If log₂(4x + 6) = 4, then x = ____
You may enter the exact value or round to 4 decimal places.
Answers
Answer: -1/2
Step-by-step explanation: To solve this problem, we can use the properties of logarithms to isolate the variable x on one side of the equation. The properties of logarithms tell us that the logarithm of a product is the sum of the logarithms of the factors, and that the logarithm of a power is the exponent times the logarithm of the base.
If log₂(4x + 6) = 4, we can rewrite the left side of the equation as follows: log₂(4x + 6) = log₂(2^4 * (2x + 3))
Then, using the property of logarithms that the logarithm of a product is the sum of the logarithms of the factors, we can simplify the equation as follows: log₂(4x + 6) = 4 + log₂(2x + 3)
Now, we can use the property of logarithms that the logarithm of a power is the exponent times the logarithm of the base to simplify the equation even further: log₂(4x + 6) = 4 + 1 * log₂(2x + 3)
Since the logarithm of a power is the exponent times the logarithm of the base, this means that the logarithm of a number is the logarithm of that number divided by the logarithm of the base. Therefore, we can divide both sides of the equation by log₂ to isolate the variable x on one side of the equation:
log₂(4x + 6) / log₂ = 4 + 1 * log₂(2x + 3) / log₂
(4x + 6) / 1 = 4 + (2x + 3) / 1
4x + 6 = 4 + 2x + 3
4x + 6 = 2x + 7
2x = -1
x = -1/2
Therefore, if log₂(4x + 6) = 4, then x = -1/2.
Related Questions
Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.
Answers
You decide to buy a refurbished computer for $550.00 plus 6% sales tax. BB Electronics allow you to take out a no-interest loan for 12 months, and after that the interest rate is a 13.25% APR. You must make payments of $25/month, and if you miss one payment you are assessed a late fee of $29.00 plus 13.25% APR interest beginning from the date of purchase.
You missed the second payment. What is the amount of interest of the bill you will receive?
Answers
The interest on the bill will be calculated as follows:
Amount of Loan = $550
Sales Tax = 6% of $550 = $33
Total Loan = $550 + $33 = $583
Interest = 13.25% APR x $583 = $77.13
Late fee = $29
Total Interest = $77.13 + $29 = $106.13
Given the ratio 8 ounces to 1 cup,how many ounces are in 4 cups?
Answers
Answer:
32 oz
Step-by-step explanation:
Given the ratio 8 ounces to 1 cup, how many ounces are in 4 cups?
4 * 8 oz = 32 oz
describe the sampling of p hat. Assume that the size of the population is 25000 n= 300 p=0.7
Answers
The mean of the given sample data is 210, and the standard deviation is 7.937.
Given size 'n' = 300
The population proportion 'p' = 0.7
Let 'x' be the random variable of the binomial distribution
a) mean of the binomial distribution = n p = 300 × 0.7
μ = 210
b) variance of the binomial distribution
⇒ n p q
⇒ 300 × 0.7 ×0.3
⇒ σ² = 63
The standard deviation of the binomial distribution:
⇒ √n p q = √63 = 7.937
Thus, the mean of the given sample data is 210, and the standard deviation is 7.937.
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The question seems to be incomplete the correct question would be:
describe the sampling of p hat. Assume that the size of the population is 25000 n= 300 p=0.7 a) Determine the mean of the sampling distributionb) Dtermine the standard deviation of the sampling distribution
Isaiah is trying to buy dry-erase markers for his teachers during teacher appreciation week. He
is able to collect 12 markers a day and started off with 15. How many days will it take him to get
to 135 markers? Make an equation to solve the problem using m for markers and d for days.
Answers
Answer:
It will take him 10 days to get to 135 markers.
[tex]d=12m+15[/tex]
Step-by-step explanation:
(attached)
On Saturday, the Milleman Family had dinner at a restaurant. They ordered 3 pizzas and 2 cheeseburgers for $41.50. The following weekend, the Anderson Family had dinner at the same restaurant where they ordered 2 pizzas and 5 cheeseburgers for $43.25. Which system of equations can be used to determine the cost of one pizza (p) and one cheeseburger (c)?
Answers
Answer: $8.64 and $7.79 respectively.
Step-by-step explanation: To determine the cost of one pizza and one cheeseburger, we can set up the following system of equations:
3p + 2c = 41.50
2p + 5c = 43.25
The first equation represents the total cost of the Milleman Family's meal, where 3p represents the cost of 3 pizzas, 2c represents the cost of 2 cheeseburgers, and 41.50 represents the total cost of the meal. The second equation represents the total cost of the Anderson Family's meal, where 2p represents the cost of 2 pizzas, 5c represents the cost of 5 cheeseburgers, and 43.25 represents the total cost of the meal.
By solving this system of equations, we can determine the cost of one pizza and one cheeseburger. For example, we can use the elimination method to solve the system of equations as follows:
First, we can multiply the first equation by 5 and the second equation by 3 to get the following equations:
15p + 10c = 207.50
6p + 15c = 129.75
Next, we can subtract the second equation from the first equation to eliminate the c terms and find the value of p as follows:
15p + 10c = 207.50
6p + 15c = 129.75
9p = 207.50 - 129.75
9p = 77.75
p = 77.75 / 9
p = 8.64
Finally, we can substitute the value of p that we found into one of the original equations to find the value of c as follows:
3p + 2c = 41.50
3(8.64) + 2c = 41.50
25.92 + 2c = 41.50
2c = 41.50 - 25.92
2c = 15.58
c = 15.58 / 2
c = 7.79
Therefore, the cost of one pizza is $8.64 and the cost of one cheeseburger is $7.79.
18=6h+2h pls help me with this answer im not understandin it
Answers
Answer:2.25 or 9/4
first we need to add 6h and 2h together, and we get 8h, and we divide 8 both side will get the fraction 18/8 and we can simplify will get 9/4 if you want more simple and will become 2.25
Add a term to the expression so that it becomes a perfect square trinomial.
x2-22x +
Answers
Answer:
Step-by-step explanation:
is times 43
At as sale, suits were sold for $72 each. This price was 45% of a suits original price. How much did a suit originally cost?
Answers
Answer: 1680. The answer is 1680 because 56% of 3000 is 1680 people.
Answer:
The suit orginally costed $160 dollars.
Step-by-step explanation:
PLEASE ASAP I NEED HELP
Given the inequality 4x ≤ 28, which of the following is a solution that makes the inequality true?
Answers
The value of the inequality equation is x ≤ 7
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
4x ≤ 28 be equation (1)
Now , on simplifying the equation , we get
Divide by 4 on both sides of the inequality equation , we get
x ≤ 7
Therefore , the value of x is less than or equal to 7
All the numbers less than or equal to 7 satisfies the condition for x
The value of the equation x ≤ 7 is shown in the graph below
Hence , The value of the inequality equation is x ≤ 7
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Will give brainliest
Answers
Answer:
-5
Step-by-step explanation:
y (4) need to times 2.5 to be 10
so, x (-2) needs to times 2.5 to be the answer
-2 * 2.5 = -5
nswer the question.
The table shows the amount of fabric needed to make each item of doll clothes. Tamara is making 5 of
Fabric for Doll Clothes
Item Amount of Fabric Needed (feet)
Blouse2/12
Jacket 7/12
Skirt 7/12
How many feet of fabric are needed to make 5 of each item? Move numbers to the boxes to show the answer. If there is no whole number
put a 0 in the first box.
Answers
Equation:
5 x (2/12 + 7/12 + 7/12) = f f = amount of fabric needed
Solve:
10/12 + 35/12 + 35/12 = f
80/12 = f
Simplify:
6 8/12
Answer:
Tamara needs 6 ft and 8 inches of fabric to make five of each item.
Use two different methods to find and explain a formula for the area of a trapezoid
that has parallel sides of length a and b and height h. Consider these ideas or others: (a)
Combine two copies of the trapezoid to make a parallelogram. (b) Subdivide the trapezoid
into two triangles, one with base b and one with base a.
Answers
The two possible ways to find the area are -
A = (1/2) × {a + b} × {h}A = {b x h} - (1/2) x {(b - a} x h}What is trapezoid?
A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides.
Area : ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sidesPerimeter : sum of lengths of sides of trapezoidNumber of vertices : 4Number of edges : 4Properties : Convex polygonType : QuadrilateralSum of interior angles : 360°We have a trapezoid.
Now, we can find the area in two ways -
[1] -
A = (1/2) × {a + b} × {h}
[2] -
A = {b x h} - (1/2) x {(b - a} x h}
Therefore, the two possible ways to find the area are -
A = (1/2) × {a + b} × {h}A = {b x h} - (1/2) x {(b - a} x h}To solve more questions on trapezoids, visit the link below -
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Algebra
will mark brainliest
Answers
The inequality for which the order pair (-5, -7) is a solution will be x + y ≤ 3. Then the correct option is B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Let's check all the options, then
A) y ≤ (1/4)x - 1
At (-5, -7), we have
-7 ≤ (1/4)(-5) - 1
-7 ≤ -2.25
This is incorrect.
B) x + y ≤ 3
At (-5, -7), we have
-5 + (-7) ≤ 3
-12 ≤ 3
This is correct.
The inequality for which the order pair (-5, -7) is a solution will be x + y ≤ 3. Then the correct option is B.
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find the slope and y-intercept of the line 3x - 5y = 15
Answers
The slope of the given line, 3x - 5y = 15, is 3/5 and the y-intercept is -3
Determining the slope and y-intercept of a lineFrom the question, we are to determine the slope and y-intercept of the given line.
The given line is
3x - 5y = 15
To determine the slope, we will write the equation in the slope-intercept form of a line.
The slope-intercept form of a line is given as
y = mx + b
Where m is the slope
and b is the y-intercept
Now, we will express the given equation in this form
3x - 5y = 15
-5y = 15 - 3x
Divide through by - 5
y = -3 + 3/5x
y = 3/5x - 3
By comparing to the slope-intercept form of a line,
m = 3/5
and b = -3
Hence, the slope is 3/5 and the y-intercept is -3
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Find the quadratic equation whose parabola has vertex (3, –2) and y-intercept (0, 16). Give your answer in vertex form, and show your work.
Please Help!!
Answers
Answer:
y = 2(x-3)^2-2
Step-by-step explanation:
We can find the quadratic equation by using the vertex form. The vertex form of a quadratic equation is:
[tex]y=a(x-h)^2+k[/tex], where x and y are any point on the parabola, a is the constant (indicating whether the parabola opens up or down), and h and k are the coordinates of the vertex.
Since we already have the y-int (an x and y coordinate lying on the parabola) and the vertex, we can plug in both to find a:
[tex]16=a(0-3)^2-2\\16=a(-3)^2-2\\16=9a-2\\18=9a\\2=a[/tex]
Thus, the equation is:
[tex]y=2(x-3)^2-2[/tex]
Solve for m.
m+15<−123
Responses
m>−11315
m is greater than negative 1 and 13 over 15
m>−1715
m is greater than negative 1 and 7 over 15
m<−1715
m is less than negative 1 and 7 over 15
m<−11315
and show work
Answers
The solution to the inequality is m < −1 13/15 . m is less than negative 1 and 7 over 15
How to solve for the inequalityIn this question we have to solve for the inequality that is given as m + 1/5 < -1 2/3
We would have to rewrite the equation using the math tool
[tex]m +\frac{1}{5}\leq 1\frac{2}{3}[/tex]
The mixed fraction can be properly rewritten as improper fraction
[tex]m +\frac{1}{5}\leq \frac{5}{3}[/tex]
subtract 1/5 from 5/3
[tex]m\leq -\frac{5}{3} -\frac{1}{5}[/tex]
we have to carry out the subtraction of the fraction
[tex]m < \frac{-25-3}{15}[/tex]
[tex]m < \frac{-28}{15}[/tex]
This can be written in mixed fraction as
[tex]m < -1\frac{13}{15}[/tex]
Hence the solution of m is D. m < −1 13/15
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Complete question
m + 1/5 < -1 2/3
Responses
A. m > −1 13/15
m is greater than negative 1 and 13 over 15
B. m > −1 7/15
m is greater than negative 1 and 7 over 15
C. m < −1 7/15
m is less than negative 1 and 7 over 15
D. m < −1 13/15
m is less than negative 1 and 7 over 15
A professor had students keep track of their social interactions
for a week. The number of social interactions over the week is
shown in the grouped frequency distribution. Identify the lower
limit of the fifth class.
The lower limit of the fifth class is
(Type a whole number.)
Answers
The lower limit of the fifth class for the track of social interactions
for a week is 50.
Explain the term lower limit of the class?The frequency distribution has an upper class limit and a lower class limit for each class.The smallest data point that really can correspond to a class is known as the lower class limit. The largest data object that can be a member of a class, or upper class limit.Allow the class intervals to be 30 - 34, 35 - 39, 40 - 44, 45 - 49, 50 - 54, etc. for some aggregated data.
In this case, the distribution is continuous, and all of the class intervals overlap.
Fifth class ; 50 - 54,
The class boundaries of the range from 50 - 54, 50 is the lower limit while 54 is the upper limit.
Thus, the lower limit of the fifth class for the track of social interactions
for a week is 50.
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John brings $15 to the candy store. He buys a bag of jelly beans for $4 and plans to buy some chocolate that costs $5 per pound. Write an inequality to solve for all the possible values of x, the number of pounds of chocolate John could buy.
Use the on-screen keyboard to type the inequality that represents this situation in the box below.
Answers
Answer:
Step-by-step explanation:
he could buy 2 pounds of chocolates and save $1.
What is the value of Negative 3 squared + (negative 4 + 7) (2)?
–28
–3
3
15
I am on a unit test hurry please
Answers
-3^2+(-4+7)(2)
answer = 15
Answer:
15
Step-by-step explanation:
a negative number squared is positive, so its 9 + (-4 + 7)*2. 7-4 is 3, which we then multiply by 2 to get 6. Now add that to 9 to get 15.
Hope this helps!
The ratio of brownies to cookies is 3:5. If there are 75 cookies, how many brownies are there?
Group of answer choices
45
15
60
32
Answers
Answer:
15:25 or 15 brownies
Step-by-step explanation:
25 / 5 = 5 (scale factor)
3 * 5 = 15
chris is 5 years older than 4 times arins age. the sum of their ages is less than 40. what is the oldest arin could be?
Answers
Answer: 6 years old.
Step-by-step explanation:
Chris: 5+4a
c + a<40
5 + 4a + a < 40
5a<35
a<7
For the oldest, let's assume Arin is 6, because it is the highest number that is less than 7.
Arin can be maximum of 6 years old.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Let the Arin's age be x.
So, Chris age is 4x + 5
Now, the sum of their ages is less than 40.
x+ 4x+ 5 < 40
5x < 35
x < 7
Hence, Arin can be maximum of 6 years old.
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Find the area of a Shaded portion
Answers
Find the area of a Shaded portion.
D. 68
Which expression is equivalent to 27 + 63 ? 3(9 + 18) 9(3 + 7) 21(7 + 3) 7(21 + 9)
Answers
Which expression is equivalent to 27 + 63 ?
3(9 + 18)
9(3 + 7)
21(7 + 3)
7(21 + 9)
(3.76x 10-8 )-(2.94 x 10-8)
Write your answer in scientific notation
Answers
The perimeter of a rectangle is 54 inches and the length of one of its sides 6 inches. What is the combined length of the other three sides, in feet?
Answers
Answer:
4 ft
Step-by-step explanation
the combined length of the other three sides can be found with 54-6 is 48 inches
48 inches can be turned into feet by dividing by 12.
48in / 12=4ft
Mia is traveling from her house to her sister’s home. She took the bus to the car rental lot and is now driving the rest of the way at a constant rate of speed. What does the -intercept represent in this problem?
the distance (mi) that Mia traveled on the bus to the car rental before she started driving the car
the distance (mi) that Mia traveled from the car rental lot to her sister's home
the amount of time (hr) elapsed for every mile the car travels from the car rental lot
the distance (mi) the car travels from the car rental lot for every 1 hour elapsed
Answers
Answer:
The distance (mi) the car travels from the car rental lot for every 1 hour elapsed.
Step-by-step explanation:
What occurs when you are dealing with objects that are round
static friction
sliding friction
rolling friction
Answers
5. -4h + 3 + Th ≥ 9h - 21
Answers
A cafeteria sold 36 cartons of regular flavored milk. If the ratio of regular milk sold to chocolate milk sold was 9:4, what is the combined amount of chocolate and regular milk sold?
Answers
Answer:
The combined amount of chocolate and regular milk sold was 52 cartons.
Step-by-step explanation:
1. Divide
36 ÷ 9 = 4
(This means that the ratio has a unit rate of 4. That means):
2. Second ratio rate
4 x 4 = 16
(Because the unit rate is 4).
3. Add
(Now, we add the original 36 cartons with the 16 cartons we found because the first step was just for finding the unit rate).
36 + 16 = 52 cartons.
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