10) Determine which point is a solution of the linear inequality.
92 + 3y < 6
O (1, -1)
O (2, -2)
• (1,1)
• (1,3)

The function of the area of the figure is M(x) = (x + 2)(3/2x - 2)

The total area of the composite figure is the sum of the areas of the individual shapes

So, we have

Area = Rectangle + Triangle

Using the area formula, we have

M(x) = (x + 2)(x - 2) × 1/2 × x ×  (x + 2)

Factorize the expression to get the function

M(x) = (x + 2)(x - 2 + x/2)

So, we have

M(x) = (x + 2)(3/2x - 2)

Hence, the function of the area of the figure is M(x) = (x + 2)(3/2x - 2)

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As per the given scenario, the amplitude of the tip of King Arthur's Sword is equal to the length of the side of either the regular hexagon or the regular pentagon.

To decide the amplitude of the tip of King Arthur's Sword, we want to locate the gap from the center of the regular hexagon and pentagon to one in every of their vertices.

A regular hexagon has six identical aspects and 6 same angles. The distance from the center to one of the vertices of a everyday hexagon is identical to the length of its side.

Thus, a everyday pentagon has 5 equal facets and 5 same angles. The distance from the middle to one of the vertices of a everyday pentagon is also equal to the length of its aspect.

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All the values are,

sin π = 0

cos π = - 1

tan π = 0

sin π/2 = 1

cos π/2 = 0

tan π/2 = ∞

We have to given that;

⇒ θ = π

⇒ θ = π/2

Hence, All the values of sine, cosine and tangent of θ are,

At θ = π;

sin θ = sin π

      = 0

cos θ = cos π

         = - 1

tan θ = tan π

        = 0

At  θ = π/2;

sin θ = sin π/2

      = 1

cos θ = cos π/2

         = 0

tan θ = tan π/2

        = ∞

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To solve the inequality 6(x−1)>−18, we need to isolate x on one side of the inequality. We can do this by dividing both sides of the inequality by 6, but since we're dividing by a negative number, we need to flip the inequality sign:

6(x−1)>−18

x - 1 > -3

Adding 1 to both sides of the inequality gives us:

x > -2

Therefore, the solution to the inequality is x > -2.

Answer: x > -2

Step-by-step explanation:

     To solve the inequality, we will isolate the given variable.

Given:

     6(x − 1) > −18

Distribute the 6 into (x - 1):

     6x − 6 > −18

Add 6 to both sides of the inequality:

     6x > -12

Divide both sides of the inequality by 6:

     x > -2

ANSWER:

768

Step-by-step explanation:

He has 1,200. We need to find 8% of 1,200. 8%x1,200=96x8 years= 768

The image of the point (-3, -7) after a reflection over the x-axis is (-3, 7)

From the question, we have the following parameters that can be used in our computation:

Point = (-3, -7)

Transformation rule

A reflection over the x-axis

The rule of a reflection over the x-axis is

(x, y) = (x, -y)

Using the above as a guide, we have the following:

Image = (-3, 7)

Hence the image of the point after a reflection over the x-axis is (-3, 7)

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The greatest common factor is 3x² and GCF form of polynomial is

3x²(3x-2).

The given polynomial is

9x³ - 6x²

We can write it as;

3x²(3x-2)

We know that

The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor (HCF) is another name for it.

Therefore 3x² is its GCD.

Divide each term of polynomial 3c,

6c³ ÷ 3c = 2c² and  -9c ÷ 3c = -3

Thus,

3x²(3x-2) is the factored version of the polynomial with the highest common factor.

Also if GCD is 1 then after dividing each term by 1 we get same result

thus the polynomial be 3x²(3x-2).

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Answer:

To solve this problem using spherical coordinates, we need to parameterize the region E using rho, theta, and phi. The cone z = x^2 + y^2 becomes phi = arctan(sqrt(x^2+y^2)/z), and the sphere x^2 + y^2 + z^2 = 1 becomes rho = 1, while x^2 + y^2 + z^2 = 64 becomes rho = 8. Then, we can integrate over the bounds rho = 1 to rho = 8, theta = 0 to theta = 2pi, and phi = 0 to phi = arctan(sqrt(x^2+y^2)/z), using the integrand x^2 + y^2 + z^2. The final result is a numerical value that represents the volume of the region E.

Answer:

1 - ($73,310.56/$73,608.40)^12 = .047

= 4.7%

The image of vertex C under the given similarity transformation is (4, 2).

To apply the given similarity transformation, we need to perform two transformations: a rotation of 90 degrees counterclockwise about the origin (denoted by R) and a dilation by a factor of 2 (denoted by D2). We perform the transformations in order: first the rotation, then the dilation.

The image of a point (x, y) after a rotation of 90 degrees counterclockwise about the origin is (-y, x).

Thus, the image of C after the rotation is:

C' = (-(-2), 1) = (2, 1)

To find the image of C' after the dilation by a factor of 2, we multiply each coordinate by 2:

C" = (22, 21) = (4, 2)

Therefore, the image of vertex C under the given similarity transformation is (4, 2).

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Answer:

The 13.2 meters from that point on the ocean floor to the wreck.

Step-by-step explanation:

As given

A ship's sonar finds that the angle of

depression to a ship wrack on the bottom of the ocean is 12.5°.

If a point on the ocean floor is 60

meters.

Now by using the trigonometric identity.

tano = Perpendicular /Base

As shown in the figure given below.

Perpendicular CB

Base AC = 60 meters

0 = 12.5°

Put in the identity CB

tan 12.5°

AC

tan 12.5° CB 60

tan 12.5° 0.22

tan 12.5° = 0.22

0.22 CB 60

CB = 60 × 0.22

CB= 13.2 meters

Therefore the 13.2 meters from that point on the ocean floor to the wreck.

The value of x in the diagram given 42°

Using angle theorems, the angles are opposite and the reflex angles can be calculated thus :

Recall :

Sum of reflex angles is 360°

(x + x + (3x+12) + (3x + 12) ) = 360°

2x + 6x + 24 = 360

8x = 360 - 24

8x = 336

x = 336/8

x = 42°

Hence, the value of x is 42°

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350 feet of fencing is needed to Enclose the backyard

To calculate the amount of fencing needed to enclose the backyard, we need to find the length of the three long sections of the fence.

Since the yard has a width of 65 feet and the two short sections of the fence each measure 10 feet, the total width of the yard plus the short sections of the fence is:

65 + 10 + 10 = 85 feet

Next, we need to find the length of the yard plus the two short sections of the fence. Since the length of the yard is 80 feet, and there are two short sections of the fence that are each 10 feet long, the total length of the yard plus the short sections of the fence is:

80 + 10 + 10 = 100 feet

Now we can calculate the length of the three long sections of the fence by adding up the perimeter of the yard plus the short sections of the fence and then subtracting the lengths of the two short sections of the fence:

2(85 + 100) - 2(10) = 350 feet

Therefore, 350 feet of fencing is needed to enclose the backyard.

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The number line is shown below.

Here's a number line with 3.5, -3.5, and 0 plotted:

     -4     -3     -2     -1      0      1      2      3      4

       |       |        |       |       |       |       |       |       |

       |               o      o             o                       |

       |                               o                              |

As you can see, 3.5 is to the right of 0, while -3.5 is to the left of 0.

They are also equidistant from 0, meaning that their distance from 0 is the same.

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The value of x that makes the equation true is 0.2.

We have the Equation,

0.17x - 0.03 = 0.03x - 0.002

Simplifying the equation by adding 0.002 to both sides, we get:

0.17x - 0.028 = 0.03x

Subtracting 0.03x from both sides, we get:

0.14x - 0.028 = 0

Adding 0.028 to both sides, we get:

0.14x = 0.028

Dividing both sides by 0.14, we get:

x = 0.2

Therefore, the value of x that makes the equation true is 0.2.

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The confidence interval based on the given values (x = 45, n = 96, Confidence level = 95%.

The confidence level (95%), sample size (n = 96), and sample mean (x = 45), we can calculate the margin of error and the confidence interval. Here's how:

1. Margin of Error:

The margin of error represents the maximum expected difference between the true population parameter and the sample estimate. It depends on the confidence level and the standard deviation (which we don't have in this case).

Since the standard deviation is unknown, we can use the t-distribution to estimate it. With a sample size of n = 96, the degrees of freedom are (n - 1) = 95. Considering a 95% confidence level, the critical value for a two-tailed test is approximately 1.984 (referencing a t-distribution table or calculator).

The margin of error (E) can be calculated using the following formula:

E = critical value * (standard deviation / sqrt(n))

However, since we don't have the standard deviation, we can't compute the margin of error in this case.

2. Confidence Interval:

The confidence interval represents a range of values within which the true population parameter is likely to fall.

The confidence interval can be calculated using the formula:

CI = x ± (critical value * standard deviation / sqrt(n))

The confidence interval based on the given values (x = 45, n = 96, confidence level = 95%.

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a) The solution to the equation is given as follows: x = -12.

b) The solution to the inequality is given as follows: -12 ≤ x < 7.

The equation for this problem is given as follows:

f(x) = g(x).

The point of intersection of the functions f(x) and g(x) is given as follows:

(-12, -7).

Hence the solution is given as follows:

x = -12.

For the inequality, we have that:

Hence the solution to the inequality is given as follows:

-12 ≤ x < 7.

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Answer:

Easy

Step-by-step explanation:

Let the time taken by Badri to complete the work be B. Then Amit can complete the work in 2.25 days, so we can write:

A = 2.25/B

Chetan takes double that of Badri to complete the work, so we can write:

C = 2B

Das takes double that of Chetan to complete the work, so we can write:

D = 2C = 4B

Let the first group consist of Amit and Das, and the second group consist of Badri and Chetan. Then the time taken by the first group to complete the work is:

T1 = A + D = 2.25/B + 4B

The time taken by the second group to complete the work is:

T2 = B + C = B + 2B = 3B

The difference between the times taken by the two groups to complete the work is:

T2 - T1 = 3B - (2.25/B + 4B) = 3B - 2.25/B - 4B

To minimize this difference, we take the derivative with respect to B and set it equal to zero:

d/dB (3B - 2.25/B - 4B) = 0

3 + 2.25/B^2 - 4 = 0

2.25/B^2 = 1

B = sqrt(2.25) = 1.5

Therefore, the time taken by Badri to complete the work is B = 1.5 days. Amit takes 2.25/1.5 = 1.5 days, Chetan takes 2B = 3 days, and Das takes 4B = 6 days.

To minimize the difference between the times taken by the two groups, we can take the faster group to consist of Amit and Badri, and the slower group to consist of Chetan and Das. The faster group takes 1.5 + 1.5 = 3 days to complete the work, and the slower group takes 3 + 6 = 9 days to complete the work. Therefore, the composition of the faster group could be Amit and Badri.

Answer: 2500

Step-by-step explanation: Step-by-step explanation: If you calculate out 5x6 that equals 30 and 5x5-5 equals 20, when you do 30+20 that equals 50 and 50 to the 2nd power is 50x50 and that would equal 2500

For this reason, 968 grams of coffee are needed to make a grande cup, and 998 grams are needed to make a jumbo cup.

Let's call the amount of coffee required to make a grande cup "g" and the amount of coffee required to make a jumbo cup "j". We want to find the values of g and j.

From the first piece of information, we know that:

60g + 59j = 61,644

From the second piece of information, we know that:

60g + 74j = 71,184

We can solve this system of equations by using the method of elimination. To eliminate g, we can subtract the first equation from the second equation:

(60g + 74j) - (60g + 59j) = 71,184 - 61,644

Simplifying, we get: 15j = 9540

Dividing by 15, we get: j = 636

Now that we know j, we can substitute it into either equation to find g. Let's use the first equation:

60g + 59(636) = 61,644

Simplifying, we get: 60g = 59,880

Dividing by 60, we get: g = 998

Therefore, the amount of coffee required to make a grande cup is 968 grams, and the amount of coffee required to make a jumbo cup is 998 grams.

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Answer:

I don't understand you

Answer: n = 412

Step-by-step explanation:

If the last two digits of a number are divisible by 4, the whole number is divisible by 4 since any multiple of 100 is divisible by 4. The largest number that can be created is 421 since the largest number is in the hundreds place and then the second largest number is in the tens place, but 21 is not divisible by 4. The second largest number, 412, still has the greatest number as the hundreds place, but the tens place is now smaller. 12 is divisible by 4, so 412 is divisible by 4. We know that 412 is the largest possible number for n because there is only one larger number than 412, which is 421 and it is not divisible by 4.

Answer:

-----------------------------

Divisibility rule for 4:

We have 3 digits and the greatest number can be made by these digits is 421. But it has to be divisible by 4, hence we rearrange it to 412. Since 12 is divisible by 4, the number is divisible by 4.

Now, we choose 9 as the fourth digit. It will be a first digit from left and form the largest possible number n:

How to compare fractions is explained in the solution below.

One way to compare fractions is to convert them into their decimal form and decide which is the smaller of the two.

Example: 7/10 and 3/5 become 0.7 and 0.6.

Hence 3/5 is smaller than 7/10.

The other way is to convert them into fractions with identical denominator.

For that multiply the denominator of one fraction with the numerator and denominator of the other.

Do the same with the other denominator and the other fraction. Then decide which fraction is the smaller of the two.

Example: 7/8 and 13/15 become (7*15)/(8*15) = 105/120 and

(13*8)/(15*8) = 104/120.

Hence 13/15 is smaller than 7/8.

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Step-by-step explanation:

Based on the given tables for x = 1, 2, 3, and 4:

A. x: 1, 2, 3, 4. y: 1/2, 1, 1 1/2, 2

B. x: 1, 2, 3, 4. y: 1, 1/2, 1/3, 1/4

C. x: 1, 2, 3, 4. y: 7, 9, 13, 21

D. x: 1, 2, 3, 4. y: 0, 6, 16, 30

A linear function has a constant rate of change (slope). Let's calculate the differences in y-values for each table:

A. 1 - 1/2 = 1/2, 1 1/2 - 1 = 1/2, 2 - 1 1/2 = 1/2 (constant differences)

B. 1 - 1/2 = 1/2, 1/2 - 1/3 = 1/6, 1/3 - 1/4 = 1/12 (not constant)

C. 9 - 7 = 2, 13 - 9 = 4, 21 - 13 = 8 (not constant)

D. 6 - 0 = 6, 16 - 6 = 10, 30 - 16 = 14 (not constant)

Table A represents a linear function, as the differences in the y-values are constant (1/2).

The solution set of this inequality is {x| x > -6.1}

Here we have the inequality:

2x + 8 > -4.2

To find the solution set, we need to isolate the variable x in one of the sides of the inequality. Doing that we will get:

2x + 8 > -4.2

2x > -4.2 - 8

2x > -12.2

x > -12.2/2

x > -6.1

So the set of all numbers larger than -6.1, this in number form is:

{x| x > -6.1}

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Answer:

41

Step-by-step explanation:

Given

Perimeter of a square ( P ) = (x + 7) cm

Side length ( L ) = 12 cm

To find : The value of x

Formula :

Perimeter of a square = 4L

4 * 12 = x + 7

48 = x + 7

x + 7 = 48

x = 48 - 7

x = 41

From the given Venn diagram the value of P(A or B) is 0.

From the given Venn diagram, we have P(A)=14, P(B)=10 and (P and B)=24.

We know that, P(A or B)=P(A)+P(B)-P(A and B)

P(A or B)=14+10-24

P(A or B)=0

Therefore, from the given Venn diagram the value of P(A or B) is 0.

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Answer:

C. x =8; y = -4

Step-by-step explanation:

To find the x and y intercepts, substitute with zero.

8x - 16y = 64

Finding the x-intercept:

8x - 16(0) = 64

8x = 64

Divide both sides by 8.

x = 8

Finding y-intercept:

8(0) - 16y = 64

-16y = 64

Divide both sides by -16.

y = -4

Hello !

Answer :

Explanation :

[tex] \to \boxed{ ({x}^{a}) {}^{b} = {x}^{ab} } [/tex]

[tex] \to \boxed{ {x}^{ \frac{1}{n} } {}^{} = \sqrt[n]{x} } [/tex]

[tex] ({x}^{4} ) {}^{ - \frac{2}{3} } = {x}^{- \frac{2}{3} \times 4} \\ \boxed{= {x}^{ - \frac{8}{3} } } \\ \boxed{= \sqrt[3]{ {x}^{ - 8} }} \\ \boxed{ = \sqrt[3]{ ({x}^{ 4}) {}^{ - 2} }}[/tex]

Have a nice day ;)