Answer:
The first three terms in the geometric sequence are 18, 24, 32.
Step-by-step explanation:
A number when added to [tex]x,y,z[/tex] that yields consecutive terms of a geometric sequence is an unknown number [tex]t\in \mathbb{Z}[/tex]
Given
[tex]x = 1, y = 7, z = 15[/tex]
We know
[tex]\alpha _1 = 1+t[/tex]
[tex]\alpha _2 = 7+t[/tex]
[tex]\alpha _3 = 15+t[/tex]
Recall that a geometric sequence is in the form
[tex]\boxed{a_n = a_1 \cdot r^{n-1}}[/tex]
Therefore, once [tex]\alpha_1, \alpha_2, \alpha_1[/tex] are consecutive terms,
[tex]15+t = (1+t) r^{3-1} \implies 15+t = (1+t) r^2[/tex]
To find the ratio, for
[tex]\dots a_{k-1}, a_k, a_{k+1} \dots[/tex]
we know
[tex]\dfrac{a_k}{a_{k-1}} =\dfrac{a_k}{a_{k-1}} =r[/tex]
Therefore,
[tex]\dfrac{(7+t)}{(1+t)} =\dfrac{(15+t)}{(7+t)} \implies (7+t)^2 = (15+t)(1+t)[/tex]
[tex]\implies 49+14t+t^2=15+16t+t^2 \implies -2t=-34 \implies t=17[/tex]
The ratio is therefore
[tex]r=\dfrac{4}{3}[/tex]
Therefore, the first three terms in the geometric sequence are 18, 24, 32.
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
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
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.
Write the equation of the line for the graph shown below.
Answer:
The answer is C
Step-by-step explanation:
y=-5x-3
Hope this helped
Answer:
I believe the answer is y = -5x -3
Step-by-step explanation:
The formula is y=mx+b
m= rise over run
b= starting point
and seeing how the dot is on -3 I assume that the answer is y= -5x -3
also m should be in fraction form and if it isn't, you automatically put a 1 as the denominator.
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
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
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.
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:
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 :)
8 and 1/3divided by 3 and 4/7
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
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.
⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆
THAT IS THE RIGHT ANSWER
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 %
Is the relationship shown by the data linear? If so, model the data with an equation.
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:
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 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
#SPJ6
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 !!!!!!!!!!
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
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
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
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
simplify 4x + 3y - 2x
Answer:
2x+3y
Step-by-step explanation:
4x + 3y - 2x
Combine like terms
4x-2x +3y
2x +3y
Zane wants to enlarge two of his photos to frame on his bedroom wall. He has 184 photos from rock concerts he's been to and 88 photos of city
skylines
How many possible combinations of 1 rock concert photo and 1 city skyline photo could Zane choose from?
Answer:
B
Step-by-step explanation:
184*88=16,192
PLEASE HELP! much appreciated :D
Find the value of x.
Answer:
a
Step-by-step explanation:
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)
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
Does the graph below represent a proportional relationship?
———————————————
A. Yes, because the graph is a straight line
B. No, because it crosses the y -axis
C. Yes, because it crosses the y -axis
D. No, because the line doesn't pass through the origin, point (0,0)
Answer: D. No, because the line doesn't pass through the origin, point (0,0)
Explanation:
A direct proportional graph is always a straight line through the origin.
Algebraically, the form of any direct proportion equation is y = kx, where k is some constant. It plays the role as the slope.
We can rewrite y = kx as y = kx+0 to see that the y intercept is always 0 for these types of equations.
Unfortunately, this line shown has a y intercept of 2 instead of 0. So it's not a direct proportion.
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.
