area = pi x r^2
615.75 = 3.14 x r^2
r^2 = 615.75/3.14 =196.0987 round to 196.1
r = sqrt(196.1) = 14.00357 round to 14
radius = 14 kilometers
For the past two years Lynda Santana has recorded the costs of operating her car. They total $1,600 (fixed costs) and $2,134 (variable costs). She has driven a total of 14,000 miles. What was her cost per mile?
A certain forest covers an area of 1800 km2. Suppose that each year this area decreases by 8.5%. What will the area be after 14 years? Use the calculator provided and round your answer to the nearest square kilometer.
[tex]519km^{2}[/tex] will be the area after [tex]14[/tex] years.
What is area?
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
According to questions, a certain forest covers an area of [tex]1800[/tex] [tex]km^{2}[/tex]. Each year this area decreases by [tex]8.5[/tex]%.
We have to find the area after 14 years.
Area after 14 years can be found using the below formula
[tex]A=I(1-r)^{t}[/tex]
[tex]=1800(1-0.085)^{14}[/tex]
[tex]=1800[/tex]×[tex]0.288[/tex]
[tex]=519km^{2}[/tex]
Hence, [tex]519km^{2}[/tex] will be the area after [tex]14[/tex] years.
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If 3 times a certain number is increased by 4 the result is 28. What is the number?
If x is "the number," which of the following equations could be used to solve for the number?
c.3x + 4 = 28
b.3(x + 4) = 28
a.3x = 4 + 28
x = number
the equation to use is: 3x+4=28
3x+4=28
3x=24
x-24/3 =8
x=8
the question isssssssss
The length of a rectangle is 4 cm greater than its width. the perimeter is 32 cm. find the length of the rectangle. 12 cm 18 cm 10 cm 6 cm
Type the correct answer in the box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use / for the fraction bar. Simplify the expression. tan(-x) cos(-x) =
Answer:
The correct simplification of the given expression [tex]tan(-x){\times}cos(-x)[/tex] is [tex]-sinx[/tex].
Step-by-step explanation:
The given expression is:
[tex]tan(-x){\times}cos(-x)[/tex]
Now, simplifying the above given expression, we get
=[tex]\frac{sin(-x)}{cos(-x)}{\times}cos(-x)[/tex] (because [tex]tanx=\frac{sinx}{cosx}}[/tex])
=[tex]sin(-x)[/tex]
Also, we know that [tex]sin({-\theta})=-sin{\theta}[/tex], tehrefore teh expression becomes
=[tex]-sinx[/tex]
Hence, the correct simplification of the given expression [tex]tan(-x){\times}cos(-x)[/tex] is [tex]-sinx[/tex].
Use the graph below to fill in the blank with the correct number:
f(−2) = _______
Numerical Answers Expected!
Answer for Blank 1:
Which ordered pairs make both inequalities true? Check all that apply.
(–2, 2)
(0, 0)
(1,1)
(1, 3)
(2, 2)
Answer:
the answers are c and e 1,1 and 2,2
Step-by-step explanation:
Answer:
(1,1) (2,2)
Step-by-step explanation:
(05.07 MC)
The net of a square pyramid is shown:
What is the surface area of the figure?
0.65 square inch
0.50 square inch
0.40 square inch
0.25 square inch
Answer:
0.65 square inch
Step-by-step explanation:
Each triangle has an area given by ...
A = 1/2bh = 1/2·(0.5 in)(0.4 in) = 0.10 in²
The square base has an area given by ...
A = s² = (0.5 in)² = 0.25 in²
The total area is that of the square base and 4 triangles:
S = 0.25 in² + 4×0.10 in² = 0.65 in²
Answer:
0.65 square inch
Step-by-step explanation:
5 radians is the same as _____.
Answer:
286.5 degrees
Step-by-step explanation:
We want to change radians to degrees
2 pi radians = 360 degrees
5 radians * 360/ 2 pi
900/pi degrees
286.4788976 degrees
286.5 degrees
Answer: 286.48 degrees
Step-by-step explanation: We are trying to find the number of degrees. The equation to convert radians to degrees radian x 180/π. Plug in 5 for x.
5 x 180/π = 286.48
5 radians is the same as 286.48 degrees.
Let , −3−8 be a point on the terminal side of θ . find the exact values of sinθ , cscθ , and cotθ .
The exact values for sinθ, cscθ, and cotθ given the point (-3, -8) are sinθ = -8/√73, cscθ = √73/-8 (because sinθ and cscθ are negative in the third quadrant), and cotθ = 3/8 (positive since sin and cos signs cancel out).
The question involves finding the values of sinθ, cscθ, and cotθ given a point (-3, -8) on the terminal side of an angle θ. To find these values, we first need to determine the radius (r) of the corresponding right triangle formed by the point (-3, -8) and the origin (0, 0). The radius can be calculated using the Pythagorean theorem:
r = √((-3)2 + (-8)2) = √(9 + 64) = √73
Using the definitions of the trigonometric functions:
sinθ = opposite/hypotenuse = -8/√73cscθ = 1/sinθ = √73/-8cotθ = adjacent/opposite = -3/-8 = 3/8Note that θ is in the third quadrant where both sine and cosine are negative; hence, sinθ and cscθ are negative, while cotθ is positive due to both the numerator and denominator being negative.
HELP ROUND 87671.5613658 TO THE NEAREST THOUSAND
Which one of the binomials is a factor of this trinomial?
x^2-13x+40
A. x-8
B. x+8
C. x-4
D. x+4
Derive the equation of the parabola with a focus at (2, –1) and a directrix of y = – .5
help me please!! Find the measure of angle 2. Image attached
opposite angles = 180
180-49 = 131
angle 2 = 131 degrees
A principal of $4700 is invested at 6% interest compounded annually. How much will the investment be worth after 12 years Use the calculator provided and round your answer to the nearest dollar.
Solve the equation by completing the square. Round to the nearest hundredth if necessary x^2+3x=25
Answer:
The solutions are: [tex]x= 3.72, -6.72[/tex]
Step-by-step explanation:
[tex]x^2+ 3x = 25\\ \\ x^2+3x+(\frac{3}{2})^2 = 25 +(\frac{3}{2})^2\\ \\ (x+\frac{3}{2})^2 = 25+\frac{9}{4}\\ \\ (x+\frac{3}{2})^2 =27.25\\ \\ \sqrt{(x+\frac{3}{2})^2} =\pm \sqrt{27.25} \\ \\ x+1.5= \pm \sqrt{27.25} \\ \\ x= -1.5 \pm \sqrt{27.25}\\ \\ x=-1.5+ \sqrt{27.25}=3.72015... \approx 3.72\\ \\ or\\ \\ x=-1.5-\sqrt{27.25} =-6.72015...\approx -6.72[/tex]
So, the solutions are: [tex]x= 3.72, -6.72[/tex]
someone help I don't get it
The value of a camcorder bought new for $2000 decreases 20% each year. Identify the function for the value of the camcorder. Does the function represent growth or decay?
A) V(t) = 2000(0.8)t; growth
B) V(t) = 2000(0.8)t; decay
C) V(t) = 2000(1.2)t; decay
D) V(t) = 2000(1.2)t; growth
Answer: V(t) = 2000(0.8)t; decay
Step-by-step explanation:
A movie theater sold 1200 tickets and made $6400 in one night. If an adult ticket costs $7 and a children's ticket costs $3, how many adult tickets were sold?
A. a + c = 1200
7a + 3c = 6400
B. a c = 1200
7a 3c = 6400
C. a + c = 6400
7a + 3c = 1200
D. a + c = 10
7a + 3c = 7600
The data in the form of the equation can be written as a + c = 1200 and 7a + 3c = 6400. The correct option is A.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a movie theatre sold 1200 tickets and made $6400 in one night. If an adult ticket costs $7 and a children's ticket costs $3.
The expression in the form of the equation can be written as below,
a + c = 1200
7a + 3c = 6400
The correct system of equations will be option A.
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The formula is used to find the area of a parallelogram. if the base of a parallelogram is doubled and its height is doubled, how does this affect the area?
Issac is standing 174 feet from the base of the South Carolina State House in Columbia. The angle formed by the ground and the line segment from his position to the top of the building is 46°. How tall is the SC State House? Round to the nearest foot.
Using the tangent function of trigonometry, the height of the South Carolina State House is calculated to be approximately 180.2 feet. When rounded, the building stands at an estimated 180 feet tall.
To calculate the height of the South Carolina State House, we can use trigonometry. Given that Issac is standing 174 feet from the base and the angle of elevation to the top of the building is 46°, we can use the tangent function to determine the height of the building. The tangent of an angle in a right triangle is the ratio of the opposite side (the height of the building in this case) to the adjacent side (the distance from Issac to the building).
Using the formula:
tangent (angle) = opposite/adjacent
The equation would be:
tangent (46°) = height of building / 174 feet
Solving for the height of the building:
height of building = 174 feet * tangent (46°)
Using a calculator with the tangent function:
height of building = 174 * 1.035530 (approx value of tangent (46°))
So:
height of building ≈ 180.2 feet
Rounded to the nearest foot, the height of the South Carolina State House is approximately 180 feet.
Outside a home, there is a 6-key keypad that can be used to open the garage if the correct four-digit code? is entered. (a) How many codes are possible? (b) What is the probability of entering the correct code on the first try, assuming that the owner doesn't remember the code?
Answer:
The total number of codes is found with
[tex]P_{n}^{r} =n^{r}[/tex]
This formula is applied when we have to find combinations where the order matters, and each element can be used more than once, as happens with codes, there can be repetitions of numbers.
So, [tex]n[/tex] represents the total number of elements which are 6, and [tex]r[/tex] represents the total digits per code, which are 4.
Replacing these values, we have
[tex]P_{6}^{4} =6^{4}=1296[/tex]
This means there are 1296 possible codes.
Now, if the owner doesn't remember the code, the probability of entering the correct code on the first try would be
[tex]P=\frac{1}{1296}=0.0008 (or \ 0.08\%)[/tex]
This means that it's nearly impossible to enter the right code at once.
Write the equation of a hyperbola with vertices (3, -1) and (3, -9) and co-vertices (-6. -5) and (12, -5).
Convert 28.7251° to degrees, minutes, and seconds. Round to the nearest second.
28.7251 =
28 degrees
then take the decimal and multiply by 60 to get the minutes
so 0.7251 *60 = 43.506, use the whole number (43)
so now you have 28 degrees, 43 minutes
now take the remaining decimal ( 0.506) and multiply by 60
0.506*60= 30.36
when you have a decimal left over for the seconds, keep that as is.
so you now have 28 degrees, 43 minutes and 30.36 seconds
use ' for minutes and " for seconds
28 degrees 43' 30.36"
rounded to the nearest second would be 28 degrees 43 minutes and 30 seconds
Here is 1 red marble, 2 green marbles, and 5 blue marbles.you draw two marbles from the urn, but replace the first marble before drawing the second. find the probability that the first mable is blue and the second is green.
Triangle PIG was rotated to create triangle P'I'G'. Describe the transformation using details and degrees.
What is best definition of combining like terms
At a crime scene police find a person in Myrtle Beach shot while sunbathing on the pier. The pier is 20 feet high. The shot came 20 degrees from the parallel. How far was the shooter standing down the beach when the gun was fired?
Select one:
a. 30 feet away
b. 45 feet away
c. 55 feet away
d. 70 feet away
A person was hiking on a trail in Greenville County Park they were shot in the leg. Before he was shot, he had climbed to a height 45 vertical feet from the bottom of the mountain. The shooter was at angle of 40 degrees parallel to the mountain. How far was the shooter when he shot the person?
Select one:
a. 32 feet
b. 87 feet
c. 54 feet
d. 18 feet
A police officer shot a man running from a crime scene on a bridge that was 100 feet high. The bullet struck the victim 25 degrees to the parallel. Approximately how far away was the police officer when she fired her weapon?
Select one:
a. 500 feet
b. 380 feet
c. 217 feet
d. 78 feet
Solve 3(2x - 4) < 2(x + 4)