The wingspan of the model airplane is 16cm having a scale factor of 1:75.
What is scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.
Given, the original airplane wingspan is 12 meter.
The scale factor given is 1:75
Let us consider the wingspan of the model plane to be 'l'
Thus, model wingspan/original wingspan = 1/75
⇒ l/12 = 1/75
⇒ l = 12/75
⇒ l = 0.16
Wingspan is 0.16 m or 16cm
The wingspan of the model airplane is 16cm having a scale factor of 1:75.
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The area of a rectangle is 35 m², and the length of the rectangle is 3 m more than double the width. What is the dimensions of the rectangle?
The dimensions of the rectangle with area 35 m² is
length = 7.6 m and width = 4.6 m
How of find the dimension of the rectangleThe dimension of the rectangle is calculated using the formula for area of rectangle
= length x width
where
length = 3 + w width = warea of rectangle
35 = (w + 3) * w
35 = w² + 3w
w² + 3w - 35 = 0
solving for w gives
w = 4.6 OR -7.6
using the positive value, the w = 4.6 m, l = 4.6 + 3 = 7.6 m
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l
How do type an exponent on a chromebook laptop?
Step-by-step explanation:
Press ''CTRL + /'' to access the list of features.
Find the “Text Formatting” section.
Choose “Superscript” from the list of options.
On the right-hand side, you'll see the ''CTRL +. '' shortcut. Use it to make the number or letter in your text appear in exponent form.
Step-by-step explanation:
1. Place your cursor where you want an exponent. For example, if you want to place an exponent after the number 10 in a document, place your cursor directly after the 10 with no space.
2. Type Alt+0185 for the exponent 1. For example, you can type the number 10¹ holding the Alt key and typing 0185.
3. Type Alt+0178 for the exponent 2. For example, you can type the number 10² holding the Alt key and typing 0178.
4. Type Alt+0179 for the exponent 3. For example, you can type the number 10³ by holding the Alt key and typing 0179.
A side of the equilateral triangle 'A' is twice the length of a side of
another equilateral triangle 'B'. How many triangles of 'B' will fit
into triangle 'A'?​
Total four triangles of B fit into triangle A as length of the equilateral triangle A is twice the length of triangle B.
As given in the question,
Types of triangles : Equilateral triangle
Number of triangle = 2
Triangle A and Triangle B
Let 'x' be the length of the triangle A
And 'y' be the length of the triangle B
As per given condition:
x = 2y
Area of equilateral triangle A = (√3/4)x²
Area of equilateral triangle B = (√3/4)y²
Now x = 2y
⇒Area of equilateral triangle A = (√3/4)(2y)²
⇒Area of equilateral triangle A = (√3/4)4y²
⇒Area of equilateral triangle A = 4 [(√3/4)y²]
⇒Area of equilateral triangle A = 4 ( area of equilateral triangle B)
Therefore, total number of four equilateral triangle of B fit into equilateral triangle A.
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Identify the radical expression for the perimeter and area of the orange triangle inscribed in the square shown below. Simplify each expression in radical form. No decimals!
The perimeter and area of the figure are 10+6√5 and 20
What is meant by perimeter?The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter. The sum of the lengths of all the sides in a rectangle is its perimeter, or P. A rectangle's opposite sides are equal, hence it has two equal lengths and two equal widths. The following formula is used to determine a rectangle's perimeter: Diameter is equal to the sum of the following dimensions: length, width, height, and width.
There are numerous practical uses for calculating the perimeter. The size of the fence needed to enclose a yard or garden is known as the calculated perimeter. The circumference of a wheel or circle, which measures its perimeter, indicates how far it may travel in a single rotation.
AC=√4²+2²=√20=2√5
AB=√8²+4²=4√5
BC=√8²+6²=√100=10
Perimeter=a+b+c
=AC+AB+BC
=2√5+4√5+10
=10+6√5
Area=20
The perimeter and area of the figure are 10+6√5 and 20
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A chi-square test of independence is used when both variables are ___.Group of answer choices a. ratio b. ordinal c. interval d. nominal
For statement 'A chi-square test of independence is used when both variables are ___.'
b. ordinal
d. nominal
In this question we have been given a statement 'A chi-square test of independence is used when both variables are ___.'
We need to select the correct choices for the given statement.
We know that the Chi-Square Test of Independence is used to test if two categorical variables are associated.
It is a nonparametric test.
It can only compare categorical variables.
The categorical variables are classified as nominal and ordinal variables.
Chi-Square Test is used to test for a statistically significant relationship between nominal and ordinal variables.
Therefore, for a chi-square test of independence is used when both variables ordinal and nominal.
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Hellllllp meeee please
Answer: 3
Step-by-step explanation: schoology whack
Quadrilateral ABCD is translated to get quadrilateral A′B′C′D′. Vertex A is at (-5, 2), and vertex A′ is at (2, -2).
Quadrilateral ABCD is translated
. If vertex B is at (-6, 5), then vertex B′ is at
The vertex B' is at (1, 1)
How to find the calculation?Let's update the guidelines for translating a point.
The image of the point (x, y) is (x + h, y) T (x, y) (x + h, y) if the point (x, y) is translated horizontally to the right by h units.The image of the point (x, y) is (x - h, y) T (x, y) if the point (x, y) is translated horizontally to the left by h units (x - h, y)The image of the point (x, y) is (x, y + k) (x + h, y) T (x, y) (x, y + k) if the point (x, y) is translated vertically up by k units.The image of the point (x, y) is (x, y - k) T (x, y) if the point (x, y) is translated down vertically by k units (x, y - k)Let's apply the guidelines to resolve our issue.
Vertex A equals (-5, 2)
Vertex A' equals (2, -2)
The two points' coordinates changed, indicating that the
horizontal and vertical translations of a quadrilateral
A's x-coordinate is equal to -5.
A' has an x-coordinate of 2
Which indicates it goes to the right, therefore adhere to the first guideline presented above.
The translation formula is T (x, y) (x + h, y).
∴ x → x + h
x = -5, and x + h = 2.
∴ -5 + h = 2
Increase both sides by 5.
∴ -5 + 5 + h = 2 + 5
∴ h = 7
∴ The quadrilateral is moved seven units to the right.
A has a y-coordinate of 2
A"s y-coordinate is equal to -2.
Which means it descends, therefore apply the fourth rule listed above.
T (x, y) is the translational rule (x, y - k)
∴ y → y - k
Because y = 2 and y - k = -2,
∴ 2 - k = -2
Increase K on both sides.
∴ 2 - k + k = -2 + k
∴ 2 = -2 + k
Increase both sides by 2.
∴ 2 + 2 = -2 + 2 + k
∴ 4 = k
The quadrilateral is down four units.
Let's locate B.
T (x, y) (x + h, y - k) is the translational rule.
∵ B = (-6, 5) (-6, 5)
∵ h = 7 and k = 4
∴ B' = (-6 + 7, 5 - 4)
∴ B' = (1, 1) (1, 1)
Vertex B is located at (1, 1).
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A The numbers 14 and 29 have more than one common factor
B The number 29 is odd
C The greatest common factor of 14 and 29 is 1
D The number 14 is even
Answer:
The greatest common factor of 14 and 29 is 1
Step-by-step explanation:
Hope this helped you
I NEED HELP THIS IS DUE TONIGHT
Answer:
The park has 20 climbing activities.
Step-by-step explanation:
Given,
Total activities = 50
Percent of climbing activities = 40%
Number of climbing activities = 40% of total activities
Number of climbing activities = 40/100 * 50
Number of climbing activities = 0.40 * 50 = 20
Hope this helps!!
Im order to save money for prom this weekend Tom is going to walk his neighbors dog for 6 per hour
The system of inequalities represents this solution is:
6c + 7.5d ≥ 75
d + c ≤ 15.
What is inequality?A statement of an order relationship, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.
Now it is given that,
Money from walking neighbor's dog = $6 per hour
Money from car wash = $7.5 per hour
Total Number of hours of work not more than 15 hours
Now, if d represents the number of hours walking his neighbor's dog and c represents the number of hours washing car
So, money from walking neighbor's dog = 6c
and money from car wash = 7.5d
Therefore total money saved = 6c + 7.5d
∵ Total Number of hours of work is not more than 15 hours
⇒ d + c ≤ 15
∵ Tom needs to make at least $75 to cover prom expenses
⇒ 6c + 7.5d ≥ 75
The system of inequalities represents this solution is:
6c + 7.5d ≥ 75 ;
d + c ≤ 15.
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The complete question is as follows:
To save money for prom this weekend, Tom is going to walk his neighbor's dog for $6 per hour and wash cars for $7.50 per hour. His mother said he can work no more than 15 hours to ensure he keeps up with his homework. Tom needs to make at least $75 to cover prom expenses. If d represents the number of hours walking his neighbor's dog and c represents the number of hours washing cars, which system of inequalities represents this solution?
There are a total of 58 reindeer and elves helping Santa get ready for Christmas. Each reindeer has 4 legs and each elf has 2 legs. Frosty the Snowman, who doesn’t have any legs, counted 158 legs when all the reindeer and elves were in Santa’s workshop helping Santa. How many elves are helping Santa? Enter your answer as a number only.
Solving a system of equations, we will see that there are 37 elves helping Santa, and 21 reindeer.
How many elves are helping Santa?
Let's define the variables:
x = number of elves.y = number of reindeer.We know that there are 58 of them, then we can write:
x + y = 58
We also know that between all of them they have 158 legs, so we can write the equation:
x*2 + y*4 = 158
Then the system of equations is:
x + y = 58
x*2 + y*4 = 158
To solve this system of equations, we can isolate x on the first equation to get:
x = 58 - y
Replacing that in the other equation we will get:
(58 - y)*2 + y*4 = 158
Now we can solve this equation for y.
(58 - y)*2 + y*4 = 158
116 - 2y + 4y = 158
116 + 2y = 158
2y = 158 - 116
2y = 42
y = 42/2
y = 21
Then the value of x is:
x = 58 - y
x = 58 - 21
x = 37
there are 37 elves.
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Rewrite the expression 3(12+6) using the distributive property of multiplication over addition.
Answer:
The answer is 3x12 + 3x6
Step-by-step explanation:
You have to multiply each number inside the brackets by the number outside the brackets
3(12+6)
= 3x12 + 3x6
= 36 + 18
= 54
The numbers below to put them in order from least to greatest: -19 13 -15 -8 -11 -13
The arrangement of the given numbers in ascending order is -19, -15, -13, -11, -8, 13
What is Ascending Order?
Ascending order refers to the arrangement of numbers in ascending order, from least to greatest. We must first compare numbers before we may arrange them in any order. Compare first, then order. Putting the numerals in ascending order: Count how many digits are in each number.
Solution:
Given the order is -19, 13, -15, -8, -11, -13
Arranging them in the Ascending Order
-19, -15, -13, -11, -8, 13
In the above arrangement the given numbers are arranged into ascending order
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A laser rangefinder is locked on a comet approaching Earth. The distance g(x) , in kilometers, of the comet after x days, for x in the interval 0 to 42 days, is given by g(x)=300,000csc(π42x)
The value of the function at day 5 is 822000 and it means that the laser rangefinder locked on the comet is at a distance of 822000 km
How to evaluate the value of the function at day 5?From the question, we have the following parameters that can be used in our computation:
g(x) = 300,000csc(π/42x)
Also from the question, we have
Number of days = 5
This means that
x = 5
Substitute x = 5 in the equation g(x) = 300,000csc(π/42x)
So, we have the following representation
g(5) = 300,000csc(π/42 x 5)
Evaluate the products
So, we have the following representation
g(5) = 300,000csc(5π/42)
Evaluate the cosec expression
g(5) = 300,000 * 2.74
So, we have
g(5) = 822000
Hence, the value of the function is 822000
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Complete question
A laser rangefinder is locked on a comet approaching Earth. The distance g(x) , in kilometers, of the comet after x days, for x in the interval 0 to 42 days, is given by g(x) = 300,000csc(π/42x)
Evaluate g(5) and interpret the information
y = 24 - 4x
2x - 3y = -2
2x - 3 (24
) = -2
Substitution
The values of x and y for the linear equations of y = 24 - 4x and 2x - 3y = -2 are x=5 and y=4.
What is a linear equation?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
Given, the equations are y = 24 - 4x and 2x - 3y = -2
Replacing the value of the first equation of y, which is, y = 24 - 4x, in the second equation, we get:
2x - 3(24-4x) = -2
⇒ 2x - 72 + 12x = -2
⇒ 14x = 70
⇒ x = 70/14
⇒ x = 5
Substituting the value of x=5 in y = 24 - 4x, we get,
y = 24 - 4(5)
⇒ y = 24 - 20
⇒ y = 4
Thus, the values of x and y for the linear equations of y = 24 - 4x and 2x - 3y = -2 are x=5 and y=4.
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If y varies directly with x and y=20 when x=4, what is the value of y when x=20?
The value of y will be;
⇒ y = 100
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
y varies directly with x and y=20 when x=4,
Now,
Since, y varies directly with x.
Hence, We get;
⇒ y = kx
Where, k is constant of proportionality.
Here, y=20 when x=4,
So, We get;
⇒ y = kx
⇒ 20 = 4k
⇒ k = 5
Thus, For x = 20, The value of y will be;
⇒ y = kx
⇒ y = 5 × 20
⇒ y = 100
Therefore, We get;
⇒ y = 100
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for the range c6:c41, create a new conditional format that changes the font color to red for values that are greater than or equal to 50.
The following steps would apply conditional formatting to the range:
Select the range of cells C6 : C41Click Conditional Formatting on the Home tabSet the conditionPoint to Color Scales, and then select the font color as red colorHow to apply the conditional formatting?The given parameters in the question are:
Range = C6 : C41Condition = cell that are greater than or equal to 50.Action = font color as red colorThe Conditional Formatting is located on the home tab
So, the first step to select the range and locate the Conditional Formatting option
Then set the necessary conditions and formats
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Assuming the two clocks start synchronized, how much do sidereal and solar clocks differ after one day?
a. about 4 minutes
b. about an hour
c. about two hours
d. 24 hours
e. none of the above
If we assume the two clocks start synchronized , then the sidereal and solar clocks differ after one day , (a) about 4 minute .
What is Solar Day ?
The rotation period of the Earth with respect to the Sun, is called the solar day .
What is Sidereal Day ?
The sidereal day can be defined in terms of the rotation period of the Earth with respect to stars.
To complete a solar day, the Earth needs to rotate an additional amount, that is equal to 1/365 of a full turn.
So , the time required for this extra rotation will be 1/365 of a day, or about 4 minutes.
Hence , the solar day is about 4 minutes longer than the sidereal day.
Therefore , the correct option is (a) about 4 minutes .
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Rather than being irrelevant or unhelpful, residuals in a simple linear regression model can be quite informative. Which of the following, in your opinion, residuals might indicate about the underlying population and the model?
Regression analysis will indicate about the underlying population and the model.
It is one of the most used and most powerful multivariate statistical techniques for it infers the existence and form of a functional relationship in a population. Once you learn how to use regression, you will be able to estimate the parameters { the slope and intercept } of the function that links two or more variables. With that estimated function, we will be able to infer or forecast things like unit costs, interest rates, or sales over a wide range of conditions.
Though the simplest regression techniques seem limited in their applications, statisticians have developed a number of variations on regression that greatly expand the usefulness of the technique. And again, the t-distribution and F-distribution will be used to test hypotheses.
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URGENT PLEASE ANSWER
Answer:
y = 371.17×1.15^x1135 in month 8Step-by-step explanation:
You want an exponential regression function for the data in the table.
a. Exponential regressionA regression function of most any kind can be found using a graphing calculator or spreadsheet. The attachment shows the function is approximately ...
y = 371.17 × 1.15^x
where y is the number sold, and x is the month.
b. Number soldUsing x=8, the predicted number sold for month 8 is ...
y = 371.17 × 1.15^8 ≈ 1135.4175 ≈ 1135
Sales for month 8 will be about 1135.
What is the sum of this equation
Answer:
The answer is A
Step-by-step explanation:
Add up
can someone help i will give brainlest:)
A. Width = 16.5 ft B.Width = 55.25 ft
Height = 9.3 ft Height = 91 ft
Area = 153.45 ft² Area = 5027.75 ft²
The formula for Area of rectangle:The area of the rectangle is a place covered by a rectangle in a 2D plane
The formula for Area of the rectangle is given by
Area = Length × WidthHere we have
1 in = 3 feet and 1 cm = 6.5 ft
Calculation for rectangle A :
In rectangle A
Width = 5.5 in
=> Width in feet = 5.5 × 3 feet = 16.5 ft
Height = 3.1 in
=> Height in feet = 3.1 × 3 feet = 9.3 ft
By the given formula
Area = 16.5 ft × 9.3 ft = 153.45 ft²
Calculation for rectangle B :
In rectangle B
Width = 8.5 cm
=> Width in feet = 8.5 × 6.5 feet = 55.25 ft
Height = 14 cm
=> Height in feet = 14 × 6.5 feet = 91 feet
By the given formula
Area = 55.25 ft × 91 ft = 5027.75 ft²
Therefore,
A. Width = 16.5 ft B. Width = 55.25 ft
Height = 9.3 ft Height = 91 ft
Area = 153.45 ft² Area = 5027.75 ft²
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Many movie theaters show advertisements before feature
films to increase concession sales. However, many
customers complain about the length the advertisements
add to their time at the theater. To understand the effect of
advertising, a movie theater manager chooses random
days during the month when the concession
advertisements are not shown. On the remaining days,
the concession advertisements are shown as usual. The
manager then records the concession sales for each day.
What is the explanatory variable in this scenario?
the movie theater patrons
the concession advertisements
* the daily theater attendance
the amount of money collected at the concession
stand
*THE CORRECT ANSWER IS B*
The explanatory variable in this scenario is B. the concession advertisements.
What is an explanatory variable?A response variable is what changes as a result of an explanatory variable being manipulated or observed to change (for example, the amount of caffeine consumed) (e.g., reaction times). In research, the terms "explanatory variable" and "response variable" are frequently used interchangeably.
Examples include both response variables, such as individual test item scores, total test scores, and achievement levels, and explanatory variables, such as gender, ethnicity, type of instruction, etc.
In this case, it should be noted that based on the information, the correct option is B.
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The measures of the angles of a triangle are shown in the figure below. Solve
for X.
Answer:
x = 4
Step-by-step explanation:
The sum of the interior angles of a triangle equal 180.
2x + 15 + 67 + 90 = 180 Combine like terms
2x + 172 = 180 Subtract 172 from both sides
2x + 1752 - 172 = 180 - 172
2x = 8 Divide both sides by 2
[tex]\frac{2x}{2}[/tex] = [tex]\frac{8}{2}[/tex]
x = 4
Answer:
x= 4
Step-by-step explanation:
To Find: Angle Measure X67+2x+15+90=180 (Sum of measures of a Triangle)
2x + 172 = 180
2x=180-172
2x=8
x=[tex]\frac{8}{2}[/tex]
x= 4
Mark Me BrainliestFind the equation of the line through the point (3,5) that cuts off the least area from the first quadrant?
The equation of the line through the point (3,5) that cuts off the least area from the first quadrant is 5x +3y -30 = 0.
An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is the slope and c is the y-intercept.
There are basically two intercepts, x-intercept and y-intercept. The point where the line crosses the x-axis is the x-intercept and the point where the line crosses the y-axis is the y-intercept.
The equation of the line, which intersects the y-axis at a point is given by:
y = mx + c
Suppose the line passes through (t,0) and (3,5), where t>3. Then the y-intercept is at (0, 5t/t-3).
So the area of the triangle is:
[tex]\frac{1}{2}[/tex]×[tex]t[/tex]×[tex]\frac{5t}{t-3}[/tex] [tex]=[/tex][tex]\frac{5(t^{2} )}{3(t-3)}[/tex]
Then:
d(5t²/2(t-3))/dt = (5t/t-3) - 5t²/2(t-3)²
= 5t²(2(t-3)-t)/2(t-3)²
=5t(t-6)/2(t-3)²
Since we require t >3, the zero of the derivative that we see is when t=6.
We can write the equation of this line as: 5x +3y -30 = 0
Thus, the equation of the line through the point (3,5) that cuts off the least area from the first quadrant is 5x +3y -30 = 0.
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If the slant height of a triangular face of a square based pyramid of side
16cm is 17cm, find the volume of the pyramid.
Answer must be 1280 cube cm
Answer:
1280 cm³
I presume you are looking for the solution steps and these are below
Step-by-step explanation:
If the each side of the square pyramid is 16 and the slant height is 17, then the height of the pyramid, half the side and the slant edge form a right triangle.
The height of the pyramid can be computed using the Pythagorean theorem
Let a be each side, h the height and s the slant height
[tex]s^2 = h^2 + (a/2)^2\\\\\\s^2 = h^2 + \dfrac{a^2}{4}\\\\\textrm{Plugging in known values,}\\17^2 = h^2 + \dfrac{16^2}{4}\\\\289= h^2 + 64\\\\h^2 = 289 - 64\\\\h^2 = 225\\\\h = \sqrt{225} = 15\\\\[/tex]
The volume, V of a square pyramid of side a and height h is given by the formula:
[tex]V = \dfrac{1}{3}a^2h\\\\\\\textrm{Plugging in values,}\\\\V = \dfrac{1}{3}\cdot 16^2 \cdot 15\\\\[/tex]
[tex]V = \dfrac{1}{3} \cdot 256 \cdot 15\\\\V = 256 \cdot 5\\\\V = 1280[/tex]
The volume of the pyramid is 1280 cubic cm.
Given the slant height of the pyramid is 17 cm and the length of square base of the pyramid is 16 cm.
Now we know the volume of the pyramid with a square base = [tex]\frac{1}{3}[/tex]×area of the base×height.
So we need the values for area of the base and height of the pyramid.
Area of the square base=16×16 sq. cm.= 256 sq. cm.
Again we can apply the relation to find the value of height,
(Slant height)² = (Height)² + ([tex]\frac{1}{2}[/tex]×Length of the base)²
So, putting the values we get,
[tex](17)^2 = (height)^2 +(\frac{16}{2})^2[/tex]
⇒ [tex]289 = (height)^2+64[/tex]
⇒ [tex](height)^2= 225[/tex]
⇒ [tex]height = 15cm[/tex]
Now by appyling the volume of the pyramid we get,
Volume = [tex]\frac{1}{3} \times 256 \times 15[/tex] cubic cm. = 1280 cubic cm.
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√100 +4, √81 + A, √64 + 6, √49 + B, √36 +8, √25+ C
Answer:
Step-by-step explanation:
Simplifying square roots
Example
Let's simplify \sqrt{75}
75
square root of, 75, end square root by removing all perfect squares from inside the square root.
We start by factoring 757575, looking for a perfect square:
75=5\times5\times3=\blueD{5^2}\times375=5×5×3=5
2
×375, equals, 5, times, 5, times, 3, equals, start color #11accd, 5, squared, end color #11accd, times, 3.
We found one! This allows us to simplify the radical:
\begin{aligned} \sqrt{75}&=\sqrt{\blueD{5^2}\cdot3} \\\\ &=\sqrt{\blueD{5^2}} \cdot \sqrt{{3}} \\\\ &=5\cdot \sqrt{3} \end{aligned}
75
=
5
2
⋅3
=
5
2
⋅
3
=5⋅
3
So \sqrt{75}=5\sqrt{3}
75
=5
3
square root of, 75, end square root, equals, 5, square root of, 3, end square root.
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Practice
PROBLEM 1.1
Simplify.
Remove all perfect squares from inside the square root.
{\sqrt[]{12}}=
12
=root, start index, end index, equals
Explain
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Simplifying square roots with variables
Example
Let's simplify \sqrt{54x^7}
54x
7
square root of, 54, x, start superscript, 7, end superscript, end square root by removing all perfect squares from inside the square root.
First, we factor 545454:
54=3\cdot 3\cdot 3\cdot 2=3^2\cdot 654=3⋅3⋅3⋅2=3
2
⋅654, equals, 3, dot, 3, dot, 3, dot, 2, equals, 3, squared, dot, 6
Then, we find the greatest perfect square in x^7x
7
x, start superscript, 7, end superscript:
x^7=\left(x^3\right)^2\cdot xx
7
=(x
3
)
2
⋅xx, start superscript, 7, end superscript, equals, left parenthesis, x, cubed, right parenthesis, squared, dot, x
And now we can simplify:
\begin{aligned} \sqrt{54x^7}&=\sqrt{3^2\cdot 6\cdot\left(x^3\right)^2\cdot x} \\\\ &=\sqrt{3^2}\cdot \sqrt6 \cdot\sqrt{\left(x^3\right)^2}\cdot \sqrt x \\\\ &=3\cdot\sqrt6\cdot x^3\cdot\sqrt x \\\\ &=3x^3\sqrt{6x} \end{aligned}
54x
7
=
3
2
⋅6⋅(x
3
)
2
⋅x
=
3
2
⋅
6
⋅
(x
3
)
2
⋅
x
=3⋅
6
⋅x
3
⋅
x
=3x
3
6x
Practice
PROBLEM 2.1
Simplify.
Remove all perfect squares from inside the square root.
\sqrt{20x^8}=
20x
8
=square root of, 20, x, start superscript, 8, end superscript, end square root, equals
Explain
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More challenging square root expressions
PROBLEM 3.1
Simplify.
Combine like terms and remove all perfect squares from inside the square roots.
2\sqrt{7x}\cdot 3\sqrt{14x^2}=2
7x
⋅3
14x
2
=2, square root of, 7, x, end square root, dot, 3, square root of, 14, x, squared, end square root, equals
Explain
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Suppose that the consumer expenditure E (in dollars) depends on the market price p per unit (in dollars) according toE = 6,400p − 80p2.a)Because E represents consumer expenditure, only values of E ≥ 0 have meaning. For what p-values is E ≥ 0? (Enter your answer using interval notation.)
As per the given expenditure, the p value is 80
The term p value refers a number, calculated from a statistical test, that describes how likely you are to have found a particular set of observations if the null hypothesis were true.
Here we have given that suppose that the consumer expenditure E (in dollars) depends on the market price p per unit (in dollars) according to
E = 6,400p − 80p2.
where E represents consumer expenditure, only values of E ≥ 0 have meaning.
And we need to find value of P.
Through the given question we have identified the function of the following,
=> E = 6,400p − 80p²
Here we have to take p as common variable then we get,
=> E = p (6400 - 80p)
Now, take 80 as the common value then we get
=> E = 80p(80 - p)
When we equate this one with zero, then ew get
=> 80p(80-p) = 0
=> 80 - p = 0
Therefore, p is 80.
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What is ab as shown in the attached question
Answer:
(c) -42
Step-by-step explanation:
You want the product ab given that ...
f(x) = 3x³ +ax² -5x +7g(x) = -3x⁴ +2x³ +3x² +bx +12(f+g)(x) = -3x⁴ +5x³ +9x² -12x +19Comparing coefficientsThe function (f+g)(x) is the sum of the other two functions. For the purpose here, we only need to look at terms that involve 'a' and 'b'.
Comparing coefficients of x², we have ...
ax² +3x² = 9x²
a = 9 -3 = 6
Comparing coefficients of x, we have ...
-5x +bx = -12x
b = -12 +5 = -7
The product is ...
ab = (6)(-7) = -42
look at the picture
The quadratic inequality (18 / 7) · x² + (54 / 7) · x - 180 / 7 < y contains all the ordered pairs outside the parabola.
What is parabola?
A parabola could be a U-shaped plane curve wherever any purpose is at an equal distance from a hard and fast purpose (known because the focus) and from a fixed line that is understood because the directrix.
Main body:
In this problem we must determine a quadratic inequality of the form:
a · x² + b · x + c < y
Where a, b, c are the real coefficients of the inequality.
First, determine the coefficients of the quadratic inequality (parabola) by solving the system of linear equations:
25 · a - 5 · b + c = 0
4 · a + 2 · b + c = 0
a + b + c = - 18
(a, b, c) = (18 / 7, 54 / 7, - 180 / 7)
Second, write the quadratic in equation:
(18 / 7) · x² + (54 / 7) · x - 180 / 7 < y
hence , the equation is (18 / 7) · x² + (54 / 7) · x - 180 / 7 < y
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