Write the prime factorization of each number in e-g.
e. 25
f. 100
g. 16
Answers
Answers:
25 = 5*5 which is the same as 25 = 5^2
100 = 2*2*5*5 which is the same as 100 = 2^2*5^2
16 = 2*2*2*2 which is the same as 16 = 2^4
====================================================
Explanation:
To find the prime factorization of 25, we divide by prime numbers. We see that 25/2 = 12.5 isn't a whole number, and neither is 25/3 = 8.33 (approx). But 25/5 = 5 is a whole number. The result is a prime number so we can stop here. This shows that 25 = 5*5 = 5^2
------------
We'll do the same for 100 as well. Start with dividing over 2
100/2 = 50
50/2 = 25
we can't do 25/2 as mentioned earlier, but we can say 25/5 = 5
So basically 100 = 2*2*25 = 2*2*5*5 = 2^2*5^2
-------------
The same will happen with 16 as well. We divide by 2 until we arrive at a prime number result
16/2 = 8
8/2 = 4
4/2 = 2
We have three 2's as denominators and that last result 2 is included in the set of prime factors as well to say 16 = 2*2*2*2 = 2^4
-------------
The factor tree for each is shown below. For something like 100, there are a few ways to draw out the tree. The same applies for 16 as well.
Related Questions
To combine integers with different signs find their _ _ then _ the smaller absolute value from the larger one give the sum the sign of the number with the _ absolute
Answers
Answer:
absolute valuessubtractlargestStep-by-step explanation:
To combine integers with different signs find their absolute values then subtract the smaller absolute value from the larger one. Give the sum the sign of the number with the largest absolute value.
Compute $(1 + i)(2 + i)(3 + i).$
Answers
Answer:
10i
Step-by-step explanation:
Step 1: Expand first 2
(1 + i)(2 + i)
2 + i + 2i + i²
2 + 3i + (-1)
1 + 3i
Step 2: Expand again
(1 + 3i)(3 + i)
3 + i + 9i + 3i²
3 + 10i + 3(-1)
3 + 10i - 3
10i
6(n - 2) - 8 = 22 + 4(2-n)
Answers
Answer:
5
Step-by-step explanation:
6n -12 -8=22+8-4n
6n-20=30-4n
6n=50 -4n
10n = 50
5
There are 30 names in a hat. If two names are picked without replacement, which expression shows the probability that Jack and Jill will be picked?
Answers
Answer: Choice C)
(1/30)*(1/29)
Explanation:
Jack has a 1/30 chance of being picked since he is 1 person out of 30 total. After his name is picked, and not put back, there are 30-1 = 29 names left. The chances Jill is picked is 1/29. The two fractions are multiplied to get the overall probability both are picked.
Twelve decreased by twice a number is -8. Find the number
Answers
Let the number be "x" , then according to the question :
• 2x - 12 = -8
Further solving
→ 2x = -8 + 12
→ 2x = 4 .
→ x = 2
★ Solution :
Let number be n.
[tex]\rule{130}{1}[/tex]
☯ [tex]\underline{\boldsymbol{According\: to \:the\: Question\:now :}}[/tex]
[tex]:\implies\sf 2n - 12 = -8 \\\\\\:\implies\sf 2n = -8 + 12\\\\\\:\implies\sf 2n = 4\\\\\\:\implies\sf n = \dfrac{4}{2}\\\\\\:\implies\underline{\boxed{\sf n = 2}}\:\:\:\:\:\Bigg\lgroup\bf{Required\: number}\Bigg\rgroup[/tex]
[tex]\therefore\:\underline{\textsf{The required number is \textbf{2}}}.[/tex]
Fatima has 2 gallons of milk she wants to pour all milk into glasses which each hold 1 cup (1/16 gallon). how many cups can she fill
Answers
Answer:
32 cups
Step-by-step explanation:
1 cup= 1/16 gallon
? cup= 2 gallon ( crisscross)
⇒[tex]\frac{2*1}{\frac{1}{16} }\\ \frac{2}{\frac{1}{16}} \\2*16=32 cups[/tex]
Mrs. Taylor is making new football uniforms for Fridays nights homecoming game. The trim fro the sleeves of one uniform requires 26 inches of fabric. Mrs Taylor needs to make 63 uniforms total. How many yards of fabric should she buy?
Answers
Answer:
Mrs Taylor should buy 45.5 yards of fabric ( 45.5364 actually but rounded to the nearest tenth)
Step-by-step explanation:
Here in this question, we are interested in calculating the total yards of fabric that Mrs Taylor should buy.
From the question, we are made to know that one uniform requires 26 inch of fabrics and she wants to make a total of 63 uniforms
The total inches of fabric needed is thus; 26 * 63 = 1,638 inches of Fabrics
But we want our answer in yards.
Mathematically;
1 inch = 0.0278 yard
1638 inches = x yard
x = 1638 * 0.0278 = 45.5364 yards which is approximately 45.5yards
Round off to three significant digits: 4.53619
Answers
Answer:
4.54
Step-by-step explanation:
The 4th digit (6) is greater than 4, so the 3rd digit (3) is increased by 1 before you drop the remaining digits:
4.54
Can someome please help me solve this my teacher hasn't done a good with teaching us this.
[tex](5.{10}^{2)} + (3 \times {10}^{4}) [/tex]
Answers
Answer:
30500 = 3.05·10^4
Step-by-step explanation:
Your calculator can do this for you. You may need to set the display to scientific notation, if that's the form of the answer you want.
__
This can be computed by converting both numbers to standard form:
(5·10^2) +(3·10^4)
= 500 +30000 = 30500 = 3.05·10^4
__
Addition of numbers in scientific notation in general requires that they have the same power of 10. It may be convenient to convert both numbers to the highest power of 10.
5·10^2 + 3·10^4
= 0.05·10^4 +3·10^4 . . . . now both have multipliers of 10^4
= (0.05 +3)·10^4
= 3.05·10^4
I need help again help me pllsssssss
Answers
Answer: you end up at (2,2)
Step-by-step explanation:
Answer:
2,2
Step-by-step explanation:
go down to the bottom right corner (5,-5)
move over left 3 boxes
and then up 7 boxes
hope this helps :P
Your hotel sells four types of rooms: double queen beds for $140/night; king bed for $160/night; junior suite for $220, and full business suites for $285. If there are 200, 150, 100, and 50 of each, respectively, what is your average price per room?
Answers
Answer:
$176.50
Step-by-step explanation:
Take each room type and multiply the number of rooms by the price of the room. Add the total for prices and add the total for the number of rooms. Divide the total prices by the total number of rooms.
Type of room Number Cost Total
Double queen 140 $200.00 $28,000.00
King 160 $150.00 $24,000.00
Junior Suite 220 $100.00 $22,000.00
Full business 285 $50.00 $14,250.00
$500.00 $88,250.00
Average cos per room $176.50
an object is dropped from the top of a cliff 675 meters high. its height above the ground t seconds after it is dropped is 675-4.9t^2. determine its speed 7 seconds after it is dropped, the speed if the object 7 seconds after it's dropped in m/sec
Answers
Answer:
V= 68.6 m/s
Step-by-step explanation:
height above the ground t seconds after it is dropped is 675-4.9t^2
For seven seconds
Height above ground= 675-4.9(7)²
height above ground= 675-240.1
Height above ground= 434.9 m
But it's dropped from a cliff and we need to find the distance traveled from the too of the cliff
Distance= 675-434.9.
Distance= 240.1
To determine it's speed
V²= U² +2gs
V= velocity we are looking for
U= initial velocity= 0
G= acceleration due to gravity= 9.8 m/s²
s= distance covered
V²= U² +2gs
V²= 0+2(9.8)(240.1)
V²= 4705.96
V= 68.6 m/s
4x + 6 - 11 help needed
Answers
Answer:
4x-5Step-by-step explanation:
[tex]4x+6-11\\\\\mathrm{Add/Subtract\:the\:numbers:}\:6-11=-5\\=4x-5[/tex]
If someone could plz help. p÷5=3.
Answers
Answer:
p=2
Step-by-step explanation:
so how to find this u take the five and three and u subtract them both and whatever is left over that is your answer
I'm genuinely lost in any problems like this and my teachers are no help, I need help doing exponents in general, everything to do with them. I genuinely need help
Answers
Answer:
See below.
Step-by-step explanation:
4)
So we have the expression:
[tex](-6n^{-3})^2[/tex]
We can use the power of a product property, where:
[tex](ab)^n=a^n\cdot b^n[/tex]
So:
[tex]=(-6)^2\cdot(n^{-3})^2[/tex]
For the left, -6 squared is the same as -6 times -6. This equals positive 36.
For the right, we can use the power of a power property. The property says that:
[tex](a^n)^k=a^{nk}[/tex]
So:
[tex](n^{-3})^2=n^{(-3)(2)}\\=n^{-6}[/tex]
So, all together, we have:
[tex]=(-6)^2\cdot(n^{-3})^2\\=36n^{-6}[/tex]
6)
We have the expression:
[tex]-\frac{3x^0}{x^4}[/tex]
First, note that anything to the zeroth power (except for 0) is 1, thus, x^0 is also 1. Simplify:
[tex]=-\frac{3}{x^4}[/tex]
And that's the simplest we can do :)
Notes for 6)
We can put the x^4 to the numerator. Recall that when you put an exponent to opposite side, you put a negative. In other words:
[tex]x^n=\frac{1}{x^{-n}}[/tex]
And vice versa:
[tex]\frac{1}{x^{-n}}=x^n[/tex]
So, we can write the above as:
[tex]=-\frac{3}{x^4}\\=-\frac{3}{x^{-(-4)}}\\=-3x^{-4}[/tex]
However, traditionally, we want only positive exponents, so this wouldn't be correct.
Answer:
Step-by-step explanation:
x^m×x^n=x^{m+n}
x^m÷x^n=x^{m-n}
[tex]\frac{1}{x^m} =x^{-m}\\x^{-n}=\frac{1}{x^n} \\(xyz)^m=x^m\times y^m \times z^m \\(x^m)^n=x^{mn}[/tex]
[tex]x^0=1[/tex]
(4 + 2i) + (-3 – 5i) show your work
Answers
Answer:
[tex] \boxed{ \bold{ \huge{\boxed{ \sf{ - 3i + 1}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{(4 + 2i) + ( - 3 - 5i)}[/tex]
When there is a ( + ) in front of an expression in parentheses, there is no need to change the sign.
That means the expression remains the same.
Just remove the parentheses
[tex] \sf{4 + 2i - 3 - 5i}[/tex]
Collect like terms
⇒[tex] \sf{ - 3i + 4 - 3}[/tex]
Calculate the difference
⇒[tex] \sf{ - 3i + 1}[/tex]
Hope I helped!
Best regards!!
9514 1404 393
Answer:
1 -3i
Step-by-step explanation:
For purposes of addition or subtraction, the i can be treated as though it were a variable. Terms can be collected in the usual way.
4 +2i +(-3 -5i) = 4 +2i -3 -5i
= (4 -3) +i(2 -5) = 1 -3i
Find two numbers in-between 0.004 and 0.005
Answers
The 14 digits of a credit card are written in the boxes shown.If the sum of any three consecutive digits is 20, what is the
value of A?
Answers
Answer:
9
Step-by-step explanation:
Working backwards, the blank box between the 7 and 4 at the end must be 9 in order for the three digits to equal 20. Then we see the pattern of 947 repeated. The whole number would be 94794794794794. That way, any three consecutive numbers would be 20. The number in the box marked a would be 9.
Evaluate 1/3m−1−1/2n when m=21 and n=12
Answers
Answer:
[tex]0[/tex]
Step-by-step explanation:
[tex] \frac{1}{3}m - 1 - \frac{1}{2}n = \frac{1}{3}(21) - 1 - \frac{1}{2}(12) = 7 - 1 - 6 = 6 - 6 = 0[/tex]
Answer:
0
Step-by-step explanation:
1/3m - 1 - 1/2n
= 1/3(21) -1 1/2(12)
= 7 - 1 - 6
= 0
3+g=a/3h
what does a equal
Answers
Answer:
a = 3gh+9hStep-by-step explanation:
[tex]3+g = \frac{a}{3h} \\\\Cross\:Multiply\\\\3h(3+g) = a\\9h +3gh = a\\\\a = 3gh+9h[/tex]
Need help with this question. I tried simplifying the radical, but apparently it’s not the answer
Answers
Answer:
-1/5+(√3)/20i or -0.2+0.05√3i
Step-by-step explanation:
[tex]\dfrac{-8+\sqrt{-12}}{40}=-\dfrac{8}{40}+\dfrac{2\sqrt{3}i}{40}=\boxed{-\dfrac{1}{5}+\dfrac{1}{20}\sqrt{3}\,i=-0.2+0.05\sqrt{3}\,i}[/tex]
_____
Comment on answer form
Satisfying the input format requirements of a computer is always problematic. One never knows if fractions or decimals are preferred, whether radicals must be simplified, and so on. If no clues are offered by general instructions, other questions, or previous experience, then it might be useful to consult your instructor.
12d^2 + 3dx + x
- (-4d^2 + 2dx - 8x)
Answers
Answer:
dx+9x+16d^2 dont know it it helps any but i tried
Step-by-step explanation:
Simplify. 1/2−3(12+1)2 Enter your answer, as a simplified fraction, in the box.
Answers
Answer: -506.5 or -253.25
Step-by-step explanation:
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Hi my lil bunny!
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[tex]\frac{1}{2}-3\ \left(12\ +\ 1\right)^2[/tex]
[tex]= \frac{1}{2}-3 (13^2)[/tex]
[tex]= \frac{1}{2} - (3) (169)[/tex]
[tex]= \frac{1}{2} - 507[/tex]
[tex]= \frac{-1013}{2}[/tex]
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Have a great day/night!
❀*May*❀
Brett and Max are diving. Brett is 34 feet below the surface and Max is 25 feet below the surface. How many feet above Brett isMax?
Answers
Answer:
Max is 9 ft above Brett
Step-by-step explanation:
Brett is 34 feet below the surface = -34
Max is 25 feet below the surface = -25
Subtract the heights
-25 - -34
-25 +34
9
Max is 9 ft above Brett
can someone help me graph this.
Answers
Answer:
Use a graphing calc.
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
For the third equation, m = 2
y = 2x + b
3 = 3(2) + b
3 = 6 + b
b = -3
y = 2x - 3
Jay just bought a new 75" television for his apartment. The opening in the entertainment center (where the tv will be placed) is only 70 inches by 35 inches. If the newer television has an aspect ratio of 16:9, will the new tv fit in the old entertainment center? Justify your answer by finding the width and height of the new television.
Answers
Answer:
Width of the new tv= 65.44 inches
Height of the new tv = 36.41 inches
If the newer television has an aspect ratio of 16:9, will the new tv fit in the old entertainment center?
Since the old entertainment set has a dimension of 70 inches by 35 inches
,new TV set, has dimension of 65.44 inches by 36.81 inches, the new TV may not be able to fit into the old entertainment set properly because it is 1.81 inches higher than the entertainment set.
Step-by-step explanation:
The newer TV set has an aspect ratio of 16: 9 and it is 75 inches
We are going to make use of Pythagoras theorem
= Width² + Height ² = Size of TV²
Width = 16x
Height = 9x
75² = (16x)² + (9x)²
5625 = 256x² + 81x²
5625 = 337x²
x² = 5625/337
x² = 16.691394659
x = √16.691394659
x = 4.0855103303
Approximately = 4.09
Hence, we can find the width and height of the new TV
Width = 16x
Width = 16 × 4.09
Width = 65.44 inches
Height = 9x
Height = 9 × 4.09
Height = 36.81 inches
Hence, the dimensions of the new TV set = 65.44 inches by 36.81 inches
If the newer television has an aspect ratio of 16:9, will the new tv fit in the old entertainment center?
Since the old entertainment set has a dimension of 70 inches by 35 inches
,new TV set, has dimension of 65.44 inches by 36.81 inches, the new TV may not be able to fit into the old entertainment set properly because it is 1.81 inches higher than the entertainment set.
2/3x+15=17 please and thank you
Answers
Answer:
x=3
Step-by-step explanation:
2/3x+15=17
first subtract 15 from both sides
2/3x=2
multiply by 3 to eliminate the fraction
2x=6
divide by 3
x=3
Answer:
x=3
Step-by-step explanation:
2/3x +15 = 17
2/3x = 17-15
2/3x = 2
x = 2 / 2/3
x = 2/1 * 3/2
x = 6/2
x = 3
Order the following expressions by their values from least to greatest.
Answers
Answer:
-2, b, a+c
Step-by-step explanation:
Answer:
All you have to do is switch A + C and B around. (basically if you wrote it out, it would look like this: -2, B, A + C.)
5 pizzes are shared equally between 10 people. What fraction of a pizza does each person receive?
Answers
Answer:
1/2
Step-by-step explanation:
Is x^4+3x^3-x+7 in standard form
Answers
Answer:
yes
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
The standard form of a polynomial has the exponents decreasing left to right. Here, the exponents are 4, 3, 1, 0, so are decreasing left to right. The expression is in standard form.