Answer:
Step-by-step explanation:
The cross section of a right rectangular pyramid is a trapezoid if the pyramid is sliced perpendicularly to the base and NOT passes trough the vertex.
If the pyramid is sliced through the top vertex and perpendicular to the base, the cross section is a triangle that does not have the same dimension as the pyramid
do these problems and get 100 points 1. Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which two numbers the length of the third side must fall.) Write an inequality. c 22 and 15 2 Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which two numbers the length of the third side must fall.) Write an inequality. d 13.2 and 6.7 3 Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which two numbers the length of the third side must fall.) Write an inequality. e 34 and 12 4 Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which two numbers the length of the third side must fall.) Write an inequality. f 23 and 44
Answer:
[tex]7 < x < 37[/tex] -- Triangle 1
[tex]6.5 < x < 19.9[/tex] -- Triangle 2
[tex]22 < x < 46[/tex] -- Triangle 3
[tex]21 < x < 67[/tex] -- Triangle 4
Step-by-Step Explanation:
Given
2 sides of a triangle
1. 22 and 15
2. 13.2 and 6.7
3. 34 and 12
4. 23 and 44
Required
Determine the range of the third side in the above triangles
Triangle 1: 22 and 15
Represent the third side with x
We'll make use of the following conditions to calculate the range of the third side;
[tex]22 + x > 15[/tex]
[tex]22 + 15 > x[/tex]
[tex]15 + x > 22[/tex]
Solving
[tex]22 + x > 15[/tex]
Make x the subject of formula
[tex]x > 15 - 22[/tex]
[tex]x > -7[/tex]
Solving
[tex]22 + 15 > x[/tex]
[tex]37 > x[/tex]
Solving
[tex]15 + x > 22[/tex]
Make x the subject of formula
[tex]x > 22 - 15[/tex]
[tex]x > 7[/tex]
The next step is to dismiss the inequality with negative digit; So, we're left with
[tex]37 > x[/tex] and [tex]x > 7[/tex]
Rewrite both inequalities
[tex]x < 37[/tex] and [tex]7 < x[/tex]
Combine the two inequalities
[tex]7 < x < 37[/tex]
Triangle 2: 13.2 and 6.7
Represent the third side with x
We'll make use of the following conditions to calculate the range of the third side;
[tex]13.2 + x > 6.7[/tex]
[tex]13.2 + 6.7 > x[/tex]
[tex]6.7 + x > 13.2[/tex]
Solving
[tex]13.2 + x > 6.7[/tex]
Make x the subject of formula
[tex]x > 6.7 - 13.2[/tex]
[tex]x > -6.5[/tex]
Solving
[tex]13.2 + 6.7 > x[/tex]
[tex]19.9 > x[/tex]
Solving
[tex]6.7 + x > 13.2[/tex]
Make x the subject of formula
[tex]x > 13.2 - 6.7[/tex]
[tex]x > 6.5[/tex]
The next step is to dismiss the inequality with negative digit; So, we're left with
[tex]19.9 > x[/tex] and [tex]x > 6.5[/tex]
Rewrite both inequalities
[tex]x < 19.9[/tex] and [tex]6.5 < x[/tex]
Combine the two inequalities
[tex]6.5 < x < 19.9[/tex]
Triangle 3: 34 and 12
Represent the third side with x
We'll make use of the following conditions to calculate the range of the third side;
[tex]34 + x > 12[/tex]
[tex]34 + 12 > x[/tex]
[tex]12 + x > 34[/tex]
Solving
[tex]34 + x > 12[/tex]
Make x the subject of formula
[tex]x > 12 - 34[/tex]
[tex]x > -22[/tex]
Solving
[tex]34 + 12 > x[/tex]
[tex]46 > x[/tex]
Solving
[tex]12 + x > 34[/tex]
Make x the subject of formula
[tex]x > 34 - 12[/tex]
[tex]x > 22[/tex]
The next step is to dismiss the inequality with negative digit; So, we're left with
[tex]46 > x[/tex] and [tex]x > 22[/tex]
Rewrite both inequalities
[tex]x < 46[/tex] and [tex]22 < x[/tex]
Combine the two inequalities
[tex]22 < x < 46[/tex]
Triangle 4: 23 and 44
Represent the third side with x
We'll make use of the following conditions to calculate the range of the third side;
[tex]23 + x > 44[/tex]
[tex]23 + 44 > x[/tex]
[tex]23 + x > 44[/tex]
Solving
[tex]23 + x > 44[/tex]
Make x the subject of formula
[tex]x > 23 - 44[/tex]
[tex]x > -21[/tex]
Solving
[tex]23 + 44 > x[/tex]
[tex]67 > x[/tex]
Solving
[tex]23 + x > 44[/tex]
Make x the subject of formula
[tex]x > 44 - 23[/tex]
[tex]x > 21[/tex]
The next step is to dismiss the inequality with negative digit; So, we're left with
[tex]67 > x[/tex] and [tex]x > 21[/tex]
Rewrite both inequalities
[tex]x < 67[/tex] and [tex]21 < x[/tex]
Combine the two inequalities
[tex]21 < x < 67[/tex]
In the picture down below
Answer:
Option C. f¯¹(x) = x + 3
Step-by-step explanation:
f(x) = x – 3
To find the inverse, f¯¹(x) of f(x), we simply do the following:
f(x) = x – 3
Replace f(x) with y
y = x – 3
Interchange y and x
x = y – 3
Make y the subject by rearranging
x + 3 = y
y = x + 3
Replace y with f¯¹(x)
f¯¹(x) = x + 3
Therefore, the inverse of f(x) = x – 3 is f¯¹(x) = x + 3
Translate into an algebraic expressions: A number increased by a % and decreased by 80% is 400. What is the number ?
Answer:
(x*(1+a))*0.8 = 400; x = 500/1+a
Step-by-step explanation:
First, increase the number (which we will call x) by a%
x*(1+a) -> You do 1 + a because if you wanted to increase let's say 5 by 20% you would do 5 + 5*0.2 and if you factor that out it becomes 5(1+0.2)
Next, decrease it by 80%.
(x*(1+a))*0.8
Finally, make it into an equation.
(x*(1+a))*0.8 = 400
If you solve it, you get:
x(1+a) = 500
x = 500/1+a
PLEASE help me with this question! No nonsense answers and answer with full solutions please!
Answer: b) {-3, 0.5}
Step-by-step explanation:
The new equation is the original equation plus 6. Move the original graph UP 6 units. The solutions are where it crosses the x-axis.
[tex]\text{Original equation:}\quad f(x)=\dfrac{15}{x}-\dfrac{9}{x^2}\\\\\\\text{New equation:}\quad\dfrac{15}{x}+6=\dfrac{9}{x^2}\\\\\\.\qquad \qquad f(x)= \dfrac{15}{x}-\dfrac{9}{x^2}+6[/tex]
+6 means it is a transformation UP 6 units.
Solutions are where it crosses the x-axis.
The curve now crosses the x-axis at x = -3 and x = 0.5.
4. You work for an advertising company and have been hired to place a blimp above a football stadium. The angle of elevation from a point directly under the goal post is 72° and the blimp will be directly above the 50 yard line. a. Which trigonometric ratio would you use to calculate how high the blimp will be above the 50 yard line? b. How high above the ground is the blimp? c. In order to be able to read the advertisement on the side of the blimp the highest the blimp can be is 150 feet. Will the fans be able to read the advertisement? If not, what possible angle of elevation could we use? d. What is the exact angle if the blimp is at 150 feet?
Answer:
tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]
The height of the blimp above the ground is h = 153.884 yard
No, the fans will not be able to read the advertisement.
The exact angle if the blimp is at 150 feet is 45.74°
Step-by-step explanation:
From the summary of the information given :
The angle of elevation from a point directly under the goal post is 72° and the blimp will be directly above the 50 yard line.
That statement above being illustrated in the attached diagram below for better understanding.
a. Which trigonometric ratio would you use to calculate how high the blimp will be above the 50 yard line?
The trigonometric ratio that can be used to calculate how high the blimp will be above the 50 yard line is :
tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]
b. How high above the ground is the blimp?
Using the above derived trigonometric ratio,
tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]
[tex]tan \ 72^0 = \dfrac{h}{50}[/tex]
[tex]h =tan \ 72^0 \times {50}[/tex]
[tex]h =3.07768 \times {50}[/tex]
h = 153.884 yard
The height of the blimp above the ground is h = 153.884 yard
c. In order to be able to read the advertisement on the side of the blimp the highest the blimp can be is 150 feet.
Will the fans be able to read the advertisement?
No, the fans will not be able to read the advertisement.
This is because, 153.884 yard to feet
= 153.884 × 3
= 461.652 feet which is more than the maximum given 150 feet.
If not, what possible angle of elevation could we use?
The possible angle of elevation can be determined by taking the tangent of the trigonometric ratio.
SO
tan θ = [tex]\dfrac{h}{150}[/tex]
tan θ = [tex]\dfrac{153.884}{150 \ feet}[/tex]
tan θ = 1.026
θ = tan ⁻¹ (1.026)
θ = 45.74°
d. What is the exact angle if the blimp is at 150 feet?
The exact angle if the blimp is at 150 feet is 45.74°
what is the explicit formula for this sequence ?
Answer:
B
Step-by-step explanation:
common difference is 3
explicit formula is
first term + ( n-1 ) * common difference
= -7 + ( n-1) * 3
I WILL GIVE BRAINLIEST!!!! A teacher is grading the final exam. He notices that the mean test score is 61, and the standard deviation is 10. The test scores were normally distributed. if there were 450 students in the data sample, how many would have a test score between 61 and 71 *Round your answer to the nearest full value.
Answer:
153.586 close to 154 students
Step-by-step explanation:
mean=61
standard deviation =10
sample 450 students , x between 61 and 71
(x-mean)/deviation for score 61 and 71
61-61/10=0
71-61/10=1
the z-scores is between 0 and 1 ( use calculator)
the percentage is 0.3413 close to 34%
number of students that score between 61 and 71=
450*0.3413= 153.586 close to 154 students
Choose the equation that is equivalent to the equation shown below. y = 2x + 4a/6b A. x = 2x - 3by B. c = ax-by/z C. b = 6y/2x+4a D. a = 3by-x/2
Answer:
Step-by-step explanation:
y = 2x + 4a/6b y=(12xb+4b )/6b
6yb=12x+4a
a=(-12xb+6yb)/4=
a=3yb/2 -3xb
x=y/2-a/3b
b=2a/(3y-6x)
the solution is for every variable
Can someone please explain The measure of angle A to the nearest tenth of a degree is:
Answer:
A =19.5
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin A= opp/ hyp
sin A = 3/9
Take the inverse sin of each side
sin ^-1 sin A = sin ^-1 (3/9)
A =19.47122063
To the nearest tenth of a degree
A =19.5
Answer:
19
Step-by-step explanation:
inverse sin (1/3) = 19.47122060852
Find all solutions of the equation in the interval [0, 2pi).
2 cos 0 - 13 = 0
Write your answer in radians in terms of t.
If there is more than one solution, separate them with commas.
Answer:
The solutions of 2·cos(θ) - √3 = 0in the interval [0, 2pi) are;
π/6, 13/6·π
Step-by-step explanation:
The given that the equation is 2·cos(θ) - √3 = 0
The solution of the above equation in the interval [0, 2pi) are required
Therefore, the domain includes 0 ≤ θ < 2pi
2·cos(θ) - √3 = 0
2·cos(θ) = √3
cos(θ) = √3/2
Therefore;
θ = cos⁻¹(√3/2)
The values are;
[tex]\theta =\dfrac{12 \cdot \pi \cdot n_1 +\pi }{6} \, or \, \theta =-\dfrac{12 \cdot \pi \cdot n_1 +\pi }{6}[/tex]
Where the domain is 0 ≤ θ < 2pi, we have;
π/6, 13/6·π
Which of the following represents a function
help please .........
Answer:
30.045
Step-by-step explanation:
the length of rectangle=140 which is also the diameter of circle
R=d/2=140/2=70 ( which is the width of rectangle)
perimeter of rectangle=2l+2w=140+280=420
perimeter of semicircle=πr+d=70π+140=359.911
the difference between two perimeter
(perimeter of rectangle- perimeter of semi circle) =
420-359.911=60.089
since only one shaded area :
60.089/2=30.0445 close to 30.045
Give the greatest common divisor of $6^3$ and $3^6$.
Answer:
27
Step-by-step explanation:
Since 3^6 is only divisible by 3 and powers of 3(including 1) the gcd of 3^6 and 6^3 mus be a power of 3 hence we need to find the highest powers of 3 that divide 6^3 and that divide 3^6, which are respectively 3^3 and 3^6, hence, taking the smaller one (since we want it to divide both), our answer is 3^3=27.
Answer:
Step-by-step explanation:
Greatest common divisor is the largest positive integer that divides each integer in the given problem
6³ = (2* 3)³ = 2³ * 3³
3⁶ = 3³ * 3³
Greatest common divisor = 3³ = 3* 3* 3 = 27
Which option is equal to 7 1/5
Answer:
D. is the answerStep-by-step explanation:
Question:
7^1/5
The number given has an exponent of a fraction: fraction exponent = 1/5
So, when you have a fraction - you always have a square root - Important!!Since the top is one, the number 7 stays the same. = 7^1 = 7
The bottom is a 5. This means it is to the fifth root.
Answer = D
Hope this helped,
Kavitha
Answer: If 36/7 is one of the options, choose that one.
If the question involves an exponent, you should use the "caret" which is ^ found above the 6 on a keyboard. [Shift + 6]. That helps avoid confusion.
Step-by-step explanation: 7 is equal to 35/5 because 7×5=35
Add 1/5 and you end up with 36/5. A Common rational number.
7^(1/5) = the 5th root of 7. A very small irrational number!
n Fill in the blank. The _______ for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further. The (1) for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further.
Answer: sample space
Step-by-step explanation: In determining the probability of a certain event occurring or obtaining a particular outcome from a set of different possible outcomes, such as in the toss of coin(s), rolling of fair die(s), the sample space comes in very handy as it provides a simple breakdown and segmentation of all possible events or outcomes such that in Calculating the probability of occurrence of a certain event, the event(s) is/are located in the sample space and the ratio taken over the total number of events.
How would 7/2 be written as a complex number
Answer:
We could rewrite 7/2 as 7a + 2
Step-by-step explanation:
Complex numbers is when real numbers [i.e: 1, 1/2, 200, 5/7, etc..) and an imaginary numbers [numbers that give a negative result when squared] are combine together.
This is really confusing I need help with this.
Answer:
Step-by-step explanation:
can you at least telllus what is in the drop box
A Prince came to an Evil Wizard to ask for the release of his beloved Princess, who is locked behind one of three doors. The Evil Wizard offered to release the Princess if the Prince was able to correctly guess which door she was behind. And with this offer, the Evil Wizard gave three hints: 1) The Princess is locked behind door 1 2) A fire-breathing Dragon is locked behind door 2. 3) There is also someone locked behind door 3 The Prince realized that all three hints were false, and with the help of logic, understood which door the Princess was locked behind. Which door was it?
Answer:
Princess is behind 2
Step-by-step explanation:
If all 3 hints are false, then the princess is not behind 1 ( so it must be 2 or 3)
The dragon is not behind 2 ( so it must be 1 or 3)
The is no one behind 3
That means the princess cannot be behind 3 and the dragon cannot be behind 3
The princess is behind 2 and the dragon is behind 1
Please help! I got 14 but it says it's incorrect! Find the maximum number of real zeros of the polynomial. f(x)=2x^(6)-3x^(3)+1-2x^(5)
Answer:
6
Step-by-step explanation:
The Fundamental theorem of Algebra states that a polynomial of degree n has n roots. These can be real, complex or both.
f(x) = 2[tex]x^{6}[/tex] - 3x³ + 1 - 2[tex]x^{5}[/tex] ← is a polynomial of degree 6
Thus the maximum number of real roots is 6
evaluate:
(5-6)^2 x (4+3)
Answer:
7
Step-by-step explanation:
( -1 ) ^ 2 = 1 * ( 4 + 3 ) 1 * ( 4 + 3 ) = 71 * 7 = 7i Hope this helps
Answer:
7Step-by-step explanation:
[tex] {(5 - 6)}^{2} \times (4 + 3)[/tex]
Calculate the difference
[tex] = {( - 1)}^{2} \times (4 + 3)[/tex]
Add the numbers
[tex] = {( - 1)}^{2} \times 7[/tex]
Evaluate the power
[tex] = 1 \times 7[/tex]
Any expression multiplied by 1 remains the same
[tex] = 7[/tex]
Hope this helps...
Best regards!!
The local theatre production company sells advance tickets (a) for $16 per seat. On the night of the performance, tickets (t) are sold for $22 each. If the company sold 648 tickets for at total of $11,826, write an equation that expresses the total income from ticket sales.
Answer:
16a + 22t = 11826
Step-by-step explanation:
Cost of 1 (a) ticket = $16
Cost of 1 (t) ticket = $22
Total tickets sold = 648
Cost of 648 tickets = $11826
So eqn will be => 16a + 22t = 11826
What is the area of the trapezoid shown below?
Answer: 78 units²
Step-by-step explanation:
Use Pythagorean Theorem to find the base of the triangle:
x² + 12² = 15²
x² + 144 = 225
x² = 81
x = 9
Now, separate the figure into two shapes --> triangle and rectangle.
[tex]A_{\triangle}=\dfrac{base\times height}{2}=\dfrac{9\times 12}{2}=54\\\\A_{\square}=length \times width = 12 \times 2 =24\\\\A_{trapezoid}=A_{\triangle}+A_{\square}=54+24=\large\boxed{78}[/tex]
You can also use the trapezoid rule:
[tex]A=\dfrac{b_1+b_2}{2}\cdot h\\\\\\.\quad = \dfrac{(9+2)+(2)}{2}\cdot 12\\\\\\.\quad = \dfrac{13}{2}\cdot 12\\\\\\.\quad =13\cdot 6\\\\\\.\quad = \large\boxed{78}[/tex]
1. The total area within any continuous probability distribution is equal to 1.00.
A. True
B. False
2. For any continuous probability distribution, the probability, P(x), of any value of the random variable, X, can be computed.
A. True
B. False
3. For any discrete probability distribution, the probability, P(x), of any value of the random variable, X, can be computed.
A. True
B. False
Answer:
1. True
2. False.
3. True.
Step-by-step explanation:
1. The total area within any continuous probability distribution is equal to 1.00: it is true because the maximum probability (value) is one (1), therefore, the total (maximum) area is also one (1).
Hence, for continuous probability distribution: probability = area.
2. For any continuous probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: False because it has an infinite number of possible values, which can not be counted or uncountable.
Hence, it cannot be computed.
3. For any discrete probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: True because it has a finite number of possible values, which are countable or can be counted.
Hence, it can be computed.
What is the real interest rate if the nominal interest rate is 1 when the rate of inflation is 2
Answer:
Real interest rate = -1%
Step-by-step explanation:
Real interest rate=Nominal interest rate - inflation rate
From the above,
Nominal interest rate=1%
Inflation rate=2%
Real interest rate=Nominal interest rate - inflation rate
=1% - 2%
= -1%
Real interest rate = -1%
Real interest rate shows you what it really costs borrowers to pay back their loans.
if the real interest rate is greater than zero, the amount you pay back is worth more in real terms than the money you borrowed.
if the real interest rate is below zero as in the above case, the amount you will pay back is less worth in real terms than the money you borrowed.
Determine the nature of the roots 4x^2 + 13x + 6 = 0 a.no real solutions b.cannot be determined c.a unique real solution d.two distinct real solutions
Answer:
D
Step-by-step explanation:
Try factoring the equation
Answer:
D Edge 2020-2021
Step-by-step explanation:
I got it right on the quiz
Ten turns of a wire are helically wrapped around a cylindrical tube with outside circumference 4 inches and length 9 inches. The ends of the wire coincide with ends of the same cylindrical element. Find the length of the wire. (a) 41 inches (b)36 inches (c) 40 inches (d) 90 inches
Answer:
b) 36 inches
Step-by-step explanation:
Length of the wire = Outside circumference of the cylindrical tube * length of the cylinder
= 4 * 9
= 36 inches
Length of the wire will be same to the surface area of the cylinder
Surface area of cylinder = circumference * length
if you drop a tennis ball from the height of 100in and the rebound is 58in what is the height on the 10th bounce?
Answer:
0.431 inches
Step-by-step explanation:
We were given the following values:
Height the tennis ball was dropped = 100in
Rebound height = 58in
We have to find the rebound ratio
= 58in/100in = 0.58
The formula to be used
Height on nth bounce = Initial height × (Rebound ratio)ⁿ
Where n = number of bounce
Height on the 10th bounce = 100 × (0.58)^10
Height on the 10th bounce = 0.4308042069inches
Approximately, the height on the 10th bounce = 0.431 inches.
Given a graph of a system that has exactly one solution, how would you estimate the solution to the tenths place? Explain the process.
Answer:
First determine the integers the x-coordinate and the y-coordinate are between. Then look at each to decide which integer the x- or y-value is closer to, and approximate the coordinate value to the tenths place.
Step-by-step explanation: Sample Response on Edge
The estimation of the solution to the tenths place is given below.
What is rounding off?
Rounding numbers refers to changing a number's digits such that it approximates a value. The provided number is more simply represented by this value. For instance, 700,000 rather than 698,869 could be used to express a town's population.
Given that;
A graph of a system that has exactly one solution.
Now,
Let a solution of the graph of a system = (2.37, 1)
So, We can estimate the solution of the system to tenth place as;
⇒ 2.37 = 2.4 (round to tenth place)
Thus, The solution of the system to the tenths place will be;
⇒ (2.3 , 1)
Learn more about the rounding number visit:
https://brainly.com/question/1620496
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Cece works at a dress shop and needs to calculate the discounts for dresses on sale using the formula d=(p−c)÷2, where d is the discount, p is the original price, and c is the store's cost for the dress. If the store's cost for a dress is $50 and the original price of the dress is $120, what is the discount on the dress?
Answer:
$35
Step-by-step explanation:
Using the formula provided, d=(p−c)÷2 (where d is the discount, p is the original price, and c is the store's cost for the dress.) we can determine the discount.
The original price is 120,
d=(120−c)÷2
The store's cost is 50,
d=(120−50)÷2
So we subtract 120 and 50 to get
d=(70)÷2
70 divide by two is
d= 35
The discount is $35
PLEASE! I need help! I am really confused with this.
Answer:
It's the first option
Step-by-step explanation:
They've constructed two angle bisectors and have shown you where they meet. Their point of intersection is the center of the inscribed circle (the incenter). Therefore, the last step is finding the altitudes (perpendicular lines) from the incenter to all the sides.