Answer:
12th term = -61
Step-by-step explanation:
Given sequence,
→ 5, -1, -7, ...
Now we have to,
→ Find the 12th term of the sequence.
The common difference is,
→ d = a2 - a1
→ d = -1 - 5
→ [ d = -6 ]
Formula we use,
→ an = a1 + (n - 1)d
Then value of 12th term will be,
→ an = a1 + (n - 1)d
→ a12 = 5 + (12 - 1) × (-6)
→ a12 = 5 + 11 × (-6)
→ a12 = 5 - 66
→ [ a12 = -61 ]
Therefore, the 12th term is -61.
1. For
what value of x is the
3(x + 2)-2x = 12 true?
A. 6
B. 10
C. 12
D. 14
E. 18
1.4.1 Set
the equation
Answer: A. 6
Step-by-step explanation:
Answer: I think D.
Step-by-step explanation: why not pick D…..
Hope this helps^^
The perimeter of a triangle is 39 inches. If the length of the shortest side is 1/2 the length of the longest side, and the length of the third side is 1 less than the length of the longest side, what is the length of each side?
Question 1
Identify the function type represented by the graph. Explain your reasoning, and include at least one key feature to
support your choice.
The function type of the graph with asymptotes, x = 2, and y = 0 is a rational polynomial, where the degree of the numerator is less than the degree of the denominator, and (x - 2) is a factor of the denominator, which is a function of the form;
[tex]f(x) = \frac{1}{(x - 2)}[/tex]
What is an asymptote?An asymptote is a line to which the output value of a function approaches as the input value becomes very large approaches infinity.
The function type represented by the graph is a polynomial function that has an horizontal asymptote of y = 0, and a vertical asymptote of x = 2
A function has a vertical asymptote at the location at which the denominator approaches zero.
The vertical asymptote of x = 2 , indicates that the denominator approaches zero when x = 2, therefore, (x - 2) is a factor of the denominator
A function has an horizontal asymptote which is the value the function approaches as the input value approaches infinity.
Therefore, the horizontal asymptote of y = 0, indicates that the the degree of the numerator is less than the degree of the denominator
The function type in the question is therefore;
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A cone has a volume of 30 in ³.
What is the volume of a cylinder with the same radius
and height?
Answer:
[tex]90 \ in^{3}[/tex]
Step-by-step explanation:
The volume of a cone is ¹/₃ the volume of the cylinder of a given radius and perpendicular height
[tex]V_{C} = volume \ of \ cylinder \\\\ V_{c} = volume \ of \ cone\\\\ r = radius \\\\ h = perpendicular \ height[/tex]
[tex]V_{C} = \pi r^{2}h \\\\ V_{c} = \frac{1}{3}\pi r^{2}h[/tex] → [tex]3V_{c} = \pi r^{2}h = V_{C}[/tex]
So if r and h are the same, then:
[tex]V_{C} = 3V_{c}[/tex]
Therefore:
[tex]V_{C} = 3(30) \\\\ V_{C} = 90[/tex]
Painted Pots lets customers choose and paint their own potter
y. The store has teapots in multiple sizes. Rebecca chose to paint the largest teapot offered, which cost $18. She also painted 4 small teacups to go with her teapot. Rebecca spent a total of $42 on pottery.
Which equation can you use to find c, the cost of each teacup?
What was the cost of each teacup
The value of the equation is y = 4c + 18 , where c is the cost of each teacup and c = $ 6
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
The total cost Rebecca spend on teacups = $ 42
The cost of the large teapot = $ 18
The cost of small teacups be = c
The number of small teacups = 4
So , the equation will be
Total cost Rebecca spend on teacups = cost of the large teapot + ( number of small teacups x cost of small teacups )
Substituting the values in the equation , we get
42 = 18 + 4c
y = 4c + 18 be equation (1) , where y is the total cost
On simplifying the equation , we get
Subtracting 18 on both sides of the equation , we get
4c = 24
Divide by 4 on both sides of the equation , we get
c = $ 6
Therefore , the cost of each teacup is $ 6
Hence , the equation is y = 4c + 18
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NEED HELP ASAP PLEASE! What is the equation of the function shown in the table?
Input x: -2 -1 0 1 2
Output y: -3 -1 1 3 5
A: y = -2 x + 1
B: y = 2 x + 1
C: y = 2 x - 2
D: y = - 1/2x - 1
The equation of the function shown in the table is y=2x +1, the correct option is B.
What is the equation of a line passing through two given points in 2 dimensional plane?Suppose the given points are (x_1, y_1) and (x_2, y_2), then the equation of the straight line joining both two points is given by
[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
We are given that;
The x and y of the function
Input x: -2 -1 0 1 2
Output y: -3 -1 1 3 5
Now,
The general equation of line
y=mx+c
Here, m= 5-3/2-1
m=2
Substituting the value of m in general equation.
y=2x +1
Therefore, the equation of line will be y=2x +1
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How many possible triangles can be created if measure of angle B equals pi over 6 comma a = 20, and b = 10?
0 triangles
2 triangles
1 triangle
Cannot be determined based on the given information
Based on the given information,
only one triangle is possible.
The correct option is C.
What is a 30-60-90 triangle?It is a triangle with constant angles of 30, 60, and 90. This triangle is always a right triangle, as one of the angles is 90 degrees. Thus, a right-angled triangle is formed by these angles. Additionally, the right angle is equal to the sum of two acute angles, which will have a 1: 2 or 2: 1 ratio.
Given:
The angle measure of B = π/6 = 30°.
a = 20, and b = 10
That means,
m∠A = 2∠B = 2 x 30 = 60°.
Now, there is only one possibility of a triangle, and that triangle is 30-60-90 triangle.
Hence, only one triangle is possible.
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Find the missing values.
Select two answers.
Answer:
a= 12, b=4, Choices B and F
Step-by-step explanation:
2/2=1
8/2=4
12/2=6
I want the answer pleaseee
Answer:
8.6 m
Step-by-step explanation:
DE = 2 7/10 m
= 2 + 7/10
= 2 + 0.7
DE = 2.7 m
EF = 5 9/10 m
= 5 + 9/10
= 5 + 0.9
EF = 5.9 m
DF = DE + EF
= 2.7 + 5.9
= 8.6 m
How long is a movie if it starts at 2:25pm and ends at 16:41 pm
Answer:
It would be a little over 2 hours or so since 16:41 is just 4:41.
2 hours and 16 minutes
Step-by-step explanation:
You're welcome.
Maya had $32. She spent all the money on buying 3 notebooks for x dollars each and 4
packs of index cards for y dollars each. If Maya had bought 5 notebooks and 5 packs of
index cards, she would have been short $18. Which system of equations represents this
situation?
O 3x + 4y = 32 and 5x + 5y = 50
O 3x+4y= 32 and 5x + 5y = 18
O 3x + 4y = 50 and 5x - 5y = 18
O 3x - 4y= 32 and 5x - 5y = 50
The system of equations which represents this
situation is 3x+4y= 32 and 5x + 5y = 18.
The correct answer choice is option B
Which system of equations represents the situation?Amount with Maya = $32
Amount spent on each notebook = x
Number of notebook = 3
Amount spent on each pack of index cards = y
Number of index cards = 4
Maya bought 5 notebooks and 5 packs of
index cards
$18 short = $32 - $18
= $14
3x + 4y = 32
5x + 5y = 14
In conclusion, the system of equation is 3x+4y= 32 and 5x + 5y = 18.
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After four years in college, Josie owes $50000 in student loans. The interest rate on the federal loans is 2.8% and the rate on the private bank loans is 4.8%. The total interest she owes for one year was $1,600.00.What is the amount of each loan?
Federal loan at 2.8% account = $
Private bank loan at 4.8% account = $
The federal loan at 2.8% is approximately 11000, and the private bank loan at 4.8 percent is around 39000 (which is 50000 - 11000).
How to solve the problem?Let's use f and p to denote the amounts of Josie's federal and private bank loans, respectively.
We know that the total amount of loans is 50000, so:
f + p = 50000
We also know that the interest on federal loans at 2.8% and the interest on private bank loans at 4.8% add up to 1600 per year. The interest on the federal loans is 0.028f and the interest on the private bank loans is 0.048p, so:
0.028f + 0.048p = 1600
We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for p:
p = 50000 - f
Substituting this into the second equation, we get:
[tex]0.028f + 0.048(50000 - f) = 1600[/tex]
Simplifying and solving for [tex]f[/tex], we get:
[tex]f = \frac{1600 - 0.048 \cdot 50000}{0.02} \approx 11000[/tex]
Therefore, the federal loan at 2.8% is approximately 11000, and the private bank loan at 4.8% is approximately 39000 (which is 50000 - 11000).
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help please i don’t know what to do
Answer:
Add 3 and then multiply by 5.
Step-by-step explanation:
The problem looks like this to me:
[tex] \dfrac{m}{5} - 3 = 8 [/tex]
If this is correct, then the operations are:
Add 3 to both sides.
Multiply both sides by 5.
I don't see that answer. The picture is not very clear to me. What is the denominator of the fraction?
Car = V-8 sedan
Year driven = third
Miles driven = 10,000
The depreciation for this vehicle using method 2 will be $
The depreciation of the vehicle at third year with miles driven 10,000 is $590.
What is depreciation cost?A fixed asset's depreciated cost is equal to its value less the total amount of accumulated depreciation that has been recorded against it.
The depreciated cost is used to calculate an asset's value after its useful life is over.
The depreciated cost helps organizations examine their capital spending patterns and their accounting technique.
The depreciated cost is also known as the "residual value," "net book value," or "changed cost base."
The depreciation cost per mile for the third year is given as 5.9 cents.
The miles driven = 10,000
The depreciation for the vehicle is:
(5.9)(10,000) = 59000 cents.
Converting into dollars:
59000/100 = $590.
Hence, the depreciation of the vehicle at third year with miles driven 10,000 is $590.
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In fall 2006, Pace University in New York raised its annual tuition from $25,000 to $29,750. Freshman enrollment declined from 1,475 in fall 2005 to 1,130 in fall 2006. Assuming that the demand curve for places in the freshmen class at Pace did not shift between 2005 and 2006, use this information to calculate the price elasticity of demand LOADING... . Use the midpoint formula in your calculation.
Answer:The answer is 20000
Step-by-step explanation:
Please help me. I'll give brainliest.
Answer: The final balance is $11,015.84.
The total compound interest is $3,845.84.
Name
2-Step Word Problems
There were 24 polar bears and 38
penguins swimming in the ocean. 15
polar bears got out of the water.
How many polar bears and penguins
are left playing in the water?
polar bears and penguins
My brother made 46 snowballs and I
made 59 snowballs. My sister joined
us and made 25 more snowballs.
How many snowballs do we have
altogether?
i
My mother had a collection of 51
snow globes. She received 8 more
snow globes for her birthday. My
brother and I started fighting and
broke 12 snow globes. How many
snow globes does my mother have
left?
snowballs
snow globes
-
ate:
There were 83 adult penguins and
69 baby penguins playing on the hill.
55 mother penguins went home.
How many penguins are left playing
on the hill?
penguinsi
There are 47 polar bears and penguins in the water.
The number of snowballs made altogether is 130 snowballs.
The number of snow globes your mother has left is 47 snow globes.
The number of penguins left playing is 97 penguins.
How to solve word problems?Number of polar bears= 24
Number of penguins = 38
No. of polar bears that got out of the water= 15
Total polar bears and penguins in the water = (24 + 38) - 15
= 47
Number of snowballs made by your brother = 46
Number of snowballs made by you = 59
Number of snowballs made by your sister, brother and you = 25
Total snowballs made= 46 + 59 + 25
= 130 snowballs
Number of snow globes mother has = 51
Number of additional snow globes received = 8
Number of snow globes broken = 12
The number of snow globes your mother has left= (51 + 8) - 12
= 59 - 12
= 47 snow globes
Number of adult penguins(mother and father) = 83
Number of baby penguins = 69
Number of mother penguins that went home = 55
Number of penguins left playing = (83 + 69) - 55
= 97 penguins.
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what is the value of 8.4n - 3.2p, when n=4 and p=-2
Answer:
33.6-(-6.4)=40
Step-by-step explanation:
1. 8.4×4
2. 3.2x-2
3. 33.6-(-6.4)
4. 40
the two negatives become positive
How can credit cards be safer than cash? a. It is harder to lose a single credit card than a large number of bills. b. A credit card requires a signature, so it is impossible for anyone other than you to use. c. If a merchant does not hold up their end of an agreement, you can call the credit company and dispute the charges. d. Cash can be miscounted, but credit cards cannot.
If a merchant does not hold up their end of an agreement, you can call the credit company and dispute the charges. This way, credit cards can be safer than cash.
What is credit card?
A credit card is a small plastic payment card that is provided by a person's bank and enables the cardholder to pay a merchant for products and services depending on the cardholder's accumulated debt.
To be on the safe side in the event that a merchant breaches an agreement, a cardholder may contact the credit bureau to resolve the disputed charges.
So, this way credit cards can be safer than cash.
Hence, option C is the correct solution.
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Find the value of C that makes 16x^2 -24x + C a perfect square
The required value of C is 3 which makes 16x² - 24x + C a perfect square.
What is Perfect Square?A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.
The expression is given in the question, as follows:
16x² - 24x + C
(4x)² - 24x + C
As we know that the factoring identity:
(a - b)² = a² - 2ab + b²
After comparing, we have a = 4x and 2ab = 24x
Solving for b:
2(4x)b = 24x
b = 24x/8x
b = 3
So 16x² - 24x + 3 = (4x - 3)²
This means the required value of C is 3 which makes a perfect square.
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Aubrey broke a cell sample into 15 batches, each way 1.3×10 to the -7th grams. How much did the original sample weigh? Use scientific notation to express your answer.
Answer:
Step-by-step explanation:
1.3 * 10 ^-7
is 0.00000013
0.00000013 times 15 is
0.00000195.
0.00000195 in scientific notation is
1.95*10^-6
What shape is this, why?
The shape is most specifically a trapezoid because it has a pair of parallel sides
How to determine the type of the shapeFrom the question, we have the following parameters that can be used in our computation:
The figure
From the figure, we have the following highlights:
The sides with lengths 21 and 24 are parallel sideThe other sides are non parallelUsing the above as a guide, we have the following:
The shape is most specifically a trapezoid
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find the vertical asymptotes
Answer: Vertical asymptotes are = [tex]-4, 1,4[/tex]
Horizontal asymptote = [tex]y=0[/tex]
Step-by-step explanation:
If you need explanation just say you want...
Kim Kardashian pays a $600 fee to own a cell phone. She also has to pay $0.15 per minute of cell phone usage. If she talked for 1000 minutes how much would her bill be?
Answer:
$750
Step-by-step explanation:
The cost of cell phone usage for 1000 minutes would be 1000 minutes * $0.15 per minute = $150.
Adding the initial fee of $600, Kim Kardashian's total bill would be $600 + $150 = $750.
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
Eighteen low-fat wheat crackers have 3 grams of fat. How many grams of fat do 63 of these crackers have?
Answer:
10.5
Step-by-step explanation:
18/3 = 63/x
18 * x = 63
18 * 3.5 = 63
3 * 3.5 = 10.5
Which one of the following items is not necessary in preparing a statement of cash flows?
O Determine the cash provided by operations
O Determine cash from financing and investing activities
O Determine the cash in all bank accounts
Determine the change in cash
The cash flow statement shows the cash the business has generated from operations, investments, and financing. Net cash flow is the name given to this sum.
What is meant by statement cash flows?In financial accounting, a cash flow statement, often called a statement of cash flows, is a financial statement that breaks down the analysis into operating, investing, and financing operations. It illustrates how changes in balance sheet accounts and income effect cash and cash equivalents.
A cash flow statement lists all of an organization's cash inflows from current operations and outside investment sources. The cash flow statement shows the cash the business has generated from operations, investments, and financing. Net cash flow is the name given to this sum.
Functionally speaking, cash flows are categorized according to the nature of the underlying transaction. The statement's main goal is to give pertinent details about the agency's cash inflows and outflows during a given time period.
Therefore, the correct answer is option d) Determine the change in cash.
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The area of a rectangular wall of a barn is 110 square feet. Its length is 12 feet longer than twice its width. Find the length and width of the wall of the barn.
width= =feet
The length and width of the rectangular wall of a barn given the area is 22 feet and 5 feet respectively.
What is the length and width of the wall of the barn?Area of the rectangular wall of a barn = 110 square feet
Width of the barn = w
Length of the barn= 2w + 12
Area of a rectangle = length × width
110 = (2w + 12) × w
110 = 2w² + 12w
equate to 0
2w² + 12w - 110 = 0
w² + 6w - 55 = 0
using factorization method of solving quadratic equation
w² + 11w - 5w - 55 = 0
w(w + 11) - 5(w + 11) = 0
(w - 5) (w + 11) = 0
w = 5 or w = -11
The width of the rectangular barn cannot be negative
Therefore,
Width of the barn = w
= 5 feet
Length of the barn= 2w + 12
= 2(5) + 12
= 10 + 12
= 22 feet
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Which of the following statements proves the series 250 – 150 + 90 – 54 + … is geometric?
r equals five thirds
r equals three fifths
r equals negative three fifths
The given series is geometric when r equals negative three-fifths.
What is geometric series?
The geometric series refers to the total of terms with a common ratio between every pair of neighbouring terms. Geometric series can be of two different types: finite and infinite. The sequence is of the form {a, ar, ar², ar³, …….} where, a is the first term, and r is the "common ratio".
where, r = ar/a = (second term)/(first term)
Given, the series 250 – 150 + 90 – 54 + …
So, r = (-150)/250 = -3/5
or, r = 90/(-150) = -3/5
Hence, for the geometric series, r should be equal to negative three-fifths.
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Examine the figure below, find the length of b, round to the nearest whole
number.
32°
L
b
M
The length of the side using cosine rule and approximating to a whole number gives 23
How to use Cosine Rule?The law of cosines is used to find the missing parts of an oblique triangle when either the two-sided measurements and the included angle measure are known (SAS) or the lengths of the three sides (SSS) are known.
This is expressed as;
b² = a² + c² - 2ac cos b
Plugging in the relevant values gives;
b² = 28² + 41² - 2(28 * 41) cos 32
b² = 2465 - 1947.118
b² = 517.882
b = √517.882
b = 22.757 ≈ 23
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Simplify the following expression using rational exponents. Assume all variables are positive.
a3/5⋅a3/4
Answer:
The simplified expression is a^(21/20).
Step-by-step explanation:
To simplify the expression, we can use the rule for multiplying two powers with the same base, which is to add the exponents.
a^(3/5) * a^(3/4) = a^(3/5 + 3/4) = a^(6/5 + 3/4)
We can then simplify the fractional exponent by finding a common denominator for the numerators, which is 20 in this case:
a^(6/5 + 3/4) = a^(6/20 + 15/20) = a^(21/20)
The simplified expression is a^(21/20).
