Answer:
1^0+5^0+9^0 = 3
Step-by-step explanation:
1^0 = 1
5^0 = 1
9^0 = 1
1^0+5^0+9^0= 1+1+1 = 3
Question -
If the ratio of the sums of first n^th terms of two AP's is (7n + 1):(4n + 27) find the ratio of their m^th terms.
[tex]\rule{200}4[/tex]
Answer : The required ratio is (14m-6):(8m+23) .
[tex]\rule{200}4[/tex]
Here we are given that the ratio of sum of first n terms of two AP's is (7n + 1):(4n + 27) .
That is.
[tex]\small\sf\longrightarrow \dfrac{S_1}{S_2}=\dfrac{7n +1}{4n +27} \\[/tex]
As , we know that the sum of n terms of an AP is given by ,
[tex]\small\sf\longrightarrow \pink{ S_n =\dfrac{n}{2}[2a +(n-1)d]} \\[/tex]
Assume that ,
First term of 1st AP = a First term of 2nd AP = a'Common difference of 1st AP = dCommon difference of 2nd AP = d'Using this we have ,
[tex]\small\sf\longrightarrow \dfrac{S_1}{S_2}=\dfrac{\dfrac{n}{2}[2a + (n-1)d]}{\dfrac{n}{2}[2a' +(n-1)d'] } \\[/tex]
[tex]\small\sf\longrightarrow \dfrac{7n+1}{4n+27}=\dfrac{2a + (n -1)d}{2a' + (n -1)d' } . . . . . (i) \\[/tex]
Now also we know that the nth term of an AP is given by ,
[tex]\longrightarrow\sf\small \pink{ T_n = a + (n-1)d}\\[/tex]
Therefore,
[tex]\longrightarrow\sf\small \dfrac{T_{m_1}}{T_{m_2}}= \dfrac{ a + (n-1)d }{a'+(n-1)d'}. . . . . (ii)\\[/tex]
[tex]\longrightarrow\sf\small \dfrac{T_1}{T_2}=\dfrac{2a + (2n-2)d}{2a'+(2n-2)d'} . . . . . (iii)\\[/tex]
From equation (i) and (iii) ,
[tex]\longrightarrow\sf\small n-1 = 2m-2\\[/tex]
[tex]\longrightarrow\sf\small n = 2m -2+1 \\[/tex]
[tex]\longrightarrow\sf\small n = 2m -1 \\[/tex]
Substitute this value in equation (i) ,
[tex]\longrightarrow \sf\small \dfrac{2a+ (2m-1-1)d}{2a' +(2m-1-1)d'}=\dfrac{7(2m-1)+1}{4(2m-1) +27}\\[/tex]
Simplify,
[tex]\longrightarrow\sf\small \dfrac{ 2a + (2m-2)d}{2a' +(2m-2)d'}=\dfrac{14m-7+1}{8m-4+27}\\[/tex]
[tex]\longrightarrow\sf\small \dfrac{2[a + (m-1)d]}{2[a' + (m-1)d']}=\dfrac{ 14m-6}{8m+23}\\[/tex]
[tex]\longrightarrow\sf\small \dfrac{[a + (m-1)d]}{[a' + (m-1)d']}=\dfrac{ 14m-6}{8m+23}\\[/tex]
From equation (ii) ,
[tex]\longrightarrow\sf\small \underline{\underline{\blue{ \dfrac{T_{m_1}}{T_{m_2}}=\dfrac{ 14m-6}{8m+23}}}}\\[/tex]
[tex]\rule{200}4[/tex]
45:60 as its simplest form
Answer :
3/4.
Explanation
Find the GCD (or HCF) of numerator and denominator
GCD of 45 and 60 is 15
Divide both the numerator and denominator by the GCD
45 ÷ 15
60 ÷ 15
Reduced fraction: 3/4
Therefore, 45/60 simplified to lowest terms is 3/4.
Hi! I hope you are enjoying your day!
In order to simplify this ratio (and 45:60 is a ratio), we should divide both sides of the ratio by 5 (because both 45 and 60 are evenly divisible by 5)
Divide:
9:12
Is the ratio in its simplest form? No.
Why?
Because 9 and 12 can be divided by 3:
3:4
Now the ratio IS in its simplest form.
Hence, the answer is
[tex]\boxed{\boxed{\bold{3:4}}}[/tex]
Hope everything is clear.
If you have any questions, please comment.
#LearningIsFun
Find m
?/1
U
T
30
19
s
97°
R
21
Answer:
Sis 97,U is 30,Tis19,R is 21and m is 37
What type of triangle is a 30, 40, 50
Answer:
Pythagoras's Theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides. Actually a 30 , 40 , 50 triangle is just a scaled up 3 , 4 , 5 triangle, which is a well known right angled triangle
Step-by-step explanation:
please mark me as brainlist please
HELPPPP
F(x)=-x^2-3x+1
The quadratic function, f(x )or g(x) has the greater maximum value ??
Answer:
The quadratic function, f(x) has the greater value.
Step-by-step explanation:
The given function written to us is in standard form, meaning it is easy to graph this function.
Since this function is going to open down-ward, we start with negative numbers.
[tex]f(-1)=3\\[/tex]
Since 3 is a greater value than 2, which we can see is the maximum value of g(x) by viewing the graph, f(x) is greater.
Please help me out. I'll give BRAINLIEST, 5 stars and thanks!
Think a moment about factoring a polynomial by finding the GCF.
Explain the role of the GCF in factoring a polynomial.
Where is the GCF placed after factoring the GCF?
How do you verify factoring is correct?
Answer/Step-by-step explanation:
Explain the role of the GCF in factoring a polynomial.
The role of the GCF in factoring a polynomial is the largest monomial that divides evenly into each term. GCF is a factor that is shared by all terms within a polynomial. For instance, if we have a polynomial of the form A*B + A*C, the GCF is A since both terms have A as a factor.
Where is the GCF placed after factoring the GCF?
After factoring out the GCF, it's placed outside the parentheses, in front of the rest of the polynomial. Like the sample we previous use A*B+A*C = A(B+C).
How do you verify factoring is correct?
To Verify factoring is correct distributing the GCF to the polynomial within the parentheses.
~Learn with Lenvy~
brainliest for free if you can solve this equation 3+5 +7 -6
Answer:
The answer is
→ 9
Step-by-step explanation:
[tex]3+5+7-6=9[/tex]
Therefore, 9 is your answer.
3x +y = –15
-3x - 4y = 30
Which variable will eliminate in the system?
Answer:
x should be eliminated
hope it helps
Which can be the first step in finding the equation of the line that passes through the points (5, negative 4) and (negative 1, 8) in slope-intercept form?
Calculate StartFraction 8 minus (negative 4) Over negative 1 minus 5 EndFraction = StartFraction 12 Over negative 6 EndFraction = negative 2..
Calculate StartFraction negative 1 minus 5 Over 8 minus (negative 4) EndFraction = StartFraction negative 6 Over 12 EndFraction = negative one-half..
Find that the point at which the line intersects with the line y = 0 is (3, 0).
Find that the point at which the line intersects with the line x = y is (2, 2).
Answer:
Step-by-step explanation:
its A :)
Answer= y=2x+6
The slope-intercept form of an equation of a line: y=mx+b
m - slope
b - y-intercept
We have the points (5, -4) and (-1, 8). Substitute:
m= [tex]\frac{8-(-4)}{-1-5}[/tex] =[tex]\frac{12}{-6}[/tex] =-2
Put the value of the slope and the coordinates of the point (5, -4) to the equation of a line,
-4=-2(5)+b
=-10+b
6=b
y=2x+6
Britney is buying a shirt and a hat at the mall. The shirt costs $31.99, and the hat costs $19.89. If Britney gives the sales clerk $100.00, how much change should she receive? (Ignore sales tax.)
A. $45.02
B. $57.87
C. $48.12
D. $51.88
Answer:
C
Step-by-step explanation:
100-31.99-19.89=48.12
Please help me!!!! Both questions! Find the GCFs:!!
Answer:
See below.
Step-by-step explanation:
28x^2yz and 16xy^2
GCF of 28 and 16: 4
GCF of x^2yz and xy^2: xy
The GCF is 4xy.
5x^2y^4, 10x^3y^5, and 15xy^2
GCF of 5, 10, and 15: 5
GCF of x^2y^4, x^3y^5, and xy^2: xy^2
The GCF is 5xy^2.
-hope it helps
Hi! Hope you're enjoying your day!
First of all, the G.C.F. stands for
Greatest Common Factor
So we need to find the Greatest Common Factor of the polynomials.
And yea, polynomials have Greatest Common Factors as well.
So, let's find all the Greatest Common Factors. :)
First, we have
[tex]\bold{28x^2yz}[/tex] and [tex]\bold{16xy^2}[/tex]
What are the common factors of these polynomials?
Well, there are plenty of them, like 2, 2x, y...
What is the Greatest Common factor?
Is it Option A, 12xy?
No, because neither 28 nor 16 is divisible by 12.
So we cross out Option A.
Is it Option B, 8xy?
No, because 28 isn't divisible by 8, and remember, if a number is evenly divisible by another number, then that number is a factor.
Example: 8 is a factor of 16 (16÷8=2); 8 is not a factor of 28, because
28÷8=3.5 (a decimal, not a whole number)
Is it Option C, 4xy?
Yeah, it seems like Option C is the right option.
[tex]\huge\checkmark[/tex]Both 28 and 16 are divisible by 4
[tex]\huge\checkmark[/tex]Both polynomials have an x and a y in them
[tex]\rule{250}{2}[/tex]
Find the GCF:
[tex]\bold{5x^2y^4,\:10x^3y^5, \:and\:15xy^2}[/tex]
Once again, is it Option A, 5x^3y^5?
No, because
✘ 5 and 10 aren't divisible by 3
✘ None of the 3 polynomials has a 3y term
In other words, Option A is wrong.
How about Option B?
You should see right off the bat that 5 and 15 aren't divisible by 10.
So now we have 2 options left.
Is it Option C, 5xy²?
Well,
✓All 3 polynomials are divisible by 5
✓ All 3 polynomials have a y² term
✓ All 3 polynomials have an x term.
Hence, the answers are
[tex]\boxed{\boxed{\bold{1. \;Option\;C; 2.\;Option\;C.}}}[/tex]
Hope everything is clear.
If you have any questions, please comment.
#LearningIsFun
[tex]\rule{200}{2}[/tex]
please help me again I have 2 tries again please and explain, please
Answer:
8
Step-by-step explanation:
→ Find width of first painting
48 ÷ 6 = 8
→ Find length of second painting
64 ÷ 8 = 8
ANSWER ASAP!!!! BRAINLIEST FOR THE PEOPLE WHO MAKE IT
Answer:
no idea
Step-by-step explanation:
The total remodeling budget for Central Square Tower is 1.5×106 dollars. The owners of the building have set aside 6×105 dollars for upgrading just the lobby. What percent of the budget will be spent on the lobby? Write your answer in standard form. Do not write exponents.
Answer:
40%
Step-by-step explanation:
assuming you actually mean 10^5 and 10^6, to find percentages you do
part/total x percent/100
you have (6x10^5/1.5x10^6) x (x/100)
cross multiply, and you have 6x10^7=1.5x10^6x
divide on both sides by 1.5x10^6
x=40
so the answer is 40%
Calculate the volume of this prism
Answer:
800 cm³
Step-by-step explanation:
The volume is the product of the base area and the "height" of the prism. Here, the base can be considered to be a 10 cm × 12 cm rectangle with a 4 cm × 5 cm cutout. Its area will be ...
A = (10 cm)(12 cm) -(4 cm)(5 cm) = 120 cm² -20 cm² = 100 cm²
The product of this base area and the 8 cm height of the prism is ...
V = Bh = (100 cm²)(8 cm) = 800 cm³
The volume of the prism is 800 cm³.
The circumference of a circle is 7.5. What is it’s diameter?
What is the sum of 12-5i and 3 + 4i?
•-16 + 63
•9-i
•9-9i
•15-9i
Answer: 2nd option: 9-i
Step-by-step explanation:
We can add the numbers and the terms with i separately.
12 - 5i - 3 + 4i = (12 - 3) + (-5i + 4i)
= 9 + (-i)
*Adding a negative is essentially subtracting a positive*
= 9-i
Daina gives of his money to Carol. Carol gives of this money to Zak.
What fraction of Daina's money does Zak get?
Step-by-step explanation:
yo question doesn't make sense.
5 times 5 to the power of 2 in index form
Answer:
=5x5x5
Step-by-step explanation:
5x5^2
=5x(5x5)
=5x5x5
Answer:
625
Step-by-step explanation:
5×5 to the power of 2
25 to the power of 2
25×25 = 625
-.27(x-2.9t)^2+2.56 in standard form?
Please provide steps. Thank you!
Answer:
[tex]-\frac{27(-\frac{20t}{10}+x)^{n} }{50} +2.56[/tex]
Step-by-step explanation:
What is the slope of line a?
Answer:
1/3
Step-by-step explanation:
The slope of a line represents the variation in height per variation in length.
In our case, for every square you move up, you have to move 3 horizontally. The slope is thus
m= (vertical change) / (horizontal change) = 1/3
Answer:
1/3
Step-by-step explanation:
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
12y - 9x = -36
length=9in width=2in height=3in. what is the surface area
Answer:
102in2
Step-by-step explanation:
The formula for surface area is 2(wl+hl+hw). So plug in the measurements of the prism into the formula to get 102.
Sarah has two sets of cards. The first set of 26 cards is labeled with all the letters of the English Language. The second set of 10 cards is numbered 0 through 9.
If Sarah draws one lettered card and one numbered card at random, what is the probability of her drawing a letter in her name and an odd number? (Enter answer as a reduced fraction).
Answer:
1/13
Step-by-step explanation:
Probability of Sarah drawing a letter in her name
= number of letters in her name: S, A, R and H / total number of letters
= 4/26
Probability of drawing an odd number
= odd numbers / total numbers
= 5/10
Combining the above, Probability of her drawing a letter in her name and an odd number = 4/26 * 5/10
= 1/13
Total Alphabetical cards Sarah has ⇢ 26
Total Letters Sarah's name has ⇢ 4
Probability of getting a card with one of the letter in her name ⇢ 4/26
Total numerical Cards Sarah has ⇢ 10
Total odd numbers in those cards⇢5
Probability of getting a card with an odd number⇢ 5/10
probability of her drawing a letter in her name and an odd number⇢ 4/26 x 5/10 = 1/13
need help can anyone help
Answer:
1: 23
2: 15/3 which reduces to 5
3: 12/4 which reduces to 3
Step-by-step explanation:
used a calculator
What is the circumcenter of ΔABC, if A(-7, 3); B(9, 3); and C(-7, -7)?
Answer: (1,-2)
Step-by-step explanation:
What is the value of e
Answer:
E = 27.125
Step-by-step explanation:
Hope this helps you.
Answer:
e=56
Step-by-step explanation:
since the denominator is 8, what can you divide by 8 to get something that you can add to 23 and get 30.
30-23=7
56//8=7
Find the hypotenuse round to the nearest hundredth
Answer:
8.94
Step-by-step explanation:
hypotenuse=h
h=4^2+8^2
h=16+64
h=80
h=√80
h=8.94
Answer:
Step-by-step explanation:
[tex]hypotenuse=\sqrt{4^2+8^2} =\sqrt{16+64} =\sqrt{80}\approx 8.94[/tex]
5²+1=x, what is x? please help
Answer:
26
Step-by-step explanation:
[tex]5^{2}[/tex] = 5 · 5 = 25
then add 1
Answer:
26
Step-by-step explanation:
(5 x 5) + 1
25 + 1
26
Have an amazing day!!!
PLEASE RATE AND MARK BRAINLIEST!!!
please help me ASAP please help me with my homework please solve this please both Problem A and B please I beg you
Answer:
A.
1. x = -5
2. x = -1
3. x = -2
4. x = 25/9
5. x = 1
B.
1. x ≤ 2
2. - 3≤ x ≤ 6
3. x ≤ 2
4. x ≤ 33/2
5. x ≤ 17/3
Step-by-step explanation:
Brainliest me please I answer it!!
A.
1. 5x + 12=2x-3
5x-2x= -12-33x/3= -15/3x = -52. 3x+6= -2x+1
3x+2x= -6+15x/5= -5/5x= -13. (x/2-4x=7)x2
2(x/2) - 2(4x)=7x2x-8x=14-7x/-7=14/-7x= -24. 1.4x - 0.4x=6.2+3.8
1x/1=10/1x=105. 5x-10+2x=7x+28-38
5x+7x-10=7x+28-3812x-10=7x+28-3812x-7x=28+10-385x=38-385x/5=0/5x=0B.
1. 2x/2 ≤ 4/2
x=22. 2x+3 > -3
2x+3< 15
x= -3x= 6X=(-3,6)3. 5x-4 >6
5x>6+45x/5 >10/5x >24. (2x./3+1/2>x-5)x6
6(2x/3)+6(1/2) > 6(x-5)4x+3 > 6x-304x-6x>-30-3-2x/-2 > -33/-2x< 33/25. 0.8+0.6x ≥4.2
0.6x≥4.2-0.80.6x/0.6 ≥3.4/0.6x= 5.666666667