x)\text{ =}\lvert\sin x\rvert[/tex]On a map which is a scale of 1 inch to 12 feet the area of the restaurant is 60 and two squared Han says the actual area of the restaurant is 720 ft.² do you agree or disagree? Explain your reasoning.
Han is therefore mistaken in what he claims. The area is 8640 [tex]feet^{2}[/tex]
What is area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Given Data
Let "x" represent the restaurant's actual space.
You are aware that the map's scale is 1 inch to 12 feet. As a fraction, this is written as follows:
[tex]\frac{1inch}{12feet}[/tex]
Calculate the restaurant's scale drawing area. Such is:
([tex]\frac{1inch}{12feet}[/tex]) ² = [tex]\frac{1inch^{2} }{144feet^{2} } }[/tex]
We can set up this percentage and then solve for "x" to determine the precise location of the restaurant because the restaurant's location is indicated on the map.
Such is:
[tex]\frac{144}{1}[/tex] = [tex]\frac{x}{60}[/tex]
60 (144) = x
x = 8640 [tex]feet^{2}[/tex]
Han is therefore mistaken in what he claims.
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how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?
It should be noted that when the graph of a relationship is a line that passes through the origin, then it is proportional.
How to illustrate the information?A connection is proportional if its graph is a line that goes through the origin. The ratio is not proportionate if it is not a line or ray that doesn't accomplish this. K = y/x is the equation for the proportionality constant. The equation for the slope of a straight line with respect to the origin is the same as this.
A relationship is proportionate if its graph is a line or ray that passes through the origin. It is not proportionate if the line or ray does not go through the origin. Additionally, something is not proportionate if it is not linear.
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List the first 6 common multiples of 8
List the first 6 common multiples of 12
The first six common multiples of 6 and 8 are :
24,48,72, 96, 120 and 144.
The first six common multiples of 12 and 18 are :
24, 36, 72, 108, 144, 216.
In order to resolve this, we shall use the multiples idea.
(A) The two numbers given are 6 and 8.
Six is the first multiple of which there are the following: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, and 144.
multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, and 144.
Therefore, common multiples are: 24, 48, 72, 96, 120 and 144.
(B) The two numbers given are 18 and 12.
The first few multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, and 240.
Similarly, the multiples of 18 are: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, and 270.
Therefore, common multiples are: 24, 36, 72, 108, 144, 216.
Hence we get the required common multiples.
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Find the difference: 11/21 - 3/7
We will operate as follows:
[tex]\frac{11}{21}-\frac{3}{7}=\frac{2}{21}[/tex]Compute P9, 2 please help me solve this
Answer:
72
Step-by-step explanation:
Formula: P (n,r) = n! ÷ (n - r)!
n = Total number of objects in a set
r = The number of items you choose
!/Factorial = Product of all positive numbers less than or equal to the given positive number
9! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9
7! = 1 x 2 x 3 x 4 x 5 x 6 x 7
P (9,2) = 9! ÷ (9-2)!
362,880 ÷ 5,040 = 72
There was a jar of cookies on the table. First Ken came along. He was hungry
because he missed lunch, so he ate half the cookies in the jar. Mary came in the
kitchen next. She didn't have dessert at lunch so she ate one third of the cookies
left in the jar. Karen followed her to the cookie jar and she took three fourths of
the remaining cookies. Susan ran into the kitchen, grabbed one cookie from the
jar and ran out again. That left one cookie in the jar. How many were in the jar to
begin with?
Answer:
There were 24 cookies in the jar at the beginning.
Step-by-step explanation:
There is 1 cookie left add the one susan took that is two. Two is 1/4 of 8. Eight is 2/3 of 12. Twelve is 1/2 of 24. 24 is the answer. You can also check it by going back.
y=x2^+9x+7 in vertex form
Answer: (-9/2,-53/4)
Step-by-step explanation:
Answer:
[tex]y=\left(x+\dfrac{9}{2}\right)^2-\dfrac{53}{4}[/tex]
Step-by-step explanation:
Vertex form of a quadratic equation:
[tex]\boxed{y=a(x-h)^2+k}[/tex]
where:
(h, k) is the vertex.a is the leading coefficient.To find the vertex form of a quadratic equation, complete the square.
Given quadratic equation:
[tex]y=x^2+9x+7[/tex]
Add and subtract the square of half the coefficient of the term in x to the right side of the equation:
[tex]\implies y=x^2+9x+\left(\dfrac{9}{2}\right)^2+7-\left(\dfrac{9}{2}\right)^2[/tex]
[tex]\implies y=x^2+9x+\dfrac{81}{4}+7-\dfrac{81}{4}[/tex]
[tex]\implies y=x^2+9x+\dfrac{81}{4}-\dfrac{53}{4}[/tex]
Factor the perfect square trinomial formed by the first 3 terms:
[tex]\implies y=\left(x+\dfrac{9}{2}\right)^2-\dfrac{53}{4}[/tex]
What are the coordinates of a point 4/5 of the way B to A
A(3,-4)
B(13,11)
[tex]\textit{internal division of a segment using a fraction}\\\\ B(\stackrel{x_1}{13}~,~\stackrel{y_1}{11})\qquad A(\stackrel{x_2}{3}~,~\stackrel{y_2}{-4})~\hspace{8em} \frac{4}{5}\textit{ of the way from B to A} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_2}{3}-\stackrel{x_1}{13}~~,~~ \stackrel{y_2}{-4}-\stackrel{y_1}{11})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment BA}}}{\left( -10 ~~,~~ -15 \right)} \\\\[-0.35em] ~\dotfill\\\\ \left( \stackrel{x_1}{13}~~+~~\frac{4}{5}(-10)~~,~~\stackrel{y_1}{11}~~+~~\frac{4}{5}(-15) \right) \\\\\\ (13~~ - ~~8~~,~~11~~ - ~~12)\implies {\Large \begin{array}{llll} (5~~,~~-1) \end{array}}[/tex]
The water pressure on a submerged object is given by P = 64d, where P is the pressure in pounds per square foot, and d is the depth of the object in feet.
a. solve the formula for d.
b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.
60 and 274.
Step-by-step explanation:
1.25x + 1.49 = 100.
The value of x comes to 78.808 after solving the given expression 1.25x + 1.49 = 100.
What are expressions?Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)A single term or a collection of terms can be used to create an algebraic expression. For instance, 4x and y are the two terms in the expression 4x + y.So, 1.25x + 1.49 = 100:
Now, solve as follows:
1.25x + 1.49 = 1001.25x = 100 - 1.491.25x = 98.51x = 98.51/1.25x = 78.808Therefore, the value of x comes to 78.808 after solving the given expression.
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There are two bags of marbles. The first contains one blue, one yellow and two reds. The seconds contains one red, one blue and two yellows. A random marble from each bag is removed. What is the probability of removing a blue and yellow? Give answer as a fraction.
Answer:
3/16
We assume that the marbles are drawn without replacement.
P(blue and yellow)
= P(b1 and y2) + P(y1 and b2)
= P(b1) P(y2) + P(y1) P(b2)
= (1/4)(1/2) + (1/4)(1/4)
= 1/8 + 1/16 = 2/16 + 1/16 = 3/16
Estimate 5.209 + 2.667 by rounding to the nearest whole number.
Answer:
I'm pretty sure it would be 8 though forgive me if I'm wrong
How many lines of symmetry does the figure at the right have?
Lines of symmetry, a line that divides a figure into two mirror parts, for example:
As we can see, the only line of symmetry that we can draw in our figure is:
Answer: One
Each pair of polygons is similar. Write a similarity statement for the polygons. Then, find the measure of x, the
measures of the indicated sides, and the scale factor.
CB and AB
D
2.4
729
2
610
E
2.6
F
C
3.6
A
72⁰
3x-0.6
2x
61 B
2
| ADEF - AABC;x=15;CB=39; AB=3; 3
2
ADEF-ACBA; x = 3; CB=3; AB=3.9; 3
2
ADEF-ACBA; x = 1; CB = 3.9; AB = 3; 3
3
ADBF - AABC;x=1.5; CB=3; AB=3.9; 2
Scale factor means ratio of the sides of the triangle then the measures of the indicated sides, and the scale factor of CB and AB exists ΔDEF - ΔABC; x = 1.5; CB = 3.9; AB = 3.
What is meant by scale factor?A scale factor is the amount by which an object is multiplied to produce a second object of different size but with the same appearance. The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
Each pair of given polygons are similar.
Similarity statement for the given polygons:
In ΔDEF and ΔABC,
∠D = ∠A (Angle)
∠E = ∠B (Angle)
Therefore, ΔDEF ΔABC (by AA similarity)
If two triangles are similar, then their sides are proportional.
[tex]$\Rightarrow \frac{D F}{A C}=\frac{D E}{A B}$[/tex]
[tex]$\Rightarrow \frac{2.4}{3.6}=\frac{2}{2 x}$[/tex]
By using cross multiplication, we get
⇒ 2.4 × 2x = 2 × 3.6
simplifying the above equation, we get
⇒ 4.8x = 7.2
⇒ x = 1.5
Therefore, the value of x = 1.5.
Substitute x = 1.5 in CB and AB,
CB = 3x – 0.6 = 3(1.5) – 0.6 = 3.9
AB = 2x = 2(1.5) = 3
Scale factor means ratio of the sides of the triangle.
⇒ DF/AC = 2.4/3.6 = 2/3
Therefore, the correct answer is option a) ΔDEF - ΔABC; x = 1.5; CB = 3.9; AB = 3.
The complete question is:
Each pair of polygons is similar. Write a similarity statement for the polygons. Then, find the measure of x, the measures of the indicated sides, and the scale factor.
[tex]$\overline{C B}$[/tex] and [tex]$\overline{A B}$[/tex]
a) ΔDEF - ΔABC; x = 1.5; CB = 3.9; AB = 3;
b) ΔDEF - ΔCBA; x=3 ; C B=3 ; A B=3.9 ; 2/3
c) ΔDEF - ΔCBA; x=1 ; C B=3.9 ; A B=3 ; 2/3
d) ΔDEF - ΔABC; x=1.5 ; C B=3 ; A B=3.9 ; 3/2
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solve for x. 7/13=x/48
Answer:
25.7
Step-by-step explanation:
7/13=x/48. By cross multiplication 13 x=326 = 25.7
Only 1 and 9 please show work THANK YOU
Simplification of the given expression to single complex number are as follow :
1. 3i
2. 4i
3. 24
4. 15
5. 1 + √3 i
6. 2 + [tex]\sqrt{5}i[/tex]
As given,
Simplify the following expression to a single complex number,
1) [tex]\sqrt{-9}[/tex] = [tex]\sqrt{9}\sqrt{-1}[/tex] = 3i
where i is the complex number representing [tex]\sqrt{-1}[/tex]
2) √-16 = 4i
3) √-6 √-24
= √6 ×6 ×4
= 6 ×4
= 24
4) √-3 √-75
=√ 3×75
= √3 × 3 ×25
= 3 ×5
=15
5) [tex]\frac{2 +\sqrt{-12} }{2}[/tex]
= (2 + 2√-3) /2
= 1 + √3 i
6) [tex]\frac{4+\sqrt{-20}}{2}[/tex] = [tex]\frac{4+\sqrt{20}\sqrt{-1}}{2}[/tex] = [tex]\frac{4+(2\sqrt{5}\sqrt{-1})}{2}[/tex] = [tex]\frac{4+(2\sqrt{5}i)}{2}[/tex] = [tex]\frac{2(2+\sqrt{5}i)}{2}[/tex] = 2 + [tex]\sqrt{5}i[/tex]
where i is the complex number representing [tex]\sqrt{-1}[/tex]
Therefore, simplification of the given expression to single complex number are as follow :
1. 3i
2. 4i
3. 24
4. 15
5. 1 + √3 i
6. 2 + [tex]\sqrt{5}i[/tex]
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Consider the expressions (2.4 x 10/8) and (9.2 x 10/6) Find the difference of the expressions.
Find the product of the expressions
The difference of the values is -12.9 while the product of the expression is 45.9
How to solve for the differenceWe have to solve for
2.4 x 10/8
= 2.4 x 1.25
= 3
(9.2 x 10/6)
= 9.2 x 1.667
= 15.3
The difference between the values wpuld be
3 - 15.3
= -12.3
The product of the expressions would be solved by
3 x 15.3
= 45.9
Hence we would say that the difference that is in the values that we have here is -12.9 while the product of these values is given as 45.9
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1. the interest on $2,00 for 2 years is 320 what is the simples interest rate
2. if the interest earned on an account after 2 years is $15, how much would it be after 10 years?
1. The simple interest rate is 80%
2. The interest earned on the account after 10 years is $75
What is simple interest?Simple interest can be defined as a mathematical or arithmetic method of calculating the charge of interest on a given loan.
The formula for simple interest is expressed as;
I = PRT/100
Where;
I is the simple interestP is the principal or initial amountR is the interest rateT is the time taken for the interestFrom the information given, we are to determine the interest rate, R
Substitute the values into the formula, we have;
320 = 200 × R × 2/100
Now, cross multiply, we have;
320(100) = 400R
Find the product of the values
400R = 32000
Divide both sides by the coefficient of the interest rate, we get
R = 32000/400
Find the quotient
R = 80%
If the interest for 2 years is $15
Then in 10 years = $x
cross multiply
x = 150/2
Find the quotient
x = $75
Hence, the rate is 80%
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7. Jill was 80th in a class of 200, whereas Nathan, who is in the same class, has a percentile rank of 80. Which student has the higher standing in the class?
The student that has the higher standing in the class is Jill
How to determine the student that has the higher standing in the class?The given parameters are:
Number of students = 200
Jill's position =80th
Nathan's position = Percentile rank of 80
The above means that
Nathan's position = 80 percentage of the number of students in the class
Substitute the known values in the above equation
So, we have the following equation
Nathan's position = 80 percentage of 200
Rewrite as
Nathan's position = 80 percentage * 200
Express as percentage
Nathan's position = 80% * 200
Express 80% as decimal
Nathan's position = 0.80 * 200
Evaluate the product
Nathan's position = 160
So, we have
Jill's position =80th
Nathan's position = 160th
By comparing the positions, 80th is greater than 160th
Hence, Jill has the higher standing in the class
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Given the function h(x) = x^2 – 7x + 6, determine the average rate of change of the function over the interval 3 < x < 7.hurry please need answer.
Answer:Explanation:
The average rate of change = 3
The average rate of change for a function f(x) is an intervale a < x < b can be calculated using the following equation:
[tex]\frac{f(b)-f(a)_{}}{b-a}[/tex]Therefore, the average rate of change of the function h(x) = x^2 – 7x + 6 in the interval 3 < x < 7 is:
[tex]\frac{h(7)-h(3)}{7-3}[/tex]Where h(7) and h(3) are equal to:
[tex]\begin{gathered} h(7)=7^2-7(7)+6 \\ h(7)=49-49+6 \\ h(7)=6 \\ h(3)=3^2-7(3)+6 \\ h(3)=9-21+6 \\ h(3)=-6 \end{gathered}[/tex]So, the average rate of change is:
[tex]\frac{6-(-6)}{7-3}=\frac{6+6}{4}=\frac{12}{4}=3[/tex]Therefore, the answer is 3.
Help!
A. 5
B. 3
C. 4
D. 16
Answer: the andwer to that is C
Step-by-step explanation:
using the path method for multivariable limits, demonstrate that the limit doesn't exist:
[tex]lim_{(x,y) \to (1,1)} \frac{x y - x - y + 1}{x^2 + y^2 - 2 x - 2 y + 2}[/tex]
Demonstrating that the limit doesn't exist
What is Limits?
The value that a function approaches when the input approaches a certain value is known as a limit. Calculus and mathematical analysis are not possible without limits, which are used to define continuity, derivatives, and integrals.
The limit exists only if the value of the limit along every direction that leads to (1,1) is same.
So by calculating,
lim xy -x-y + 1 / x^2 + y^2 - 2x - 2y + 2
x->1
calculating the limit along the line x = 1
Similarly,
lim xy -x-y + 1 / x^2 + y^2 - 2x - 2y + 2
x->1
calculating the limit along the line y = 1
And the last limit you calculated is along line y=x.
To answer your question, the calculation of the limit along y=1 would not have been necessary. It is sufficient to demonstrate the absence of a limit by giving just two cases in which it appears to vary along several directions.
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