Consider the system of linear equations.

−4x+6y = 4

2x−3y = k

Determine the constant so that the system of linear equations has infinitely many solutions. (Hint: Graph the equations in the same coordinate plane. What should you see in order for the system to have infinitely many solutions?)

The distance between the centers of the circle is [tex]3\sqrt{2}[/tex] units.

It is required to find the distance between the centers of the circle.

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. The perimeter around the circle is known as the circumference.

Given:

Radius =5 units

XY = 8

According to given question we have

XY=

[tex]\sqrt{3^{2}+3^{2} } \\\\=\sqrt{18} \\\\=\sqrt{9.2} \\\\=3\sqrt{2}[/tex]

Therefore, the distance between the centers of the circle is [tex]3\sqrt{2}[/tex] units.

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Step-by-step explanation:

The formula for finding the length between two points is as follows:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

All we have to do is plug in our values and solve:
[tex]D=\sqrt{(-4-(-1))^2+(-4-2)^2}\\D=\sqrt{(-3)^2+(-6)^2}\\D=\sqrt{9+36}\\D=\sqrt{45}\\ D=6.71[/tex]

Answer: [tex]\frac{7}{32}[/tex]

Step-by-step explanation:

You want your numbers to have a common denominator which you can get by doubling both sides of the second number ([tex]\frac{1}{16} = \frac{2}{32}[/tex]).

[tex]\frac{9}{32} - \frac{2}{32} \\= \frac{7}{32}[/tex]

A rectangle measuring 8 inches by 6 inches needs squares of side. A function in an in which the box's volume is 4a³-28a²+48a.

Given that,

A square measuring 8 inches by 6 inches needs squares of side. A cut out of each corner so that the sides can be folded into a box without a top.

How much area a box can occupy is determined by its volume. You need to know a box's length, width, and height in order to compute its volume. By multiplying the base area by the box's height, one can get the volume of a box.

The measurement of how much space an object may occupy is called volume, which is also known as capacity. Both regular and irregular objects may be present. Cubes, blocks, cylinders, pyramids, cones, and spheres are examples of common objects.

A:  area of the base

L: Length of the base

W: Width of the base

V(a)= (8-2a) (6-2a) (a)

V(a)= (48-16a-12a+4a²) (a)

V(a)= (48-28a+4a²) (a)

V(a)= 48a-28a²+4a³

V(a)=4a³-28a²+48a

Therefore, a function in an in which the box's volume is 4a³-28a²+48a.

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[tex] \eta \times \eta \times \eta = 60 \\ \eta {}^{3} = 60 \\ \eta = \sqrt[3]{60} \approx3.91487[/tex]

Answer: -6

Step-by-step explanation:

8t+30-2t-16=-22

8t-2t+30-16=-22

6t+30-16=-22

6t+14=-22

6t=-22-14

6t=-36

t=-6

Answer:

x = 3.

Step-by-step explanation:

ADE and ABC are similar right isoceles triangles.

Step-by-step explanation:

12 / 3 = 12 / X

The number of watts will be 4700 watts to the nearest 100 watt.

It should be noted that 1 watt equals to 3.41 Btu per hour.

In this case, the air conditioner is rated at 16000 BTU per hour.

Therefore, the number of watt will be:

= 16000/3.41.

= 4692

= 4700 watts to the nearest 100 watt.

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The gallons of a 80​% antifreeze solution must be mixed with 70 gallons of ​25% antifreeze to get a mixture that is ​70% ​antifreeze is  x=315

Use a weighted average........ let x = an unknown number of gallons of the 80​% solution.

then     {x(80​%) + 70 (25%)}/{x +70} =70% ​

{x*[tex]\frac{80}{100}[/tex] + 70*[tex]\frac{25}{100}[/tex]}/{x +70} =70% ​

{[tex]\frac{4x}{5}[/tex] +17.50}/{x +70} =70% ​

[tex]\frac{4x+87.5}{5x+350}[/tex] = [tex]\frac{70}{100}[/tex]

40x+875 = 35x + 2450

40x-35x = 2450-875

5x = 1575

x=315

Keep in mind that the substance with the highest concentration is the solvent.

There are numerous varieties of solutions. A solute, for instance, could be a gas, a liquid, or a solid. Additionally, solvents can be solids, liquids, or gases.

The behavior of several types of solutions at the microscopic level is depicted in the following illustrations. You'll see that the solute particles are evenly spaced out among the solvent particles in each instance.

A solution is a homogeneous mixture of one or more solutes dissolved in a solvent. solvent: the substance during which a solute dissolves to produce a homogeneous mixture. solute: the substance that dissolves during a  solvent to produce a homogeneous mixture. The solute is the substance that is being dissolved, while the solvent is the dissolving medium. Solutions are often formed with many different types and forms of solutes and solvents.

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Answer: 99% 62%

Step-by-step explanation: Multiply the decimal by 100 to get a percentage.

The value of the points in the graph is a (2,80).

According to the statement

We have to find that the points on the graph.

So, For this purpose, we know that the

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.

From the given information:

f(x)=x^3+6x^2+17x+14​; slope of the tangent line=5

Then

f(x)=x^3+6x^2+17x+14

Now find the drivative then

f'(x)=3x^2+12x+17

Then slope of the tangent line=5

Now,

3x^2+12x+17 = 5

3x^2+12x+12 = 0

x^2+4x+4 = 0

Now solve the equation then

x^2+2x+2x+4 = 0

x(x+2) +2(x+2) = 0

(x+2) (x+2) = 0

Here the values of the x become -2,-2.

Then

When x = 2

f(x)=2^3+6(2)^2+17(2)+14

f(x)=8+24+34+14

f(x) = 80.

So, The value of the points in the graph is a (2,80).

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Answer:

x = 7

Step-by-step explanation:

The dashes on each side of the rectangle indicate congruency.

This means that PS = QR, or 2x - 3 = 11.

Now we would solve for this like normal.

2x - 3 = 11 add 3 to each side

+ 3 + 3

--------------

2x = 14 now divide by 2 to find x

÷ 2 ÷2

--------------

x = 7

Answer:

X = 36.5

Z = 19

Angle RIG is 69

angle ZIM is 126.5

Step-by-step explanation:

angle AIZ and ZIP

x + 3x - 56 = 90

    4x - 56 = 90

            4x = 90 + 56

            4x/4 = 146/4

                x  = 36.5

Plugin the value of x in (3x -56)

      3x - 56

     (3(36.5) - 56)

     (109.5 - 56) =  53.5

       Angle AIZ = 53.5

Angle RIG is 4z + 7. Convert the letter x in (x + 2)  to Z and solve for z

4z + 7 + z + 2 = 90

         5z + 9 = 90

                5z = 90 - 9

                5z/5 = 81/5

                   z = 16.2

                        Z + 2

                      16.2 + 2 = 18.2

           Angle GIM is 18.2 degrees

  Plugin the the value of z into 4z + 7 for angle RIG

   4z + 7

   (4(16.2) + 7) = 71.8

 Angle RIG = 71.8 degrees

Answer:

EX1: 4×(-1/3)=-4/3

EX2: (-2/3)(-1/2)(-3/5)= -1/5

Answer:

Step-by-step explanation: This vould be the answer because it could have been turned into an epression

The area of ΔTUV, to the nearest square inch is given as 267 square inch

Given data

ΔTUV, = 24 inches, = 29 inches and ∠T=130°

let the Area of the triangle = A

let the two sides be a and b

let the given angle be β

A = a * b * sin β / 2

A = 24 * 29 * sin 130 / 2

A = 696 * 0.7660 / 2

A = 696 * 0.3830 = 266.583

A = 266.583 square inch

A = 267 square inch ( to the nearest square inch )

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By solving a system of equations we conclude that they need to use 22 ounces of the 10% alloy and 33 ounces of the 20% alloy.

First, let's define the variables we will use to solve this problem:

We know that they want to get 55 ounces, then:

x + y = 55

And the concentration of these 55 ounces must be 16%, then we can write other equation:

0.1*x + 0.2*y = 0.16*55

Then we have a system of equations:

x + y = 55

0.1*x + 0.2*y = 0.16*55

Isolating x on the first equation we get:

x = 55 - y

Now we can replace that in the other equation so we get:

0.1*(55 - y) + 0.2*y = 0.16*55 = 8.8

Now we can solve this for y.

5.5 - 0.1*y + 0.2*y = 8.8

5.5 + 0.1*y = 8.8

y = (8.8 - 5.5)/0.1 = 33

Then the value of x is:

x = 55 - y = 55 - 33 = 22

We conclude that they need to use 22 ounces of the 10% alloy and 33 ounces of the 20% alloy.

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Answer:

79 boxes

Step-by-step explanation:

1500-155= 1345

1345/17=79.11

The information translated to algebraic expression  is 12 - x

Algebraic expressions are simply known as expressions composed of variables, terms, factors, constants and coefficients.

They are also made up of arithmetic operations such as multiplication, division, addition, subtraction, bracket, etc

From the information given, we have;

Let 'x' be the number

Let 'x' be subtracted from 132

This can be expressed as;

12 - x

Thus, the information translated to algebraic expression  is 12 - x

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The expression using factoring is 4 * (33 + 57)

The expression is given as

(132 + 228)

Factor out 2 from the expression

So, we have

(132 + 228) = 2 * (66 + !14)

Factor out 2 from the expression

So, we have

(132 + 228) = 2 * 2 * (33 + 57)

This gives

(132 + 228) = 4 * (33 + 57)

Hence, the expression using factoring is 4 * (33 + 57)

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4.3659392

hope this helps

Answer:

17.04 x 6.2= 105.648

Hope this helps :)

The decimal form of the fraction 10 / 66 is 0.15.

Fractions represent the parts of a whole or collection of objects.  

In other words fractions are represented as a numerical value, which defines a part of a whole.

Fractions has a numerator and a denominator.

The numerator is at the top while the denominator is below.

A decimal is a number that consists of a whole and a fractional part.

Therefore, let's convert the fractions 10 / 66 to decimal.

Hence,

10 / 66 ÷ 2 / 2 = 5 / 33

Therefore,

5 / 33 = 0.15151515151 = 0.15

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The measurement of angle ∠D in parallelogram CDEF would be 89° and

the measurement of angle ∠D in parallelogram ABCD would be 57°.

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

In parallelogram CDEF,

∠C = ∠D

87 = 93 + 2x

2x = 87 - 93

2x = -6

x = -3

So the measurement of ∠D = 93 + 2(-2) = 89

In parallelogram ABCD,

∠A =∠C

57 = 3x + 21

3x = 57 - 21

3x = 36

x = 12

So the measurement of ∠C = 3(12) + 21 = 57

Hence, the measurement of angle ∠D in parallelogram CDEF would be 89° and the measurement of angle ∠D in parallelogram ABCD would be 57°.

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the distance, d from the top of the platform to the  beach ball is equal to 10.29 m.

We are given that:

Height of the platform = 5 m

distance between bas of the platform and the beach = 9 m

We need to find the distance from the top of the platform to the beach ball.

We know that this distance d will be the hypotenuse of the triangle formed.

So, we have:

Perpendicular = 5 m

Base = 9 m

Hypotenuse = d

So, by using the Pythagoras theorem, we get that:

d² = 5² + 9²

d² = 25 + 81

d² = 106

d = √ 106

d = 10.29 m.

Therefore, we get that, the distance, d from the top of the platform to the  beach ball is equal to 10.29 m.

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The explicit rule for the arithmetic sequence that represents the number of miles that Abby will run in week n is:

[tex]a_n = 15 + 2n[/tex]

Using this rule, it is found that she will run 39 miles during her 12th week of training.

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

On the first week, she runs 15 miles, and for each subsequent week this amount increases by 2 miles, hence the first term and the common difference are given as follows:

[tex]a_1 = 15, d = 2[/tex]

The explicit rule for the arithmetic sequence that represents the number of miles that Abby will run in week n is:

[tex]a_n = 15 + 2n[/tex]

During the 12th week, the number of miles that she will run is found as follows:

[tex]a_{12} = 15 + 2(12) = 39[/tex]

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The expression 1-cotx/tanx-1 is cot x.

Given,

1-cotx/tanx-1

cot x = 1/tan x

1-cotx/tanx-1 = 1- (1/tan x) / tan x-1

                     = [(tan x -1 )/tan x ]/ [tan x -1]

                     = (tan x -1 )/ [tan x (tan x -1)]

                     =  1/tan x

                     = cot x

Expressions in mathematics are mathematical assertions that comprise at least two phrases that contain numbers, variables, or both, and are connected by an operator in between. Addition, subtraction, multiplication, and division are examples of mathematical operators. For example, x + y is an expression in which x and y are terms separated by an addition operator. There are two sorts of expressions in mathematics: numerical expressions, which contain simply numbers, and algebraic expressions, which contain both numbers and variables.

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The order of expressions from the least to greatest is [tex]\sqrt{3}[/tex], [tex]\sqrt{pie}[/tex] and 2

In order to find the value of these given expressions, we will have to convert them into a standard form, therefore we will find the value of these expressions by removing the root and finding its actual value

Value of 2 will remain the same as it is already in standard form

Value of [tex]\sqrt{3}[/tex] in standard form = 1.732

Value of [tex]\sqrt{pie}[/tex] in standard form = [tex]\sqrt{3.1459}[/tex] = 1.77

No ordering these expressions we find that 2 is the greatest, followed by 1.77 and 1.732

Hence, the expressions from least to greatest is [tex]\sqrt{3}[/tex], [tex]\sqrt{pie}[/tex] and 2

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