The x-coordinate of point T is 7. Thus, point T is (7, 3).
To solve for x, we will use the concept of slope. The slope between any two points on a line remains constant. Let's find the slope between points R(-5, -3) and S(-1, -1):
Slope (m) = (y2 - y1) / (x2 - x1)
m = (-1 - (-3)) / (-1 - (-5))
m = (2) / (4)
m = 1/2
Now, we will use the slope between points S(-1, -1) and T(x, 3):
m = (3 - (-1)) / (x - (-1))
1/2 = (4) / (x + 1)
Now, we will solve for x:
1/2 (x + 1) = 4
x + 1 = 8
x = 7
So, the x-coordinate of point T is 7. Thus, point T is (7, 3).
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A ninja star, or shuriken, is usually constructed using four congruent isosceles triangles that are placed along the sides of a square. What is the value of x?
a.) 46
b.) 56
c.) 62
d.) 118
The measure of angle x of the ninja star is given by x = 56°
Given data ,
Let the ninja star be represented as an isosceles triangle
Now , it is constructed using four congruent isosceles triangles that are placed along the sides of a square
And , the vertex angle of the triangle is x
In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle
So , the measure of x = 180° - ( 62° + 62° )
On simplifying , we get
x = 56°
Hence , the angle of triangle is x = 56°
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How do I solve for X with the base numbers on a right triangle. (Please give an explanation and an answer, I need to know how it works.)
Let's label the 3 points as A;B;C, where BC is the hypotenuse and AB is the shortest side, and x as AH.
We can see that triangle AHC is similar to triangle CAB, and triangle ACH is similar to triangle BCA, so therefore triangle AHC is similar to triangle CHA (i might've messed up the order but you get it)
Because they are similar, we get the ratio : x/12 = 40/x, or x^2 = 480.
So, x = [tex]\sqrt{480}[/tex], or 21.9 (1 d.p)
Answer:
21.9 units-----------------------
According to the right triangle altitude theorem:
the altitude on the hypotenuse is equal to the geometric mean of line segments formed by altitude on the hypotenuse.We see x is the altitude and 12 & 40 are the segments formed on the hypotenuse.
Applied to the given triangle, we get following equation:
[tex]x=\sqrt{12*40} =\sqrt{480} =21.9\ units[/tex]The volume of this rectangular prism is 3 cubic feet. What is the surface area?
Answer:
27
Step-by-step explanation:
Convert the rectangular coordinates (0, 6√3) into polar form. Express the angle using radians in terms of over the interval 0 ≤ 0 < 27, with a positive value of r.
Answer:
The polar form of the rectangular coordinates (0, 6√3) with a positive value of r, over the interval 0 ≤ θo < 27 and in terms of radians, is (6√3, 1.58).
Step-by-step explanation:
To convert the rectangular coordinates (0, 6√3) to polar form, we can use the following formulas:
r = √(x^2 + y^2)
θ = tan^(-1)(y/x)
Substituting the given values, we get:
r = √(0^2 + (6√3)^2) = 6√3
θ = tan^(-1)((6√3)/0) = π/2
However, note that the angle θ is not well-defined since x=0. We can specify that the point lies on the positive y-axis, which corresponds to θ = π/2 radians.
Thus, the polar form of the rectangular coordinates (0, 6√3) is:
r = 6√3
θ = π/2
To express the angle θ in terms of θo, where 0 ≤ θo < 27 and in radians, we can write:
θ = π/2 = (π/54) × 54 ≈ (0.0292) × 54 ≈ 1.58 radians
Therefore, the polar form of the rectangular coordinates (0, 6√3) with a positive value of r, over the interval 0 ≤ θo < 27 and in terms of radians, is (6√3, 1.58).
At the beginning of spring, jin planted a small sunflower in his backyard. the sunflower's height in inches, h after w weeks, is given by the equation h=18+2.5w. what could the number 18 represent in the equation
After considering all the given data provided by the question we conclude that the number 18 present in the given equation is constant .
The equation for the sunflower's height is h = 18 + 2.5w.
Here, the number 18 shows the height of the sunflower during the time it was planted, so it is the constant term present in the equation and hence it does not relie on the duration of weeks that have passed.
The coefficient of w is 2.5, which represents the rate at which the sunflower grows in height per week.
Therefore, after one week, the sunflower would be 20.5 inches tall (18 + 2.5 x 1), after two weeks it would be 23 inches tall (18 + 2.5 x 2), after four weeks it would be 28 inches tall (18 + 2.5 x 4), and after six weeks it would be 33 inches tall (18 + 2.5 x 6).
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if integrate f(x) dx = 1/3 * x ^ 3 - 2x ^ 2 + 3x - 5 then the value of f(-2) = ...
A. -9
B. -1
C. 7
D. 15
E. 23
please
pleasee
The value of f(-2) is 15.
Hence option D is correct.
The given expression is
[tex]\int\limits {f(x)} \, dx[/tex] = (1/3)x³ - 2x² +3x - 5
To find expression of f(x)
Differentiate it with respect to x
f(x) = x² - 4x + 3
Now put x = -2
f(-2) = (-2)² - 4(-2) + 3
= 4 + 8 + 3
= 15
Hence,
f(-2) = 15
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4 3 (1)/(5 )2 (3)/(5 )1 (4)/(5)
ecplict formula, in slope intercept form (4)/(5)
The explict formula, in slope intercept form is an = n/5
Calculating the explict formula, in slope intercept formThe given sequence is 1/5, 2/5, 3/5.
We can observe that this is an arithmetic sequence, where the first term is 1/5, the common difference is 1/5
To find the explicit formula for an arithmetic sequence, we can use the formula:
an = a1 + (n-1)d
Substituting the values we know for this sequence, we get:
an = 1/5 + (n - 1)*(1/5)
Evaluate
an = n/5
Thus, the nth term of this sequence can be found by substituting the value of n in the formula an = n/5
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Complete question
1/5 2/5 3/5
What is the explicit formula in slope intercept form
Quadrilateral klmn is similar to quadrilateral opqr. find the measure of side op.
round your answer to the nearest tenth if necessary.
n
13
m
r
57
q
27
k
p
0
answer:
submit answer
The measure of side OP in quadrilateral OPQR is 0.
To find the measure of side OP in quadrilateral OPQR, which is similar to quadrilateral KLMN, follow these steps:
1. Identify the corresponding sides in both quadrilaterals. In this case, side OP corresponds to side KL, side OQ corresponds to side KM, side PQ corresponds to side LN, and side QR corresponds to side MN.
2. Determine the scale factor between the quadrilaterals by comparing the lengths of corresponding sides. Since we have the lengths of sides KM (13), LN (27), and MN (57), we can use the ratio of KM/LN (13/27) or MN/LN (57/27) as the scale factor.
3. Apply the scale factor to the length of side KL (0) to find the length of side OP. Since the length of side KL is 0, multiplying by the scale factor (either 13/27 or 57/27) will still result in a length of 0 for side OP.
4. Round your answer to the nearest tenth if necessary. In this case, the length of side OP is 0, so rounding is not necessary.
So, the measure of side OP in quadrilateral OPQR is 0.
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Find the Circumference and area of the circle with the center C=(-1, 6) and a point on the circle A(3, 9). Round to the nearest tenth
Circumference of circle is 31.4 and area of circle is 78.6
Given, C(-1,6) is center and A(3, 9) is a point on circle.
CA is the radius of the circle.
Using Distance Formula
[tex]r=\sqrt{(3-(-1))^2+(9-6)^2}[/tex]
[tex]r=\sqrt{(4)^2+(3)^2}[/tex]
[tex]r=\sqrt{16+9}[/tex]
[tex]r=\sqrt{25}=5[/tex]
We know the the formula for circumference of circle C = 2πr
C = 2*22/7*5
= 31.428
Rounding to nearest tenth
C = 31.4
Area of the circle = [tex]\pi r^2[/tex]
[tex]A=\frac{22}{7}(5)^2[/tex]
= 78.571
Rounding to nearest tenth
A = 78.6
Hence, circumference of circle is 31.4 and area of circle is 78.6.
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Prove that the triangle FGH is right-angle des at F
The Pythagorean Theorem is used to prove that triangle FGH is a right triangle at angle F.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.Considering the equivalent side lengths, the proportional relationship for the side lengths in this problem is given as follows:
4/4.8 = FH/3.6 = 5/6.
Hence the length FH is given as follows:
4/4.8 = FH/3.6
FH = 3.6 x 4/4.8
FH = 3.
If the Pythagorean Theorem is respected, the triangle is a right triangle, hence:
3² + 4² = 5²
9 + 16 = 25
25 = 25. -> right trianglge.
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It costs $ 35 per hour to rent a boat at the lake. You also need to pay a $ 25 fee for safety equipment. You have $ 200 . How long can you rent the boat? CLEAR CHECK Write the equation that represents the situation. 35 + = $ 200 Solve for h . h = hours
Answer: H = 5
the equation would be, 35h - 25 = $200
Step-by-step explanation:
Helpppppppppppppppppppppppp
Answer:
Point in the original figure: (5,4)
Point in the final figure: (0,-2)
Step-by-step explanation:
hope this works and helps! :)
If a spinner will land on red 45% of the time, yellow 15% of the time, and blue 40% of the time, what are the chances it wont land on red
Answer:
55%
Step-by-step explanation:
Chances it wont land on red = chances of blue + chances of yellow
= 55%
Use Mean value theorem to prove √6a + 3 < a + 2 for all a > 1.
Using methods other than the Mean Value Theorem will yield no marks. {Show all reasoning).
√6a + 3 < a + 2, we have proven that √6a + 3 < a + 2 for all a > 1 using the Mean Value Theorem.
To use the Mean Value Theorem to prove √6a + 3 < a + 2 for all a > 1, we first note that the function f(x) = √6x + 3 is continuous on the interval [1,a].
Next, we need to find a point c in the interval (1,a) such that the slope of the line connecting (1,f(1)) and (a,f(a)) is equal to the slope of the tangent line to f(x) at c.
The slope of the line connecting (1,f(1)) and (a,f(a)) is given by:
(f(a) - f(1)) / (a - 1) = (√6a + 3 - √9) / (a - 1) = (√6a) / (a - 1)
To find the slope of the tangent line to f(x) at c, we first find the derivative of f(x):
f'(x) = (1/2) * (6x + 3)^(-1/2) * 6 = 3 / √(6x + 3)
Then, we evaluate f'(c) to get the slope of the tangent line at c:
f'(c) = 3 / √(6c + 3)
Now, by the Mean Value Theorem, there exists a point c in (1,a) such that:
f'(c) = (√6a) / (a - 1)
Setting these two expressions for f'(c) equal to each other, we get:
3 / √(6c + 3) = (√6a) / (a - 1)
Solving for c, we get:
c = (a + 2) / 6
(Note that c is indeed in (1,a) since a > 1.)
Now, we can evaluate f(a) and f(1) and use the Mean Value Theorem to show that:
√6a + 3 - √9 < (√6a) / (a - 1) * (a - 1)
Simplifying, we get:
√6a + 3 < a + 2
as desired.
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Subtract 1/4- 5/14 = type an integer or fraction
Answer:
-3/28
Step-by-step explanation:
In order to subtract fractions you first have to get a common denominator. The common denominator between 4 and 14 is 28 since 4(7) = 28 and 14(2) = 28. Then multiply the top and bottom of (1/4) by (7/7) and (5/14) by (2/2). This gives a common denominator and since you multiply by a fraction equal to 1, it doesn't change the value. Therefore, we get 7/28 - 10/28 = -3/28.
What is the maximum height of of Anna's golf ball? The equation is y=x−0. 04x2
The maximum height of Anna's golf ball is approximately 7.81 units.
Find the maximum height of Anna's golf ball with equation y=x−0. 04x2
The equation y = [tex]x - 0.04x^2[/tex] represents the height of Anna's golf ball, where x is the horizontal distance the ball has traveled.
To find the maximum height of the ball, we need to determine the vertex of the parabolic equation. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = -0.04 and b = 1.
x = -b/2a = -1/(2(-0.04)) = 12.5
So, the maximum height of the ball occurs when it has traveled a horizontal distance of 12.5 units. To find the maximum height, we substitute x = 12.5 into the equation:
[tex]y = 12.5 - 0.04(12.5)^2 = 7.81[/tex]
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A basket contains 8 green apples, 11 red apples, 5 nectarines, and 12 oranges. Akhil takes a piece of fruit, eats it,
then grabs another. What is the P(two oranges)?
The probability of Akhil picking two oranges is 11/105 OR 10.476%.
To find the probability of Akhil picking two oranges, we need to consider the total number of fruits and the number of oranges in the basket.
The total number of fruits is 8 green apples + 11 red apples + 5 nectarines + 12 oranges = 36 fruits.
The probability of picking the first orange is 12 oranges / 36 fruits = 1/3.
After eating the first orange, there are now 35 fruits left and 11 oranges.
The probability of picking the second orange is 11 oranges / 35 fruits.
So, the probability of Akhil picking two oranges (P(two oranges)) is the product of the individual probabilities: (1/3) * (11/35) = 11/105.
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what are the values of m and n, and what does the plotted graph look like?
The values of m and n are
m = 0 and n = 3.125
The graph is attached
How to find the values of m and nThe values of m and n are solved using the relationship between miles and kilometers. This type of relationship is a linear proportional relationship. Linear relationship implies the graph will be a straight line graph.
This relationship is that 1 mile equals 0.625 km hence the linear equation is
y = 0.625x
when x = 0, we have that
y = 0.625 * 0
y = 0
when x = 5, we have that
y = 0.625 * 5
y = 3.125
Where x is kilometers and y is miles
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Your doing practice 5
5.) The dimensions of the banner whose perimeter is given is listed below:
length = 134in
width = -59in
How to determine the dimensions of the rectangular banners?To calculate the dimensions of the rectangular banner, the formula for the perimeter of rectangle should be used and it's given below;
Perimeter of rectangle = 2(length+width)
length = 16-2a
width = a
perimeter = 160in
That is;
160 = 2(16-2a+a)
160 = 32-4a+2a
160 = 42-2a
2a = 42-160
2a = -118
a = 118/2
= -59
Length = 16-2(-59)
= 16+118
= 134in
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Yuriy and anduray will mail rectangular packages that meet the weight and height requirements of their delivery service. their packages are described in
the table.
yurly's package
package
height
4 in.
7 in.
length
21 in.
18 in.
width
9 in.
14 in.
part 1. the delivery service also requires that both the length and width of the packages to be 22 inches or less and that the length plus the width be no
more than 30 inches. write a system of inequalities to represent this situation. don't forget to define your variables and show your work
The complete system of inequalities for Anduray's package is:
x ≤ 22
y ≤ 22
x + y ≤ 30
14xy ≤ 3696
Let's define:
x: length of the package in inches
y: width of the package in inches
Then, the system of inequalities that represents the delivery service requirements is:
x ≤ 22 (length must be 22 inches or less)
y ≤ 22 (width must be 22 inches or less)
x + y ≤ 30 (length plus width must be no more than 30 inches)
We also know that Yuriy's package has a height of 7 inches, so we can add the following constraint:
4xy ≤ 840 (the product of length, width, and height must be no more than 840 cubic inches)
Therefore, the complete system of inequalities for Yuriy's package is:
x ≤ 22
y ≤ 22
x + y ≤ 30
4xy ≤ 840
Anduray's package has a height of 14 inches, so we can add the following constraint to his system of inequalities:
14xy ≤ 3696 (the product of length, width, and height must be no more than 3696 cubic inches)
Therefore, the complete system of inequalities for Anduray's package is:
x ≤ 22
y ≤ 22
x + y ≤ 30
14xy ≤ 3696
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Lola is in a hot air balloon that has just taken off and is now floating 7 meters above its launching point. Julian is standing on the ground, 6 meters away from the launching point. How far apart are Lola and Julian? If necessary, round to the nearest tenth.
what value of x is y/z
a-13
b-77
c-103
d-154
Answer:
I got you
Step-by-step explanation:
it's c -103 cause you first have to get 180 degrees
the population of a city with 750,000 people is devastated by a unknown virus that kills 20% of the population per day. How many people are left after 1 week
The number of people left after one week is approximately 157286.
How to find the number of people left?The population of a city with 750,000 people is devastated by a unknown virus that kills 20% of the population per day.
Therefore, each day, 20% of the people are killed by the virus.
Hence, let's find the number of people left as follows:
Therefore,
7 days = 1 week
number of people left = 750,000(1 - 20%)⁷
number of people left = 750,000(1 - 0.2)⁷
number of people left = 750,000(0.8)⁷
number of people left = 750,000(0.2097152)
number of people left = 157286.4
Therefore,
number of people left after 1 week = 157286.4
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find the number of triangles that can be formed using 14 points in a plane such that 4 points are collinear?
The number of triangles that can be formed using 14 points in a plane such that 4 points are collinear is 360.
If 4 points are collinear, then we can choose any 3 of those points to form a line segment, which cannot be extended to form a triangle.
we need to choose 3 points from the 14 points such that no 3 of them are collinear.
The number of triangles that can be formed from n non-collinear points in a plane is given by the formula:
C(n,3) = n(n-1)(n-2)/6
where C(n,3) is the binomial coefficient for choosing 3 items out of n.
So, to find the number of triangles that can be formed using 14 points in a plane such that 4 points are collinear,
we first need to find the number of ways to choose 3 points from 14 points, and then subtract the number of ways to choose 3 points from the 4 collinear points.
That is:
Total number of triangles = C(14,3) - C(4,3)
Total number of triangles = 364 - 4
Total number of triangles = 360
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A website’s profit as a function of visitors is represented in the table. the function is quadratic.
visitors (thousands). monthly profit ($ thousands)
0. 0
0. 5. −10
1. 0
2. 80
3. 240
select from the drop-down menu to correctly complete the sentence.
the y-intercept represents
options:
the number of visitors when the publisher breaks even
the maximum amount of profits
the amount of profit when there are 0 visitors
The amount of profit when there are 0 visitors.
In the context of the given quadratic function, the y-intercept represents the amount of profit when there are 0 visitors.
To explain, the y-intercept is the point at which the function intersects the y-axis. This occurs when the x-value (number of visitors in thousands) is 0. In the given table, the y-intercept corresponds to the data point (0, 0), meaning there is a profit of $0 thousands when there are 0 visitors.
Looking at the table, we can see that when the number of visitors is 0, the profit is also 0. Therefore, the y-intercept of the function represents the amount of profit when there are 0 visitors.
So the correct option is: "the amount of profit when there are 0 visitors".
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The monthly demand function for product sold by monopoly is p 2,220 1x2 dollars, and the average cost is C = 900 + 14x + x2 dollars. Production is limited to 1,000 units, and x is in hundreds of units_ Find the revenue function, R(x)_ R(x) Find the cost function, C(x): C(x) Find the profit function, P(x) P(x) (a) Find P'(x) . P'(x) Considering the limitations of production, find the quantity (in hundreds of units) that will give the maximum profit. hundred units (b) Find the maximum profit
To find the revenue function, we need to multiply the price (p) by the quantity (x):
R(x) = xp = (2220 - x^2) x
Expanding this expression, we get:
R(x) = 2220x - x^3
To find the cost function, we can simply use the given formula:
C(x) = 900 + 14x + x^2
To find the profit function, we subtract the cost from the revenue:
P(x) = R(x) - C(x)
= (2220x - x^3) - (900 + 14x + x^2)
= -x^3 + 2206x - 900
To find P'(x), the derivative of P(x) with respect to x, we take the derivative of the expression for P(x):
P'(x) = -3x^2 + 2206
Setting P'(x) equal to zero and solving for x, we get:
-3x^2 + 2206 = 0
x^2 = 735.333...
x ≈ 27.104
We can't produce a fraction of a hundred units, so we round down to the nearest hundredth unit, giving x = 27.
To confirm that this value gives a maximum profit, we can check the sign of P''(x), the second derivative of P(x) with respect to x:
P''(x) = -6x
When x = 27, P''(x) is negative, which means that P(x) has a local maximum at x = 27.
Therefore, the quantity that will give the maximum profit is 2700 units (27 x 100).
To find the maximum profit, we evaluate P(x) at x = 27:
P(27) = -(27)^3 + 2206(27) - 900
= 53,955 dollars
Therefore, the maximum profit is $53,955.
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In a group of students,
[tex] \frac{8}{13} [/tex]
of the group are scouts and the rest are police cadets. If
[tex] \frac{3}{8} [/tex]
of the scouts or 15 of them are prefects, calculate the number of police cadets in the group
The calculated number of police cadets in the group is 25
Calculating the number of police cadets in the groupFrom the question, we have the following parameters that can be used in our computation:
Scouts = 8/13
Police cadets = the rest
This means that
Police cadets = 1 - 8/13
Evaluate
Police cadets = 5/13
Also, we have
Prefects = 3/8 or 15 of scouts
This means that
3/8 * Scouts = 15
Scouts = 40
So, we have
Total = 40/(8/13)
Total = 65
Recall that
Police cadets = 5/13
So, we have
Police cadets = 5/13 * 65
Evaluate
Police cadets = 25
Hence, the number of police cadets in the group is 25
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Determine the intercepts of the line.
Do not round your answers.
-5x - 4y = 10
Step-by-step explanation:
-5x - 4y = 10
Intercept-y (x = 0)
-5 (0) - 4y = 10
-4y = 10
y = - 5/2
(0, -5/2)
Intercept-x (y = 0)
-5x - 4 (0) = 10
-5x = 10
x = -2
(-2, 0)
#CMIIWwhat should be added to a-2b 3c to get 2a 3b-4c
Answer:
a + 5b - 7c
Step-by-step explanation:
Let the number to be added by X
then,
a - 2b + 3c + X = 2a + 3b - 4c
X = a + 5b - 7c
Molly has 250 trading cards. she gives n trading cards to her friend carol. marcus has 430 trading cards. he gives away three times as many cards as molly does. how many trading cards did molly give away if molly and marcus have the same number of trading cards left?
a.) 70 trading cards
b.) 80 trading cards
c.) 90 trading cards
d.) 180 trading cards
Molly gave away 90 trading cards, which is option (c).
Let's start by figuring out how many trading cards Marcus gave away. We know that Molly gave away n trading cards, so she has 250 - n cards left. Marcus gave away three times as many cards as Molly did, so he gave away 3n cards. That means he has 430 - 3n cards left.
We also know that Molly and Marcus have the same number of trading cards left, so:
250 - n = 430 - 3n
Simplifying and solving for n, we get:
2n = 180
n = 90
Therefore, Molly gave away 90 trading cards, which is option (c).
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