What is the image of the point (-6,4) after a rotation of 180° counterclockwise about the origin?

-1 is the domain of the following

Answer:

see explanation

Step-by-step explanation:

1

1 + [tex]\frac{x-5}{2}[/tex] - [tex]\frac{x+3}{5}[/tex] ≤ 0

multiply through by 10 ( the LCM of 2 and 5 ) to clear the fractions

10 + 5(x - 5) - 2(x + 3) ≤ 0 ← distribute parenthesis on left side and simplify

10 + 5x - 25 - 2x - 6 ≤ 0

3x - 21 ≤ 0 ( add 21 to both sides )

3x ≤ 21 ( divide both sides by 3 )

x ≤ 7

2

[tex]\frac{6x}{5}[/tex] - [tex]\frac{2}{3}[/tex] ≥ 4

multiply through by 15 ( the LCM of 5 and 3 ) to clear the fractions

18x - 10 ≥ 60 ( add 10 to both sides )

18x ≥ 70 ( divide both sides by 18 )

x ≥ [tex]\frac{70}{18}[/tex] , that is

x ≥ [tex]\frac{35}{9}[/tex]

3

[tex]\frac{x}{10}[/tex] - [tex]\frac{2}{8}[/tex] ≥ 1

multiply through by 40 ( the LCM of 10 and 8 ) to clear the fractions

4x - 10 ≥ 40 ( add 10 to both sides )

4x ≥ 50 ( divide both sides by 4 )

x ≥ [tex]\frac{50}{4}[/tex] , that is

x ≥ [tex]\frac{25}{2}[/tex]

Answer:

[tex]\textsf{1.} \quad x \leq 7[/tex]

[tex]\textsf{2.} \quad x \geq \dfrac{35}{9}[/tex]

[tex]\textsf{3.} \quad x \geq \dfrac{25}{2}[/tex]

Step-by-step explanation:

Given inequality:

[tex]1+\dfrac{x-5}{2}-\dfrac{x+3}{5} \leq 0[/tex]

[tex]\textsf{Add \; $\dfrac{x+3}{5}$ \; to both sides}:[/tex]

[tex]\implies 1+\dfrac{x-5}{2}-\dfrac{x+3}{5} +\dfrac{x+3}{5}\leq 0+\dfrac{x+3}{5}[/tex]

[tex]\implies 1+\dfrac{x-5}{2}\leq \dfrac{x+3}{5}[/tex]

[tex]\textsf{Rewrite $1$ as $\dfrac{2}{2}$}:[/tex]

[tex]\implies \dfrac{2}{2}+\dfrac{x-5}{2}\leq \dfrac{x+3}{5}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies \dfrac{2+x-5}{2}\leq \dfrac{x+3}{5}[/tex]

[tex]\implies \dfrac{x-3}{2}\leq \dfrac{x+3}{5}[/tex]

Cross multiply:

[tex]\implies 5(x-3)\leq 2(x+3)[/tex]

[tex]\implies 5x-15\leq 2x+6[/tex]

Subtract 2x from both sides:

[tex]\implies 5x-15-2x\leq 2x+6-2x[/tex]

[tex]\implies 3x-15\leq 6[/tex]

Add 15 to both sides:

[tex]\implies 3x-15+15\leq 6+15[/tex]

[tex]\implies 3x\leq 21[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3x}{3}\leq \dfrac{21}{3}[/tex]

[tex]\implies x \leq 7[/tex]

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

Given inequality:

[tex]\dfrac{6x}{5}-\dfrac{2}{3} \geq 4[/tex]

[tex]\textsf{Add \; $\dfrac{2}{3}$ \; to both sides}:[/tex]

[tex]\implies \dfrac{6x}{5}-\dfrac{2}{3} +\dfrac{2}{3}\geq 4+\dfrac{2}{3}[/tex]

[tex]\implies \dfrac{6x}{5}\geq \dfrac{12}{3}+\dfrac{2}{3}[/tex]

[tex]\implies \dfrac{6x}{5}\geq \dfrac{12+2}{3}[/tex]

[tex]\implies \dfrac{6x}{5}\geq \dfrac{14}{3}[/tex]

Cross multiply:

[tex]\implies 3(6x) \geq 14(5)[/tex]

[tex]\implies 18x \geq 70[/tex]

Divide both sides by 18:

[tex]\implies \dfrac{18x}{18} \geq \dfrac{70}{18}[/tex]

[tex]\implies x \geq \dfrac{70}{18}[/tex]

Reduce the fraction by dividing the numerator and the denominator by 2:

[tex]\implies x \geq \dfrac{70 \div 2}{18 \div 2}[/tex]

[tex]\implies x \geq \dfrac{35}{9}[/tex]

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

Given inequality:

[tex]\dfrac{x}{10}-\dfrac{2}{8} \geq 1[/tex]

[tex]\textsf{Add \; $\dfrac{2}{8}$ \; to both sides}:[/tex]

[tex]\implies \dfrac{x}{10}-\dfrac{2}{8} +\dfrac{2}{8}\geq 1+\dfrac{2}{8}[/tex]

[tex]\implies \dfrac{x}{10}\geq \dfrac{8}{8}+\dfrac{2}{8}[/tex]

[tex]\implies \dfrac{x}{10}\geq \dfrac{8+2}{8}[/tex]

[tex]\implies \dfrac{x}{10}\geq \dfrac{10}{8}[/tex]

Cross multiply:

[tex]\implies 8(x) \geq 10(10)[/tex]

[tex]\implies 8x \geq 100[/tex]

Divide both sides by 8:

[tex]\implies \dfrac{8x}{8} \geq \dfrac{100}{8}[/tex]

[tex]\implies x \geq \dfrac{100}{8}[/tex]

Reduce the fraction by dividing the numerator and the denominator by 4:

[tex]\implies x \geq \dfrac{100 \div 4}{8 \div 4}[/tex]

[tex]\implies x \geq \dfrac{25}{2}[/tex]

The monthly payment of Jason with no additional charge is found as  $1,556.53.

The formula for the calculation of the compound interest is;

CI = A - P

A = P(1 + r/100n)∧nt

Where,

The given values are;

Put the values in the formula;

CI = $3,561.05(1 + 18.2/24×100)∧24×2 - $3,561.05

Simplifying;

CI =  $3,561.05×1.43 - $3,561.05

CI = $5117.58 -  $3,561.05

CI = $1,556.53

Thus, the monthly payment of with no additional charge is found as  $1,556.53.

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Answer:

f = 90 + 32

= 122° (exterior angle)

Answer: d

Step-by-step explanation:

im new at this but i am pretty sure it would be d

An individual has a body fat percentage of 14.4% and weighs 148 pounds,

total pounds of her weight is made up of fat is 21.3pounds (nearest tenth).

As given in the question,

Total weight of an individual =148pounds

Percentage of her weight made up of fat = 14.4%

Pounds  of her weight is made up of fat = 14.4% of 148

                                                                  = ( 14.4 / 100 ) × 148

                                                                  = 21.3 pounds (nearest tenth)

Therefore, an individual has a body fat percentage of 14.4% and weighs 148 pounds, total pounds of her weight is made up of fat is 21.3pounds(nearest tenth).

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Answer:

y - intercept = 14

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 10x + 14 ← is in slope- intercept form

with y- intercept c = 14

Answer:

These pairs are called vertical angles, and they always have the same measure. ∠1 and ∠3 are vertical angles. ∠2 and ∠4 are vertical angles.

Step-by-step explanation:

Point M has the same distance from point A and point B (option d).

Given,

Line segment CD is the  perpendicular bisector of line segment  AB

AB ⊥ CD

Assume the conjecture that the set of  points equidistant from A

and B is the  perpendicular bisector of AB is true

Here,  line segment CD intersect line segment AB at M

Then, M is the mid-point of line segment AB

So, the length of  line AM = the length of line MB

That is, Point M has the same distance from both point A and point B.

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When Ramona reflect the original figure over the x-axis, the coordinate of point T' will be (-2, -4). When Elias reflect the original figure over the y-axis, the coordinate of point T' will be (2, 4).

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In Mathematics, a reflection over the x-axis is given by this transformation rule:

(x, y)                   →               (x, -y)

Point T = (-2, 4) → Point T' = (-2, -4)

In Geometry, a reflection over the y-axis of a graph is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, the coordinates of point T' after a reflection over the y-axis is as follows:

Point T = (-2, 4) → Point T' = (-(-2), 4) = (2, 4)

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Answer: 5 more!

Step-by-step explanation:

Due to the lack of numbers your could do about 4 - 5 more security numbers!

Answer:

I think 81

Step-by-step explanation:

I'm not too sure since 9 x 9 is 81 but im not sureeee

The rate of change of y with respect to x for this linear function is 1/5 or 0.2

A linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate. This ultimately implies that, a linear function is typically used for uniquely mapping an input variable to an output variable.

Mathematically, the average rate of change (slope) of a linear function can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

Average rate of change = (3 - 2)/(10 - 5) = (4 - 3)(15 - 10)

Average rate of change = 1/5 or 0.2

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Answer: 6.782

Step-by-step explanation:

Answer:  x=11

Step-by-step explanation:

Answer:

[tex] \sf \: x = 11[/tex]

Step-by-step explanation:

Given equation,

→ 0.3(4 + x) = 4.5

Now the value of x will be,

→ 0.3(4 + x) = 4.5

→ 1.2 + 0.3x = 4.5

→ 0.3x = 4.5 - 1.2

→ 0.3x = 3.3

[tex] \sf \rightarrow \: x = \frac{3.3}{0.3} [/tex]

→ [ x = 11 ]

Hence, the value of x is 11.

Answer:

A. A reflection occurs when a point and its image are equidistant from a line on the opposite sides of the line and the line segment joining the two points is perpendicular to the line.

Hope this helps! :)

When 67,000 is rounded to the nearest ten thousand then we get 70,000

When you round to the nearest 10 thousand. Find the number in the 10 thousand place, that would be the  6 in this case, now look at the number to the right of it, if that number is 5 or higher, then your 67,000 becomes 70,000.

If the number to the right of place value is lower than 5 then it would have been rounded to 60,000.

The digits in the thousands, hundreds, tens, and ones should be changed to 0 if the number is less than 5, but the other digits should remain the same. If it is 5 or more, increase the digit in the tens of thousands by 1 and replace the digits in the thousands, hundreds, tens, and ones with 0.

Hence the nearest round of to ten thousand is 70,000.

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Algebraic equation - The cost of each bag of Oranges =  $6.63

What is Algebraic equation ?

An algebraic equation, sometimes known as a polynomial equation, in mathematics is a formula of the form P=0, where P is a polynomial with coefficients in some field, typically the field of the rational numbers.

Let the cost one bag of oranges be x

Given,

Total amount she pays =  $59.53

Total amount she pays for ice cream = $6.49

Since the total amount for 8 bag of oranges = 8x  

Therefore, the equation of the following will be

8x + 6.49 = 59.53

Now by solving the equation we get the cost of each bag of oranges

8x = 59.53 - 6.49

8x = 53.04

x   = 53.04 / 8

x   = 6.63

Hence, The cost of each bag of oranges will be $6.63

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We have the following:

Multiplication is the product between two numbers, it is the number of times the number to be multiplied is repeated. In this case, it would be 1 time 1

The answer is 1

Answer:

k = 53.13°

Step-by-step explanation:

[tex]{ tan (k) = \dfrac{\text{side opposite k}}{\text{side adjacent k}}}[/tex]

[tex]= \dfrac{35}{JK}\\\\\textrm{Since JK is a right triangle, by the Pythagorean theorem }\\JK = \sqrt{IK^2 - IJ^2}}\\\\= \sqrt{35^2 - 28^2}\\\\\\ =\sqrt{1225 - 784}\\\\= \sqrt{441}\\\\= 21[/tex]

[tex]\tan(k) = \dfrac{28}{21} = 1.333\\\\k = \tan^{-1}(1.333)\\\\= 53.13^\circ[/tex]

Step-by-step explanation:

1 inch = 25 miles

or as ratio

1 inch : 25 miles

1 : 25 or 1/25

a ratio is nothing else than a fraction (just with special meaning, but the handling, calculation, transformation and simplification is the same).

the checked distance is 20 miles.

so, we need to transform the ratio (in the same way as we transform fractions) to show 20 instead of 25 in the denominator.

25 × f = 20

f = 20/25 = 4/5

remember, we need to multiply 1/25 by f/f to keep the original value of the ratio unchanged.

1/25 × 4/5/4/5 = (4/5)/(25×4/5) = (4/5)/20

so, the distance on the map is 4/5 in.

The system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped are:

50x+80y=1750

y = x+4 ,

where x represent the number of small boxes of paper and y represent the number of large boxes of paper.

We have:

Weight of small box of paper = 50 pounds

Weight of large box of paper = 80 pounds

Total weight of boxes = 1750 pounds

Let us consider that  the number of small boxes of papers be x.

The number of large boxes of papers be y.

Then, according to question

50x+80y=1750

y = x+4  

Therefore, the equations 50x+80y=1750 and y = x+4 can be used to determine the number of small boxes and large boxes of paper shipped.

where, x represent the number of small boxes of paper and y represent the number of large boxes of paper.

Answer:

y=3x=16/3

Step-by-step explanation:

Answer:

x= -9, y= -4

Step-by-step explanation:

Solving a linear equation can be done by two main methods, namely elimination and substitution. Elimination works by making the numerical value of one of the variable's coefficient the same, such that we can subsequently eliminate (or remove) the variable by subtracting or adding the two equations together.

Start by labelling the 2 given equations:

2x -5y= 2-----(1)

3x -7y= 1-----(2)

I will be working to eliminate the x term here, since we would be dealing with smaller numbers in this case. Eliminating the y term would also work.

The lowest common multiple of 2 and 3 is 6, thus multiply equation (1) by 3 and (2) by 2 so that the coefficient of x in both equations is 6. Then label the equations.

(1) ×3:

6x -15y= 6 -----(3)

(2) ×2:

6x -14y= 2 -----(4)

Since the coefficient of x in both equations is positive 6, we can subtract one equation from the other to eliminate the x term. If both coefficients have different signs (e.g. +6 and -6), the addition of the two equations would eliminate the term.

(3) -(4):

6x -15y -(6x -14y)= 6 -2

Expand:

6x -15y -6x +14y= 4

-y= 4

Divide both sides by -1:

y= -4

Then use substitution to find the value of y. Note that at this point, you could work to eliminate the y term from equations (1) and (2) to solve for x but it is commonly understood that when a question states solve by elimination, it is only for the first variable.

Substitute y= -4 into (1):

2x -5(-4)= 2

2x +20= 2

Subtract 20 from both sides:

2x= 2-20

2x= -18

Divide both sides by 2:

x= -9

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The distance between the 2 given points is √45.

So, the distance between (3, 2) and (0, -4) is:

Now, substitute the values in the formula and solve as follows:

Therefore, the distance between the 2 given points is √45.

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Answer:

A

Step-by-step explanation:

In a case whereby  two members of the math competition team solve at the rate  13 problems in 1 hour, the members that are needed to solve 39 problems in 1 hour is 6 member of the team.

Since two members solve 13 problems in 1 hour, which implies that

2 members= 13 problem/ hr

Then if we want to calculate the number of the team that will be able to solve the problem at the rate of 39 problems in 1 hour, we can represent the number required as X.

Then X = 39 problems/hr.

2 members= 13 problem/ hr

Then in this case we can cross multiply as follows:

13 problem/ hr * X =  39 problems/hr * 2

Then we can make X the subject of the formular as X =( 78 /13)

= 6 member of the team.

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Answer:

Grace

Step-by-step explanation:

48 is the LCM, 4 is the GCF

Answer: DF

Step-by-step explanation:

Remember that

We know that:

This way,