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Given:

The equation of parallel line is:

[tex]3x-2y=5[/tex]

The required line passing through the midpoint of the line segment joining the points (-4,2) and (2,4).​

To find:

The equation of required line.

Solution:

Midpoint of  line segment joining the points (-4,2) and (2,4) is:

[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

[tex]Midpoint=\left(\dfrac{-4+2}{2},\dfrac{2+4}{2}\right)[/tex]

[tex]Midpoint=\left(\dfrac{-2}{2},\dfrac{6}{2}\right)[/tex]

[tex]Midpoint=\left(-1,3\right)[/tex]

It means the required line passes through the point (-1,3).

The slope of line [tex]Ax+By=C[/tex] is:

[tex]m=\dfrac{-A}{B}[/tex]

The given equation is:

[tex]3x-2y=5[/tex]

Here, A=3 and B=-2. So, the slope of the line is:

[tex]m=\dfrac{-3}{-2}[/tex]

[tex]m=1.5[/tex]

Slope of parallel lines are same. So, the slope of the required line is 1.5.

The required line passes through the point (-1,3) with slope 1.5. So, the equation of the line is:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-3=1.5(x-(-1))[/tex]

[tex]y-3=1.5(x+1)[/tex]

[tex]y-3=1.5x+1.5[/tex]

Adding 3 on both sides, we get

[tex]y=1.5x+1.5+3[/tex]

[tex]y=1.5x+4.5[/tex]

Therefore, the equation of the required line is [tex]y=1.5x+4.5[/tex].

Answer:

$3.30

Step-by-step explanation:

Shirt price * city sales tax = sales tax amount on shirt. $39.95 * 0.0825 = $3.30

Answer: it should be 252 in.

Step-by-step explanation:

Answer:

(2,1)

Step-by-step explanation:

When we translate to the right, we are simply adding a value to the x axis value corresponding to the units of translation

We have the translation by 1 unit, so we are to add 1 to the value of the x-coordinate

Thus, we have this as ;

(-3 + 1, 1)

= (-2,1)

When we reflect a point (x,y) over the y-axis, its new coordinates become (-x,y)

Applying this to what we have above, the coordinate of the final point will be (2,1)

Answer:

140x+420

Step-by-step explanation:

7(x+3)20

=140x+420

Answer:

14x+420

Step-by-step explanation:

7(x+3)(20)

=140x+420

Answer:

It's B

Step-by-step explanation:

B makes the most sense to me

Given:

The figure of a triangle.

To find:

The measure of angle 1.

Solution:

Exterior angle theorem: In a triangle, the measure of an exterior angle of a triangle is equal to the sum of two opposite interior angles.

Using Exterior angle theorem, we get

[tex]101^\circ =31^\circ +m\angle 1[/tex]

[tex]101^\circ -31^\circ =m\angle 1[/tex]

[tex]70^\circ =m\angle 1[/tex]

Therefore, the measure of angle 1 is 70 degrees.

Answer:

Natural numbers , whole numbers, Integers

Answer: 21.6 m

Step-by-step explanation:

Given

A football field measures [tex]100\ m\times 72\ m[/tex]

If a football field similar in shape to a full size  has a length [tex]l=30\ m[/tex]

The ratio of the length of the original to the small field is the same

Assume the width of the small field is  w

[tex]\therefore \dfrac{100}{30}=\dfrac{72}{w}\\\\\Rightarrow w=30\times \dfrac{72}{100}\\\\\Rightarrow w=21.6\ m[/tex]  

Thus, the width of the field is 21.6 m

Answer:

Leading coefficient is the coefficient of the highest power of x.

[tex]x^5[/tex] is the highest power.

Therefore, leading coefficient = [tex]\frac{1}{4}[/tex]

Option D

Answer:1/4

Step-by-step explanation:

Answer:

0% chance

Step-by-step explanation:

if the cube is 1-6 then 6 is the highest number. there is non higher.

Fabric B is a more durable fabric because it has a higher double rub rating than fabric A.

We have given that,

Researchers for a textile company carried out an experiment comparing the longevity of two new fabric blends.

An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried.

They carried out a series of usage tests, known as double rubs, on 100 pieces of each type of material.

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Answer:

Fabric B is a more durable fabric because it has a higher double rub rating than fabric A.

The sales department can refer to fabric B as a medium-duty fabric.

Step-by-step explanation:

edmentum :)

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{2x + 12 = 40}[/tex]

[tex]\large\text{SUBTRACT 12 to BOTH SIDES}[/tex]

[tex]\large\textsf{2x + 12 - 12 = 40 - 12}[/tex]

[tex]\large\text{CANCEL out: \textsf{12 - 12} because that gives you \textsf{0}}[/tex]

[tex]\large\text{KEEP: \textsf{40 - 12} because that helps solve for \textsf{x}}[/tex]

[tex]\large\textsf{40 - 12 = \bf 28}[/tex]

[tex]\large\text{New EQUATION: \textsf{2x = 28}}[/tex]

[tex]\large\text{DIVIDE 2 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{2x}{2}=\dfrac{28}{2}}[/tex]

[tex]\large\text{CANCEL out: }\mathsf{\dfrac{2}{2}}\large\text{ because that gives you 1}[/tex]

[tex]\large\text{KEEP: }\mathsf{\dfrac{28}{2}}\large\text{ because gives you the value of x}[/tex]

[tex]\mathsf{x = \dfrac{28}{2}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: \bf \huge x = 14}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Step-by-step explanation:

V = l.W.H

3(5)(4) = 60 units

The volume of rectangular prism is given by the product of its dimensions hence the correct option is 3(5)(4) = 60 units

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder or a sphere. Different shapes have different volumes.

Given that, we need to determine the correct calculation for the volume of the prism,

We know that, the volume of a rectangular prism is the  product of its dimensions = length x width x height

Therefore, the correct formula is 3(5)(4) = 60 units

Hence, the correct option is 3(5)(4) = 60 units

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Answer:

it will decrease

Step-by-step explanation:

if theres not enough food water, ect for all 55 to survive and only enough to support 40 wolves they will die down

Answer:

It will decrease

Step-by-step explanation:

There are 55 wolves means the wolf population will decrease as the place have only sufficient resources to 40 wolves and will eventually die.

I think this is the answer.

Answer:B

Step-by-step explanation:

Answer:

Step-by-step explanation:

980

Answer:

[tex]Pr = \frac{1}{2}[/tex]

Step-by-step explanation:

Given

[tex]S = \{1,2,3,4,5,6\}[/tex] --- the faces of the dice

[tex]n(S) = 6[/tex]

Required

Pr(Multiple of 8)

The multiples of 8 in the given dataset are:

[tex]Multiples = \{1.,2,4\}[/tex]

[tex]n(Multiples) = 3[/tex]

So, we have:

[tex]Pr = \frac{n(Multiples)}{n(S)}[/tex]

[tex]Pr = \frac{3}{6}[/tex]

Simplify

[tex]Pr = \frac{1}{2}[/tex]

Answer:

last option:  y = 1/6x+3; y = 1/2x+3

Step-by-step explanation:

6y = x + 18

Solve the above for 'y' to get:

y = 1/6x + 3

2y - x = 6

Solve the above for 'y' to get:

2y = x + 6

y = 1/2x + 3

The solution is Option A

The equation of Charlene's age is 3x - 4

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let Charlene's age be C

The age of Mary is = x

Now , the equation is

Charlene's age is 4 less than 3 times Mary's age

Substituting the values in the equation , we get

C = 3 x ( Mary's age ) - 4

On simplifying the equation , we get

C = 3x - 4    be equation (1)

Therefore , the value of C is 3x - 4

Hence , the age of Charlene's age is 3x - 4

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Answer:

For problem one:

a. 11

b. 3/11

c. 2/11

d. there are only 2 chips

e. 3/11