Answer:
630.
Find the Prime factorization of 45, 3 x 3 x 5
Find the prime factorization of 70, 2 x 5 x7
Multiply each factor the greater number of times it occurs.
You get 630.
LCM of 45 and 70 :
= 45 ÷ 5 , 70 ÷ 5 ( Both the numbers are being divided by 5 ; which is their smallest common factor )
= 14 , 9
= 14 ÷ 14 , 9 ( We are dividing 14 by 14 as both 9 and 14 dont have have a common factor )
= 1 , 9
= 1 , 9 ÷ 3 ( 9 is being divided by 3 )
= 1 , 3
= 1 , 3 ÷ 3 ( 3 is being divided by 3 )
= 1 , 1
LCM of 45 and 70 = 5 × 14 × 3 × 3
LCM of 45 and 70 = 630
Therefore , the LCM of the 45 and 70 = 630 .
f(x) = x^2- 51 when f (-7)
Answer:
f(x)= -2
Step-by-step explanation:
f(x) = x^2- 51
-7^2-51
49-51
-2
f(x)= -2
Find the product of each expression using properties of complex numbers.
1. (x + 3i)(x − 3i)
2. (x − 4i)(x + 4i)
3. (x + 8i)(x − 8i)
Answer:
[tex](x+3\mathbf{i})(x-3\mathbf{i})=x^2+9[/tex]
[tex](x-4\mathbf{i})(x+4\mathbf{i})=x^2+16[/tex]
[tex](x+8\mathbf{i})(x-8\mathbf{i})=x^2+64[/tex]
Step-by-step explanation:
Complex Numbers
The complex numbers are known by having an 'imaginary' part along with the real part. They can be expressed like a + bi, where
[tex]\mathbf{i}=\sqrt{-1}[/tex]
Or, equivalently:
[tex]\mathbf{i}^2=-1[/tex]
Let's find the result of the following products. On each one of them, there is a sum of a binomial multiplied by the subtraction of a binomial with the very same terms. It leads to a well-known polynomial identity:
[tex](a+b)(a-b)=a^2-b^2[/tex]
1. [tex](x+3\mathbf{i})(x-3\mathbf{i})[/tex]
Applying the above-mentioned identity:
[tex](x+3\mathbf{i})(x-3\mathbf{i})=(x^2-(3\mathbf{i})^2)[/tex]
[tex]=x^2-9\mathbf{i}^2[/tex]
Since [tex]\mathbf{i}^2=-1[/tex]
[tex](x+3\mathbf{i})(x-3\mathbf{i})=x^2-9(-1)[/tex]
[tex]=x^2+9[/tex]
2. [tex](x-4\mathbf{i})(x+4\mathbf{i})[/tex]
Proceed in the same way as before:
[tex](x-4\mathbf{i})(x+4\mathbf{i})=(x^2-16\mathbf{i}^2)[/tex]
[tex]=(x^2-16(-1))[/tex]
[tex]=x^2+16[/tex]
3. [tex](x+8\mathbf{i})(x-8\mathbf{i})[/tex]
[tex](x+8\mathbf{i})(x-8\mathbf{i})=(x^2-64\mathbf{i}^2)[/tex]
[tex]=(x^2-64(-1))[/tex]
[tex]=x^2+64[/tex]
Three families bought food at the baseball game. The Smith family spent $16.50 on 3 hot dogs, 2 sodas, and 1 candy bar. The Patterson family spent $26 on 4 hot dogs, 4 sodas, and 2 candy bars. The Nguyen family spent $13.75 on 2 hot dogs, 1 soda, and 3 candy bars. Which of the following systems of equations could be used to determine the price of each item?
Answer:
Step-by-step explanation:
Let
Price of
Hotdogs = x
Sodas = y
Candy bar = z
Smith family
Hotdogs = 3
Sodas = 2
Candy bar = 1
Total cost = $16.50
3x + 2y + z = 16.50
Patterson family
Hotdogs = 4
Sodas = 4
Candy bar = 2
Total = $26
4x + 4y + 2z = 26
Nguyen family
Hotdogs = 2
Sodas = 1
Candy bar = 3
Total cost = $13.75
2x + y + 3z = 13.75
The equations
3x + 2y + z = 16.50 (1)
4x + 4y + 2z = 26 (2)
2x + y + 3z = 13.75 (3)
Multiply (1) by -2
-2(3x + 2y + z = 16.50)
-6x - 4y - 2z = -33
-6x - 4y - 2z = -33 (1a)
4x + 4y + 2z = 26 (2)
Add (1a) and (2)
-6x + 4x = -33 + 26
- 2x = -7
x = -7/-2
= 3.5
x = $3.5
Multiply (3) by -4
-4(2x + y + 3z = 13.75) (3)
-8x - 4y - 12z = -55 (3a)
Add (3a) and (2)
-8x - 4y - 12z = -55 (3a)
4x + 4y + 2z = 26 (2)
-8x + 4x -12z + 2z = -55 + 36
-4x - 10z = -29
Substitute the value of x into
-4x - 10z = -29
-4(3.5) - 10z = -29
-14 - 10z = -29
-10z = -29 + 14
-10z = - 15
z = -15 / - 10
= 1.5
z = $1.5
Substitute values of x and z into (1)
3x + 2y + z = 16.50
3(3.5) + 2y + 1.5 = 16.50
10.5 + 2y + 1.5 = 16.50
12 + 2y = 16.50
2y = 16.50 - 12
2y = 4.50
y = 4.50 / 2
y = $2.25
Of the 50 students in the cafeteria, 7 have red hair. Suppose there are 750 students in the school. Write a proportion that could be used to predict the number of students who have red hair. Use x to represent the number of students who have red hair.
Given:
Of the 50 students in the cafeteria, 7 have red hair.
Total number of students = 750
To find:
The proportion that could be used to predict the number of students who have red hair.
Solution:
Let x represent the number of students who have red hair.
The ratio of student having red hair to the total number of students are
[tex]Ratio_1=\dfrac{7}{50}[/tex]
[tex]Ratio_2=\dfrac{x}{750}[/tex]
The number of students having red hair is proportional to the total number of students. So, the above ratios are equal.
[tex]\dfrac{x}{750}=\dfrac{7}{50}[/tex]
Multiply both sides by 750.
[tex]\dfrac{x}{750}\times 750=\dfrac{7}{50}\times 750[/tex]
[tex]x=7\times 15[/tex]
[tex]x=105[/tex]
Therefore, the required equation is [tex]\dfrac{x}{750}=\dfrac{7}{50}[/tex] and the number of students who have red hair is 105.
How much is the number 727731000 in percent form
I need yall to answer this question quickly you will recieve a ton of points if you do.
Answer:
72773100000%
Step-by-step explanation:
"Percent" means "per 100" or "over 100". So, to convert 727731000 to percent we rewrite 727731000 in terms of "per 100" or over 100.
Multiply 727731000 by 100/100. Since 100/100 = 1, we are only multiplying by 1 and not changing the value of our number.
7277310001×100100=72773100000100
72773100000/100 is 72773100000 over 100 and means 72773100000 per 100. 72773100000 "per 100" means 72773100000 "percent" or 72773100000%
Therefore, we have shown that
727731000 = 72773100000%
Simplified Conversion:
Multiply by 100 and add the percent sign %
727731000 × 100 becomes 72773100000%
Shortcut Conversion:
Move the decimal point 2 places to the right and add the percent sign %
727731000 becomes 72773100000%
I need someone to solve this pls
Answer:
linear
Step-by-step explanation:
I WILL MARK AS BRAINLLIEST TO WHOEVER ANSWER THIS RIGHT AWAY:)!
and 50 points
The distributive property can be used to rewrite the expression 3(4 + 2) as 3(4) + 3(2).
True or False
Answer:
18
Step-by-step explanation:
On a coordinate plane, a curved line with a minimum value of (5.1, negative 7) and a maximum value of (0, 25), crosses the x-axis at (negative 3.4, 0), (3.9, 0), and (6, 0), and crosses the y-axis at (0, 25).
Which statement is true about the local minimum of the graphed function?
Over the interval [–4, –2], the local minimum is 0.
Over the interval [–2, –1], the local minimum is 25.
Over the interval [–1, 4], the local minimum is 0.
Over the interval [4, 7], the local minimum is -7.
Answer:
D
Step-by-step explanation:
The rest of the question is the attached figure and the statement options.
A. Over the interval [–4, –2], the local minimum is 0.
B. Over the interval [–2, –1], the local minimum is 25.
C. Over the interval [–1, 4], the local minimum is 0.
D. Over the interval [4, 7], the local minimum is -7.
============================================================
According to the graph, we will check the options:
A. Over the interval [–4, –2], the local minimum is 0. (Wrong)
Because the minimum is -12
B. Over the interval [–2, –1], the local minimum is 25. (Wrong)
Because the minimum is 18
C. Over the interval [–1, 4], the local minimum is 0. (Wrong)
Because the minimum is at x = 4 less than zero
D. Over the interval [4, 7], the local minimum is -7. (True)
Answer:
The answer would be D
Step-by-step explanation:
Multiply. Enter the product in simplest form.
17/8 x 14/51
Answer:
7/12 or in decimal form it is .583
Step-by-step explanation:
Please mark brainliest!
hope this helps!
Find the next three numbers in the pattern.
1,4,9,16,
Answer:25,36,49
Step-by-step explanation:
Answer:
25 , 36 , 49Step-by-step explanation:
1 , 4 , 9 , 16 , 25 , 36 , 49
1 + 3 + 5 + 7 + 9 + 11 + 13 = ↑
Hope this helps! <3
which single transformation could be used to map quadrilateral EFGH to quadrilateral EFGH
Answer:
H
Step-by-step explanation:
how is 0.0000267 written in scientific notation
Answer: 6.7*10^-5
Step-by-step explanation:
Answer:
-5
2.67x10
Step-by-step explanation:
that's the answer brainliest plsss
I have been stuck on this for 1 hours someone plz help me
Answer:
answers in PDF
Step-by-step explanation:
What would the points be if y=2x-5 domain's are : -2, -1, 0, 1, 2,
Answer:
-9, -7, -5, -3, -1
I will give you branilest!
Here is a circle with center H and some line segments and curves joining points on the circle. Identify ONE example of each of the following.
a. Diameter
__________
b. Radius
_________
(Be sure that your book includes your written reasoning.)
Answer:
a) line [EA]
b) line [HA]
Step-by-step explanation:
Answer:
a) line(EA)
b) line(HA)
Step-by-step explanation:
You are a screenwriter who is writing a script for an hour-long police drama. You have written 20 1/2 pages for act 1 and 5 1/2 pages for act 2.
How many pages have you written in total?
Answer:
You have written 26 pages in total.
Step-by-step explanation:
I always enjoyed adding fractions. Something about it is so... simple.
The problem is basically asking us to add 20 1/2 and 5 1/2 together.
I would first suggest adding both halves together, to make 1.
That way, we're left with 20 + 5 + 1. That seem easier, doesn't it?
Then we would add 20, 5 and 1 together, to get 26 whole pages.
And that, to an extent, is how I did it.
Hope this helps! :D
Answer:
Given:
Written pages for Act 1 = 20 1/2
Written pages for Act 2 = 5 1/2
For making mixed numbers like this easier to add, let's convert them first into an irrational number with this formula,
((Whole Number × Denominator) + Numerator)/Denominator
Thus,
for 20 1/2
((20 × 2) + 1)/2 = 41/2
for 5 1/2
((5 × 2) + 1)/2 = 11/2
Then we add,
41/2 + 11/2
Since, they have the same denominator, no more conversions need, proceed adding the numerators,
(41 + 11)/2 = 52/2 = 26
You've written 26 pages in total.
20 POINTS AND 5 STARS
Find the quadratic function.
You decide to borrow a loan of $2,500 to go on vacation. The banks loans you the money at 9%for 7 months. How much interest will you pay?
Answer:
umm 1500? hmqmmmmmm
ye
#1 What is the difference between
an expression and an equation?
please please help me!!
Answer:
C. f(x)=3x-4
Step-by-step explanation:
slope formula is (y2-y1)/(x2-x1)
(-1+4)/(-1-0)
3/1=3
The slope is going up and to the right so it is positive
Ben bought 1 2/3 pounds of jelly beans and 2 3/8 pounds of jolly ranchers. What are the total pounds of candy that Ben bought?
Answer:
4 1/24
Step-by-step explanation:
1 2/3 +2 3/8 = 5/3 +2 3/8 = 5/3 + 19/8 = 97/ 24 =4 1/24
I don't understand this...
Answer:
If x is 55, z is also 55. Now subtract, and boom! you get 15 degrees
Step-by-step explanation:
I think the whole triangle is 125* total, and has three sides, one smaller than the rest. Hope this helps!
AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH sombody help me:(
Answer:
Step-by-step explanation:
5.
a+2=b
b-5=c
c-3=d
d+4=e
e=2-5-3+4
e=-2 (a loss of 2 yards)
6.
-2+2.5=0.5
Jason bought 4 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 39 cards left. How many cards did Jason start with?
Answer:
78
Step-by-step explanation:
What are the Slope and the Equation of the Image?
change in y/change in x
y2-y1/x2-x1
-1--5/0-2
-1+5/-2
4/-2
-2
slope is -2
now take one ordered pair and plug it into the equation (for this example i will use the SECOND ordered pair
y = -2x +b
-1 = -2(0)+b
-1 = b
the equation is
y = -2x - 1
The product of 12 and a number is greater than 24.
NEED HELP IM BEGGING YOU PLEASE !!!!!
Answer:
1.5t+2=4 and 2/3
1.5t=2 and 2/3
t= 1 and 7/9
1/2 1/7 2/5 in mixed number simplified
Answer:
They are all in simplest form. Is that what you mean?
i find the difference of
the two sum
14581 +4 185 41 and 23427+23243
Answer:
by adding 14581+418541=433,122
by adding 23427+23243=46,670
by substraction of both Numbers=
difference between both number is 386,452