The value of the logarithm expressions [tex]log_{2} 8 - log_{2} 4[/tex] is 1.
Using only two logarithms at a time, from left to right, use the product property or quotient property of logarithms to rewrite logarithms of the form [tex]log_{b} A - log_{b} B = log_{b} (\frac{A}{B} )[/tex]
The logarithm expressions is [tex]log_{2} 8 - log_{2} 4[/tex].
Use the properties to rewrite logarithm expressions as a single logarithm
Using only two logarithms at a time, from left to right, use the product property or quotient property of logarithms to rewrite logarithms of the form [tex]log_{b} A - log_{b} B = log_{b} (\frac{A}{B} )[/tex]
= [tex]log_{2} 8 - log_{2} 4 = log_{2} (\frac{8}{4} )[/tex]
=[tex]log_{2} 2[/tex]=1
thus the expressions value is 1.
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if the length of a rectangle is four less than twice its width and the perimeter is 220 inches, what is the width of the rectangle?
Answer:
Let's denote the length of the rectangle to be L and the width to be W.
The first sentence tells us that the length, L, is "4 less than twice the width". "4 less than" implies we subtract 4 from some quantity. What is that quantity? Well that's "twice the width." We can rewrite this sentence in terms of L and W as: L = 2W - 4.
Now we know the length of the rectangle in terms of the width.
The area of a rectangle is given by A = L x W. Using this equation, we can substitute our values for area and length:
A = L x W
96 = (2W - 4) x W
From this we can solve for W and subsequently solve for L using algebra:
96 = (2W - 4) x W
96 = 2W^2 -4W
96 = 2(W^2 - 2W)
48 = W^2 - 2W
W^2 - 2W - 48 = 0
(W - 8)(W + 6) = 0
W = 8 or W = -6
Since W is the side-length of a rectangle, we can disregard the negative solution. Therefore W = 8 ft.
If W = 8, then L = 2W - 4 = 2(8) - 4 = 12 ft.
Lastly, we know the Perimeter of a rectangle is given as P = 2L + 2W. Substituting into this equation we solve for the perimeter:
P = 2L + 2W = 2(12) + 2(8) = 40 ft.
Step-by-step explanation:
Simplify
√18 +√50 + √8
Answer: 4√2
Step by step explanation:
√8 + √50 - √18
√4√2 + √25√2 - √9√2
2√2 + 5√2 - 3√2
4√2
A periods of 4 hour 30 minute is what percent of a day
Answer:
It's 4.5 divide by 24 , multiply by 100 you get 18.75%The manufacturing cost of a cell phone was $136. Sellers first marked up the cost by 25 percent. Sales were poor, so sellers decreased the markup to 17 percent. Calculate the old and new selling prices.
Answer:
old price was $170; new price is $159.12
Step-by-step explanation:
1) Formula given:
Selling price = original cost + mark up value
2) Old price = original cost + 25% (original cost)
Old price = $136 + 35% ($136) = $136 + 0.25×$136 = $136 + 34 = $170
3) New price = original cost + 17% (original cost)
= $136 + 17% ($136) = $136 + 0.17×$136 = $136 + $23.12 = $159.12
Answer:
old price was $170; new price is $159.12
**Sometimes you are given the information for a part-to-part
relationship, but are asked about a part-to-whole relationship.
When this happens, just add another row to your ratio table.
The ratio of mammals
to reptiles at the pet
I store is 3:7. If there are
90 animals at the pet
I store, how many of the
animals are reptiles?
Show answer in a ratio table
The number of reptiles will be 63.
In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7).
The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be positive.
Let the number of mammals and reptiles be 3x and 7x
the store has total 90 animals
so total number of animals will be
90= 3x+7x
90= 10x
so x will be 9
number of mammals will be 3×9= 18
number of reptiles will be 7×9= 63.
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LOTS OF POINTS PLS ANSWER
The answer is Discrete
Answer:
B
Step-by-step explanation:
help, I'm very lost. I dont know what to do.
Answer:
x=11
Step-by-step explanation:
(3x-1)+(6x-8)= 90
9x- 9= 90
+9 +9
9x=99
/9 /9
x=11
Find the Least Common Denominator of 5/6 and 3/8, show all of your work:
To find the LCD of (5/6, 3/8) we need to find the Least Common Multiple (LCM), which in this case is (6, 8). So we want to find the values of the numerical part of each term. We need to select the largest one, which in this case is 8
Then multiply them together to get the current total. In this case, the current total is 48
Current Total = 48
Multiply the numeric part of the denominators together.
Current Total = 8 + 8 = 16
Again, multiply the numeric part of the denominators together.
Current Total = 16 + 8 = 24
Check each value in the numerical part of each term against the current total. Since the current total is evenly divisible, return it. That is the least common denominator of the numerical part of the fraction.
So the Lowest Common Denominator (LCD) is 24
Someone please help i don’t understand
Answer: you just add all the sides
Step-by-step explanation:
make 40,50,40,20 and 15 into 100
solution:
Answer:
40,40,20
Step-by-step explanation:
40+40+20=100
Answer:
20 + 40 + 40 = 100
50 * (40/20) = 100
chapter 8 HELPPPPPPPPPP!!!!!!!!!!!!!!!!!
Find the circumference of each circle. Use your calculator's value of [pi]. Round your answer to the nearest tenth.
Answer:37.68/18.84
Step-by-step explanation:.
area of a circle s pier^2 or just 1/2pie r^2 so 1/2*3.148*2answer is 37.68.Un club de rentar películas cobra una membresía mensual de $15 y cobra 2$ por cada película rentada Si n representa el número de películas rentados en mayo entonces el cargo para este mes puede ser representado por
Based on the cost of membership per month and the number of movies rented, the charge for the month of May can be represented as 15 + 2n.
What is the charge for the month?The movie rental club charges a flat $15 for membership per month.
The movies rented incur a charge of $2 per rental.
The total cost for May and any other month is:
= Membership fee + 2 x number of movies rented
Number of movies rented is n so the equation for the cost of May is:
= 15 + 2n
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A truck can be rented from Company A for $70 a day plus $.5 per mile. Company B charges $30 a day plus $.9 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
100 miles in a day the truck should have to cover so that the rental costs for company A and company B are same
Company A rented a truck for $70 a day and $.5 per mile will be added accordingly. Similarly, Company B rented a truck for $30 a day and $.9 per mile will be added as per distance covered.
Let the number of miles travelled by the truck be x.
Then, we can depict the given information in terms of equation and will equate them further to solve according to the question need.
So, total rent to be pay to company A = $(70+0.5x)
and total rent to be pay to company B = $(30+0.9x)
Now, the number of miles in a day at which the rental costs for Company A and Company B are the same will be
70+0.5x = 30+0.9x .............(1)
Now, solve equation (1) in order to calculate the value of x.
70-30 = 0.9x-0.5x
40 = 0.4x
40/0.4 = x
400/4 = x
100 = x
∴ x = 100
Hence, 100 miles in a day the truck should have to cover so that the rental costs for company A and company B are same.
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at the supermarket you can fill your own honey bear container. a customer buys 12 oz of honey for $5.40
The price of the honey per ounce will be $0.45 per ounce.
How to calculate the value?From the information given, at the supermarket you can fill your own honey bear container and a customer buys 12 oz of honey for $5.40
Therefore, the price per ounces will be:
= Total price / Number of ounces
= $5.40 / 12
= $0.45 per ounce
Therefore, the price of the honey per ounce will be $0.45 per ounce.
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how much more does $1,000 earn in 8 years
Answer:
ur question doesnt make sense
Step-by-step explanation:
Help me find the answer
The answer will be 16 minutes.
In mathematics and statistics, the arithmetic mean or arithmetic average, or just the mean or the average, is the sum of a collection of numbers divided by the count of numbers in the collection
An arithmetic average is the sum of a series of numbers divided by the count of that series of numbers. If you were asked to find the class (arithmetic) average of test scores, you would simply add up all the test scores of the students and then divide that sum by the number of students.
The arithmetic mean or mean is the simplest way to calculate the average for the given set of numbers. It is classified into two different types, namely simple arithmetic mean and weighted arithmetic mean.
leave at 7 a.m.=
x₁= 32+28+35+26+39/5
⇒ 160/5
⇒ 32 minutes.
x₂ = 46+44+52+50+48/5
⇒ 240/5 = 48 min
Δx = x₂- x₁
= 48-32
= 16minutes.
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3. Larry made a list of his assets and liabilities
and determined his net worth. He got a
bonus at work and paid off his credit card
debt and student loan. What is his net worth
after he made these two payoffs?
Item
Value (S)
cash
875.00
764.00
1,022.00
6,500.00
2,896.00
3,800.00
2,500.00
1,299.00
clothes
jewelry
savings
credit card debt
car payoff
student loan
motorcycle payoff
Find the length of each arc. Round your answers to the nearest tenth.
Based on the calculations, the length of the arc of this circle is equal to: C. 11.5 ft.
What is an arc?In Geometry, an arc can be defined as a trajectory that is generally formed when the distance from a given point has a fixed numerical value.
How to calculate the length of the arc?In Mathematics, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.
Mathematically, the length of an arc formed by a circle is given by:
Arc length = 2πr × θ/360
Where:
r represents the radius of a circle.θ represents the central angle.Substituting the given parameters into the formula, we have;
Arc length = 2 × 3.142 × 11 × 60/360
Arc length = 11.520 ≈ 11.5 feet.
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Write the statement "the sum of a number and 12.6 is more than −3.5" as an inequality.
−3.5 + b ≥ 12.6
−3.5 + b < 12.6
b + 12.6 > −3.5
b + 12.6 ≤ −3.5
Answer:
c
Step-by-step explanation:
For the given statement "the sum of a number and 12.6 is more than −3.5" the inequality is b + 12.6 > −3.5. Option C is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.For the inequality, we have to apply the arithmetic operation.
It is given that the sum of the number 12.6 is more than −3.5.
If the two numbers are b and 12.6 their sum is represented as b + 12.6 and the sum of the number is more than −3.5.
The obtained relation in form of inequality is,
b + 12.6 > −3.5
When we are unsure if the value of a variable is greater than a specific value, we use the "Greater than " symbol in linear inequalities. It is represented by the character ">"
Thus, for the given statement "the sum of a number and 12.6 is more than −3.5" the inequality is b + 12.6 > −3.5. Option C is correct.
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This morning, Milan's car had 19.57 gallons of fuel. Now, 3.8 gallons are left. How much fuel did Milan use?
gallons
X
S
Answer: 15.77
Step-by-step explanation: We know that Milans car had 19.57 gallons of fuel, so I subtracted 19.57 - 3.8 to get my answer.
A middle school has 240 girls and 160 boys. What percent of the total students are girls?
Karissa had 48 t-shirts. Exactly 58 of Karissa's shirts were blue. Karissa gave 13 of her blue t-shirts to her friend Amy. What fraction of Karissa's t-shirts were blue after she gave the shirts to Amy?
Step-by-step explanation:
What did the Rana rulers do to please the British rulers?
Anita Marquez's annual gross pay is $55,520 as a property
analyst. She is married with 2 dependents. How much is
withheld from her biweekly paycheck for state income taxes?
Based on the graduated state tax table and the personal allowance table, the amount withheld from Anita Marquez's biweekly paycheck for state income taxes is $103.50
What amount is withheld?First, Anita is married and will receive a personal allowance of $4,000. She will also receive $2,000 per dependent. Total allowances are:
= 55,520 - 4,000 - 2,000 - 2,000
= $47,520
Total annual tax is:
= (1.50% x 1,000) + (3% x 2,000) + (4.50% x 2,000) + (5% x (55,520 - 1,000 - 2,000 - 2,000 ))
= $2,691
The biweekly tax is:
= 2,691 / (52 / 2)
= $103.50
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I am running two times around a circle of distance 25 meters through out. What is the distance two times from the mid center of that circle
Answer:
[tex]{ \tt{c = \pi d}} \\ { \tt{25 = 2(3.14d)}} \\ { \tt{d = 3.98 \: m}}[/tex]
The isosceles
triangle theorem states that if two sides
congruent, then the angles opposite those sides are
of a triangle are
Answer:
If two sides of a triangle are congruent, then the angles opposite to these sides are congruent.
Step-by-step explanation:
Congruent/Congruency: having the same size and shape congruent triangles.
Theorem 1: If a line is drawn parallel to one side of a triangle to intersect the midpoints of the other two sides, then the two sides are divided in the same ratio.
I hope this helped, have a great day <3
10 cm of a normal specimen of human blood contains 1.2
g of hemoglobin. How many grams does 36 cm³ of the
same blood contain?
The 36cm of specimen will contain an amount of 4.32 grams of blood.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that 10 cm of a normal specimen of human blood contains 1.2 g of hemoglobin. The amount of hemoglobin in 36 cm will be calculated as below:-
10 cm = 1.2g
1 cm = 1.2 / 10 = 0.12 g
36 cm = 36 x 0.12
36 cm = 4.32 grams
Therefore, the 36cm of specimen will contain an amount of 4.32 grams of blood.
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please help!! its really hard and i don't understand what my teacher says
3 x 1, 250 expanded form
The Expanded form of 3×1=3 is 3
The Expanded form of 250 is 200+50+0
Expanded form is nothing more than a method for rewriting a number such that the digit values are included. A place value exists for each number. It calculates that digit's value based on where it is in the number. As we move from left to right in a number, a digit's value rises. In comparison to the digits on the right, the ones on the left have a lower place value. The position of the number is used to calculate each number's value. We can comprehend the place value notations if we read them from right to left.
250=200(hundreds place)+50(tens place)+0(ones place)
Therefore, the Expanded form of 250 is 200+50+0.
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Is y=- 11 linear or nonlinear?
help me with math hw
The value of T will be√74.1
The number line contain point T as shown in the figure. The number line has 7, 8, and 9 marked
There is line in the middle of point 8 and 9
Point T is located away from 8.5.
Since 8 is the square root of 64. And number 9 is the square root of 81. So the 64 and 81 are the perfect square number.
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 32 and can be written as 3 × 3.
Since 8.5 is not a perfect square number so it must be a square between the number 64-81.
Point T is located away from 8.5
So therefore the answer will be √74.1
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