Given that the 10th term of an AP is 45 and that the sum
of the first 10 terms is 270 find
a) The first term
b) The common difference
c) The sum of the first 15 terms
A) The first term of the AP is; 9
B) The common difference of the AP is; 4
C) The sum of the first 15 terms of the AP is; 555
Formula for nth term of an AP is;
a_n = a + (n - 1)d
Where;
a is first term
n is number of terms
d is common difference between consecutive terms
We are told the 10th term is 45
Thus;
45 = a + (10 - 1)d
a + 9d = 45 - - - (1)
Formula for sum of n terms of an AP is;
S_n = (n/2)(2a + (n - 1)d)
Sum of first 10 terms is 270. Thus;
270 = (10/2)(2a + (10 - 1)d)
5(2a + 9d) = 270
2a + 9d = 270/5
2a + 9d = 54 - - - (2)
Solving both equations simultaneously gives;
a = 9 and d = 4
Thus;
First term = 9
Difference = 4
Sum of first 15 terms is;
S_15 = (15/2)(2(9) + (15 - 1)4)
S_15 = 7.5(18 + 56)
S_15 = 555
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Will the sign of the product of two negative numbers be negative or positive? Explain your answer.
A.
Cannot tell; the sign depends on the absolute values of the factors.
B.
Negative; if either of the factors is negative, their product is negative.
C.
Negative; if the signs of the two factors are the same, their product is negative.
D.
Positive; if the signs of the two factors are the same, their product is positive.
Answer:
A
Step-by-step explanation:
Answer:
D if the signs of two factors are the same, their product is positive
Which list orders the numbers from least to greatest?
–2.6, 5.1, 0.8, –2.16, 0.58
0.58, 0.8, –2.16, –2.6, 5.1
–2.16, –2.6, 0.8, 0.58, 5.1
–2.16, –2.6, 0.58, 0.8, 5.1
–2.6, –2.16, 0.58, 0.8, 5.1
Answer:
-2.6,-2.16,0.58,0.8,5.1
Step-by-step explanation:
Trust me
Answer:
d
Step-by-step explanation:
A 100 - sqaure grid has 70 shaded sqaures . Explain how you could express this model as a fraction , percent , and decimal.
Answer:
Would it be 70/100 as a fraction and 0.7 as a decimal and 70% as a percentage?
Step-by-step explanation:
If you have 100 squares and 70 of those squares are shaded, your answer would 70/100.
20 point if you get it right I’ll mark brainiest
Answer:
8 , - 4 , 1
Step-by-step explanation:
Coefficient of 8x³ = 8
Coefficient of (-4x²) = -4
Coefficient of x = 1
What is the equation of the line that passes through the point (1,3) and has a slope of 6
awensr ex y=-x+6
Answer:
Y=6x+-3
Step-by-step explanation:
Deltamath
Select the correct answer.
A basketball team played 15 games and won 80% of them. If the team expects to play 30 games in all, how many more games must it win to
finish the season with a 90% winning percentage?
A.12
B.14
C.15
D.27
Answer:
C
Step-by-step explanation:
First find how many games they need to have 90% by multiplying .9(30)=27
then, 15(.8)=12
Then 27-12=15
Answer:
c
Step-by-step explanation:
One angle of a parallelogram measures 15º. What are the measures of the other three angles in
the parallelogram?
Answer:
The opposite angle is 15 degrees. So that leaves you with 330 degrees for the last two sides which is 115 degrees each.
What is 903 divided by 72?
33 POINTS FOR THIS QUESTION!!
Answer:
12.5416667
Step-by-step explanation:
Solve 2x2 - 126 = 0. Make sure to simplify if
necessary.
-122
sorry if i am wrong but have a good day<3
A rotation by 2520° is how many full rotations?
O 10
O 5
07
O 14
7
a full rotation is 360°
divide 2520 by 360 it gives u 7.
7×360=2520
There are 7 complete rotations at 2520 degrees. Then the correct option is C.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
A rotation by 2520°.
Then the number of the rotations will be
⇒ 2520° / 360°
⇒ 7 rotation
Thus, the correct option is C.
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PLEASE HELP
This is due TODAY
Answer:
10) m = rise/run = 3/4 11) y = 2x - 3
Step-by-step explanation:
A jewelry maker is designing a crown. The crown must have at least 45 gems, only using emeralds, rubies, and diamond the number of diamonds must be 4 less than the number of rubies. Which inequality could the jewelry maker use to find the fewest numbers of emeralds, x, that can be placed on the crown
Answer:
X is the variable and x means multiplication symbol.
X + (X x 3 - 1) + (X x 3 - 1) - 4) ≥ 45 is the answer I got.
The answer to that inequality would be
X ≥ 7
Step-by-step explanation:
I am not good at math I just tried my best sorr if it is wrong.
Answer:
Diamonds: 20 Emeralds: 1 Rubies: 24
Step-by-step explanation:
45 = Total
Diamonds = 20 (4 less than rubies)
Emeralds = 1 (made into the smallest number)
Rubies = 24 (4 more than diamonds)
Tip! To help find the answer I divided 45 into three groups so the diamonds, emeralds, and rubies all started with 15. I then started to work it into place where diamonds were ALWAYS 4 less than rubies and just kept taking away from emeralds.
<3 Enjoy,
Dea
I DESPERATELY NEED HELP PLZ ANSWER THESE QUESTIONS I AM TIMED AND DON"T HAVE MUCH TIME LEFT
Answer:
Ok I will help you answer the first one the rest yourself?
Step-by-step explanation:
So the question is
6(r-s+t)
we have to time each number by 6
6r-6s+6t
That's how we can simply so the answer is 6r-6s+t
Same thing goes with the others
Hope it helps 0w0
A number divided by 43 has a quotient of 3 with 28 as a remainder. Find the number.
The number when divided by 43 has a quotient of 3 with 28 as a remainder is 157
The number is 157
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 number be = A
Now , the equation will be
A number divided by 43 has a quotient of 3 with 28 as a remainder
So , A / 43 = 3 + 28/43 be equation (1)
On simplifying the equation , we get
A / 43 = 3 + 28 / 43
A/43 = ( 3 x 43 + 28 ) / 43
Multiply by 43 on both sides of the equation , we get
A = 3 x 43 + 28
A = 129 + 28
A = 157
Therefore , the value of A is 157
Hence , The number when divided by 43 has a quotient of 3 with 28 as a remainder is 157
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x delivery persons carry a total of B bags of groceries up the stairs. They can each carry y bags at a time, and they each make 2 trips up the stairs.
Write an equation that relates x, B, and y.
Answer:
B= 2xy
Example:
2 delivery persons carry a total of 4 bags of groceries up the stairs. they can each carry 1 bag at a time, and they make 2 trips up the stairs.
The equation relaated to x, B, and y is B= 2xy.
What is an equation?
An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
2 delivery persons carry a total of 4 bags of groceries up the stairs. they can each carry 1 bag at a time, and they make 2 trips up the stairs. Then the equation is,
B =2xy
Here, B = Total Bags , x = Delivery persons and y = Number of bags.
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Use the information in the figure. Find m
Answer:
Its 32
Step-by-step explanation:
you need to get 180 degrees altogether
819 3/10 simplified?
Answer: 819.3
Step-by-step explanation:
Answer:
Exact form: 8193/10 Decimal form: 819.3 Mixed number form: 819 3/10
Step-by-step explanation:
I believe this is the answer idk... UwU
In one weekend, a theatre sells 61,366 tickets to a new movie. Write the values for each of the 6s in 61,366.
The values of the 6s are
Answer:
60,000, 60, 6.
Step-by-step explanation:
just separate the numbers into sections and boom
whats the answer giving brainliest to the c o rect anwers
Answer:
A
Step-by-step explanation:
9/3 is 3
36-3 is 33
PLZ HELP!!!!
A circle has a diameter of 5 inches show your work to find to fallowing (use 3.14 for pi) A) area of circle B) circumference of the circle
Answer:
Area:19.63
circumference:15.71
Step-by-step explanation:
A=πr2
d=2r
A=1/[tex]\frac{1}{4} \pi d^{2}[/tex]4π d2=1 4·π·52≈19.63495
C=2πr
d=2r
c=[tex]\pi[/tex]d=[tex]\pi[/tex]·5=15.70796
Answer:
I think its A) Fresh
Step-by-step explanation:
Srry if its wrong
The segments shown below could form a triangle.
A. True
B. False
answer TRUE because they would make a triangle
If P= {2, 3, 5, 7, 11, 13, 17, 19}, what is n(P)?
Answer:
Mark a s brainliest
Step-by-step explanation:
We are given the set:
P = {2, 3, 5, 7, 11, 13, 17, 19}
The n( ) function of a set is used to find out the number of elements in a set [also known as the cardinality of a set]
To find out the cardinality of a set, we usually count the number of terms in the set but keep in mind that ∅ (null) is an element of every set there is. So, the given set can be re-written as:
P = {∅, 2, 3, 5, 7, 11, 13, 17, 19}
From this, we can clearly see that there are 9 elements in this set
Therefore, the n(P) (cardinality) of this set is 9
how many times does 4 go into 55
Answer:
13 times
Step-by-step explanation:
4 * 13 is 52 and 55 - 52 is 3 if you add 4 to 52 it would be 56 not 55
can someone please solve this 5+2x=7+3x
Simplifying
2x + -7 = 3x + 5
Reorder the terms:
-7 + 2x = 3x + 5
Reorder the terms:
-7 + 2x = 5 + 3x
Solving
-7 + 2x = 5 + 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation.
-7 + 2x + -3x = 5 + 3x + -3x
Combine like terms: 2x + -3x = -1x
-7 + -1x = 5 + 3x + -3x
Combine like terms: 3x + -3x = 0
-7 + -1x = 5 + 0
-7 + -1x = 5
Add '7' to each side of the equation.
-7 + 7 + -1x = 5 + 7
Combine like terms: -7 + 7 = 0
0 + -1x = 5 + 7
-1x = 5 + 7
Combine like terms: 5 + 7 = 12
-1x = 12
Divide each side by '-1'.
x = -12
Simplifying
x = -12
What is 17/40 written as a decimal?
Answer:
0.425
Step-by-step explanation:
division of 17/40
Twice a number q minus 1 is less than 5
Answer:
2q - 1 < 5
If you're trying to solve for q...
q < 3
Step-by-step explanation:
I'm not sure if you were asking for the inequality or the answer for q... but I'll gladly explain either if you need :)
Rewrite the expression by factoring out (y-8).
3y^2(y-8)+7(y-8)
Answer
(y-8)x(3y^+7)
Step-by-step explanation:
3y^2(y-8)+7(y-8)
(y-8)x(3y^+7)
An expression is defined as a set of numbers, variables, and mathematical operations. The given expression 3y²(y-8)+7(y-8) can be rewritten by factoring out (y-8) as (3y²+7)(y-8).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression can be rewritten by factoring out (y-8) as,
3y²(y-8) + 7(y-8)
= (3y²+7)(y-8)
Hence, The given expression 3y²(y-8)+7(y-8) can be rewritten by factoring out (y-8) as (3y²+7)(y-8).
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Is 5/6 larger or 2/3? Pls help.........
Answer:
yes 5/6 is bigger
Step-by-step explanation:
Estimate 1/3 times 28
Answer:
9.333333
Step-by-step explanation:
28/3=28(1/3)
Answer
About 9
Explanation
1/3 times 28 is 9 1/3.
9 1/3 is closest to 9.