Answer:
Yes, this is an arithmetic sequence.
The difference is -3, so a(n+1) = a(n) - 3
The 21st term is -53, calculated as follows:
a(21) = 7 + (21 - 1)(-3) = -53
The next three terms are -5, -8, and -11.
Please answer all 8 questions and show work, thank you.
1. A square classroom has 10 square yards more than 5 times the area of the hallway outside it. The classroom and hallway have a combined area that’s 50 square yards less than 10 times the area of the hallway. Find the length of each side of the classroom.
2. The area of a magenta circle is 100 square meters more than four times the area of a yellow circle. If the magenta circle has an area of 1,500 square meters, what is the radius of the yellow circle?
3. A cubed-shaped box has a volume of 343 cu. ft. What is the surface area of the box?
4. Ace and Charles are salesmen. If Ace had made another $20 in sales, he would have sold three times as much as Charles. Combined, they sold $80 less than 7 times Charles’s sales. How much money did Ace sell?
5. Maria, Dawn, and Hina painted a fence for a total of $480. Since they spent different amounts of time painting, they divided this total in the ratio 3:5:8 (Dawn, Maria, Hina.) How much more did Maria earn than Dawn?
6. 10 years ago, Charlotte was 40 years old, while Mark was 14 years old. When will Charlotte be 8 years more than twice Mark’s age?
7. Rewrite the volume of a cone’s formula to solve for the radius, then solve for the radius when the volume is 300in cubed and the height is 4in.
8. The area of a pink square is 20 square yards more than one-third the area of a purple square. If the pink square has an area of 300 square yards, what is the length of each side of the purple square?
Thank you so much to anyone who helps.
how I answer this using Commutative and Associative Properties of Addition can help you evaluate the expression.
The value of the fraction given as - 1 3/4 - (-8 1/3) - (- 4 1/4) will be 10 5/6.
How to calculate the fraction?It should be noted that a fraction is simply used to represent the numbers that aren't whole.
Based on the information given, the fraction is illustrated as:
= - 1 3/4 - (-8 1/3) - (- 4 1/4)
Note that (-) × (-) = +
Therefore,
= - 1 3/4 - (-8 1/3) - (- 4 1/4)
= - 1 3/4 + 8 1/3 + 4 1/4
The LCM of the denominator is 12
= - 1 9/12 + 8 4/12 + 4 3/12
= 12 7/12 - 1 9/12
= 10 10/12
= 10 5/6
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There are thirty three students in the chess club. There are five more boys than girls in the club. Write and solve a system of equations to find the number of boys and girls in the chess club.
There are 14 girls and 19 boys in the chess club.
Step-by-step explanation:Let x be girls and y be boys in the chess club. First, we need to write the system.
We know there are 33 students in total.
x + y = 33
We also know there are five more boys than girls in the club.
x + 5 = y
Here is our system of equations and the solving process:x + y = 33
x + 5 = y
First, we will solve for y with substitution:
x + y = 33
x + (x + 5) = 33
2x = 28
x = 14
Now, we will plug in this x-value:
x + y = 33
(14) + y = 33
y = 19
There are 14 girls and 19 boys in the chess club.
Demuestra las funciones trigonométricas de 45o a partir de un cuadrado con longitud de lado igual a 1.
The most appropriate choice for trigonometric function will be given by -
sin 45° = [tex]\frac{1}{\sqrt{2} }[/tex]
cos 45° = [tex]\frac{1}{\sqrt{2} }[/tex]
tan 45° = 1
cot 45° = 1
sec 45° = [tex]\sqrt{2}[/tex]
cosec 45° = [tex]\sqrt{2}[/tex]
What are trigonometric functions?
Trigonometric functions are those functions which shows the relationship between side and angle of a right angled triangle.
There are six trigonometric functions-
[tex]sin \theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]
[tex]sin \theta[/tex] = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]
[tex]cos\theta[/tex] = [tex]\frac{Base}{Hypotenuse}[/tex]
[tex]tan\theta[/tex] = [tex]\frac{Perpendicular}{Base}[/tex]
[tex]cot\theta[/tex] = [tex]\frac{Base}{Perpendicular}[/tex]
[tex]sec\theta[/tex] = [tex]\frac{Hypotenuse}{Base}[/tex]
[tex]cosec\theta[/tex] = [tex]\frac{Hypotenuse}{Perpendicular}[/tex]
Here,
The diagram of the square has been attached with this answer
∠ABC = 90° [Side of a square is 90°}
∠BAC = [tex]\frac{90}{2}[/tex]
= [tex]45[/tex]°
Side of square = 1 unit
Length of diagonal of a square = [tex]\sqrt{2}[/tex] [tex]\times[/tex] side
= [tex]\sqrt{2}[/tex] [tex]\times[/tex] [tex]1[/tex]
= [tex]\sqrt{2}[/tex] units
From [tex]\Delta[/tex] ABC,
sin 45° = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]
= [tex]\frac{BC}{AC}[/tex]
= [tex]\frac{1}{\sqrt{2} }[/tex]
cos 45° = [tex]\frac{Base}{Hypotenuse}[/tex]
= [tex]\frac{AB}{AC}[/tex]
= [tex]\frac{1}{\sqrt{2} }[/tex]
tan 45° = [tex]\frac{Perpendicular}{Base}[/tex]
= [tex]\frac{BC}{AB}[/tex]
= [tex]\frac{1}{1}[/tex]
= 1
cot 45° = [tex]\frac{Base}{Perpendicular}[/tex]
= [tex]\frac{AB}{BC}[/tex]
= [tex]\frac{1}{1}[/tex]
= 1
sec 45° = [tex]\frac{Hypotenuse}{Base}[/tex]
= [tex]\frac{AC}{AB}[/tex]
= [tex]\frac{\sqrt{2} }{1}[/tex]
= [tex]\sqrt{2}[/tex]
cosec 45° = [tex]\frac{Hypotenuse}{Perpendicular}[/tex]
= [tex]\frac{AC}{BC}[/tex]
= [tex]\frac{\sqrt{2} }{1}[/tex]
= [tex]\sqrt{2}[/tex]
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Sebastian used his knowledge of exponents to simplify the following expression. Did he simplify correctly? If not, what mistake did
Sebastian make?
87.8-4.40
87+(-4).40
83.40
8³.0
0
Sebastian has solved the expression wrongly and the correct answer will be 536.
We are given the expression:
(87 × 8) - (4 × 40)
We need to simplify the expression.
For this, we need to follow the rule of PEMDAS.
So, we get that:
696 - 160
= 536
Sebastian has simplified it wrong as he has not followed the rule of PEMDAS and first subtracted 4 from 8.
Therefore, we get that, Sebastian has solved the expression wrongly and the correct answer will be 536.
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9. Michael needs 6 ½ feet of metal flashing to complete a household project. He has two small pieces measuring 3 1/8 feet and 1 ₴ feet. How many feet of metal flashing does Michc need to purchase?
The length of metal flashing needed to be purchase is [tex]1\frac{5}{8}[/tex] feet's.
How to find the length of feet he needs to purchase?He needs 6 ½ feet of metal flashing to complete a household project.
He has two small pieces measuring 3 1/8 feet and 1 3 / 4 feet.
Therefore, the length of metals for him to purchase can be calculated as follows;
The length he has = 3 1 / 8 + 1 3 / 4
The length he has = 25 /8 + 7 / 4
The length he has = 25 + 14/ 8
The length he has = 39 / 8 feet
Therefore
length required to purchase = [tex]6\frac{1}{2} - \frac{39}{8}[/tex]
length required to purchase = [tex]\frac{13}{2}-\frac{39}{8}[/tex]
length required to purchase = [tex]\frac{52-39}{8}[/tex]
length required to purchase = [tex]\frac{13}{8}[/tex] feet
Therefore,
length of metal flashing required to be purchase = [tex]\frac{13}{8}[/tex] feet = [tex]1\frac{5}{8}[/tex] feet
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Under her cell phone plan, Salma pays a flat cost of $55 per month and $5 per
gigabyte. She wants to keep her bill under $75 per month. Use the drop-down menu
below to write an inequality representing g, the number of gigabytes she can use
while staying within her budget.
Answer: 5
Step-by-step explanation:
The weight of meteorite A is 3 times the weight of meteorite B. If the sum of their weights is 92 tons, find the weight of each.
The weights of meteorite A and meteorite B are 69 tons and 23 tons respectively.
It is given in the question that the weight of meteorite A is 3 times the weight of meteorite B.
Also, the sum of their weights is 92 tons.
We have to find the weights of meteorite A and meteorite B.
According to the data given in the question,
Let the weight of meteorite B be x and,
The weight of meteorite A be 3x
Hence, we can write an algebraic equation,
3x + x = 92 tons
4x = 92 tons
x = 92/4 tons
x = 23 tons
Hence, 3x = 3*23 = 69 tons.
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Two fish tanks have measurements as shown.
Which tank has a greater volume? How much greater is its volume?
Use the drop-down menus to explain and show your answer.
8 ft
Choose.
Fish Tank A
The volume of fish tank A is Choose...
volume is greater by ose
Fish Tank B
Area of base: 25 ft²
Area of base: 40 ft²
4 ft
cubic feet, and the volume of fish tank B is
has a greater volume. Its
cubic feet. So fish tank Choose....
cubic feet
Step-by-step explanation:
sgshshsbhehdbdbdbsbehebebdbebd
can I get help with this one? Jaylen's equation is y=8.3x, I need help with the missing values only not the writing.
Based on Jaylen's equation and the distance, as well as the time, the missing values are:
Distance Time minutes
2.89 24.0
3 24.9
4.34 36.0
6 49.8
How to find the missing values?The missing values can be found by Jaylen's equation where y is the Time in minutes and x is the distance.
With a time of 24 minutes, the distance is:
24 = 8.3x
x = 24/8.3
= 2.89
With a distance of 3, time would be:
= 8.3x
= 8.3 (3)
= 24.9 minutes
With a time of 36 minutes:
= 36 / 8.3
= 4.34
With a distance of 6, the time is:
= 6 x 8.3
= 49.8 minutes
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What is the total surface area??
Check the picture below.
[tex]\stackrel{\textit{\LARGE Areas}}{ \stackrel{\textit{two triangles}}{2\left[\cfrac{1}{2}(\underset{b}{8})(\underset{h}{6}) \right]}~~ + ~~\stackrel{\textit{three rectangles}}{(14)(6)~~ + ~~(14)(8)~~ + ~~(14)(10)}} \\\\\\ 48~~ + ~~84~~ + ~~112~~ + ~~140\implies \text{\LARGE 384}~cm^2[/tex]
solve 11kx+13kx=6 for x
The solution of the equation 11kx+13kx= 6 is x = 1/(4k)
The given equation is 11kx+13kx = 6
To solve this equation first we have to take x as common and rearrange the equation, so we can group the like terms together
x(11k+13k) = 6
Add the like terms in the equation
x(24k) = 6
Move 24k to the right hand side of the equation
x = 6/(24k)
Here we have to simplify the value of x, for that we have to divide 6 by 24k in the equation
x = 1/(4k)
Hence, the solution of the equation 11kx+13kx= 6 is x = 1/(4k)
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Help I will. Give brainly
I really need this done in the next 10 minutes I will give 25 points please help asap
Answer:
Step-by-step explanation:
The graph starts at 70 and decreases by 5 temp after 15 mins
70
65 o
60 o
55 o
50
45
40
35
30
25
20
15
10
5 i i i
0 5 10 15 20 25 30 35 40 45 50
time
hey please help
Using the digits to (no more than once per digit), fill in the boxes to create three equivalent ratios.
You will get 15 points! or maybe even 20!
Solve question.
I will give you as many points as possible.
Answer : 3500
Reasoning 2589+2920+3500=9009
Then 9009/3 = 3003
Round 3003 to 3000 and there's your answer
A scale drawing of a car is presented in the following three scales. Order the scale drawings from smallest to largest. Explain your reasoning. (There are about 1.11.1 yards in a meter and 2.542.54 cm in an inch)
help me please ;-;
The order of the scales from smallest to largest would be,
inch, centimeter, yard, meter
In this question, we have been given a scale drawing of a car is presented in the following three scales.
We need to order the scale drawings from smallest to largest.
We know that,
1 cm = 2.54 inch
and 1 meter = 1.1 yards
We know that the metric conversion,
1 meter = 100 centimeters
And 1 cm = 2.54 inch
So, 1 meter = 254 inches
This means, meter is the largest scale and inch is the smallest scale.
1 yd = 91.44 cm
This means, yard is greater than centimeter.
Therefore, the order of the scales from smallest to largest would be,
inch, centimeter, yard, meter
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Please help, have no clue what I’m doing. Math is not my specialty
Find the three solutions to the equation y = 3x - 5 for the following values of x.
Enter your answers as an ordered pair in the form (x, y).
Enter the solution when = 0.
Enter the solution when a = -1.
Enter the solution when a = 2.
(Picture below)
Answer:
1_y=3(0)-5
y=0-5
y=-5
(0,-5)
2_y=3(-1)-5
y=-3-5
y=-8
(-1,-8)
3_y=3(2)-5
y=6-5
y=1
(2,1)
Step-by-step explanation:
jonh had 5 dish soap and shared 16 how many did he share
Answer:
16
Explanation:
It states the answer in the question. Unless you meant something else?
Hope this helps!
Have a good day :)
Answer: He shared 16.
Step-by-step explanation:
1. What value of x makes this equation true?
X/2-2= X/4+4
A. 4
B. 8
C. 16
D. 24
Please help me anyone :'( it would mean a lot!
The x value of 24 makes the equation to be true
How to determine the value of x in the equation?The equation is given as
x/2 - 2 = x/4 + 4
Add 2 to all sides of the equation
So, we have
x/2 = x/4 + 6
Subtract x/4 from all sides of the equation
So, we have
x/2 - x/4 = 6
Multiply through by 4
So, we have
2x - x = 24
So, we have
x = 24
Hence, the value of x in the equation is 24
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please help wth my mathsssssssss
Answer:
A = 1
B = 5
Step-by-step explanation:
I don't understand this can you help me?
The missing digits are 0, 4, and 5 in descending order
The complete division operation is
8 2 0 R 5
6 |4, 9 2 5
- 4 8
1 2
- 1 2
0 5
Division operationFrom the question, we are to determine the missing digits in the division operation
From the diagram,
The first two digits of the divided were divided by the divisor, this resulted into a quotient of 8 and a remainder of 1.
The divisor is 6
Let the value of the first two digits be x
Thus,
x / 6 = 8 1/6
x/6 = 49 / 6
By comparison,
The first two digits is 49
Therefore,
The dividend of the division operation is 4,925
Now, we can complete the division operation
8 2 0 R 5
6 |4, 9 2 5
- 4 8
1 2
- 1 2
0 5
Hence, the missing numbers are 0, 4, and 5
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Which of the following functions has an amplitude of 4 and a phase shift of pi over 4
The cosine function that has an amplitude of 4 and a phase shift of pi over 4 is given by:
f(x) = 4cos(2x - π/4) + 4.
How the cosine function is defined?The cosine function is defined as follows, considering it's coefficients:
y = acos(bx - c) + d.
The meaning of the coefficients is given as follows:
Coefficient a is the amplitude of the cosine function.Coefficient 2π/b gives the period of the cosine function.Coefficient c gives the phase shift of the cosine function.Coefficient d gives the vertical shift of the cosine function.In this problem, we want an amplitude of 4, hence coefficient a has a value of:
a = 4.
We also want a phase shift of π/4, hence the coefficient c has a value of:
c = π/4.
Among the given options, the one that gives a cosine function with the desired amplitude and phase shift is:
f(x) = 4cos(2x - π/4) + 4.
Which is the first option.
What is the missing information?The options are missing, and are given by the image at the end of the answer.
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suppose 39% of recent college graduates plan on pursuing a graduate degree. twenty one recent college graduates are randomly selected. a. what is the probability that no more than five of the college graduates plan to pursue a graduate degree? (do not round intermediate calculations. round your final answer to 4 decimal places.) b. what is the probability that exactly eight of the college graduates plan to pursue a graduate degree? (do not round intermediate calculations. round your final answer to 4 decimal places.) c. what is the probability that at least eight but no more than thirteen of the college graduates plan to pursue a graduate degree?
0.6054 is the probability that at least eight but no more than thirteen of the college graduates plan to pursue a graduate degree.
What are examples and probability?
It is predicated on the likelihood that something will occur. The justification for probability serves as the basic foundation for theoretical probability. For instance, the theoretical chance of receiving a head while tossing a coin is 12.this is binomial with parameter n=21 and p=0.39
a)
probability = P(X<=5)= ∑x=0x (nCx)px(1−p)(n-x) = 0.1124
b)
probability = P(X=8)= (nCx)px(1−p)(n-x) = 0.1763
c)
probability = P(8<=X<=13)= ∑x=x1x2 (nCx)px(1−p)(n-x) = 0.6054
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Can someone help and please hurry i don't have a lot of time
2.5, 10, 17, 26...
a Arithmetic, geometric, or neither?
c. Explicit:
b. Recursive:
Isaiah measured a house and made a scale drawing. In real life, the hall closet is 5 feet long. It is 10 inches long in the drawing. What is the drawing's scale factor?
Simplify your answer and write it as a fraction.
Answer: The answer is a scale factor of 6
Step-by-step explanation:
5 feet is 60 inches, and on the drawing the closet is 10 inches while the real closet is 5 feet, so just divide 60 by whatever gets you 10.
I need help with qeustion 36 please
Answer:
2x + 14
Step-by-step explanation:
8 + 2(x + 3) = 2x + 14
2x + 14 = 2x + 14
0 = 0; True
All real numbers
if tan x = -4/3 and x is in quadrant 2, then cos2x is
Step-by-step explanation:
Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. The correct option is C, -7/25.
What are Trigonometric Identities?
Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. There are several trigonometric identities relating to the side length and angle of a triangle.
Given that the value of tan(x) = -4/3 and x is in quadrant 2.
In order to find the value of cos(2x), we can use the trigonometric identity of cos(2x), therefore, for cos(2x) we can write,
\cos(2x) = \dfrac{1-\tan^2(x)}{1+\tan^2(x)}cos(2x)=
1+tan
2
(x)
1−tan
2
(x)
Since the value of tan(x) is known, substitute the value in the identity,
\begin{gathered}\cos(2x) = \dfrac{1-(-\frac{4}{3})^2}{1+(-\frac{4}{3})^2}\\\\\cos(2x) = \dfrac{1-(\frac{16}{9})}{1+(\frac{16}{9})}\\\\\end{gathered}
cos(2x)=
1+(−
3
4
)
2
1−(−
3
4
)
2
cos(2x)=
1+(
9
16
)
1−(
9
16
)
cos(2x) = (-7/9) × (9/25)
Cancelling 9 from the numerator and the denominator,
cos(2x) = -7/25
Hence, if tanx=-4/3 and x are in quadrant 2 then cos2x=-7/25.
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given f(x)=3x-4 find f(4)
Answer:
f(4) = 8
Step-by-step explanation:
Hello!
You can find f(4) by substituting 4 for x in 3x - 4.
Evaluate f(4)f(x) = 3x - 4; x = 4f(4) = 3(4) - 4f(4) = 12 - 4f(4) = 8The value of f(4) is 8.
Answer:
Step-by-step explanation:
h(x)=-2x-3 h(6)