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Answer:

M=|3x-2|+2/7

Step-by-step explanation:

Find the value of M:

Divide each term by -7. Simplify.

M=|3x-2|+2/7

Find the value of x:

Simplify both sides of the equation, then isolate the variable.

x=-7M/3 OR x=7M/3+4/3

I hope this helps! I tried. Hope you get it right!

The segment joining the midpoints of the diagonals of a trapezoid is parallel to the bases

From the figure, we have the following coordinates

B = (a, 0)

D = (d, c)

The midpoint of line segment BD is calculated as

BD = 1/2 * (x1 + x2, y1 + y2)

So, we have

BD = 1/2 * (a + d, 0 + c)

This gives

BD = ((a + d)/2, c/2)

Also, we have:

Lines MN and AB are horizontal lines

This means that they have a slope of 0

i.e.

Slope of AB = Slope of MN = 0

Parallel lines have equal slope

Hence, the segment joining the midpoints of the diagonals of a trapezoid is parallel to the bases

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Answer:

Option 3

Step-by-step explanation:

[tex]|6t-7|-8 \geq 3 \\ \\ |6t-7| \geq 11 \\ \\ 6t-7 \leq -11, 6t-7 \geq 11 \\ \\ 6t \leq -4, 6t \geq 18 \\ \\ t \leq -2/3, t \geq 3[/tex]

Answer:

109is the answer

Step-by-step explanation:

Hope it helps you

Answer: the slope would be 7

Step-by-step explanation:

Answer:

The transformation that map line RS to line R"S" is " rotation of 180° about the origin, followed by a translation (x, y) → (x + 1, y + 1)" ⇒ B

Step-by-step explanation:

Let us revise some transformationIf the point (x, y) rotated about the origin by angle 180° counterclockwise, then its image is (-x, -y) ⇒ R(180, O) (x, y) → (-x, -y) If the point (x, y) translated horizontally to the right by h units then its image is (x + h, y) ⇒ T (x, y) → (x + h, y)If the point (x, y) translated vertically up by k units then its image is (x, y + k) ⇒ T (x, y) → (x, y + k)∵ The coordinates of the point R = (-2, 4)∵ The coordinates of point R" = (3, -3)→ Both coordinates in R" have opposite signs then R∴ R rotated 180° about the origin ⇒ using the 1st rule above∴ R' = (2, -4)→ Find the difference between the x-coordinate of R" and x-coordinate  of R'∵ xR" - xR' = 3 - 2 = 1→ By using the 2nd rule above∴ R' translated 1 unit to the right → Find the difference between the y-coordinate of R" and y-coordinate  of R'∵ yR" - yR' = -3 - (-4) = -3 + 4 = 1→ By using the 3rd rule above∴ R' translated 1 unit up∴ The rule of translation is T(x, y) ⇒ (x + 1, y + 1)Let us use these 2 rules on S to find S"∵ The coordinates of the point S = (-4, -1)∵ S is rotated 180° around the origin→ By using the 1st rule above, opposite the signs of its coordinates∴ S' = (4, 1)∵ S' translated 1 unit right→ By using the 2nd rule above, add its x-coordinate by 1∵  S' translated 1 unit up→ By using the 3rd rule above, add its y-coordinate by 1∴ S" = (4 + 1, 1 + 1)∴ S" = (5,2)→ That means the rules of transformation of point R is rightThe transformation that map line RS to line R"S" is " rotation of 180° about the origin, followed by a translation (x, y) → (x + 1, y + 1)"

Translation

Explain Explain Explain Explain

A ratio shows us the number of times a number contains another number. The area of the TV will be 729 inches².

A ratio shows us the number of times a number contains another number.

Given that the aspect ratio of the 36-inch tv is 16:9. Therefore, the width of the TV will be,

Length of the TV / Width of the TV = 16 : 9

36 inches / Width of the TV = 16 : 9

Width of the TV = 20.25 inches

Now, the area of the TV will be,

Area = Length of the TV × Width of the TV

        = 36 inches × 20.25 inches

        = 729 inches²

Hence, the area of the TV will be 729 inches².

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Work Shown:

1 case = 14 reams

15*(1 case) = 15*(14 reams)

15 cases = 210 reams

Answer:

There are 210 reams of paper in 15 cases

Step-by-step explanation:

1 case = 14 reams

To find out the total of reams in 15 cases, multiple both sides by 15

15 x 1 case = 15 x 14 reams

15 cases = 210 reams

Step-by-step explanation:

since 12 < 19, we have to use the first function definition :

f(12) = -18×12 + 20 = -216 + 20 = -196

Answer:

x=0,x=-4

Step-by-step explanation:

(x+6)(x+6) =8x+36

x^2+12X+36-8X-36=0

X^2+4X=0

x(X+4)=0

You will get x=0 ,x=-4

Answer: x1=-4,x2=0

Step-by-step explanation:

x+6^2=8x+36

Expand the expression

x^2+12x+36=8x+36

Cancel equal terms

x^2+12x=8x

Move the variable to the left

x^2+12x-8x=0

Collect like terms

x^2+4x=0

Factor the expression

x x (x+4) = 0

Separate into possible cases

x=0

x+4=0

Solve the equation

x=0

x=-4

The equation has 2 solutions

x1=-4,x2=0

The equation of the line tangent to the curve is y = 19 · x - 7.

In this problem we need to find the equation of a line tangent to the function f(x) = (√x + 5) · (x² + x) for x = 1, that is, a line that only passes through one point of the entire curve. The equation of the line is introduced below:

y = m · x + b

Where:

The slope of the line can be found by evaluating the first derivative of f(x) for x = 1:

f'(x) = (1 / 2√x) · (x² + x) + (√x + 5) · (2 · x + 1)

f'(1) = (1 / 2) · 2 + 6 · 3

f'(1) = 1 + 18

f'(1) = 19

The y-coordinate of the curve is:

f(1) = (√1 + 5) · (1² + 1)

f(1) = 6 · 2

f(1) = 12

Lastly, we determine the intercept of the tangent line:

b = y - m · x

b = 12 - 19 · 1

b = - 7

The equation of the line tangent to the curve is y = 19 · x - 7.

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Therefore, the total mass of all bags of beads is 19.27 grams

Given masses of three bags of beads as

Mass of beads in bag1 = 10.3 grams

Mass of beads in bag2 = 5.23 grams

Mass of beads in bag3 = 3.74 grams

We have to calculate the total mass of all the beads as below

The total mass of all bags of beads = mass of bag1 + mass of bag2 + mass of bag3

                                                           = 10.3 + 5.23 + 3.74

                                                           = 19.27 grams

Therefore, the total mass of all bags of beads is 19.27 grams

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Answer:

A weekly salary is a function of the hourly pay rate and the number of hours worked

Step-by-step explanation:

a function is a map assigning values of a result or solution set to values of a set of initial or starting values.

we typically name these starting values x and the solution values f(x) or y (the results "created" out of x).

we often say

y = f(x)

and provide an expression or table to explain the logic of the mapping between x and f(x).

the only rule to be a function and not just a general relationship between these 2 sets :

every value in the set of starting values must have exactly one assigned solution value. not 0, not 2 (or more). one and only one.

but yes, different values of x can have the same assigned solution value. that is not a problem for a function. it just cannot be the other way around. there cannot be different solution values assigned to the same value of x.

so, a typical example of a function is a line.

e.g.

y = f(x) = 5x + 12

for every value of x you could think of (and everything else) there is exactly one result value calculated.

or the score board in a sports event :

athlete 1 : 12 points

athlete 2 : 24 points

athlete 3 : 20 points

athlete 4 : 22 points

...

the athletes are the "x". and their associated points the "f(x)" or "y".

no athlete is listed multiple times with different scores.

a typical example of not being a function is a circle. for almost every value of x inside the circle (that means for almost every point of the horizontal diameter of the circle) there are 2 values of y (that means points on the arc of the circle) : one above and one below the diameter.

or a strange score board like

athlete 1 : 12 points

athlete 2 : 24 points

athlete 3 : 20 points

athlete 2 : 22 points

athlete 4 : 22 points

...

athlete 2 is listed twice with 2 different scores.

so, this is therefore not a function.

The range of values for the expressions are given by these following compound inequalities:

A compound inequality is a combination of multiple inequalities, at least two, involving operations such as and and or, explained below.

Hence one example of a compound inequality is:

a ≤ x ≤ b.

Which is read as follows:

x is greater or equal than a and less or equal than b.

The smallest possible value is when both a and b are at their lower bounds, hence:

a + b = 2 + 1 = 3.

The greatest possible value is when both a and b are at their upper bounds, hence:

5 + 2 = 7.

Then the range is:

3 < a + b < 7.

Since the ranges of a and b are open intervals, the ranges of the operations will also be composed by open intervals.

The smallest possible value is when both a and b are at their lower bounds, hence:

a x b = 2 x 1 = 2.

The greatest possible value is when both a and b are at their upper bounds, hence:

a x b = 5 x 2 = 10

Then the range is:

2 < ab < 10.

The smallest possible value is when a is at it's lower bound and b is at it's upper bound, hence:

2 - 2 = 0

The greatest possible value is when a is at it's upper bound and b is at it's lower bound, hence:

5 - 1 = 4.

Hence the range is:

0 < a - b < 4.

The smallest possible value is when a is at it's lower bound and b is at it's upper bound, hence:

2/2 = 1.

The greatest possible value is when a is at it's upper bound and b is at it's lower bound, hence:

5/1 = 5.

Hence the range is:

1 < a/b < 5.

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Answer:

it equals 4

Step-by-step explanation:

Answer:

Step-by-step explanation:x+y=100

(2x+2.4y)/100=2.08

x=80

y=20

Answer:

Step-by-step explanation:

Step 1: We must locate the slope, by using the slope formula, which is:

[tex]\frac{y2-y1}{x2-x1}[/tex]

When we plug it in we get:

[tex]\frac{-2-10}{9-3}[/tex]

Which simplifies to a -2

Step 2: We must plug in our values in the point-slope formula which is:

[tex]y-y1=m(x-x1)[/tex]

We can plug in (3,10) or (9,-2). It doesn't matter which one, we'll end up with the same answer. For this example, we'll use (3,10)

When we plug in our values we will get:

[tex]y-10=-2(x-3)[/tex]

Step 3: Now we just need to put our equation in slope-intercept form

[tex]y-10=-2(x-3)[/tex]

[tex]y-10=-2x+6\\y=-2x+16[/tex]

Therefore, our answer is [tex]y=-2x+16[/tex]

Hope this helps!!!

The number is -4

[tex]x \times[/tex]4+4= 2[tex]x[/tex]-4

[tex]$$x \times 4+4=2 x-4$$[/tex]

Subtract 4 from both sides[tex]$x \times 4+4-4=2 x-4-4$[/tex]

Simplify

[tex]$$x \times 4=2 x-8$$[/tex]

Subtract [tex]$2 x$[/tex] from both sides [tex]$x \times 4-2 x=2 x-8-2 x$[/tex]

Simplify

[tex]$$2 x=-8$$[/tex]

Divide both sides by 2

[tex]\frac{2 x}{2}=\frac{-8}{2}$$[/tex]

Simplify

[tex]$$x=-4$$[/tex]

A strategy for teaching division is by repeated subtraction. It involves repeatedly subtracting the same integer from a big number until the result is zero. It is a fantastic approach to teach kids about division. A technique called repeated subtraction, commonly referred to as division, removes an equal amount of items from a group.

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

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The difference between 4 and the sum of a number and is equal to twice that number. The number is -4.

Given that,

The difference between 4 and the sum of a number and is equal to twice that number.

Repeated subtraction is a method for teaching division. Until the result is zero, the same integer must be repeatedly subtracted from a large number. Repeated subtraction, sometimes known as division, is a method that takes an equal number of elements out of a group.

Division's opposite is multiplication. If 3 groups of 4 total up to 12, then 4 are in each group when 12 is divided into 3 equal groups. The fundamental goal of division is to produce equal groups or to determine how many individuals are in each group following a fair distribution.

x×4+4=2x-4

Subtracting 4 on both sides

4x+4-4=2x-4-4

4x=2x-8

Now, substracting 2x from both sides

4x-2x=2x-8-2x

2x=-8

x=-4

Therefore, The number is -4.

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Answer:

39cm

Step-by-step explanation:

7+7+7+9+9 = 39 - hope this works: )

Answer:

53

Step-by-step explanation:

Add all of number you have right now then pick a number and add it then divide it by 4 and keep going until reach 80

The reasonable domain of the given situation is 0≤ x ≤2 that is 0 to 2 hours.

We see that x is represented as the number of phone hours used, therefore it has to be a number larger or equal to zero, but not a negative number. So, on one end we have that the number of phone hours used (x) must be larger or equal to zero. On the other hand, when the battery goes to zero, there are no more phone hours to use. We can find what is that other limit by making the battery percent (y variable) equal to zero, and solve the equation for x, thus giving us the upper limit of usable phone hours:

=> y = 0 = 100 - 50x

=> 100 = 50x

=> x = 100/50

=> x = 2

Therefore, the phone can be used for a maximum of 2 hours and the situation may be written as 0≤ x ≤2.

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The snake would be 30 months old when his length is 5 feet 1 inches.

• Algebra is a branch in mathematics  which deals with symbolic and the rule for manipulation of those symbols. Algebra is also divided into some sub branches such as advanced algebra, abstract algebra , linear algebra, elementary algebra etc.

• The basics of algebra contains numbers, variables, constants, expressions and equations. The basic operations in mathematics are addition, subtraction, multiplication, division.

The length L of an Brazilian snake m months after birth is given by

L(m) = 3(m-8) -5 inches

We need to find how much the snake is old the snake Is when it is 5 feet 1 inches long

L(m) = 5 feet 1 inches

We know that 1 feet = 12 inches

L(m) =  5*12+1

= 61 inches

61 = 3(m-8)-5

66 = 3(m-8)

m-8 = 22

m = 30

The snake would be 30 months old when his length is 5 feet 1 inches.

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Answer:

Point J

Step-by-step explanation:

Collinear means in a line

Point J is on the same line with E and H

Answer:

Step-by-step explanation:

318 feet per second

So 19080 feet per minute

So 1,114,800 feet per hour

So 216.818181... miles per hour

Marvin Co. sells a total of 12 flashlights and 84 pens

Price of pen sold by Marvin Co. = $6

Price of flashlight sold by Marvin Co. = $10

Total sales = $624

Let the number of flashlights be x and the number of pens be y

Formulating the equations:

10x + 6y = 624

It is given that customer bought 7 times as many pens as flashlights, therefore:

y = 7x

Putting y = 7x in the equation we get,

10x + 6(7x) = 624

10x + 42x = 624

52x = 624

x = 12

So, the number of flashlights sold is 12 and the number of pens sold is 84

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Answer:

what will happen if we bought corrupt people

Answer:

13.94 seconds

Step-by-step explanation:

The greatest number with 2 decimal places that can be rounded to 13.9 is 13.94.

Answer: 13.94 seconds

The announcer said that Ingrid has won the race in 13.9 seconds, then the slowest time she could have run is 13.94 seconds.

Something similar to something else but not precisely the same is called an approximation. By rounding, a number can be roughly estimated.

By rounding the values in a computation before carrying out the procedures, an estimated result can be obtained.

13.94 is the largest number that can be rounded to the nearest two decimal places and be equal to 13.9.

Because after the second decimal, that is 4 the number has to increase as per the rules of approximation. That's why the number 13.94 up to two decimal places is correct.

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