Use the properties of logarithmic functions to simplify the expression on the left side of the equation and determine the values of x and y. Then evaluate the simplified expression.
The value of x is , and the value of y is. The value of the expression, rounded to nearest hundredth, is
Answers
Properties of exponents tell us that:
log7(2) / log7(5) = log5(2)
x = 5
y = 2
Answer = 0.43
By using the logarithmic property the solution of the given function will be 0.43.
What is Logarithm?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division
The solution of the given expression is given as:-
Log7(70) - log7(35) = log7(70/35) = log7(2)
Properties of exponents tell us that:
log7(2) / log7(5) = log5(2)
x = 5
y = 2
Answer = 0.43
Therefore using the logarithmic property the solution of the given function will be 0.43.
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Related Questions
Can someone please help me with #2 and 4 please thanks
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4. 2x^4+11x^2+12= (2x+3)(x+4)
What is the side length of the smallest square plate on which a 30-cm chopstick can fit along a diagonal without any overhang?
Answers
Answer:
21.2
Step-by-step explanation:
math xl said so
The side length of the smallest square plate is 21.2 units.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given that, length of diagonal on the square is 30 cm.
Let the side of a square be x.
Now, x²+x²=30²
2x²=900
x²=450
x=√450
x=21.2 units
Therefore, the side length of the smallest square plate is 21.2 units.
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Shen needs to memorize words on a vocabulary list for german class. he has memorized 12 of the words, which is two-thirds of the list. how many words are on the list?
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2/3x = 12
x = 12 / (2/3)
x = 12 * 3/2
x = 36/2
x = 18 <=== there are 18 words on the list
I need help to figure this problem out
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keeping in mind that, "x" is just a length unit, and thus it cannot be negative.
Which angles are corresponding angles?
a. ∠7 and ∠3
b. ∠8 and ∠3
c. ∠3 and ∠11
d. none of this
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Angles 7 and 3 are vertical angles.
The answer is C, angles 3 and 11 are corresponding angles.
Investigators at the scene of a crime strongly suspect that a handwritten promissory note for $10,000.00 has been altered to read $40,000.00. how might this be proven?
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To prove that there is altering made on the promissory note, the investigators should test the ink on a piece of TLC. This would tell them when the ink was used and how long ago it was used so they can compare.
PLEASE HELP:::
Louise used this figure to model the expression 20/4.
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You buy a bookshelf. The label on the box says the bookshelf is 5151 inches tall. How tall is it in feet?
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1 foot = 12 inches
so 5151 inches divided by 12 = 429.25 feet tall
that is too tall for a normal house so hopefully you meant 51 inches
51 / 12 = 4.25 (4 1/4) feet tall
there are 40 girls on a softball team. 3 out of every 5 prefer chocolate over vanilla milkshakes .
how many girls prefer chocolate milkshakes
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24 girls prefer chocolate milkshakes out of 40 girls.
Ratio and proportionsFrom the given information, you can see that we have a total of 40 girls
If 3 out of every 5 prefer chocolate over vanilla milkshakes, hen;
3girls = every 5 prefer chocolate
x = 40 girls
Cross multiply
5x = 3 * 40
5x = 120
x = 24
Hence 24 girls prefer chocolate milkshakes
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After reviewing her driving record for the past 3 years, Cindy’s insurance company offers her a good driver discount of 4.5%. Her original policy was based on the premiums listed below. What is her new annual premium including the discount?
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Cindy's new annual premium including the discount would be given by: Option A: $504.24
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
The table given is:
Type of Insurance Coverage= {Coverage Limits} and {Annual Premiums}
Bodily Injury $50/100,000 $31. 75
Property Damage $25,000 $120. 50
Collision $500 deductible $275. 75
Comprehensive $100 deductible $100. 00
Her total annual premium = 31.75 + 120.50 + 275.75 + 100 = $528
Discount offered to her = 4.5% of $528 = (in dollars)
The new premium that she needs to pay after discount = Old premium - discount = $528 - $23.76 = $504.24
Therefore, Cindy's new annual premium including the discount would be given by: Option A: $504.24
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The complete question is ;
After reviewing her driving record for the past 3 years, Cindy’s insurance company offers her a good driver discount of 4. 5%. Her original policy was based on the premiums listed below. What is her new annual premium including the discount? Cindy's Auto Insurance Policy Type of Insurance Coverage Coverage Limits Annual Premiums Bodily Injury $50/100,000 $31. 75 Property Damage $25,000 $120. 50 Collision $500 deductible $275. 75 Comprehensive $100 deductible $100. 00 a. $504. 24 b. $523. 50 c. $528. 00 d. $551. 76.
A hose fills a tank at a rate of 20 gallons per minute.
What is the rate in liters per hour?
(1 gallon ≈ 3.79 liters)
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Answer:
[tex]\frac{4548}{1}[/tex] liters per hour.
Step-by-step explanation:
Given : A hose fills a tank at a rate of 20 gallons per minute.
To find : What is the rate in liters per hour?
Solution : We have given
A tank can fill hose in 1 minute = 20 gallon .
1 gallon = 3.79 liters.
20 gallon = 20 * 3.79 = 75.8 liters.
20 gallon = 75 .8 liters.
So,
A tank can fill hose in 1 minute = 75.8 liters.
A tank can fill hose in 60 minute = 75.8 * 60 liters = 4548 liters.
A tank can fill hose in 1 hour = 4548 liters.
Rate = [tex]\frac{4548}{1}[/tex] liters per hour.
Therefore, [tex]\frac{4548}{1}[/tex] liters per hour.
are relations always functions
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A meteorologist was accurate 90% of the time, reporting accurately on 45 days. how many days of weather did he report? 50
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Which graph represents the solution set of the system of inequalities?
{−2x+y≤4
y>x+2
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The correct graph is:
First graph
Step-by-step explanation:The first inequality is:
[tex]-2x+y\leq 4[/tex]
The graph of this inequality is a straight solid line ( since the inequality is a inequality with a equality sign i.e. not strict ) which passes through (-2,0) and (0,4) and the shaded region is towards the origin as it passes the zero point test.
The second inequality is:
[tex]y>x+2[/tex]
is a dotted straight line (since the inequality is strict) which passes through (-2,0) and (0,2) and the shaded region is away from the origin as it fails the zero point test.
Hence, the correct graph is the first graph.
Please calculate −0.5(7b−12a)−(8.4a−14b) if a=−10; b=−6.
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help help help please
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The length of XY is 4
The length of ZW is 6
Because we don't get the same length (for XY and ZW), this means that the segments are not congruent.
-------------------------------------------------------------
To find the length of segment XY, you can count the number of spaces between -7 and -3 to get 4 units. Or you can subtract and use the absolute value notation to ensure the result is positive
|-7-(-3)| = |-7+3| = |-4| = 4
Do the same for segment ZW.
|2-8| = |-6| = 6
A rectangle is cut in half along the diagonal to form a triangle. if the area of the triangle is (2x + 10) cm^2, what is the area of the rectangle? Please provide steps and reason for your answer too!
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the triangle's area (a)=(1/2)*(b) (the rectangle's area) we can multiply 2 to both sides to get 2*a=b. Since a is (2x+10), we can plug it in and use the distributive property (since we just can't add up variables and integers) to get
2*(2x+10)=4x+20=b
An airplane over the Pacific Ocean sights an atoll at an 7° angle of depression. If the plane is 663 m above the water, how many kilometers is it from a point 663 m directly above the atoll
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distance = 663 / tan (7)
distance = 663 / 0.12278
distance = 5,400 meters = 5.4 kilometers
The perimeter of a rectangle is 900 yards. what are the dimensions of the rectangle if the length is 70 yards more than the width?
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900:4= 225
So, now we know each side is 225 Yards first..
Now, since the length is 70 yards longer than the width, we know that:
Length: 225+70= 295
Respectively, we also know that the width is 70 yards shorter since the length is already 70 yards longer:
Width: 225-70=155
Checking answer: (295*2) + (155*2) = 900 Yards
As our final answer, the dimension of the rectangle is 295 yards (Length) by 155 yards (Width)
Hope this help with your studies.
You want to make five-letter codes that use the letters a, f, e, r, and m without repeating any letter. what is the probability that a randomly chosen code starts with a?0.100.150.200.25
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Answer:
Option C is the right answer
Step-by-step explanation:
The probability that a randomly chosen code starts with A is 0.20
4/5 - 2/7 find difference
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hope this is what u r looking for
A company manufactured a 16-oz box of cereal. Boxes are randomly weighted to ensure the correct amount. If the discrepancy in weight is more than 0.15 oz, the production is stopped. What is the range of acceptable values for production to continue?
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Answer:
The acceptable range will be : 15.85 oz to 16.15 oz
Step-by-step explanation:
Let the weight of the box be = x
As given,
If the discrepancy in weight is more than 0.15 oz, the production is stopped.
And if the discrepancy in weight is less than 0.15 oz then the production will continue.
We can express this as : If [tex]|x-16| \leq 0.15[/tex] ; the production continues
[tex]|z| \leq a[/tex] or we can say
[tex]-a\leq z\leq a[/tex]
Now, z = x-16, and a=0.15, then the value becomes,
[tex]-0.15 \leq x-16 \leq 0.15[/tex]
Solving for x:
We get the final range as :
[tex]-0.15+16 \leq x-16+16 \leq 0.15+16[/tex]
[tex]15.85\leq x \leq 16.15[/tex]
Therefore, the answer is : [tex]15.85\leq x \leq 16.15[/tex]
It should be noted that the range that's acceptable will be 15.85 oz and 16.15 oz.
How to calculate the range.From the information, the discrepancy in weight is about 0.15 oz. The lowest weight will be:
= 16 - 0.15 = 15.85 oz
The highest weight will be:
= 16 + 0.15 = 16.15 oz.
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Which number is prime?
27
14
91
59
Which trinomial is a perfect square trinomial?
a2 – 8a + 64
a2 – 4a + 64
a2 – 4a + 16
a2 – 8a + 16
Answers
I believe it is the first one
Final answer:
The number 59 is prime, and the trinomial a^2 - 4a + 4 is a perfect square trinomial.
Explanation:
Prime number: The number 59 is prime because it is only divisible by 1 and itself, while the other numbers have factors other than 1 and themselves.
Perfect square trinomial: The trinomial a2 - 4a + 4 is a perfect square trinomial because it can be factored to (a - 2)(a - 2), making it a square of a binomial.
Wyatt’s eye-level height is 120 ft above sea level, and Shawn’s eye-level height is 270 ft above sea level. How much farther can Shawn see to the horizon? Use the formula mc024-1.jpg, mc024-2.jpg with d being the distance they can see in miles and h being their eye-level height in feet.
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d = √ [ 3h / 2], for h > 0
where d is the distance they can see in miles, and h is their eye-level height in feet.
In the case of Wyatt, h = 120 ft
=> d = √ [ 3(120) ] / 2 = √180 = 13.42 miles
In the case of Shawn, h = 270 ft
=> d = √ [ 3 (270) / 2 ] = √ 405 = 20.12 miles
Given that the question is how much farther Shawn can see to the horizon, you must find the difference:
20.12 miles - 13.42 miles = 6.7 miles
Answer: 6.7 miles
Answer:
3 sqrt5
Step-by-step explanation:
1. Clara grew 2 1/8 inches from her ninth birthday to her tenth birthday. If she was 53 2/3 inches when she turned nine. How tall was she when she turned ten?
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53 + 2 = 55
2/3 + 1/8 = 16/24 + 3/24 = 19/24
55 + 19/24 = 55 19/24 inches <==
Trina and Jessie went on a vacation. Trina went scuba diving with an elevation of -85.6. Jessie went hand gliding with an altitude of 87.9 meters . Which is above sea level
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so anything above sea level is positive and anything below sea level is negative. So Jessie, who is at an altitude of 87.9 meters, is above sea level
A regular 18-sided polygon is rotated with the center of rotation at its center.
What is the smallest degree of rotation needed to map the polygon back on to itself?
Is it 180 degrees or 20 degrees? Or are both my answers wrong? :(
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360 degrees / 18 sides = 20 degrees
the answer is 20 degrees
Julie owns a video store. Her monthly expenses, including rent, average $1,168. This year she made $34,416 in revenue. What is the difference between her average monthly revenue and her average monthly expenses?
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2868-1168=1700
Joann works in a publicity office at the state university. she is paid $ 13.00 $13.00 an hour for the first 35 35 hours she works each week and $ 19.50 $19.50 an hour for every hour after that. if she makes $ 650.00 $650.00 one week, how many hours did she work?
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A line passes through the point (4, –2) and has a slope of mc010-1.jpg.
What is the value of a if the point (–4, a) is also on the line?
–6
–5
5
6
Answers
The value of a if the point (–4, a) is also on the line is -6
What is the value of a if the point (–4, a) is also on the line?If a line passes through the point (4, –2) and has a slope of 1/2, its equation can be written in point-slope form as:
y - (-2) = 1/2(x - 4)
Simplifying the equation gives:
y + 2 = 1/2x - 2
To find the value of a, substitute x = -4 and y = a into the equation:
a + 2 = 1/2(-4) - 2
a + 2 = -4
a = -6
Hence, the value of a is -6
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Question
A line passes through the point (4, –2) and has a slope of 1/2 What is the value of a if the point (–4, a) is also on the line?