For the given infinite geometric sequence,
(a) the two expressions for r are [tex]r=\frac{6}{m-1}[/tex] and [tex]r= \frac{m+8}{6}[/tex]
(b) The two possible values of m are -8 and 5.
(c) The two possible values of r are [tex]-\frac{2}{3}[/tex] and [tex]\frac{3}{2}[/tex]
What are Geometric Series?
A geometric sequence's finite or infinite terms are added together to form a geometric series. The geometric series that corresponds to the geometric sequence a, [tex]a,ar, ar^{2} ,..., ar^{n-1} ,...[/tex] is [tex]a+ar+ar^{2}+...+ar^{n-1} +...[/tex] Clearly, "series" means "sum." The phrase "geometric series" refers specifically to the total of words with a common ratio between every adjacent pair of them. Finite and infinite geometric series are both possible.What is the Common Ratio of an Infinite Geometric Sequence?
The common ratio (r) of a geometric sequence or series is defined as the ratio between the two consecutive terms of it.The common ratio of an infinite geometric sequence, [tex]a_{0} , a_{1} ,a_{2} ,a_{3} ,...[/tex] is given as [tex]r=\frac{a_{1} }{a_{0} } =\frac{a_{2}}{1}[/tex]In the question, the first three terms of an infinite geometric sequence are given as, m-1, 6, m+8
[tex]\implies a_{0} =m-1, a_{1}=6,[/tex] and [tex]a_{2}=m+8[/tex]
So, the common ratio is calculated as,
[tex]r=\frac{6}{m-1}=\frac{m+8}{6}[/tex]
Here, there are two expressions,
[tex]r=\frac{6}{m-1}[/tex] ------(1), and [tex]r= \frac{m+8}{6}[/tex] ------(2)
Simplifying (1), we get
[tex]r(m-1)=6[/tex] -----(3)
Simplifying (2), we get
[tex]6r=m+8\\\implies r= \frac{m}{6}+\frac{8}{6}[/tex] ------(4)
Now, substituting the values of (4) in (3), we get
[tex](\frac{m}{6}+\frac{8}{6})(m-1)=6\\\implies \frac{m^{2} }{6}-\frac{m}{6} +\frac{2m}{3}-\frac{2}{3} =6\\\implies m^{2}+3m-4=36\\[/tex]
Solving further, we get
[tex]\implies m^{2}+3m-40=0\\\implies m=5, m=-8[/tex]
So, when [tex]m=5, r=\frac{6}{5-1}=\frac{3}{2}[/tex]
Also, when [tex]m=-8, r=\frac{6}{-8-1}=-\frac{2}{3}[/tex]
Therefore, (a) the two expressions for r are [tex]r=\frac{6}{m-1}[/tex] and [tex]r= \frac{m+8}{6}[/tex]
(b) The two possible values of m are -8 and 5.
(c) The two possible values of r are [tex]-\frac{2}{3}[/tex] and [tex]\frac{3}{2}[/tex]
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How to graph p(x)=-3x-1
The graph of the equation p(x) = -3x- 1 has been plotted
The equation is given that
p(x) = -3x - 1
We know the slope intercept form of the line
y = mx + b
Where m is the slope of the line
b is the y intercept
Compare both equation
The slope of the line m = -3
The y intercept b = -1
At x = 1
The value of p(1) = -3(1) -1
= -3 - 1
= -4
At x = 2
The value of P(2) = -3(2) -1
= -6 - 1
= -7
Substitute the value for x and find the value of y.
Draw the graph using the points
Hence, the graph of the equation p(x) = -3x- 1 has been plotted
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PLEASE HELPP!!! MORE POINTS AND BRAINIEST MARK!
Mr. Gonzales would like to create a playground in his
backyard. He has 20 ft of fencing to enclose the play
area. Use this information for Items 10-13. S
10, Write a quadratic function in standard form that
models f(x), the total area of the playground in
square feet in terms of its width x in feet. Then
graph f(x).
11. Write the x- and y-intercepts of f(x) and interpret
them in terms of the problem.
12. Give the reasonable domain and range of f(x) as
inequalities, in interval notation, and in set
notation. Explain how you determined the
reasonable domain and range..
13. What is the maximum area for the playground?
What are the dimensions of the playground with
the maximum area?
Please, I need this tmr!
The quadratic equation is −x²+10x. Domain for the given equation is (0,10) and the Range is (0,25]. The x-intercept is (0,10) and the area is 10.
What is equation?Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.
Here,
quadratic function in standard form that models f(x), the total area of the playground in square feet in terms of its width x in feet,
f(x)=−x²+10x
The graph is given below,
Domain=(0,10)
range=(0,25]
To determine the domain that must exist between them, we used the xx-intercepts. We excluded them from the domain because the area at the x-intercepts is 0.
Since an area must be greater than 0, y>0y>0 follows. Remembering that the vertex of the graph of f(x) has the maximum point of (5,25) the maximum value for y is 25.
−x²+10x is the quadratic equation. The domain and range of the given equation are (0,10) and (0,25), respectively. (0, 10) is the x-intercept, and 10 is the area.
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Solve this equation using the "Distributive Property".
[tex] \sf 3(x - 2) = 21[/tex]
Answer:
x = 9
Step-by-step explanation:
Start by dividing both sides by the singular number, 3. We divide by 3 and not 21 because 21 is the result of the equation, not the coefficient.
[tex]\frac{3\left(x-2\right)}{3}=\frac{21}{3}[/tex]
We got 21 over 3 because you cannot divide 3 times an unknown number subtracted by 2 by 3. This is because we do not know the number. So that's where 21 comes in.
Next, simplify this equation by dividing whole numbers.
[tex]\frac{3}{3} = 1[/tex]
[tex]1\left(x-2\right) = \left(x-2\right)[/tex]
[tex]\frac{21}{3} = 7\\= x-2 = 7[/tex]
Lastly, add 2.
[tex]x - 2 + 2 = 7 + 2\\2 + 2 = 4\\7 + 2 = 9\\= x - 4 = 9\\x = 9[/tex]
Why x - 4 is 0: We assume x is always equal to 1, since 4 does not go into 1, the result would be 0. x - 0 = 0. Therefore, the problem became x = 9.
Hope this helps!
I need to write the second equation, the first is right
Step-by-step explanation:
well that is the really easy one :
the number of produced drills cannot be more than 210 per day.
while the first inequality addressed the work hours, the second simply addresses the number of drills.
therefore,
x + y <= 210
Which of the following graphs are identical?
[tex]y = \sqrt{x} \\ y = \sqrt[3]{x} \\ y = \sqrt{ - x} \\ y = - \sqrt{x} \\ y = \sqrt[3]{x} [/tex]
We can easily see that two similar equation of under cube root of x.
So, the graph of cube root of x is identical.
Explain graph of under root x?
The graph of under root x is positive half of parabola, consist of origin (0, 0). Its symmetric on the positive x-axis.
Explain the graph of under cube of x?The graph of the cube root function f(x) = ∛x.Take the numbers -8, -1, 0, 1, and 8 in the x column calculate the cube root of each of these numbers, and fill them in the column labeled y. Then we have 5. Just plot them and join them by a curve. As this curve is not complete, just extend it on both sides.
According to given data in question:We can easily see that two similar equation of under cube root of x.
So, the graph of cube root of x is identical.
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Answer:
D F on edge
next one is A C D
Step-by-step explanation:
trust
Directions: State all the possible rational zeros for each function.
f(x) = 3x² + 2x - 1
The possible rational zeros are x = -1 and x = 1/3 for the given function f(x) = 3x² + 2x - 1.
What is a quadratic function?The quadratic function is defined as a function containing the highest power of a variable is two.
The function is given in the question as:
f(x) = 3x² + 2x - 1
To determine possible rational zeros for the given function.
f(x) = 3x² + 2x - 1
For finding rational zeros, f(x) = 0
3x² + 2x - 1 = 0
3x² + 3x - x - 1 = 0
3x(x +1) - 1(x +1) = 0
(x +1)(3x - 1) = 0
(x +1) = 0 and (3x - 1) = 0
x = -1 and 3x = 1
x = -1 and x = 1/3
Thus, the possible rational zeros are x = -1 and x = 1/3 for the given function f(x) = 3x² + 2x - 1.
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A jungle has 594 monkeys.
It also has 62 birds.
How many more monkeys than birds are there?
Answer:
532
Step-by-step explanation:
594 [monkeys] - 62 [birds] = 532
Can anyone help me with this problem
the answer would be a= -1
ASAP! exponent rules.
The error occurs in Litas work is in step 3 and step 4.
What is Exponential Function?An exponential function is a mathematical function of the following form:
f ( x ) = aˣ where x is a variable, and a is a constant called the base of the function.
The given expression is
25⁻⁴/(5⁻²)²
The given steps are
Step 1,
25⁻⁴/(5⁻²)²
Step 2,
(5²)⁻⁴/(5⁻²)²
Step 3,
(5²⁻⁴)/(5⁻²⁺²)
The step 3 is wrong because the exponents should be multiplied but not added.
The actual step should be
(5⁻⁸)/(5⁻⁴)
Hence the error occurs in Litas work is in step 3 and step 4.
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Janette is placing a rectangle in the coordinate plane. She
knows that the longer side of the rectangle is 2 times its shorter
side. She places the longer side on the x-axis.
What coordinates should she assign to the top-right vertex of the
rectangle?
Enter your answer in the boxes.
Answer:
(2a,a)
Step-by-step explanation:
Hope this helps!
14. A baker needs to make 3 batches of
3 cups of
cupcakes. If each recipe uses
sugar, how much sugar will the baker need?
(Example 5)
The baker needs [tex]\frac{25}{12}[/tex] cups of sugar.
Number of batches of cupcakes a baker needs to make = [tex]3 \frac{1}{8}[/tex]
Number of cups of sugar each recipe uses = [tex]\\\frac{2}{3}[/tex]
Quantity of sugar required to make [tex]3 \frac{1}{8}[/tex] batches of cupcakes = [tex]3 \frac{1}{8}[/tex] × [tex]\\\frac{2}{3}[/tex]
= [tex]\frac{25}{8}[/tex] × [tex]\frac{2}{3}[/tex]
= [tex]\frac{25}{12}[/tex]
Therefore, the quantity of sugar required to make [tex]3\frac{1}{8}[/tex] batches of cupcakes is [tex]\frac{25}{12}[/tex] cups.
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Transform y=-2x + 5 into an equivalent equation that is in standard form
Answer: The standard form of a linear equation is Ax+By=C. To change an equation written in slope-intercept form (y=mx+b) to standard form, you must get the x and y on the same side of the equal sign and the constant on the other side. Use inverse operations to move terms.
Step-by-step explanation:
Denise bake 14 cookies for Wednesday night book club for 4 people how many cookies should she bake next time if 12 people are coming
Answer: The answer is 56
Step-by-step explanation: bc 14 cookies is for 4 ppl and there are 12 ppl next time 4x3=12 so 14+14+14+14= 56 u would add 3 more 14's bc 14 cookies for 4 ppl and to check it 56 divided by 4 is 14.
What is f(9) when the slope is 3
Answer:
27
Step-by-step explanation:
it's a function with 3 as the slope and x as 9. So it's 27.
What is the standard form of a quadratic function passing through the points (2,4) , (3,5) and (4,3)
The standard form of a quadratic function is y = 3/2x² + 17/2x - 7
How to determine the quadratic equation?From the question, the points on the quadratic equation are given as
(2,4), (3,5) and (4,3)
The standard form of a quadratic equation is represented as
y = ax² + bx + c
So, we have
Point (2,4):
4a + 2b + c = 4
Point (3,5):
9a + 3b + c = 5
Point (4,3):
16a + 4b + c = 3
Solving using an online calculator. we have
a = 3/2, b = 17/2 and c = -7
Substitute a = 3/2, b = 17/2 and c = -7 in y = ax² + bx + c
y = 3/2x² + 17/2x - 7
Hence, the equation is y = 3/2x² + 17/2x - 7
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Here are two closed containers and four balls just fit in each container. Container A Container B Curved surface area of a cylinder is 2лrh Each ball has a diameter of 60 mm. Which container has the smaller surface area? You must show your working (using mm). Your final line should say either, 'A is smaller' or 'B is smaller'.
There are two closed containers and four balls can just fit in each of the containers, then container A has a smaller surface area.
What is volume?A three-dimensional solid shape's capacity is referred to as its volume. It is difficult to visualize in any shape, yet this can be evaluated among forms.
As per the data in the question,
Radius, r = 30 mm
Height, h = 60 × 4 = 240 mm
Use the equation of the surface area of the cylinder, SA = 2πr² + 2πrh
SA = 2π(30)² + 2π (30)(240)
SA = 50,868.
Now, calculate the area of a rectangular prism,
Area of top and bottom,
= (60 + 60) × (60 + 60) × 2
= 120 × 120 × 2 = 28,800
Area of 2 sides,
= 2 × (60 × 120) = 14,400
Area of front and back,
= 2 × (60 × 120) = 14,400
Total Surface Area = 28,800 + 14,400 + 14,400 = 57,600
Therefore, A has a smaller surface area.
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The area of a rectangle i 223. 2 m2. If the length i 16 m, what i the perimeter of the rectangle?
The perimeter of the rectangle is 59.9 m.
The area of the rectangle is = 223.2 m²
the length(L) of the rectangle is = 16 m
we know that the area of the rectangle is given by
Area = Length x Breadth
A = LB
therefore ,
LB= 223.2
16 x B = 223.2
B = 223.2/ 16
B = 13.95 m
∴ breadth or the rectangle is 13.95 meter.
Now , we know that the perimeter of the rectangle is given by ,
(P) perimeter = 2( Length + Breadth )
P = 2(L + B)
P = 2( 16 + 13.95)
P = 2( 29.95)
P = 59.9 m
So the perimeter of the rectangle is 59.9 meter.
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a sugar solution was made by mixing 8 gal of a 11% sugar solution and 4 gal of a 89% sugar solution. what is the concentration of the mixture ?
This is my last question help me please
Answer:
Line 1: [tex]y=-x+2[/tex]
Line 2: [tex]y=2x-1[/tex]
Step-by-step explanation:
Line 1
Staring with line one, let's find the slope!
Between the two known points, the rise, or change in y, is 2, and the run, or change in x, is -2. The slope is the rise over the run, so:
[tex]-\frac{2}{2} =-1[/tex]
The slope is negative 1! The line crosses the y-axis at [tex]y=2[/tex], so 2 is the y-intercept. Using the slope-intercept formula, the equation is:
[tex]y=-x+2[/tex]
Line 2
To find the slope of line 2, find the rise and the run between the two known points! The rise is 4, and the run is 2. Simplified, this is:
[tex]\frac{4}{2} =2[/tex]
The slope is 2! The line crosses the y-axis at [tex]y=-1[/tex], so -1 is the y-intercept. Using the slope-intercept formula, the equation is:
[tex]y=2x-1[/tex]
Answer:
y=2x-1 , y=x+2 , the solution of the system is (1,1)
Step-by-step explanation:
Lines can be expressed in the form y=mx+b where m is the slope and b is the y-intercept.
m= rise/run
Looking at the blue line:
m =2/1 =2
The slope is 2 since you rise 2 squares and run to the right one square.
We see that the line crosses the y-axis at (0,-1) so the y-intercept is -1.
Putting it all together: y=2x-1
Looking at the red line:
m = -1 / 1 = -1
We see that the line crosses the y-axis at (0,2) so the y-intercept is 2.
Putting it all together: y=1x+2 or simply y=x+2
The solution to the system is the point that satisfies both equations. Rather than solving it algebraically, we can simply look at the graph and find a point that is on both lines, aka the intersection. In this case, the intersection is (1,1).
On Friday, a local hamburger shop sold a combined total of 303 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Friday?
Answer:
101
Step-by-step explanation:
Since the total number of cheeseburgers was twice the number of hamburgers, let the number of sold hamburgers be h
Twice of h = 2(h)
Hence,
2(h) + h = 303
2h + h = 303
3h = 303
Divide both sides by the coefficient of h
h = 101
Therefore, the total number of hamburgers sold was 101
A school is arranging a field trip to the zoo. The school spends 526.26 dollars on passes for 47 students and 2 teachers. The school also spends 401.38 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student
The total amount of money spent on pass and lunch for each student is $19.28.
How much is spent on lunch and a pass?The first step is to determine the amount that was spent on a pass for each student. The cost of one pass can be determined by dividing the total amount spent on passes by the total number of teachers and students.
Cost of one pass = total amount spent on one pass / total number of people
Cost of one pass = 526.26 / (47 + 2)
Cost of one pass = 526.26 / 49
Cost of one pass = $10.74
The second step is to determine the amount spent on lunch for one student. This can be determined by dividing the total amount spent on lunch by the total number of students.
Cost of one lunch = total cost of lunch / total number of students
401.38 / 47 = $8.54
Total amount spent on pass and lunch for each student = cost of lunch for one student + cost of a pass for one student
$8.54 + $10.74 = $19.28
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if g (x) = 3x +5, for which value of x does g (x) =17?
Answer:
x = 4
Step-by-step explanation:
g (x) = 3x + 5
3x + 5 = 17
subtract 5 from both sides
3x = 12
divide by 3
x = 4
what is 32 times 45 and what does uprising mean
The solution of the mathematical statement is 1440 and uprising is a change in direction of a point in the coordinate plane
How to evaluate the expression?From the question, we have the following mathematical statement that can be used in our computation:
"what is 32 times 45"
This means that
32 times 45
Express as numbers
So, we have
32 x 45
Evaluate the product
So, we have
1440
Hence, the result is 1440
The meaning of uprisingThere is no direct term for uprising in mathematics.
However, the closest synonyms to uprising is revolution (in this case, it is rotation)
Rotation (uprising) implies that we change the direction of a shape, figure or object.
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A chef got 8 bags of onions. The red onions came in bags of 2 and the yellow onions came in bags of 6. If the chef got a total of 28 onions, how many bags of each type of onion did he get?
Answer: First you have to think about what to multiply 9 by to get a number that ends with 6. The answer to that is 3. So 9*3=36. Then you need to subtract 36 from 86. You get 50. So now you need to divide. 36/9=3 and 50/10=5. So the chef bought 3 bags of red onions and 5 bags of yellow onions.
Step-by-step explanation:
Answer:
3 yellow onion bags, 5 red onion bags
Step-by-step explanation:
hope it helped!
Which size bag of raisins has the lowest cost per gram?
A
100 g at $1.00
B
250 g at $2.00
C
500 g at $3.00
D
750 g at $6.00
Answer: A
Step-by-step explanation:
A for 1 gram it is $1.00
B for 1 gram it is $1.25
C for 1 gram it is $1.66
D for 1 gram it is $1.25
HELPPP so the man bought a tv worth $1,700, and then each week he continued to spend $700 weekly WHAT IS THE EXPRESSION???? HELP (variable is X)
Answer:
1700 - 700x
Step-by-step explanation:
assuming x is the number of weeks, the equation is 1700 - 700x equals the amount you are trying to solve for. You can say you are solving for y.
Anna is working two summer jobs, making $9 per hour washing cars and $12 per
hour landscaping. Last week Anna worked a total of 7 hours and earned a total of
$78. Determine the number of hours Anna worked washing cars last week and the
number of hours she worked landscaping last week.
By solving a system of equations we will see that Anna works 2 hours washing cars and 5 hours landscaping.
How to determine the number of hours in each job?
First, we need to define the variables that we will be using, these are:
x = number of hours washing cars.y = number of hours landscaping.We know that she works 7 hours in total and earns $78 in total, so we can write the system of equations:
x + y = 7
x*$9 + y*$12 = $78
Isolating x on the first equation we get:
x = 7 - y
Replacing this on the other equation we get:
(7 - y)*$9 + y*$12 = $78
$63 - $9*y + $12*y = $78
$63 + $3*y = $78
$3*y = $78 - $63
$3*y = $15
y = $15/$3 = 5
Then the value of x is:
x = 7 - y = 7 - 5 = 2
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A study was conducted on the effect of daytime running lights on cars. Researchers gathered data from a random sample of 3,248 drivers and measured quite a few variables, in addition to the explanatory variable of daytime running lights and the response variable of less accidents. According to a newspaper article summarizing the study, those cars that had daytime running lights were more likely to be operated by drivers who were confident and attentive. Drivers whose cars did not have daytime running lights were about 22% more likely to have an accident. What conclusion can we draw from this study? explain.
The correct choice is (a). The conclusion from the study is causality cannot be inferred because there is no control group.
Treatment in a study involves administering a stimulus, known as a treatment, to a group or portion of the sample while the rest of the sample is excluded from the stimulus. A successful treatment manipulation is one in which members of the treatment group perform better than members of the control group on the measures measured in study.
Given that the investigators collected data from a random sample of drivers and measured several variables, including the study's explanatory variables, it was possible to closely examine the cannot suggest a cause-and-effect relationship. No control group exists.
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Complete question:
A study was conducted on the effect of daytime running lights on cars. Researchers gathered data from a random sample of 3,248 drivers and measured quite a few variables, in addition to the explanatory variable of daytime running lights and the response variable of less accidents. According to a newspaper article summarizing the study, those cars that had daytime running lights were more likely to be operated by drivers who were confident and attentive. Drivers whose cars did not have daytime running lights were about 22% more likely to have an accident. What conclusion can we draw from this study? Explain.
a. We can infer a cause-and-effect relationship because the sample was selected randomly.
b. We cannot infer a cause-and-effect relationship because we do not have a control group.
c. We can infer a cause-and-effect relationship because multiple variables were included.
d. We cannot infer a cause-and-effect relationship because treatments were not assigned randomly.
e. We cannot infer a cause-and-effect relationship because the treatments imposed were not blocked correctly.
Answer:
We cannot infer a cause-and-effect relationship because treatments were not assigned.
Step-by-step explanation:
Got it right on test
Use the figure below for the following problems (not drawn to scale).
Given: m/1 = 70.
What is m25?
O a
.Ob
Oc
Od
125⁰
40°
70°
55°
2
76
The value of m∠5 is 125°. option A is the correct answer
From the question, we have
m∠1=70°
As the sides are equal.
∠2=∠3=(180°-70°)/2
= 55°
∠5 = 180°-55° (Linear pair)
= 125°
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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What is the value of the expression -23 - 12 - (-33)?
A: -2
B: 22
C: -68
D: 44
Answer: -2 ==> A
Step-by-step explanation:
-23 - 12 - (-33) =
-23 - 12 + 33 = ==> subtracting by a negative number is basically adding by the positive number
-(23 + 12) + 33 =
-35 + 33 =
-(35 - 33)=-2 ==> A
Answer: -2
Step-by-step explanation: