Cutting squares with side length approximately 3.8 inches from each corner will result in a box with the maximum volume.
What is the value of x that will maximize the volume of the box?To determine the value of x that will maximize the volume of the box, we can start by visualizing the box and expressing its volume in terms of x.
When we cut out squares with side lengths x from each corner of the rectangular cardboard, the resulting shape, when folded, will form the box without a top. The height of the box will be equal to the side length of the squares, which is x. The length and width of the base of the box will be the dimensions of the cardboard after the squares are cut out, which will be (30 - 2x) and (10 - 2x) respectively.
The volume of the box can be calculated by multiplying the dimensions of the base and the height:
V(x) = (30 - 2x)(10 - 2x)x.
To find the value of x that maximizes the volume, we can take the derivative of V(x) with respect to x, set it equal to zero, and solve for x.
dV/dx = 0.
Let's calculate the derivative of V(x):
dV/dx = [(30 - 2x)(10 - 2x)]'x + (30 - 2x)(10 - 2x) * 1.
Simplifying and setting it equal to zero:
[(30 - 2x)(10 - 2x)]'x + (30 - 2x)(10 - 2x) = 0.
Solving for this;
x = 3.8 inches
Learn more on maximizing volume of square here;
https://brainly.com/question/30351524
#SPJ1
Helppp me asap pleaseeeee
The Inequalities are:
1. 4x + 10y ≥ 280, x + y ≤ 52
2. 8t + 3c ≤ 200 , 2t + c ≤ 60
1. Let x be the number of tables that seat 4 people.
Let y be the number of tables that seat 10 people.
The total number of people should be equal to or less than the total number of seats:
4x + 10y ≥ 280
The total number of tables should be equal to or less than the maximum number of tables available:
x + y ≤ 52
The number of tables of each type should not be negative:
x ≥ 0
y ≥ 0
2. Let t be the number of tables.
Let c be the number of chairs.
The total assembling hours used for tables and chairs should be less than or equal to the available assembling hours per week:
8t + 3c ≤ 200
The total finishing hours used for tables and chairs should be less than or equal to the available finishing hours per week:
2t + c ≤ 60
Non-negativity constraint:
The number of tables and chairs should not be negative:
t ≥ 0
c ≥ 0
The graph for both inequality is attached below.
Learn more about Inequality here:
https://brainly.com/question/31946010
#SPJ1
Convert 600 to radians
π/4
π/6
π/3
3π/2
π/2
Answer:
π/3
Step-by-step explanation:
There are [tex]360^\circ[/tex] in a circle, and 2π radians in a circle.
So, to convert from degrees to radians, you multiply by π and then divide by [tex]180^\circ[/tex]
Therefore,[tex] 60^\circ \times \frac{\pi}{180^\circ} = \boxed{\frac{\pi}{3}}[/tex] radians.
The table below shows a company's Manufacturing Cost, Overhead, Total
Sales, Profit, and Dividend per Shareholder over 4 years. Assume the
relationships among Manufacturing Cost, Overhead, Total Sales, Profit,
and Dividend per Shareholder remain the same over the years.
What should have been the Dividend per Shareholder in 2017,
assuming the number of Shareholders has remained unchanged
during the period 2017-2020?
SELECT ONE ANSWER
$17.45
$19.50
$20.00
$25.00
The Dividend per Shareholder in 2017 is $20.
As, Dividend per Shareholder = Profit / Number of Shareholders
Since the number of shareholders is assumed to have remained unchanged during the period 2017-2020, we can calculate the dividend per shareholder in 2017 using the profit value for that year.
Based on the given table, the profit for 2017 is $7,000.
Dividend per Shareholder in 2017
7000/x = 15500 / 44.29
7000/x = 349.966
x = 7000/349.966
x= 20.01
Learn more about Shares problem here:
https://brainly.com/question/30475800
#SPJ1
A class has two guinea pigs. Fluffy weighs 11 kilograms, Marshmallow weighs kilogram less than Fluffy.
How much does Marshmallow weigh? Make an equation that can be used to find Marshmallow's weight in kilograms. Move a number or a symbol to each blank to make the equation. If there is no whole number, put a 0 in the first blank after the equals sign.
Answer:
Marshmallow weighs 10 kilograms.
Step-by-step explanation:
Let's use the variable "M" to represent Marshmallow's weight in kilograms.
Based on the information given, we know that Marshmallow weighs 1 kilogram less than Fluffy, whose weight is 11 kilograms. Therefore, we can write the equation:
M = 11 - 1
Simplifying the equation:
M = 10
So, Marshmallow weighs 10 kilograms.
Using the region names in the image below, select all regions that represent:
A ∪ B ∪ C'
3 group Venn Diagram with Roman numeral labeled regions
A union B union not C. Region I: Items only in group A, not in B or C. Region II: Items in A and B, but not C. Region III: Items only in B, not in A or C. Region IV: Items in A and C, but not B. Region V: Items in A, B, and C. Region VI: Items in B and C, but not A. Region VII: Items only in C, not in A or B. Region VIII: Items not in any of the groups.
In the 3 group Venn Diagram with Roman numeral labeled regions
A ∪ B ∪ C = V: Items in A, B, and C. Region
What is union of sets?The union of sets refers to the operation of combining or merging two or more sets to create a new set that contains all the distinct elements from the original sets.
It is denoted by the symbol "∪"
when you take the union of two sets A and B and C, the resulting set, denoted as A ∪ B ∪ C, consists of all the elements that are present in either set A or set B or set C, or in the three sets.
hence the right choice is V: Items in A, B, and C. Region
Learn more about Venn Diagram at
https://brainly.com/question/2099071
#SPJ1
You have to decide whether to apply Darius's method (determining which
brand's team cleaned the fastest) or Julia's method (determining which brand
was most absorbent) when determining the winner.
Answer the following questions in your response:
• Which method should be applied to determine the winner? Why?
• Based on that analysis, which brand should be declared the winner
and promoted in the commercial?
Justify your choice of the winner with computations from the data
represented in Table 2.
Table 2 provides information about the outcomes of all of the previous similar experiments. In order to determine whether to apply Darius's method, we must first understand what the method entails and how it relates to the data in Table 2.
Darius's method involves a set of steps that are designed to optimize the outcome of an experiment. It involves carefully selecting variables, setting up the experiment in a controlled manner, and analyzing the results in a way that allows for meaningful conclusions to be drawn.The data in Table 2 provides information about the outcomes of previous similar experiments. This information can be used to help us determine whether Darius's method is likely to be effective. If the previous experiments were conducted using similar methods and variables, then the data in Table 2 can be used to identify patterns and trends that can be used to optimize the experiment.For example, if the data in Table 2 shows that a particular variable had a significant impact on the outcome of the previous experiments, then we can use this information to carefully control that variable in our own experiment. Similarly, if the data shows that certain methods or techniques were more effective than others, then we can use this information to optimize our own approach.Overall, the decision to apply Darius's method will depend on a number of factors, including the nature of the experiment, the available resources, and the specific goals of the project. However, by carefully analyzing the data in Table 2 and using it to inform our decisions, we can increase the likelihood of a successful outcome.For such more question on variables
https://brainly.com/question/28248724
#SPJ8
x y
5 8
8 12.8
9 14.4
Direct Variation: Divide `y` by `x` to find constant of variation, `k`. y/x=k
Indirect Variation: Multiply `x` and `y` to find constant of variation, `k`. xy=k
Determine if the given data are a direct or indirect variation. SHOW YOUR WORK
The given data represents a direct variation, as when x increases, y increases.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:
y = kx.
The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.
The constant for this problem is given as follows:
k = 8/5 = 1.6.
Hence the equation is given as follows:
y = 1.6x.
Which is a direct proportional relationship, as when x increases, y also increases.
A similar problem, also featuring proportional relationships, is presented at https://brainly.com/question/7723640
#SPJ1
Mrs. Tilmos creates a new garden in her yard in the shape of a triangle. One side of the garden measures 13 feet and is perpendicular to a second side which is twice as long. Before she plants her flowers, she wants to mix a fertilizer into the soil, whose directions say to use 1 cup per every 20 square feet. How many cups of fertilizer should she use? Enter your answer as a decimal, rounded to the nearest 1/2 cup.
Mrs. Tilmos should be used 8.5 cups of fertilizer.
Now, we can use the formula:
Area = (base x height) / 2
Since, We have to given that,
One side of the garden measures 13 feet and is perpendicular to a second side which is twice as long, we can use the Pythagorean theorem to find the length of the third side,
a² + b² = c²
13² + (2b)² = c²
169 + 4b² = c²
Simplifying:
4b² = c² - 169
The length of the third side is therefore:
c = √(4b² + 169)
Since the second side is twice as long as the first, we can write:
b = 2(13)
b = 26
Now we can substitute:
c = √(4(26²) + 169)
c = √(4(676) + 169)
c = √(2705)
c ≈ 52.0 feet
So the base of the triangle-shaped garden is 26 feet, and the height can be found using the formula:
Area = (base x height) / 2
Area = (26 x height) / 2
Area = 13 x height
So, the height of the garden is 13 feet.
The area of the garden is,
Area = (base x height) / 2
Area = (26 x 13) / 2
Area = 169 square feet
Now, the cups of fertilizer needed,
Cups of fertilizer = Area / 20
Cups of fertilizer = 169 / 20
Cups of fertilizer ≈ 8.4
Hence, Mrs. Tilmos should be used 8.5 cups of fertilizer.
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ1
In the following function defined by an equation in the form y = a x squared + b x + c, identify the values of a, b, and c. y = negative 2 x squared a. a = negative 2, b = 0, c = 0 b. a = negative 2, b = negative 2, c = negative 2 c. a = 0, b = negative 2, c = 0 d. a = 0, b = 0, c = negative 2 Please select the best answer from the choices provided A B C D
The values of a, b and c on the quadratic function are given as follows:
a. a = -2, b = 0, c = 0.
How to obtain the coefficients of a quadratic function?The standard definition of a quadratic function is given as follows:
y = ax² + bx + c.
The coefficients are given as follows:
a, b and c.
The function in this problem is given as follows:
y = -2x².
Hence the coefficients are given as follows:
a = -2, b = 0, c = 0.
Hence option a is the correct option in the context of this problem.
More can be learned about quadratic functions at https://brainly.com/question/1214333
#SPJ1
Find the volume of the sphere
Answer:
Volume = 108 cm³
Step-by-step explanation:
The formula for the volume of a sphere is [tex]\frac{4}{3}[/tex] π r³.
The directions say to use 3 for π.
The diagram shows that the diameter of the sphere is 12 cm, but the formula needs the radius. To find the radius, you divide the diameter by 2.
r = diameter/2 = 12cm/2 = 6 cm
>Now that we know all the parts of the formula, we can plug everything in.
Volume = [tex]\frac{4}{3}[/tex] × 3 × 3³
>We can rewrite 3³ as 3 × 3 × 3.
Volume = [tex]\frac{4}{3}[/tex] × 3 × 3 × 3 × 3
>Now we can multiply everything.
Volume = [tex]\frac{4}{3}[/tex] × 81
Volume = 108 cm³
What is the equation of the line that passes through the point (5, -20) and has a slope of -6
Answer:
Step-by-step explanation:
given m=-6
(x1,y1)=5,-20
equation of line is given by
y-y1=m(x-x1)
substituting
y-(-20)=-6(x-5)
y+20=-6x+30
6x-y+10=0 is equation of line
Calculator
What are the endpoint coordinates for the midsegment of
ABCD that is parallel to BC?
Enter your answer, as a decimal or whole number, in the boxes.
and D
B
-5-4-3
3
4
2-1
4-
5
3
2
1
A
D
-4
6
7
C
2 3
8
9
3₂₂
To find the endpoint coordinates for the midsegment of ABCD that is parallel to BC, we need to determine the midpoints of the corresponding sides.
Let's start by finding the midpoint of BC. The coordinates of B are (-5, 4) and the coordinates of C are (2, 3). To find the midpoint, we average the x-coordinates and the y-coordinates separately:
Midpoint of BC:
x-coordinate: (-5 + 2) / 2 = -3/2 = -1.5
y-coordinate: (4 + 3) / 2 = 7/2 = 3.5
So, the midpoint of BC is (-1.5, 3.5).
Now let's find the midpoint of AD. The coordinates of A are (-4, 6) and the coordinates of D are (8, 9).
Midpoint of AD:
x-coordinate: (-4 + 8) / 2 = 4 / 2 = 2
y-coordinate: (6 + 9) / 2 = 15 / 2 = 7.5
So, the midpoint of AD is (2, 7.5).
Therefore, the endpoints of the midsegment of ABCD that is parallel to BC are (-1.5, 3.5) and (2, 7.5).
Learn more about x-coordinates on:
https://brainly.com/question/28913580
#SPJ1
Describe in words the transformations of the graph of the parent function f(x) = x2 that
would result in the graph of
g(x) = 3(x - 5)^2 + 2.
Describe in words the transformations of the graph of the parent function f(x) = x2 that
would result in the graph of
g(x) = 1/3(x + 6)^2- 4.
2. The transformations are given as follows:
Vertical stretch by a factor of 3.Translation right 5 units.Translation up 2 units.3. The transformations are given as follows:
Vertical compression by a factor of 3.Translation left 6 units.Translation down 4 units.How to define the transformations?For item 2, the transformations in this problem are given as follows:
Vertical stretch by a factor of 3, due to the multiplication by 3.Translation right 5 units, as x -> x - 5.Translation up 2 units, as y -> y + 2.For item 3, the transformations are given as follows:
Vertical compression by a factor of 3, due to the multiplication by 1/3.Translation left 6 units, as x -> x + 6.Translation down 4 units, as y -> y - 4.More can be learned about translations at brainly.com/question/28174785
#SPJ1
Write the equation of the circle graph below.
Answer:
x^2 + (y-3)^2 = 2.25
Step-by-step explanation:
(x – h)2 + (y – k)2 = r2
(x - 0)2 + (y - 3)2 = r2
x^2 + (y - 3)^2 = (1.5)^2
x^2 + (y-3)^2 = 2.25
343 es = a 114 +
[tex]343 es = a 114 + [/tex]
the answer lyes in the cave at the end of a island
The ratio of red pens to blue pens in maxs drawer is 4 to 5 how many red pens and how many blue pens are there in the drawer if there are 342 pens altogether? HELP PLEASE
There are 152 red pens and 190 blue pens in Max's drawer, given that there are a total of 342 pens altogether.
Let's solve the problem step by step:
Identify the given information:
The ratio of red pens to blue pens is 4 to 5.
There are a total of 342 pens in the drawer.
Set up the ratio equation:
Let's assume the number of red pens is 4x, and the number of blue pens is 5x.
Here, 'x' is a scaling factor that allows us to find the actual number of pens.
We can write the equation as: 4x + 5x = 342.
Simplify and solve the equation:
Combining like terms, we have 9x = 342.
Divide both sides of the equation by 9 to solve for 'x':
x = 342 / 9 = 38.
Calculate the number of red pens and blue pens:
Now that we have the value of 'x', we can find the number of red and blue pens:
Number of red pens: 4x = 4 × 38 = 152.
Number of blue pens: 5x = 5 × 38 = 190.
For similar questions on pens
https://brainly.com/question/16820350
#SPJ8
The ratio of the sides of two figures is 5/8, what is the ratio of their areas
The ratio of the areas of the figures is 25/64
How to determine the ratio of their areasFrom the question, we have the following parameters that can be used in our computation:
The ratio of the sides of two figures is 5/8,
The ratio of their areas is calculated as
Ratio = Side ratio²
substitute the known values in the above equation, so, we have the following representation
Ratio = (5/8)²
Evaluate
Ratio = 25/64
Hence, the ratio of their areas is 25/64
Read more about ratio at
https://brainly.com/question/21003411
#SPJ1
what is the value of x?
The value of x in the triangle is 20 units.
How to find the side of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
Using triangle proportional theorem, If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
Hence,
11 / 121 = 10 / 5x + 10
cross multiply
11(5x + 10) = 1210
55x + 110 = 1210
55x = 1210 - 110
55x = 1100
divide both sides of the equation by 55
x = 1100 / 55
x = 20
Therefore,
x = 20
learn more on triangle here: https://brainly.com/question/31304267
#SPJ1
the isosceles trapezoid ABCDE is part of an isosceles triangle ACE. What is true about isosceles triangles?
The measure of the vertex angle of ΔACE is: D. 50°.
The two side lengths of all isosceles triangles are the same and the angles facing these side lengths are congruent.
What is an isosceles triangle?In Mathematics and Geometry, an isosceles triangle simply refers to a type of triangle with two (2) sides that are equal in length and two (2) equal angles.
Since the isosceles trapezoid ABCDE belongs to isosceles triangle ACE, we can reasonably infer and logically deduce that the measure of angle BDE (∠BDE) is equal to 115 degrees.
∠BDE + ∠BDC = 180° (sum of angles on a straight line).
115° + ∠BDC = 180°
∠BDC = 180° - 115°
∠BDC = 65°
Based on isosceles triangle ACE, we can logically deduce the following congruent angles;
∠BDC ≅ ∠CBD = 65°
Now, we can determine the measure of the vertex angle of ΔACE:
∠BDC + ∠CBD + ∠ACE = 180°
∠ACE = 180° - (∠BDC + ∠CBD)°
∠ACE = 180° - (65 + 65)°
∠ACE = 180° - 130°
∠ACE = 50°.
In conclusion, the two side lengths of all isosceles triangles are typically the same (equal) and the angles facing these side lengths are congruent.
Read more on isosceles triangle here: brainly.com/question/19238666
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Find the 14th term of the geometric sequence 10, 40, 160,
A 188 cm tall man has a waistline of 91cm. Which measure best approximates the volume of the man when using a cylinder to approximate the man's shape Round your answer to the nearest cm³.
The volume of the man when using a cylinder to approximate the mans shape is 1222110 cm³.
How to find the volume of a cylinder?A 188 cm tall man has a waistline of 91cm. Therefore, the measure that best approximates the volume of the man when using a cylinder to approximate the man's shape can be calculated as follows:
Modelling the mans shape to a cylinder,
volume of the cylinder = πr²h
where
r = 91 / 2 = 45.5 cm
h = 188 cm
Therefore,
volume of the cylinder = 3.14 × 45.5² × 188
volume of the cylinder = 3.14 × 2070.25 × 188
volume of the cylinder = 1222109.98
volume of the cylinder = 1222110 cm³
learn more on volume here: https://brainly.com/question/274953
#SPJ1
y = f(x) = -1x
find f(x) when x = 3
Hello!
f(x) = -1x
f(3) = -1*3 = -3
The unadjusted trial balance of Sheridan Exposure Inc. had these balances for the following select accounts: Supplies $4,300, Unearned Service Revenue $9,250, and Prepaid Rent $1,920. At the end of the period, a count showed $960 of supplies on hand. Services of $4,100 had been performed related to the unearned revenue account, and one month’s worth of rent, worth $40, had been consumed by sheridan exposure. Record the required adjusting entries related to these events. (List all debit entries before credit entries. If no entry is required, select “No Entry” for the account titles and enter 0 for the amounts. Credit account titles are automatically indented when the amount is entered. Do not indent manually.)
Recording the required adjusting entries related to the balances and events of the select accounts is as sfollows:
Adjusting Journal Entries:Debit Supplies Expense $3,340
Credit Supplies $3,340
(To record supplies expense for the period.)
Debit Rent Expense $40
Credit Prepaid Rent $40
(To record rent expense for the period.)
Debit Uneared Service Revenue $4,100
Credit Service Revenue $4,100
(To record earned service revenue.)
What are adjusting entries?Adjusting entries are period-end records in the general journal that recognize income and expenses for the period that do not have cash effects.
Some of the adjusting entries include accrued revenues, accrued expenses, unearned revenues, prepaid expenses, and depreciation expenses.
Transaction Analysis:Supplies Expense $3,340 Supplies $3,340 ($4,300 - $960)
Rent Expense $40 Prepaid Rent $40
Uneared Service Revenue $4,100 Service Revenue $4,100
Learn more about adjusting journal entries at https://brainly.com/question/13035559.
#SPJ1
Solve 2^x = 3^x +1. What are the exact and approximate solutions
The equation's close approximation [tex]2^x = 3^{(x+1)[/tex]is x ≈ -2.713.
To solve the equation [tex]2^x = 3^{(x+1)[/tex] for x, we can use logarithms.
If we take the logarithm of both sides of the equation (base 2), we get:
[tex]log2(2^x) = log2(3^{(x+1)})[/tex]
Using the properties of logarithms, we can simplify this equation as:
[tex]x = (x+1) \times log2(3)[/tex]
Expanding further:
[tex]x = x log2(3) + log2(3)[/tex]
Now, we can isolate the x terms on one side of the equation:
[tex]x - x \times log2(3) = log2(3)[/tex]
Factoring out x from the left side:
x(1 - log2(3)) = log2(3)
Dividing both sides by (1 - log2(3)), we find:
x = log2(3) / (1 - log2(3))
This gives us the exact solution for x.
We can change log2(3) = 1.585 into the equation to get an approximation of the answer:
x ≈ 1.585 / (1 - 1.585)
Simplifying further:
x ≈ 1.585 / (-0.585)
x ≈ -2.713
For similar question on logarithm.
https://brainly.com/question/30226560
#SPJ8
Question 3 of 5
Given a sphere with a diameter of 6.2 cm, find its volume to the nearest whole
number.
OA. 39 cm³
OB. 125 cm³
OC. 70 cm³
OD. 998 cm³
Answer:
option B
125 cm³
Step-by-step explanation:
volume of sphere = 4/3πr³
where r = d/2
= 6.2/2 = 3.1
thus,
v = 4/3 * 3.14 * (3.1)³
= 4/3 * 3.14 * 29.79
= 124.72 cm³
rounding off to the nearest whole number,
= 125 cm³
Factorize the given expression:
27x3 − 63x2 + 49x − 34327
The Factorization of the given expression gives:
(1/27) (9x - 7)³
How to factorize a given expression?Factorization is the process of finding factors which when multiplied together results in the original number or expression.
We have:
27x³ - 63x² + 49x - 343/27
Step 1:
Factor out (1/27) from the expression
= (1/27) { 27 · 27 x³ - 27· 63x² + 27· 49x - 343)
= (1/27) { 729 x³ - 1701x² + 1323x - 343)
Step 2:
Rewrite terms in the expression
= (1/27) { 9³ x³ - 3·7·9²x² + 3·7²·9x - 7³ }
= (1/27) { (9x)³ - 3(9x)²7 + 3(9x)7² - 7³}
Step 3:
Use (a - b)³ = a³ - 3a²b + 3ab² - b³ where a = 9x , b = 7
= (1/27) { 9³ x³ - 3.7.9²x² + 3.7².9x - 7³ }
= (1/27) (9x - 7)³
Thus,
27x³ - 63x² + 49x - 343/27 = (1/27) (9x - 7)³
Learn more about Factorization on:
https://brainly.com/question/29322055
#SPJ1
Combine like terms to create an equivalent expression.
Enter any coefficients as simplified proper or improper fractions or integers.
−
2
3
�
+
5
6
�
−
1
6
−
3
2
a+
6
5
a−
6
1
The final simplified equivalent expression is:
(3/2)a - (1/6)
To combine the like terms in the expression a(2/3) + (5/6)a - (1/6), we add the coefficients of the like terms.
The like terms in the expression are:
a(2/3) and (5/6)a
The coefficient of a(2/3) is 2/3, and the coefficient of (5/6)a is 5/6.
Adding these coefficients, we get:
(2/3) + (5/6)
To add these fractions, we need to find a common denominator, which in this case is 6.
Converting (2/3) to have a denominator of 6:
(2/3) × (2/2) = 4/6
Now we can add the fractions:
(4/6) + (5/6) = 9/6
The combined expression, with like terms combined, is:
(9/6)a - (1/6)
We can simplify this expression further by dividing both the numerator and denominator of (9/6) by their greatest common divisor, which is 3.
(9/6) ÷ (3/3) = (9/6) ÷ 1
= 9/6
For similar questions on equivalent
https://brainly.com/question/2972832
#SPJ8
I need help a s a p ………..
The solution of the given expression is x = 1
The given expression:
[tex]6^{2x-6} = 36^{3x -5}[/tex]
We can write,
⇒ [tex]6^{2x-6} = 6^{2(3x -5)}[/tex]
Since we know that,
Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself.
According to the law of exponent
⇒ 2x - 6 = 2(3x - 5)
Expanding it we get
⇒ 2x - 6 = 6x - 10
Subtracting 2x both sides we get
⇒ -6 = 4x - 10
Adding 10 both sides we get,
⇒ 4x = 4
Dividing by 4 both sides,
⇒ x = 1
To learn more about exponent visit:
https://brainly.com/question/31242910
#SPJ1
NO LINKS!! URGENT HELP!!
Calculate the AREA of the following figures.
Answer:
A. 12 units square
B. 12 units square
C. 20 unit square
Step-by-step explanation:
A. Coordinate of Traingle F(-2,-3),G(-2,3) and H(2,0)
ANS:
The distance formula is used to find the distance between two points in a coordinate plane. The formula is:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
where:
d is the distance between the two points[tex]x_1[/tex] and [tex]y_1[/tex]are the coordinates of the first point[tex]x_2[/tex] and [tex]y_2[/tex]are the coordinates of the second pointUsing the distance formula, we can find the lengths of the sides of the triangle.
The distance between F and G is:
a=FG=[tex]\sqrt{(-2 - (-2))^2 + (3 - (-3))^2} = \sqrt{ 36} = 6[/tex]
The distance between G and H is:
b=[tex]GH = \sqrt{(2 -(- 2))^2 + (0 - 3)^2}= \sqrt{16+9}=5[/tex]
The distance between F and H is:
c=[tex]FH = \sqrt{(2 - (-2))^2 + (0 - (-3))^2} = \sqrt{16 + 9}= \sqrt{25} = 5[/tex]
Now that we know the lengths of the sides of the triangle, we can use the formula for the area of a triangle to find the area of the triangle.
The formula for the area of a triangle is:
[tex]A = \sqrt{s(s - a)(s - b)(s - c)}[/tex]
where:
A is the area of the triangles is the semi-perimeter of the triangle a, b, and c are the lengths of the sides of the triangleThe semi-perimeter of the triangle is:
[tex]s = \frac{a + b + c}{2} = \frac{6+5+5}{2}=8[/tex]
Plugging in the values for s, a, b, and c, we get:
[tex]A=\sqrt{8(8-6)(8-5)(8-5)}=12[/tex]
Therefore, the area of the triangle is 12 units square.
B, Coordinate of rectangle T(1,-2),U(4,1),V(2,3) and W(-1,0)
ANS:
We can find the lengths of the sides of the rectangle using the distance formula. The distance formula is:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
where:
d is the distance between the two points[tex]x_1[/tex] and [tex]y_1[/tex]are the coordinates of the first point[tex]x_2[/tex] and [tex]y_2[/tex]are the coordinates of the second pointUsing the distance formula, we can find the lengths of the sides of the rectangle as follows:
[tex]UT=\sqrt{(4 - 1)^2 + (1 - (-2))^2} = 3\sqrt2[/tex]
[tex]UV = \sqrt{(2 - 4)^2 + (3 - 1)^2}= 2\sqrt2[/tex]
[tex]VW= \sqrt{(-1 - 2)^2 + (0 - 3)^2} =3\sqrt2[/tex]
[tex]WT = \sqrt{(1 - (-1))^2 + ((-2) - 0)^2}= 2\sqrt2[/tex]
since the opposye side are equal, so it's a rectangle.
Finding the area of the rectangle:
Area = length * width
where:
Area is the area of the rectanglelength is the length of one of the sides of the rectanglewidth is the length of one of the sides of the rectanglePlugging in the values for length and width, we get:
[tex]length=3\sqrt2[/tex]
[tex]breadth=2\sqrt2[/tex]
[tex]Area = 3\sqrt2 * 2\sqrt2 = 12[/tex]
Therefore, the area of the rectangle is 12 units square.
C. Coordinate of square Q(-4,0),R(-2,4),S(2,2),T(0,-2)
ANS:
Finding the length of one of the sides:
We can find the length of one of the sides of the square using the distance formula. The distance formula is:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
where:
d is the distance between the two points
[tex]x_1[/tex] and [tex]y_1[/tex]are the coordinates of the first point
[tex]x_2[/tex] and [tex]y_2[/tex]are the coordinates of the second point
Using the distance formula,
[tex]QR= \sqrt{(-2 - (-4))^2 + (4 - 0)^2} = 2\sqrt5[/tex]
[tex]SR= \sqrt{(-2 - 2)^2 + (4 - 2)^2} = 2\sqrt5[/tex]
[tex]TS= \sqrt{(0 - 2)^2 + (-2- 2)^2} = 2\sqrt5[/tex]
[tex]QT= \sqrt{(0 - (-4))^2 + (-2- 0)^2} = 2\sqrt5[/tex]
Since all the side are equal, so its a square having length [tex]2\sqrt5[/tex]
we have
Area of square = side²
Area is the area of the squareside is the length of one of the sides of the squarePlugging in the value for side, we get:
[tex]Area = (2\sqrt5)^2 = 20[/tex]
Therefore, the area of the square is 20 unit square.
Data was collected for 300 fish from the North Atlantic. The length of the fish (in cm) is summarized in the histogram below.
20
40
60
80
100
length of fish (mm)
160
170
180
190
200
210
220
230
Frequency
[Graphs generated by this script: setBorder(61,40,20,5); initPicture(151,230,0,108);axes(1000,20,1,1000,20); fill="blue"; stroke="black"; textabs([165,0],"length of fish (mm)","above");line([160,-2.16],[160,2.16]); text([160,0],"160","below");line([170,-2.16],[170,2.16]); text([170,0],"170","below");line([180,-2.16],[180,2.16]); text([180,0],"180","below");line([190,-2.16],[190,2.16]); text([190,0],"190","below");line([200,-2.16],[200,2.16]); text([200,0],"200","below");line([210,-2.16],[210,2.16]); text([210,0],"210","below");line([220,-2.16],[220,2.16]); text([220,0],"220","below");line([230,-2.16],[230,2.16]); text([230,0],"230","below");textabs([0,115],"Frequency","right",90);rect([160,0],[170,1]);rect([170,0],[180,16]);rect([180,0],[190,71]);rect([190,0],[200,108]);rect([200,0],[210,83]);rect([210,0],[220,18]);rect([220,0],[230,3]);]
What is the class midpoint for the fourth class?
class midpoint =
The class midpoint for the fourth class is given as follows:
195 mm.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.
For the fourth class, the bounds are given as follows:
190 mm.200 mm.The class midpoint for the fourth class is the mean of the bounds, hence it is given as follows:
(190 + 200)/2 = 195 mm.
More can be learned about the mean of a data-set at brainly.com/question/1156334
#SPJ1
