[tex] \qquad \qquad \qquad \frac{1}{x} + \frac{3}{x } = 16[/tex]
This is how to solve your problem:
Combine fracrions with common denominator[tex] \qquad \qquad \frac{1}{x} + \frac{3}{x} = 16[/tex]
[tex] \qquad \qquad \frac{1 + 3}{ x} = 16[/tex]
Add the numbers[tex] \qquad \qquad \qquad\frac{1 + 3}{x} = 16[/tex]
[tex] \qquad \qquad\frac{4}{x} = 16 [/tex]
Multiply all terms by the same value to eliminate fraction denominators[tex] \qquad \qquad \qquad \color{skyblue}{ \frac{4}{x} = 16}[/tex]
[tex] \qquad \qquad \qquad \color{gold}{x .\frac{4}{x} = x.16}[/tex]
Cancel multiplied terms that are denominator[tex] \qquad \qquad \: x.\frac{4}{x} = x.16 [/tex]
[tex] \qquad \qquad 4 = x.16[/tex]
Re-order terms so constants are on the left[tex] \qquad \qquad4 = x.16[/tex]
[tex] \qquad \qquad 4 = 16x[/tex]
Divide boths sides by the same factor[tex] \qquad \qquad4 = 16x[/tex]
[tex] \qquad \qquad\frac{4}{16} = \frac{16x}{16} [/tex]
Simplifydivide the numbersCancel terms that are in both the numerator and denominatorMove the variable to the left[tex] \qquad \qquad x = \frac{1}{4} [/tex]
the final answer is :
[tex]x = \frac{1}{4} [/tex]
4. For v = -2i – 7j, find the unit vector in the direction of y, and write your answer as a linear combination of the standard unit vectors i and j
5. Find u•v if u = i + 2j and v = -i + 5j.
4. If v = -2i - 7j, then its magnitude is
||v|| = √((-2)² + (-7)²) = √53
and the unit vector in the direction of v is
[tex]\dfrac{v}{\|v\|} = \boxed{-\dfrac2{\sqrt{53}} \, \vec\imath - \dfrac7{\sqrt{53}} \, \vec\jmath}[/tex]
5. Given u = i + 2j and v = -i + 5j, we have
u • v = (i + 2j) • (-i + 5j) = -(i • i) - 2 (j • i) + 5 (i • j) + 10 (j • j)
Since i and j are orthogonal unit vectors, we have i • i = j • j = 1 and i • j = 0, so the product reduces to
u • v = -1 - 0 + 0 + 10 = 9
A fabric store is having a sale. The price of every item in the store has been reduced by 30%. Which equation shows the
proportional relationship between the regular price, r, of an item and its sale price, s?
Equation to show the proportional relationship between the regular price, r, of an item and its sale price, s is 10s -7r=0.
What is sale price?A sale price is the discounted price at which goods or services are being sold. This price is usually offered for a limited period of time, typically to spur sales during a slow period or to sell off excess inventory.
Let the regular price be r and sale price be 's'
Since price of every item reduced by 30%.
So, sale price will be
[tex]s= r- 30% of r[/tex]% of r
[tex]s= r- \frac{30}{100} *r[/tex]
s= r - 0.3 r
s= 0.7 r
s-0.7r=0
or, 10s -7r=0
Thus, equation shows the proportional relationship between the regular price, r, of an item and its sale price, s :10s -7r=0
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Out of 270 students in 6th grade, only 60% are going on the field trip. How many students are NOT going on the field trip
Step-by-step explanation: answer: 108
270
[tex]270 \times \frac{60}{100} [/tex]
[tex]27 \times 6 = 162[/tex]
270=60%
60% =162
40% = not going
270 students - 60% 162= 108
→108 students are not going
Answer:
270 students - 60% 162= 108
Step-by-step explanation:
Please help! Evaluate y = (x + 3)(x – 2) at x = r1 and then at x = r2. Show your work below.
The values of the function y = (x +3)(x - 2) at x = 1 and x = 2 are -4 and 0, respectively
How to evaluate the function?The function is given as:
y = (x +3)(x - 2)
When x = 1, we have:
y = (1 +3)(1 - 2)
y = -4
When x = 2, we have:
y = (2 +3)(2 - 2)
y = 0
Hence, the values of the function y = (x +3)(x - 2) at x = 1 and x = 2 are -4 and 0, respectively
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A carton of half & half costs $.98 for 4 cups. What is the cost per cup?
Answer:
$00.245
Step-by-step explanation:
.98/4=00.245
please mark brainliest
A triangle has a base length of 6ac² and a height 3 centimeters more than the base length. Find the
area of the triangle if a = 2 and c=3.
Hey there!
EQUATION:
6ac^2
ASSUMING:
= 6(2)(3)^2
SOLVING:
= 6(2)(3^2)
= 12(3^2)
= 12(3 * 3)
= 12(9)
= 108
Therefore, the answer should be: 108
Good luck on assignment & enjoy your day!
~Amphitrite1040:)
The sun came out and the temperature quickly rose 18 degrees. The a thunderstorm hits and the temperature drops 6 degrees. The sun comes back out the temperature raises 12 degrees. The temperature is now 94 degrees. What was the starting temperature?
Answer:
70
Step-by-step explanation:
Just do it backwards.
94 - 12 = 82.
82 + 6 = 88.
88 - 18 = 70.
The scale factor of a model car to the actual car is 300. If the model car is 2in tall, how tall is the actual car?
Answer:
600 inches or 50 feet
Step-by-step explanation:
Scale factor = model car : actual car = 1 : 300
We have a 2 inch model car.
2 in. : actual = 1 : 300actual = 2 × 300actual = 600 inches or 600/12 = 50 feetFind the surface area of a cylinder with a base radius of 5 cm and a height of 8 cm.
Use the value 3.14 for , and do not do any rounding.
Be sure to include the correct unit.
Answer:
408.40704
Step-by-step explanation:
Robert delivers papers every morning. On Sundays he has to deliver 65 papers and on each of the other days he only has to
deliver 38 papers. How many papers does Robert deliver each week?
A. 455
B. 331
C. 255
D. 293
Answer:
D. 293
Step-by-step explanation:
He delivers 38 papers each day of the week except sunday, so six days a week
38 x 6 = 228
228 + the 65 he delivers on sunday = 293 papers a week
This is had can you help me
Answer:
#9 is 6 #10 is 1 #11 is 7 #12 is 6
Step-by-step explanation:
what is 4,649 divided by 39
Answer:
[tex]4649 \div 39 = 119.205128295[/tex]
Step-by-step explanation:
I hope it's help u
Answer:
119 R 8
Step-by-step explanation:
convert 4649 to tens place, write 1
46 - 39 = 7
drop the 4 in the tens place, write 1
74 - 39 = 35
drop the 9 in the ones place, write 9
359 - 351 = 8
• For each time we got 39 or another number, we wrote the multiple of that number we used to get the result.
• We got the remainder by the general subtraction.
find the value of 7x+2y when x=2 and y=-9
Answer:
32
Step-by-step explanation:
7×18+2×18=32
x=14
y=18
Have a great day!
josiah is running a marathon which is 26 1/5 miles Long. At four 1/4 miles from the start, he meets his wife, who is cheering him on. 7 1/2 miles further down the marathon course, he sees some Friends from his running club volunteering at a water stop. Once he passes his friends, how many more miles does Josiah have left to run?
Once he passes his friends, The miles Josiah has left to run would be 10.95 miles.
What is addition?The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
Josiah is running a marathon which is 26 1/5 miles long.
At four 1/4 miles from the start, he meets his wife, who is cheering him on.
7 1/2 miles further down the marathon course.
26 1/5 = 131/ 5
7 1/2 = 15/2
The marathon run by Josiah
= 1/4 + 15/2
= 15.25
The miles Josiah has left to run
= 131/ 5 - 15.25
= 10.95
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(05.07) A square pyramid is shown. What is the surface area?
A square based pyramid, with bases labeled 3.5 centimeters and side length of triangle labeled 7 centimeters.
19.25 cm2
30.625 cm2
49.625 cm2
61.25 cm2
The surface area of the square based pyramid is 61.25 centimetre square
How to find the surface area of a square base pyramid?surface area of the pyramid = A + 1 /2 ps
where
A = area of the base
p = perimeter of the base
s = slant height
Therefore,
A = 3.5² = 12.25 cm²
p = 4(3.5) = 14 cm
s = 7 cm
Therefore,
surface area of the pyramid = 12.25 + 1 /2 × 14 × 7
surface area of the pyramid = 61.25 cm²
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help me plssssssssssssssssssssss
What is the value of x?
Answer:
a) 20
Step-by-step explanation:
90 - 46 = 44
44 - 4 = 40
40/2 = 20
A teacher bought 8 books at (p - 1500) each book and 2 pens at (p + 1000) each pen. If the teacher spent 53,000 altogether, how much money did he spend on the books?
Answer:
38400/=
Step-by-step explanation:
8(p-1500)=8p-12000
2(p+1000)= 2p+2000
8p-12000+2p+2000=53000
10p-10000=53000
10p=53000+10000
10p=63000
p=6300/=
8 books=8(6300-1500)
=38400/=
need help on my aleks chapter 5 lesson 3
Answer:
65º
Step-by-step explanation:
Angles in a triangle add to 180º so:
180- 44 - 71 = 180 - 115 = 65º
Full‐me Ph.D. students receive an average of $12,837 per year. If the
average salaries are normally distributed with a standard deviation of $1500, find these
probabilities.
a. A student makes more than $15,000.
b. A group of 36 students makes between $13,000 and $14,000.
Answer:
.0022
Step-by-step explanation:
can anyone answer this? i’ve had multiples tutors and none have been able to help.
Answer:
Area = 3430
Step-by-step explanation:
Graphing y = 28x - x^2 with it's limit interval (0<x<28). They ask for four sub-interval of LRAM.
Divide the base of 28 into 4 equal rectangles.
Area = (Base * Height) + (Base * Height) + (Base * Height) + (Base * Height)
Area = (0 * 7) + (147 * 7) + (196 * 7) + (147 * 7)
Area = 3430
3x + 2 = 14
Which number makes the equation true?
1
2
2
4
6
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
[tex]3x+2=14\\\\3x+2-2=14-2\\\\3x=12\\\\\displaystyle \frac{3x}{3}=\frac{12}{3}\\ \\ x=4[/tex]
There is a population of 15,500 bacteria in a colony. If the number of bacteria doubles every 234 hours, what will
che population be 936 hours from now?
bacteria
Answer:
2,48,000
Step-by-step explanation:
Initial population of bacteria = 15,500Bacteria doubles after every 234 hoursSo, after 0 (zero) hours, no of bacteria = 15,500After 234 hours, no. of bacteria = 2(15,500) = 31,000After 468 hours, no. of bacteria = 2(31,000) = 62,000 (2*234 = 468)After 702 hours, no. of bacteria = 2(62,000) = 124,000 (3*234 = 702)After 936 hours, no. of bacteria = 2(124000) = 2,48,000 (4*234 = 936)A snail crawls 83 cm due west and then
78 cm due north.
Work out the bearing of the snail from its
starting point.
Give your answer to the nearest degree.
Answer:
313°
Step-by-step explanation:
The reference angle (α) can be found using the tangent relation:
Tan = Opposite/Adjacent
__
In this problem, that means ...
tan(α) = 78/83
α = arctan(78/83) ≈ 43° . . . . . . angle from -x axis
The bearing angle will be this value added to 270°, since bearing angles are measured clockwise from north.
bearing = 270° +43° = 313°
PLS HELP ASAP WILL GIVE BRAINLIEST
Answer:
C
Step-by-step explanation:
None of the others are vertical angles
a is supplementary angles
b is supplementary angles
d is alternate interior angles
A car originally priced at $8,900 is on sale at 15% off. If the sales tax rate is 8.25%, how many dollars is the sale price of the car
If there is 15% off and the sales tax rate is 8.25%. Then the price of the car will be $ 8,189.11.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
A car originally priced at $8,900 is on sale at 15% off. If the sales tax rate is 8.25%.
The cost after 15% off will be
→ 0.85 × $8,900
→ $ 7,565
Then the final cost after the sale tax of 8.25% will be
Cost = $ 7,565 × 1.0825
Cost = $ 8,189.11
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last question before I go. [tex]x^{2} -y[/tex] when [tex]x = 4, y = 2[/tex].
Hey there!
x^2 – y
= 4^2 – 2
= 4 * 4 - 2
= 16 - 2
= 14
Therefore, the answer should be: 14
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
How many integers from 1 to 100 have a factor of 3?
Answer: 33 integers
Step-by-step explanation:
The numbers with a factor of 3 must be a multiple of 3. Therefore, since 99 is the greatest multiple of 3 that is less than 100, we can divide 99 by 3 to get 33 integers (for every 3 consecutive integers, there is one multiple of 3). We can also divide 100 by 3 to get 33 1/3, which rounds to 33 integers.
I hope this helps!
A circular tabletop has a circumference of 94.2 inches. What is its approximate area?
Answer:
1st choice : 706.5 square inches
Step-by-step explanation:
circumference is pi times diameter
divide 94.2 by pi to get diameter = 29.9847912785
diameter 29.9847912785 divided by 2 is
14.9923956393 which is the radius
area is pi times radius times radius again
pi times 14.9923956393 times 14.9923956393 =
706.141834613
Solve for -5v+6 = -12v+62 Simplify your answer as much as possible.
Hey there!
Answer :[tex] \displaystyle \blue{\boxed{\green{\bold{v = 8}}}} [/tex]
[tex] \\ [/tex]
Explanation:-5v + 6 = -12v + 62
[tex] \\ [/tex]
▪️Subtract 6 from both sides :
-5v + 6 - 6 = -12v + 62 - 6
-5v = -12v + 56
▪️Add 12v to each side :
-5v + 12v = -12v + 56 + 12v
7v = 56
▪️ Divide both sides by 7 :
7v / 7 = 56 / 7
v = 8
[tex] \\ [/tex]
Therefore, our answer is v = 8.
[tex] \\ [/tex]
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Answer:
v = 8
Step-by-step explanation:
Hello!
We can solve the equation by moving all terms of V to one side, and all integer values to the other.
Solve-5v + 6 = -12v + 62-5v + 6 + 12v = -12v + 62 + 12v7v + 6 = 627v + 6 - 6 = 62 - 67v = 56v = 56/7v = 8The value of v is 8.
We can plug back 8 into the original to check our answer:
-5(8) + 6 = -12(8) + 62-40 + 6 = -96 + 62-34 = -34Since both sides match, the solution of v = 8 is correct.