What is the equation of the line?
A) x + 3y = 9
B) 3x - y = 9
C) x - y = 9
D) 3x + y = 9
Which of the following equations can be used to solve for the radius (r)
Answer:
The last option is the correct answer: [tex]r=\sqrt{\frac{A}{\pi}}[/tex]
Step-by-step explanation:
The area of a circle is given by :
[tex]A=\pi r^{2}[/tex] ; where r is the radius.
Now, lets find the radius.
[tex]\frac{A}{\pi } =r^{2}[/tex]
[tex]\sqrt{\frac{A}{\pi}} =r[/tex]
or [tex]r=\sqrt{\frac{A}{\pi}}[/tex]
Therefore, the last option is the correct answer.
Each morning papa notes the birds feeding on his bird feeder. so far tis month he has seen 59 blue jays, 68 black crows, 12 red robins and 1 cardinal. if 300 birds list papa's birdfeeder, how many blue jays can we expect to see?
The perimeter of the rectangle is 64 cm. Find the value of x.
A. 7
B. [tex] \frac{64}{33} [/tex]
C. 32
D. 50
The value of x is 7 and the right option is A. 7.
What is perimeter?Perimeter is the total distance around an object.
To find the value of x, we use the formula of the perimeter of a rectangle.
Formula:
P = 2(L+W)............... Equation 1Where:
P = Perimeter of the rectangleL = Length of the rectangleW = Width of the rectangleFrom the question,
Given:
L = 3xW = 11 cmP = 64 cmSubstitute these values into equation 1 and solve for x
64 = 2(11+3x)64 = 22+6x6x = 64-226x = 42x = 42/6x = 7Hence, the value of x is 7 and the right option is A. 7.
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Help plz and explain. ..........
If i give my sister 17 dollars, then we will have the same amount of money. if instead she gives me 23 dollars, then i'll have three times as much money as she will have. how much money does she currently have (in dollars)
The total number of dollars my sisters have is $60.
Given that, if I give my sister 17 dollars, then we will have the same amount of money.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of dollars I have be x and number of dollars my sisters have be y.
Now, if I give my sister 17 dollars, then we will have the same amount of money
y-17 = x
x - y = -17 ---------(1)
If she gives me 23 dollars, then I'll have three times as much money as she will have.
3(x-23) = y
3x-69 = y
3x-y = 69 ---------(2)
Subtract equation (1) from (2)
3x-y-(x-y) = 69 - (-17)
⇒ 2x = 86
⇒ x = $43
Put x = 43 in equation (1), we get
43 - y = -17
43+17 = y
y = $60
Therefore, the total number of dollars my sisters have is $60.
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Select the locations on the number line to plot the points 4 1/ 3 and −1 1/3 .
Answer:
The locations of given number are shown on the below number line.
Step-by-step explanation:
The given numbers are
[tex]4\dfrac{1}{3} and -1\dfrac{1}{3}[/tex]
We need to plot these points on the given number line.
In the given number write the integers -4,-3,-2,-1,0,1,2,3,4 on points indicated and two sub point between two consecutive points divides the line in three equal parts.
[tex]4\dfrac{1}{3}=4+\dfrac{1}{3}[/tex]
It means [tex]4\dfrac{1}{3}[/tex] lies next to 4 on right side.
[tex]-1\dfrac{1}{3}=-(1+\dfrac{1}{3})=-1-\dfrac{1}{3}[/tex]
It means [tex]-1\dfrac{1}{3}[/tex] lies next to -1 on left side.
Therefore, the locations of given number are shown on the below number line.
How do you prove cotx/(cscx-sinx)=secx
If you take Coleman's test grade and divide by 2 and add 27, you get 67. Write and solve an equation to find Coleman's test grade.
To find Coleman's test grade, set up the equation x/2 + 27 = 67, solve for x by first subtracting 27 and then multiplying by 2 to get x = 80.
Explanation:The student is asking to find Coleman's test grade given that if you take Coleman's test grade, divide by 2, and add 27, the result is 67. To solve for Coleman's test grade, we can set up an equation where Coleman's test grade is represented by x. The equation based on the provided information would be x/2 + 27 = 67. We can solve for x by first subtracting 27 from both sides of the equation to get x/2 = 40, and then multiplying both sides by 2 to find x. Therefore, x = 80, which means Coleman's test grade is 80.
To find Coleman's test grade, we can set up an equation: (x/2) + 27 = 67. By solving this equation, we find that Coleman's test grade is 80.
Explanation:To find Coleman's test grade, we can set up an equation using the information given. Let's represent Coleman's test grade as 'x'. We have the equation: (x/2) + 27 = 67.
To solve this equation, we need to isolate 'x'. We can start by subtracting 27 from both sides of the equation: (x/2) = 40.
Next, we need to get rid of the fraction by multiplying both sides of the equation by 2: x = 80.
So Coleman's test grade is 80.
There were some pencils in a pencil box. Zoe added 7 more pencils to the pencil box. Now there are 24 pencils in the box. How many pencils were in the box to start with?
△ABC is reflected to form △A′B′C′ . The vertices of △ABC are A(3, 1) , B(1, 5) , and C(6, 9) . The vertices of △A′B′C′ are A′(−1, −3) , B′(−5, −1) , and C′(−9, −6) . Which reflection results in the transformation of △ABC to △A′B′C′ ? reflection across the x-axis reflection across the y-axis reflection across y = x reflection across y=−x
A shipping tube is shaped like a triangular prism. The bases are equilateral triangles with edges of 6 inches and a height of 5.2 inches. The tube is 14 inches long. Find the lateral surface area of the shipping tube.
The lateral surface area of the equilateral triangular prism shaped shipping tube is 252 square inches.
Explanation:The question pertains to the calculation of the lateral surface area of a triangular prism shaped shipping tube, more specifically an
equilateral triangular prism
. The lateral area of a triangular prism can be calculated using the formula: Perimeter of the base x length of the prism. Here, the base of the prism is an equilateral triangle, so the perimeter of the base will be 3 x the length of one edge, which in this case is 3 x 6 inches = 18 inches. The length of the prism is given to be 14 inches. Hence, by substituting these values into the formula, the lateral surface area = 18 inches x 14 inches =
252 square inches.
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Multiply.
638 × 49
_____
From an airplane at an altitude of 1200m the angle of depression to a rock on the ground measures 28. Find the distance from the plane to the rock
The distance from the plane to the rock can be calculated using trigonometry. Here, the tangent of the given angle is used, with the formula: Distance = 1200m / tan(28°).
Explanation:The subject matter in the question relates to trigonometry. We can use the tangent of the given angle to find the distance to the rock. We are given an altitude of 1200m (which is equivalent to the opposite side in a right angle triangle) and an angle of depression of 28°. We know from trigonometry that the tangent of an angle is equal to the opposite side divided by the adjacent side (tan(θ) = opposite / adjacent).
Since we want to know the distance from the plane to the rock, we're trying to find the length of the hypotenuse. This forms a right-angled triangle with the height of the plane as the opposite side, and the line of sight to the rock as the hypotenuse.
We can use the following formula which is derived from the principles of trigonometry:
Distance to the rock (hypotenuse) = Opposite side / tan(θ)
Plugging the given values into this formula gives:
Distance to the rock = 1200m / tan(28°) This calculation will give the answer.
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Which of the following is the image of C after a rotation of 180° about the origin?
(-5, 2)
(-5, -2)
(-2, 5)
Answer:
Option A.(-5, 2).
Step-by-step explanation:
Picture attached in the question we know the coordinates of the point C are (5, -2). Now we rotate C with a rotation of 180° about the origin.
As we can see a line connecting C and a new point C'. This line shows the rotation of the poit by 180°.
Therefore the new coordinates of C will be C'(-5, 2).
Option A is the correct option.
How to find the derivative of a fraction without using the quotient rule?
Final answer:
To find the derivative of a fraction without using the quotient rule, you can use the chain rule and the product rule.
Explanation:
To find the derivative of a fraction without using the quotient rule, you can use the chain rule and the product rule. Here's an example:
Let's differentiate the function f(x) = (3x + 2) / (2x + 1).
First, identify the numerator and the denominator. In this case, the numerator is 3x + 2 and the denominator is 2x + 1.Apply the product rule by differentiating the numerator and the denominator separately. The derivative of the numerator is 3, and the derivative of the denominator is 2.Next, apply the chain rule by multiplying the derivative of the numerator by the denominator, and subtracting the derivative of the denominator multiplied by the numerator. In this case, the derivative of f(x) is (3 * (2x + 1) - (2 * (3x + 2))) / ((2x + 1)^2).Simplifying further, the derivative of f(x) is (6x + 3 - 6x - 4) / ((2x + 1)^2) = -1 / ((2x + 1)^2).
Given the arithmetic sequence an = −3 + 9(n − 1), what is the domain for n? all integers where n ≥ 1 all integers all integers where n ≥ 0 all integers where n > 1
Bill is able to save $35/week after working part-time and paying his expenses. These two formulas show his weekly savings: f(1) = 35, f(n) = f(1) + f(n-1) for n > 1 f(n) = 35n Which one of these formulas show the sequence written rercursively and which shows it written explicity? Justify your explanantions. Use the recursive formula to make a table of values for 1 ≤ n ≤ 5. Show your calculations. Use the explicit formula to demonstrate the most direct method to find f(40). Explain why you chose that method and what your answer means. Show your calculations. Given the sequence of numbers: 5, 6, 8, 11, 15, 20, 26, 33, 41,… Explain whether or not this sequence can be considered a function.
The value of f(40) is 1400 .The sequence can be considered a function because each position has a unique value.
Let's analyze the given formulas for Bill's savings:
The recursive formula is: f(1) = 35, f(n) = f(1) + f(n-1) for n > 1
The explicit formula is: f(n) = 35n
A recursive formula defines each term based on the previous terms, which we see in f(n) = f(1) + f(n-1). An explicit formula provides a direct calculation, shown in f(n) = 35n.
Recursive Formula Table for 1 ≤ n ≤ 5n = 1: f(1) = 35n = 2: f(2) = 35 + f(1) = 35 + 35 = 70n = 3: f(3) = 35 + f(2) = 35 + 70 = 105n = 4: f(4) = 35 + f(3) = 35 + 105 = 140n = 5: f(5) = 35 + f(4) = 35 + 140 = 175Using the Explicit Formula to Find f(40)The explicit formula f(n) = 35n allows us to directly calculate:
f(40) = 35 * 40 = 1400
This method is chosen because it provides a straightforward calculation without needing to compute all the preceding values.
Analyzing the Sequence 5, 6, 8, 11, 15, 20, 26, 33, 41, ...This sequence can be considered a function because each input (position in the sequence) has a unique output (value in the sequence).
@ajaylounsber Jennifer has been saving for college for 57 months. The first month, she saved $11. She was able to save more money each month than the month before. She ended up saving $19,779.00. How much more did she save each month?,
what is the slope? 0 or undefined
15. A restaurant has one type of milk that has 2% fat and another that has 7% fat. how many quarts of each type does the restaurant need to make 40 quarts of a milk mixture that is 5% fat?
a. 24 quarts of the 2% milk and 16 quarts of the 7% milk
b. 16 quarts of the 2% milk and 24 quarts of the 7% milk
c. 16 quarts of the 2% milk and 16 quarts of the 7 milk
d. 24 quarts of the 2% milk and 24 quarts of the 7% milk,
Esther and Jim plan to add a pond to their property. The area of the pond is 11 square meters. What is the radius?
True of False: If the measure of theta is A radians and B degrees, then A = 180B/pi. Please explain!
I understand that the remainder is 0, I kinda guessed and it told me.
But we're using long division or synthetic division.
Can you explain to me what the quotient is?
Thanks!
The base of a regular pyramid is a hexagon. The figure shows a regular hexagon with center C. An apothem is shown as a dashed segment perpendicular to an edge and is labeled as a. A dashed line segment joins the center with the left vertex of the edge perpendicular to the apothem. This segment has a length of 8 centimeters. The angle formed by the edge and the segment measure 60 degrees. What is the area of the base of the pyramid? Enter your answer in the box. Express your answer in radical form.
The area of the base of the pyramid which is a hexagon with given parameters is; 96√3
How to find the area of a Polygon?We are told that the base of the pyramid is a hexagon.
Now, from the given image we can find the base length of the right angle triangle from trigonometric ratio which is;
x/8 = cos 60°
x = 8 cos 60°
x = 4
Thus, length of side of hexagon is;
s = 4 * 2
s = 8
Formula for area of hexagon is given by;
A = ((3√3) * s²)/2
Where;
s is length of a side of hexagon
A = ((3√3) * 8²)/2
A = 96√3
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Hakim invests $700 in a bank that pays 5% simple interest annually. After one year he uses the money in his account to buy a computer. The original cost of the computer is $750.00. The computer is on sale for a 20% discount off of the original cost. The sales tax is 4% of the sale price. After purchasing the computer, how much does Hakim have left in his bank account? Show your work.
What is the area of the polygon??
A dress that retails for 160 dollars was on sale 96 dollars by what percent was the dress discounted?
Julia surveyed her friends to find the number of hours they spend on homework during the week. The data from her survey is displayed in the first table. She then took a random sample of five responses from the population as shown in the second table. Compare the mean of the population with the mean of the given sample.
Population Data
4
5
3
1
3
2
2
3
5
7
3
6
3
0
1
5
0
4
3
6
Sample Data
5
4
6
2
1
What is the difference between the mean of the sample and the mean of the population?
0.2
0.3
0.4
0.5
Solution:
we are given with two kind of data set , one is Population data and the other is sample data.
we have been asked to Compare the mean of the population with the mean of the given sample.
Given Population Data
is
[tex] 4
, 5
, 3
,1
,3
,2,2
,3
,5
,7
,3
,6
,3
,0
,1
,5
,0
,4
,3
,6 [/tex]
Its mean can be calculated as below
[tex] Mean=\frac{4+5+3+1+3+2+2+3+5+7+3+6+3+0+1+5+0+4+3+6}{20} \\\\\Mean=\frac{66}{20}=3.3\\ [/tex]
Now the Sample data is
5,4,6,2,1
[tex] Mean=\frac{5+4+6+2+1}{5}\\\\Mean=\frac{18}{5}= 3.6\\ [/tex]
Hence the value of difference of the Mean is [tex] =3.6-3.3=0.3 [/tex]
Answer:
The answer is B. 0.3
Step-by-step explanation:
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Briyana has a $500 bond with a 6% coupon. Briyana purchased this bond for $460. What is the yield of this new bond?
A. 6%
B. 4.6%
C. 6.3%
D. 6.5%
Answer:
The correct answer is: 6.5%
Step-by-step explanation: