What is the slope of a line perpendicular to the line whose equation is 6x + 2y = -32. Fully simplify your answer.

The measures of the following angles are:

∠6 = 124°,  ∠2 =124°,  ∠3 = 124° ∠5 = 56°,  ∠7 = 124° ∠1 = 56°

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal).

∠4 = 56° ( corresponding angles are equal)

∠1 =∠4 ( vertically opposite angles are equal)

∠1 = 56°

∠7 + 56° = 180 ( angles on a straight line sum up to 180°)

∠7 = 180 - 56

∠7 = 124°

∠7 = ∠6 ( vertically opposite angle are equal)

∠6 = 124°

∠3 = ∠6 ( alternate angles are equal)

∠3 = 124°

∠2 = ∠3 ( vertically opposite angle)

∠2 = 124°

∠5 = 56° ( vertically opposite angles)

The unknown angles are: ∠1 = 56° ∠2 = 124°, ∠3 = 124°, ∠4 = 56°, ∠5 = 56°, ∠6 = 124° ∠7 = 124°

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The exponential form is  [tex]10^\frac{3}{2}= \sqrt{1000}[/tex].

Given expression is [tex](\sqrt{10})^3[/tex]

We know that

[tex](\sqrt{x})^n = x^\frac{n}{2}[/tex]

Therefore, [tex](\sqrt[]{10})^3 = 10^\frac{3}{2}[/tex]

Now, let's simplify the exponential form of this expression.

We know that [tex]a^\frac{m}{n} = nth root of a^m[/tex]

Therefore,

[tex]10^\frac{3}{2} =(\sqrt{10})^3[/tex]

[tex]10^\frac{3}{2}= \sqrt{1000}[/tex]

 Hence, the exponential form of the expression [tex](\sqrt{10})^3[/tex] is [tex]10^\frac{3}{2}= \sqrt{1000}[/tex] which simplifies to [tex]10^\frac{3}{2}[/tex].

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O Carys gets to Norwich station at 0750. To know how long will she have to wait for a train directly to Colchester.

Lets assume the values to be

a = 0848

b = 1 hour 2 minutes

c = 5 minutes

And let us look into it in detail as below

a = The first train arrive in London is 0848

b = Norwich to Colchester gets the trains in 1 hour 2 minutes

c = Carys gets to Norwich at 0750

So she need to wait for 5 minutes in a a train to get directly to Colchester.

Hence the answer is 5 minutes.

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Answer:

y=6 x=3

Step-by-step explanation:

−2(−7x−y=−27)

1(−14x+10y=18)

14x+2y=54

−14x+10y=18

12y=72

y=6

−7x−y=−27

−7x−6=−27

−7x=−21

x=3

Answer:

0.282kg/m3

Step-by-step explanation:

density=mass/volume

mass=32.5kg

volume=lxbxh

volume=2.4mx60cmx80cm

convert 60cm and 80cm to m:

60cm=6m

80cm=8m

volume= 2.4mx6mx8m

volume=115.2m3

density=32.5/115.2m3

density=0.28211kg/m3

round to nearest three decimal places:

= 0.282kg/m3

Answer:

Yes, the relation is proportional

Step-by-step explanation:

For a proportional relation, the ratio of X/Y (and thus Y/X) should be constant. You can verify, for examply dividing each Y by the corresponding X:

9 / -3 = -3

6 / -2 = -3

-3 / 1 = -3

-6 / 2 = -3

-9 / 3 = -3

As you can see, the ratio is the same, so the relation is proportional.

The length of the third side of the triangle is 2√14 units.

According to the question,

We have the following information:

Note that the complete question will be related to the right angled triangle with hypotenuse 15 units and perpendicular 13 units.

(More to know: Pythagoras theorem can only be used in right-angled triangle.)

We can use the Pythagoras theorem to find the base of the right-angled triangle.

Let's denote the base with b, perpendicular with p and hypotenuse with h.

[tex]b^{2} = h^{2}- p^{2}[/tex]

[tex]b^{2} = 15^{2} -13^{2}[/tex]

[tex]b^{2} }[/tex] = 225-169

b = √56

b = 2√14 units

Hence, the length of the third side of the triangle is 2√14 units.

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The equation that describes Joe’s monthly income is I = 500 + 20n. This function is Linear and discrete.

Joe makes each month = $500

The extra income per account he solicits = $20

No. of accounts he solicits = n

Income, I = 500 + 20n

It's a linear and discrete function.

A linear function in mathematics is one that has either one or two variables and no exponents. On a graph, it creates a straight line.

When the domain and range of a function are discrete sets of values rather than intervals, the function is said to be discrete.

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Answer:

m = 180d -20

Step-by-step explanation:

m = miles

d = days

Answer:

3034 grams

Step-by-step explanation:

to find one serving divide the total grams by grams per serving:

106200/35

=3034.28571429=3034(rounded to nearest whole number)

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Answer:

I believe it would be 4.9 inches

Step-by-step explanation:

14.7 divided by 3

Answer: 4.9 inches

Step-by-step explanation: 14.7 divided by 3 is 4.9

The volume of a cone having the same radius and same height as that of the cylinder is equal to 100 cm³.

Given that:

The volume of a cylinder is 300 cm³.

We assume that,

The radius of the cylinder = radius of the cone = r cm.

Height of cylinder = height of cone = h cm.

We have to find the volume of a cone having the same radius and same height as that of the cylinder.

The formula for the volume of a cylinder is = π x radius² x height

The formula for the volume of a cylinder is = πr²h cm³ = 300 cm³ ..... (1)

We know that,

The formula for the volume of cone = (1/3) x π x (radius)² x h

Volume of cone = (1/3) x π x (radius)² x h

Volume of cone = (1/3) x (πr²h)

Putting the value of πr²h from equation (1).

Volume of cone = (1/3) * 300

Hence, the volume of the cone is equal to 100 cm³.

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Inequality: 23x + $8 ≤ $110

Inequality:

$110 = Amount of money they have

$8 = Parking Cost

$23 = Cost of tickets per person

23x + $8 ≤ $110

23x=$110-8

23x=$102

In mathematics, a courting among expressions or values that aren't the same as every other is referred to as 'inequality. This term is used to examine the significance, wide variety, and intensity of two values or expressions. Equations and inequalities are both mathematical sentences fashioned by using referring to two expressions for every difference. In an equation, the two expressions are deemed equal's shown with the aid of the symbol =.

whereas in inequality, the two expressions aren't necessarily the same that's indicated by means of the symbols: >, <, ≤ or ≥. Inequality is critical to poverty due to the fact the relative role of people or families in society is taken into consideration as a crucial aspect of their welfare.

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Answer:

<8, <1, <4 are all 96

<6,<7,<3, <2 are all 84

Step-by-step explanation:

The congruency postulates for the given triangles are;

1) ASA Congruency postulate.

2) SSS congruency postulate.

3) AAS congruency postulate.

4) SAS Congruency postulate.

5) Triangles are not congruent

There are different triangle congruency postulates such as AAS, ASA, SSS, SAS, RHS.

1) We are given 2 corresponding angles and the included congruent side and as such, the congruency rule here is ASA Congruency postulate.

2) We are given 3 corresponding congruent sides for both given triangles and as such we can say that the triangle congruence postulate here is SSS congruency postulate.

3) We are given 2 corresponding angles and the non-included congruent side and as such, the congruency rule here is AAS Congruency postulate.

4) We are given two congruent sides and the include congruent angle and as such the congruency rule here is SAS Congruency postulate.

5) We are given three congruent angles but there is no mention of any of the sides being congruent and as such the triangles are not congruent.

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After 25 minutes will both aquariums contain the same amount of water.

Given:

Aquarium a contains 4. 6 gallons of water. Louise will begin filling aquarium a at a rate of 1. 2 gallons per minute. Aquarium b contains 54. 6 gallons of water. Isaac will begin draining aquarium b at a rate of 0. 8 gallon per minute.

Let y be the minutes

A(y) = 4.6 + 1.2y

B(x) = 54.6 - 0.8y

Same amount of water:

A(x) = B(x)

4.6 + 1.2y = 54.6 - 0.8y

1.2y + 0.8 y = 54.6 - 4.6

2y = 50

divide by 2 on both sides

2y/2 = 50/2

y = 25 minutes.

Therefore after 25 minutes will both aquariums contain the same amount of water.

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The angle of half past eight between the hour and minute hands of a clock is 255°.

Given that,

We have to find look for the smaller angles half past eight between the hour and minute hands of a clock.

We know that,

The clock is in circle.

A clock has 12 different parts. Between any two divisions, there is a 30° angle. Each division is then divided into 5 equal pieces, each of which is divided by an angle of 60° and equals 1 minute.

We know the total angle of the circle is 360°.

So, 12 hours is 360°.

Then 1 hours is

1 hour= 360/12=30°

So, 1 hour is 30°

60mins=1 hour

60 mins = 30°

1 min =30/60

1 min=1/2

So,

8 hour and 30 min

(8× 1 hour)+( 30×1 min)

(8×30)+(30×1/2)

240+15

255°

Therefore, The angle of half past eight between the hour and minute hands of a clock is 255°.

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Answer:23

Step-by-step explanation:

Reflection in the x-axis and translation 2a units up, translation a units up, followed by a reflection in the line y = a translation a units up, followed by a reflection in the line y = 2

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph. It's a common type of problem in algebra, specifically the modification of algebraic equations.

transformations that do not result in mapping (a,-a) to (a, a) when a > 0. are

reflection in the x-axis and translation 2a units up, translation a units up, followed by a reflection in the line y = a translation a units up, followed by a reflection in the line y = 2

Hence reflection in the x-axis and translation 2a units up, translation a units up, followed by a reflection in the line y = a translation a units up, followed by a reflection in the line y = 2

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Answer:x

2

−

2

x

+

1

=

x

2

−

2

x

+

1

2

=

(

x

−

1

)

2

A perfect square trinomial is the square of a binomial, so will take the form:

a

2

+

2

a

b

+

b

2

since

(

a

+

b

)

2

=

a

2

+

2

a

b

+

b

2

So a perfect square trinomial satisfies the following conditions:

(1) Two of the terms are squares.

(2) The other term is twice the product of the square roots (positive or negative) of the other two terms.

If the two square terms are

a

2

and

b

2

then the trinomial is either

(

a

+

b

)

2

or

(

a

−

b

)

2

depending on the sign of the third term.

Answer:

2\3

Step-by-step explanation:

Hope this helps!!

Step-by-step explanation:

2² - 12z +c

4 -12z + c

c = -4+12z

Answer:

  a.  9.56 × 10^3

Step-by-step explanation:

You want the sum (3.45 × 10^3)+ (6.11 ×10^3).

Distributive property

The distributive property works when adding numbers in scientific notation:

  (3.45 × 10^3)+ (6.11 × 10^3) = (3.45 +6.11) × 10^3 = 9.56 × 10^3

Answer:

The answer has to be 8.999

The constant, k is $2500 and 7 months of work will be needed to earn $17,500.

According to the question,

We have the following information:

We have a table where months and the salary in dollars is given.

Now, the salary is increasing constantly with number of months.

So, we have the following expression:

9) Amount of dollars is directly proportional to number of months.

Dollars = k*months

2500 = k*1

k = 2500

10) Now, the amount given is $17,500.

So, we have:

k*months = 17,500

Months = 17500/2500

Months = 7

Hence, the constant, k is $2500 and 7 months of work will be needed to earn $17,500.

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Answer:

Series calculator is a free online tool that gives the summation value of the given function for the given limits.

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The sum of two positive numbers is 120. The product of those numbers will be maximum if both numbers are equal to 60 and the maximum value is 3600.

Suppose we have a function f(x). At the extreme point (maximum/minimum), it holds:

      f ' (x) = 0

In the given problem, let the two numbers be a and b. Then,

a + b = 120 or

a = 120 - b   (equation 1)

f(b) = a x b = (120 - b) x b

f(b) = -b² + 120b

At the maximum point, the derivative with respect to b is zero,

f ' (b) = 0

-2b + 120 = 0

b = 120 / 2 = 60

Substitute b = 60 to equation 1,

a = 120 - 60 = 60

Hence, the two numbers that give maximal value of the product is 60 and 60. The product is 60 x 60 = 3600.

We can conclude that the maximum value of the product of those two numbers is 3600.

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The first quadrant that lies between the circle x² + y² =4 is 1.09587

The graph of x² +y² = 4 is a circle of radius 2, centered at (0, 0). In polar coordinates, this equation becomes simply r = 0.

The second equation requires a bit more work. To convert it to a polar equation, we

substitute, r cos θ for x and r sin θ for y:

r²cos ²θ + r²sin ²θ

   = 2r cos Ф

⇒r² = 2r cos θ

⇒r = 2 cos θ

This is the polar equation for a circle of radius 1, centered at the point (x, y) = (1, 0). (This can be seen directly from the original equation by completing the square, which results in the equation (x − 1)²+ y² = 1.)

To describe the region between the circles in polar coordinates, we can let θ range from 0 to π/2. Our values for r should range from the smaller circle to the larger one

Recalling again that x = r cos θ and dA = rdrdθ, our integral becomes

∫ ∫ₐ  x DA  = 8/3 - π/2

We can get a rough check of this answer as follows. The area of the region D is easily computed to be π/2. The average value of the function x in the region is somewhat less than 1, since D is thicker on the left. Doing these sorts of visual estimates can be very tricky, but let’s say the average value of x in D is about 0.70. Thus

∫∫ₐ x dA ∼=π/2· 0.70 ∼= 1.09956

Since 8/3 − π/ 2∼= 1.09587, this estimate agrees quite well with our answer.

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