Answer:
S₆ = - 364
Step-by-step explanation:
the sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 2 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-6}{2}[/tex] = - 3 , then
S₆ = [tex]\frac{2((-3)^{6}-1) }{-3-1}[/tex]
= [tex]\frac{2(729-1)}{-4}[/tex]
= [tex]\frac{2(728)}{-4}[/tex]
= [tex]\frac{1456}{-4}[/tex]
= - 364
Explain how you would estimate the value of 57−−√ by determining the two consecutive whole numbers that it lies between. Write the two numbers and explain the process you used to select them.
The two consecutive whole numbers that it lies between are 28 and 29.
What are the consecutive numbers?The consecutive numbers are those number which follow each other continuously in the order from smallest to largest numbers.
Let the two consecutive numbers be x and x + 1
x + x + 1 = 57
Combine like terms;
2x + 1 = 57
Now Subtract 1 from both sides;
2x = 57- 1
2x = 56
Divide both sides by 2
x = 56/2
x = 28
Thus, x + 1 = 28 + 1 = 29
The two consecutive whole numbers that it lies between are 28 and 29.
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-4x^2 +2x-5(1+x)
What expression is equivalent to the given expression?
Blank x^2+Blank x+Blank
The expression -4x² + 2x - 5(1 + x) is equivalent to the expression - (4x² + 3x + 5).
What is an equivalent expression?The equivalent is the expression that is in different forms but is equal to the same value.
The quadratic expression is given below.
⇒ -4x² + 2x - 5(1 + x)
Simplify the expression, then the expression will be given as,
⇒ -4x² + 2x - 5(1 + x)
⇒ -4x² + 2x - 5 - 5x
⇒ -4x² - 3x - 5
⇒ - (4x² + 3x + 5)
The expression -4x² + 2x - 5(1 + x) is equivalent to the expression - (4x² + 3x + 5).
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Angle Relationship
Find mLTSU if SU bisects LTSV,
mLTSU = 4y + 11, and m∠USV = 6y + 5.
< TSU = 4y + 11 = 23 degrees
What does angle relationship mean?
We talk of angle relationships because we are comparing position, measurement, and congruence between two or more angles. For example, when two lines or line segments intersect, they form two pairs of vertical angles
we have to find m < TSU if SU bisects < TSV, m < TSU = 4y + 11, m < USV = 6y + 5
SU bisects < TSV
=> < TSU = < USV
4y + 11 = 6y + 5
-2y = -6
y = 3
< TSU = 4y + 11 = 23 degrees ( put the value of y=3)
∠USV = 6y + 5 = 23 degrees ( put the value of y=3)
Hence ,< TSU = 4y + 11 = 23 degrees
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Find x and y, i only need the answer so no need to show work
Step-by-step explanation:
X=48 becase 42+90=132
180-132= 48
Solve first principle of y=X^3
Answer:
3x^2
Step-by-step explanation:
Explained in image.
All students in the 6th grade either purchased their
lunch or brought their lunch from home on Monday.
• 24% of the students purchased their lunch.
• 190 students brought their lunch from home.
How many students are in the 6th grade?
i need a really detailed answer
The number of students in the 9th grade is 250.
How to calculate the value?Based on the information, the percentage of those who brought their good from home will be:
= 100 - 24%
= 76%
Therefore, 76% of x = 190
0.76x = 190
x = 190/0.76
x = 250
Therefore, the number of students in the 9th grade is 250.
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left parenthesis 3 plus 4 right parenthesis plus 5 equals 3 plus left parenthesis 4 plus 5 right parenthesis is an example of the ______________property.
1. inverse
2. associative property
3. identity property
4. commutative property
Answer:
2 associate property
Step-by-step explanation:
(3 + 4) + 5 3 + (4 + 5) On the left side, the 4 is "associating" with the 3", but on the left side the 4 is "associating;" with the 5.
h is a trigonometric function of the form h(x) = a sin(bx + c) + d.
Below is the graph h(x). The function intersects its midline at (-4pi,2.5) and has a maximum
point at(-5pi/2,6)
Find a formula for h(x). Give an exact expression.
The expression acquired is h(x) = 3.5 sin(1/3x ₊ 4π/3)₊2.5
Given h(x) = a sin(bx ₊ c) ₊ d
The h(x) function intersects its mid line at (₋4π , 2.5)
and has its maximum points at (₋5π/2 , 6)
therefore, x₂ ₋ x₁ = ₋5π/2 ₋ (₋4π)
= ₋5π/2 ₊ 4π
= 3π/2
⇒ 2π/b = 3π/2 4
⇒ 2π/b = 6π
⇒b = 1/3
hence, a = b ₋ 2.5
a = 3.5
now h(x) = 3.5 sin(1/3x ₊ c) ₊ 2.5
x = ₋4π
h(₋4π) = 3.5 sin( ₋4π/3 ₊ c) ₊ 2.5
₋4π/3 ₊ c = 0
c = 4π/3
therefore, h(x) = 3.5 sin(1/3x ₊ 4π/3)₊2.5
hence after solving the equation we get the expression for h(x) as
h(x) = 3.5 sin(1/3x ₊ 4π/3)₊2.5
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Complete the problems. Find the a) employee’s total annual contribution, and b) employee’s monthly deduction. 1. Dorsey Williams has a single plan. His PPO annual premium is $4,325. His employer pays 65%
Employee’s total annual contribution is $1513.75
And, Employee’s monthly deduction is $126.15
Here,
Dorsey Williams has a single plan.
And, His PPO annual premium is $4,325.
His employer pays 65%.
We have to find the Employee’s total annual contribution.
And, Employee’s monthly deduction.
What is Annual contribution?
The amount credited to Account balance after the end of each Plan Year for which the Performance Goals are achieved is called Annual contribution.
Now,
His PPO annual premium is $4,325.
And, His employer pays 65%
Hence,
Employee’s total annual contribution = 4,325 (1 - 65%)
= 4,325 (35%)
= 4,325 x 35/100
= 1513.75
And, Employee’s monthly deduction = 1513.75 ÷ 12 = 126.15
Therefore, Employee’s total annual contribution is $1513.75
And, Employee’s monthly deduction is $126.15
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20 cm
13 cm
7 cm what is the area of the shape?
Answer:
270cm2
Step-by-step explanation:
you have to split the figure into 2.
the triangle above is = 1/2 x20cmx13cm=130cm2
the rectangle is = 20cmx7cm=140cm2
total area=140cm2+130cm2
=270cm2
priya and tyler are discusising the figures shown below . priya thinks that b,c and d are scaled
For the given figures, both Priya and Tyler's opinions are incorrect.
What is meant by scale factor/scaling?Scaling is the process of measuring as well as assigning numbers to objects according to predefined rules.
Scaling is the process of locating the measured items on the continuum, an ongoing sequence of numbers with which the objects are assigned.
As, for the given question;
Figure D is the sole shape that can be considered a scaled replica of Figure A. This is due to the observation that all segments in figure D are times 2 of the correlating segments in figure A.When we compare figure B and C to figure A, we see that not all of their segments are twice as long as the correlating segments in figure A.As a result, both Priya as well as Tyler are incorrect. None of them are acceptable to us.
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The complete question is-
Priya and Tyler are discussing the figures shown below. Priya thinks that B, C, and D are scaled copies of A. Tyler says B and D are scaled copies of A. Do you agree with Priya, or do you agree with Tyler? Explain your reasoning.
the table shows the estimated sales for two different prices of bags of chips. Calculate the profit per bag for the bags sold at 3$ each
The profit per bag for the bags sold at 3$ each is $1.5 per bag.
How to calculate the profit?The total cost will be:
= $300000 + (1 × $600000)
= $900,000
The revenue will be:
= $3 × 600000
= $1,800,000
Therefore, the profit per bag will be:
= ($1800000 - $900000) / 600000
= $900000/600000
= $1.5
The profit is $1.5.
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They wrote the model `n=40\cdot1.5^{t}` , where `n` is the total number of squirrels and `t` is the number of years since the biologists started counting. How many squirrels do the biologists predict there will be `2` years after they started counting
The number of squirrels that the biologists predict there will be 2 years after they started counting will be 43 squirrels.
How to illustrate the information?It should be noted that a function is used to show the relationship between the variables.
It should be noted that the function that's given is illustrated as:
n = 40 + 1.5t
In this case, it should be noted that t = 2 years.
Therefore, the number of squirrels that the biologists predict there will be 3 years after they started counting will be:
n = 40 + 1.5t
n = 40 + 1.5(2)
n = 40 + 4
n = 43
Therefore, the number of squirrels that the biologists predict there will be 2 years after they started counting will be 43 squirrels.
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A mural measures 95 feet long by 285 feet high. Find the ratio of the height to the perimeter of this mural.
The ratio of the height to the perimeter of this mural 57 : 152.
We are given that:
Length = 135 feet
height = 285 feet
Mural is of a rectangular shape
We will first find the perimeter.
Perimeter = 2(l + w)
Perimeter = 2(95 + 285)
Perimeter = 2(380)
Perimeter = 760 feet
We will now find the ratio of the height to the perimeter of this mural.
Height : perimeter = 285 : 760
Reduce to lowest terms
Height : perimeter = 57 : 152
Therefore, we get that, the ratio of the height to the perimeter of this mural 57 : 152.
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The length of a rectangular garden is 10 feet longer than its width. The garden's perimeter is 188 feet. Find the width of the garden.
Answer: width of the garden is 42
Step-by-step explanation:
let's say "x" = the garden's length
and "y" = the garden's width
the length of the garden is 10 feet longer than its width
x-10=y
the garden's perimeter is 188 feet
we can set up a new equation like this:
2x+2y=188
now we have two equations and we can solve using the system of equations.
x-10=y
add 10 on both sides to isolate "x"
x=y+10
2x+2y=188
substitue x for y+10 in the second equation
2(y+10)+2y=188
expand
2y+20+2y=188
combine like terms
4y+20=188
subtract 20 from both sides
4y=168
divide by four on both sides
y=42
the width of the garden is 42 feet
PLEASE HELP!!! BRAINLIEST TO WHOEVER IS FIRST!
Answer:
It's the first one: 7 to the fourth over 3 to the tenth.
Step-by-step explanation:
Answer:
I think it is the first one
Step-by-step explanation:
Find each of the following by first summing all the negative and positive numbers separately
and then combining the final positive and negative. Show your work.
(a) -8+-9+7+4
(b)-18+6+-22+28
(c) 24+19+-6+10+-12
(d) -18+32+14+21+-50
Applying addition of integers, the final results of the expressions are given as follows:
a) -6.
b) -6.
c) 35.
d) -1.
How do we add two integers?To add two integers, we have to keep in mind their signals, if they are the same or different, as follows:
If they have the same signal, we keep the signal and add the numbers.If they have the different signal, we take the signal of the largest absolute number(largest number without the signal), then subtract the amounts.Hence, for item a, we have that:
-8 - 9 = -17.7 + 4 = 11.-17 + 11 = -6.For item b, the solution is found as follows:
-18 - 22 = -40.6 + 28 = 34.34 - 40 = -6.For item c, the solution is found as follows:
-6 - 12 = -18.24 + 19 + 10 = 53.53 - 18 = 35.For item d, the solution is found as follows:
-18 - 50 = -68.32 + 14 + 21 = 67.67 - 68 = -1.More can be learned about addition of integers at https://brainly.com/question/17695139
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If tan a = x + 1 and tan ß = x - 1, then verify that: 2cot(a - B) = x²
[tex]
\cot(a-b)=\frac{\frac{1}{(x+1)(x-1)}+1}{\frac{1}{x-1}+\frac{1}{x+1}} \\ \\ =\frac{1-1+x^2}{2} \\ \\ =\frac{x^2}{2} \\ \\ \therefore 2\cot(A-B)=x^2[/tex]
Answer:
See below for proof.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Trigonometric Identities}\\\\$\cot \theta=\dfrac{1}{\tan \theta}$\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]
[tex]\begin{aligned}\implies 2\cot (\alpha - \beta) & =\dfrac{2}{\tan (\alpha - \beta)}\\\\ & =\dfrac{2}{\dfrac{ \tan \alpha - \tan \beta}{1+\tan \alpha \tan \beta}}\\\\ & =\dfrac{2(1+\tan \alpha \tan \beta)}{ \tan \alpha - \tan \beta}\\\\ & =\dfrac{2(1+(x+1)(x-1))}{ (x+1) - (x-1)}\\\\& = \dfrac{2(1+(x^2-x+x-1))}{x+1-x+1}\\\\& = \dfrac{2(1+(x^2-1))}{2}\\\\& = \dfrac{2x^2}{2}\\\\& = x^2\end{aligned}[/tex]
Hence verifying that 2cot(α - β) = x².
Round 3.691 to the nearest hundredth
Answer: 3.69
Step-by-step explanation:
Answer:
3.69
Step-by-step explanation:
If the last digit in the fractional part of 3.691 is less than 5, then simply remove the last the digit of the fractional part.
You're to prepare 850 mL of D8W form D10W and sterile water for injection. How many milliliters of D10W will you need?
The volume of D10W solution required to be diluted to make 850 mL of D8W solution is 680 mL.
How can the dilution contents be calculated?The dilution formula can be presented as follows;
[tex]C_1 \cdot V_1 = C_2 \cdot V_2[/tex]
Where;
[tex]C_1 = Initial \: concentration = D10W [/tex]
[tex]V_1 = Initial \: volume [/tex]
[tex]C_2 = Final \: concentration = D8W[/tex]
[tex]V_2= Final \: volume = 850 \: mL [/tex]
Which gives;
[tex]V_1 = C_2 \cdot V_2/C_1[/tex]
V1 = 8×850/10 = 680
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Randi went to Lowe’s to buy wall-to-wall carpeting. She needs 111.02 square yards for downstairs, 31.82 square yards for the halls, and 161.92 square yards for the bedrooms upstairs. Randi chose a shag carpet that costs $15.01 per square yard. She ordered foam padding at $3.12 per square yard. The carpet installers quoted Randi a labor charge of $3.77 per square yard.
What will the total job cost Randi?
Round your answer to the nearest cent.
help please
Using proportions, it is found that the total job cost for Randi is of $6,674.24.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
The total amount of square yards that she needs is given by:
111.02 + 31.82 + 161.92 = 304.76.
The cost per square yard is given by:
15.01 + 3.12 + 3.77 = $21.9.
Hence the total cost is given by:
304.76 x 21.9 = $6,674.24.
The total job cost for Randi is of $6,674.24.
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Solve for x.
5(2+1)<5x+3
What number makes the
equation true?
23+5= + 18
the number that makes it correct is 10
let's write it like this
23+5=x+18
28=x+18
you would subtract 18 from each side to get x
28-18=10
18-18=0
x=10
What is the area, in square units, of the parallelogram shown below? D A 7 units C H5 units O 20 square units O 25 square units 30 square units O 35 square units B
Answer: The answer is C
Step-by-step explanation:
11. A trader bought 2 cows and 9 goats for a total of ksh. 98 200. If she had bought 3 cows and 4 goats, she would have spent ksh. 2200 less a) Taking C to be the number of cows and G to be the number of goats, form two equations to represent the above information. b) use substitution method to represent the above information
By using subtraction method we get 55.157.8987
What is subtraction method?
In mathematics, subtraction refers to the act of removing something from a set of related objects or numbers. What is left in the group decreases as a result of subtraction.
Let cost of each cow=x
cost of each goat =y
Given 2x+9y=98200------------(equation 1)
9y=98200-2×Y=98200-2x/9-----------(equation 2)
Also 3x+4y= 9800+2200
3x+4y=1004004y=100,
400-3xY=100400-3x/4---------(equation 3)
From equation 2 and 3 we get
Y=Y98200-2x/9
=100400-3x/4
=196,400-8x
=301200-27x
=19x
=104,800
=x=55.157.8987
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Put these winning lottery numbers in the correct order.
Select the boxes and type in the correct answers.
lowest
48
5
23
11
9
20
after seven years , an intitial investment of $600 earned $84 find the interest rate
The interest rate 2% per year
How to calculate the interest rate ?The time period is 7 years
The initial investment is $600
The current investment is $84
The interest rate can be calculated as follows
84/600 × 7
= 84/4200
= 0.02
The interest rate is
= 0.02 × 100
= 2%
Hence the interest rate is 2%
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Can someone please help me I will mark u brilliant I need the points for Q R and S
Is (1, 10) a solution to the inequality y ≤ 4x + 1?
Answer:
(1,10) is not a solution to the inequality.
Step-by-step explanation:
First, you want to insert the values of x and y in the inequality.
So, [tex]10\leq 4(1) +1[/tex]
[tex]10\leq 5[/tex]
That inequality is not true, so we know that (1,10) is not a valid solution.
Is this true
4. When you subtract two numbers, if you reduce the first number in the subtraction by one, the result is one less. For example, 12 – 4 is 8 and 11 – 4 is 7
When you subtract two numbers, if you reduce the first number in the subtraction by one, the result is one less. This is true.
How to calculate the value?It should be noted that in subtraction when you reduce the first number, you will get a value that's lesser by 1.
In this case, if we have 20 - 5 = 15, then 19 - 5 = 14. We can see that 14 and 15 is a difference of 1.
Therefore, when you subtract two numbers, if you reduce the first number in the subtraction by one, the result is one less. This is true.
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