Answer:
n=10
Step-by-step explanation:
The given equation is
[tex]10+12+14+...+2n=90[/tex] ...(1)
Let nth term is 2n.
We need to find the values of n.
It is clear that [tex]S_n=10+12+14+...+2n[/tex] is sum of A.P., whose first term is 10 and common difference is 2.
Sum of A.P. is
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
where, a is first term and d is common difference.
Substitute a=10 and d=2 in the above formula.
[tex]S_n=\dfrac{n}{2}[2(10)+(n-1)2][/tex]
[tex]10+12+14+...+2n=n[10+n-1][/tex]
[tex]10+12+14+...+2n=n[9+n][/tex] ...(2)
From (1) and (2), we get
[tex]n(9+n)=90[/tex]
[tex]n^2+9n-90=0[/tex]
Splitting middle term, we get
[tex]n^2+15n-6n-90=0[/tex]
[tex]n(n+15)-6(n+15)=0[/tex]
[tex](n+15)(n-6)=0[/tex]
[tex]n=-15,6[/tex]
Since, n represents the number of terms so n cannot be a negative number, therefore number of term is 6.
Note: nth term and variable n both are different.
[tex]a_n=a+(n-1)d[/tex]
[tex]a_6=10+(6-1)2=10+10=20[/tex]
Sixth term is 20. So,
[tex]2n=20[/tex]
[tex]n=10[/tex]
Therefore, the value of n is 10.
What is the value of the expression 9×4−(2×12)? Enter your answer in the box.
Answer:
12
Step-by-step explanation:
9x4-(2x12)
= 36-24
= 12
which of the following descriptions represent the transformation shown in the image? Part 1b
Answer: b) 2 units left, 4 units up, reflect across y-axis
Step-by-step explanation:
The easiest way to do this is to graph the black triangle using the the given options to see which one lands on the red triangle.
The second option is the one that works.
Leshawn has $580 in a savings account that pays 3% interest.
How much interest will be earned in 5 years?
How much interest will be earned in 6 months?
Answer:
For 5 years $87
For 6 months $8.7
Step-by-step explanation:
To calculate the interests, we use the simple interest formula
Mathematically;
I = PRT/100
where P is the amount invested called the principal = $580
R is the rate = 3%
Time differs which may be 5 years or 6 months according to the question.
kindly note that 6 months is 0.5 year
For 5 years, we have
I = (580 * 3 * 5)/100 = $87
For 6 months, we have;
I = (580 * 3 * 0.5)/100 = $8.7
Ms. Jenks bought 1.75 pounds of ham and 0.8 pound of turkey from the deli. How many more pounds of ham than turkey did she buy?
Which is equivalent to One-fourth x? StartFraction 1 over 8 EndFraction x + StartFraction 1 over 8 EndFraction x StartFraction 1 over 8 EndFraction x + StartFraction 1 over 8 EndFraction StartFraction 1 over 8 EndFraction + StartFraction 1 over 8 EndFraction One-half x + one-half x
Answer:Its A
Step-by-step explanation:
Its A because its right believe me
equivalent to One-fourth x is One-half x + one-half x; equation 7 is correct
what is equivalent expression?Equivalent expression is the expression of two equation when the way of representation of the two equation is different but the result is same. The given equation is equivalent to the expression one half and one half x.
Given information;
The expression given in the problem is,
(1/4) x [tex]x[/tex]
Equivalent expression;
Equivalent expression is the expression of two equation when the way of representation of the two equation is different but the result is same.
For given expression,
1/4 x [tex]x[/tex]
As the above function is the function of x. Thus it can be written as,
f(x)= 1/4 x [tex]x[/tex]
The number four is the product of number 2 and number 2. Thus,
f(x)=(1/2x2) x [tex]x[/tex]
f(x)=(1/2 x 1/2) x [tex]x[/tex]
Hence the given equation is equivalent to the expression one half and one half x.
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A file that is 246 megabytes is being downloaded. If the download is 12.5% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth
Answer:
30.8
Step-by-step explanation:
We can mutiply 246 by 0.125 to get the answer.
246 * 0.125 = 30.75 = 30.8
Answer:
30.8 megabytes
Step-by-step explanation:
We know that 12.5% of the 246 megabytes have been downloaded.
Of, means multiply. Therefore, we must multiply 12.5% and 246.
12.5%*246
Convert 12.5% to a decimal. Divide 12.5 by 100, or move the decimal place two spots to the left.
12.5/100=0.125
12.5–> 1.25 —> 0.125
0.125*246
Multiply
30.75
We need to round to the nearest tenth. The 5 in the hundredth place indicates that we must round the 7 in the tenth place up to a 8.
30.8
30.8 megabytes have been downloaded.
Which is a correct first step in solving 5 - 2x < 8x - 3?
5 < 6x-3
3x < 8x - 3
5 < 10x - 3
2 - 2x < 8x
Answer:
5< 10x -3
add like terms first
make sure X's are on one side and numbers on the other
Answer:
5 < 10x - 3
Step-by-step explanation:
5 - 2x < 8x - 3?
Add 2x to each side
5 - 2x+2x < 8x - 3+2x
5 < 10x - 3
select the equation that has a y-intercept value of 3
Answer:
The y-intercept is the point of which the graphed line passes through the y axis.
Step-by-step explanation:
First person to give me Brainliest wins the official contest!! Hurry!! Please give me Brainliest, I just started using this and really want it.
Please help with this question
Answer:
the SSS similarity theorem
Step-by-step explanation:
The triangles are not indicated as being right triangles (even though we know they are), so we cannot use the HL theorem.
The ratios of corresponding sides are the same, so the applicable theorem is ...
the SSS similarity theorem
__
3/(3+6) = 4/(4+8) = 5/15 = 1/3 . . . the ratio of shorter sides to corresponding longer sides.
_____
Additional comment
You recognize the smaller triangle as a 3-4-5 right triangle, and notice that the larger triangle is 3 times that size. If angle C were marked as the right angle it is, then the HL similarity theorem could also be used.
w
b
Х
What is the value of c?
4
4 units
a
с
0 5 units
Y
6 units
3
Z
O 7 units
The length c is the hypotenuse of the triangle WYZ, and the value of c is 5 units
How to determine the value of c?Considering the triangle WYZ, we make use of the following Pythagoras theorem
c² = 4² + 3²
Evaluate the exponents
c² = 16 + 9
Evaluate the sum
c² = 25
Take the positive square root of both sides
c = 5
This means that the value of c is 5 units
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plz hurry and answer i will give brainliest
what is 2*2+6/2*3
Answer:
This would equal 13.
2x2=4, 6/2=3, 3x3=9, 9+4=13
Which of the following reasons can be used to justify statement #3 in the proof?
A Given
B the vertical angel theorem
C the reflexive property of congruence
D SSS
c because it is accuet.
hope it helps
Option C . The reflexive property of congruence is the correct reason that can justify statement 3 . BD≅BD
What is the reflexive property of congruence?The reflexive property of congruence states that every side, every angle, every line segment and every shape is congruent to itself.
To prove that ΔABD is congruent to ΔCBD where given that
1.Line segment AB ≅ Line segment CB (Given)
2. Then we can write AD ≅CD ; Given : D is the mid point of AC
3. line segment BD ≅ Line segment BD , this is true by reflexive property of congruence which states that every line segment or side is congruent to itself.
BD can be considered as side of both the given triangles
Therefore, the reason that can justify statement 3 is option C.
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Solve 4x- 9 = k for x.
A. x= k+ 9
B. X=
K-9
4
C. X=
k+9
4
D. x = 4 + 9
Answer:
x = (k+9)/4
Step-by-step explanation:
4x - 9 =k
Add 9 to each side
4x-9+9 = k+9
4x = (k+9)
Divide each side by 4
4x/4 = (k+9)/4
x = (k+9)/4
Answer:
The answer is C
Explanation:
you first add 9 to both sides, you equation will then be 4x = k+9
you then divide both sides by for to get rid of the four from the left side, that will leave you with the equation of x = k+9 over 4
in fantasy football, Real Performance statistics from actual players are used to generate mock scores for Imaginary teams and virtual games. What kind of data source is this?
Answer:
[tex]\fbox{\begin{minipage}{8em}Option B: Survey\end{minipage}}[/tex]
Step-by-step explanation:
The data is collected from actual players, from real world, not simulation.
=> Option A-Simulation is incorrect.
The data is all collected subjectively from actual players, and has not been manipulated purposely, like in an experiment, yet.
=> Option C-Experiment is incorrect.
The data is collected subjectively and used directly to generate mock scores without any manipulation.
The data can be considered the results of survey.
=> Option B-Survey is correct
Hope this helps!
:)
Answer: Simulation
Step-by-step explanation:
I took the quiz
i need help!How would i find the value of X?
HELP PLEASE !! NEED HELP ASAPPP !! Will give brainliest !!!
1. Find the measure of angle b (image attached below)
2. Find the measure of angle b (image attached below)
Answer:
1. 37° 2. 140
Step-by-step explanation:
They are supplementary angles, so the angle measures equal a straight line, or 180 degrees. 180 - 143 = 37
olivia has 2 gallons and 3 quarts of vanilla ice cream and 1 gallon and 2 quarts of ice cream left over form the party how many gallons and quarts does she have left
Answer:
She has 4 gallons and 1 quart left
Step-by-step explanation:
4 quarts equals a gallon. Add the 2 gallons with the one gallon and it's 3 gallons. Then add the 3 quarts with the other 2 quarts for another gallon with a quart left over. Add that gallon with the other three and she has 4 gallons and 1 quart. Hope this helps :>
What is the simplified form of this expression?
Answer:
B. -7[tex]x^{2}[/tex] + 3x + 5
Step-by-step explanation:
(-3[tex]x^{2}[/tex] + x + 5) - (4[tex]x^{2}[/tex] - 2x)
-3[tex]x^{2}[/tex] + x + 5 - 4[tex]x^{2}[/tex] - 2x
Combine like terms
-3[tex]x^{2}[/tex] - 4[tex]x^{2}[/tex] = -7[tex]x^{2}[/tex]
x - -2x = x + 2x = 3x
5
-7[tex]x^{2}[/tex] + 3x + 5
I hope this helps :))
Use Venn diagram notations to describe the shading of
Answer:
A intersection B or A Π B
Step-by-step explanation:
The intersection of A and B is the set of all those elements which belong to both A and B.
In given Venn diagram describe the shading region is A intersection B or A ∩ B
What is Venn diagram?A Venn diagram is an illustration that uses circles to show the commonalities and differences between things or groups of things Venn diagrams, also called Set diagrams or Logic diagrams, are widely used in mathematics, statistics, logic, teaching, linguistics, computer science and business. Many people first encounter them in school as they study math or logic, since Venn diagrams became part of “new math” curricula in the 1960s. These may be simple diagrams involving two or three sets of a few elements, or they may become quite sophisticated, including 3D presentations, as they progress to six or seven sets and beyond. They are used to think through and depict how items relate to each within a particular “universe” or segment. Venn diagrams allow users to visualize data in clear, powerful ways, and therefore are commonly used in presentations and reports. They are closely related to Euler diagrams, which differ by omitting sets if no items exist in them. Venn diagrams show relationships even if a set is empty.
According to the question
The intersection of A and B is the set of all those elements which belong to both A and B.
Hence, the given Venn diagram describe the shading region is A intersection B or A ∩ B
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Awnser needed thank you!
Answer:
Step-by-step explanation:
I think 33°
Answer:
its 34 i think
Step-by-step explanation:
Carter has 123 songs on a playlist. He's categorized them in the following manner: 11 gospel, 25 country, 21 blues, 6 folk, 16 pop. 14 jazz.
and 30 rock. If Carter begins listening to his playlist on shuffle, what is the probability that the first song played is a gospel song? Express
your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Plsssss help
Answer:
11/123
Step-by-step explanation:
P( gospel) = number of gospel songs/ total
= 11/123
Jonathan’s family took a road trip to the Grand Canyon.Jonathan fell asleep after they had travelled 260 miles. If the total length of the trip was 400 miles,what percentage of the total trip had they travelled when Jonathan fell asleep??
Answer:
Step-by-step explanation:
for 140
miles he had slept
An oil company fills 1/10
of a tank in 1/5, hour. At this rate, which expression can be used to determine how long it will take for the tank to fill completely?
10
10 hours
01
. 5 hours
10
.
1
10
hour
5
5-10 hours
Answer:
So if the company fills in 1/10 of a tank in 1/5 hour. We should multiply by 10
so that means that the tank will be 100% full because 10/10 = 100%
That also means we need to multiply it by 1/5. 1/5*10 = 10/5.
Therefore we get 2 hours.
Thanks for the question. I am working my way up to brainliest and and Master Answerer
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST
Linda made 5 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 5 necklaces was $18.50 . If the beads cost $1.50 for each necklace, how much did each pendant cost?
Answer:
$2.20
Step-by-step explanation:
If the beads cost $1.50 for each necklace, then we have to do $1.50 X 5 = $7.50
Then, $18.50 - $7.50 = $11
Then $11/ 5 = $2.2
Need Help. Order of operation 1/35 * 1/22 I get a different answer
Answer:
[tex]\frac{1}{770}[/tex]
Step-by-step explanation:
[tex]\frac{1}{35} *\frac{1}{22} =\frac{1}{770}[/tex]
Answer:
1 / 770.
Step-by-step explanation:
1/35 * 1/22
= 1*1 / 35*22
= 1 / 770.
A. A worker with 1700 hours of training is paid $40 per month.
B. A worker who works 40 hours is paid $1700.
C. There are 40 workers who are paid $1700 per month.
D. A worker with 40 hours of training is paid $1700 per month
Answer:
d.
Explanation:
Look at the title of the categories in the chart. 40 is categorized under “hours of training,” meaning 40 hours of training. 1700 is categorized under “monthly pay.” Put the information together and it means $1,700 for 40 hours that month.
X = 4/5 (x+10)
Find x
Answer:
[tex]x=40[/tex]
Step-by-step explanation:
[tex]x=\frac{4}{5}\left(x+10\right)\\\mathrm{Expand\:}\frac{4}{5}\left(x+10\right):\quad \frac{4}{5}x+8\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=\frac{4}{5},\:b=x,\:c=10\\=\frac{4}{5}x+\frac{4}{5}\cdot \:10\\=\frac{4}{5}x+10\cdot \frac{4}{5}\\10\cdot \frac{4}{5}=8\\10\cdot \frac{4}{5}\\\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}\\=\frac{4\cdot \:10}{5}\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:10=40\\=\frac{40}{5}[/tex]
[tex]\mathrm{Divide\:the\:numbers:}\:\frac{40}{5}=8\\=\frac{4}{5}x+8\\x=\frac{4}{5}x+8\\\mathrm{Subtract\:}\frac{4}{5}x\mathrm{\:from\:both\:sides}\\x-\frac{4}{5}x=\frac{4}{5}x+8-\frac{4}{5}x\\Simplify\\x-\frac{4}{5}x=\frac{4}{5}x+8-\frac{4}{5}x\\\mathrm{Simplify\:}x-\frac{4}{5}x:\quad \frac{1}{5}x\\x-\frac{4}{5}x\\\mathrm{Factor\:out\:common\:term\:}x\\=x\left(1-\frac{4}{5}\right)\\1-\frac{4}{5}=\frac{1}{5}\\=\frac{1}{5}x\\1-\frac{4}{5}[/tex]
[tex]\mathrm{Convert\:element\:to\:fraction}:\quad \:1=\frac{1\cdot \:5}{5}\\=\frac{1\cdot \:5}{5}-\frac{4}{5}\\\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{1\cdot \:5-4}{5}\\1\cdot \:5-4=1\\1\cdot \:5-4\\\mathrm{Multiply\:the\:numbers:}\:1\cdot \:5=5\\=5-4\\\mathrm{Subtract\:the\:numbers:}\:5-4=1\\=1\\=\frac{1}{5}\\=\frac{1}{5}x\\\mathrm{Simplify\:}\frac{4}{5}x+8-\frac{4}{5}x:\quad 8\\\frac{4}{5}x+8-\frac{4}{5}x[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:\frac{4}{5}x-\frac{4}{5}x=0\\=8\\\frac{1}{5}x=8\\\mathrm{Multiply\:both\:sides\:by\:}5\\5\cdot \frac{1}{5}x=8\cdot \:5\\\mathrm{Simplify}\\x=40[/tex]
Answer:
40
Step-by-step explanation:
x+10= x 5/4
x +10= 5x/4
4x+40= 5x
40= x
x=40
Help me with this question please
Answer:
x < 6
Step-by-step explanation:
There is an open circle ( no equals) at 6 and the line goes to the left
This means that it is less than 6
x < 6
please help for brainliest answer
Answer:
3360 cm^2
Step-by-step explanation:
24 times 14 times 10 = 3360
I WILL MARK YOU BRAINLIEST!!!
Answer:
A
Step-by-step explanation: