The result of the log function [tex]log_a (m * n ^ 2)[/tex] is 60
According to the law of logarithm if [tex]log_ab=y[/tex] then [tex]b=a^y[/tex]
Given the following expressions
[tex]log_am=10\\log_an=25[/tex]
This can be expressed as
[tex]m =a^{10} \ and \ n = a^{25}[/tex]
Substitute the value of m and n into the expression [tex]log_a (m * n ^ 2)[/tex] to have:
[tex]log_a (m * n ^ 2) = log_a(a^{10}\times a^{50})\\=log_aa^{60}\\=60log_aa\\=60(1) \\= 60[/tex]
This shows that the result of the log function [tex]log_a (m * n ^ 2)[/tex] is 60
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10, 18, 26, 34, 42, ...
Write the simplified formula (expression) for the given Arithmetic Sequence
Answer:
[tex]10 + (n - 1) 8[/tex]
Step-by-step explanation:
All arithmetic sequence can be written as:
[tex]a_{n} = a_{1} + (n - 1)d[/tex]
Where [tex]a[/tex] is the [tex]n^{th}[/tex] term of the sequence, [tex]a_{1}[/tex] the first term of the sequence and [tex]d[/tex] the common difference between terms.
So in our sequence we have [tex]a_{1} = 10[/tex] and for find the difference substract two sequence terms.
[tex]d = a_{n+1} - a_{n} = 18 - 10 = 8[/tex]
Now replace the knowns terms in the general form:
[tex]a_{n} = 10 + (n - 1)8[/tex]
The simplified formula for the given arithmetic sequence is:
a(n) = a + 8 (n - 1)
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
We have,
The common difference between any two consecutive terms in an arithmetic sequence is constant.
In this case, the common difference is 8, as each term is obtained by adding 8 to the previous term.
Let the first term of the sequence be 'a', then the second term is 'a + 8', the third term is 'a + 16', and so on.
Therefore, the nth term of the sequence can be expressed as:
a + (n-1)d
where d is a common difference, which is 8 in this case.
So, the simplified formula for the given arithmetic sequence is:
a(n) = a + 8 (n - 1)
where a is the first term of the sequence and n is the position of the term in the sequence.
Thus,
The simplified formula for the given arithmetic sequence is:
a(n) = a + 8 (n - 1)
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The Perimeter of a triangle is 24cm and the length of the three sides are in the ratio 3:4:5 Find the length of the three sides
Answer:
6, 8, and 10 cm
Step-by-step explanation:
3+4+5=12
24/12=2
2*3=6
2*4=8
2*5=10
Check here LOADING... for instructional material to complete this problem.
Evaluate the formula z=
p−p
pq
n when p=
388
1386, n=1386, p=0.30, and q=1−p
Answer:
-1.63
Step-by-step explanation:
Plug in the values listed into the equation
([388/1386] - 0.30) / √(0.30[1-0.30)/1386
-0.02006/0.01231
-1.63
Simplify the expression.
x - 9 - 5x+7 - 2y
Answer:
add the like terms then look for a gcf to take out atleast for this one
so -9+7= -2
-5x + 1x = -4x
and -2y
we can take -2 out of all those
so our answer is -2(2x+y+1
The height of an experimental plant after x days can berepresented by the formula 3(4x+2). The height of a second plant can be represented by the formula 6(2x+2). Is it possible that the two plants will ever be the same height? Explain.
Answer: No
Step-by-step explanation:
The question is whether 3(4x+2) could ever equal 6(2x+2). So let's set them equal to each other and find if there is a value of x, the days, where they are equal.
3(4x+2) = 6(2x+2)
12x + 6 = 12x+2
6 = 12?? No
They will bnever be at the same height. They are growing at the same rate (12x) but starting at different heights (6 and 12)
cody spent 3 hours and 5 minutes looking for his missing cat if he finally found it at 7:35 what time was it when he originally started
Answer:
4:30
Explanation:
Three hours before 7:35 is 4:35, but you also have to subtract the extra 5 minutes to make it 4:30
Human bones make up 18% of our body mass. Jason's mass is 59.2 kg. What is the mass of his bones?
Answer:
Bone Mass, Density and Bone Weight
"Bone weight is about 15 percent of your body weight, but determining bone weight is complicated and it does not give us useful information. It is much more important to know about bone density, which is the best way to measure bone mass and bone health," says Dr. Ford.
Step-by-step explanation:
Hope its helps you
Answer:
10.656Step-by-step explanation:
18%*59.2=10.656
4. Jenny sells two types of lanyards, solid color or
striped. She charges more for striped lanyards than
for solid color lanyards. The amount of money, in
dollars, that she collects from selling x lanyards of
one type and y lanyards of the other type can be
modeled by the expression 3x + 5y.
What does the variable y represent in this
situation?
A. The number of solid color lanyards sold.
B. The number of striped lanyards sold.
C. The selling price of one solid color lanyard.
OD. The selling price of one striped lanyard.
Answer:
The selling price of one striped lanyard
helppppppp pleaseeeee
if somebody can answer this I'll really really appreciate it
Answer:
What is the question?
Step-by-step explanation:
in the inequality 4> -4 which number appears farther right on a number line and why?
Answer:
4
Step-by-step explanation:
It is a positive number meanwhile -4 in negative.
Name the congruent triangles.
Answer:
ΔOGD≅ ΔPRC
Step-by-step explanation:
PLEASE HELP ME WILL MARK BRAINLIEST THIS IS DUE IN A HOUR
Answer:
There is no Question or no images...
Step-by-step explanation:
Without solving the system of equations how can you
determine if the two systems have the same solution?
3x + 6y = 12
x+y = 7
And
6x +12y = 24
x + y = 7
Answer:
Step-by-step explanation:
First Pair.
If you divide the top equation by 3 you get
x + 2y = 12
x + y = 7 From that I get that y = 5
Second pair
Do the same thing to the top equation only this time divide by 6
x + 2y = 4
x + y = 7
If you subtract again you get y = - 3
656nm into m plzzzzzzzz
Answer:
[tex]6.56\times10^{-7}[/tex]
Step-by-step explanation:
[tex]1nm[/tex] is equal to [tex]1\times 10^{-9}m[/tex] so you have the next relation
[tex]\frac{1nm}{1\times 10^{-9}m} = \frac{656nm}{x}[/tex]
Then isolating [tex]x[/tex] you have
[tex]x = \frac{6.56\times 10^{2}nm \cdot 1\times 10^{-9}m}{1nm} = 6.56\times 10^{-7}m[/tex]
if you are graphing a system of equations, but the graph doesn't give you enough space to plot the y intercept or slope, what do you do? HELP ASAP
HELP PLEASE DONT GIVE THE WRONG ANSWER
Answer:
120 minutes
Step-by-step explanation:
find the LCM
first find the GCF using prime factorization
15=3*5 12=2*2*3 10=2*5
GCF is 5 and 2 respectively
remove from each and multiply
3*2*2*2*5=120
What is the closed form definition for the sequence below?
4, -12, 36, -108,...
Note that 4 is considered the 1st term.
Answer:-108
Step-by-step explanation:
you need to put them in order from least to greatest 4, 36, -12, -108
horizontal translation 5 unitss left
Answer:
The Rule for Horizontal Translations:
if y = f(x), then y = f(x-h) gives a vertical translation. The translation h moves the graph to the left when h is a postive value and to the right when h is a negative value.
Step-by-step explanation:
First, let us look at the parent function f(x) = |x|. The graph of this function looks like the following.
Notice that it is symmetric about the y-axis and looks like a v. Now, that we have the parent function and its graph. Let's look at thow the four transformations happen.
Part I: Horizontal and Vertical Translations
First, we must have a definition of the two types of translations. A vertical translation moves the graph up or down. An example of that would be:
Here, the red graph has been moved up 10 units and the blue graph has been moved down 10 units. These are the two types of vertical translations.
The other type of translation is a horizontal translation. A horizontal translation moves the graph left or right. An example of this would be:
Here, the red graph has been moved to the left 10 units and the blue graph has been moved to the right 10 units.
Now that we have seen some examples of the these, let's see if we can figure out why these translations happen.
Here is an equation of one of the vertical translations: , which of the graphs do you think it is? If you said the red one, you are correct.
Now, what do you think the equation of the blue graph is? If you said, , then you are correct again.
What does this lead us to any generalizations about how to make vertical translations with regard to our parent function? If you need a little more help, click here to start a movie of the parent function moving through vertical translations.
Now, we have hopefully come up with a generalization for our parent funcion, f(x) = |x|.
The Rule for Vertical Translations:
if y = f(x), then y = f(x) + k gives a vertical translation. The translation k moves the graph upward when k is a postive value and downward when k is negative value.
Here is an equation of one of the horizontal translations: , which of the graphs do you think it is? If you said the red one, you are correct.
Now, what do you think the equation of the blue graph is? If you said, , then you are correct again.
What does this lead us to any generalizations about how to make vertical translations with regard to our parent function? If you need a little more help, click here to start a movie of the parent function moving through horizontal translations.
Now, we have hopefully come up with a generalization for our parent funcion, f(x) = |x|.
The Rule for Horizontal Translations:
if y = f(x), then y = f(x-h) gives a vertical translation. The translation h moves the graph to the left when h is a postive value and to the right when h is a negative value.
Hope this helps, have a nice day/night! :D
If it helped, please mark as brainliest!
MODELING REAL LIFE The diagram shows the number of quarts of blood the
human heart pumps per minute,
Pumps 5
quarts of
blood per
minute
a How many quarts of blood does the human heart pump per hour?
quarts per hour
b. How many liters of blood does the human heart pump per minute?
Answer:
a)300 quarts per hour
b)4.73 (rounded to the nearest hundredth) liters or 5 (rounded to the nearest whole number liters
Step-by-step explanation:
a)f the heart pumps 5 quarts per minute, and we want it in quart per hour, all we have to do is multiply 5x60 (quarts-per-minute x minutes-per-hour) =300 quarts per hour
b)1 quart is .946liters
using that conversion we get that 5 quarts is ≈4.73 litera
Can someone help me plzz
cuanto es "y=2x + 5" ??
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-(2*x+5)=0
STEP1:
Equation of a Straight Line
1.1 Solve y-2x-5 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-2x-5 = 0 and calculate its properties
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 5/1 so this line "cuts" the y axis at y= 5.00000
y-intercept = 5/1 = 5.00000
Calculate the X-Intercept :
When y = 0 the value of x is 5/-2 Our line therefore "cuts" the x axis at x=-2.50000
x-intercept = 5/-2 = -2.50000
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 5.000 and for x=2.000, the value of y is 9.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 9.000 - 5.000 = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 4.000/2.000 = 2.000
Geometric figure: Straight Line
Slope = 4.000/2.000 = 2.000 x-intercept = 5/-2 = -2.50000 y-intercept = 5/1 = 5.00000i need help i can’t understand how to solve it so pls help
=====================================================
Work Shown:
1st term = -42nd term = -2*(1st term)+6 = -2*(-4)+6 = 143rd term = -2*(2nd term)+6 = -2*14+6 = -224th term = -2*(3rd term)+6 = -2*(-22)+6 = 50The first four terms are: -4, 14, -22, 50
The idea is to start with the first term (-4) and use the template [tex]\text{nth term} = -2*(\text{previous term}) + 6[/tex] to generate each new term. We multiply the previous term by -2, then add on 6. This is exactly what the recursive equation [tex]a_n = -2(a_{n-1})+6[/tex] is indicating.
help will give brainliest
Answer:
The bar for Spain is between 0 and 50 billion, but is slightly closer to 0 than to 50 so the value will be 20 billion dollars.
I need help pleaseeeeee
ok for the first one says
f(x)= 2 which is our Y, now we see when y is 2 our x = 1
f(x)=0 so when y= 0 , x = 2
f(1) = 2
X/2-1/5=x/3+1/4
Plz I need fast
Answer:
X= - 6/20
Step-by-step explanation:
Find the lcm in both sides,,,
Do a cross multiple of the sides,
Is -3/4 greater than -0.25
Answer: No
Step-by-step explanation:
you should know that 3/4 is the same as 0.75. -0.75 is smaller than -0.25 because when dealing with negative numbers, what would be the “smaller” number in positive negative integers is actually the larger number as it is closer to 0.
Answer:
-0.25 is greater than -0.75
Step-by-step explanation:
usually if they were positive 0.75 would be bigger but since there negative decimals, -0.25 is greater. By the way, -0.75 is -3/4.
helppppppppppppppppppppppppppppppppppppppppp
Answer:
if $15.98----> 2kg
$x --------> 7kg
cross multiply
$x= (15.98 x 7)/2
x = $55.93
IF F(x) is ax + x² – 152-18
as show that F(3)=0
(
b) Find the factors of F(x).
[tex]x = 3[/tex]
[tex]a(3) \: + \: 3 {}^{2} - 152 - 18[/tex]
[tex]3a \: + \: 9 \: - 134[/tex]
[tex]3a \: - 134 + 9[/tex]
[tex]3a - 143[/tex]
Step-by-step explanation:
Hope this helps you XD ✌️Carry on learning !!A fruit basket contains oranges and grapefruits. 1/3 of oranges and 1/4 of the grapefruits were spoiled. You threw away 4 oranges and 7 grapefruits. How many pieces of fruit were in the basket before you threw out the spoiled ones?
Answer:
Below.
Step-by-step explanation:
1/3 is equivalent to 4 oranges so number of oranges = 3 * 4 = 12.
In the same way there are 7 * 4 = 28 grapefruit.
Total pieces of fruit = 12 + 28
= 40.
Solve one third plus seven ninths equals blank
Question 1 options:
ten twenty sevenths
eight ninths
ten ninths
nine thirds
Answer:
the answer is 10/9.
Step-by-step explanation:
Please give BRANIEST and 5 stars if correct!
Answer:
ten ninths
Step-by-step explanation:
"one third plus seven ninths" can be rewritten symbolically as
1/3 + 7/9 and we note that the LCD is 9. Thus,
1/3 + 7/9 = 3/9 + 7/9 = 10/9 (or "ten ninths")