The algebraic expression can be used to find the nth term of the sequence is:
[tex]a_n = 5+3n[/tex]
Where, [tex]n\geq 1[/tex] and n is a positive whole number
Solution:
Given sequence is:
8, 11, 14, 17, 20, 23
Let us find the common difference between terms
11 - 8 = 3
14 - 11 = 3
17 - 14 = 3
20 - 17 = 3
23 - 20 = 3
Thus the common difference between successive term and previous term is constant
Thus this is a arithmetic sequence
The formula for nth term term of arithmetic sequence is given as:
[tex]a_n = a_1+(n-1)d[/tex]
Where,
[tex]a_n[/tex] is the nth term of sequence
[tex]a_1[/tex] is the first term of sequence
d is the common difference between terms
Here in this sequence, 8, 11, 14, 17, 20, 23
[tex]a_1 = 8\\\\d = 3[/tex]
Therefore,
[tex]a_n = 8+(n-1)3\\\\a_n = 8+3n -3\\\\a_n = 5+3n[/tex]
Where, [tex]n\geq 1[/tex] and n is a positive whole number
Thus algebraic expression can be used to find the nth term of the sequence is found
What’s 2percent of 300
Answer:
6
Step-by-step explanation:
2%=0.02
0.02*300=6
Solve please!
−3(x+5)=−9
To solve this, you need to isolate/get the variable "x" by itself in the equation:
-3(x + 5) = -9 Distribute/multiply -3 into (x + 5)
(-3)x + (-3)5 = -9
-3x - 15 = -9 Add 15 on both sides
-3x - 15 + 15 = -9 + 15
-3x = 6 Divide -3 on both sides to get "x" by itself
[tex]\frac{-3x}{-3} =\frac{6}{-3}[/tex]
x = -2
I just realized I took unnecessary steps....you could've just divided -3 then subtracted 5
-3(x + 5) = -9 Divide -3 on both sides [two negative signs cancel each other out and become positive]
x + 5 = 3 Subtract 5
x = -2
If A = {1, 2, 4} and B = {2, 4, 6, 8, 10}, find A ∩ B.
1. {1, 6, 8, 10}
2. {}
3. {2, 4}
4. {1, 2, 4, 6, 8, 10}
A∩B = {2, 4}
Step-by-step explanation:
Step 1: Given A = {1, 2, 4} and B = {2, 4, 6, 8, 10}Step 2: To find A∩B, find the number of common elements in both the sets.⇒ A∩B = {2, 4}
Find the area of the figure.( sides meet at right angles)
if 4x + 2 equals 4 what is the value of 2x + 1
To find the value of 2x + 1, we first solved for x in the equation 4x + 2 = 4, which yielded x = 1/2. Substituting this value into 2x + 1, the final answer is 2.
Explanation:The question seeks a solution for the value of 2x + 1 given that 4x + 2 = 4. We start by solving for x in the initial equation. Subtract 2 from both sides to get 4x = 4 - 2, which simplifies to 4x = 2. Dividing both sides by 4 yields x = 2 / 4, which simplifies to x = 1/2. Now that we have the value of x, we substitute it into the expression 2x + 1. So, 2(1/2) + 1 equals 1 + 1, which equals 2.
To find the value of 2x + 1, we need to determine the value of x first. Given that 4x + 2 = 4, we can start by subtracting 2 from both sides to isolate the 4x term. This gives us 4x = 2. Next, we divide both sides by 4 to solve for x. So x = 2/4 = 1/2.
Now that we know the value of x, we can substitute it into the expression 2x + 1. Plugging in x = 1/2, we get 2(1/2) + 1 = 1 + 1 = 2.
Therefore, the value of 2x + 1 is 2.
Find the sine...... Pls
Answer:
72/97
Step-by-step explanation:
Sinus is calculated by dividing opposite by hypotenuse so the answer is 72/97
Answer:
72/97
Step-by-step explanation:
Sin(X) = opposite/hypotenuse
Sin(X) = 72/97
how much do u need to subtract from 41/6 to make 6
What is the square root of 81
Answer:9
Step-by-step explanation:
Remember, 9•9=81, that’s how you know what the square root is.
Answer:
9
Step-by-step explanation:
which is 9.5 expressed as a fraction in simplist form
A.19/2
B.46/5
C. 86/9
D.64/7
Answer:19/2
Step-by-step explanation:
19/2=9.5
Other are not in its very simplest form
Answer:
19/2
Step-by-step explanation:
The other answers are not in the simplest form!
When rolling a number cube numbered 1 to 6, how would you describe the chances of rolling a number greater than or equal to 3 versus rolling a number less than 3?
A. more likely to roll a number greater than or equal to 3
B. more likely to roll a number less than 3
C. equally likely events
D. none of the above
Point e is between points D and F. If DE = x-4, EF= 2x+5 and DF= 4x-8 find x
What’s 6 1/4 minus 2 3/4
Answer: 3.5
Step-by-step explanation:
yes
A total of $5500 was invested in two accounts. Part was invested in a CD at 2% annual
interest rate and part was invested in a money market fund at 3% annual interest rate. If
the total simple interest for one year was $250, then how much was invested in each
account?
How many 1/5 liter glasses can Lin fill with a 1 1/2 liter bottle of water?
Answer:
The number of 1/5 liter glasses that Lin can fill is [tex]7\frac{1}{2}[/tex]
Step-by-step explanation:
we know that
To find out how many 1/5 liter glasses can Lin fill with a 1 1/2 liter bottle of water, divided 1 1/2 by 1/5
so
[tex]1\frac{1}{2} :\frac{1}{5}[/tex]
Convert mixed number to an improper fraction
[tex]1\frac{1}{2}=1+\frac{1}{2}=1\frac{1*2+1}{2}=\frac{3}{2}[/tex]
substitute
[tex]\frac{3}{2} :\frac{1}{5}[/tex]
Multiply in cross
[tex]\frac{5*3}{2*1}=\frac{15}{2}=7.5[/tex]
Convert to mixed number
[tex]7.5=7+\frac{1}{2}=7\frac{1}{2}[/tex]
Lin can fill 7.5 glasses of water from a 1 1/2 liter bottle. However, if only full glasses are counted, Lin can fill 7 full glasses.
Explanation:The question asks how many 1/5 liter glasses can be filled with a 1 1/2 liter bottle of water. To answer this, we need to perform a division of the total volume of the water by the volume of each glass.
First, express both quantities in the same units, in liters. The bottle has 1 1/2 liters, which is the same as 1.5 liters. Now, divide the total volume of the water by the volume of one glass:
1.5 liters / (1/5 liter per glass) = 1.5 * 5 = 7.5 glasses.
Therefore, Lin can fill 7.5 glasses of water from a 1 1/2 liter bottle, if we consider that partial glasses can be filled. If only full glasses can be filled, Lin can fill 7 full glasses.
Construct a triangle ABC where BC =4cm ,B=60° and AB+AC=6cm
Answer:
Below is the step-by-step explanation.
Step-by-step explanation:
To determine:
Construct a triangle ABC
Information Fetching and Information Steps:
From the given data,
[tex]BC\:=\:4\:cm[/tex][tex]B=60^{\circ }[/tex][tex]AB+AC=6\:cm[/tex]Procedure:
First draw a line segment [tex]BC\:=\:4\:cm[/tex]Then construct angle of [tex]m[/tex] ∠ [tex]60^{0}[/tex] at [tex]B[/tex] on [tex]BC[/tex].Taking [tex]B[/tex] as center with [tex]6\:cm[/tex] radius, draw an arc which cuts the ray of [tex]m[/tex] ∠ [tex]60^{0}[/tex] at [tex]X[/tex].Then Join [tex]X[/tex] and [tex]C[/tex].The draw a perpendicular bisector of [tex]XC[/tex].Wherever this perpendicular bisector intersect [tex]BX[/tex], name that point as [tex]A[/tex]Join [tex]A[/tex] and [tex]C[/tex].Thus, ∆ [tex]ABC[/tex] will be a required triangle.
Keywords: triangle, perpendicular bisector, angle
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Consider the function f(x)=x3+6x2−20x+450.
What is the remainder if f(x) is divided by (x−12)? Report your answer as a number only. Do not include (x−12) in your answer.
Answer:
Therefore reminder = 2802
Step-by-step explanation:
f(x)=x³+6x²-20x+450
x-12)x³+6x²-20x+450(x²+18x+196
x³-12x²
____________________
+18x²-20x+450
18x²-216x
_______________
196x +450
196x-2352
_____________
2802
Therefore reminder = 2802
The first figure is dilated to form the second figure.
Which statement is true?
The scale factor is 0.25.
The scale factor is 4.
The scale factor is 4.35.
The scale factor is 7.25.
A diamond with a side length of 5.8. An arrow points to a smaller diamond with a side length of 1.45
Answer:
The scale factor is 0.25.
Step-by-step explanation:
We have two side lengths.
First figure: A diamond with a side length of 5.8
This is the object length.
Second figure: Then a smaller diamond with a side length of 1.45
This is the image length.
The scale factor is
[tex]k = \frac{image \: length}{object \: length} [/tex]
[tex]k = \frac{1.45}{5.8} [/tex]
[tex]k = 0.25[/tex]
0.25 hope this helps
12 years ago left it was twice as old as Hester Lester is 21 years older than Hester what would be the sun in 5
Answer:
The sum of their ages in 5 years will be 97 years
Step-by-step explanation:
The correct question is
Twelve years ago, Lester was twice as old as Hester. Lester is 21 years older than Hester. What will the sum of their ages be in 5 years?
Let
x ----> Lester's age
y ----> Hester's age
we know that
Twelve years ago, Lester was twice as old as Hester
so
[tex]x-12=2(y-12)[/tex]
[tex]x-12=2y-24[/tex]
[tex]x-2y=-12[/tex] ----> equation A
Lester is 21 years older than Hester
so
[tex]x=y+21[/tex] ----> equation B
substitute equation B in equation A
[tex]y+21-2y=-12[/tex]
solve for y
[tex]-y=-12-21\\-y=-33\\y=33[/tex]
Find the value of x
[tex]x=33+21=54[/tex]
therefore
Lester's age is 54 years and Hester's age is 33 years
The sum of their ages in 5 years will be
[tex](54+5)+(33+5)=97\ years[/tex]
A survey of 260 families show that 99 had dog 76 had cat 34 had dog and cat 98 had neither a cat nor a dog nor a parakeet 8 had a cat a dog and a parakeet
The number of parakeet is 21.
The calculation is as follows:
Let us assume the families had parakeet only be X
A survey of 260 families show that:
The families had a dog and a cat only it means
= 34 - 8
= 26
The families had a dog only is
= 99 - (26 + 8 )
= 65
The families had a cat only is
= 76 - (26 + 8)
= 42
So,
X = 260 - ( 98 + 8 + 26 + 65 + 42 )
= 260 - 239
= 21
Therefore, the families had a parakeet only is 21.
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The question pertains to the analysis of survey data relating to pet ownership among a set of families. It requires understanding of data analysis in mathematics.
Explanation:The question is about finding the total number of families that have each specified type of pet (dogs, cats, both dogs and cats, or a dog, a cat, and a parakeet). The given data from the survey states that among the 260 families:
99 had a dog 76 had a cat 34 had both a dog and a cat 98 had neither a dog nor a cat nor a parakeet 8 had a dog, a cat, and a parakeet
Using this data, you can compute and analyze the number of families owning each type of pet or combination of pets. It's important to understand that some families may fall into multiple categories - for example, families with a dog and a parakeet would count both towards the 'dog' total and the 'dog, cat, and parakeet' total.
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What two numbers multiplies to -51 and adds to -14?
Answer: -17 and 3
Step-by-step explanation:
First try and find numbers that are divisible by -51 and see if they work. Then you'll find -17, leading to you multiplying -17 with 3, then you get -51, and if you add them, then you get -14.
You roll a pair of fair dice. Classify the probability for each of the outcomes as Impossible, Unlikely, Likely, or Certain.
Answer:
THE DIFFERENCE OF THE NUMBERS IS 6~ likely
THE SUM ON EACH DIE IS 5~ unlikely
THE NUMBER ON EACH DIE IS A WHOLE NUMBER~ Certain
THE NUMBER ON EACH DIE IS LESS THAN 6~ likely
THE SUM OF THE NUMBERS IS 14 OR GREATER~ impossible
Please answer the question in the photograph
Mr. Sam's swimming pool is in the shape of a parallelogram, as shown.
What is the area of his swimming pool?
A. 189 ft²
B. 234 ft²
C. 279 ft²
D. 585 ft²
Answer:
234 ft²
Step-by-step explanation:
Area of parallelogram = base x height
in our case, base length = 26 feet and height = 9 feet
hence,
Area of parallelogram = 26 x 9 = 234 ft²
Answer:
234 ft²
Step-by-step explanation:
I just finished the test and I got 100% correct.
Both circle A and circle B have a central angle measuring 50°. The area of circle A's sector is 36π cm2, and the area of circle B's sector is 64π cm2. Which is the ratio of the radius of circle A to the radius of circle B?
A) 3/4
B) 3/7
C) 4/3
D) 5/7
Answer:
A) 3/4
Step-by-step explanation:
Given: Both circle A and circle B have a central angle measuring 50°.
The area of circle A's sector is 36π cm2.
The area of circle B's sector is 64π cm2.
We know, area of the circle= [tex]\pi r^{2}[/tex]
lets assume the radius of circle A be "[tex]r_1[/tex]" and radius of circle B be "[tex]r_2[/tex]"
As given, Area of circle A and B´s sector is 36π and 64π repectively.
Now, writing ratio of area of circle A and B, to find the ratio of radius.
⇒[tex]\frac{\pi r_1^{2} }{\pi r_2^{2} } = \frac{36\pi }{64\pi }[/tex]
Cancelling out the common factor
⇒ [tex]\frac{r_1^{2} }{r_2^{2} } = \frac{36 }{64}[/tex]
⇒ [tex](\frac{r_1 }{r_2} )^{2} = \frac{36 }{64}[/tex]
Taking square on both side.
Remember; √a²= a
⇒ [tex](\frac{r_1 }{r_2} ) =\sqrt{ \frac{36 }{64}}[/tex]
⇒ [tex](\frac{r_1 }{r_2} ) = \frac{6}{8}[/tex]
⇒[tex]\frac{r_1 }{r_2} = \frac{3}{4}[/tex]
Hence, ratio of the radius of circle A to the radius of circle B is 3:4 or 3/4.
Ben bowled 121 and 184 in his first two games. What must he bowl in his third game to have an average of at least 170?
Answer:
205
Step-by-step explanation:
Were gonna start by writing an equation (121+184+x)/3=170 because were adding a 3rd value to the average and x is going to be our value that were looking for. If you solve that, you get 205. Hope this helps.
For Ben to have an average of at least 170 in his third game, he must bowl a score of 205.
Explanation:To find out what Ben must bowl in his third game to have an average of at least 170, we can use the formula for average: average = total score/number of games.
In this case, Ben has played two games and wants to have an average of 170. So we can set up the equation: 170 = (121 + 184 + x) / 3, where x represents his score in the third game.
To solve for x, we can multiply both sides of the equation by 3 to get rid of the fraction: 510 = 121 + 184 + x.
Then, we can combine the numbers on the right side: 510 = 305 + x.
Finally, subtracting 305 from both sides gives us: 205 = x.
Therefore, Ben must bowl a score of 205 in his third game to have an average of at least 170.
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Which statement is best supported by the dot plot? Choose ONE and explain your
answer.
I. The range of the number of miles Amanda skated in August is less than the range
of the number of miles she skated in July.
II. The distribution of data is approximately symmetrical in both sets of data.
III.The mode of the number of miles Amanda skated in July is equal to the mode of
the number of miles skated in August.
Answer:
The statement that is best supported by the dot-plot is iii)
The mode of the number of miles Amanda skated in July is equal to the
mode of the number of miles skated in August.
This is a true statement.
The mode of the number of miles Amanda skated in July is equal to 1.
The mode of the number of miles Amanda skated in August is equal.
Step-by-step explanation:
i) The range of the number of miles Amanda skated in August is less than the
range of the number of miles she skated in July.
This is a true statement.
the range of the number of miles Amanda skated in August is 1 to 3
the range of the number of miles Amanda skated in July is 1 to 4
ii) The distribution of data is approximately symmetrical in both sets of data.
This is NOT a true statement.
the distribution of data of the number of miles Amanda skated in August
is not symmetrical.
the distribution of data of the number of miles Amanda skated in August
is approximately symmetrical.
iii) The mode of the number of miles Amanda skated in July is equal to the
mode of the number of miles skated in August.
This is a true statement.
The mode of the number of miles Amanda skated in July is equal to 1.
The mode of the number of miles Amanda skated in August is equal.
Which of the following must be true in order for SAND to be in a rhombus? Select all that apply
a) Consecutive sides must be congruent, for SAND to be in a rhombus
For the word "SAND" to form a rhombus, certain conditions must be met based on the properties of a rhombus:
a) Consecutive sides must be congruent: True. In a rhombus, all sides are congruent, so consecutive sides must also be congruent.
b) Diagonals do not bisect the angles: False. In a rhombus, the diagonals bisect the angles. This is a property of rhombuses.
c) All interior angles add up to 360: False. In a rhombus, all interior angles are equal, but their sum is not necessarily 360 degrees. However, the sum of all interior angles in any quadrilateral (including a rhombus) is indeed 360 degrees.
Therefore, the correct statement is:
a) Consecutive sides must be congruent
Which expression has a negative value?
A. -1×-2
B. 1×−2×−3×−4×−5
C. −1×2×−3×4×−5
D. 1×−2×3×−4×5
Please answer correctly! Oh, and fail to satisfy me with your answer will result in someone being reported.
The expression -1 × 2 × -3 × 4 × -5 has a negative value ⇒ C
Step-by-step explanation:
Let us revise the products of negative and positive
(+) × (+) = (+)(-) × (-) = (+)(-) × (+) = (-)(+) × (-) = (-)The product of three (-) is (-) ⇒ -2 × -3 × -1 = -6 (-2 × -3 = 6 × -1 = -6)The product of four (-) is (+) ⇒ -2 × -3 × -1 × -4 = 24 (-2 × -3 = 6 × -1 = -6 × -4 = 24)If there are even negative signs, then the product will be positiveIf there are odd negative signs, then the product will be negativeA. -1 × -2
∵ There are two negative signs
∵ 2 is an even number
∴ -1 × -2 has a positive value
B. 1 × -2 × -3 × -4 × -5
∵ There are four negative signs (-2 , -3 , -4 , -5)
∵ 4 is an even number
∴ 1 × -2 × -3 × -4 × -5 has a positive value
C. -1 × 2 × -3 × 4 × -5
∵ There are three negative signs (-1 , -3 , -5)
∵ 3 is an odd number
∴ -1 × 2 × -3 × 4 × -5 has a negative value
D. 1 × -2 × 3 × -4 × 5
∵ There are two negative signs (-2 , -4)
∵ 2 is an even number
∴ 1 × -2 × 3 × -4 × 5 has a positive value
The expression -1 × 2 × -3 × 4 × -5 has a negative value
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Ramesh says that based on the pattern 7^-5 =-16,807 which statement explains were her Ramesh is correct?
Ramesh is not correct because as the exponents decrease, the previous value is divided by 7 .
Explanation:
An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
Exponents are superscript numerals that let you know how many times you should multiply a number by itself. Some real world applications include understanding scientific scales like the pH scale or the Richter scale, using scientific notation to write very large or very small numbers and taking measurements.
Answer:
D. Ramesh is not correct because as the exponents decrease, the previous value is divided by 7, so 7 Superscript negative 5 = 1 divided by 7 divided by 7 divided by 7 divided by 7 divided by 7 = StartFraction 1 Over 16,807 EndFractionStep-by-step explanation:
EDGE 2020
a. The seats are divided into 40 different sections thats are given in only 5 sections, what
is the probability of a guest's sitting in a section that gets a hat?