Answer:
A
Step-by-step explanation:
Our equation is:
[tex]\frac{2}{3} *(\frac{1}{2} x+12)=\frac{1}{2} *(\frac{1}{3} x+14)-3[/tex]
Let's first distribute the left side. When distributing, we essentially find the sum of the product of the outside term with each of the inside terms. Here, the outside term is 2/3 and the inside terms are 1/2x and 12. So:
[tex]\frac{2}{3} *(\frac{1}{2} x+12)=\frac{2}{3} *\frac{1}{2} x+\frac{2}{3} *12=\frac{1}{3} x+8[/tex]
Now distribute the right side. Here, the outside term is 1/2 and the inside terms are 1/3x and 14, so:
[tex]\frac{1}{2} *(\frac{1}{3} x+14)-3[/tex]
[tex]\frac{1}{2} *(\frac{1}{3} x+14)-3=\frac{1}{2} *\frac{1}{3} x+\frac{1}{2} *14-3=\frac{1}{6} x+7-3=\frac{1}{6} x+4[/tex]
We now have:
[tex]\frac{1}{3} x+8=\frac{1}{6} x+4[/tex]
Isolate the variable by bringing 1/6x to the left and bringing 8 to the right:
[tex]\frac{1}{3} x-\frac{1}{6} x=4-8[/tex]
[tex]\frac{2}{6} x-\frac{1}{6} x=-4[/tex]
[tex]\frac{1}{6} x=-4[/tex]
x = -4 * 6 = -24
The answer is A.
Steps to solve:
2/3(1/2x + 12) = 1/2(1/3x + 14) - 3
~Distribute
1/3x + 8 = 1/6x + 7 - 3
~Combine like terms
1/3x + 8 = 1/6x + 4
~Subtract 1/6x to both sides
1/3x + 8 - 1/6x = 1/6x + 4 - 1/6x
~Simplify
1/6x + 8 = 4
~Subtract 8 to both sides
1/6x + 8 - 8 = 4 - 8
~Simplify
1/6x = -4
~Multiply 6 to both sides
1/6x * 6 = -4 * 6
~Simplify
x = -24
Best of Luck!
consider the following three equations:
linear: y=20x+300
Quadratic: y=5x^2
Exponential: y=10(1.4)^x
use the equations to answer the following questions. Support your answers with work.
1. At an x-value of 11, which equation has the largest y-value?
2. what is the smallest integer value of x for which the value of the exponential equation is greater than the values of both the linear and quadratic functions?
Answer:
1.
y = 20(11) + 300 = 520
y = 5(11)(11) = 605
y = 10(1.4)^11 = 404.96
hence the quadratic formula - y = 5x^2 has the largest y-value
2.
y = 20 (14) + 300 = 580
y = 5 (14) (14) = 980
y = 10(1.4)^ 14 = 1111.20 > this is greater than both equations above
14 is the smallest value of x for which the value of the exponential equation is greater than the values of both the linear and quadratic functions
Step-by-step explanation:
Answer:
1. Quadratic
2. x = 14
Step-by-step explanation:
1. At x = 11
linear: y=20(11) + 300 = 520
Quadratic: y=5× 11² = 605
Exponential: y=10(1.4)¹¹ = 404.956517
2. 10(1.4^x) > 20x + 300
1.4^x > 2x + 30
1.4^x - 2x - 30 > 0
Using trial method:
x > 11
10(1.4^x) > 5x²
1.4^x - 0.5x² > 0
Using trail method:
x > 13
The smallest positive integer which satisfies both inequalities is 14
mike had a balance of $175 in his bank account at the start of the week.He withdrew $65.00 on Monday, $43.25 on Wednesday, and $56.45 on Thursday.On Friday he deposited $165.30.
1.At the end of the week, does Mike have more or less money in his savings account than he had at the beginning of the week?
2.How much more or less?
3.Show all of your work to support your answers.
Answer:
1. Mike has more money in his savings account than he had at the beginning of he week
2. $0.6 more
3. Current Balance is $175 + $165.30 - $164.7 = $175.6
Step-by-step explanation:
The question is of the format of a word problem, hence we have;
Initial balance in Mike's bank account = $175
Withdrawal on Monday = $65.00
Withdrawal on Wednesday = $43.25
Withdrawal on Thursday = $56.45
Deposit on Friday = $165.30
Total withdrawal = $164.7
Therefore we have;
Current Balance = Initial balance + total deposit - total withdrawal
∴ Current Balance = $175 + $165.30 - $164.7 = $175.6
1. Therefore, based on the above calculations, Mike has more money in his savings account than he had at the beginning of he week
2. Mike has $0.6 more.
3. Current Balance = Initial balance + total deposit - total withdrawal
∴ Current Balance = $175 + $165.30 - $164.7 = $175.6.
Use the given circle. Find the length s to the nearest tenth.
a) 10.5 in
b) 5.2 in
c) 3.3 in
d) 20.9 in
Answer: its A
Step-by-step explanation:
Any smooth curve connecting two points is called an arc. The length of arc s to the nearest tenth is 10.5 in.
What is the Length of an Arc?Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,
[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360} = 2\pi r \times \dfrac{\theta}{2\pi}[/tex]
where θ is the angle, which arc creates at the center of the circle in degree.
The length of the given arc s, with an angle made at the center equal to (2/3)π and radius of 5 inches can be represented as,
[tex]\text{Length of Arc} = 2\pi r \times \dfrac{\theta}{2\pi}[/tex]
[tex]\text{Length of Arc s} = 2\pi \times (5)\times \dfrac{\frac23\pi}{2\pi}[/tex]
[tex]=10.472\approx 10.5\rm\ in[/tex]
Thus, the length of arc s to the nearest tenth is 10.5 in.
Learn more about Length of an Arc:
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Pythagorean Theorem: How many yards will the players have to run?
Answer:
≈ 125.3
Step-by-step explanation:
If we're using the Pythagorean Theorem to solve this, then the formula is:
[tex]a^{2}+ b^{2} =c^{2}[/tex]
So basically, by using this formula, you're finding the length that the soccer players will run diagonally. Plug in the numbers:
[tex]110^2 + 60^2 = c^2[/tex]
12100 + 3600 = [tex]c^2[/tex]
15700 = [tex]c^2[/tex]
Take the square root:
15700 = [tex]c^2[/tex]
[tex]\sqrt{15700} = \sqrt{c^2}[/tex]
125.3 ≈ c
The shark dove down 48 feet in 6 minutes. How many feet did the shark dive down per minute?
Answer:
8 ft per minute
Step-by-step explanation:
Take the number of feet and divide by the number of minutes
48 ft / 6 minutes
8 ft per minute
is it true that energy never moves
Answer:
False
Step-by-step explanation:
Energy is transferred from one object to another when a reaction takes place. Energy comes in many forms and can be transferred from one object to another as heat, light, or motion, to name a few.
Mr. Eichmann 's salary is $42,000. This year, he receives a raise of 7%. What will be his salary this year?
What's the numerator for the following rational
expression?
7/v+3/v=?/v
Answer:
54inches 43inches are the 53364inches rye 5t337 the earth stud is 37feet of the 368feet
Answer:
10
Step-by-step explanation:
they all have the same denominator so the only focus is adding the 7+3
Solve the equation using the quadratic formula: 2x^2-5x+2=0
Answer:
x= 2, 1/2
Step-by-step explanation:
x= b±√b²-4ac/2a
x = [5±√(-5)²-4·(2·2)]/2·2
x = (5±3)/4
x= 2, 1/2
Students in grade 7 and 8 were asked which food they liked best the results are shown in the table below?
Answer:
55% if the students like hotdods
Answer:
55%
Step-by-step explanation:
Enter all answers to the nearest tenth.
A day care program has an average daily expense of $75.00. The standard deviation is $5.00. The owner takes a sample of 64 bills. What is the probability the mean of his sample will be between $70.00 and $80.00?
Step 1. Calculate a z-score for $70.00 -
Step 2. Give the probability for step 1. %
Step 3. Calculate the z-score for $80.00 +
Step 4. Give the probability for step 3. %
Step 5. Add the probabilities from steps 2&4. %
Answer:
What is the probability the mean of his sample will be between $70.00 and $80.00? = 64/64 =1
s1) = 99% =z score = 127/128
s2)64/64 = 1
s3)95% of 64 = 123/128
s4) p) step 3 = 95% of 64 = 60.08 /64 = 60/64 = 93.75%
s5) P)of 2+4 = 283/292 = 96.92%
Find the surface area of the figure. Round the the nearest hundredth.
Answer:
Step-by-step explanation:
surface area of cylinder=2πrh
SA=1/2×2×π×3×25+2 ×(1/2×π×3²)=75π+9π=84π≈84×3.14≈263.76 cm²
if lowerside is also counted then area of lower side=25×6=150
total surface area=263.76+150=413.76 cm²
if we take π=22/7
84 π=84×22/7=12×22=264 cm²
if base is also counted then area=264+150=414 cm²
help me answer this question
Answer: Sorry i whould help but I cant see it can you put it more bigger
Step-by-step explanation:
If P(A) = 0.25, P(B) = 0.60 and P(A and B) = 0.15, are the event A and B independent? Explain/show work.
Answer:
event A and B are independent because P(A and B) = P(A) x P(B) = 0.15
Step-by-step explanation:
When two events are independent, the probability of both occurring is the product of their separate probabilities, as expressed below;
P(A and B) = P(A) x P(B)
Given;
P(A) = 0.25
P(B) = 0.60
P(A and B) = 0.15
Now, let's check if P(A and B) will be equal to P(A) x P(B)
P(A) x P(B) = 0.25 x 0.60 = 0.15
P(A and B) = P(A) x P(B), thus event A and B are independent.
2. Simplify.
–48
O A. 4213
OB. -4213
O C.-4v3
OD. 4V3
Solve the system of equations using any appropriate method: 5x + 2y = -4 and -x + 2y = 8
Plz help:(
A)(-2,3)
B)(1,3)
C)(3,2)
D)(6,12)
Answer:
A
Step-by-step explanation:
-x + 2y = 8
5x + 2y = -4
+ x. -2y. -8
6x = -12
÷6. ÷6
x = -2
5(-2) + 2y = -4
-10 + 2y = -4
+10. +10
2y = 6
÷2. ÷2
y = 3
which statement must be true
Answer:
(C)
Step-by-step explanation:
AD and BC are parallel to each other. They are the same distance but they never touch.
Your best answer would be C.
Brainilest appreciated.
Calculate:|a|−|b|+|c|, if a=−8; b=−5; c=1
Answer:
The answer is 4.
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
|x| just means positive x so the equation turns into 8-5+1
8-5 = 3
3+1 = 4
What is the slope of the line represented by y=3/4x-1 ? A. –1 B. -3/4 C. 3/4 D. 1
Answer:
3/4
Step-by-step explanation:
In the above equation the y-intercept is -1 and the slope of the equation is 3/4
Answer:
The answer is C or 3/4.
Step-by-step explanation:
This equation is in point-slope form or Y= mx+b. The variable m represents slope. So, just look for the number that stands in place of m. Hope this helps! Please mark Brainliest! :)
Which two terms are interchangeable
Answer:
C hope this helped :D if not plz let me know..
The terms that are interchangeable are axioms and postulates.
What are Axioms and Postulates ?"In mathematics or logic, an axiom is an unprovable rule or first principle accepted as true because it is self-evident or particularly useful. “Nothing can both be and not be at the same time and in the same respect” is an example of an axiom"
"The term is often used interchangeably with postulate, though the latter term is sometimes reserved for mathematical applications (such as the postulates of Euclidean geometry). It should be contrasted with a theorem, which requires a rigorous proof."
By the definition of Axiom and postulates,
It is clear that Axiom and postulates are interchangeable, since they both used as a unprovable rule.
Hence A is the correct option.
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what is the inequality
Answer:
An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. a ≠ b says that a is not equal to b. a < b says that a is less than b. a > b says that a is greater than b.
A number is multiplied by 4. That results is added to 12. The final number is 40. What is the original number.
A.) 2
B.) 7
C.) 13
D.) 22
Answer:
B.) 7
Step-by-step explanation:
7 x 4 = 28
28 + 12 = 40
:)
Using multiplication, the original number is 7.
What is multiplication?Multiplication is "the process multiplying that the integer is multiplied by number of time".
According to the question,
A number is multiplied by 4. The results is added to 12. The final number is 40. In order to find original number.
4x + 12 = 40
4x = 40 -12
4x = 28
x = 28/4
x = 7.
Hence, using multiplication, the original number is 7.
Learn more about multiplication here
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Complete the following ratios:
Answer:
700/821, 429/821, 700/429
Step-by-step explanation:
SOH, CAH, TOA
Sin= opp/hyp
Cos= adj/hyp
Tan= opp/adj
need help mark brain 30 points
Answer:
(6000)(0.03)(5)=$900
(1500)(0.0425)(4)=$255
(580)(0.02)(6)=$69.60
(1200)(0.039)(2.5)=$117
will give brainliest plz helppp!!!!
Answer:
A. True
B. False
C. False
D. False
Step-by-step explanation:
How much will the guitar be worth in 10 years?
Answer:
$44487
Step-by-step explanation:
If you plug in 10 for t, you are left with the following equation:
[tex]V=12000(1.14)^{10}=12000\cdot 3.7072\approx 44487[/tex]. Hope this helps!
Answer: $44,487
Step-by-step explanation:
To solve this, substitute t (the variable for time in the equation) with 10 to represent the value of the guitar after 10 years.
[tex]V = 12000(1.14)^{10}\\V = 12000*3.7072\\\\V = 44487[/tex]
The guitar will be worth $44,487 in 10 years.
HELP PLEASE!!
There are 12 students in a class: 7 boys and 5 girls. If the teacher picks a group of 5 at random, what is the probability that everyone in the group is a boy?
Answer:
0.027Step-by-step explanation:
The number of groups of 5 boys that we can have from 7 boys is 7C5 = 21
The number of groups of 5 boys that we can have from 12 students is
12C5 = 792
then the probability = 21/792 = 0.026515151515
by the way you can calculate 12C5 and 7C5 using a calculator.
Which set of numbers is correctly ordered from least to greatest?
24 x 63
5.7 15.758,956 V
63
24 x
S
15.758
4.956 Ve
9566 15.753, 24, 49
63
956 /
15.758
24 x
5
Answer:
The set of numbers that is correctly ordered from least to greatest is 5.7, 15.758, 24, 49, 63. Is there anything else you would like to know?
I will mark brainliest! The question is the image attached, please help!
Answer:
x=20 and y=128.Option 2
Step-by-step explanation:
Since,the angles are vertically opposite,they are equal(property)
Therefore,
(3x-8)=(2x+12)
3x-8=2x+12
3x-2x=12+8
x=20,
Now,
Since,the angles are formed in a straight line,their sum is equal to 180(property)
Therefore,
y+(2x+12)=180
y+2×20=180-12
y=168-40
y=128
Therefore,x=20 and y=128
option 2 would be your answer because it explains the missing part where y is.
Michael has $10 in his savings account. Option 1 will add $100 to his account each week. Option 2 will double the amount in his account at the end of each week. Michael wants to have at least $700 in his account at the end of 7 weeks to buy a mountain bike.
Answer:
i am thinking option 1
Step-by-step explanation:
i may be wrong if i am correct me
