Which graph represents the solution of -3m < 15?

Considering the given translation, the vertex that is not part of the image is:

H(3,0).

The translations to an image are represented as follows:

The vector notation of a translation is given as follows:

{x ± a, y ± a}

In this problem, this notation is:

{3, -3}.

Hence the rule applied to each vertex of the image is:

(x,y) -> (x + 3, y - 3).

The vertices of the original figure are as follows:

( -7, 3), (- 4,6), ( -1, 3) and (-4, 0)

Applying the translation rule, the vertices of the image are given as follows:

(-4, 0), (-1, 3), (2, 0), (-1, -3).

The lone coordinate without a vertex of the image is H(3,0).

The problem is given by the image at the end of the answer.

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The solution to the compound inequality is x < 3 and x >6. The graph of the solution is shown.

The relation between two unequal expressions is defined as inequality.

The given inequalities are 3x + 6 < 15 and  2x - 5 >7.

Solve the first inequality:

3x + 6 <15

3x < 15 -6

3x < 9

x < 3

Solve the second inequality:

2x - 5 > 7

2x > 7 + 5

2x > 12

x > 6

Hence, the solution to the compound inequality is x < 3 and x >6.

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The seal's new position relative to the surface of the ocean is 47 meters below.

It is important to note that that question has to do with elevation which is the change in position with regards to the sea or ocean level.

In this case, the harbour seal dives 35 metres below the ocean's surface and then it dives down an additional 12 metres

The new position will be;

= -35 - 12

= -47

This implies that it's 47 meters below the ocean surface.

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Answer:

5 pounds

Step-by-step explanation:

1 kg = 2.205 lbs.

2.25×2.205

⇒4.96125

For isosceles triangle RST  the measure of angle T is 34 degree

In this question, we have been given a isosceles triangle RST with RS = RT.

So, by isosceles triangle theorem,

angle S = angle T

So, angle T = (3x - 2)°

We know that the sum of all angles of triangle is 180°

∠R + ∠S + ∠T = 180°

9x + 4 + 3x - 2 + 3x - 2 = 180°

15x + 4 - 4 = 180°

15x = 180°

x = 12

So, 3x - 2 = 3(12) - 2

                = 34°

Therefore, for triangle RST  the measure of angle T is 34 degree

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The area of the given figure is 25cm².

Area of rectangle

Area = length x width

Perimeter of rectangle

Perimeter = length + length + width + width

Hence, we have

length = 5cm

width = 5cm

then, by applying the Area of the rectangle, we get

Area = length x width

Area = 5 x 5

      = 25cm²

Hence, The area of the given figure is 25cm².

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Step-by-step explanation:

the solution to a system of functions (lines or any other form of curve) is the point (or points), where they intersect.

in this case : the point (2, 0)

FYI : if there is no intersection, then there is no solution at all (like with parallel lines).

if the curves fully overlap for at least some distance, then we have infinitely many solutions (at least for real numbers). like for identical lines.

The exponential growth of 16.63% will take approximately 10.80 years to reach a population of 1134

An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on.

Data;

f(x) = P(1 + r)ˣ

x = time

Substituting the values

1134 = 215(1 + 0.1663)^ˣ

x = 10.80

It will take approximately 10.8 years to reach a growth of 1134

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Answer: The correct answer is "10.0 years"

Step-by-step explanation:

I took the test

The probability that the fish is at most 0.5 meters away from the center of the container, considering the volume of the cube, is given as follows:

0.0723 = 7.23%.

The volume of a cube of side length s is given by the side length cubed, that is:

V = s³.

The cube in this problem has a side length of 1.2 meters, hence the volume is given as follows:

V = 1.2³ = 1.728 cubic meters.

Considering only the inner 0.5 meters of the cube, the volume is given as follows:

V = 0.5³ = 0.125 cubic meters.

A probability is given by the division of the number of desired outcomes by the number of total outcomes, hence:

p = 0.125/1.728 = 0.0723 = 7.23%.

(desired volume is of 0.125 m³, total is of 1.728 m³).

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If Abigail Henderson has $3400.00 budgeted for spending money on an upcoming trip .The currency needed is 200 euro and 500 pounds.

Formulate an equation

1.30x + 1.60y = 3400

Hence,

x =4y Equation 1

1.30x + 1.60y = 3400 Equation 2

Substitute eq1 into eq2

1.30(4y) + 1.60y = 3400

5.2y +1.60y =3400

6.8y =3400

Divide both side by 6.8y

y =3400/6.8

y = 500

Number of euro

4y where y = 500

4(500)

=2000

Therefore  the answer in practical terms is : 2000 euro of European currency and 500 pounds of Britain currency are needed.

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The length of the segment CB in triangle ABC where [tex]\overline{AM}[/tex] is a median line and CM = 5·x - 2, MB = 3·x + 12, CM = MB, is 66 units

A median line is a line that is drawn from a vertex of a triangle to the middle of the opposite side such that the it bisects the opposite side.

The parameters are; [tex]\overline{AM}[/tex] = A median line

Length of segment CM = 5·x - 2

Length of segment MB = 3·x + 12

Required; The length of segment CB

The median line [tex]\overline{AM}[/tex] bisects the segment CB

Therefore; CM = MB

CB = CM + MB (Angle addition postulate)

Which gives; 5·x - 2 = 3·x + 12 (substitution property of equality)

2·x = 14

x = 14 ÷ 2 = 7

CB = CM + MB

CB = (5·x - 2) + (3·x + 12)

Which gives; CB = 8·x + 10

x = 7

CB = 8×7 + 10 = 66

The length of segment CB =  66

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The correct statement:  

1/3 equal to 4/12; 4/6 equal to 2/3; 2/5 equal to 5/10

incorrect statement:  2/5 equal to 1/3

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

a) 4/12

Writing into Simplest form

4/12 = 1/3

b) 4/6

Writing into Simplest form

4/6 = 2/3

c) 2/5 cannot be simplified to 1/5

d) 5/10

Writing into Simplest form

5/10= 1/2

Hence, The correct statement:  1/3 equal to 4/12; 4/6 equal to 2/3; 2/5 equal to 5/10 and incorrect statement:  2/5 equal to 1/3.

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Answer:

[tex]y+10=\frac{13}{8}(x-20)[/tex]

Step-by-step explanation:

The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex].

The solution for the given inequality has been graphed in detail.

A linear inequality can be gives the values for a variable in an interval of numbers.

Given inequalities are as below,

2x - 7 > 3 and 4 - x < -4

They can be simplified as,

2x - 7 > 3    

=> 2x > 10    

=> x > 5

And,  

4 - x < -4

=> x - 4 > 4

=> x > 8

The solution of the given inequality is the intersection of two solutions x > 5 and x > 8, which is x > 8.

This is graphed as follows,

Hence, the given inequality has solution x > 8 which has been graphed.

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Option B. The appropriate conclusion at the 5% significance level is to Reject the null hypothesis, the population mean is significantly different from 123

H0: mean = 123

H1 : mean ≠ 123

We have the p value of the statistics stated already in the question as p value = 0.0037.

The level is significance that we have been given in the question is 5% = 0.05

We are to test here if the true mean is different from 123.

Hence we would be testing the p value against the significance level.

We can see that P value is  < level of significance.

0.0037 < 0.05

Hence we would reject the null hypothesis.

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Mr. Pinello wants each container to contain the same number of coloured pencils and markers, the most containers he can create is 16.

What is the Greatest Common Factor?

The biggest positive integer that divides evenly into all the numbers with no remainder is the greatest common factor (GCF, GCD, or HCF) of a collection of whole numbers.

We have,

The number of coloured pencils Mr. Pinello has = 80.

The number of markers and pencils Mr. Pinello has = 60.

The most containers Mr. Pinello can create to ensure that each one contains an identical amount of coloured pencils and markers.

The GCD of the number of coloured pencils and markers will be the largest number of containers to have the same number of items when the same number of items must be preserved.

Calculating the gcd of  and 80 and 64 is:

The greatest common divisor (GCD) of both 80 and 64 is 16.

∴ GCD = 16

Therefore, If Mr. Pinello wants each container to contain the same number of coloured pencils and markers, the most containers he can create is 16.

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The first mechanic worked for 10 hours and second mechanic worked for 5 hours.

Given,

Price of first mechanic service =$85/hr

Price of second mechanic service=$45/hr

Total time they worked together=15 hours

Total combined price charged=$1075

Let

Time spend by first mechanic on work =x

Time spend by second mechanic on work =y

Price charged by first mechanic on total work =85x

Price charged by second mechanic on total work=45y

Equation for total time spend by them together on work can be written as,

[tex]x+y=15.....i\\\\y=15-x[/tex]

Equation for total price charged by them can be written as,

[tex]85x+45y=1075\\[/tex]

Substituting y,

[tex]85x+45(15-x)=1075\\\\85x+675-45x=1075\\\\40x+675=1075\\\\40x=1075-675\\\\40x=400\\\\x=10\\[/tex]

Substituting x in eq.[tex]i[/tex],

[tex]10+y=15\\\\y=15-10\\\\y=5[/tex]

Hence, the first mechanic worked for 10 hours and second mechanic worked for 5 hours.

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The statement that correctly describes the graph of the relationship is (d) A line that goes through (0, 0) and (4.3, 17.2).​

The table of values is given as

x 4.3 9.2 3.4

y 17.2 36.8 13.6

The table shows a proportional relationship

This means that the line of the graph must pass through the origin i.e. (0, 0)

From the table of values, we have the following point

(4.3, 17.2)

This means that the line of the graph goes through (0, 0) and (4.3, 17.2).​

Hence, the true statement is (d)

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Answer:

No, it is not proportional because 9.2 over 18.4 does not equal 17.6 over 52.8.

Step-by-step explanation:

The total number of movies that the students saw is 105.

I got the answer by adding all of the values that the students saw. So I add 14,10,16,15...etc. which gives me the total of 105.

Answer:

68°

Step-by-step explanation:

The angles are equal to each other.  Set them equal and solve for x

5x + 18 = 8x - 12  Subtract 5x from both sides of the equation

18 = 3x - 12  Add 12 to both sides of the equation

30 = 3x  Divide both sides by 3

10 = x

Now that you have found x plug is back into  5x + 18

5(10) + 18

50 + 18 = 68

Answer:

∠ FLJ = 68°

Step-by-step explanation:

∠ EKG and ∠ FLJ are alternate exterior angles and are congruent , then

8x - 12 = 5x + 18 ( subtract 5x from both sides )

3x - 12 = 18 ( add 12 to both sides )

3x = 30 ( divide both sides by 3 )

x = 10

Then

∠ FLJ = 5x + 18 = 5(10) + 18 = 50 + 18 = 68°

Answer:

There isn't one. There is no solution.

Step-by-step explanation:

There are multiple ways to solve this system, but here's what I did:

Solve the both equations for s:

   s/2 + 5t = 3 + 5t  ⇒  s = 6

   3t - 6s = 9 + 3t  ⇒  s = -3/2

Since s cannot equal both 6 and -3/2 at the same time, there is no real solution to this system.

Answer: C.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

It will take 80 gallons of water to fill the fish tank.

The amount of space occupied by a three-dimensional object or region of space.

Given that, Anna is going to clean the fish tank, which measures 48 inches long by 11 inches wide by 35 inches high

The fish tank is cuboidal,

Volume of cuboid = length*width*height

Therefore, volume of fish tank = 48*11*35 = 18,480 in³

1 gallon = 231 in³

So, 18,480  in³ = 18,480/231 gallons = 80 gallons

Hence, Volume of tank = 80 gallons

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68 calls she received in each evening .

A straight line equation and equations with a maximum order of one are referred to as "linear equations." The formula for the linear equation can be written as Y = mx + b, where m is the slope of the line, b is the y-intercept, and x and y are the variables. Slopes tell us the direction and steepness of a line. The value of y when x is 0 is referred to as the y-intercept because (0,y) is the point where the line crosses the y-axis.

Let's say the number of calls on the second night was x.

The first evening was then x+7.

The third evening she received 4x calls.

Add them up to make 109 calls....

x + x+7 + 4x = 109

6x + 7 = 109

6x = 102

x = 17 calls

x+7 = 24 calls

4x = 68 calls

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The equivalent rational expression with the same denominator as given will be 8(c - 8)/[(c - 3)(5c - 9)(c - 8)] and  2c(c - 3)/[(c - 3)(5c - 9)(c - 8)].

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

As per the given expression,

8/(5c² - 6c - 27) , 2c/(5c² - 31c - 72)

Now, take the first denominator,

5c² - 6c - 27 = 5c² - 15c + 9c - 27

⇒ 5c(c - 3) - 9(c - 3)

⇒ (c - 3)(5c - 9)

Take the second denominator

5c² - 31c - 72 = 5c² - 40c + 9c - 72

⇒ 5c(c - 8) + 9(c - 8)

⇒ (c - 8)(5c + 9)

Therefore, the expression converts as,

8/[(c - 3)(5c - 9)] , 2c/[(c - 8)(5c + 9)]

8/[(c - 3)(5c - 9)] = 8(c - 8)/[(c - 3)(5c - 9)(c - 8)]

2c/[(c - 8)(5c + 9)] = 2c(c - 3)/[(c - 3)(5c - 9)(c - 8)]

The denomiantor of both expression are same.

Hence "The equivalent rational expression with the same denominator as given will be 8(c - 8)/[(c - 3)(5c - 9)(c - 8)] and  2c(c - 3)/[(c - 3)(5c - 9)(c - 8)]".

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The structured question below,

Using trigonometric ratios, tan a + cot a = (cos a + sin a) / sin a * cos a

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trigonometric ratios are evaluated with respect to sides and angles.

In the question given, the trig ratio is

tan a + cot a

We can simplify this as

tan a = sin a / cos a

cot a = 1 / tan a = 1 / sin a / cos a = cos a / sin a

Adding both ratios together

tan a + cot a = (sin a / cos a) + (cos a / sin a)

tan a + cot a = (cos a + sin a) / sin a * cos a

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