Answer:
[tex]A=2044[/tex]
Step-by-step explanation:
Note that [tex]x\in\mathbb{W}[/tex] denotes that [tex]x[/tex] is a whole number.
By definition, consecutive numbers follow each other when we count up (e.g. 1, 2, 3).
Let's consider our conditions:
A, B, and C are consecutive whole numbers greater than 2,000A is a multiple of 4B is a multiple of 5C is a multiple of 6Since B is a multiple of 5, the ones digit of B must be either 0 or 5. However, notice that the number before it, A, needs to be a multiple of 4. The ones digit of a number preceding a ones digit of 0 is 9. There are no multiples of 4 that have a ones digit of 9 and therefore the ones digit of B must be 5.
Because of this, we've identified that the ones digit of A, B, and C must be 4, 5, and 6 respectively.
We can continue making progress by trying to identify the smallest possible whole number greater than 2,000 with a units digit of 6 that is divisible by 6. Notice that:
[tex]2000=2\mod6[/tex]
Therefore, [tex]2000-2=1998[/tex] must be divisible by 6. To achieve a units digit of 6, we need to add a number with a units digit of 8 to 1,998 (since 8+8 has a units digit of 6).
The smallest multiple of 6 that has a units digit of 8 is 18. Check to see if this works:
[tex]C=1998+18=2016[/tex]
Following the conditions given in the problem, the following must be true:
[tex]A\in \mathbb{W},\\B\in \mathbb{W},\\C\in \mathbb{W},\\A+1=B=C-1,\\A=0\mod 4,\\B=0\mod 5,\\C=0\mod 6,[/tex]
For [tex]C=2016[/tex], we have [tex]B=2015[/tex] and [tex]A=2014[/tex]:
[tex]A\in \mathbb{W},\checkmark\\B\in \mathbb{W},\checkmark\\C\in \mathbb{W},\checkmark\\A+1=B=C-1,\checkmark\\A=2014\neq 0\mod 6, \times\\B=2015=0\mod 5,\checkmark\\C=2016=0\mod 6\checkmark\\[/tex]
Not all conditions are met, hence this does not work. The next multiple of 6 that has a units digit of 8 is 48. Adding 48 to 1,998, we get [tex]C=1998+48=2046[/tex].
For [tex]C=2046[/tex], we have [tex]B=2045[/tex] and [tex]A=2044[/tex]. Checking to see if this works:
[tex]A\in \mathbb{W},\checkmark\\B\in \mathbb{W},\checkmark\\C\in \mathbb{W},\checkmark\\A+1=B=C-1,\checkmark\\A=2044=0\mod 4,\checkmark\\B=2045=0\mod 5,\checkmark\\C=2046=0\mod 6\checkmark[/tex]
All conditions are met and therefore our answer is [tex]\boxed{2,044}[/tex]
If f(x) = 3x + 5 and g(x) = -2x2 - 5x + 3, find (f + g)(x).
Answer:
A
Step-by-step explanation:
(f+g)(x) simply means you add f(x) and g(x).
[tex]-2x^2-5x+3x+3+5=(f+g)(x)[/tex]
We can then simplify by combining like terms to get
[tex]-2x^2-2x+8[/tex]
A is correct!
PLEASE HELP! URGENT. the law of cosines is a2+b2-2abcosC=c2. Find the value of 2abccosC.
Answer:
D
Step-by-step explanation:
2ab*cos(C)=a^2+b^2-c^2
2ab*cos(C)=5^2+4^2-2^2=25+12=37
Answer:
The answer is 37
Step-by-step explanation:
3 1/2 + (-5 2/3 ) ÷ ( 1 3/4)²
are there any inputs that cannot be evaluated by the function 6/x-3?
Answer:
as written
[tex]\frac{6}{x} -3[/tex] zero would not be allowed....
BUT !!! I think that your question
is ......
[tex]\frac{6}{x-3}[/tex] then the answer is "3"
Step-by-step explanation:
Find the height of the triangle
Answer:
The height is 12 cm
Step-by-step explanation:
Hi there!
We are given a triangle with the 3 sides marked as 15, 20, and 25 and we want to find the height of it (marked as x in the problem).
This problem can seem a bit difficult, but let's see if the triangle is a right triangle first off.
One way to figure out if it is a right triangle is to apply the converse of the Pythagorean theorem.
Let's label the sides, where a is the shortest side, b is the second shortest side, and c is the longest side:
a=15
b=20
c=25
Now square a and b, then add the result together. If it's the same as c squared, then the triangle is a right triangle
15²+20²=25²
225+400=625
625=625
So we can safely say that the triangle is a right triangle
This makes the problem way easier, as there are 2 ways to find the area of a right triangle:
The first way is to multiply the legs (the sides that make up the right angle) together, then divide the result by 2
The other way is to multiply the height and the hypotenuse (the side OPPOSITE to the right angle) together, and then divide the result by 2
First, we need to figure out which sides are the legs, and which side is the hypotenuse
By the triangle inequality theorem, the hypotenuse of a right triangle is the longest side, which means that the 25 cm side is the hypotenuse, and that leaves 15 cm and the 20 cm sides as the legs
So let's find the area of the triangle using the legs
A=[tex]\frac{15*20}{2}[/tex]=[tex]\frac{300}{2}[/tex]=150
So the area of the triangle is 150 cm²
However, as mentioned above, we can also find the area of the triangle by multiplying the hypotenuse by the base, then dividing the result by 2
Which means that the area is also:
A=[tex]\frac{25x}{2}[/tex] cm²
As these both equal the area of the triangle, we can set them equal to each other. This is possible via a property known as transitivity (if a=b and b=c, then a=c)
[tex]\frac{25x}{2}=150[/tex]
Multiply both sides by 2
25x=300
Divide both sides by 25
x=12 cm
So the height of the triangle is 12 cm
Hope this helps!
The question is
"Mia has a large bag of sweets, If i share the sweets equally among 1,2,3,4,5 or 6 people, there will always be 1 sweet left over"
with step by step pls :(
Answer:
61
or
421
Step-by-step explanation:
Find the L.C.M. of 2,3,4,5,6 and add 1.
2| 2-3-4-5-6
-------------------
2| 1-3-2-5-3
---------------------
3| 1-3-1-5-3
----------------------
5| 1-1-1-5-1
----------------------
| 1-1-1-1-1-1
L.C.M.=2×2×3×5=60
reqd. number=60+1=61
if i distribute between 2,3,4,5,6 people then reqd number is 61
if Mia is also among those people or she gets also share
then the people are2,3,4,5,6 or 7
L.C.M. of 2,3,4,5,6,7=60×7=420
so reqd number is 420+1=421
melanie is cutting a 6 1/2 inch piece of yarn from a string that is 15 3/4 inches long how much yarn will be left
Answer:
9 1/4 inches would be left
Step-by-step explanation:
Evaluate C(6, 3)
120
720
20
Answer:
20
Step-by-step explanation:
C(6,3) = 6!/[3!(6-3)!]
= 20
Which property of equality would be used to isolate the variable b in this equation?
3/4 x b = 12
A. addition property of equality
В. subtraction property of equality
C. multiplication property of equality
D. symmetric property of equality
Answer:
C. multiplication property of equality
Step-by-step explanation:
3/4b = 12
Multiply each side by 4/3 using the multiplication property of equality
4/3* 3/4b = 12*4/3
b = 16
help me please
[tex] \frac{ \cos(80) }{ \sin(10) } + \frac{ \sin(20) }{ \cos(70) } = 2 \\ \\ \frac{ \cot(40) }{ \tan(50) } + \frac{ \cos(65) }{ \sin(115) } = 2[/tex]
Answer:
[tex] \frac{ \cos(80) }{ \sin(10) } + \frac{ \sin(20) }{ \cos(70) } = 2 \\ \frac{ \cos(90 - 10) }{ \sin(10) } + \frac{ \sin(20) }{ \cos(9 0 - 20) } = 2 \\ \frac{ \sin(10) }{ \sin(10) } + \frac{ \sin(20) }{ \sin(20) } = 2 \\ 1 + 1 = 2 \\ 2 = 2 \\ \\ \frac{ \cot(40) }{ \tan(50) } + \frac{ \cos(65) }{ \sin(115) } = 2 \\ \frac{ \cot(90 - 50) }{ \tan(50) } + \frac{ \cos(65) }{ \sin(90 + 65) } = 2 \\ \frac{ \tan(50) }{ \tan(50) } + \frac{ \cos(65) }{ \cos(65) } = 2 \\ 1 + 1 \\ = 2[/tex]
What is the answer in scientific notation?
(5.1 × 106) x (4.3 × 105)
A 0.8 × 106
B 0.8 × 105
C 4.67 × 105
D 4.67 × 106
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{\star \ (5.1 \times10^6) \times (4.3 \times 10^5)\ \star}[/tex]
[tex]\huge\boxed{10^6}[/tex]
[tex]\huge\boxed{= 10 \times 10 \times10 \times10 \times10 \times 10}[/tex]
[tex]\huge\boxed{= 100\times 100\times100}[/tex]
[tex]\huge\boxed{= 10,000\times100}[/tex]
[tex]\huge\boxed{= \bf 1,000,000}[/tex]
[tex]\huge\boxed{\star\ (5.1 \times 100,000) \times(4.3 \times 10^5)\ \star}[/tex]
[tex]\huge\boxed{10^5}[/tex]
[tex]\huge\boxed{= 10 \times 10 \times10 \times 10 \times 10}[/tex]
[tex]\huge\boxed{= 100\times100\times 10}[/tex]
[tex]\huge\boxed{= 10,000\times10}[/tex]
[tex]\huge\boxed{= \bf 100,000}[/tex]
[tex]\huge\boxed{\star \ (5.1 \times 1,000,000) \times (4.3\times 100,000)\ \star}[/tex]
[tex]\huge\boxed{5.1 \times 1,000,000}[/tex]
[tex]\huge\boxed{= \bf 5,100,000}[/tex]
[tex]\huge\boxed{4.3 \times 100,000}[/tex]
[tex]\huge\boxed{= \bf 430,000}[/tex]
[tex]\huge\boxed{\star\ 5,100,000 \times 430,000\ \star}[/tex]
[tex]\huge\boxed{= \bf 2,193,000,000,000}[/tex]
[tex]\huge\boxed{0.8 \times 10^6}[/tex]
[tex]\huge\boxed{= \bf 800,000}[/tex]
[tex]\huge\boxed{0.8 \times 10^5}[/tex]
[tex]\huge\boxed{= \bf 80,000}[/tex]
[tex]\huge\boxed{4.67\times10^5}[/tex]
[tex]\huge\boxed{= \bf 467,000}[/tex]
[tex]\huge\boxed{4.67 \times 10^6}[/tex]
[tex]\huge\boxed{= \bf 4,670,000}[/tex]
[tex]\huge\boxed{\textsf{Therefore, this makes the answer: \bf NONE}}\\\hug\boxed{\textsf{of the \bf ABOVE}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}}[/tex]
Find the value of x and y
[tex]\\ \rm\Rrightarrow \dfrac{x}{2}=3[/tex]
[tex]\\ \rm\Rrightarrow x=2(3)[/tex]
[tex]\\ \rm\Rrightarrow x=6[/tex]
And
[tex]\\ \rm\Rrightarrow \dfrac{y}{2}+1=3[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{y}{2}=3-1=2[/tex]
[tex]\\ \rm\Rrightarrow y=2(2)[/tex]
[tex]\\ \rm\Rrightarrow y=4[/tex]
Answer:
x=6 y=4
Step-by-step explanation:
Equating corresponding terms , we get
x/2=3
or, x=6
Also,
y/2+1=3
or, (y+2/2)=3
or, y+2=6
or, y=6-2
y=4
Therefore, x=6 and y=4.
please solve it
find the value of x
Answer:
The measure of angle x is 25 degrees.
Step-by-step explanation:
Since triangle ABC is an isosceles triangle, the measure of angle BAC is equal to the measure of angle ACB. Angle ABC = 80 degrees, leaving 100 degrees to be divided equally for the measures of the other two angles. Now that you know that angle ACB = 50 degrees, you can calculate the value of angle ACD and determine that angle ACD = 130 degrees. Triangle ACD is also an isosceles triangle, and the two equal legs are AC and CD. Since angle ACD = 130 degrees, the other two angles have a total of 50 degrees. Splitting the 50 degrees equally between the two angles gives you 25 degrees as the value of angle CAD, which is labeled "x."
What is the least common multiple of 70, 60, and 50?
Answer:
2100
Step-by-step explanation:
LCM of 70, 60, and 50?
First, find the prime factorization of each number.
70 = 2 * 5 * 7
60 = 2^2 * 3 * 5
50 = 2 * 5^2
The LCM is the product of some of the factors above. These are the factors you need to multiply together.
Choose factors that are common with the highest exponent and also factors that are not common.
Common factors: There is a 2, a 2^2, and a 2. Use the 2^2.
There is a 3. Use it.
There is a 5 and a 5^2. Use the 5^2.
There is a 7. Use it.
LCM = 2^2 * 3 * 5^2 * 7
LCM = 2100
Answer: 2100
What is the solution of the system of equations?
y = –3x + 7
y = 2x – 8
Answer:
(3,-2)
Step-by-step explanation:
The easiest way to solve this is to realize that in both equations, the ys must have the same value. So the right side of each equation can be equal.
-3x + 7 = 2x - 8 Add 8 to both sides
-3x + 7 + 8 = 2x Combine
-3x + 15 = 2x Add 3x to both sides
15 = 2x + 3x Combine and exchange sides
5x = 15 Divide by 5
x = 15/5
x = 3
Use y = 2x - 8 to solve for y
y = 2(3) = 8
y = 6 - 8
y = - 2
Correct answer gets 5 stars and brainliest
Answer:
Does the answer help you?
Answer:
D
Step-by-step explanation:
Using the converse of Pythagoras' identity.
If the square of the longest side is equal to the sum of the squares on the other two sides then the triangle is right.
longest side = 12 and 12² = 144
5² + 8² = 25 + 64 = 89
Since 5² + 8² ≠ 12² , then triangle is not right → D
help lol i forgot everything of the summer time
fill in the table using this function rule
Answer:
hope it help you
Step-by-step explanation:
mark me brailiest answer
17 + 5x = -23
please help
Answer:
x= -8
Step-by-step explanation:
Answer:
[tex]17 + 5x = - 23 \\ 5x = - 23 - 17 \\ 5x =-4 0 \\ x = \frac{ - 40}{5} \\ \boxed{x = - 8}[/tex]
Therefore, the value of x is -8.PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Convert 110011 no decimal number System
(110011)2 = (51)10
Step by step solution
Step 1: Write down the binary number:
110011
Step 2: Multiply each digit of the binary number by the corresponding power of two:
1x25 + 1x24 + 0x23 + 0x22 + 1x21 + 1x20
Step 3: Solve the powers:
1x32 + 1x16 + 0x8 + 0x4 + 1x2 + 1x1 = 32 + 16 + 0 + 0 + 2 + 1
Step 4: Add up the numbers written above:
32 + 16 + 0 + 0 + 2 + 1 = 51.
So, 51 is the decimal equivalent of the binary number 110011.
round 2.034 to the nearest whole number
Answer:
2
Step-by-step explanation:
2.034
We are rounding to the ones place.
To round, look at the digit to the right of which we are rounding. In this case, it is 0.
0 is less than 5, so we just keep the 2.
I hope this helps!
pls ❤ and mark brainliest pls!
Answer:
2
Step-by-step explanation:
2.034 can be rounded to 2.000, or 2. This is because the digit after the two in the tenths place, 0, is less than 5.
Brainliest, please!
Find two different integers such that the square of the integer is 12 less than seven times the integer
9514 1404 393
Answer:
3, 4
Step-by-step explanation:
If x represents the integer, then the relationship required is represented by the equation ...
x^2 = 7x -12
x^2 -7x +12 = 0 . . . . put in standard form
(x -3)(x -4) = 0 . . . . . factor
The values of x that make this relation true are x=3 and x=4.
The two integers are 3 and 4.
I need help with this question
Answer:
m
Step-by-step explanation:
If a school camp has enough food for 150 students over 5 days
How long would the food last for is only 100 students are there
Answer:
It is over 7 days
hope it helps
Find X
A. 3
B. sqrt6
C. 3sqrt3
D. 3sqrt2/2
Answer:
B. sqrt 6 is the answer.maja
What is the image of (-5,-5) after a dilation by a scale factor of 3 centered at the origin
Answer:
(-15,-15)
Explanation:
The dilation of 3 to the image means that each coordinate point is multiplied by 3. So, multiplying -5*3 gets you -15.
Find the surface area of the composite figure
Answer:
144 cm²
Step-by-step explanation:
This figure is formed by rectangles and triangles, so we need to find the surface area of they and add all to have the surface area of the figure:
area of the rectangles:
4×3 = 12, and there are two of these rectangles
6×3 = 18, and there are just one of that
4×6 = 24, and there are two of these
5×3 = 15, and there are two of these
Now the area of a triangle:
6×4/2 = 12, and there are two of these
12×2 + 18 + 24×2 + 15×2 + 12×2 = 144 cm²
Simplify the expression
Answer:
B
Step-by-step explanation:
[tex] \frac{{3}^{5} }{ {3}^{3} } = {3}^{5 - 3} = {3}^{2} = 9 [/tex]
right answers only!!!
Step-by-step explanation:
7
Find the length of the third side. If necessary, round to the nearest tenth.
4
Submit Answer
Answer:
attempt 1 out of 2
PLS HELP ASAP
Answer:
5
Step-by-step explanation:
p=4 b=3 h=?
h²=p²+b²
=4²+3²
=16+9
h²=25
h=5
