The value of x in the given equation using laws of exponents is; x = -9
How to use laws of exponents?We want to solve the problem correctly expressed as;
3^(4x) = 27^(x - 3)
Now, some of the laws of exponents are;
1) Product of powers rule.
2) Quotient of powers rule.
3) Power of a power rule.
4) Power of a product rule.
5) Power of a quotient rule.
6) Zero power rule.
7) Negative exponent rule.
Now, 27^(x - 3) can also be expressed as;
3^(3(x - 3))
Now, according to power of power rule, if a base raised to a power is being raised to another power, the exponents are multiplied and the base remains the same. Thus;
3^(3(x - 3)) = 3^(3x - 9)
Thus, we now have;
3^(4x) = 3^(3x - 9)
4x = 3x - 9
3x - 4x = 9
-x = 9
x = -9
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1. Which of the fractions are closer to 1 than to 0?
2. Which of the fractions are closer to 0 than to 1?
3. Write two fractions with a denominator of 8 that are closer to 0
than to 1.
4. Use the benchmark and the fractions and to write three
comparison statements.
Answer:
where’s the options??
Step-by-step explanation:
The last customer of the day calls telling you they purchased 80 meters of fencing to fence in
a circular area around their flagpole. They want to know how much area of concrete they'd
need to buy to cover the entire circular pad around the flagpole. Using their fence as the
circumference, calculate how much area they will need to cover with the concrete for their
circular pad.
The area of circle that is needed to be filled with concrete is 509 m².
What is the definition of a circle?
A circle is a kind of ellipse with zero eccentricity and two coinciding foci. The locus of points drawn at equal distances from the centre is also known as a circle. A circle's radius is the distance between its centre and its outer line. A circle's diameter is the line that divides it into two equal halves and is equal to twice its radius.
A circle in the plane has the following equation:
(x-h)^²+ (y-k)² = r²
When the coordinate points are aligned (x, y)
(h, k) is the centre of a circle's coordinate.
r denotes the radius of a circle.
where 2πr is the circumference of the circle
πr²=circle's area
Now,
Given that circumference of the area=80 m
2πr=180
2*22/7*r=80
r=80*7/44
r=140/11 m
then area of the circular pad=πr²
=22/7*140/11*140/11
=2*20*140/11
=5600/11
=509 m²
hence,
The area of circle that is needed to be filled with concrete is 509 m².
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2. The area of a garden plot can be represented by
the expression 85.2z - 58.8. The garden will be
divided into six sections for planting six different
vegetables. The sections will be equal in area.
Write an expression that represents the area of
each section.
The expression that represents the area of each section is 14z-9
How to find the expression?The expression to denote the area of each section would be: 14z -9
Given that,
The expression for the area of plot area 84z -54
The number of equal sections in which it is divided 6
To find,
The expression for each section = ?
The area of each section = (total area of the garden(/number of equal sections
= (84x-54)/6
= 6(14z-9)/6
=14z - 9
Thus, is the expression that would represent every section's area.
Which of the following are roots of the polynomial function?
Check all that apply.
F(x)=3-2-5x-3
A. 3-√√2
B. 1-√√3
□ C. -1
D. 3
DE 1+√3
F. 3+√√2
Answer:B
Step-by-step explanation:
Label each figure correctly. Area is understood to be square feet and perimeter is understood to be feet.
1. Area of the figure = 702 square feet.
Perimeter = 114 feet
2. Area of the figure = 20 square inches.
Perimeter = 24 inches.
How to Find the Area and Perimeter?Area of a rectangle = length * width
Perimeter of a shape = length of all the surrounding of a figure.
1. Area = area of rectangle 1 + area of rectangle 2 = 27 * 24 + 9 * 6
= 702 square feet.
Perimeter = 30 + 27 + 24 + 18 + 6 + 9 = 114 feet
2. Area = area of rectangle 1 + area of rectangle 2 = 7 * 2 + 3 * 2
= 20 square inches.
Perimeter = 7 + 2 + 3 + 3 + 2 + 3 + 2 + 2
= 24 inches.
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Whats the correct answer answer asap for brainlist
The sentence that uses the word "obstinancy" incorrectly is: if we eat out too often, its result in obstinancy and poor health. The Option C is correct.
Definition of the word "obstinancy", its uses and example:Obstinancy is a noun that refers to the quality of being stubborn or resolutely unyielding. It describes a person's refusal to change their views, opinions, or actions, even in the face of compelling evidence or persuasive arguments. Example of its use: despite the pleas of his family, the man's obstinancy led him to continue his dangerous lifestyle.
We often use the word "obstinancy" for the followings:
to describe someone's persistence in pursuing a particular course of action despite obstacles or challenges.to describe someone's reluctance to change their opinion or attitude in light of new evidence.to describe someone's refusal to give in to the demands or requests of others.Read more about Obstinancy
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PLEASEE HELPPP!!! 3 QUESTIONS
Consider the function below.
f(x)=8/x−6
What would be the output if the input is 8?
responses:
-1/4
-4
-8/14
-8/6
What is the average rate of change of the function f(x)=3x^2−5 over the interval [2, 6]?
responses:
-3
-48
-12
-24
The average mass of a certain type of microorganism is 2.4×10^−6
grams. What is the approximate total mass of 5,000 of these microorganisms?
responses:
-0.00012 g
-0.0012 g
-0.012 g
-0.12 g
A. The value of the function at x = 8 will be 4. Then the correct option is B.
B. The average rate of change of the function in the interval of [2, 6] will be 24. Then the correct option is D.
C. The total mass of 5,000 of these microorganisms will be 0.012 g. Then the correct option is C.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
A. The function is f(x) = 8 / (x - 6), then the value of the function at x = 8 is given as,
f(8) = 8 / (8 - 6)
f(8) = 4
Then the correct option is B.
B. The function is f(x) = 3x² - 5, then the average rate of change of the function in the interval of [2, 6] is given as,
Average rate = [3(6² - 4²)] / (6 - 2)
Average rate = 24
Thus, the correct option is D.
C. The average mass of a certain type of microorganism is 2.4 × 10⁻⁶ grams. Then the total mass of 5,000 of these microorganisms is given as,
⇒ 2.4 × 10⁻⁶ × 5,000
⇒ 0.012 grams
Thus, the correct option is C.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A rectangle is shown with length x plus 10 and width 2 x plus 5. The inside of the rectangle is shaded other than an unshaded square with length x plus 1 and width x plus 1.
Write an expression for the area of the shaded region in its simplest form. Show all of your steps.
Answer:
x² + 23x + 49
Step-by-step explanation:
area of rectangle = length × width
Area of outer rectangle:
(x + 10) × (2x + 5) = 2x² + 5x + 20x + 50 = 2x² + 25x + 50
Area of unshaded square:
(x + 1)² = x² + 2x + 1
shaded area = area of outer rectangle - area of square
shaded area = 2x² + 25x + 50 - (x² + 2x + 1) =
= 2x² + 25x + 50 - x² - 2x - 1
= x² + 23x + 49
Graph the following conditions. Click on the graphic to choose the correct answer. [(x, y): x + y = 5) 4 -3 -2 -1 YA 6 5 4 3 2 + T -2 -3 A 5 19 - K 2 3 4 5 6 X
A graph of the equation under this condition {(x, y): x + y = 5)} is shown in the image attached below.
What is an ordered pair?In Mathematics, an ordered pair simply refers to a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.
Next, we would determine the ordered pairs that satisfies the given linear function in standard form.
When the value of x = 1, the output value of this linear function is given by;
y = 5 - x
y = 5 - 1
y = 4 ⇒ (1, 4)
When the value of x = 0, the output value of this linear function is given by;
y = 5 - x
y = 5 - 0
y = 5 ⇒ (0, 5).
When the value of x = 2, the output value of this linear function is given by;
y = 5 - x
y = 5 - 2
y = 0 ⇒ (2, 3).
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Regular pentagons ABCDE and PQRST are congruent to each other. What is the perimeter of pentagon PQRST?
The perimeter of the pentagon PQRST will be equal to the perimeter of the pentagon ABCDE.
What is the perimeter of the regular polygon?The regular polygon's edges are all identical to one another. The relationship between the number of sides to the mean distance determines the regular polygon's perimeter when it has n sides.
Then the perimeter of the pentagon ABCDE is given as,
P = AB + BC + CD + DE + EA
And the perimeter of the pentagon PQRST is given as,
P = PQ + QR + RS + ST + TP
Regular pentagons ABCDE and PQRST are congruent with each other. Then the perimeter of the pentagons will be identical to each other.
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1. For
what value of x is the
3(x + 2)-2x = 12 true?
A. 6
B. 10
C. 12
D. 14
E. 18
1.4.1 Set
the equation
Answer: A. 6
Step-by-step explanation:
Answer: I think D.
Step-by-step explanation: why not pick D…..
Hope this helps^^
A research firm estimates the number of people who watch a television show. One rating point means that about 1,800,000 households watched the show. The top-rated television show during a certain week had a rating of 10.2. About how many households watched the show that week?
Based on the rating information of 10.2, a total of 1,800,000 households watched the show that week is 18360000 household.
How do ratings work?An evaluation of something's quality or appeal is given a rating. a 10 out of 10 value-for-money rating, as an illustration. The president's standing among the public is at its lowest point since assuming office.
Position is synonymous with ranking, evaluation, appraisal, and categorisation. Additional Ratings
Since 1 rating point is given = 1,800,000
Rating point = 1,800,000 household
Rating point = 10.2 × 1,800,000 household.
Rating point =18360000 household.
Therefore, correct to state that the number of households that watched the show that week are 18360000 household.
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Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 70 miles per hour, with a standard deviation of 3 miles per hour. Estimate the percent of vehicles whose speeds are between 64 miles per hour and 76 miles per hour.
Answer:
The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.
In this case, the mean speed is 70 mph and the standard deviation is 3 mph. So, we can estimate the percent of vehicles whose speeds are between 64 mph and 76 mph as follows:
64 mph = 70 mph - 3 mph * 1
76 mph = 70 mph + 3 mph * 1
Since the speeds are within one standard deviation of the mean, we can use the Empirical Rule to estimate that approximately 68% of the vehicles have speeds between 64 mph and 76 mph.
So, the answer is approximately 68%.
17.1
What is the solution to the equation --+?
X=-5
X=-4
X-5
Save and Exit
the solution of the given equation will be x =1
What is a System of Equations?
A system of equations in algebra is made up of two or more equations that are solved together. "A group of equations satisfied by the same set of variables are called a system of linear equations. Finding the values of the variables employed in the system of equations is the first step towards solving it. While maintaining the balance of the equations on both sides, we compute the values of the unknown variables. Finding a variable whose value makes the condition of all the given equations true is the primary goal of solving an equation system.
The given equation x -5 = -4
add +5 in both side we get
x = -4+5
x=1.
Hence the solution of the given equation will be x =1
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Janet is shopping for bottles and formula for her
baby. Last month, the price of her favorite brand
of formula was $15 per can. She bought six
bottles last month. This month, the price of the
cans of formula has increased by 20%. As a
result, she will buy 50% fewer new bottles.
The cross-price elasticity for the new bottles
calculated using the cross-price elasticity
formula is
and the goods are
2.5; substitutes
1.2; substitutes
-2.5; complements
-1.2; complements
Answer:
Step-by-step explanation:
Cross-price elasticity of demand is a measure of the relationship between the prices of two goods and the quantity demanded of each. It is used to determine how changes in the price of one good affect the demand for another good.
In this scenario, Janet is shopping for formula and bottles for her baby. The price of her favorite brand of formula has increased by 20%, causing her to buy 50% fewer new bottles. The cross-price elasticity for the new bottles calculated using the cross-price elasticity formula is -2.5.
A negative cross-price elasticity value of -2.5 means that the two goods, formula and bottles, are complements. This indicates that an increase in the price of one good (the formula) leads to a decrease in the demand for the other good (the bottles). In other words, when the price of formula increases, Janet is less likely to buy as many new bottles because she is spending more on formula.
On the other hand, if the cross-price elasticity were positive, it would indicate that the two goods are substitutes. In that case, an increase in the price of one good (the formula) would lead to an increase in the demand for the other good (the bottles) as people switch to the cheaper alternative.
In summary, cross-price elasticity of demand is a useful tool for understanding the relationship between the prices of two goods and the quantity demanded of each, and can help businesses make informed decisions about pricing and product strategy.
The cross-price elasticity is -3.66., complements.
What is elasticity of demand?A demand that is elastic experiences a significant shift in quantity demanded as a result of a price adjustment. When the amount sought changes little as a result of a price adjustment, the demand is said to be inelastic.
The percentage change in the quantity demanded for one good has an impact on the percentage change in the price of another good, which is measured by the cross elasticity of demand.
Based on the values given above, the cross elasticity of demand will be:
= [(3 - 6) / (18 - 15)] × [(15 + 18) / (6 + 3)]
= (-3/3) × (33/9)
= -1 × 3.66
= -3.66%
Since it's a negative value, the goods are complement.
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Solve for x with the given measures
a rectangular sheet of dimensions 44cm *14cm is rolled along its length and a cylinder is fromed find the surface area of the cylider
The total surface area of cylinder formed is 924 cm²
We are given a rectangular sheet of paper of dimensions 44 cm* 14 cm is rolled along its length
So, height of formed cylinder = Length of rectangular sheet = 14 cm
Circumference of base of cylinder = Breadth = 44 cm
Circumference of circle = 2πr
So,
2 × (22/7) × r =44
r = (44×7)/(22×2)
Radius of cylinder is 7 cm
Height = 14 cm
Total surface area of cylinder = 2πr(h+r)
= 2 × 22/7 × 7 (14 +7 )
= 924 cm²
Hence the total surface area of cylinder formed is 924 cm² .
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x + 17 = -50 + x + 34 + 33
PLEASE HELP ASAP IF YOUHELP QUICK I WILL
GIVE BRANLIST In a repeated experiment, Kim rolled a fair die twice. The theoretical probability of both rolls equaling a sum greater than 10 is Predict how many times
36
the rolls will result in a sum greater than 10 if the experiment is repeated 108 times
OPTIONS
3
9
10
1&
The theoretical probability that a sum greater than 10 is obtained is given as follows:
p = 1/12.
Out of 108 trials, the expected number of trials with a sum greater than 10 is given as follows:
9.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The 36 total outcomes for the pair of dices is given as follows:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)Out of these outcomes, three of them, (5,6), (6,5) and (6,6) have a sum greater than 10, hence the probability is given as follows:
p = 3/36
p = 1/12.
Then the expected number is given as follows:
E(X) = 108 x 1/12
E(X) = 9.
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Answer:
9
Step-by-step explanation:
experiment, Kim rolled a fair die twice. The theoretical probability of both rolls equaling a sum greater than 10 is Predict how many times.
Therefore the experement is 9
write a number or expression in each empty box to create a true equation 15 + 10 = _____ (3 + 2)
Answer:
5(3-2)
Step-by-step explanation:
15-10
5×3-5×2
Shen is riding in a bike race that goes through a valley and a nearby mountain range.
The table gives the altitude (in feet above sea level) for the five checkpoints in the race.
Use the table to answer the questions.
Checkpoint Altitude
(feet above sea level)
1 3,459
2 1,499
3 668
4 -202
5 -99
(a) The top of a hill rises 66 feet above Checkpoint 4.
What is the altitude of the top of the hill?
(b) How much higher is Checkpoint 1 than Checkpoint 5?
1) Note that the altitude of the top of the hill is -136 feet above sea level.
2) Note that Checkpoint 1 is 3,558 feet higher than Checkpoint 5.
What is the rationale for the above response?Altitude or height is a distance measurement between a reference datum and a point or object, generally in the vertical or "up" direction. The precise definition and reference datum vary depending on the circumstance.
1) Checkpoint 4 has an altitude of -202 feet above sea level. The top of the hill rises 66 feet above Checkpoint 4. Therefore, the altitude of the top of the hill is:
-202 + 66 = -136 feet
So, the altitude of the top of the hill is -136 feet above sea level.
2) To find the difference in altitude between Checkpoint 1 and Checkpoint 5, we need to subtract the altitude of Checkpoint 5 from the altitude of Checkpoint 1.
Altitude difference = Altitude of Checkpoint 1 - Altitude of Checkpoint 5
Substituting the values given in the table, we get:
Altitude difference (AD) = 3,459 - (-99)
AD = 3,459 + 99
Thus, AD = 3,558
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differentiate (1+2x²)⁴
Answer:
16x(1+2x^2)^3
Step-by-step explanation:
f(x)=(1+2x^2)^4
Use chain rule
4(1+2x^2)^3(4x)
Find the value of x
(to
the nearest ten th).
31°
x
9
The value of x from the given triangle is 17.5 units.
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
We know that, sinθ= Opposite/Hypotenuse
Here, sin31°=9/x
0.515=9/x
x=9/0.515
x=17.5
Therefore, the value of x is 17.5 units.
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The "-8" and "+8" on the left
cancel, leaving x by itself. What
number do we get on the right?
Enter the number that belongs in the green box.
X-8=6
+8+8
x = [?]
ha
Sophia ate 18 candies in 4.5 minutes. How many candies did she eat per minute
what is it
Graph the function f(x) = -x² - 2. Complete the table of function values below. x f(x) -2 -1 0 1 2 Use the graphing tool to graph the function.
The graph of the quadratic function is on the image at the end.
How to graph the quadratic function?Here we want to graph the quadratic function:
f(x) = -x² - 2
To do so, we can complete the table of values by evaluating the function.
if x = ±2 then:
f(±2) = -(±2)² - 2 = -4 - 2 = -6
if x = ±1
f(±1) = -(±1)² - 2 = -1 - 2 = -3
if x = 0
f(0) = -(0)² - 2 = - 2 = -2
Then we have the points:
(-2, -6), (-1, -3), (0, -2), (1, -3), (2, -6)
Now just graph these points and connect them with a curve. The graph of the parabola is below.
Draw a rectangular fraction model to explain your thinking. 1/2 of 2/3 = 1/2 of_ third(s) =_ third(s)
A rectangle that has been divided into equal parts is referred to as a rectangular fraction. Depending on how many equal pieces you divide the whole into, the equal parts may be divided into halves, thirds, fourths, and so on.
1/2 of 2/3 is equal to 1/3
What is the equation?
The equation is defined as a mathematical statement with at least two terms that contain variables or values that are equal.
To represent the multiplication of 1/2 and 2/3, we can draw a rectangle and divide it into equal parts.
1) First, we draw a rectangle.
2) Then, we divide it into 2 equal parts horizontally.
3) Next, we divide each half vertically into 3 equal parts.
4) Now we can see that each small rectangle represents 1/6 of the whole rectangle.
So, 1/2 of 2/3 is equal to 1/2 of 1/3.
Therefore, 1/2 of 2/3 is equal to 1/3.
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The sixth-graders at Liam's school got to visit either the science museum or the history museum. 10 students picked the science museum and 39 students picked the history museum. What is the ratio of the number of sixth-graders who visited the science museum to the number of sixth-graders who visited the history museum?
The ratio of the number of sixth-graders who visited the science museum to the number of sixth-graders who visited the history museum is
10:39.
What is meant by the ratio of two quantities?
A ratio displays the multiplicity of two numbers. Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent." In general, a: b, which can be interpreted as "a is to b," is used to denote a ratio between two quantities, let's say "a" and "b."
Given,
Number of students who picked the science museum = 10
Number of students who picked the history museum = 39
The ratio of students who visited the science museum to students who visited the history museum = 10:39.
Therefore the ratio of the number of sixth-graders who visited the science museum to the number of sixth-graders who visited the history museum is 10:39.
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To encourage bulk buying, a company reduces the list price of $2,000 per unit by nine cents times the number of units bought. Write a function statement for the company's revenue (R) from a particular distributor that buys x units
The company’s revenue (R) from a particular distributor that buys x units is R(x) = 8999.93x
What is algebra?Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
Given:
original price = $9000 per unit.
let the number units bought be x
then amount= 9000x.
If the price reduces the list price by seven cents times the number of units bought .
7cents= 0.07 dollar
Then,
R(x) = 9000x - 0.07x
R(x) = 8999.93x
Hence, R(x) = 8999.93x.
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Please work these out, If possible can someone just work out 1 providing solutions. Thanks
Answer:
See below for solution steps for parts (a) and (c)
Step-by-step explanation:
The trick here is to get all the roots to have the same radical. Each of the lowest radical is the square root pf a prime so cannot be reduced further
For example, in a, the lowest is [tex]\sqrt{3}[/tex]
So get all the others to this level a[tex]\sqrt{3}[/tex] and then you can just add up the non-radicals and use the radical as the common expression
I will solve a couple and that will give you a general idea of solving the rest
Let's do a.
[tex]5\sqrt{3} , \sqrt{3}[/tex] are already at the lowest radical level of [tex]\sqrt{3}[/tex] so let's reduce 108 to have [tex]\sqrt{108}[/tex] to have [tex]\sqrt{3}[/tex] as one of its components
We can factor 108 as follows;
108/3 = 36
So 108 = 36 x 3
√108 = √36 × √3 = 6√3
Therefore the original expression becomes
[tex]5\sqrt{3} - 6\sqrt{3} + \sqrt{3} = (5 - 6 + 1)\sqrt{3} = 0 \sqrt{3} = 0[/tex]
[tex]-------------------------------[/tex]
c.
[tex]2\sqrt{20} - 7\sqrt{5} + \sqrt{45}[/tex]
Lowest radical is [tex]\sqrt{5}[/tex] whose coefficient is 7
Factor 20 = 4 x 5
[tex]2\sqrt{20} = 2\sqrt{4 \times 5} = 2\sqrt{4} \times \sqrt{5} = 2\times 2 \times \sqrt{5}\\= \bold{4\sqrt{5}}[/tex]
Factor 45:
45 = 9 x 5
[tex]\sqrt{45} = \sqrt{9} \times \sqrt{5} = \bold{3\sqrt{5}}[/tex]
Original expression becomes:
[tex]4\sqrt{5} - 7\sqrt{5} + 3\sqrt{5}\\\\=(4 - 7 + 3)\sqrt{5}\\\\= 0 \sqrt{5}\\\\= 0\\----------------------------[/tex]
I am sure you can do the rest. If not post them as another question. Maybe someone else will answer a few of the ones I did not.
All the best
