Answer:
On edg it's 2kpi
Step-by-step explanation:
i took the test
The exact solution of the equation will be;
⇒ x = 2kπ
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ sin²x + 3cos x - 1 = 2
Now,
Since, The equation is,
⇒ sin²x + 3cos x - 1 = 2
We know that;
⇒ sin²x = 1 - cos²x
Substitute above value in equation (i), we get;
⇒ 1 - cos²x + 3cos x - 1 = 2
⇒ cos²x - 3 cos x + 2 = 0
⇒ cos²x - (2 + 1)cos x + 2 = 0
⇒ cos²x - 2cos x - cos x + 2 = 0
⇒ cos x (cos x - 2) - 1 (cos x - 2) = 0
⇒ (cos x - 2) (cos x - 1) = 0
This gives two solution,
⇒ cos x = 2
But it is not possible because the value of cos x is in between - 1 and 1.
⇒ cos x = 1
⇒ x = 2kπ + 0°
⇒ x = 2kπ
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A circular swimming pool has a radius of 28 feet there’s a path all the way around the pool dad 4 feet wide inference is going to be built around outside edge of the pool by about how many feet of fencing are needed to go around the pool path
Answer:
201.06 (2 decimal places)
Step-by-step explanation:
new radius 28 + 4 = 32
diameter = 64
circumference of the fence
= pi x d
= pi x 64
= 201.0619
Mandy built a pyramid for her project on Egypt with a volume of 483
4
in.3 Find the area of the base of the pyramid.
Answer
We have,
Volume of pyramid = 4834 in³
Base area of the pyramid = ?
Assuming height of the pyramid = 20 in
We know that
Volume of pyramid =[tex]\dfrac{hlw}{3}[/tex]
[tex] 4834=\dfrac{20\time lw}{3}[/tex]
l w = 725.1 in²
Hence, area of the base of the pyramid is equal to 725.1 in².
At the start of the week, you could complete 12 push-ups. By the end of the week, you could complete 17 push-ups. Which proportion could you use to find the percent increase in the number of push-ups you can complete? ( please pick one of these answers) A) 5/17=n100 B) 12/5=n100 C) 12/17=n100 D) 5/12=n100
Recall the formula S A = 2 pi r squared + 2 pi r h.
216 pi inches squared
252 pi inches squared
630 pi inches squared
648 pi inches squared
Answer: The surface area for this cylinder is 252*pi square inches.
Step-by-step explanation:
The surface area of a cylinder can be calculated by using the following formula:
surface area = 2*pi*r² + 2*pi*r*h
Applying the data from the problem, we have:
surface area = 2*pi*(6)² + 2*pi*(6)*15
surface area = 2*pi*36 + 180*pi
surface area = 72*pi + 180*pi
surface area = 252*pi
The surface area for this cylinder is 252*pi square inches.
Step-by-step explanation: edge 2021
The surface area of the cylinder, given h = 15 inches and r = 6 inches, is 252π square inches.
To find the surface area (SA) of a cylinder, we use the formula [tex]\(SA = 2\pi r^2 + 2\pi rh\)[/tex], where r is the radius and h is the height. Given h = 15 inches and r = 6 inches, we substitute these values into the formula:
[tex]\[SA = 2\pi(6)^2 + 2\pi(6)(15)\][/tex]
[tex]\[SA = 2\pi(36) + 2\pi(90)\][/tex]
[tex]\[SA = 72\pi + 180\pi\][/tex]
[tex]\[SA = 252\pi\][/tex]
Thus, the surface area of the cylinder is 252π square inches. This includes the areas of the two circular bases and the lateral surface area formed by the curved surface.
factor the trinomial (worth 10 points)
X^2-4x+3
Answer:
The factors are..
1,3
Step-by-step explanation:
Hence we see that:
x2+4x+3= (x+3)(x+1)
Therefore the factors are
x= 3 or 1
Answer:
(x-1)(x-3)
Step-by-step explanation:
-3 times -1 equals 3 which is the number at the end
and -3-1=-4 which is the number in the middle
the put -3 and -1 into 2 different parentheses
(x-3)(x-1)
PLEASE HELP ME
Mean: $620 Median: $610 Mode: $600
The following statistics represent weekly salaries at the Midtown Construction Company: First quartile: $580
Third quartile: $645 85th percentile $685
c. About what percent of employees’ salaries surpassed $645?
d. About what percent of employees’ salaries surpassed $685?
e. If the company has 100 employees, what is the total weekly salary of all employees?
The mean, median, and mode of the weekly salaries at the Midtown Construction Company are provided. We can use this information to answer questions about the percentage of salaries surpassing certain values and the total salary of all employees.
Explanation:To answer the question, we need to understand what each statistical term means.
The mean is the average of a set of numbers. In this case, the mean salary is $620.
The median is the middle value of a set of numbers when they are arranged in ascending order. In this case, the median salary is $610.
The mode is the value that appears most frequently in a set of numbers. In this case, the mode salary is $600.
Now, let's answer the questions:
c. To find the percentage of employees' salaries that surpassed $645, we need to calculate the percentage of values that are greater than $645 in the data set. Since the third quartile is $645, we know that 75% of the salaries are less than or equal to $645. Therefore, about 25% of the salaries surpassed $645.
d. To find the percentage of employees' salaries that surpassed $685, we need to calculate the percentage of values that are greater than $685 in the data set. Since the 85th percentile is $685, we know that 85% of the salaries are less than or equal to $685. Therefore, about 15% of the salaries surpassed $685.
e. To find the total weekly salary of all employees, we need to multiply the mean salary ($620) by the number of employees (100). Therefore, the total weekly salary of all employees is $62,000.
Does anyone know what
-3*14^(7x-2)+8=-53 is?
Answer:
Step-by-step explanation: i know i take this
answer quick for brainliest.
Answer:
the slope is 5 the y intercept is 5
Step-by-step explanation:
slope intercept form makes this true
please mark brainliest :)
Answer:
The slope is 10 and the eqation is y+5x Please pray that it is right
Step-by-step explanation:
Find the radius of the circle given the circumference. Use 3.14 for pi. Round to the nearest hundredth.
C = 28 ft.
Answer:
4.46
Step-by-step explanation:
As the circumference of a circle is pi multiplied by the diameter to work out the radius you would first divide the circumference of 28 by pi, which gives you 8.92. This is the diameter, however the question is asking for the radius. To work out the radius you would divide the diameter by 2, which gives you 4.46. This is because the radius is half of the diameter.
1) Divide 28 by pi.
[tex]28/\pi =8.92[/tex]
2) Divide 8.92 by 2.
[tex]8.92/2=4.46[/tex]
I need number 3 only please help me!!
The answer is 9 times. This is because if the radius of A is r, and the radius of B is 3r, the radii will be squared while finding the formula. So, r will become r squared, while 3r will become 9r squared.
What’s 7 and what’s 9?
Answer:
7. A- 5√2
9. C- 6√2
Step-by-step explanation:
Let's begin with question 7 asking to simplify √50.
We need to ask ourselves the question if 50 has a factor that is a square. It does!
We can break √50 into √25·2. Since 25 is a square, we can take it out of the radical by taking out its square root like this:
5√2.
For question 9, we can simply do the same exact process. √72 can be broken into a factor that is a perfect square as well!
√72 --> √36·2
Now, take the square root of 36 out of the radical to become:
6√2
Here are your answers!
Answer:
7 is A
Step-by-step explanation:
50 can be turned into 2 and 25 and you can simplify 25 into 5 giving you 5 to the square root of 2
12 cookies are in a bag. 6 children will share a bag of cookies. The children want to know how many cookies they will each get. Which number sentence would they use to answer the question?
Answer:
12 / 6 = 2
Step-by-step explanation:
If there are a total of 12 cookies, and these cookies will be divided evenly among 12 children, to find how many cookies each children will have, we just need to divide the total number of cookies by the total number of children:
Number of cookies per children = number of cookies / number of children
Number of cookies per children = 12 / 6 = 2
So each children will get 2 cookies.
The diagram shows the number of dollars each child in a family has. A balance diagram going from 1 to 9. 2 circles are above 5 and 2 circles are above 9. How can they redistribute the money so that each child has the same amount? Check all that apply. Each child who has $9 must give away $4. Each child who has $9 must give away $2. Each child who has $5 must be given $4. Each child who has $5 must be given $2. When fairly balanced, each child has $7. When fairly balanced, each child has $8. BRAINLIEST BABY!!
Answer:
B D E
Step-by-step explanation:
i did the quiz
Answer:
2,4,5 choices
Step-by-step explanation:
I did the quiz
Rewrite the expression 2-bx2<56 to get the variable b alone on one side of the equation.
Answer:
b >-54/x^2
Step-by-step explanation:
2-bx^2<56
Subtract 2 from each side
2-2-bx^2<56-2
-bx^2 <54
Divide by -1, remembering to flip the inequality
bx^2 > -54
Divide each side by x^2
bx^2/x^2 > -54/x^2
b >-54/x^2
Answer:
b > -54/x²
Step-by-step explanation:
2 - bx² < 56
2 - 56 < bx²
-54 < bx²
-54/x² < b
b > -54/x²
If AC=16 and BC=13 what is the radius
Answer:
Radius AB = 9.3 units
Step-by-step explanation:
Given:
BC (tangent) make right angle with radius AB.
AC = 16 units
BC = 13 units
Find:
Radius AB = ?
Computation:
Using Pythagoras theorem:
[tex]Hypotenuse^2 = Perpendicular^2 +Base^2\\\\AB =\sqrt{AC^2 -BC^2}\\\\ AB =\sqrt{16^2 -13^2}\\\\AB =\sqrt{256 -169}\\\\AB =\sqrt{87}\\\\AB =9.327[/tex]
Radius AB = 9.3 units
The question lacks clear context for the radius calculation, but assuming AC and BC are sides of a right triangle with the hypotenuse as the diameter of a circle, the radius can be found using the Pythagorean theorem. The calculated radius would be approximately 10.307764.
Explanation:The question seems to be asking for the radius of a circle given certain measurements from a triangle. However, the information provided is ambiguous as it lacks context and specifics such as which geometric scenario we are dealing with. Nonetheless, assuming that AC and BC are legs of a right triangle, and if the hypotenuse is the diameter of a circle, we can calculate the radius using the Pythagorean theorem.
To find the radius (R), we would expect to have a right triangle with sides AC and BC, and a hypotenuse that is twice the radius. However, the lengths given in the question (AC=16 and BC=13) do not correspond to one of the formulae provided which suggests using the lengths in a Pythagorean relationship. Instead, if these lengths are for a right-angled triangle, we would calculate the hypotenuse as follows:
√(AC² + BC²) = √(16² + 13²) = √(256 + 169) = √425 ≈ 20.615528
Therefore, if the hypotenuse is the diameter of the circle, the radius R would be approximately half of this value, or 10.307764.
PLEASE HELP!!!Will mark BRAINLIEST for 5 and 6
Answer:
5. yes
6. no
Step-by-step explanation:
5. yes
You know this because you're familiar with the first few Pythagorean triples:
(3, 4, 5), (5, 12, 13), (7, 24, 25), ...
If you're not, you can use the Pythagorean theorem to check. The sides will form a right triangle if and only if they satisfy the Pythagorean theorem.
13^2 = 12^2 +5^2
169 = 144 + 25 . . . . . . true
__
6. no
Your knowledge of numbers tells you that these numbers cannot satisfy the Pythagorean theorem.* The sum of an even and and odd number cannot be even. (The square of a number has the same parity as the number itself.)
_____
* Thanks to Brainly, I recently figured out that you can apply a parity test to candidates for right triangle sides. The number of odd-length sides must be even. There cannot be a right triangle with integer side lengths, only one of which is odd.
Enter the exponential expression as a decimal.
[tex]10^{4}[/tex]
Answer:
3.4
Step-by-step explanation:
A circle is centered on point (-2,-1). The circle passes through the point (-7,-7). What is its radius?
Answer:
-The answer for the radius:
[tex]\sqrt{61} = r[/tex]
Step-by-step explanation:
-The equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex] (where the center is known as [tex](h,k)[/tex], the point is [tex](x,y)[/tex] and the radius known as [tex]r[/tex]).
-Use both the center (-2,-1) and the point (-7,-7) for the equation:
[tex](-7+2)^2+(-7+1)^2=r^2[/tex]
-Then, solve the equation to get the radius:
[tex](-7+2)^2+(-7+1)^2=r^2[/tex]
[tex](-5)^2+(-6)^2=r^2[/tex]
[tex]25+36=r^2[/tex]
[tex]61 = r^2[/tex]
[tex]\sqrt{61} = \sqrt{r^2}[/tex]
[tex]\sqrt{61} =r[/tex]
So, therefore the radius is [tex]\sqrt{61}[/tex] .
2x + y = 4
y = 3x - 1
Is (1, 2) a solution to both equations?
yes or no?
Answer: yes
Step-by-step explanation:
2x+y=4 x=1 and y=2 2(1)+2=4
y=3x-1 3(1)-1=2
A bag contains 2 blue marbles and 5 red marbles. You choose one marble and
without replacing it, youchoose a second marble. What is the probability of
choosing: A). A red marble first, then a blue marble second? B). A blue marble
GIVEN that a red marble was chosen first?
Answer:
A) 5/7 and 2/6 B) 4/7
Step-by-step explanation:
First find the total and then establish probability for each color: 2+5 = 7 total marbles. [tex]\frac{2}{7}[/tex] for blue and [tex]\frac{5}{7}[/tex] for red. Because you don't replace the marble you took out the total will do down one but the number of blue will not be affected to it just changed from [tex]\frac{2}{7} to \frac{2}{6}[/tex]
On part b I'm a little confused, are you putting a blue marble in the bag and then finding red's probability? If so, you are in theory replacing the first red marble so the total will be 7 again but since it's a blue marble your probabilities change to [tex]\frac{3}{7}[/tex] for blue and [tex]\frac{4}{7}[/tex] for red.
A number cube labeled one though six is rolled and a letter is selected from
the word MUSIC. Find each probability. P(6 and consonant)
Answer:
1/10
Step-by-step explanation:
In the question above we are given two data sets
a) A number cube labelled and it rolled, 1 to 6
b) A word called Music
We are asked to find the probability of
obtaining a 6 from the rolled dice and picking a consonant.
Step 1
Probability = Number of Possible Outcomes/ Number of events
Probability of obtaining a 6 from the rolled cube = P(6) = 1/6
Step 2
Probability = Number of Possible Outcomes/ Number of events
In the Letter MUSIC, we have 5 letters,
2 Vowels and 3 consonants
The Probability of Obtaining an Consonant = Number of possible outcomes ( Number of consonants) ÷ Number of events ( Number of letters in MUSIC)
P ( Consonant) = 3/5
Step 3
This is the final step
And we are to find the Probability of P(6 and consonant)
P( 6 and Consonant ) = P (6) × P ( Consonant)
P ( 6 and Consonant) = 1/6 × 3/5
= 3/30 = 1/10
Therefore, the Probability of obtaining P(6 and consonant) = 1/10.
Final answer:
The probability of rolling a 6 on a six-sided die and selecting a consonant from the word MUSIC is 1/10.
Explanation:
The probability of rolling a 6 on a number cube and selecting a consonant from the word MUSIC is found by multiplying the probabilities of the two independent events. The probability of rolling a 6 on a six-sided die is 1/6. The word MUSIC has three consonants: M, S, and C. The probability of choosing a consonant from MUSIC is 3/5, since there are 5 letters in total and 3 of them are consonants.
Therefore, the probability of both events occurring is:
P(6 and consonant) = P(6) × P(consonant) = (1/6) × (3/5) = 1/10.
Find the volume of a pyramid with a square base, where the side length of the base is 8.7 cm and the height of the pyramid is 13.1 cm
Answer:
V = 330.513 cm^3
Step-by-step explanation:
Area = l x w and with a square the length and width are the same, additionally the volume of a pyramid can be found by using the formula (L)(w)(h)/3 so
8.7 x 8.7 = 75.69cm^2
75.69 x 13.1 = 991.539
991.539 ÷ 3 = 330.513 cm^3
Mark as brainliest please :)
Final answer:
The volume of a pyramid with a square base of side 8.7 cm and height 13.1 cm is calculated using the formula for volume, resulting in 330.35 cm³.
Explanation:
To find the volume of a pyramid with a square base, you can use the formula V = (1/3) × base area × height, where the base area for a square is given by side length × side length.
In this case, the side length of the base is 8.7 cm, and the height of the pyramid is 13.1 cm.
First, calculate the area of the base:
Base Area = 8.7 cm × 8.7 cm = 75.69 cm²
Then, calculate the volume of the pyramid:
Volume = (1/3) × 75.69 cm² × 13.1 cm = 330.35 cm³
Therefore, the volume of the pyramid is 330.35 cm³.
In the equation y = -2x - 3, find x if y= 5.
Answer:
-4
Step-by-step explanation:
y= -2x - 3
First, plug in 5 for y
5= -2x - 3
+3 +3
8= -2x
Divide by -2
-4= x
Final answer:
To find x when y = 5 in the equation y = -2x - 3, the solution is x = -4.
Explanation:
In the given equation y = -2x - 3, to find x when y = 5, substitute y with 5 in the equation:
5 = -2x - 3
Solve for x:
Add 3 to both sides: 5 + 3 = -2x
8 = -2x
Divide by -2: x = -4
equation for a parabola with a focus of (2, -2) and a directrix of y=-8
Answer:
y=1/8(-x^2+4x+44
Step-by-step explanation:
In this question the given focus is (2,4) and a directrix of y = 8 and we have to derive the equation of the parabola.
Let (x,y) is a point on the given parabola.Then the distance between the point (x,y) to (2,4) and the distance from (x,y) to diractrix will be same.
Distance between (x,y) and (2,4)
= √(x-2)²+(y-4)²
And the distance between (x,y) and directrix y=8
= (y-8)
Now √(x-2)²+(y-4)² = (y-8)
(x-2)²+(y-4)² = (y-8)²
x²+4-4x+y²+16-8y = y²+64-16y
x²+20+y²-4x-8y = y²-16y+64
x²+20-4x-8y+16y-64=0
x²+8y-4x-44 = 0
8y = -x²+4x+44
Find the area of the semicircle. Round your answer to the nearest whole number, if necessary.
40 cm
Answer:
To the nearest hundredth : 628.32 [tex]cm^2[/tex]
To the nearest whole number : 628 [tex]cm^2[/tex]
Step-by-step explanation:
The formula for the area of a circle is : [tex]\pi*radius^2[/tex]
To work out the area you would first need to work out the radius. You can do this by dividing the diameter of 40 cm by 2, this gives you 20 cm. This is because the radius is half of the diameter.
Now that we have worked out the radius, the next step would be to work out the area. You can do this by multiplying pi by the radius of 20 squared, this gives you 1256.64.
The final step is to work out the area of this semi-circle. You can do this by dividing the area of 1256.64 by 2, this gives you 628.32 [tex]cm^2[/tex]. This is because a semi-circle is half of a circle.
1) Divide 40 by 2.
[tex]40/2=20 cm[/tex]
2) Multiply pi by 20 squared.
[tex]\pi*20^2=1256.64 cm^2[/tex]
3) Divide 1256.64 by 2.
[tex]1256.64/2=628.32 cm^2[/tex]
The area of the semicircle is approximately 628 square centimeters.
To find the area of a semicircle with a given diameter, we need to use the formula for the area of a circle and then divide it by 2, since a semicircle is half of a circle.
The formula for the area of a circle is:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle. Given the diameter is 40 cm, we can find the radius by dividing the diameter by 2:
[tex]\[ r = \frac{40 \, \text{cm}}{2} = 20 \, \text{cm} \][/tex]
Now, we can calculate the area of the full circle:
[tex]\[ A_{\text{circle}} = \pi (20 \, \text{cm})^2 = 400\pi \, \text{cm}^2 \][/tex]
Since the semicircle is half of the full circle, the area of the semicircle is:
[tex]\[ A_{\text{semicircle}} = \frac{1}{2} A_{\text{circle}} = \frac{1}{2} \times 400\pi \, \text{cm}^2 = 200\pi \, \text{cm}^2 \][/tex]
Using [tex]\(\pi \approx 3.14159\)[/tex]
[tex]\[ A_{\text{semicircle}} \approx 200 \times 3.14159 \, \text{cm}^2 \approx 628.32 \, \text{cm}^2 \][/tex]
Rounding to the nearest whole number:
[tex]\[ A_{\text{semicircle}} \approx 628 \, \text{cm}^2 \][/tex]
40 points!!!! The space allowed for the mascot on a school web page is 120 pixels wide by 70 pixels high. It’s digital image is 600 pixels wide by 350 pixels high. What is the largest image of the mascot that will fit in the web page
Answer:
120 pixels wide by 70 pixels high
Step-by-step explanation:
Think about it...
The image is 600/350
that is equivalent to 12/7 or 7:12
The space provided is 120/70
that is equivalent to 12/7 or 7:12
Since the ratios are the same the largest possible size the image can be is 120/70
The largest image of the school mascot that will fit in the web page is 120 pixels wide by 70 pixels high, which is the same aspect ratio as the original image size of 600 pixels wide by 350 pixels high.
Explanation:Your task is to determine the biggest possible size for the school mascot image on the school web page. The spot for the mascot on the webpage is restricted to 120 pixels wide by 70 pixels high, while the actual digital image is 600 pixels wide by 350 pixels high.
The image needs to keep its aspect ratio (the ratio of width to height) in order to prevent distortion. The aspect ratio of the digital image is 600/350 (or 60/35 when simplified), which equals 12/7. Therefore, the mascot image also needs to have a 12/7 ratio to fit in the webpage space perfectly.
The way to do this is to scale down the image. Scaling works equally on both width and height of the image, therefore, we can start by scaling down the width from 600 pixels to 120 pixels. To calculate the scale factor, we divide 120 (the width of the webpage space) by 600 (the width of the image). The scale factor is 0.2 or 20%.
Applying this scale factor to the height: Scale factor * height of image = 0.2 *350 = 70 pixels, which is exactly the height of the webpage space. So, the largest image of the mascot that will fit in the webpage is 120 pixels wide by 70 pixels high, which maintains the same aspect ratio as the digital image.
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Do,k = (9,6) --> (3,2)
The scale factor is?
1/3
3
6
Answer:
the answer is 1/3
Step-by-step explanation:
If you dilate (3,2) by 3 it will come out a (9,6). Therefore, the scale factor is 1/3
Question 4 (1 point)
What is the solution to the equation 3(2x + 5) = 3x + 4x?
a
x = 0
b
x = 4
с
x = 15
d
x= 5
Answer:
x=15
Step-by-step explanation:
3(2x+5)=3x+4x
6x+15=3x+4x. *multiplied parentheses by 3*
15=3x+4x+-6. *moves all x to one side*
15=× * added
x=15
Write a formula for r in terms of θ based on the image below.
The angle in the figure is a central angle in radians.
Answer:
R=7[tex]\pi[/tex]/Ф
7Pi/Theta
Which of the following fractions has the same value as the decimal number 0.65?
20/13
13/20
5/13
13/5
Answer:
13/20
Step-by-step explanation:
To find this, divide 13 by 20 to get .65
Hope this helped!
Answer:
13/20
Step-by-step explanation: