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There are 3 methods to find the lowest common multiple (LCM)
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Method 1
List out the multiples of 6 and 8
multiples of 6 = {6, 12, 18, 24, 30, 36, 42, 48, ...}
multiples of 8 = {8, 16, 24, 32, 40, 48, ...}
We see that 24 is the smallest number in both sets at the same time. So this is the LCM.
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Method 2
Write the prime factorization of 6 and 8
prime factorization of 6 = 2*3
prime factorization of 8 = 2*2*2
The unique prime factors here are 2 and 3. We have 2 show up at most three times meaning that 2*2*2 = 8 is a factor of the LCM. The number 3 is also a factor meaning that 8*3 = 24 is the LCM.
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Method 3
Multiply the denominators 6 and 8 to get 6*8 = 48
48 is a common multiple, but its not the smallest
we can divide 48 over the GCF 2 to get 48/2 = 24, which is the actual LCM.
So when you have 2 different denominators, you can multiply their values and then divide by the GCF to get the LCM.
The density of Venus, compared to Earth having a density of 1,
is 0.943. The density of Mercury is 0.983, compared to the
density of Earth. Which planet has a greater density, Venus or
Mercury?
Answer:
Mercury
Step-by-step explanation:
We'll translate this into ratios.
First, V:E = 0.943:1
Then, M:E = 0.983:1
We already have their density in terms earth's density. They are in the same unit. So, we can compare them directly, with greater ratio means greater density. It's clear that Mercury has the greater density.
find the square root of 2304 by division method
Answer:
Hope it helps you ♥️
Step-by-step explanation:
Solve the formula 4x + 7y = 5 for y.
Answer:
39x
Step-by-step explanation:
Just multiply 7 by 5 and that equals-35
now you just add 4x by 35 and that equals-39x
3.
Which of the following equations does not have a real solution?
(A) x + x = 1
(B) x + x=0
(C) x*x=0
(D) x*x=-1
Answer:
I think the right answer is d
Answer:
The last equation (D): doesn't have a real solution
Step-by-step explanation:
Notice that equation A has for solution x = 1/2
Equation B has for solution x = 0
Equation C has for solution x = 0
There is no real number that multiplied by itself can render a negative value.
Write this number in expanded form. 268,741
Answer:
200000+60000+8000+700+40+1
Step-by-step explanation:
268,741
2 is in the hundred thousands place 200000
2 is in the ten thousands place 60000
8 is in the thousands place 8000
7 is in the hundreds place 700
4 is in the tens place 40
1 is in the one place 1
Add these together
200000+60000+8000+700+40+1
Answer:
[tex](2\times100000)+(6\times10000)+(8\times 1000)+(7\times100)+(4\times10)+(1\times1)[/tex]
Step-by-step explanation:
So we want to write 268,741 in expanded form.
To do so, first take a look at what each digit means starting from the right.
268,741
This means 1 1s.
268,741
This means 4 10s.
268, 741
This means 7 100s.
268,741
This means 8 1000s.
268,751
This means 6 10,000s.
and 268,751.
This means 2 100,000s.
Therefore, 268,741 is 2 100,000s plus 6 10,000s plus 8 1000s plus 7 100s plus 4 10s plus 1 1s.
In expression form, this would be:
[tex](2\times100000)+(6\times10000)+(8\times 1000)+(7\times100)+(4\times10)+(1\times1)[/tex]
For one of their science experiments students needed 10 1/2 liters of water. If there were 7 groups
doing the same experiment, how much water did they need for all of the groups?
Answer:
73.5 liters of water
Step-by-step explanation:
10 1/2× 7= 73.5
The amount of water that they need for all of the groups will be 73.5 liters.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
For one of their scientific tests, understudies required 10 ¹/₂ liters of water. Assuming there were 7 gatherings doing likewise analysis.
The amount of water that they need for all of the groups will be calculated as,
⇒ (10 ¹/₂) x 7
Simplify the expression, then we have
⇒ (10 ¹/₂) x 7
⇒ (10 + ¹/₂) x 7
⇒ (21/2) x 7
⇒ 147/2
⇒ 73.5 liters
The amount of water that they need for the gatherings will be all 73.5 liters.
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The formula for the volume V of a rectangular prism is V = ℓwh, where ℓ represents the length, w represents the width, and h represents the height. Rearrange the quantities in this formula to give a new formula for the width of the rectangular prism.
Answer:
w = V / lh
Step-by-step explanation:
V = ℓwh
Where,
V=volume of a rectangular prism
l= length of the rectangular prism
w= width of the rectangular prism
h= height of the rectangular prism
Rearrange the quantities in this formula to give a new formula for the width of the rectangular prism.
V = ℓwh
It can be written as
V = l * w * h
w = V ÷ l * h
= V / lh
w = V / lh
Width of a triangular prism equals Volume of the rectangular prism divided by length of the rectangular prism times height
A jogger leaves his house runs 15 km on a straight track in a North westerly direction to a lake. The lake is 2.9 km north of the joggers house. find the bearing of the lake from the joggers house correct to the nearest degree
Answer: 281.1 degree
Step-by-step explanation:
Given that a jogger leaves his house runs 15 km on a straight track in a North westerly direction to a lake. The lake is 2.9 km north of the joggers house.
Using pythagorean theorem to find the third side, which is 14.72
The angle at the lake side will be achieved by using sine rule.
Please find the attached file for the solution and explanation.
While solving an equation, if the variable term becomes zero, and the equation make a false statement, then the solution is
Answer:
no solution
Step-by-step explanation:
Then there is no solution.
Answer:
No solution.
Step-by-step explanation:
Then the equation has no solution.
For example
2x - 2 = 2x + 1
-2x - 2x
-2 = 1.
What is the distance between (6, 2) and (-3, -2)?
Answer:
√97 ≈ 9.85 units
Step-by-step explanation:
The distance formula can answer this question.
d = √((x2 -x1)^2 +(y2 -y1)^2) = √((-3-6)^2 +(-2-2)^2) = √(81 +16) = √97
The distance between the points is √97 ≈ 9.85 units.
Alice has 2 dogs, ollie and taffy, ollie eats 2/3 of a tin of dog food every day and taffy eats 2/5 of a tin everyday, Alice buys a crate of 24 tins. How many whole days should the crate last?
Answer:
Step-by-step explanation:
2/3 + 2/5 = 10/15 + 6/15 = 16/15 tins per day
24 tins divided by 16/15 = 24/1 divided by 16/15
To divide one fraction by another, take reciprocal of the other and then multiply.
24/1 x 15/16 = 360/16 = 22 1/2 days
Please Help. I really don’t get this concept, if you could explain it in detail it would be very appreciated
=================================================
Explanation:
Sine is given to be negative, and so is tangent. This only happens in quadrant Q4
Recall that y = sin(theta), so if sin(theta) < 0, then we're below the x axis.
If tan(theta) < 0, then this means cos(theta) > 0
So we have y < 0 and x > 0 which places the angle somewhere in Q4.
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Draw a right triangle as shown below in the attached image. We have AC = 25 and BC = 7. Use the pythagorean theorem to find that AB = 24
So this is what your steps may look like
a^2+b^2 = c^2
7^2+b^2 = 25^2
b^2+49 = 625
b^2 = 625-49
b^2 = 576
b = sqrt(576)
b = 24
So because AB = 24, we know that the cosine of the angle is adjacent/hypotenuse = 24/25
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As an alternative, you could use the trig identity
sin^2(x) + cos^2(x) = 1
and plug in the given value of sine to solve for cosine. The cosine value result will be positive since we're in Q4.
So,
sin^2(x) + cos^2(x) = 1
(-7/25)^2 + cos^2(x) = 1
(49/625) + cos^2(x) = 1
cos^2(x) = 1 - (49/625)
cos^2(x) = (625/625) - (49/625)
cos^2(x) = (625-49)/625
cos^2(x) = 576/625
cos(x) = sqrt(576/625)
cos(x) = sqrt(576)/sqrt(625)
cos(x) = 24/25
This is effectively a rephrasing of the previous section since the pythagorean trig identity is more or less the pythagorean theorem (just in a trig form)
What’s the square root of 10 to the nearest thousandth
Answer:
3.162
Step-by-step explanation:
on a calculator type in sqrt of 10 and round it to three decimal places
kevin has 70 cents in his pocket. one coin is a quarter, and the others are nickels. how many nickels does he have?
Answer:
Step-by-step explanation:
25 +5+5+5+5+5+5+5+5+5=70
Answer: 9nickels
In Niagara-on-the-Lake, you can ride a horse-drawn carriage for a fixed price plus a variable amount that depends on the length of the trip. The variable cost is $10/km and a 2.5-km trip costs $40. a) Determine the equation relating cost, C, in dollars, and distance, d, in kilometres. b) Use your equation to find the cost of a 6.5-km ride. c) Graph this relation. d) Use the graph to find the cost of a 6.5-km ride.
Answer:
Step-by-step explanation:
a) The cost of a product is given as:
Cost = a + bx
Where a is the fixed cost, b is the variable cost, x is the independent variable.
In this case, the independent variable is the distance(d), therefore:
Cost (C) = a + bd
C = a + bd
But the variable cost is $10/km, therefore:
C = a + 10d
A 2.5 km trip cost $40, therefore:
40 = a + 10(2.5)
40 = a + 25
a = 40 - 25 = 15
The fixed cost is $15. Therefore the equation for cost is:
C = 15 + 10d
b) C = 15 + 10d
For 6.5 km ride:
C = 15 + 10(6.5) = 15 + 65 = 80
It would cost $80 for a 6.5 km drive.
6. Christopher can make enough iced coffee for one
person by mixing two teaspoons of espresso
with 4 ounces of water. How many tablespoons
of espresso would he need to make enough iced
coffee for 24 people? (3 teaspoons =
1 tablespoon
A) 12
B) 16
C) 48
D) 144
R
Answer:
B) 16
Step-by-step explanation:
Espresso required for one person:
2 teaspoonsEspresso required for 24 people:
2*24 = 48 teaspoons3 teaspoons = 1 tablespoon
48 teaspoons = 48/3 = 16 tablespoons
Christopher needs 16 tablespoons of espresso.
Correct answer choice: B) 16
b. Simplify (1-3) (⅓+√3), leaving your answer in the form P+Q√3
Answer:
6
Step-by-step explanation:
Ally sliced 32 \text{ kg}32 kg32, start text, space, k, g, end text of watermelon for a party. She divided the watermelon slices equally between 888 large bowls
Complete question :
Ally sliced 32 kg of watermelon for a party. She divided the watermelon slices equally between 8 large bowls.
How many grams of watermelon did Ally put in each bowl?
Answer:
4000g
Step-by-step explanation:
Given the following :
Mass of water melon sliced = 32kg
Number of bowls water melon was shared equally in = 8
Therefore, mass of water melon on each bowl :
Mass of water melon / number of bowls
= 32kg / 8
= 4kg
Note:
1000g = 1kg
Therefore,
4kg = (4 * 1000)
= 4000 grams
Therefore, amount in gram of watermelon put in each bowl is 4000g
Calculate the area of this diagram
[tex]A=\frac{1}{2}\cdot a\cdot b\cdot \sin\angle AB\\\\A=\frac{1}{2}\cdot6\cdot6\cdot\sin38^\circ\\\\A=18\cdot0.616\\\\\boxed{A=11.0819}[/tex]
Please help I do not get
Answer:
(a) 51%
(b) 41%
Step-by-step explanation:
We can simplify this problem down by realizing that the amount of girls over 200 will get us our percentage as a decimal.
Looking at this table, we can see that [tex]30+72=102[/tex] girls were asked. So, [tex]102\div200=0.51[/tex], and [tex]0.51\cdot100=51[/tex].
We can also see that [tex]30+52=82[/tex] people preferred video games, so [tex]82\div200=0.41[/tex], and [tex]0.41\cdot100=41[/tex].
Hope this helped!
Answer:
[tex]\Large \boxed{\mathrm{(a) \ 51\% }} \\ \\ \Large \boxed{\mathrm{(b) \ 41\%}}[/tex]
Step-by-step explanation:
(a) To find the percentage of the students that are girls:
[tex]\displaystyle \sf \frac{total \ number \ of \ girls}{number \ of \ students }[/tex]
[tex]\displaystyle \sf \frac{30+72}{200 }= \frac{102}{200 } =51\%[/tex]
(b) To find the percentage of students that prefer playing video games:
[tex]\displaystyle \sf \frac{total \ number \ of \ students \ that \ prefer \ playing \ video \ games}{number \ of \ students }[/tex]
[tex]\displaystyle \sf \frac{30+52}{200 }=\frac{82}{200} = 41\%[/tex]
A number minus 4 equals 19. Which equation fits this statement?
A 4-X=19
BX-4 = 19
C 4 = X-19
D 19 - X=4
please help :) Write the number shown in standard notation. 6.6 x 10 to the 5 power A. 6,600 B. 660,000 C. 66,000 D. 6,600,000
Answer: Hi!
The equation given is 6.6 * 10^5.
First, we will solve the exponent.
10^5 = 100,000
Next, we will multiply 100,000 by 6.6.
100,000 * 6.6 = 660,000
Therefore, your answer is b), 660,000.
Hope this helps!
Given that El bisects ZCEA, which statements must be
true? Select three options,
mZCEA = 90°
mZCEF = m ZCEA + m ZBEF
mZCEB = 2(m ZCEA)
ZCEF is a straight angle.
ZAEF is a right angle.
Question: Given that BE bisects ∠CEA, which statements must be true? Select THREE options.
(See attachment below for the figure)
m∠CEA = 90°
m∠CEF = m∠CEA + m∠BEF
m∠CEB = 2(m∠CEA)
∠CEF is a straight angle.
∠AEF is a right angle.
Answer:
m∠CEA = 90°
∠CEF is a straight angle.
∠AEF is a right angle
Step-by-step explanation:
Line AE is perpendicular to line CF, which is a straight line. This creates two right angles, <CEA and <AEF.
Angle on a straight line = 180°. Therefore, m<CEA + m<AEF = m<CEF. Each right angle measures 90°.
Thus, the three statements that must be TRUE are:
m∠CEA = 90°
∠CEF is a straight angle.
∠AEF is a right angle
The correct statements from the given diagram is m∠CEA = 90°, m∠CEF = m∠CEA + m∠BEF and m∠CEB = 2(m∠CEA)
Lines and anglesFrom the given diagram, we have the following information
∠CEF is a straight angle.
∠AEF is a right angle.
Line AE is perpendicular to line CF, which is a straight line. This creates two right angles, <CEA and <AEF.
Since the angle on a straight line is 180 degrees, hence;
<CEA + m<AEF = m<CEF
Hence, the three statements that must be TRUE are m∠CEA = 90°, ∠CEF is a straight angle and ∠AEF is a right angle
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A new youth center is being built in erie. The perimeter of the rectangular playing field is 274 yards. The length of the field is 4 yards less than double the width. What are the dimensions of the playing field? need width and length in yards
Answer:
width is 47 and the length is 90
Step-by-step explanation:
Hello!
You find the perimeter by adding all the sides
l + l + w + w = p
The perimeter is 274
l + l + w + w = 274
It says the length is 4 less than double the width
l = 2w - 4
We can put this into the original equation
2w - 4 + 2w - 4 + w + w = 274
Now we solve
Combine like terms
6w - 8 = 274
Add 8 to both sides
6w = 282
Divide both sides by 6
w = 47
We can put w into the orginal equation to find l
l + l + 47 + 47 = 274
Combine like terms
2l + 94 = 274
Subtract 94 from both sides
2l = 180
Divide both sides by 2
l = 90
The answer is the width is 47 and the length is 90
Hope this helps!
Answer:
lenght: 90 yards
width: 47 yards
Step-by-step explanation:
perimeter = 2(length + width)
274 = 2(h + w)
h = 2w - 4
h = length
w = width
then:
274 = 2((2w-4) + w)
274/2 = 2w - 4 + w
137 = 3w - 4
137 + 4 = 3w
141 = 3w
w= 141/3
w = 47 yd
h = 2w - 4
h = 2*47 - 4
h = 94 - 4
h = 90 yd
probe:
274 = 2(47 + 90)
274 = 2(137)
A function f(x) has range {yer 1-50}. Explain why reflecting the function vertically would not affect the range
Answer:
For the reflection property, we have;
For reflection vertically, which is equivalent to reflection across the y-axis, we have;
Let the location or point of the pre-image before, reflection be (x, y), then, the location or point of the image after reflection will be (-x, y)
Therefore, the y-coordinates remains the same
Given that the range of the function is the value of f(x) or y from 1 - 50, which are the y-coordinate values of the function, it will not be affected by the vertical reflection of the function.
Step-by-step explanation:
A store polled its customers about the fit of jeans they preferred. the two-way frequency table shows the result of the poll.
doing this because its already answered and I need points. But to be safe, Itds the second option going to the right. (aka the top right option)
Step-by-step explanation:
The two-way frequency table shows the result of the poll is in option "B".
What is frequency table?Frequency refers to the number of times an event or a value occurs. A frequency table is a table that lists items and shows the number of times the items occur.
According to the question
A store polled its customers about the fit of jeans they preferred.
The two-way frequency table shows the result of the poll.
As the frequency table have 4 columns and 3 rows
In which columns have : Regular , Slim , Bootcut , Total
In which rows have : Male , Female ,Total
To check which option is correct we will check whether total is correct for column is row or not
Option A :
This option is incorrect
1st column is not correct as total should be 1 but it is 0.5 .
Option B:
This option is correct as total is correct for column and row .
Option C:
This option is incorrect as total of column Bootcut is not correct .
Option D:
This option is incorrect as total of all columns are incorrect .
Hence, the two-way frequency table shows the result of the poll is in option "B".
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a way to make a approximation to a given number by using fewer digits is called.
Answer:
Rounding
Step-by-step explanation:
Rounding is a way to make an approximation to a given number by using fewer digits.
Answer:
Rounding
Step-by-step explanation:
A way to make a approximation to a given number by using fewer digits is called rounding
How you round:If the next smallest place value is greater than or equal to five (5, 6, 7, 8, or 9), you increase the value of the digit you're rounding to by one (+1). Any remaining digits before the decimal point become zeros, and any that are after the decimal point are dropped.Find the exact area of the shaded region. A. 16π−8 cm² B. 42.3 cm² C. 92.5 cm² D. 84.6 cm2
Answer:
A = (16π - 8) cm^2
Step-by-step explanation:
The shaded area is trhe area of the circle minus rthe area of the truiangle,.
A = πr^2 - bh/2
A = π(4 cm)^2 - (4 cm)(4 cm)/2
A = 16π cm^2 - 8 cm^2
A = (16π - 8) cm^2
The exact area of the shaded region is (16π - 8) [tex]cm^{2}[/tex].
Option (A) is correct.
To find the shaded area.
What is circle?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”.
Given that:
Height of triangle is same as that of base because is equal to radius of circle.
The shaded area is area of the circle minus the area of the triangle.
A = π[tex]r^2 - bh/2[/tex]
A = π[tex]4^{2}[/tex] - (4 cm)*(4 cm)/2
A = (16π - 8 )[tex]cm^{2}[/tex]
A = (16π - 8) [tex]cm^{2}[/tex]
The exact area of the shaded region is (16π - 8) [tex]cm^{2}[/tex].
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If A = {1, 2, 3} and B = {1, 2, 2, 3}, is B ⊆ A? If so, is A = B?
Answer:
yes, yes
Step-by-step explanation:
B={1,2,3} it doesn't matter if it has ten 2's or one!
so A=B and A⊆B
What is the value of the expression below?
Negative 8 + 19 + 8
A. 0
B. 11
C. 19
E. 35
I believe it's 19 but next thing you know it's a complete different equation :
Answer:
c .19
Step-by-step explanation: