Answer:
B) 3 radians
Step-by-step explanation:
The arc length is the product of the radius and angle. You have ...
... 3 radians = 1 × angle
so
... 3 radians = angle
_____
Comment on units
The formula is
... s = rθ . . . . . where s is the arc length, r is the radius, and θ is the central angle in radians.
The units of both s and r are units of length, so the units of angle are ...
... (length units)/(length units) = <no units>
That is, "radians" are fully equivalent to "no units."
The trouble with this problem statement is that it expresses "arc length" in units of "radians." This only works if the units of the radius of the unit circle are "no units". Ordinarily, that would not be the case. The length of the radius of the unit circle is usually "one length unit." If the central angle is 3 radians, then the arc length is "3 length units," not "3 radians."
Huntington Park officials approved a rectangular plot of land for a Japanese Zen garden. Is it sufficient to know that opposite sides of the garden plot are congruent and parallel to determine that the garden plot is rectangular? Explain
Answer: No, it is not sufficient to know that opposite sides of the garden plot are congruent and parallel to determine that the garden plot is rectangular.
Step-by-step explanation:
1. You have the following information given in the problem:
- Opposite sides of the garden plot are congruent.
- Opposite sides of the garden plot are parallel.
2. Therefore, keeping the information above on mind, you can conclude that the description is about a parallelogram, but to determine that it is rectangular, you need to know that the four interior angles measure 90° and the diagonals are congruent.
One square tile on your kitchen floor is 11.2511.25 inches long. It takes 12.512.5 tiles to cover the length of the floor. About how long is the floor?
Answer:
Length of the floor is about 11.75 feet.
Step-by-step explanation:
It is given that, it takes 12.5 tiles to cover the length of the floor.
The length of each square tile is 11.25 inches. So, if 12.5 tiles each of length 11.25 inches are joined, we will get to know the length of the floor.
So, the length of the floor is,
[tex]11.25 \times 12.5[/tex]
[tex]=140.625 \text {in}[/tex]
So the length of the floor is 140.625 inches or we can say roughly about 141 inches.
We can convert this length into feet.
1 feet = 12 inches, so the length of the floor in inches is,
[tex]\frac{141}{12} =11.75 \text {ft}[/tex]
So the length of the floor is 11.75 feet.
Please help on this one ?
Answer:
A
Step-by-step explanation:
The expansion of (x +y)⁴ is ...
... x⁴ +4x³y +6x²y² +4xy³ +y⁴
The expansion coefficients are 1, 4, 6, 4, 1; the sum of exponents is always 4, and there are 5 terms.
C = F Based on the given information, choose the similarity statement that you would use to say ABC~DEF. If you could NOT conclude the triangles similar, then choose NOT. AA SAS SSS NOT
Answer:
Might not be congruent
Step-by-step explanation:
You don't have enough information
Answer with explanation:
It is given that,In ΔABC and Δ DEF
∠C =∠F⇒⇒[Given]
To prove that two triangles are similar, we can use following Similarity axiom which are
a.→ AA
b.→S AS
c.→SSS
→Ratio of sides of two triangles should be proportional while proving similarity of two triangles.
But, Here between two triangles , only one angle is congruent ∠C and ∠F.So, we can't conclude that these two triangles that is, ΔABC and Δ DEF are similar.
Option D:→ Not
The number of students at Marita`s school decreased to 90% of last year's number. Last year, there were 1,500 students. How many students are there this year
Answer:
1350
Step-by-step explanation:
We can write a proportion to find the total amount in the school this year using the information given. A proportion is two equivalent ratios set equal to each other. If 10% has decreased, then 90% is now left.
[tex]\frac{10}{100}=\frac{y}{1500}[/tex]
We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.
10(1500)=100(y)
15000=100y
y=150
Y is the number of students who are now gone. We subtract 1500-150=1350
Sue buys material for a costume she buys 1.75 yards of red material. . She buys 1.2times as much yards of material. How many yards of blue material will she need
Answer:
2.1 yards of blue material will she need.
Step-by-step explanation:
As per the given statement: Sue buys material for a costume she buys 1.75 yards of red material.
As she bought 1.75 yards of the red material.
For blue material she bought 1.2 times as much as yard of the red material.
"times" represents multiply
Blue material she will need = [tex]1.2 \times 1.75 = 2.1 yards[/tex]
therefore, 2.1 yards of blue material will she need.
Anthony who is 5 feet tall stands 20 feet from a lamppost and casts a shadow that is 10 feet long. If he moves 5 feet closer to the lamppost how long will his shadow be?
Factor the trinomial below
6x^2-9x-6
A. 3(2x+1)(x-2)
B. 3(2x=6)(x-1)
C. 3(2x+2)(x-1)
D. 3(2x+1)(x-6)
For this case we must factor the following expression: [tex]6x ^ 2-9x-6[/tex]
We test the options:
Option A:
[tex]3 (2x + 1) (x-2) =[/tex]
We apply distributive property for the first parenthesis:
[tex](6x + 3) (x-2) =[/tex]
We apply distributive property of the form:
[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]
[tex]6x ^ 2-12x + 3x-6 =[/tex]
Different signs are added and the sign of the major is placed.
[tex]6x ^ 2-9x-6[/tex]
So, [tex]3 (2x + 1) (x-2) = 6x ^ 2-9x-6[/tex]
Answer:
Option A
Consider the function f(x)=−23x+1.
What is f(3)?
Each unit costs 14p how much does942 cost?????????????????????????????????????????????????????????????????????????????????????????????????????????????????
Answer:
13188
Step-by-step explanation:
The distance from the school to the corner is 0.9 kilometers. How many meters is this?
Nancy is 5 yrs younger than her brother stan last year she was half as old as he was how old are they both
Answer: 11 and 6
Step-by-step explanation:
I think this is it because she is 5 years younger and last year she was half of his age so he was 10 then you have to add another year to their age because that was last year, 5+1=6, 10+1=11. but im not completely sure so if you can wait for someone else or if you agree go ahead and answer it.
We'll call the ages n and s
Nancy is 5 yrs younger than her brother Stan
n = s - 5
Last year she was half as old as he was
n - 1 = (1/2) ( s - 1 )
We substitute for n
s - 5 - 1 = (1/2) (s - 1)
2s - 12 = s - 1
s = 11
n = s - 5 = 6
Answer: Nancy is 6, Stan is 11
Check:
Clearly they're five years apart. Last year they were 5 and 10, half, good.
Find h(x) if it is known that h(x+5)=3x+18.
[tex]h(x+5)=3x+18\\\\h(x)=mx+b\to h(x+5)=m(x+5)+b=mx+5m+b\\\\\text{Therefore we have}\ m=3\ \text{and}\\\\5m+b=18\to5(3)+b=18\\\\15+b=18\qquad\text{subtract 15 from both sides}\\\\b=3\\\\Answer:\ \boxed{h(x)=3x+3}[/tex]
To find the function h(x) when given h(x+5)=3x+18, we substitute x with (x-5) in 3x+18 to make h(x) = 3x+3.
Explanation:To find the function h(x), we need to replace (x+5) in the equation with x. The given equation is h(x+5)=3x+18.
We know that if we substitute x+5 with x in h(x+5), we must also substitute the x in 3x+18 with (x-5) to keep the equation and function consistent.
So, we replace x with (x-5) in 3x+18, and our new equation will be 3(x-5)+18.
This simplifies to 3x - 15 + 18, which further simplifies to 3x+3.
Consequently, the function h(x) = 3x+3.
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Real estate values in a town are increasing at a rate of 14% per year.
Mrs. Knoxville purchased a building for $590,000 in 2012.
How much can she expect to sell the building for in 2020, assuming this trend continues?
Enter your answer in the box.
Round to the nearest whole dollar.
Answer:
$1,093,026
Step-by-step explanation:
We have been given that real estate values in a town are increasing at a rate of 14% per year. Mrs. Knoxville purchased a building for $590,000 in 2012.
We are told that real estate values are increasing at a rate of 14%, this means that values of real estates are increasing exponentially.
Since we know that an exponential function is in form: [tex]y=a*b^x[/tex]; for growth b=(1+r), where r= growth rate in decimal form.
a= Initial value.
Let E(t) be value of real estates t years after 2012. Now let us substitute our given values in exponential function form.
Upon converting our increase rate to decimal form we will get,
[tex]14\text{ percent}=\frac{14}{100}=0.14[/tex]
[tex]E(t)=590,000*(1+0.14)^t[/tex]
[tex]E(t)=590,000*(1.14)^t[/tex]
Now let us substitute the value for building in 2020 by substituting t=8 as 2020-2012=8.
[tex]E(2020)=590,000*(1.14)^8[/tex]
[tex]E(2020)=590,000*2.8525864220672256[/tex]
[tex]E(2020)=1,683,025.989019663104\approx 1,683,026[/tex]
Now let us subtract 590,000 from 1683026 to find the amount that Mrs. Knoxville can get from selling the building.
1,683,026-590,000=1,093,026
Therefore, Mrs. Knoxville can get $1,093,026 from selling the building.
Find the cos(Θ) of an angle in standard position if the terminal side passes through the point (4, -8).
Note: Answer choices attached below
Look at the picture.
[tex]r=\sqrt{x^2+y^2}-\text{from the Pythagorean theorem}\\\\\sin\theta=\dfrac{y}{r}\\\\\cos\theta=\dfrac{x}{r}\\\\\tan\theta=\dfrac{y}{x}\\\\\cot\theta=\dfrac{x}{y}[/tex]
We have the point
[tex](4,\ -8)\to x=4,\ y=-8[/tex]
Calculate r:
[tex]r=\sqrt{4^2+(-8)^2}=\sqrt{16+64}=\sqrt{80}=\sqrt{16\cdot5}=\sqrt{16}\cdot\sqrt5=4\sqrt5[/tex]
Substitute:
[tex]\cos\theta=\dfrac{4}{4\sqrt5}=\dfrac{1}{\sqrt5}\to\boxed{C)}[/tex]
Phyllis Doran worked at Symmes Medical Center for 7 1/2 hours on Monday and from 8:00 a.M. Until 1:00 p.M. On Tuesday What is the total number of hours she worked
Final answer:
Phyllis Doran worked a total of 12.5 hours between Monday and Tuesday at Symmes Medical Center.
Explanation:
Phyllis Doran worked a total of two different shifts across Monday and Tuesday. On Monday, she worked for 7 1/2 hours. On Tuesday, she started at 8:00 a.m. and finished at 1:00 p.m., which is a 5-hour shift.
To find the total number of hours Phyllis worked, we add the hours from both days together.
Monday: 7.5 hours
Tuesday: 5 hours (since 1:00 p.m. is 5 hours after 8:00 a.m.)
Now, we sum these up:
Total hours worked = 7.5 hours + 5 hours = 12.5 hours.
So, Phyllis Doran worked a total of 12.5 hours between Monday and Tuesday at Symmes Medical Center.
Which expression is equivalent to 5x - 5x + 3x - 3x?
A) -16x
B) -4x
C) 4x
D) 0 what the answer
The simplification form of the expression 5x - 5x + 3x - 3x is 0 option (D) is correct.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The linear expression is:
= 5x - 5x + 3x - 3x
After simplification:
= 0 + 3x - 3x
= 0
All terms are canceled out,
Thus, the simplification form of the expression 5x - 5x + 3x - 3x is 0 option (D) is correct.
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The centre of each semicircle is on DC.
Work out the area of the shaded region.
Give your answer correct to 3 significant figures.
The shaded region, which is approximately 251.74 cm².
For the area of the shaded region, we need to calculate the area of a trapezium and the area of two semicircles.
Given data: AB = 28 cm , DC = 12cm and h = 14 cm
The formula for the Area of Trapezium:
Area of trapezium = 1/2 × (AB + DC) × h
Substituting the given values:
Area of trapezium = 1/2 × (28 + 12) × 14 = 280 cm²
The formula for the Area of a Semicircle:
Area of semicircle = πr²/2
Given that the radius r is 3 cm:
Area of two semicircles = 2 × π × 3²/2 = 28.26 cm²
Area of the Shaded Region:
Area of shaded region = Area of trapezium - Area of two semicircles
Area of shaded region = 280 - 28.26 ≈ 251.74 cm²
Therefore, the area of the shaded region is approximately 251.74 cm².
Six groups of students at 162 balloons at school carnival with three students in each group
Answer:
9 balloons per student and 27 per group of 3 students.
Step-by-step explanation:
We have 6 groups of students with 3 students in each group. This means in group 1 there is 3. Groups 2 has 3. Group 3 has 3. Group 4 has 3. Group 5 has 3. Group 6 has 3.
So there are 3+3+3+3+3+3=18 total students.
The school carnival has 162 balloons, how much will each student have?
We will divide 162 balloons by the total number of 18.
162/18=9
9 balloons per student and 27 per group of 3 students.
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If AB is congruent to BC, can you prove the triangles congruent by SAS. Please explain why or why not.
Answer:
no
Step-by-step explanation:
SAS stands for side angle side. so in this question we know that one side is equal to another side, but we don't know wether or not there is another angle and another side that is congruent. so for that reason it is not congruent by SAS.
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You need a 70% alcohol solution. On hand, you have a 200 mL of a 35% alcohol mixture. You also have 90% alcohol mixture. How much of the 90% mixture will you need to add to obtain the desired solution?
Add 350 mL of the 90% alcohol mixture to obtain a 70% alcohol solution.
Let V be the volume of the 90% alcohol solution needed
Set up the equation
The final mixture volume will be 200 + V mL.
- The total amount of alcohol in the final mixture should be 70% of the total volume.
Calculate the total amount of alcohol
- Amount of alcohol from 200 mL of 35% solution: 0.35 * 200 = 70 mL.
- Amount of alcohol from V mL of 90% solution: 0.90 * V mL.
Total amount of alcohol in the final solution
- Total alcohol = 70 + 0.90V mL.
Set up the equation for the final concentration
- Final concentration: 70%
0.70 *(200 + V) = 70 + 0.90V
Solve the equation
0.70 * (200 + V) = 70 + 0.90V
140 + 0.70V = 70 + 0.90V
140 - 70 = 0.90V - 0.70V
70 = 0.20V
V = 70 / 0.20 = 350 mL.
Mr. Andrews has a classroom of 45 students. He wants to divide them equally into 5 teams for a group project.
How many students will be on each team? what the answer
Answer:
9
Step-by-step explanation:
45/5 = 9
Please help! Urgent!
What is the measure of angle B?
-78°
-92°
-102°
-282°
If Tonya bought 1/6 pounds of bologna and 3/8 pounds of ham and 2/4 pound turkey and that cost $5.99 what is the total number of pounds of meat processed
Answer:
25/24 pounds of total meat processed.
Step-by-step explanation:
We have been given pounds of bologna and 3/8 pounds of ham and 2/4 pound turkey
And we need to find the total number of pounds of meat processed.
The total number will be calculated by finding their sum of all the meats which is
1/6+3/8+2/4
Taking LCM of (6,8,4)=24 hence, we get:
1/6+3/8+2/4= 25/24
The lee family buys a new car that has a sales price of 35,000. If the car dealer requires minimum down payment of 15% what is the minimum down payment the lees must pay for their car?
Answer:5250.00
Step-by-step explanation: percents are a multiplication so 35,000×15=5250.00
Answer:
$5,250
Step-by-step explanation:
The less must pay a minimum down payment that is equivalent to 15% the sales price of the new car.
Given that the price of the new car is $35,000, the product of 15% with this amount will equal the down payment.
As such, the down payment
= 15% * $35,000
= 0.15 * $35,000
= $5,250
Apple stock plummets and now you have to decide if you hold onto your stock in the hopes that it goes back up, or sell it at a loss. Apple stock is now selling or $54.76 a share. You have 2 shares. When you first bought them their total value was $226.10. What is their total value now?
The total value of 2 Apple shares at $54.76 each is $109.52, resulting in a loss of $116.58.
To calculate the total value of your Apple stock now, we'll first determine the total value of your shares at their current price and then compare it to their original total value.
Current price per share: $54.76
Number of shares you own: 2
Total value of your shares now:
= Current price per share × Number of shares
= $54.76 × 2
= $109.52
Original total value of your shares: $226.10
Now, let's compare the current total value with the original total value:
Current total value: $109.52
Original total value: $226.10
As the current total value is less than the original total value, it indicates a loss.
To find out the loss incurred, we subtract the current total value from the original total value:
Loss = Original total value - Current total value
= $226.10 - $109.52
= $116.58
Therefore, the total value of your Apple stock now is $109.52, and you have incurred a loss of $116.58.
The total value of your 2 shares of Apple stock now is $109.52.
To determine the total value of your Apple stock now, we first need to calculate the total value of the stock when you first bought it and then compare it to the current value.
1. Initial Total Value: You initially bought 2 shares of Apple stock. Let's denote the initial price per share as P. The total value initially is the product of the number of shares and the initial price per share.
Initial total value = Number of shares * Initial price per share
Initial total value = 2 shares * Initial price per share = $226.10
2. Initial Price per Share: To find the initial price per share, we divide the initial total value by the number of shares.
Initial price per share = Initial total value / Number of shares
Initial price per share = $226.10 / 2 shares = $113.05 per share
3. Current Total Value: Now, we find the current total value of your 2 shares at the current price per share, which is $54.76.
Current total value = Number of shares * Current price per share
Current total value = 2 shares * $54.76 per share = $109.52
So, the total value of your 2 shares of Apple stock now is $109.52.
What are the next three terms of 50,150,450,1350,...
Answer: 4,050, 12,150, 36,450
Step-by-step explanation: multiply each following number by 3
Answer:
4050; 12150; 36450
Step-by-step explanation:
[tex]a_5 = 50.3^4 \\\ a_5 = 4050 \\\ a_6 = 50.3^5 \\\ a_6 = 12150 \\\ a_7 = 50.3^6 \\\ a_7 = 36450[/tex]
I hope I helped you.
If there are 150 students surveyed and 23% is English 30% Science 15% Social Studies and Music is 12% What would the percent be for math be?
Answer:
it would be 20%
Step-by-step explanation:
out of 100% you would subtract the 23%, 30%, 15% and, 12% and you would get 20%
a new car has a sticker price of 20950 while the invoice price paid was 18750. what is the dealer markup
11.73%
Step-by-step explanation:
What is the value of x in the equation 2^2x = 2^3?
A.) x = 1.5
B.) x = 3
C.) x = 64
D.) x = 0.28
Answer:
B
Step-by-step explanation: