The value of [tex]\log_5{125}[/tex] is 3.
Solution:
Step 1: Given expression is [tex]log_5{125}[/tex].
125 can be expressed as [tex]5^3.[/tex]
[tex]\log_5{125}=\log_5{5}^3[/tex]
Step 2: Using log rule: [tex]\log_a{x^b}=b\log_a{x}[/tex]
[tex]\log_5{5}^3=3\log_5{5}[/tex]
Step 3: Using log rule: [tex]\log_a{a}=1[/tex]
[tex]\log_5{5}= 1[/tex]
⇒ [tex]3\log_5{5}= 3(1)[/tex]
⇒ [tex]3\log_5{5}= 3[/tex]
∴ [tex]\log_5{125}=3[/tex]
Hence the value of [tex]\log_5{125}[/tex] is 3.
Which mathematical symbol would best fill in the blank to compare the two real numbers?
square root of 2 blank 1.8 repeating
<
>
=
≈
Which shows the prime factorization of 36?
A.) 2 x 2 x 2 x 3
B.) 2 x 2 x 3 x 3
C.) 2 x 2 x 9 x 1
D.) 2 x 3 x 3 x 3
Thanks, after TWO people answer I will pick the best answer and give brainlest, don't bug me for it in your answer please!
Answer:
the answer is b.)
Step-by-step explanation:
2×2=4×3=12×3=36
Raphael runs every day for several weeks. He runs for 35 days in a row. How many weeks did he run?
Answer:
5 weeks
Step-by-step explanation:
There are 7 days in a week.
5 weeks * 7 days = 35 days.
Raphael ran for a total of 5 weeks.
To calculate how many weeks Raphael ran, we need to divide the number of days he ran by the number of days in a week.
Raphael ran for 35 days.
Since there are 7 days in a week, we divide 35 by 7:
35 days / 7 days per week = 5 weeks
Therefore, Raphael ran for 5 weeks.
Joe made a scale drawing of the community pool in his town. the pool has a perimeter of 77 meters, what is the length and width in meters?
Answer:
The length of the pool is 28 meters and the width of the pool is 10.5 meters.
Step-by-step explanation:
In the scale drawing of Joe, the community pool has (length : width) = 8 : 3
Let the actual length of the pool is 8x meters and the actual width is 3x meters.
Now, given that the actual pool has a perimeter of 77 meters.
So, 2(8x + 3x) = 77
⇒ 22x = 77
⇒ x = 3.5
So, the length of the pool is 8x = 8(3.5) = 28 meters and the width of the pool is 3x = 3(3.5) = 10.5 meters. (Answer)
Answer:
The length of the pool is 28 meters and the width of the pool is 10.5 meters.
Step-by-step explanation:
What percent of your budget of $6000 would your rent be if you pay $600 in rent?
Answer:
ur answer ( I think so it will be correct)
Step-by-step explanation:
$6000 percent $600
= 6000/600
= 60÷6 percent
= 10 percent
I THINK ITS HELPFULL TK YOU
y=6x-10=x-4 what is x
Answer:
x=6/5
Step-by-step explanation:
y=6x-10
y=x-4
-----------
6x-10=x-4
6x-x-10=-4
5x-10=-4
5x=-4+10
5x=6
x=6/5
y=6/5-4=6/5-20/5=-14/5
Part A: Write an equation of a line that is perpendicular to the line y = 2/3x + 5 and passes through the point (4, 0).
Part B: Explain how you determine the equation in 3-4 sentences using at least 6 of the words below.
Slope
y-intercept
x-intercept
perpendicular
opposite
reciprocal
substituted/substitution
slope-intercept
ordered pair
Step-by-step explanation:
First you need to make a line perpendicular to y=2/3x+5. To do that you have to know that, if we use y=ax+b, a1*a2=-1. That is if a1 and a2 are perpendicular. So we get 2/3*a2=-1. -1/ 2/3=a2. a2=-1.5. We get y=-1.5x+b. Fill in (4,0) on y=-1.5x+b abd we get 0=-1.5(4)+b. b=6
Answer:
y = (-3/2)x - 6
Step-by-step explanation:
slope of the line y= 2/3x + 5
slope = 2/3
for two perpendicular lines
slope1*slope2 = -1
so, slope2 = (-1)*(3/2) = -3/2
hence for it to pass (4,0)
slope2=(y2 - y1)/(x2 - x1)
-3/2 = (y - 0)/(x - 4)
cross multiplying
-3x -12 = 2y
the equation of the line is
y = (-3/2)x - 6
Is 25/176 a repeating or terminating decimal
It repeats since it can't be simplified.
During a bake sale 1 1/2 dozen cookies were sold in 1/3 of an hour. What is the unit rate for the dozens of cookies sold in an hour
Answer:
4.5 dozen cookies per hour
Step-by-step explanation:
I just had my sister help me and she said this was the answer but didnt tell me how she got it.LOL
i am faceing north west. if i turn 180 clockwise i will be facing what
Answer:
south
Step-by-step explanation:
it’s half way turn because 180 is half of one 360 and north is right across from south:)
Answer:
South
Step-by-step explanation:
You will be facing south because if you are facing north and you turn 90 clockwise you will face east. Turn 90 degrees again and you'll face south.
Bonita said that the product of 56 × 123 is 73. How can you tell that her answer is wrong?
Answer:
It is wrong because the answer should be way greater than the factors.
by the way the anwer is 6888
Step-by-step explanation:
Answer:
5/6 of a number cannot be greater than the number.
Step-by-step explanation:
Find the coordinates of the midpoint of the line segment with the endpoints C(1,0) and D(5,4)
Answer:
(3, 2 )
Step-by-step explanation:
Given the endpoints are (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
[ 0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) [
Here (x₁, y₁ ) = (1, 0) and (x₂, y₂ ) = (5, 4), thus
midpoint = [0.5(1 + 5), 0.5(0 + 4) ] = (0.5(6), 0.5(4)) = (3, 2 )
Answer:
(3,2)
Step-by-step explanation:
To find a midpoint of two given points, we can use the formula:
[tex](x_{m} ,y_{m} ) = (\frac{x_{1} +x_{2} }{2} , \frac { y_{1} +y_{2}}{2})[/tex]
(i.e. we just take the average of the x coordinates, and similarly, the average of the y coordinates).
so we get:
midpoint = ( (1+5)/2, (0+4)/2 )
= (3, 2)
3x +y = 14
Rewrite equation in slope intercept form solve for y
To rewrite the equation in slope-intercept form and solve for y, we isolate y on one side of the equation by subtracting 3x from both sides. The resulting equation is y = -3x + 14.
Explanation:To rewrite the equation in slope-intercept form and solve for y, we need to isolate y on one side of the equation.
Given the equation 3x + y = 14, we can start by subtracting 3x from both sides to get y alone.
The equation becomes y = -3x + 14, which is now in slope-intercept form (y = mx + b) where the slope (m) is -3 and the y-intercept (b) is 14.
Learn more about rewriting equations in slope-intercept form here:https://brainly.com/question/29095684
#SPJ2
Are 17 heartbeats in 15 seconds and 68 heartbeats in 60 seconds Equivalent
Answer:
1.133.
Step-by-step explanation:
Yes because if you divide 17 by 15 you get about 1.133 and if you divide 68 by 60 you also get about 1.133.
Answer:
Step-by-step explanation:
17/15 = 1 2/15
68/60 = 1 2/15
yes, they are equivalent
A. Suppose you have just inherited a sum of money. Let’s say you choose to invest the money. How much did you inherit? Choose an amount between $1000 and $100,000. Do not choose an increment of 1000. In other words, do not choose $1000, $2000, $5000, $14000, etc.
B. What is your interest rate? Choose a rate between 0.5% and 3%.
C. Using yearly compounding, calculate the accrued value after 5 years, 10 years, and 15 years. Show all work. You may show your work as an inserted image.
Amount =$48003.20
Step-by-step explanation:
Here apply the compound interest formula;
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
where;
P=Principal amount invested = $37500
r=rate of interest as a decimal, 2.5% =0.025
n=number of compounding per year=1
t=time period the amount in invested=10
In our case, the amount after investing will be;
[tex]A=37,500(1+0.025)^{10} \\\\A=37,500(1.025)^{10} \\\\A=48003.20[/tex]
Interest earned after the period= $48003.20-$37500 =$10503.20
Learn More
Compound Interest formula application: https://brainly.com/question/7014337
Keywords: inherit, sum, money, interest
#LearnwithBrainly
A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries 12.5, 2.5, 0.5, 0.1, 0.02.
Which exponential function is represented by the table?
f(x) = 0.2(0.5x)
f(x) = 0.5(5x)
f(x) = 0.5(0.2x)
f(x) = 0.2(0.2x)
Answer:
[tex]f(x)=0.5\cdot (0.2)^x[/tex]
Step-by-step explanation:
Given the table
[tex]\begin{array}{cc}x&f(x)\\ \\-2&12.5\\ -1&2.5\\0&0.5\\1&0.1\\2&0.02\end{array}[/tex]
The exponential function can be written [tex]f(x)=a\cdot b^x.[/tex] To find [tex]a[/tex] and [tex]b,[/tex] substitute some values:
When [tex]x=0,\ f(x)=0.5,[/tex] then
[tex]0.5=a\cdot b^0\Rightarrow a=0.5\ [ b^0=1][/tex]
When [tex]x=1,\ f(x)=0.1,[/tex] then
[tex]0.1=0.5\cdot b^1\Rightarrow 0.5b=0.1,\ b=0.2[/tex]
Thus,
[tex]f(x)=0.5\cdot (0.2)^x[/tex]
Check remaining values:
[tex]f(-2)=0.5\cdot 0.02^{-2}=0.5\cdot 5^2=0.5\cdot 25=12.5\\ \\f(-1)=0.5\cdot 0.2^{-1}=0.5\cdot 5=2.5\\ \\f(2)=0.5\cdot 0.2^2=0.5\cdot 0.04=0.02[/tex]
Broccoli costs $1.50 per pound at a store. How much money does 32
ounces of broccoli cost?
Answer:
2 pounds
Step-by-step explanation:
Answer:$3
Step-by-step explanation:32 ounces is equal to 2 pounds. 1.50 times 2
(-5, -5), 6x - y = 1
Write an equation of the lines that passes through the given point and is parallel to the given line.
Answer:
Step-by-step explanation:
6x - y = 1
6x - 1 = y.....rearrange
y = 6x - 1......slope is 6. A parallel line will have the same slope.
y = mx + b
slope(m) = 6
(-5,-5)...x = -5 and y = -5
now we sub and find b, the y int
-5 = 6(-5) + b
-5 = -30 + b
-5 + 30 = b
25 = b
so ur equation is : y = 6x + 25 <==
3.) mr. smith’s class sold wrapping paper for $3.50 each and mr. davis’ class sold magazines for $2.75 each. together, the classes sold 72 items and earned $222 for their school. a. write and solve a system of equations that model the problem. show all your work. Need answer ASAP!!!!!
Answer:
The number of wrapping paper sold was 32 and the number of magazines sold was 40
Step-by-step explanation:
Let
x ----> the number of wrapping paper sold
y ----> the number of magazines sold
we know that
The classes sold 72 items
so
[tex]x+y=72[/tex] ----> equation A
The classes earned $222 for their school
so
[tex]3.50x+2.75y=222[/tex] ----> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
using a graphing tool
The solution is (32,40)
see the attached figure
therefore
The number of wrapping paper sold was 32 and the number of magazines sold was 40
what is the value of (5r+1/5) squared when r=0
Answer:1/5
Explanation The answer is 1/5 because 05×0 is zero so 0+1/5 equals 1/5
Answer:
1/5
Step-by-step explanation:
What time is past 13 hours past 1:00 am
Answer:
Therefore the answer is 14:00 hours or we can also write this as
14:00 - 12:00 = 2 : 00 pm.
Step-by-step explanation:
13 hours past 1:00 am is equal to 13 + 1 = 14.
Therefore the answer is 14:00 hours or we can also write this as
14:00 - 12:00 = 2 : 00 pm.
Answer: That would be 2.00 P.M
Step-by-step explanation:
A store is having a sale on jelly beans and almonds. For 6 pounds of jelly beans and 2
pounds of almonds, the total cost is $16 . For 3 pounds of jelly beans and 5 pounds of almonds, the total cost is $13. Find the cost for each pound of jelly beans and each pound of almonds.
The cost of each pound of jelly beans is $ 2.25 and cost of each pound of almond is $ 1.25
Solution:
Let the cost of each pound of jelly beans is "a"
Let the cost of each pound of almond is "b"
For 6 pounds of jelly beans and 2 pounds of almonds, the total cost is $16
Therefore, we frame a equation as:
6 pounds of jelly beans x cost of each pound of jelly beans + 2 pounds of almonds x cost of each pound of almond = 16
[tex]6 \times a + 2 \times b = 16[/tex]
6a + 2b = 16 --------- eqn 1
For 3 pounds of jelly beans and 5 pounds of almonds, the total cost is $13
Therefore, we frame a equation as:
3 pounds of jelly beans x cost of each pound of jelly beans + 5 pounds of almonds x cost of each pound of almond = 13
[tex]3 \times a + 5 \times b = 13[/tex]
3a + 5b = 13 ----------- eqn 2
Let us solve eqn 1 and eqn 2
Multiply eqn 2 with 2
6a + 10b = 26 --------- eqn 3
Subtract eqn 1 from eqn 3
6a + 10b = 26
6a + 2b = 16
( - ) -------------------------
8b = 10
[tex]b = \frac{10}{8} = 1.25[/tex]
b = 1.25Substitute b = 1.25 in eqn 1
6a + 2(1.25) = 16
6a + 2.5 = 16
6a = 13.5
a = 2.25Thus cost of each pound of jelly beans is $ 2.25 and cost of each pound of almond is $ 1.25
Solve for x and y:
28x-49y=35
4x-7y=5
A.The solution is (0, 0).
B.There are an infinite number of solutions.
C.X=3,y=1
D.There is no solution.
Answer:
D
Step-by-step explanation:
The lines are parallel, this means that they will never meet.
Answer: D no solution
Step-by-step explanation:
the first one is wrong because if they were both 0 than they would have to equal 0
the second one is wrong because no number works
the third one is wrong because it works on the second one but when you plug it into the first equation you get 95 = 35 which is incorrect.
D is the correct choice.
PLZ HELP 20 points and brainliest
Select TWO equations that have infinitely many solutions.
A.
2(7 – 4x) = 4(5 – 2x) – 6
B.
6(x – 9) = 6x – 54 + x
C.
4(x + 4) = 2(2x + 5) + 6
D.
5(x – 8) + 10 = 5(x + 2)
Answer: A. 2(7 – 4x) = 4(5 – 2x) – 6
C. 4(x + 4) = 2(2x + 5) + 6
Step-by-step explanation:
Infinitely solution means when all numbers are solutions . Checking the equations given one by one
A. 2(7- 4x ) = 4(5 - 2x ) - 6
Expanding , we have
14 - 8x = 20 - 8x - 6
14 - 8x = 20 - 6 - 8x
14 - 8x = 14 - 8x , this is just a typical example of infinitely many solutions because any value of x chosen will satisfy the equation.
B. 6(x - 9 ) = 6x - 54 + x
Expanding , we have
6x - 54 = 6x + x - 54
6x - 54 = 7x - 54
collecting the like terms
6x - 7x = -54 + 54
- x = 0
x = 0
This equation has just one solution at x = 0 , because 0 is the only value of x that will satisfy the equation
C. 4( x + 4 ) = 2 ( 2x + 5 ) + 6
4x + 16 = 4x + 10 + 6
4x + 16 = 4x + 16
This equation also have infinitely many solutions
D. 5 ( x - 8 ) + 10 = 5 ( x + 2 )
5x - 40 + 10 = 5x + 10
5x - 30 = 5x + 10
This equation has no solution.
Therefore , the equations with infinitely many solutions are equations A and C
40. Danielle's living room is a rectangle with the dimensions 16 feet
by 18 feet. If she partially covers the bare floor with a circular
throw rug with a diameter of 12 feet, what is the approximate
area of bare floor, in square feet, that remains exposed?
(Note: Assume the rug lies completely flat and does not touch
any wall.)
F. 113
G. 144
H. 175
J. 288
K. Cannot be determined without knowing the exact position
of the rug
Answer:
wanna be my friend cause you seem cool
Step-by-step explanation:
1700/85 in simplest form
Answer:20
Step-by-step explanation:
Telling of a classroom is 32 feet. The width is 75% of the lengt. Find the area of the classroom in square feet
Answer:
768 Square Feet
Step-by-step explanation:
32(.75) = 24
24 × 32 = 768
There are sparrows and cardinals that feed at Mrs. Sims bird feeder. The ratio of sparrows to cardinals is 3:1. There are at least 7, but less than 11 sparrows that eat at Mrs. Sims bird feeder. Put an S in the grid below to show the number of sparrows and a C to show the number of cardinals. There may be extra squares. (See attachment)
Answer:
Please find the grid of Sparrows and Cardinals below.
Step-by-step explanation:
Ratio 3:1 of Sparrows to Cardinals
There are at least 7, but less than 11 sparrows that eat at Mrs. Sims bird feeder
Let's build the grid for sparrows and cardinals, this way:
Sparrows = 7 - 8 - 9 - 10 - 11
Cardinals = 2 - 3 - 3 - 3 - 4
For calculating the number of cardinals we use the ratio 3:1 and round the number of cardinals to the next whole number.
Number of sparrows 7 to 11
Number of cardinals 2 to 4
what is an expression equivalent to 48+30
Answer:
Step-by-step explanation:
48 + 30 = 6(8 + 5)
Answer:78
Step-by-step explanation:
Equivalent expression is to carry out the addition process.
48 + 30 = 78
How many 3/8 go into 3/2
Answer: 3/8 can’t go to 3/2
Step-by-step explanation: