The missing second term of the given arithmetic sequence is: 2.5.
What is arithmetic progression?A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
given: -3, __, 8 is an arithmetic sequence, where a₁ = -3 and a₃ = 8
Now, as [tex]a_n=a_1+(n-1)d[/tex], for the nth term of an arithmetic sequence,
For n = 3, a₃ = -3 + (3 - 1)d
=> 8 = -3 + 2d
=> 11/2 = d
=> d = 5.5
Hence, a₂ will be given as n = 2, in the above formula
=> a₂ = -3 + (2 - 1) (5.5)
=> a₂ = -3 + 5.5
=> a₂ = 2.5
Hence, The missing second term of the given arithmetic sequence is: 2.5.
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need help solving please
Answer:
3 option
Step-by-step explanation:
To find the missing side (c) you need to do a^2 and b^2
Formula a^2 + a^2 = c^2
You and your friend are swimming against the current. You move forward 15 feet. Your friend is not a strong swimmer, so he moves back 6 feet. write each amount as the distance swam.
The amount of you swam is +15 feet and your friend swam is -6 feet.
Given that you move forward 15 feet and your friend is not a strong swimmer, so he moves back 6 feet.
The arithmetic operators means performing an addition, subtraction, multiplication, division, exponentiation, and modulus operations.
It is given that you move the forward that means you move in positive direction.
So, you move forward means you move +15 feet.
It is also given that your friend is not a strong swimmer, so he moves back that means he move in negative direction.
So, your friend moves backward means he move -6 feet.
Hence, you move forward 15 feet is +15 feet and your friend is not a strong swimmer, so he moves back 6 feet is -6 feet.
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Last month, jennifer earned $180 for her after-school job. if she was paid $7.50 per hour, how many hours did jennifer work?
Answer: 22
Step-by-step explanation: 143 divided by 6.50 = 22, therefore our answer is 22
solve for x and y
6x+5y=-10
3x+5y=20
Answer: x = -10
Step-by-step explanation:
Answer:
(- 10, 10 )
Step-by-step explanation:
6x + 5y = - 10 ( subtract 6x from both sides )
5y = - 10 - 6x → (1)
3x + 5y = 20 → (2)
substitute 5y = - 10 - 6x into (2)
3x - 10 - 6x = 20
- 3x - 10 = 20 ( add 10 to both sides )
- 3x = 30 ( divide both sides by - 3 )
x = - 10
substitute x = - 10 into (2) and solve for y
3(- 10) + 5y = 20
- 30 + 5y = 20 ( add 30 to both sides )
5y = 50 ( divide both sides by 5 )
y = 10
solution is (- 10, 10 )
Greta uses 3 cups of pasta for every 3/4 cup of sauce. How much pasta does she use per cup of sauce?
4 cups of pasta are used per cup of sauce.
Given,
Greta uses 3 cups of pasta for every 3/4 cup of sauce.
We need to find how much pasta she uses per cup of sauce.
How to compare two quantities?Example:
12 apples = 2 basket ____(1)
For 5 baskets:
We need to make 2 baskets = 5 baskets.
We can divide by 2 and multiply 5 on both sides on (1).
5/2 x 12 apples = 5/2 x 2 baskets
30 apples = 5 baskets.
We have,
3 cups of pasta = 3/4 cup of sauce
We need to make 3/4 cup of sauce as 1 cup of sauce.
Multiply 4/3 on both sides.
4/3 x 3 cups of pasta = 4/3 x 3/4 cup of sauce
4 cups of pasta = 1 cup of sauce
Thus 4 cups of pasta are used per cup of sauce.
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Solve the system:
5x-6y= -44
3x + 7y = 69
Answer:
Point form:
(2, 9)
Equation form:
x = 2,y = 9
Step-by-step explanation:
What is the difference of the two rational expressions in simplest form? State any restrictions on the variable.
b. x-1 / x+5 - x+3 / x²+6 x+5
The simplification of difference of the given two rational expressions [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex] is equal to [tex]\frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]. Restriction on the variables is given by x≠ -5, x≠ -1.
As given in the question,
Given expression is [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex]
Simplify the given two rational expressions by factorizing them,
[tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}\\\\= \frac{x-1}{x+5}-\frac{x+3}{x^{2} +5x +x+5}\\\\= \frac{x-1}{x+5}-\frac{x+3}{(x+5)(x+1)}\\\\= \frac{x^{2} -1-(x+3)}{(x+5)(x+1)}\\\\= \frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]
Restriction on the variables is given by x≠ -5, x≠ -1.
Therefore, the simplification of difference of the given two rational expressions [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex] is equal to [tex]\frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]. Restriction on the variables is given by x≠ -5, x≠ -1.
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what is the greatest common factor of 7 and 35x
Answer:
7
Step-by-step explanation:
Hope this helps!!
I need help asap!!!!
Answer:
y = 2016 - 112x
Step-by-step explanation:
because he is paying 112 dollars each month for 18 months
y= 2016 -112x
for instance, he paid it for 6 months we would say
y = 2016 - 112(6)
y = 2016 - 672
y = 1334
so, y = 2016 - 112x
Hi can anybody help with (a)? I'm struggling with this question
Determine whether the quadrilateral can always, sometimes, or never be inscribed in a circle. Explain your reasoning.
parallelogram
A rectangle as the only parallelogram that can be inscribed in a circle.
What shapes can be inscribed in a circle?Every circle has an inscribed triangle with any three given angle measurements (summing to 180°, of course), and every triangle can be inscribed in any circle (which is called its circumscribed circle or circumcircle). Every triangle has an incircle, which is a circle that has been inscribed.
The only parallelogram that can be inscribed in a circle is a rectangle. Because every rectangle can be inscribed in a (unique circle), the important point is that the radius of the circle is R. (I think). One of the properties of a rectangle is that the diagonals bisect in the 'center,' which is also the center of the circumscribing circle.
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−3/8+(−2
9/10)
Enter your answer as a simplified fraction
The simplied form of the given fraction will be -3 11/40.
What are proper and improper fractions and how to convert mixed fraction to simple fraction?There is a fraction, containing numerator(upper value) and denominator(lower value). When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction. A proper fraction is also called fraction which is less than 1 an improper fraction is ≥ 1. A mixed fraction contains a sum of whole number and a proper fraction.
WE have been given an expression as;
−3/8+(−2 9/10)
Then first we will solve the mixed fraction;
−2 9/10 = -29/10
Now solve the fraction;
−3/8+-29/10
-131/40
In mixed number form:
-3 11/40
Hence, The simplied form of the given fraction will be -3 11/40.
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Find the value of 8 1/3
Answer: The answer is 25/3.
Step-by-step explanation: 8 1/3 = 8 x 3 + 1/3 = 24 + 1 = 25/3
-------- -----------
3 3
"a
4. Mr. Jensen's class was tracking the average
temperature each month. Given the data below,
calculate the slope and explain what it means in
context.
Month
Avg. Temp (°F)
Jan Feb
42 56
Mar
70
Apr
84
The slope of the given problem is 14
It is a problem of linear regression Line
y = a +by
where a = ∑Y - b ∑X / N
and b = N ∑XY - (∑X×∑Y)/ ( N∑x²- (∑X)
Month(X) Temperature (y) X² XY
1 42 1 42
2 56 4 112
3 70 9 210
4 84 16 336
Total 10 252 30 700
Number of observation (n) = 4
So, b = 4(700) - (10)(252) / ( 120 - 10²)
= 2800-2520/20
= 280/20
= 14
b = 14
Now a= 252 - (14)10/ 4
=112 /4
= 28
So, The linear regression line is
y= 28 + 14x
Slope = 14
The slope here is positive which means increase in period or moving forward in month is increasing the average temperature of the month.
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A 90 -inch board is cut into two pieces. One piece is two times the length of the other. Find the length of the shorter piece.
Answer:
30 inches
Step-by-step explanation:
We know that the total length of the board is 90 inches and we know that the shorter piece is two times smaller than the other so we have two pieces divided into three sections 90 divided by three is 30 and since we realize that 30x2=60 and 60+30=90 it means the longer board is 60 inches and smaller one is 30 I hope this helps.
What’s the negative exponent ??
Answer:
[tex]10 { }^{ - 5} [/tex]
Step-by-step explanation:
that is the answer above
How many quarts of pure antifreeze must be added to 7 quarts of a 10% antifreeze solution to obtain a 30% antifreeze solution?
Answer: 2 quarts of pure antifreeze are needed.
Step-by-step explanation:
Write an equation to solve each problem. The first stage of a rocket burns 28 s longer than the second stage. If the total burning time for both stages is 152s , how long does each stage burn?
Answer:
From the Soldier's point of view, the American Civil War was not a continuous battle. Instead, it was long monotonous marches and long residency in camps punctuated by the terror and chaos of combat. When winter set in and the campaigning season came to a close, most Soldiers counted on a long, cold stay in a winter camp. The four log cabins at the center of the Army Heritage Trail represent the types of buildings which Soldiers in both the Union and the Confederate Armies spent the long dreary months of winter. The cabins are modeled after images from the USAHEC collection, including the Army of the Potomac's winter camp at Brandy Station and the Confederate camp at Centerville
The square root of 16 to the second power -14 to the second power
Answer:
is it -180?
I don't remember most of this stuff!
sorry if its wrong
Step-by-step explanation:
The point N lies on the segment .
Find the coordinates of N so that is 1/3 of MP.
The coordinates of N so that MN is 1/3 of MP are:
(0,7/4)
In geometry line segment is a part of a line that is bounded by two end points, and contains every point on the that is between end points.
Given, coordinates of M(-3,-2)
and coordinates of P(9,13)
so we have,
x₁ = -3
y₁ = -2
x₂ = 9
y₂ = 13
Also we know that MN is 1/3 of MP
⇒ MN/MP = 1/3 = mn
here, m= 1 and n=3
Let the coordinates of N be (x,y)
Therefore,
(x,y) = (nx₁+mx₂)/(m+n) , (ny₁+my₂)/m+n
⇒ (x,y) = (3(-3)+1(9)/1+3) , (3(-2)+1(13)/1+3)
⇒ (x,y) = (-9+9/4) , (-6+13/4)
⇒ (x,y) = (0,7/4)
Thus the coordinates of N so that MN is 1/3 of MP is (0,7/4)
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Solve the equation. 3/5 a = 1/4 or \frac{3}{5} a = \frac{1}{4}
A -3
B 3/20
C 5/12
D 2
Answer:
C. 5/12
Step-by-step explanation:
Let's solve your equation step-by-step.
3/5a= 1/4
Step 1: Multiply both sides by 5/3.
(5/3)*(3/5a)=(5/3)*(1/4)
a = 5/12
Simplify the expression 36 + 63 ÷ 9.
record the letter of each graph with the given characteristics a has a vertical axis of symmetry
A parabola with a vertical axis of symmetry is graphed at the end of the answer.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), with a vertical axis of symmetry, is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
The most simple example of this is the parabola y = x², which is graphed at the end of the answer.
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For Every $100 he earns, Grayson Pays Federal income tax of $19. how much federal income tax will he pay on earnings of $500?
One of the particles in atoms is called an electron. It has
particle in atoms is a proton. It has charge of +1.
The overall charge of an atom is the sum of the charges of the electrons and the
protons. Here is a list of common elements.
The sum of an infinite geometric series is twice its first term.
b. Find the common ratio of the series.
The sum of an infinite geometric series is twice its first term then the common ratio(r) be 1/2.
What is an infinite geometric series?An infinite geometric series is the outcome of an unlimited geometric sequence. This series wouldn't have a finish. It is possible to calculate the sum of all finite geometric series. The terms in the sequence will grow steadily larger, but adding the larger numbers together will not provide a solution if the common ratio of an infinite geometric series is greater than one.
Given: S = 2a₁
a₁ be the first term
r be the common ratio
Let the equation be S = a₁/1-r
2a₁ = a₁/1-r
substitute the values in the above equation, we get
2 = 1/1-r
2 - 2r = 1
2r = 1
The value of r = 1/2
Therefore, the common ratio(r) be 1/2.
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If a car can travel 300 miles in 4 hours, how far can it go in an hour and a half?
Answer:
112.5miles
Step-by-step explanation:
4hrs=8 half hours
And 1hr30min=3 half hours
If a car travels 300miles in 8 half hours with the mathematical expression of
300miles-8hh
Then for the 3 half hour we have
X-3hh
Comparing the two
300miles-8hh
Xmiles-3hh
By cross multiplying
8×X=3×300
8X=900
X=900/8
X=112.5miles
through: (-2,-3) and (5,-3)
Answer:
0, -7 or Slope is Undefined
Step-by-step explanation:
y2 - y1 / x2 - x1
(x2 - y2) (x1 - y1)
Select the correct answer.
The spread of data set X is greater than the spread of data set Y, and the data sets are normally distributed. Which statement is true?
OA The mean of data set XIs greater than the mean of data set Y.
OB. The median of data set X is less than the median of data set Y.
OC. The standard deviation of data set Xis greater than the standard deviation of data set Y.
OD. The range of data set X is less than the range of data set Y.
O E.
The mode of data set X is greater than the mode of data set Y.
Answer:
C
Step-by-step explanation:
Just the spread of normally distributed data tells us nothing about the mean, mode or median, so answers A, B, and E are out of question.
The range is based on the difference between the highest and lowest elements. As there can be big outliers, we have no idea if D is true, although we expect distributions with bigger spread to generally exhibit bigger ranges.
We're left with answer C. Standard deviation is a measure of "how much the data can deviate from the mean". It's also one of the measures of spread. We expect data that's more spread out (higher spread) to have a higher standard deviation.
Write each equation in slope-intercept form. Then find the slope and y -intercept of each line. - [ (1/2)x - y ] = 3/4
The slope is 1/2 and the y-intercept is 3/4 in the equation - [ (1/2)x - y ] = 3/4.
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope
We know that the equation for slope(m) and y - intercept(c) of a line is given by :
y = mx + c
Here given the equation - [ (1/2)x - y ] = 3/4, lets simplify
⇒ - [ (1/2)x - y ] = 3/4
⇒ -(1/2)x + y = 3/4
⇒ y = (1/2)x + 3/4
Hence, the slope is 1/2 and the y-intercept is 3/4 in the equation - [ (1/2)x - y ] = 3/4
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