The ladder is 29.9 feet long.
For solving this problem we have to use trigonometric ratio
We need to use the tangent function:
What is the ratio of tangent function?
[tex]tan (\theta) = opposite/adjacent[/tex]
[tex]tan 75 = opposite/8[/tex]
multiply both side by 8 so we will get,
Here, the opposite side is the length of the ladder and angle [tex]\theta =75^0[/tex]
Therefore by using the tan ratio we have,
[tex]8 * tan 75 = opposite[/tex]
[tex]29.8564065 = opposite[/tex]
Therefore, the ladder is 29.9 feet.
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3 on the outside, square root 1/5
To simplify 1/(5 + √3), multiply both numerator and denominator by the conjugate of the denominator, which is 5 - √3. This results in (5 - √3)/22, which is the simplified form of the expression.
The student has asked to evaluate the expression 1/(5 + √3). To simplify this expression, we can multiply both the numerator and the denominator by the conjugate of the denominator to get rid of the square root in the denominator. The conjugate of 5 + √3 is 5 - √3. So, we multiply the expression by (5 - √3)/(5 - √3).
The resulting expression after multiplication:
Numerator: 1 * (5 - √3) = 5 - √3Denominator: (5 + √3) * (5 - √3) which simplifies to 5² - (√3)² = 25 - 3 = 22
So our final answer after simplification is:
(5 - √3)/22
complete question given below:
Evaluate 1/(5+ square root of 3)
A 45 gram sample of a substance that's used to preserve fruit and vegetables has a k-value of 0.1109.
Find the substances half-life in days. Round your answer to the nearest tenth.
what equation of a line is perpendicular to 6x+4y=3?
what is the square root of negative one hundred.?.
If a wheel with a radius of 70 inches spins at a rate of 600 revolutions per minute, find the approximate linear velocity in miles per hour.
How many corners does a cube have? how many faces does a cube have? how many other cubes would share a given corner atom or face atom if several cubes were stacked side-to-side, front-to-back, and top-to-bottom?
Evaluate the following algebraic expressions:1.) 40y-¹, y = 5 2.) 1/m-²(m + 4), m = -8 3.) (p² – 3)-², p = 14.) (x – 1)-² / (x + 1)-², x = 2 5.) y-³ – y-², y = 2
Linear Function Graph. Express it in slope intercept form.
Drive Down is a racing video game. The game gives each player an initial amount of $5,000 in virtual money. After that, a player gets $500 in virtual money for each race won. What function represents the amount of virtual money a player has in terms of the number of races won?
The independent quantity is the , and the dependent quantity is the _________ and the dependent quantity is the _________ The function representing the situation is _________
Answer:
The game gives each player an initial amount of $5,000 in virtual money. After that, a player gets $500 in virtual money for each race won. This $5000 is fixed.
Let the races won be x
So, the function that represents the amount of virtual money a player has in terms of the number of races won becomes :
[tex]f(x)=500x+5000[/tex]
The independent quantity (x) is : the number of races won
And the dependent quantity f(x) or y is : the total virtual money earned
a basketball coach is purchasing 12 shirts for her team, each with a different number. at the checkout counter the clerk places 5 of the shirts in the first bag. how many different ways can a group of 5 shirts be placed in that first bag
Answer:
792 ways
Step-by-step explanation:
Determine the slope and y-intercept of the line.
y = 5x + 4
a.
Slope = 4, y-intercept is (0, 5)
c.
Slope = 5, y-intercept is (0, 4)
b.
Slope = -5, y-intercept is (0, 4)
d.
Slope = 4, y-intercept is (0, -5)
Please select the best answer from the choices provided
A
B
Answer:
D
Step-by-step explanation:
Correct on A P E X
Determine the type and number of solutions of 6x^2-7x-4=0
A. One real solution
B. Two real solution
C. Two imaginary solutions
D. One real solution and one imaginary solution
Of a group of students 5/8 of them are boys. The girls are put into groups so that each group has 1/6 of the total number of students. How many groups of girls are there?
how much would $140 invested at 6% interest compounded monthly be worth after 15 years? round your answer to the nearest cent
The principle amount of $140 invested at a 6% rate of interest compounded monthly be worth after 15 years will be $340.
What is compound interest?Compound interests are those interests where the principle amount always going to change.
For example, if you give $100 to anyone with 5% interest monthly then at the end of your month your value becomes $105 and this will become the principal amount.
Given that the principal amount is $140
P = $140
The rate of interest is 6%
r = 6%
Number of time period 15 years
t = 15
Now by compounding interest formula
A = [tex][1+r/100]^{t}[/tex]
By putting all value we get
A = [tex][1 + 6/100]^{15}[/tex]
A = $340 hence, $340 will be the total amount after 15 years.
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if the apothem is 6.9 mm and a side length is 8 mm what is the area of the hexagon
A function is shown in the table.
x g(x)
−2 2
−1 −3
0 2
1 17
Which of the following is a true statement for this function?
a. The function is increasing from x = −2 to x = −1.
b. The function is increasing from x = 0 to x = 1.
c. The function is decreasing from x = −1 to x = 0.
d. The function is decreasing from x = 0 to x = 1.
Only one statement is correct:
B ) The function is increasing from x = 0 to x = 1
Explanation: g ( 0 ) = 2, g ( 1 ) = 17, 2 < 17.
Simplify the expression below.
3 · -8 + 5 - 4 ÷ 2
-11.5
-21
-12.5
-27
Answer:
-21 I think
I hope i helped you!
Marisol is making a rectangular wooden frame. She wants the length of the frame to be no more than 12 inches. She has less than 30 inches of wood to use. Which system of inequalities represents the possible length, l, and the possible width, w, that her frame could have?
l ≤ 12
2l + 2w < 30
l > 12
2l + 2w < 30
l ≤ 12
l + w < 30
l > 12
l + w < 30
Answer: (A) The first option is the right answer.
Step-by-step explanation:
l ≤ 12
2l + 2w < 30
NEED HELP!!!!!!!!!!!!!!!!!!!!!
what is the sum of the geometric sequence -3, 18, -108,... if there are 7 terms?
Which linear function represents the line given by the point-slope equation y + 1 = –3(x – 5)?
In the diagram, HGF is a straight line. Given EF = 4 cm and HG = GF = 3 cm, find :
(i) tan x
(ii) sin y
What is a rule that describes the translation ABCD ⇒A' B' C' D'?
A. T <3,-2> (ABCD)
B. T <3,2> (ABCD)
C. T <2,-3> (ABCD)
D. T<-3,2> (ABCD)
A. IS WRONG
Final answer:
The question seeks the correct translation rule for the movement of quadrilateral ABCD to A'B'C'D'. Translation in geometry involves moving a shape in a consistent direction and distance. Given option A is incorrect, and considering directionality, T <-3,2> (ABCD) is another possibility for the translation.
Explanation:
The question asks for the rule that describes the translation of quadrilateral ABCD to A'B'C'D'. A translation in geometry is a type of transformation that moves every point of a shape the same distance in the same direction. Since option A, which is T <3,-2> (ABCD), is given as incorrect, let's analyze the remaining options.
To determine the correct rule for translation, we need to look at the relative position of the original points and their corresponding points after the translation. For example, if point A were at (x,y) and A' is at (x+3, y-2), this would correspond to a translation of 3 units to the right and 2 units down, which is described by the vector <3, -2>.
Since option A is incorrect and we know that the transformation corresponds to a translation and not a reflection or rotation, let's consider the other options. Looking at option D, T <-3,2> (ABCD), this would imply that every point of quadrilateral ABCD is moved 3 units to the left (because of -3) and 2 units up (because of 2), which would be the reverse of what is described in option A.
Given the vertices of ∆ABC are A (2,5), B (4,6) and C (3,1), find the vertices following each of the transformations FROM THE ORIGINAL vertices:
a. Rx-axis
b. Ry = 3
c. T<-2,5>
d. T<3,-6>
e. r(90◦, o)
a)
Reflection over x-axis.
We know that when any point is reflected over the x-axis, then the rule of transformation that is applied is:
(x,y) → (x,-y)
Hence,
A (2,5)→ A'(2,-5)
B (4,6) → B'(4,-6)
and C (3,1) → C'(3,-1)
b)
Reflection about the line y=3
We know that any point after reflection is at a fixed distance from the line as it was before reflection.
Hence,
A (2,5)→ A'(2,1)
B (4,6) → B'(4,0)
and C (3,1) → C'(3,5)
c)
T<-2,5>
The rule that is applied to this translation is:
(x,y) → (x-2,y+5)
Hence,
A (2,5)→ A'(0,10)
B (4,6) → B'(2,11)
and C (3,1) → C'(1,6)
d)
T<3,-6>
The rule that is applied to this translation is:
(x,y) → (x+3,y-6)
Hence,
A (2,5)→ A'(5,-1)
B (4,6) → B'(7,0)
and C (3,1) → C'(6,-5)
e)
r(90◦, o)
It is a rotation of a point 90 degree clockwise about the origin.
Hence, the rule that describes this transformation is:
(x,y) → (y,-x)
Hence,
A (2,5)→ A'(5,-2)
B (4,6) → B'(6,-4)
and C (3,1) → C'(1,-3)
In your own words, define each of the following terms. a. Whole number b. Digit c. Place value d. Rounded number e. Equals
The following terms are defined below:
a. Whole number, b. Digit, c. Place value, d. Rounded number, and e. Equals.
a. Whole Number: A whole number is a positive integer not having any fractional or decimal parts. Whole numbers include the set of natural numbers(non-negative integers) along with zero.
b. Digit: A digit, in mathematics, means any of the numerical symbols used to denote numbers in the decimal numeral system.
c. Place value: Place values are the values of a digit in a number based on its position or place within that number. Based on powers of ten, in the decimal numeral system, each digit's position determines its place value.
d. Rounded number: An approximation of a numerical value having been adjusted or approximated to a certain level of precision or a specific place value is called a "rounded number".
e. Equals: Mathematically, the term "equals" is utilized to represent that two quantities or expressions have the same value. The equals sign (=) is a symbol used to indicate equality between two mathematical expressions.
Thus, the above terms are defined.
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Final answer:
Whole numbers are counting numbers without fractions or decimals, digits are symbols used to represent numbers, place value is the value of a digit based on its position, a rounded number is simplified for ease of use, and equals shows that two quantities have the same value.
Explanation:
In the field of mathematics, the terms mentioned refer to basic concepts essential for understanding numbers and arithmetic operations.
a. Whole number
Whole numbers are the basic counting numbers starting from 0 and including all positive integers (1, 2, 3, ...). They do not include fractions, decimals, or negative numbers.
b. Digit
A digit is any one of the ten symbols used to write numbers. These symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
c. Place value
Place value refers to the value of a digit based on its position in a number. For instance, in the number 231.45, the place value of the digit '3' is tens, meaning it represents thirty.
d. Rounded number
A rounded number has been altered to a nearby, often simpler number. Rounding is done to make numbers easier to work with, especially when precision is not crucial.
e. Equals
The term 'equals' is used to signify that two quantities are the same in value, often represented by the symbol '='.
what shows 23^2-17^2 being evaluated using the difference of perfect squares method
Find the missing terms in the following geometric sequence. -12,__,__, -324
Answer:
The nth term for the geometric sequence is given by:
[tex]a_n = a_1 \cdot r^{n-1}[/tex]
where,
[tex]a_1[/tex] is the first term
r is the common ratio of the terms.
As per the statement:
Given the sequence
-12,__,__, -324
here, [tex]a_1 = -12[/tex] and [tex]a_4 = -324[/tex]
Solve for r:
By definition we have;
[tex]a_4 = a_1 \cdot r^3[/tex]
⇒[tex]-324 = -12 \cdot r^3[/tex]
Divide both sides by -12 we have;
[tex]27 = r^3[/tex]
⇒[tex]r = \sqrt[3]{27} =\sqrt[3]{3^3} = 3[/tex]
We have to find the missing terms [tex]a_2, a_3[/tex]
[tex]a_2=a_1 \cdot r[/tex]
⇒[tex]a_2 = -12 \cdot 3 = -36[/tex]
[tex]a_3=a_1 \cdot r^2[/tex]
⇒[tex]a_2 = -12 \cdot 3^2 = -12 \cdot 9 = -108[/tex]
therefore, the missing terms in the following geometric sequence is,
-12,_-36_,_-108_, -324
Sandra calculated the missing side length of one of these triangles using the Pythagorean Theorem. Which triangle is it?
A
B
C
D
1 over 111 as a decimal
In winter, the temperature in northern Wisconsin can be quite cold. When Lauren woke up this morning (6:00am) the temperature outside was -18°F. When she got home from school (4:00pm) the tempature outside was 4°F. What was the change in temperature from 6:00 am to 4:00 pm?