One km is equal to _______.
a.
0.62 ft
b.
3280.8 ft
c.
1.61 ft
d.
5280 ft

By using a rotation rule, the image of point P = (- 4, 1) after rotating 180° counterclockwise using center (- 3, 0) is equal to point P'(x, y) = (- 2, 1).

In this problem we find the case of a point that must be rotated 180° counterclockwise (+ 180°) about the point (- 3, 0). Rotation is a kind of rigid transformation, that is, a kind of transformation applied on a point such that Euclidean distance is conserved. The rotation formula for a point P(x, y) = (x, y) around the center O(x, y) = (Ox, Oy) is introduced below:

P'(x, y) = (Ox + (x - Ox) · cos θ - (y - Oy) · sin θ, Oy + (x - Ox) · sin θ + (y - Oy) · cos θ)

Where θ is the angle of rotation.

If we know that O(x, y) = (- 3, 0), P(x, y) = (- 4, 1) and θ = 180°, then the coordinates of the image are:

P'(x, y) = (- 3 + [- 4 - (- 3)] · cos 180° - (1 - 0) · sin 180°, 0 + [- 4 - (- 3)] · sin 180° + (1 - 0) · cos 180°)

P'(x, y) = (- 3 - [- 4 - (- 3)], - 1)

P'(x, y) = (- 3 - (- 1), - 1)

P'(x, y) = (- 2, - 1)

The coordinates of the image are P'(x, y) = (- 2, 1).

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Answer:

A

Step-by-step explanation:

On a number line, I would start at 32 and then go left on the number line 17 spaces.  This would land me at positive 15.

The unit rate of ounces of water per cup of flour for this situation is; 3 ounces per cups

From the given graph, we are expected to find the unit rate of ounces of water per cup of flour for the situation.

Now, to find the unit rate , all we need to do is to pick two coordinates on the line graph and find the slope. Thus;

Slope = (y2 - y1)/(x2 - x1)

Slope of graph = (12 - 9)/(4 - 3)

Slope = 3/1

Slope = 3

Let us pick another two points to verify;

Slope = (6 - 3)/(2 - 1)

Slope = 3/1

Slope = 3

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Answer:

125 : 1

Step-by-step explanation:

given 2 similar objects with ratio of sides a : b , then

ratio of volumes = a³ : b³

here

ratio of pot A : pot B = 15 : 3 = 5 : 1

ratio of volumes = 5³ : 1³ = 125 : 1

Answer:

Rational

Step-by-step explanation:

This statement about distance is proved.

What is distance ?

It is length of space between two points.

Okay, so the first three components of this issue involve more physics and math. So, part A received the formula Ds = R. D. Data. We have to track down S. Therefore, we simply integrate both sides equally using R. D. Data. Our data are provided. Therefore, the upon integration over our data is just R 0 Santa plus 12 beta zeta squared for part B. We'll make sure S = V T. We combine these two by using the above equation as an equal. In order to allow it to reach its roots once positive, we can see that this is Justin's equation for data. The other negative, which is naturally a positive one because it has the proper physical meaning, would indicate that the rotation is occurring in the opposite direction.

Standard units, uh, are zero point 24/7 times, so switch to the nature radio's negative six setting. Additionally, we are given the time, which is 74 minutes, or 4440 seconds. Thus, plugging everything. Injecting R 0 and data mm hmm into the expression for data. Therefore, we enter better Data. V also appears. Everything is therefore known. We can confidently conclude that the data is, um, 1.337 x 10-5 brilliant. or 2.13 x 10 to 4 revolutions, in terms of turns. Okay. We simply re-insert the numbers for beta and tr zero V into the previous expressions for omega and alpha in the final section of the problem.

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Answer:

a= (0,14) (2,-8)

Step-by-step explanation:

Answer:

22.47

Step-by-step explanation:

7/100 = 0.07 (the tax rate) 21 * 0.07 = 22.47, the tax adds on 1.47

The slope of the line is that passing through the points  (-1,-3) and (1,3) is m = 2

From the graph, we have to find the two points to find the slope of the line

The two points are (-1,-3) and (1,1)

The slope of the line m = [tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]
Where m is the slope of the line

[tex](x_{1} ,y_{1})[/tex] are the coordinates of first point

[tex](x_{2} ,y_{2})[/tex] are the coordinates of second point

substitute the values in the equation of slope of the line

The slope of the line m =[tex]\frac{1-(-3)}{1-(-1)}[/tex]

= 4/2

= 2

Hence, the slope of the line is that passing through the points  (-1,-3) and (1,3) is m = 2

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Answer:

j = 1

Step-by-step explanation:

calculate the slope m between the 2 points and equate to - [tex]\frac{7}{10}[/tex]

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, j ) and (x₂, y₂ ) = (5, - 6 )

m = [tex]\frac{-6-j}{5-(-5)}[/tex] = [tex]\frac{-6-j}{5+5}[/tex] = [tex]\frac{-6-j}{10}[/tex]

then equating gives

[tex]\frac{-6-j}{10}[/tex] = - [tex]\frac{7}{10}[/tex] ( cross- multiply )

10(- 6 - j) = - 70 ( divide both sides by 10 )

- 6 - j = - 7 ( add 6 to both sides )

- j = - 1 ( multiply both sides by - 1 )

j = 1

Equation of the first line =  [tex]y=-\frac{1}{2} x+1[/tex]

Equation of the second line = [tex]y=-\frac{5}{2} x -1[/tex]

What is the equation of the first line?

Co-ordinates of the first line (x, y) = (-2,2), (0,1), (2,0), (4,-1)

We know that,

[tex]\text{slope }=m=\frac{y_2-y_1}{x_2-x_1}\\\\= > \frac{1-2}{0+2} \\\\=-\frac{1}{2}[/tex]

The slope -intercept form of a line is given by,

y = mx + b    ---(1)

Let us substitute ( x, y )= (-2, 2) in (1)

2=(-1/2)*-2+b

2-1= b

b = 1 ----(2)

Let us substitute m and b in the slope-intercept equation (1)

[tex]y=-\frac{1}{2} x+1[/tex]

What is the equation of the second line?

Co-ordinates of the second line (x, y)=(-4,9), (-2,4), (0,-1), (2,-6)

We know that,

[tex]\text{slope }=m=\frac{y_2-y_1}{x_2-x_1}\\\\= > \frac{4-9}{-2+4} \\\\=-\frac{5}{2}[/tex]

The slope -intercept form of a line is given by,

y = mx + b    ---(3)

Let us substitute ( x, y )= (-4, 9) in (1)

9 = (-5/2)*-4+b

2 - 1 = b

b = - 1 ----(4)

Let us substitute m and b in the slope-intercept equation (3)

[tex]y=-\frac{5}{2} x -1[/tex]

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Given picture is not a graph of inequality y < 6x + 1

In this question, we have been given a graph.

We need to determine whether the picture is a graph for the inequality y < 6x + 1 or not.

We know that the graph of equation y = 6x + 1 is a straight line and we represent a straight line graph by a solid line.

This graph represents a shaded region below dotted line. This means, this is the graph of inequality.

From this graph we can see that x-intercept of the equation is (2, 0) and y-intercept is (0, - 4)

If we find the x and y-intercept of y = 6x + 1 then it would be,

x - intercept = (-1/6 , 0)

y - intercept = (0, 1)

This means, given picture is not a graph of inequality y < 6x + 1

Therefore, given picture is not a graph of inequality y < 6x + 1

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Answer:

30 markers

Step-by-step explanation:

(15 what she spent)+(3 the 3 dollors off)=

18/(3 the price of markers)=

(6 sets)*(5 how many is in a set)=

(30 final anwser)

Step-by-step explanation:

i.)add 3 in 6 which = 9

ii.) follow the negative sign of the larger value which now ur finally answer is -9

Answer:

x^2= 50 ------ (equation 1)

x^3= 37 ------- (equation 2)

dividing (equation 2) by (equation 1)

=> x^3/x^2 = 37/50

=> x = 37/50

Answer: x= 37/50

It is to be noted that the information for the completed table is given accordingly to show the perimeters in millimeters and in centimeters.

Perimeter simply refers to the total or sum of all the sides of a geometric shape. Note that the perimeter in units is obtained by counting the number of rectangles.

In the case of A:

Perimeter in Units = 10 Units.

Length is 60mm and width is 40mm
Perimeter = 30 + 20 + 30 + 20 = 100mm; and 10 cm

Recall that I cm = 10mm.

Hence, 100 /10 = 10 cm.

In the case of shape B:
Perimeter in Units = 41 Units.

Length is 400mm (that is 200 + 200)

Breath is 40mm (20 + 20)

Perimeter therefore is:

400 + 40 = 440mm
Perimeter in cm = 44

Recall, 10mm = 1cm

In the case of shape C:

Perimeter in Units = 36 Units.

Length is 10cm (that is 5 + 5)

Breath is 14mm (7 + 7)

Perimeter therefore is:

10+ 14 = 24cm
Perimeter in mm= 240

Recall, 10mm = 1cm

In the case of Shape D:

Perimeter in Units = 51 Units.

Length is 200mm (that is 100 + 100)

Breath is 100mm (50 + 50)

Perimeter therefore is:

200 + 100 = 300mm
Perimeter in cm= 230

Recall, 10mm = 1cm

In the case of Shape D:

Perimeter in Units = 53 Units.

Length is 260mm (that is 130 + 130)

Breath is 80mm (40 + 40)

Perimeter therefore is:

260 + 80 = 340mm
Perimeter in cm= 34

Recall, 10mm = 1cm

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Step-by-step explanation:

[tex](4(2) \: - 6(7) \: 5(1)) \\( 2( - 1) \: 4(5) \: - 1(2) ) \\ (8 \: - 42 \: \: 5 \\ - 2 \: \: \: 20 \: \: - 2)[/tex]

If the radius to the inside of the shell is 4 millimeters and the radius to the outside of the shell is 4.3 millimeters. the volume of the shell is 19π mm³.

v = 4 / 3πr³

dv =4 / 3π (3r²) dr

Where:

r= radius = 4 cm

dr = 4.3 -4 = 0.3

Hence,

dv = 4 / 3π (16) 3/10

dv =4 / 3π(16) 0.3

dv = 19.2π mm³

dv = 19π mm³ (Approximately)

Therefore the volume of the shell is 19π mm³.

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Answer:

-1/8>-3/8

Step-by-step explanation:

You can write it as a decimal.

-0.125 ? -0.375

Answer: See attached and/or view below.

Step-by-step explanation:

      Since we are given the equation, we can plug the values into it and solve for the unknown. We will solve by isolating the variable and using reverse operations.

      x = 1, y = 34

2x + y = 36

2(1) + y = 36

2 + y = 36

y = 34

      x = -2, y = 40

2x + y = 36

2(-2) + y = 36

-4 + y = 36

y = 40

      y = 18, x = 9

2x + y = 36

2x + (18) = 36

2x = 18

x = 9

A mathematical expression known as an algebraic expression includes variables, constants, and algebraic operations (addition, subtraction, etc.). Expressions include terms. Here, y=3x.

The idea behind algebraic expressions is to represent numbers using letters or alphabets rather than giving their exact values. In algebraic basics, we learned how to express an unknown number using letters like x, y, and z. We will refer to these letters as variables from now on. An algebraic expression may have both constants and variables. Any amount that is added to a variable before it is multiplied by another is known as a coefficient.

A mathematical expression known as an algebraic expression includes variables, constants, and algebraic operations (addition, subtraction, etc.). Expressions include terms.

There are 3 main types of the algebraic expressions which include:

For the above question:

4x3=12 , 5x3=15 , 6x3=18 ,.....

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The complete question:

"Write an equation that represents the pattern in the table

x 4,5,6,7,8

y 12,15,18,21,24 y = __ x"

Answer: y²-2y-48=(y-8)(y+6)

Step-by-step explanation:

[tex]y^2-2y-48=\\\\y^2-8y+6y-48=\\\\y(y-8)+6(y-8)=\\\\(y-8)(y+6)[/tex]

Answer:

y²-2y-48=(y-8)(y+6)

Step-by-step explanation:by factorization

y2-2y-48= y2-8y+6y48= y(y-8)+6(y-8)= (y-8)(y+6)

Answer: x = 80°, y = 50°

Step-by-step explanation:

We have an isosceles triangle.

As you can see, 130° lies on a straight line. A straight line = 180°.

The base angles of an isosceles triangle are equal. This means 180° - 130° = y.

So, y = 50°.

The total measures of any triangle is 180 degrees.

The total measure for the base angles here 100 degrees. That is, 50° + 50° =

100°.

How do we find x?

x = 180° - 100

x = 80°

Answer:

m<1 = 159° m<2 = 21° m<4 = 21°

Step-by-step explanation:

Since angle measure 3 was found, seeing that 3 and 1 are vertical angles (congruent) they equal the same, meaning angle measure 1 is also 159°. Also seeing that angle measure 3 and 2 are supplementary angles (2 or more angles that add up to 180°) subtracting 159° will give you 21°. Once again there are another set of verital angles, 2 and 4 making 4 also 21°

Answer:

In a year you can shrink 0.625cm

Step-by-step explanation:

1.7/4=0.625

Answer:

35

Step-by-step explanation:

The consecutive interior angles are supplementary, so:

[tex]3x-11+2x+16=180 \\ \\ 5x+5=180 \\ \\ x+1=36 \\ \\ x=35[/tex]