Step-by-step explanation:
1. In an arithmetic sequence, the general term can be written as
xₙ = y + d(a-1), where xₐ represents the ath term, y is the first value, and d is the common difference.
Given the third term and the fifth term, and knowing that the difference between each term is d, we can say that the 4th term is x₃+d and the fifth term is the fourth term plus d, or (x₃+d)+d =
x₃+2d. =x₅ Given x₃ and x₅, we can subtract x₃ from both sides to get
x₅-x₃ = 2d
divide by 2 to isolate d
(x₅-x₃)/2 = d
This lets us solve for d. Given d, we can say that
x₃ = y+d(2)
subtract 2*d from both sides to isolate the y
x₃ -2*d = y
Therefore, because we know x₃ and d at this point, we can solve for y, letting us plug y and d into our original equation of
xₙ = y + d(a-1)
2.
Given the third and fifth term, with a common ratio of r, we can say that the fourth term is x₃ * r. Then, the fifth term is
x₃* r * r
= x₃*r² = x₅
divide both sides by x₃ to isolate the r²
x₅/x₃ = r²
square root both sides
√(x₅/x₃) = ±r
One thing that is important to note is that we don't know whether r is positive or negative. For example, if x₃ = 4 and x₅ = 16, regardless of whether r is equal to 2 or -2, 4*r² = 16. I will be assuming that r is positive for this question.
Given the common ratio, we can find x₆ as x₅ * r, x₇ as x₅*r², and all the way up to x₁₀ = x₅*r⁵. We don't know the general term, but can still find the tenth term of the sequence
The sum of two integers is -360. One of them is 60, then the other integer is
X^2 + bx + 49 is a perfect squad trinomial what is one possible value of b? & I need help with the others also due soon!
20. (2) 14
A perfect square trinomial will factor into two expressions that are the same, for example: x^2 + 6x + 9 = (x + 3)(x + 3). Since this problem has a C value of 49, it will factor into (x + 7)(x + 7). 7 doubled is 14, therefore one possible value of B is 7.
21. (4) 2, -12
x^2 + 10x + 25 = 24 + 25
(x + 5)^2 = 49
x + 5 = +/- 7
x = 2, -12
22. (3) 3 + sqrt(17)
x^2 - 6x = 8
Complete the Square
x^2 - 6x + 9 = 8 + 9
(x - 3)^2 = 17
x - 3 = +/- sqrt(17)
x = 3 + sqrt(17), 3 - sqrt(17)
23. (1) 1, -5
x^2 + 4x - 5 = 0
x^2 + 4x = 5
x^2 + 4x + 4 = 5 + 4
(x + 2)^2 = 9
x + 2 = +/- 3
x = 1, -5
Hope this helps!
find the solution to this system of equations x+y=1
2x-y+z=1
x+2y+z=8/3
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Answer:
(x, y, z) = (1/3, 2/3, 1)
Step-by-step explanation:
We can use the first equation to write an expression for x that can be substituted into the other equations.
x = 1 -y
2(1 -y) -y +z = 1 ⇒ -3y +z = -1
(1 -y) +2y +z = 8/3 ⇒ y +z = 5/3
Subtracting the first of these equations from the second gives ...
(y +z) -(-3y +z) = (5/3) -(-1)
4y = 8/3
y = 2/3
z = 5/3 -y = 1
x = 1 -y = 1/3
The solution is (x, y, z) = (1/3, 2/3, 1).
Which of the following choices shows the complete factorization of 50?
52 • 5
2 • 25
52 • 2
None of these choices are correct.
Hello can anyone answer this question please I need help
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Answer:
maximum: 40(8/3, 8/3)Step-by-step explanation:
The graph shows the relevant vertex of the feasible region is ...
(x, y) = (8/3, 8/3).
The value of z there is ...
z = 11(8/3) +4(8/3) = (88 +32)/3
z = 40
An investor puts $800 into an account that pays 7.5% interest compounded annually. The total amount A in the account after t years is given by which function below?
A = 800(1.75) ^t
A = 800(1.075) t
A = 800(1.075)^ t
A = 800 + (1.075)^ t
Answer:
A = 800( 1.075)^(t)
Step-by-step explanation:
The equation for interest is
A = p (1+r/n) ^ nt where p is the principle, r is the interest rate, n is the number of times per year and t is the years
A = 800( 1+ .075/1)^(1*t)
A = 800( 1.075)^(t)
Let's see
[tex]\\ \tt\leadsto A=P(1+r/n)^{nt}[/tex]
n is 1[tex]\\ \tt\leadsto A=P(1+r)^t[/tex]
[tex]\\ \tt\leadsto A=800(1+0.075)^t[/tex]
[tex]\\ \tt\leadsto A=800(1.075)^t[/tex]
Option C
What is the different of (5-3x) and (5x-10)
a. 8x-5
b. 15-8x
c. 8x + 15
d. none of the above
Answer:
15 - 8x
Step-by-step explanation:
Remark
This all depends on how you read the question. In other words, which comes first 5 - 3x or 5x - 10. It's not clear.
If you do the first one first, you get
5 - 3x - (5x - 10) Remove the brackets.
5 - 3x - 5x + 10 Collect like terms
15 - 8x So that makes the middle one correct.
Now do it the other way.
5x - 10 - (5 - 3x)
5x - 10 - 5 + 3x
8x - 15
That answer isn't available here. So ..
The answer is 15 - 8x
give me examples of equivalent expressions of square root 54 with a radican of 3
Which expression is equivalent to 7√x^2/5√y^3? Assume y≠0
Answer:
Step-by-step explanation:
If the √y³ term is in the denominator, then the expression needs to be written with parentheses: 7√x²/(5√y³)
in a class, 64 offers mathematics while 94 offers chemistry , How many will offer the both course?
Answer:
30
Step-by-step explanation:
94-64=30 will offer the same course because the chemistry offers ocerride the mathematics offers
8 and 1/3divided by 3 and 4/7
Ravi bought 50kg rice at the rate of tk.40 per kg and sold it at the rate of tk.44 per kg. What is the percentage of profit
He paid 0.40 x 50 = 20
He sold it for 0.44 x 50 = 22
His profit was 22-20 = 2
Percentage was 2/20 = 0.10 = 10 %
Answer 10 %
in a small town in New York, we initiated a cohort study and followed 5,900 people for a mean follow-up of 2 years. At the end of the 2nd year, none of the participants was lost to follow-up. During this follow-up, we identified 600 cases of malaria. What was the cumulative incidence?
a. 10.1%
b. 10.1 per 1,000
c. 50.8%
d. 10 cases
Answer:
Option A
Step-by-step explanation:
From the question we are told that:
Sample size n=5900
Number of newly developed cases No.C=600
Generally the equation for Cumulative Incidence is mathematically given by
[tex]CI=\frac{No.C}{n}[/tex]
[tex]CI=\frac{600}{5900}[/tex]
[tex]CI=0.101[/tex]
[tex]CI= 10.1%[/tex]
Option A
A tennis coach divides her 9-player squad into three 3-player groups with each player in only one group. How many different sets of three groups can be made?
Answer:
84
9 choose 3
Step-by-step explanation:
Proving the Single Opposite Side Pair Theorem
Given: AD = BC and AD || BC
Prove: ABCD is a parallelogram.
Angles Segments Triangles Statements Reasons
ZBCA
ZDAC
А
Statements
Reasons
B
D
с
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
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Explanation:
1. AD ≅ BC, AD ║ BC . . . . given
2. ∠DAC ≅ ∠BCA . . . . alternate interior angles theorem
3. AC ≅AC . . . . reflexive property
4. ΔDAC ≅ ΔBCA . . . . SAS postulate
5. AB ≅ CD, ∠BAC ≅ ∠DCA . . . . CPCTC
6. AB ║ CD . . . . converse of alternate interior angles theorem
7. ABCD is a parallelogram . . . . definition of a parallelogram (has 2 pairs of parallel & congruent sides)
_____
We don't know what your tiles/choices are for statements or reasons. We have shown the triangles are congruent, so their corresponding parts (sides/angles) are congruent. That lets us claim opposite sides are congruent and parallel. YMMV
Answer:
Picture Down Below
Step-by-step explanation:
solve for "X" where x±4=12
Answer:
x = 8, 16
Step-by-step explanation:
x + 4 = 12
x = 12- 4
x = 8
x - 4 = 12
x = 12 + 4
x = 16
find the product using suitable product 854×102 step by step explanation
Answer:
87108
Step-by-step explanation:
854 x 102
= 854 x ( 100 + 2 )
= 854 ( 100 ) + 854 ( 2 )
= 85400 + 1708
= 87108
What is the remainder of 119 divided by 4
The remainder when dividing 119 by 4 is 3.
We have,
To find the remainder when dividing 119 by 4, we perform the division and observe the remainder.
When we divide 119 by 4, we get:
119 ÷ 4 = 29 remainder 3
The quotient is 29, which means that 4 goes into 119 twenty-nine times without any remainder.
However, there is a remainder of 3.
Therefore,
The remainder when dividing 119 by 4 is 3.
Learn more about expressions here:
https://brainly.com/question/3118662
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Find the value of x on this triangle
Answer:
33
a2+b2 =c2
a2+ 33 squared = 55 squared
a + 1936 = 3025
3025-1936=1089
square root of 1089 is 33
pleeeaaasssseeee mark as brainliest
A baseball is projected upward at 64 feet per second. It can be approximated by the equation -16t^2+64t. The baseball reaches it maximum height at the vertex. That can be gotten from x= −/2a . How long until the baseball reaches its full height? Note a quadratic equation can be written as ax^2+bx+c
Answer:
f(t) = -16t²+64t
t = number of secondsf(t) = height (in feet)The x-coordinate(t) of the vertex can be found using formula [tex]\frac{-b}{2a}[/tex], where:
a = -16b = 64Therefore the t-value of the vertex is:
[tex]\frac{-64}{2(-16)} =\frac{-64}{-32} =2[/tex]
The baseball will reach its maximum height after two seconds.
What is the least possible degree of a polynomial that has the root -3 + 2i, and repeated root -2 that occurs twice?
4
3
2
5
Answer:
4
Step-by-step explanation:
complex roots always occur in pairs.
so roots are -3+2i,-3-2i ,-2,-2
number of roots=4
Look at the numbers below. −9.8 −5.4 1.0 14.8 Which shows the best way to add these numbers using the Commutative and Associative Properties? A. (–9.8 + 1.0) + (–5.4 + 14.8) B. (–9.8 + 14.8) + (–5.4 + 1.0) C. (1.0 + 14.8) + (–9.8 + (–5.4)) D. (1.0 + (–9.8)) + (14.8 + (–5.4)
Answer:
B
Step-by-step explanation:
i did the test and it was correct, ur welcome
PLEASE HELP! much appreciated :D
Find the value of x.
Answer:
a
Step-by-step explanation:
Is the relationship shown by the data linear? If so, model the data with an equation.
Which sets of ordered pairs show equivalent ratios? Use the grid to help you.
Check all that apply.
A: (1, 2), (2, 3), (4, 7)
B: (2, 2), (4, 4), (6, 6)
C: (3, 1), (4, 1), (5, 1)
D: (4, 1), (8, 2), (12, 3)
E: (2, 1), (4, 3), (5, 4)
Answer:
B and D
Step-by-step explanation:
in B the ratio of x/y = 1 for all pairs.
in D the ratio of x/y = 4 for all pairs.
in all other sets there are different ratios inside the set.
Answer:
The pairs (2, 2), (4, 4), and (6, 6) have ratios of 1 and the pairs (4, 1), (4, 1), (8, 2), and (12, 3) have ratios of 4. The other pairs do not have similar ratios.
Step-by-step explanation:
Step 1; In order to pair up the pairs with equivalent rations, we first need to calculate the ratios for all the pairs by dividing the first value with the second value. The same procedure must be followed throughout to be able to pair them up.
Step 2; By dividing the values, the ratios are;
For (1, 2), the ratio is = 0.5,
For (2, 3), the ratio is = 0.6666,
For (4, 7), the ratio is = 0.5714,
For (2, 2), the ratio is = 1,
For (4, 4), the ratio is = 1,
For (6, 6), the ratio is = 1,
For (3, 1), the ratio is = 3,
For (4, 1), the ratio is = 4,
For (5, 1), the ratio is = 5,
For (4, 1), the ratio is = 4,
For (8, 2), the ratio is = 4,
For (12, 3), the ratio is = 4,
For (2, 1), the ratio is = 2,
For (4, 3), the ratio is = 1.333,
For (5, 4), the ratio is = 1.25.
Step 3; Now we pair up the sets with the same ratios, out of these 15 pairs. The pairs (2, 2), (4, 4), and (6, 6) have ratios of 1 and the pairs (4, 1), (4, 1), (8, 2), and (12, 3) have ratios of 4. The other pairs do not have similar ratios.
I hope this is right and it helps you !!!!!!!!!!
Which expression is equivalent to 7x , if b > 0?
Work Shown:
[tex]7x^2*\sqrt{2x^4}*6\sqrt{2x^{12}}\\\\7*6x^2*\sqrt{2x^4*2x^{12}}\\\\42x^2*\sqrt{4x^{4+12}}\\\\42x^2*\sqrt{4x^{16}}\\\\42x^2*\sqrt{(2x^8)^2}\\\\42x^2*(2x^8)\\\\42*2x^{2+8}\\\\84x^{10}\\\\[/tex]
So that's why the answer is choice C
The requirement that x is nonzero isn't technically necessary. The original expression simplifies to choice C even when x = 0 is the case. Also, we don't have issues such as division by zero errors that could arise. It's a bit curious why your teacher put in that condition.
Answer:
C.
Step-by-step explanation:
7x²×sqrt(2x⁴)×6×sqrt(2x¹²)
we see right away that as constant multiplication factor we have 7×6 = 42.
and then we get from each sqrt expression a sqrt(2), which leads to sqrt²(2) = 2 and therefore 42×2=84.
the only answer option with 84 is C.
now, to be completely sure, and to get some practice, let's look at the other parts :
sqrt(2x⁴) = sqrt(2)×sqrt(x⁴) = sqrt(2)×x²
sqrt(2x¹²) = sqrt(2)×sqrt(x¹²) = sqrt(2)×x⁶
=>
7x²×sqrt(2)×x²×6×sqrt(2)×x⁶ =7×6×2×x²×x²×x⁶ = 84x¹⁰
perfect. C is confirmed.
Ophelia is making homemade spaghetti sauce by combining 48 oz of tomato paste with 6 cups of water.how many cups of water are needed for every ounces of tooth paste
1 cup per 8 oz
48/6 = 8
every 1 cup of water 8 oz of tomato paste.
Singh's house the weekly consumption of milk is 6.5 liters what is their daily consumption of milk if they consume same quantity of milk every day
Answer:
Their daily consumption of milk is of 0.93 liters.
Step-by-step explanation:
Weekly consumption:
6.5 liters.
Daily consumption:
A week has 7 days.
Each day the amount consumed is the same, so the daily consumption is:
6.5/7 = 0.93
Their daily consumption of milk is of 0.93 liters.
The price of a car was decreased from $13,000 to $11,830. The price is decreased by what percentage?
Answer:
It is decreased by 9%
Step-by-step explanation:
First, find out how much money is decreased. To do this, subtract 13,000-11,830=1170. Finally, figure out how much percent 1170 is of the original price of $13,000.
The answer is 7%.
Hope this helps :)
Draw the image of the rotation of quadrilateral SORT by 270° about the origin.
I need visual help, not a number answer please :)
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Answer:
see attached
Step-by-step explanation:
A rotation 270° CCW is the same as a rotation 90° CW. To see what the figure looks like in its new location, make a copy on a semi-transparent medium, then align the +x axis on the copy with the -y axis on the original graph, keeping the origin in the same place.*
Algebraically, the transformation is ...
(x, y) ⇒ (y, -x)
For example, ...
S(7, -6) ⇒ S'(-6, -7)
In the attachment, the rotated figure is in red.
_____
* The exercise of physically doing this on paper or with transparencies can give you the insight you need to learn to do it mentally.
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THAT IS THE RIGHT ANSWER
