Find the length of the rectangle if x = 10.

M = A + |B| is the function's highest possible value. When sin or cos x equals 1, this maximum value is reached. m = A |B| is the function's lowest possible value. If either cos x or sin x is equal to 1, this minimum will be reached.

Example :

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There are no values of t for which u⃗ and v⃗ are perpendicular in the given equation.

To determine the values of t for which u⃗ and v⃗ are perpendicular, we can use the dot product of the two vectors. If the dot product is zero, it indicates that the vectors are orthogonal (perpendicular).

Let's calculate the dot product:

u⃗ · v⃗ = (8t)(i⃗ · i⃗) + (8t)(i⃗ · t^2j⃗) + (15)(j⃗ · i⃗) + (15)(j⃗ · t^2j⃗)

Now, since i⃗ · i⃗ = 1 and j⃗ · j⃗ = 1, we can simplify the expression:

u⃗ · v⃗ = 8t + 8t^3 + 15

For u⃗ · v⃗ to be zero (indicating perpendicularity), we need to solve the equation:

8t + 8t^3 + 15 = 0

This is a cubic equation that we can solve to find the values of t. However, upon closer inspection, we can see that the equation does not have any real roots. Therefore, there are no values of t for which u⃗ and v⃗ are perpendicular.

In other words, the vectors u⃗ = (8t 15)i⃗ j⃗ and v⃗ = i⃗ t^2j⃗ are never perpendicular regardless of the value of t.


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Answer:

x-intercept: (2,0)

y-intercept: (0,-4/3)

vertical asymptote: x = -3

Step-by-step explanation:

To find the x-intercepts, we can set f(x) to 0, which is y=0:

2x-4/x+3 = 0

2x-4 = 0

2x = 4

x = 2

To find the y-intercepts, we can set x to 0:

2(0)-4/(0)+3 = y

y = -4/3

To find the vertical asymptote, we can set the denominator equal to 0:

x+3 = 0

x = -3

Answer:

X = 3

Step-by-step explanation:

Best of lucks!!!

A mathematical statement that two sides of mathematical expressions are equal.

Given expression 6x+5=3x+14

Transpose variables left side and constants to right side.

 6x-3x=14-5

      3x=9

       x=9/3

       x=3

Therefore, The value of the x=3

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The coordinates of B' after the translation described by the rule T(1,4) • r(90°, 0) are (-4,6).

To find the coordinates of B' after the translation, we first need to apply the rotation rule r(90°, 0) to the coordinates of B.

Using the formula for a 2D rotation, the coordinates of B after rotating 90 degrees around the origin (0,0) are (-5,2).

Next, we apply the translation rule T(1,4) to the coordinates of B'. Adding the translation vector (1,4) to the coordinates of (-5,2), we get the coordinates of B' as (-4,6).

Therefore, the coordinates of B' after the translation described by the rule T(1,4) • r(90°, 0) are (-4,6).

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There are 6 ways to decorate the clown hat with three positions using three round pom-poms in three colors.

The worksheet shows the following possibilities:

Position Color

1 Orange

2 Yellow

3 Green

1 Yellow

2 Orange

3 Green

1 Green

2 Orange

3 Yellow

1 Green

2 Yellow

3 Orange

b) Find a better way of representing your investigation responses.

A better way of representing the investigation responses would be to use a table. The table would show the number of ways to decorate the clown hat for each color combination.

For example, the table would show that there is only 1 way to decorate the clown hat with all three pom-poms the same color (orange, yellow, or green).

The table would also show that there are 3 ways to decorate the clown hat with two pom-poms the same color and one pom-pom a different color. For example, there is 1 way to decorate the clown hat with two orange pom-poms and one yellow pom-pom,

1 way to decorate the clown hat with two yellow pom-poms and one orange pom-pom, and 1 way to decorate the clown hat with two green pom-poms and one yellow pom-pom.

The table would be a more efficient way of representing the investigation responses because it would be easier to read and understand. The table would also be easier to update if the investigation were to be repeated with different colors of pom-poms.

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Answer:

tanx= -1 is the correct answer.

Answer:

the radius of the smaller windmill is approximately 60 feet (option D).

Step-by-step explanation:

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.

For the larger windmill:

C = 660 feet

2πr = 660

r = 330/π

r ≈ 105.1 feet

For the smaller windmill:

C = 376 feet

2πr = 376

r = 188/π

r ≈ 59.8 feet

Therefore, the radius of the smaller windmill is approximately 60 feet (option D).

Answer:

D. 60 feet.

Step-by-step explanation:

Radius of big windmill = 1/3 * 210 = 105 ft.

The 2 windmills are similar in shape so

C/R = c/r    where C and R refer to big windmill and c and r are the circumference and radius of the smaller one.

So 660/105 = 376/ r

r = (105 * 376)/660

 = 60 feet.

x = 5/4   or   x = 15/4

Step-by-step explanation:

Answer:

x=-12

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

80=4x+4(−4x−16)

80=4x+(4)(−4x)+(4)(−16)(Distribute)

80=4x+−16x+−64

80=(4x+−16x)+(−64)(Combine Like Terms)

80=−12x+−64

80=−12x−64

Step 2: Flip the equation.

−12x−64=80

Step 3: Add 64 to both sides.

−12x−64+64=80+64

−12x=144

Step 4: Divide both sides by -12.

-12x/-12=144/-12

x=-12

Answer:

x = -12

Step-by-step explanation:

-4x - 16  =   -4 • (x + 4)

80 -  (4x +  -16 • (x + 4))  = 0

12x + 144  =   12 • (x + 12)

12 • (x + 12)  = 0

x+12 = 0

Answer:

66

Step-by-step explanation:

Answer: -30

Let's call the original number "x". Then, we can write the equation as follows:

-3/10 x + 1 = 10

To find the original number, we can isolate x by subtracting 1 from both sides and then multiplying both sides by 10/3:

-3/10 x = 9

x = (9 * 10)/(-3)

x = -30

So, the original number is -30.

Step-by-step explanation:

x current age of the father

y current age of the son

first equation (x-4)+(y-4)=27 so x=27+4+4-y=35-y

second equation (y+5) : (x+5)= 2:7

so (y+5)*7=(x+5)*2

let's replace x we found at the first equation with the one at second equation

(y+5)*7=(35-y+5)*2

7y+35=(40-y)*2

7y+35=80-2y

7y+2y=80-35

9y=45

y=5

x=35-y=35-5=30

The midpoint of the segment is (-15/2, -15/2)

The complete question is in the attached image

The points are given as:

(-8, -7) and (-7, -8)

The midpoint is calculated as:

(x,y) = 1/2 * (x1 + x2, y1 + y2)

So, we have:

(x,y) = 1/2 * (-8 - 7, -7 - 8)

Evaluate the difference

(x,y) = 1/2 * (-15, -15)

Evaluate the product

(x,y) = (-15/2, -15/2)

Hence, the midpoint of the segment is (-15/2, -15/2)

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A stacked histogram is a column chart that displays the number of resources required for or assigned to a project over time.

A stacked histogram is a type of column chart that represents the distribution of resources over time. It is commonly used in project management to visualize the allocation or requirement of resources for a project. The histogram consists of vertical bars, where each bar represents a specific time period, and the height of the bar corresponds to the number of resources.

In a stacked histogram, different categories or types of resources are represented by different colors or patterns within each bar. Each segment of the bar represents the quantity or proportion of a particular resource within that time period. By stacking the segments, the chart provides a visual representation of the cumulative number of resources required or assigned over time.

This type of histogram allows project managers and stakeholders to analyze resource utilization, identify periods of high demand or availability, and make informed decisions about resource allocation and scheduling. It provides a clear overview of resource distribution patterns and helps in optimizing resource management for efficient project execution.

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The Law of Sines says that for a given triangle, the ratio between the sine of an angle and the length of the opposite side is the same for all three angles in a triangle. the sine values of all three internal angles will be the samethe sine values of all three internal angles will be proportional to each otherthe ratio between the sine of the angle and the opposite side will match for all three internal anglesthe sine values of all three angles will be different

In a triangle, we have three angles and three sides. The Law of Sines says that for any triangle, the ratio between the sine of an angle and the length of the opposite side will be the same for all three angles. In other words, the sine values of each angle are proportional to the length of the opposite side.

To put this in mathematical terms, let's consider a triangle with angles A, B, and C, and sides a, b, and c respectively. The Law of Sines can be written as:

sin(A)/a = sin(B)/b = sin(C)/c

This means that if we know the length of any two sides and the measure of the angle opposite one of those sides, we can use the Law of Sines to find the measure of the other angles and sides.

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The measure of the central angle indicated is 270 degrees

The term "diameter" refers to a straight line segment that passes through the center of a circle or a sphere, connecting two points on the circumference or surface of the circle or sphere. In other words, it is the longest distance that can be measured between two points on the edge of the circle or sphere, passing through its center.

To find the measure of the central angle indicated, we need to first identify the endpoints of the diameter that contains points W, T, and X. Let's assume that this diameter is WX. Then, we can find the measure of the central angle WTX by finding the measure of the arc WT and dividing it by 2.

We know that the diameter WX passes through the midpoint of segment VT, which we can find by averaging the coordinates of V and T. Using the coordinates given in the diagram, we have:

V: (9x-2, 15x+10)

T: (15x+10, 9x-2)

Midpoint of VT: ((9x-2 + 15x+10)/2, (15x+10 + 9x-2)/2)

= (12x + 4, 12x + 4)

Since this midpoint lies on the diameter WX, we can find the coordinates of point X by reflecting the midpoint across the y-axis:

X: (-12x - 4, 12x + 4)

Now we can find the measure of the arc WT by finding the difference between the angles formed by radii WT and WX. Let's call the center of the circle O:

m∠WOT = 90 degrees (since WT is a diameter)

m∠WOX = 180 degrees (since WX is a diameter)

m∠TOX = m∠WOT - m∠WOX = -90 degrees

To convert this angle to a positive measure, we can add 360 degrees:

m(arc WT) = m∠WOT - m∠TOX + 360 degrees = 90 degrees - (-90 degrees) + 360 degrees = 540 degrees

Finally, we can find the measure of the central angle WTX by dividing the measure of arc WT by 2:

m∠WTX = m(arc WT)/2 = 540 degrees/2 = 270 degrees

Therefore, the measure of the central angle indicated is 270 degrees

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Answer: -6+13=7

Step-by-step explanation:

Answer:

3r − 9 = –6r

-9 = -6r-3r         (you change the signs when bringing +3r to the other side)

-9 = -9r

r = -9/-9

r = 1

Answer:

\(\boxed {r = 1}\)

Step-by-step explanation:

Solve for the value of \(r\):

\(3r - 9 = -6r\)

-Add \(6r\) to \(3r\):

\(3r - 9 + 6r = -6r + 6r\)

\(9r - 9 = 0\)

-Add \(9\) on both sides:

\(9r - 9 + 9 = 0 + 9\)

\(9r = 9\)

-Divide both sides by \(9\):

\(\frac{9r}{9} = \frac{9}{9}\)

\(\boxed {r = 1}\)

So, the value of \(r\) is \(1\).

The car travels 660 meters after 10 seconds of deceleration.

To solve this problem, we can use the formula: distance = initial velocity * time + (1/2) * acceleration * time^2. The initial velocity is 114 m/s, the time is 10 seconds, and the acceleration is -6 m/s^2 (negative because it represents deceleration). Plugging these values into the formula, we get:

distance = 114 * 10 + (1/2) * (-6) * 10^2

distance = 1140 - 300

distance = 840 meters

Therefore, the car travels 840 meters after 10 seconds of deceleration.

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At α=0.10, there is not enough evidence to claim that the breaking strength is less than 6000 pounds.

To determine if there is enough evidence to claim that the breaking strength of the cables is less than 6000 pounds at α=0.10, we can conduct a one-sample t-test. Given a sample size of 25 cables with an average breaking strength of 5956 pounds and a standard deviation of 138 pounds, we calculate the t-statistic using the formula t = (sample mean - population mean) / (sample standard deviation / √sample size).

Using the given values, the t-statistic is approximately -1.014. With 24 degrees of freedom (sample size minus 1), we compare this t-value to the critical t-value at α=0.10. At α=0.10, the critical t-value is -1.711.

Since the calculated t-value (-1.014) is greater than the critical t-value (-1.711), there is not enough evidence to claim that the breaking strength is less than 6000 pounds at α=0.10.

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The rules AAS, ASA, SSS and SAS are congruence rule of triangle  and the each rules has been explained

The rules AAS, ASA, SSS and SAS are congruence rule of triangle

SSS rule is side-side-side rule, it states that if three sides of the one triangle and three sides of the other triangles are equal, then both triangles are congruent

SAS rule is side-angle-side rule, it states that if two sides and one included angles between the sides of the one triangle is equal to  the two sides and one included angles between the sides of the other triangle, then both triangles are congruent

ASA rule is angle-side-angle rule, it states that if two angles and one included side between the angle of the one triangle is equal to the two angles and one included sides between the angles of the other triangle, then both triangles are congruent

AAS rules is angle-angle-side rule, it states that if two angles and one non included sides of the one triangle is equal to the two angles and one non included sides of the another triangle, then both triangles are congruent

Therefore, the AAS, ASA, SSS and SAS are the rules of congruence of the triangle

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Answer:

\( - 3 \leqslant x < 2\)

I hope I helped you^_^

X-intercept (5,0),(1,0)

Y-intercept (0,5)

Vertex (3,-4)

Axis of Symmetry x=3

The proportion of trick-or-treaters who were not dressed as cowboys is 10/13.

If three out of every thirteen trick-or-treaters were dressed as cowboys, it means that the proportion of trick-or-treaters dressed as cowboys is 3/13.

To find the proportion of trick-or-treaters who were not dressed as cowboys.

we subtract the proportion dressed as cowboys from 1 (since the total proportion of trick-or-treaters must sum to 1).

Proportion not dressed as cowboys = 1 - Proportion dressed as cowboys

Proportion not dressed as cowboys = 1 - (3/13)

Proportion not dressed as cowboys = (13/13) - (3/13)

Proportion not dressed as cowboys = 10/13

Therefore, the proportion of trick-or-treaters who were not dressed as cowboys is 10/13.

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The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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Answer:

Elsie

Step-by-step explanation:

It's kinda obvious

Answer:

Ramon

Step-by-step explanation:

Ramon walked further

Answer:

2(3.14(4)^2)

100.48

answer: 100.5

Step-by-step explanation: