[tex]\large\underline{\sf{Solution-}}[/tex]
We have to evaluate the logarithm.
Given That:
[tex] \rm = \log \bigg( \dfrac{ {a}^{3} {b}^{2} }{ {c}^{4} } \bigg) + \log \bigg( \dfrac{b {c}^{3} }{ {a}^{2} } \bigg) - \log \bigg( \dfrac{a}{c} \bigg)[/tex]
We know that:
[tex] \rm\red\longmapsto \log(x) + \log(y) = \log(xy) [/tex]
[tex] \rm \red\longmapsto \log(x) - \log(y) = \log \bigg( \dfrac{x}{y} \bigg) [/tex]
Therefore, we get:
[tex] \rm = \log \bigg( \dfrac{ {a}^{3} {b}^{2} }{ {c}^{4} } \times \dfrac{b {c}^{3} }{ {a}^{2} } \bigg) - \log \bigg( \dfrac{a}{c} \bigg)[/tex]
[tex] \rm = \log \bigg( \dfrac{ {a}^{3 - 2} {b}^{2 + 1} }{ {c}^{4 - 3} } \bigg) - \log \bigg( \dfrac{a}{c} \bigg)[/tex]
[tex] \rm = \log \bigg( \dfrac{a{b}^{3} }{c} \bigg) - \log \bigg( \dfrac{a}{c} \bigg)[/tex]
[tex] \rm = \log \bigg( \dfrac{a{b}^{3} }{c} \div \dfrac{a}{c} \bigg)[/tex]
[tex] \rm = \log \bigg( \dfrac{a{b}^{3} }{c} \times \dfrac{c}{a} \bigg)[/tex]
[tex] \rm = \log( {b}^{3})[/tex]
As we know that:
[tex]\rm \red\longmapsto \log( {x}^{n}) = n \log(x)[/tex]
Therefore, we get:
[tex] \rm = 3\log(b)[/tex]
Akram is p years old. Shazwan is
7 years older than Akram. Their
total age is 31 years. Write a linear equation to represent their
total age.
answer
Ang sagot po 38 diyan
What is the equation in slope-intercept form of a line with
slope -5/4 and y-intercept 2?
why is green anaconda a threat we should care about?
Answer:
It's dangerous
Step-by-step explanation:
Anacondas are formidable predators, king of the food chain in their native South American ecosystems. While contact with mankind and domestic animals is rare, these large, heavy-bodied constrictors pose a potential threat to anything that crosses their path. Other dangers are also associated with these large snakes.
For any linear function f(x) = mx + b, when does kf(x) = f(kx)?
Only when b = 0 or k = 1.
If f(x) = mx + b, then
f (kx) = m (kx) + b = mkx + b
while
k f(x) = k (mx + b) = kmx + kb
The two expression are identical only if
kb = b ===> kb - b = 0 ===> b (k - 1) = 0 ===> b = 0 or k = 1
Crosby had $300 in his checking
account. Over one week, he
withdrew $50, wrote a check for
$20, and deposited $60. What was
his account balance at the end of
the week?
Answer:
390
Step-by-step explanation:
so 50-20 = 30 30+60= 90
90+300 = 390
Answer:
$290
Step-by-step explanation:
300-50= 250
250-20=230
230+60=290
9(x/3+1)>6.
A.x>-5
B.x>2
C.x>5/3
D.x>-1
Answer:
D.
Step-by-step explanation:
We are given
9(x/3 + 1) >= 6
Divide 9 on both sides
x/3 + 1 >= 2/3
Subtract 1 on both sides
x/3 >= -1/3
Multiply 3 on both sides
x >= -1
The new dolphin tank at the city aquarium is in the shape of a rectangular prism. It is long by wide by deep. To make the tank livable for the dolphins, the aquarium workers treat the water using bags of salt. The amount of water a bag of salt can treat is known in cubic feet.
(a) Find the volume of water in the tank in cubic feet.
(b) To make the tank livable for the dolphins, a bag of salt must be added for each 19.4ft$ of water. The aquarium doesn't have any salt on hand and the salt can only be purchased in whole bags. How many bags of salt must be purchased to treat the water?
(c) If each bag of salt costs $4.85, how much must the aquarium pay for salt to treat all the water in the new dolphin tank?
answer quickly
The volume of water in the tank is 35,100 cubic feet.
What is the volume of the rectangular prism?Volume = length × width × height
We have the following parameters based on the information provided;
Length = 20 meters
Width = 13 meters
Height = 5 meters
Substitute the values into the formula to get
Volume = 20 × 13 × 5
Volume = 1300 cubic meters
Convert the cubic yard into cubic feet
1 cubic yard = 27 cubic foot
⇒ 1300 yards = x
⇒ x = 27 × 1300
⇒ x = 35,100 cubic feet
Therefore, the amount of water a bag of salt can treat is 35,100 cubic feet
To learn more about the volume here:
brainly.com/question/28574486
#SPJ1
The question seems to be incomplete the correct question would be
The new dolphin tank at the city aquarium is in the shape of a rectangular prism. It is 20 yds long by 13 yds wide 5yds by deep. To make the tank livable for the dolphins, the aquarium workers treat the water using bags of salt. The amount of water a bag of salt can treat is known in cubic feet.
Find the volume of water in the tank in cubic feet.
1. A package of sliced cheese costs 2.97 dollars, Their are 11 slices in each pack.
Question: how much would a package with 18 slices cost at the same price per slice? Explain or Show ur reasoning
Answer:
4.86 pack of 18
Step-by-step explanation:
If we consider adding a price to each slice from the 11 slice package. The price to each slice would be .27 cents. Now if we add 7 slices, each .27 cents each. The total price for the 18 package of sliced cheese would be 4.86
10x÷8=18
plz helppppppppppppppppppppppppppppppppppp
Hey there!
10x ÷ 8 = 18
MULTIPLY 8 to BOTH SIDES
10x ÷ 8 * 8 = 18 * 8
SIMPLIFY IT
NEW EQUATION: 10x = 144
DIVIDE 10 to BOTH SIDES
10x/10 = 144/10
CANCEL out: 10/10 because it gives you 1
KEEP: 144/10 because it helps simplify for the x-value
x = 144/10
x = 144 ÷ 2/10 ÷ 2
x = 72/5
Therefore, your answer is: x = 72/5
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Mario and 3 friends equally shared the burritos shown.
Problem
Read aloude How many burritos did each person get?
A
1 2
3
B
1 1
6
C
1 1
4
D
1 1
2
Answer:
c
Step-by-step explanation:
it would be c. because there are 4 friends and there and 5 burritos so each one gets 1 and the last one slips to 4 pieces.
Answer:
each one had 3 so C is the answer
You need a mean score of at least 90 points to get an ""A"" average. What do you need to score on your fifth test to earn at least a 90?
Answer:
85
Step-by-step explanation:
at least a 85 %bcz it's go bring you higher
find the intersection of the two lines by solving the system of equations please help I will give brainliest
Answer:
(-3, -5)
Step-by-step explanation:
We can add the two equations together so the x's cancel out:
x + y = -8
-x + y = -2
2y = -10
y = -5
We can substitute y in to get x:
x - 5 = -8
x = -3
This means the intersection is (-3, -5).
What is the GCF of 2×3³×5² and 2³×3×5²
I will give brainliest and extra points plz
[tex]\frac{4}{\sqrt{5}+3}[/tex]
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The value of given expression is :
[tex]3 - \sqrt{5} [/tex]
Solution is in attachment ~
what is the value of -4.5 degrees
Answer:30
Step-by-step explanation:
Find the value of cos 45° + sin 30° Solution: Given, cos 45° + sin 30° cos 45° + sin
30° = 1/√2 + ½ = (√2+1)/2 Question 2: Evaluate: 2 sin 60° – 4 cos 45° Solution: Given, 2 sin 60° – 4 cos 45° Since, sin 60° = √3/2 and cos 45° = 1/√2
Therefore, ⇒ 2 (√3/2) – 4 (1/√2) ⇒ √3 – 2√2 Question 3: Find Cos 45 + Cos 90. Solution: Cos 45° = 1/√2 Cos 90° = 0 Therefore, Cos 45° + cos 90° = 1/√2
if x+y=7 and xy=10 find x2+y2+5xy
Answer:
64
Step-by-step explanation:
x+y = 7
xy = 10
2x+2y+5xy = 2(x+y)+5(xy) = 2*7+5*10 = 14 + 50 = 64
work out the size of angle A
i need to know the answer to simplify 5/6
Answer: It's already in it's simplest form.
Johnny bought a Blu-Ray Disc recorder for $280. Now, it's on sale for $220. Find the percent of change in the price. Round to the nearest whole percent if necessary.
Answer -21.43
Step-by-step explanation:
-21.43
Step-by-step explanation:
cost price :$280
selling price:$220
%profit =sp-cp/cp ×100
%loss=cp-sp/cp×100
%loss=280-220/280 ×100
=60/280 ×100
=21.4285
=21
An object is thrown upwards with a speed of 20 m/s. After t seconds, its height can be solved using the formula h = 20t - 4.9t2 where h is the height and t is the time. After how many seconds is the object 19.6 meters high?
Step-by-step explanation:
h= 20t - 4.9t^2
when h=19.6m
19.6=20t - 4.9t^2
4.9t^2 -20t+19.6=0
solving quadratically
t= 1.64 seconds or t= 2.45 seconds
(3, r) and (7, 2) m = 1
Answer:
r = -2
Step-by-step explanation:
2+2 = 4
7-3 = 4
4/4 = 1
m = 1
How can you tell if an equation (for example, x=16+3y (don’t solve this)) will be represented by a straight line when graphed on a coordinate plane? Is there an easy way to tell or how do you figure that out?
Answer:
I know it is a straight line because I can convert it into standard or slope intercept form. An example of when something isn't a straight line is like y=|x|.
x=16+3y
-3y=-x+16
y=1/3x-16/3
HELP!!! I RLY NEED HELP WITH THIS!
Answer:
the first one is no solution
the second one is one solution
the third one is many solutions
Step-by-step explanation:
Which of the following is a measure of spread?
1.Range
2.Mean
3.Median
4.Mode
5.All of the above: Mean, Median, Mode, and Range
6.Mean, Median, and Mode only
Answer: 1. range
Step-by-step explanation: range is the spread of values from lowest to highest in which you will find all the values.
Find the difference (10j – 7)-(-9j + 2)
Answer:
Step-by-step explanation:
(10j – 7)-(-9j + 2)
10j-7+9j-2
19j-9
What does the expression you wrote in part d mean?
Answer:
you give us no context
Answer:
The expression means that if Harold has one pack of red sticks and one pack of blue sticks, he could distribute them equally among 4 people without having any sticks of either color leftover.
Step-by-step explanation:
if i went to school at 9:14 and only have to be there for 4 hours what time do i get out
Answer:
1:14
Step-by-step explanation:
instead of starting from 9:14 you start counting from 10:14 because that where the first hour start
Find the slope of the line that passes through (-53, -2) and (-54, 91).
Answer:
x1=-53 y1=-2
x2=-54. y2=91
slopes= y2-y1
---------
x2-x1
91-(-2)
-----------------
= -54-(-53)
91+2
= ----------
-54+53
= 93
-------
-1
A package of 6 pairs of insulated gloves costs $38.94. What is the unit price of the pairs of gloves? The unit price is $ per pair of gloves.
Answer:
6.49
Step-by-step explanation:
6 pairs of insulated gloves cost $38.94
That means 6 x (price of one glove) = 38.94
Let's say the price of on glove = x
The equation is :
6x = 38.94
x = 38.94 ÷ 6 (divide all sides by 6)
x = 6 + (2.94 ÷ 6) (Splitting numbers to multiples of 6)
x = 6 + 0.4 + ( 0.54 ÷ 6) (Splitting numbers to multiples of 6)
x = 6 + 0.4 + 0.09 (Adding all sums)
x = 6.49
Each pair of gloves cost 6.49
-Chetan K
Answer:
6.49
Step-by-step explanation:
Practice 1-2: Unit Rates (Level: Middle School)
Here, given the cost of 6 pairs pf gloves = $38.94
Now, the unit price = Price per unit of the given item
U =
[tex]\frac{38.94}{6} =6.49[/tex]
Write the equation of the line that has a slope of 4/5 and a y-intercept of -8.
The equation of any staright line can be written as y = mx + c , where m is its slope and c is its y - intercept . hence, equation of line with slope = 4/5 and y - intercept = -8 is,
→ y = 4/5x - 8
→ m - c = 4/5 + 8 = 12/5
hope this answer helps you dear take care!