Answer:
[tex]a_{n}[/tex] = 60 - 15n
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 45 and d = a₂ - a₁ = 30 - 45 = - 15 , then
[tex]a_{n}[/tex] = 45 - 15(n - 1) = 45 - 15n + 15 = 60 - 15n
An equation for the nth term of the arithmetic sequence is aₙ=60-15n.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.
The given arithmetic sequence is 45, 30, 15, 0,.....
Here, a=45 and d=30-45 = -15
Now, aₙ=45+(n-1)(-15)
aₙ=45-15n+15
aₙ=60-15n
Therefore, an equation for the nth term of the arithmetic sequence is aₙ=60-15n.
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1. Expand to write an equivalent expression: −14(8x+12y)
2. Factor to write an equivalent expression: 36a−6
Pls answer (No links)
Answer:
-112x-168y, 6(6a-1).
Step-by-step explanation:
-14(8x+12y)
-112x-168y
--------------
36a-6
6(6a-1)
In order to ride a roller coaster, a rider
must be greater than 48 inches tall. Right
now, Jeff is 45 inches tall. Write an inequality
that describes how many more inches Jeff
must grow in order to ride the roller coaster
HELPPPPPP
Answer:
Step-by-step explanation:
45+x>48
x>3
Answer:
45+x>48
x>3
Step-by-step explanation:
Good Luck! <3
2x+7 + 3x+1 +x what’s the answer
Answer:6 + 8
Step-by-step explanation:
Add the numbers
Combine like terms
Answer:
the answer is: 6x+8
Step-by-step explanation:
also can I have brainliest please? :)
3) Tell whether the triangle can have the sides with the given lengths. Explain. 6, 16,9
Write a slope intercept equation for the following table
Answer:
y= 3x+1
Step-by-step explanation:
(0,4) shows the y-intercept of +4
Use slope formula to find slope:
7-4/2-1 = 3/1 = 3
M (slope)= 3x
Answer:
y=3x+1
Since we know that the line is increasing by 3 and since when x is equal to zero, and y is equal to 1 we know that we will need to add 1.
So Y=3x+1
which of the following expressions represent the number of distinguishable permutations of the letters of the word conclusion
Answer:
See explanation
Step-by-step explanation:
In most cases, we run into the problem of arranging objects that are repeated. This often occurs when we have a word that has repeated letters.
Let us recall that permutation deals with arrangements which are distinguishable.
Hence, for the word CONCLUSION, the number of distinguishable arrangements are;
10!/2!2!2!
I need help for this problem
Answer:
(-8,-2) try it
Step-by-step explanation:
Point D is in the interior of ∠ABC. What is m∠DBC?
37.5 degrees
we know angled like this always have 180 degrees total between the 2. which means we can set up a little equation to solve for x. The equation is (3x+22)+(x-4)= 180. Initially we can take the solid numbers (22 and -4) and get rid of them by taking them to the 180. 180- 22 is 158. 158 + 4 is 162. now we have 3x + x = 162. we combine like terms. means we end up with 4x =162. We now divide by 4 which means we get 40.5. Now we know x is 40.5. Now dbc is just 40.5- 4 which is 37.5.
The measure of angle ∠DBC is,
⇒ ∠DBC = 35.5°
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Given that;
Point D is in the interior of ∠ABC.
And, ∠ABD = (3x + 22)°
⇒ ∠DBC = (x - 4)°
Clearly, Both angle make a linear pair.
Hence, We get;
⇒ ∠ ABD + ∠DBC = 180°
⇒ (3x + 22) + (x - 4) = 180°
⇒ 3x + 22 + x - 4 = 180
⇒ 4x + 18 = 180
⇒ 4x = 180 - 18
⇒ 4x = 162
⇒ x = 162/4
⇒ x = 40.5
Hence, The measure of angle ∠DBC is,
⇒ ∠DBC = (x - 4)°
⇒ ∠DBC = (40.5 - 4)°
⇒ ∠DBC = 35.5°
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The radius of the circle is 3 inches what is the area
Answer:
28.27in
Step-by-step explanation:
HELP PLEASE DUE TODAY
The total cost, c, of belonging to two different gyms for m months is shown on the graph. The lines intersect at the point (4,250). Enter numbers in the boxes to explain what the solution means in the situation.
Answer: at 4 months the cost for each gym is $250
Step-by-step explanation:
At 4 month, the cost for each gym is $250
The y axis of the graph represents the membership cost and the x axis represent the number of month.
The lines representing gym A and B intersect at (4, 250).
The point where the lines intersect is when the cost and the month for each gym are the same.
Therefore, at 4 month, the cost for each gym is $250
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Which choice shows the corresponding sides as equal ratios?
Option A, DE/AB=EF/BC=DF/AC shows the corresponding sides as equal ratios
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
From the given triangles
In triangle ABC, the lengths AB is 3, BC is 4 and CA is 5.
In triangle DEF, the lengths DE is 6, EF is 8 and DF is 10.
As the two triangles are similar.
DE/AB=6/3=2
EF/BC=8/4=2
DF/AC=10/5=2
So DE/AB=EF/BC=DF/AC=2
Hence, Option A DE/AB=EF/BC=DF/AC shows the corresponding sides as equal ratios
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This will be the last easy question I'll make. tomorrow I'll make two more easy questions.
Whoever answers, I'll give brainliest:) (i won't always choose the first person, it's random btw)
what is 100x 30?
remember to spread kindness <3
Answer: 3000
100 x 30 = 3000
Answer:
3000 is the answer
Step-by-step explanation:
Here ya go :)
A rainbow is an arc of colors that is visible in the sky, caused by the refraction and dispersion of light after rain or other water droplets in the atmosphere .The colours of the rainbow are generally said to be red
Answer:
Red, orange, yellow, green, cyan, blue and purple.
Step-by-step explanation:
The rainbow is a colorful visual and meteorological phenomenon, in which the range of colors that compose the visible light in the sky appears. The phenomenon occurs when the sun's rays fall on raindrops in the Earth's atmosphere and is an example of refraction, after reflection. Each color is refracted at a different angle inside the droplets (which act like small prisms), it undergoes a different deflection and so the visible white light is analyzed in the different colors that compose it.
what is the slope of y=-4x-8
Answer:
-4
Step-by-step explanation:
y = mx + b
Answer:
-4
Step-by-step explanation:
y=mx+b
m is slope
b is y-intercept
So you line y=mx+b and y=-4x-8
-4 is replacing m so -4 is the slope
Hope this helps!
Gary Chain has a total of 37 tapes
and records. The number of tapes
is 3 less than twice the number of
records. How many of each does he have?
How do I do this????
Answer:
5.41
Step-by-step explanation:
x - 9 = 21
What does x =
Answer:
x=30
Step-by-step explanation:
You have to isolate for x. This means you need to somehow get x on one side of the equation all alone. In this case it is x-9=21 which means some unknown number x with 9 subtracted from it is equal to 21. When we bring the -9 over to the other side to get the x all alone, we have to switch the sign of the -9 so it becomes +9. This means x=21+9, and if you add that you'll get 30!
A boat can travel 10 miles downstream in the same time it
can travel 3 miles upstream. The speed of the river
current is 2 miles per hour. Which equation could you use
to find the speed of the boat in still water?
Answer:
[tex]\frac{10}{x+2} = \frac{3}{x-2}[/tex]
Step-by-step explanation:
The 10 represents the speed traveling downsteam while the 3 represents speed upstream. Downstream you have the help of the current, so it would be x + 2, upstream you are working against the current so it would be x - 2.
Laura borrowed $48,000 at a 6% interest rate for 6 years. what was the total interest?
Answer:
$17,280
Step-by-step explanation:
Formula:
I = Prt
Given:
P = 48000
r = 0.06
t = 6
Work:
I = (48000)(0.06)(6)
I = 17280
I suck at math so thanks for helping
Answer:
7.5
Step-by-step explanation:
The square has 4 equal sides, so you take the p,(30) and divide it. 30/4 = 7.5
To check your answer add 7.5 four times since the square has 4 equal sides.
7.5 + 7.5 = 15
15 + 7.5 = 22.5
22.5 + 7.5 = 30
A lawnmower is on sale for 45% of its original price of $355 what is the sale price
Answer:
$195.25Step-by-step explanation:
Original price = $355Sale = 45%Sale price:
$355*(100 - 45)/100 = $195.25your sale price should be, $195.25
the origonal price is, $355
sale happens = 45%
Sale price:
$355 times [tex]\frac{(100-45)}{100}[/tex] = $195.25
Hope this helps!
solve the equation for the variable, show your work
11x - 16 = -49
x = _____
Answer:
x = -3Step-by-step explanation:
Given,11x - 16 = -49
=> 11x = - 49 + 16
=> 11x = -33
[tex] = > x = \frac{ - 33}{11} [/tex]
=> x = -3 (Ans)
Answer:
x=-3
Step-by-step explanation:
1. Add 16 to both sides of the equation
11−16=−49
11−16+16=−49+16
2. Simplify.
IF you add the numbers you will get:
11x=-33
3. Divide both sides of the equation by the same term
11=−33
11/11=−33/11
4. Simplify.
x=-3
Hope this helps :)
A cube has a volume of 2197 m. Its surface is to be painted. Each can of paint covers about 40 m2
How many cans of paint are needed?
Answer:
25 cans
Step-by-step explanation:
Let the side length of the cube be s m
Therefore,
[tex] {s}^{3} = 2197 \\ \\ {s}^{3} = {13}^{3} \\ \\ \implies \: s = 13 \: m \\ \\ total \: surface \: area \: of \: cube \\ = 6 {s}^{2} \\ = 6( {13})^{2} \\ = 6 \times 169 \\ = 1,014 \: {m}^{2} \\ \\ no \: of \: cans \: of \: paint \: needed \\ = \frac{1014}{40} \\ = 25.35 \: \\ \approx \: 25[/tex]
Which of the following constructions can be accomplished with paper
folding?
Check all that apply.
A. Drawing a perpendicular line segment through a given point on a
given segment
. B. Constructing a circle with a radius from a given line segment
0 C. Finding the midpoint of a segment
D. Drawing a perpendicular line segment from a given point to a
given segment
The constructions that could be accomplished with paper folding are:
A. Drawing a perpendicular line segment through a given point on a given segmentC. Finding the midpoint of a segmentD. Drawing a perpendicular line segment from a given point to a given segmentHow do you find the midpoint of a segment using paper folding?To do the above, one can fold the paper so that the two endpoints of the line segment can be seen on top of each other.
A segment perpendicular to another segment can be done using paper folding by folding the paper so that the paper is folded via the point and the segment that is seen on top of its own self.
Therefore, The constructions that could be accomplished with paper folding are:
A. Drawing a perpendicular line segment through a given point on a given segmentC. Finding the midpoint of a segmentD. Drawing a perpendicular line segment from a given point to a given segmentLearn more about line segment from
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hi please help i’ll give brainliest please
Answer:
The answer is 3.
Step-by-step explanation:
If z equals 2 then you are supposed to multiply 2 by 3 and then subtract 3 since x equals 3.
HELP PLZ
1. A new bicycle sells for $300. It is on sale for off the regular price. Select all the
expressions that represent the sale price of the bicycle in dollars.
A. 300 •1/4
B. 300 • 3/4
C. 300 - (1 - 1/4)
D. 300 – 1/4
E. 300 – 1/4•300
Answer:
Step-by-step explanation:
All of them beside D and A
What is the volume of a cone with a radius of 3 and a height of 15? Use
3.14 as pi*
Answer:
141.3 (units³)
Step-by-step explanation:
formula for volume of a cone = V=1/3πr²h
1/3* 3.14 * 3² * 15 = 141.3
hope this helps!
Simplify 52 · 59.
511
518
2511
2518
Answer:
5^11
Step-by-step explanation:
The simplification form of the given expression 5² · 5⁹ would be 5¹¹ which is the correct answer that would be an option (A).
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
We have to determine the simplification form of the expression 5² · 5⁹.
The given exponential expression below as:
⇒ 5² · 5⁹
Apply the multiplication operation, and add the exponents because the same base of the exponential expression,
⇒ 5² ⁺⁹
⇒ 5¹¹
Therefore, the simplification form of the given expression would be 5¹¹.
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CAN SOMEONE PLEASE HELP ME WITH THIS :<
Answer:
A
Step-by-step explanation: