The logarithmic property chosen here is:
[tex]log_{a}[/tex] m - [tex]log_{a}[/tex] n = [tex]log_{a}[/tex] [tex]\frac{m}{n}[/tex], and its validity is proven below:
The logarithmic properties are up to six, but one of it that is applicable here is:
[tex]log_{a}[/tex] m - [tex]log_{a}[/tex] n = [tex]log_{a}[/tex] [tex]\frac{m}{n}[/tex]
In the above expression, both the numerator and denominator have the same base number, but different powers. So in this case, dividing a number of power m by the same number but of power n would given an answer that is the same as the number to the power of the difference between m and n.
For example: Solve;
a. [tex]log_{10}[/tex] 6 - [tex]log_{10}[/tex] 3
b. [tex]log_{10}[/tex] 8 - [tex]log_{10}[/tex] 5
c. [tex]log_{b}[/tex] 6 - [tex]log_{b}[/tex] 2
Solutions:
a. [tex]log_{10}[/tex] 6 - [tex]log_{10}[/tex] 3 = [tex]log_{10}[/tex] [tex]\frac{6}{2}[/tex]
= [tex]log_{10}[/tex] 2
= 0.3010
b. [tex]log_{10}[/tex] 8 - [tex]log_{10}[/tex] 5 = [tex]log_{10}[/tex] [tex]\frac{8}{5}[/tex]
= [tex]log_{10}[/tex] 1.6
= 0.2041
c. [tex]log_{b}[/tex] 6 - [tex]log_{b}[/tex] 2 = [tex]log_{b}[/tex] [tex]\frac{6}{2}[/tex]
= [tex]log_{b}[/tex] 3
The stated examples defend the validity of the specific logarithmic property.
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help I dont understand
Answer:
all real numbers
Step-by-step explanation:
im not 100% sure haha
This wording is so weird. Why are there two maximums and minimums. What does “first maximum and minimum” mean? Which one should I use to solve for amplitude? Please help.
-x-y-2z=9
-2x+2y-2z=-8
x-y+z=5
Answer:
in order for me to solve this , you need to space it out & give me a actually problem .
pls & thnx .
Step-by-step explanation:
Compare the quantity in Column A with the quantity in Column B.
Column A Column B
slope of y = 3 slope of x = 3
A. The quantity in Column A is greater.
B. The quantity in Column B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined on the basis of the information supplied.
Answer:
D. The relationship cannot be determined on the basis of the information supplied.
what is 74 times 98 add 65?
Answer:
7317
Step-by-step explanation:
74x98+65=7317
Answer:
7317
Step-by-step explanation:
(74*98)+65=7317
Select the two statements that are true about the equation y−10=60(x−40).
a. The slope of the line is 10.
b. The slope of the line is 60.
c. One point on the line is (40, 10).
d. One point on the line is (10, 60).
Answer:
Options B and C
Step-by-step explanation:
The point-slope form of linear equations is y - y₁ = m(x - x₁) where: m = slope, and (x₁, y₁) represents a point on the line.
In reference to the definitions provided regarding the point-slope form: Given the linear equation, y - 10 = 60(x - 40):
The slope, m = 60, and one of the points (x₁, y₁) is represented by (10, 40).
Therefore, the correct answers are: Options B and C.
According to the synthetic division below, which of the following statements
are true?
Check all that apply
=================================================
Explanation:
The number in the upper left corner of the synthetic division table is the test root we're trying out. If it leads to a remainder of 0 (bottom right corner), then we have a winner. In this case, we have a root. Choice A is one of the answers.
Since 4 is a root, this leads to x-4 being a factor. Think of x = 4 becoming x-4 = 0 when we subtract 4 from both sides. Choice C is another answer.
The remaining stuff in the bottom row forms the quotient polynomial. The coefficients 3 and -1 lead to 3x+(-1) which simplifies to 3x-1.
So this means dividing 3x^2-13x+4 over x-4 yields the quotient 3x-1 with a remainder of 0. Therefore, choice E is the correct equation compared to choice D which is close but not quite there.
Which equation can be used to describe the relationship between x and y shown in the table below?
Answer:
x=+1 y=-.5
Step-by-step explanation:
What's the circumference for 4cm
Answer:
8πcm or 25.12cm
y- 5- 2x
0
1
2
3
4
5
i don’t get this plz help!
Answer:
y-5-2x quad y-5-2x
Step-by-step explanation:
y-5-2x
Wesley spent $34.60 at the grocery store. 15% of that was spent on fruit. How much did Wesley spend on fruit?
Answer:
5.19 I'm not 100% sure if it's right tho.
Answer:
$5.19
Step-by-step explanation:
15/100 = ?/34.60
15% multiplied by 34.60 divided by 100 = $5.19
Bob is buying the soccer team snacks after their game today. 8 players want cookies and 5 players want ice cream cones. If ice cream cones cost $1.25 each and cookies cost $1.75 each, how much will Bob spend on snacks for the team?
pls show steps
Answer:
$20.25
Step-by-step explanation:
8*1.75=x
x=14
5*1.25= y
y=6.25
x+y=20.25
Are the ratios 15:20 and 3:4 equivalent yes or no
Answer:
Yes they are equivalent.
Step-by-step explanation:
Find the least common denominator or LCM of the two denominators:
LCM of 4 and 20 is 20
Next, find the equivalent fraction of both fractional numbers with denominator 20
For the 1st fraction, since 4 × 5 = 20,
3
4
=
3 × 5
4 × 5
=
15
20
Likewise, for the 2nd fraction, since 20 × 1 = 20,
15
20
=
15 × 1
20 × 1
=
15
20
Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction
15
20
=
15
20
or
3
4
=
15
20
Yes, we can say that the ratio 15 : 20 and 3 : 4 are equivalent.
What are ratios?The ratio is the number that can be used to express one quantity as a fraction of the other ones. The two numbers in a ratio can only be compared when they have the same unit.
Equivalent ratios are the ratios that are the same when we compare them.
Therefore, for ratios of 15 : 20 and 3 : 4, for them to be equivalent, they must have thesame value.
15 : 20 = 15/20
divide through by 5
= 3/4 = 3 :4
Therefore , we can say that ratios 15 : 20 and 3 : 4 are equivalent.
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The surface area of a right circular cone is 15π in.. The cone is enlarged by multiplying both the radius of the base and the slant height by 4. What is the surface area of the new cone?
A. 80π in.
B. 120π in.
C. 60π in.
D. 240π in.
Can you pless add the process
Answer:
The surface area of the new cone is 240π inches² ⇒ answer D
Step-by-step explanation:
If the two cones are similar, then:
1. t1/t2=l1/l2=constant ratio
2. S.A1/S.A2=(R1/R2)^2
3. V1/V2=(R1/R2)3
The surface area of a right circular cone is 15π inches²
The cone is enlarged by multiplying both the radius of the base and the slant height by 4
The two cons are similar
R1/R2=1/4
The surface area of a right circular cone is 15π inches²
S.A1/S.A2=(R1/R2)^2
SO
15π/S.A2=(1/4)^2
15π/S.A2=1/16
By using cross multiplication:
15πX16=S.A2X1
240π=S.A2
The surface area of the enlarged cone = 240π inches²
The surface area of the new cone is 240π inches²
HOPE THAT HELPS!!
Simon spent 1/4 of his wages on rent.
He spent 20% of his wages on food.
He spent 0.15 of his wages on clothes
Work out the fraction of his wages that he had left.
Answer:
2x/5 wages is remaining.Step 1: Lets say 'x' is the total wage. Then we subtract 1/4 from the total wages.
=> 4x/4 - x/4
=> 3x/4 = Remaining Wages Left.
Step 2: Subtract 20% from 3x/4.
3x/4 - x/5 = Remaining Wages Left. [20% = 20x/100 = x/5]
=> 11x/20 = Remaining Wages Left.
Step 3: Subtract 0.15x from his remaining wages left.
=> 11x/20 - 3x/20 = Remaining Wages Left. [0.15 = 15/100 = 3/20]
=> 8x/20 = Remaining Wages Left.
Step 4: Simplify
8x/20 = 2x/5 = 0.40x
=> Simon has saved 2x/5 of the wages.
Please give me brainliest :)
Answer:
2/5 of wedgesStep-by-step explanation:
The total is 100% or 1.
Spent:
1/4 + 20% + 0.15 =0.25 + 0.2 + 0.15 = 0.6Left:
1 - 0.6 = 0.4 = 4/10 = 2/5A county with an area of 360 square miles has a population of 9,000 residents. Which rate best represents the relationship between the population of the county and the area of the county?
Answer:
600 i think
Step-by-step explanation:
simplify (9.5) (-2) (-5)
Answer:2.5
Step-by-step explanation:
Answer:
It is 95
Step-by-step explanation:
3.3-5.7n-3n+5
Help me
Answer:
8.3 -8.7n
Step-by-step explanation:
Maybe you want to simplify this expression.
First of all, recognize it is a sum of four terms. We use "sum" in the general sense, where the things being added can be positive or negative.
3.3
-5.7n
-3n
5
Two of these terms are regular decimal numbers: 3.3 and 5. They can be added together without any fuss: 3.3 +5 = 8.3.
The other two terms are products. One of the factors of the product is a constant, called the "coefficient" of the term. The other factor is the letter n, called a "variable".
You may recall that multiplication is a way to write repeated addition:
3×6 = 6 +6 +6
The factor 3 in this example tells you how many times 6 is included in the sum. We can combine such sums:
(3×6) + (2×6) = (6 +6 +6) +(6 +6) = (3+2)×6 = 5×6
If you replace 6 with n, the same thing is true:
3n +2n = (3+2)n = 5n
That is, we can combine terms containing n by adding their coefficients.
__
Your simplification problem then can be written as ...
3.3 -5.7n -3n +5
= (3.3 +5) +(-5.7n -3n) . . . . . . "like" terms are grouped together
= 8.3 +(-5.7-3)n
= 8.3 -8.7n
Mrs. Speas has $138 in her bank account during Week #1. At the end of each week, she deposits $55 into her bank account. What is the first term?
What is the difference?
What is the iterative rule for the amount of money Mrs. Speas has after n weeks? (you are NOT required to simplify)
Answer:
24
Step-by-step explanation:
is the answer.
The first term is 138
The difference is 55
The iterative rule for the amount of money Mr Speas has after n weeks is
55/2 n² + 221/2 n
During the first week she has $138 in his bank account. At the end of each week she deposited $55 into her bank account.
The first term will be 138 .
The common difference is 55 because her bank always increase by $55 dollars every week. The sequence will be 138, 193, 248, 303, 358...…
The difference = 193 - 138 = 55.
The iterative rule for the amount of money Mr Speas has after n weeks can be represented below
n = number of weeks
a = first term = 138
d = common difference = 55
Using AP formula,
sₙ = n/2(2a + (n - 1)d)
sₙ = n/2 (2(138)+ (n - 1)55)
sₙ = n /2(276 + 55n -55)
sₙ = n /2(221 + 55n)
sₙ = 55/2 n² + 221/2 n
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a family drives 1,000 miles per month with a ratio of highway to
city miles of 2:3. They’re looking forward to using less gas this year with their new hybrid car! Assuming it
costs $2.454 on average per gallon for gas, how much money should the family plan to spend on gas to
drive the hybrid car for a year? Please round all work to the thousandths place when working out solutions
with final answers rounded to the nearest hundredth.
Given:
high ways :
cities: [tex]1000 \times \frac{3}{5}= 200 \times 3= 600\ miles\\\\[/tex]
To find:
total cost=?
Solution:
Calculating all the gallons:
[tex]\to \frac{400}{48}+ \frac{600}{55} \\\\\to \frac{22000+28800 }{2640} \\\\\to \frac{50800 }{2640} \\\\\to \$ 19.2424 \ gallons \\\\[/tex]
Calculating the total cost:
[tex]\to \$19.2424 \times 2,454 \\\\\to \$47220.8496 \approx \$47.22[/tex]
Therefore, the final answer is "[tex]\$47.22[/tex]".
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1 football field = 120 yards. How many meters are in a football field? 1 meter = 1.09 yards .............ONLY TYPE THE NUMBER! DO NOT PUT METERS OR M AT THE END OF YOUR ANSWER.
Answer:
110.09174
Step-by-step explanation:
120yd/1.09meters per yard=110.09174...
The answer needs to be rounded to whatever decimal place is called for.
true or false. a dialation with a negative scale factor has the center of dialation between the pre-image and image
Answer:
It is true bc i think its turne
o
o
o
o
o
o
o
o
o
o
o
o
o
oo
Step-by-step explanation:
dont play with me just answer the question
Answer:
B
Step-by-step explanation:
write the equation of the line from the given information. through (-3,5) & (4,-2)
Answer:
y = -x + 2
Step-by-step explanation:
(-3,5) and (4,-2)
Slope: (-2-5)/(4 - - 3) = -7/7 = -1
y-intercept= -2 - (-1)(4) = -2 + 4 = 2
You earn $20 for washing 5 cars how much do you earn for washing 2 cars
Answer:
$8
Step-by-step explanation:
First we have to see how much you are paid per car. To do this we divide the money earned ($20), by the number of cars washed (5).
20÷5=4
This tells us you earn $4 per car. So, to find the amount you would earn buy washing 2 cars, you multiply the money earned per car by 2.
4·2=8
This means you would earn $8.
Would you please mark my answer brainliest if it helped you? :D
damian dilates PQR shown on the coordinate grid with a scale factor of 0.5 centered at the origin. then he translate the 1 unit up and 3 units to the right to from P' Q' R' what are the coordinates of the vertices P' Q' R'
Transformation involves changing the size and position of a shape.
The coordinates of P'Q'R' follows the transformation rule [tex]\mathbf{(x,y) \to (0.5x-3,0.5y+1)}[/tex]
First PQR is dilated by 0.5.
The transformation rule of this dilation is:
[tex]\mathbf{(x,y) \to 0.5(x,y)}[/tex]
This gives
[tex]\mathbf{(x,y) \to (0.5x,0.5y)}[/tex]
Next, the points are translated 1 unit up and 3 units right.
The transformation rule of this translation is:
[tex]\mathbf{(x,y) \to (x-3,y+1)}[/tex]
So, we have:
[tex]\mathbf{(x,y) \to (0.5x-3,0.5y+1)}[/tex]
Hence, the coordinates of P'Q'R' follows the transformation rule [tex]\mathbf{(x,y) \to (0.5x-3,0.5y+1)}[/tex]
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Help, please.
A painter painted about half a room in half a day. Coley estimated the painter would paint 4 rooms in 4 days. Is Coley's estimate reasonable? Complete the explanation.
Answer:
not reasonable, half of a room per day, and 2 rooms, I hope this helps:)
draw a graph of the line (1,2) (4,8)
Answer:
Step-by-step explanation:
11. Find the Domain and Range of the following: (6.-1) (-2.2) (18,-1) (-2,3) Domain: Range: Is this relation a function?
Answer:
solution,
R={(6,-1),(-2,2),(18,-1),(-2,3)}
domain={6,-2,18}
range={-1,2,3}
domain:range is the relation a function…
Note:-
Domain is the input.Range is the output.If an relation be (x,y) then x is the domain ,y is the range .Solution:-
[tex]\\ \sf\longmapsto D_f=\{6,-2,18\}[/tex]
[tex]\\ \sf\longmapsto R_f=\{-1,2,3\}[/tex]
No it's a relation not function
-6 3/8 - 1/4 = ? write your answer as a mixed number in simplest form.
Answer:
-6 ⁵/8. Since you are only subtracting a fraction from a negative mixed number, you would leave the whole number alone.
