Micheal solved this inequality as shown: step 1: -6(x + 3) + 10 < -2 step 2: -6x - 18 + 10 < -2 step 3: -6x - 8 < -2 step 4: -6x < 6 step 5: x > -1. what property justifies the work shown between step 3 and 4?

Answer:

y = -1/2x

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

The slope = rise/run

Let's pick 2 points (0,0) (4, -2), we see that the y decrease by 2 and the x increase by 4, so the slope is

m = -2/4 = -1/2

Y-intercept is located at (0,0)

So, our equation is

y = -1/2x

The equation in slope-intercept form is y = 3x - 8.

What is the slope-intercept form?

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point-slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.

Here, we have

Given: Line includes the points (3, 1) and (4, 4).

Slope intercept: y = mx + b

We first find the slope, m, using the point-slope

Slope(m) = (y₂ - y₁)/(x₂ - x₁) = (4 - 1)/(4 - 3) = 3

Now, we find the y-intercept, b, Using any points' x and y values in y = mx + b with the found slope.

Put the slope into y = mx + b

y = 3x + b

Now, we took points (3, 1) to get slope intercept form and we get

1 = 3(3) + b

b = -8

Now, we put the value of b in y = mx + b and we get

y = 3x - 8

Hence, the equation in slope-intercept form is y = 3x - 8.

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Using hour and minutes conversion, Pam spent 7380 seconds on the puzzle.

We can convert an hour into minutes by multiplying it by 60 since an hour is made up of 60 minutes. Therefore, if one wants to translate three hours into minutes, they can do it by multiplying three by sixty, which gives them three times sixty or 180 minutes.

On Saturday, Pam spent 1 hour and 15 minutes working on a puzzle.

On Sunday, she spent 48 minutes on the puzzle.

1 hour = 60 minutes

1 minute = 60 second

1 hour = 60 × 60 seconds

1 hour and 15 minutes = 60 × 60 seconds + 15 × 60 seconds

⇒ 3600 + 900 seconds

⇒ 4500 seconds

48 minutes = 48 × 60 = 2880 seconds

Total seconds spent = 4500 + 2800 = 7380 seconds

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The expression that shows how many baseballs Joel hit in all is y = b + 15.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that Joel hit (b) baseballs at practice and another 15 baseballs at the batting cage.

We can write the expression that shows how many baseballs Joel hit in all is given by -

y = b + 15

Therefore, the expression that shows how many baseballs Joel hit in all is y = b + 15.

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The first equation that represents 42 - p -p= 21 is correct.

An equation is a mathematical statement that express the equality between two or more number of expressions. An equal sign is mandatory for equation. An equation is used to determine unknown values in terms of variables. In our everyday life equation is used by many professionals necessarily. By using equation many complicated problems can be easily solved within a limited time.

Isaac has $42 cash in hand when arrived Saturday market.

He buys two posters that each cost selling price or SP.

when he leaved the market had $21 cash in hand.

assume, each poster has a price = p

The situation is represented by the following.

initial amount - cost for two posters = final amount

42 - p - p = 21

hence, the first equation that given in the question is correct.

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Therefore ,the solution tot he given problem of rectangle comes out to be Perimeter ABCD 68 unit and Perimeter PQRS 85 unit.

A rectangle in Euclidean physics and engineering is a shape with four sharp angles. You may also put it like this: When all of a quadrilateral's angles are equal, it is said to be equiangular. A straight angle is another another option for the parallelogram. In a square, four of the vertices are the same length. A quadrilateral with a rectangle-shaped cross section has four 90° apexes and equal neighboring sides. As a result, it is sometimes referred to as a "equirectangular rectangle". Due to the uniform and perpendicular lengths of its opposing sides, a rectangle is also known as a parallelogram.

Here,

Given : ABCD ~PQRS

From the given information We get:

Scale factor  = 4/5

and

Perimeter ABCD :

=> 2(l+b)

=> 2(20+14)

=>68

and

Perimeter PQRS:

=>2(l+b)

=>2(25 + 17.5)

=>85

Therefore ,the solution tot he given problem of rectangle comes out to be Perimeter ABCD 68 unit and Perimeter PQRS 85 unit.

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The perimeter of the triangle having vertices (0,1),(3,6), and (4,1) will be 10.83 units.

Any two-dimensional figure's perimeter is determined by the space surrounding it. By summing the lengths of the sides, we can determine the perimeter of any closed shape.

Any polygon's perimeter is equal to the sum of its side lengths. Considering a triangle

The sum of the three sides equals the perimeter.

Units are always a part of the ultimate response. The final solution should be given in centimeters if the triangle's sides are in that unit.

Because the y values between U and V differ, the distance is equal to the x value difference.

Because the x values of V and W differ, the distance equals the difference between their y values.

The hypotenuse of a right triangle, or U to W, equals sqr (sum of squares on the other two sides)

Perimeter = sum of the 3 sides

[tex]= \sqrt{34} + \sqrt{26}+ \sqrt{16}= 5.83 + 5.1 + 4 = 10.83\:units[/tex]

As the value of 34 is 5.83 squared,  26 is 5.1 squared,  16 is about 4 squared.

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The total distances add up to the triangle's perimeter is 10.00

The triangle's perimeter may be calculated by summing the distances between its three vertices. Use the distance formula to calculate the separation between the points:

d = √((x2 - x1)2 + (y2 - y1)2)

The distances between the points are as a result for the triangle with vertices (0,1), (3,6), and (4,1)

Utilizing the distance formula, determine the separation between (0,1) and (3,6):

d = √((x2 - x1) 2 + (y2 - y1) 2) = √((3-0) 2 + (6-1) 2) = √(32 + 52) = √45

Utilizing the distance formula, determine the separation between (3,6) and (4,1):

d = √((x2 - x1) 2 + (y2 - y1) 2) = √((4-3) 2 + (1-6) 2) = √(12 + 52) = √25

Utilizing the distance formula, determine the separation between (4,1) and (0,1):

d = √((x2 - x1) 2 + (y2 - y1)2) = √((0-4) 2 + (1-1) 2) = √(42 + 02) = √16

The triangle's perimeter is calculated by adding the three distances together:

Perimeter = √45 + √25 + √16 = 10.00.

Hence, the perimeter of the triangle is 10.00, rounded to the closest hundredth.

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Answer:

4 units right, 2 units up

Step-by-step explanation:

For [tex]g(x)=(x-4)^2+2[/tex], the graph of [tex]f(x)=x^2[/tex] would need to move 4 units to the right and 2 units up. Hence, the vertex would be [tex](4,2)[/tex] if we compare the function g(x) with the form [tex]y=a(x-h)^2+k[/tex].

Answer:

130 feet

Step-by-step explanation:

45 feet is one of the lengths of the rectangular garden and 20 feet is the other.

The perimeter of a rectangle is 2(l+w) and we know that these must be the lengths and widths.

Communitive property of addition states that it doesn't matter the order that we add so we know it's just 20+45 (65) then times 2 which is 130

130 feet is your answer.

If a quantity increases or decreases as per the increase or decrease in other quantity, the two quantities are said to be in a proportional relationship.

And here, the graph representing the proportional relationship is the one with positive slope (2nd graph)

The length of the mid-segment of the trapezoid for these problems is given as follows:

28. n + 12 = 17.

29. 2n + 11 = 27.

The length of the mid-segment of a trapezoid is half the sum of the lengths of the bases.

Hence the value of n for item 28 is given as follows:

n + 12 = 1/2(2n - 2 + 4n + 6)

n + 12 = 0.5(6n + 4)

n + 12 = 3n + 2

2n = 10

n = 5.

Hence the length of the mid-segment is of:

n + 12 = 5 + 12 = 17.

The value of n for item 29 is given as follows:

2n + 11 = 1/2(5n - 2 + n + 8)

2n + 11 = 0.5(6n + 6)

2n + 11 = 3n + 3

n = 8.

Hence the length of the mid-segment is of:

2n + 11 = 16 + 11 = 27.

(replacing n = 8 into 2n + 11).

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From the congruency of triangles we can prove,

A: D is the midpoint of AC,

B: Measure of ∠D = ∠E,

C: BD bisect the angle ABC.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance.

Given BD bisect ∠ABC

AB ≅ CB

from the figure, AB = CB

since BD bisects ∠ABC

∠1 = ∠2

and BD = BD (common side)

from SAS property,

ΔABD ≅ ΔCBD

Triangles can be shown to be congruent after which the final dimension can be anticipated without actually measuring the triangle's sides and angles.

from CPCT, AD = CD

since AD = CD so D should be the midpoint of AC.

B: Given B is the midpoint of AC,

AB = CB

and BD ║ AE,

so ∠1 and ∠2 are equal due to corresponding angles between parallel lines,

∠1 = ∠2

BD = AE

ΔABE ≅ ΔCBD

from CPCT, ∠D = ∠E

C: Given ∠A and ∠C are right angles,

∠A = ∠C = 90°

AD = CD

BD = BD (common side and hypotenuse of a right triangle)

from RHS property ΔABD ≅ ΔCBD

from CPCT, ∠ABD = ∠CBD

since both angles are equal so BD is the angle bisector.

Hence all the statements are proved by the congruency of triangles.

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The value of sin x is [tex]\frac{5}{13}[/tex] and the value of cos y is [tex]\frac{5}{13}[/tex]. The ratio of sin x and cos y is 1.

The Pythagorean Triples, which comprise the three positive numbers a, b, and c, are the integer solutions to the Pythagorean Theorem.

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem.

The given triangle has sides 12 and 5.

According to the Pythagorean triplet the length of the third side is 13.

The value of sin x is [tex]\frac{5}{13}[/tex].

The value of cos y is [tex]\frac{5}{13}[/tex].

The ratio of sin x and cos y is:

[tex]\frac{sin x}{cos y} = \frac{\frac{5}{13}}{\frac{5}{13}} = 1[/tex]

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Answer:

44 862,07

Step-by-step explanation:

SUM=21000*(1+8,8/100)^9

SUM=21000*(108,8/100)^9

SUM=44862,07

2600 pounds are equal to 1.3 tons.

A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.

Given,

2,600 pounds to tons

1 US ton =  2000 pound

1 pound = 1/2000 US tons

2,600 pound = 2600/2000 US tons

2600 pound = 1.3 US tons.

Hence, 1.3 US tons are there in 26000 pounds.

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Answer:

Interest = Principal x Rate x Time
($2,840)

Step-by-step explanation:

interest earned on a deposit of $800 at 3.5% interest for 7 years, you can formula: Interest = Principal x Rate x Time

In this case, the interest earned would be:

Interest = $800 x 0.035 x 7 = $2,040

So, after 7 years the deposit would be worth $800 + $2,040 = $2,840.

Answer: 87

Step-by-step explanation:

The sum of the internal angles of the polygons are

a) The sum is A = 540°

b) The sum is A = 360°

c) The sum is A = 1800°

The sum of the interior angles of a polygon is given by the formula

Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

where n is the number of sides

θ = angle in degrees

Given data ,

Let the sum of the internal angles of a polygon be represented as A

Now , the value of A is

The sum of exterior angle of n polygon is = 360°

Now ,

a)

The number of sides of the polygon = 5 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

Substituting the value of n = 5 in the equation , we get

nθ = 180° ( 5 - 2 )

nθ = 180° x 3

nθ = 540°

b)

The number of sides of the polygon = 4 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

Substituting the value of n = 4 in the equation , we get

nθ = 180° ( 4 - 2 )

nθ = 180° x 2

nθ = 360°

c)

The number of sides of the polygon = 12 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

Substituting the value of n = 12 in the equation , we get

nθ = 180° ( 12 - 2 )

nθ = 180° x 10

nθ = 1800°

Hence , the sum of the internal angles of the polygon is solved

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Answer:

the minimum temperature was furthest from the norm. it was 23.5 degrees further

Step-by-step explanation:

difference between the max and median = 115-98.6 = 16.4

difference between the median and minimum = 98.6 - 58.7 = 39.9

the difference between the median and minimum (39.9) is greater than the distance between the maximum and median (16.4). thus, the minimum temperature was furthest from the norm. the difference in differences is 39.9 - 16.4 = 23.5 degrees. this means that the minimum temperature was 23.5 degrees further away from the norm than the maximum was

Answer:

[tex]\sf \tan\left(c_2\right)=\dfrac{OD}{OC}=\dfrac{2\sqrt{66}}{19}[/tex]

Step-by-step explanation:

**Please note that if the segment AO = 3.8 cm then the 50° angle on the given rhombus is incorrect. It should be 49.46° (2 d.p.)**

In a rhombus, all four sides are equal in length.  Therefore:

Diagonals bisect each other at 90°.  Therefore:

Therefore, triangle COD is a right triangle.

To find the tangent ratio of angle c₂, first find the length of OD using Pythagoras Theorem:

[tex]\implies OC^2+OD^2=CD^2[/tex]

[tex]\implies 3.8^2+OD^2=5^2[/tex]

[tex]\implies 14.44+OD^2=25[/tex]

[tex]\implies OD^2=10.56[/tex]

[tex]\implies OD^2=\dfrac{1056}{100}[/tex]

[tex]\implies OD^2=\dfrac{1056 \div 4}{100 \div 4}[/tex]

[tex]\implies OD^2=\dfrac{264}{25}[/tex]

[tex]\implies OD^2=\dfrac{4 \cdot 66}{25}[/tex]

[tex]\implies OD=\sqrt{\dfrac{4 \cdot 66}{25}}[/tex]

[tex]\implies OD=\dfrac{\sqrt{4 \cdot 66}}{\sqrt{25}}[/tex]

[tex]\implies OD=\dfrac{2\sqrt{66}}{5}[/tex]

[tex]\boxed{\begin{minipage}{6 cm}\underline{Tan trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\end{minipage}}[/tex]

Given:

Substitute the values into the tan ratio:

[tex]\implies \sf \tan\left(c_2\right)=\dfrac{OD}{OC}[/tex]

[tex]\implies \sf \tan\left(c_2\right)=\dfrac{\frac{2\sqrt{66}}{5}}{3.8}[/tex]

Rewrite 3.8 as 19/5:

[tex]\implies \sf \tan\left(c_2\right)=\dfrac{\frac{2\sqrt{66}}{5}}{\frac{19}{5}}[/tex]

[tex]\implies \sf \tan\left(c_2\right)=\dfrac{2\sqrt{66}}{19}[/tex]

Answer:

(7,2)

Step-by-step explanation:

(3,3) 》(x+4, y-1)

3=x

3+4=7

3=y

3-1=2

=(7,2)

Answer:

(7, 2 )

Step-by-step explanation:

the translation rule (x, y ) → (x + 4, y - 1 ) means

add 4 to the original x- coordinate and subtract 1 from the original y- coordinate.

(3, 3 ) → (3 + 4, 3 - 1 ) → (7, 2 )

Furthermore, it is evident that 'every day corresponds to a distinct quantity of cans'. As a result, alternatives B and C are accurate.

A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output.

Here,

We presume Thomas only invited one buddy to participate.

The pattern for days and cans can be seen as follows:

Thomas has two cans on the first day, i.e. cans.

Thomas has four cans on the second day, i.e. cans.

Thomas has 8 cans on the third day, i.e. cans.

Thomas has 16 cans on the fourth day, i.e. cans.

This trend continues until day ten.

So, on x day, Thomas has cans, and x varies from 1 to 10.

As a result, the relevant function is.

This means that for each day (x), there is a distinct value for the number of cans:

The 'Vertical Line Test,' on the other hand, is a test in which we draw a vertical line through the graph and if it cuts the graph at exactly one place, then the graphed curve is a function.

As shown in the graph below, the vertical line intersects f(x) at precisely one location. As a result, f(x) is a function.

As a result, the sequence graph passes the vertical line test.

Furthermore, it is evident that 'every day corresponds to a distinct quantity of cans'. As a result, alternatives B and C are accurate.

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The number of mini cherry pie and mini peach pie that she sold each would be = 12

The price for each cherry pie = $4

The price for each peach pie = $3

The total price for the whole pies sold = $84

The quantity of each pie sold. is calculated as thus;

= 4+3 = 7

For cherry pie;

= 4/7 × 84

= 336/7

= $48

The number of cherry pie sold = 48/4 = 12

For peach pie;

= 3/7× 84

= 252/7

= $36

The number of peach pie sold = 36/3 = 12

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Answer:

the first box is 3 and the second box is 25

Step-by-step explanation:

Answer: Box 1: 3 Box 2:  25

Step-by-step explanation:

Box 1:

Since the top is divided by 3, you have to do the same to the bottom

9 / 3 = 3

Box 2:

The bottom is multiplied by 1 ⅔, so you do the same to the bottom

1 ⅔ x 15 = 25

The distance in miles he biked up to the point of both stops is 10 1/2 miles

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

Total distance = 24 3/4 miles

When he stops a third of the way, we have the expression to be (24 3/4)/3

So, we have the following equation

Required distance = 24 3/4 - ((24 3/4)/3 + 5 3/3)

Evaluate

Required distance = 10 1/2

Hence, the distance is 10 1/2 miles

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Answer: OC. x = -8 is not in the domain of the function f(x) = √x - 8 because the square root of a negative number is not a real number. Therefore, the only value of x that is in the domain of the function is x ≥ 0.

Step-by-step explanation:

Answer:  B has only one unique intercept.

Step-by-step explanation:  line has only one unique intercept when it is not a vertical or horizontal line, which means it has a slope.

In this case, line A has the equation x = 8, which is a vertical line and does not have a slope, thus it does not have a unique intercept.

Line B has the equation -8x - 7y = -7, which has a slope of -8/7. Since it has a slope, it has one unique intercept.

Line C has the equation 9y = 5, which is a horizontal line and does not have a slope, thus it does not have a unique intercept.

Line D has the equation -3x - 3y = 0, which has a slope of -3/-3 = 1. Since it has a slope, it has one unique intercept.

Thus, only line B has only one unique intercept.

Answer:

Step-by-step explanation 3:5 copblocking

The domain is the set of all real numbers except the x values.

And x :  denominator ≠ 0.

The collection of all conceivable independent values that a function or relation may take is known as its domain.

Let y = f(x) be a rational function.

And to find the domain of the rational function:

We have to find the all achievable values that rational function can have.

That means, we have to find the values where function is defined.

Rational function have numerator and denominator.

To find the domain of the rational function y = f(x):

Set the denominator ≠ 0 and solve for x.

The domain is the set of all real numbers except the x values ​​mentioned in the last step.

Therefore, the complete explanation is given above.

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