Consider the system of linear equations: 12x+6y=-20
-3x+y=5
Change the coefficient of y in the first equation so that the system has infinitely many solutions.

The unit rate is given by a quotient between the cost and the mass, the unit rate is 18 dollars per pound.

We want to find the unit rate for the given item, where we know that:

1/4 pound costs $4.50

To find the unit rate, we need to take the quotient between the cost and the mass.

We will get:

U = $4.50/(1/4 lb)

U = $4.50*4 /lb

U = $18 per lb

So the unit cost is 18 dollars per pound.

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The expression 5z + 5 - 6z is equivalent to the expression 5 - z.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ 5z + 5 - 6z

Simplify the expression, then we have

⇒ 5z + 5 - 6z

⇒ 5 - z

The expression 5z + 5 - 6z is equivalent to the expression 5 - z.

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Answer:

C

Step-by-step explanation:

Because the three shapes listed all have at least one right angle as a right angle triangle has one and a square and a rectangle both have two each

The distance between the trains after 30 minutes is 28.96 miles.

In 30 minutes, the train traveling at 100 miles per hour traveled 50 miles.

A train traveling at 90 miles per hour has traveled 45 miles in 30 minutes.

It is possible to think of this as a triangle with sides of 50 and 45, and an angle of 35 degrees included.

Take into account a right-angled triangle with x as one of its acute angles.

The cosine formula is then cos x = (adjacent side) / (hypotenuse), where "adjacent side" refers to the side next to angle x and "hypotenuse" refers to the longest side (the side across from the right angle) of the triangle.

By using the cosine law,

c2=a+b+2+cosC or c2=50*45*cos35=2500+2025+4500*0.82=838.82(2dp)c= sqrt 838.82=28.96 miles.

The distance between the trains after 30 minutes is 28.96 miles.

The Complete Question is distance between the trains.

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Answer:

Step-by-step explanation:

it's c

3^3 * 2^3*5

When Vessel A and Vessel B start steaming at the same time and with same speed then Vessel B will reach the Prime Meridian first as it is at a closer distance to Prime Meridian.

What is distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

The coordinates of position of Vessel A is = (83°16’N, 48°51’W)

The coordinates of position of Vessel B is = (32°43’N, 48°51’W)

The coordinates of position of Prime Meridian is = (0°0’N, 0°0’W)

First calculate the distance in kilometers for Vessel A.

From initial position (83°16’N, 48°51’W) to final position (0°0’N, 0°0’W) -

The distance in kilometers is 9516 km.

Now, calculate the distance in kilometers for Vessel B.

From initial position (32°43’N, 48°51’W) to final position (0°0’N, 0°0’W) -

The distance in kilometers is 6270 km.

The distance from Vessel A to Prime Meridian is greater than the distance from Vessel B to Prime Meridian.

Therefore, it can be seen that vessel B will reach the prime meridian first.

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Answer:

CI = Amount - Principal

CI = P (1+(r/12))121 - P

 P= principal amount

 r= interest rate

 t= time

Step-by-step explanation:

The compound interest each month is calculated using the monthly compound interest method. Return on credit is another name for compound interest. Simple interest and compound interest are identical in the initial amount of time, however the variation starts with the following phase. It is characterized as interest on interest because starting with the second intermission, it is also computed on the revenue that was thus generated on the prior time frame.

The interest is accrued directly to the principle every month using a method called monthly compounding principal, often termed as interest-on-interest equation. The ultimate sum minus the principle sum is known as total compound interest.

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Answer:

nothing is truth

Step-by-step explanation:

because this world is like a circle

Answer:

3.52, 3.48

82.633, 82.632, 82.629

438.12, 437.96

8.45, 8.46,8.47,8.48,8.49,

Answer: 9

Also could you mark my answer as brainliest? It helps and doesnt hurt

The Least Common Denominator (LCD) of fractions with denominators 27, 18, and 36 is 108. This is found by identifying the Least Common Multiple (LCM) of the three numbers, which is also 108.

The LCD, or Least Common Denominator, of fractions whose denominators are 27, 18, and 36, is the smallest multiple that all three numbers have in common. In this case, the LCD is 108.

To find the LCD, you need to find the Least Common Multiple (LCM) of the denominators. The LCM of 27, 18, and 36 is 108.

Here's how:

Therefore, 108 is the LCD of fractions whose denominators are 27, 18, and 36.

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The number of fourth graders who bought lunch in the cafeteria is given by the equation A = 107 students

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

The number of classes of fourth graders = 7 classes

The number of students in each class = 19 students

So , the total number of fourth graders = 7 x 19 = 133 students

And ,

The number of students who brought lunch from home = 26 students

Now , the number of students who bought lunch from cafeteria A = total number of fourth graders - number of students who brought lunch from home

Substituting the values in the equation , we get

The number of students who bought lunch from cafeteria A = 133 - 26

On simplifying the equation , we get

The number of students who bought lunch from cafeteria A = 107 students

Therefore , the value of A is 107

Hence , the number of students is 107 students

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One (1) centimeter into yards is equal to 0.01093613

We should know that centimeter is defined as  a metric unit of measurement used for measuring the length of an object.

It is written as cm.

A meter has 100 centimeters.

10 millimeters make one centimeter.

The centimeter can be written as cm.

While calculating the surface area of an object, the unit of measurement becomes cm².

While measuring the volume of an object, the unit of measurement becomes cm³.

1 centimeter converted into yard is 0.01093613

Yard [yd] to  Centimeter [cm]

0.01 yd 0.9144 cm

0.1 yd 9.144 cm

1 yd 91.44 cm

2 yd 182.88 cm

3 yd 274.32 cm

5 yd 457.2 cm

10 yd 914.4 cm

20 yd 1828.8 cm

50 yd 4572 cm

100 yd 9144 cm

1000 yd 91440 cm

From the table above we notice that 1 centimeter converted into yard is 0.01093613

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The decreased numbers are first number is 2. and the second number is -9.

x - y = 0

The first number decreased 5 times

-5 -y = -10

-y = -10 + 5

-y = -5

y = 5

The second number decreased 2 times

x - (-2) = -1

x + 2 = -1

x = -1 -2

x = -3

Now,

the first number is

-3 - 5 = -10

-8 = -10

10-8 = 0

2 = 0

the second number is

-3 - 5 =-1

-8 = -1

-8 +1 =0

-9 = 0

Hence, the answer is 2, -9.

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The length of the line segment AC is 20 units.

A line segment is bounded by two distinct points on a line.

The length of AC is x + 9. The actual length of the line segment AC can be found as follows:

Therefore, using equations,

AB + BC = AC

AB = 3x - 15

BC = x - 9

AC = x + 9

Hence,

AC = AB + BC

x + 9 =  3x - 15 + x - 9

x + 9 = 3x + x - 15 - 9

x + 9 = 4x - 24

x - 4x = -24 - 9

-3x = -33

divide both sides by -3

x = -33 / -3

x = 11

Therefore,

AC = 11 + 9 = 20 units

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The unknown angles of the quadrilateral are as follows:

x = 100°

y = 80°

z = 40°

A quadrilateral is a plane figure that has four sides , and also has four corners or vertices. The sum of angles in a quadrilateral is 360 degrees. Examples of quadrilateral are parallelograms, rectangle, square, rhombus etc.

Therefore, let's find the angle x, y and z in the quadrilateral as follows:

x = 100 degrees(vertically opposite angles)

adjacent angles of the quadrilateral is supplementary.

Therefore,

100 + y = 180

y = 80 - 100

y = 80 degrees

Let's find z.

z + z + 100 = 180

2z = 180 - 100

2z = 80

z = 80 / 2

z = 40 degrees

Therefore,

x = 100 degrees

y = 80 degrees

z = 40 degrees

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Since the ABCD rectangle's vertex coordinates are A(1, -2), B(4, -2), C(4, -4), and D(3, 1), option c is accurate (1,-4)

You may also refer to it as a quadrilateral that is equiangular, meaning that each of its angles is equal. Another possibility for the parallelogram is a straight angle. Four of the sides of a square are of identical length. Four 90-degree vertices and equal parallel sides make up a rectangle-shaped quadrilateral. This leads to the term "equirectangular rectangle" occasionally being used to describe it. A rectangle is also referred to as a parallelogram due to the equal and parallel lengths of its opposite sides.

given

To find the coordinates, first subtract 1 from 4 to get 3 and then add 3 to -2 to get 1.

Since the ABCD rectangle's vertex coordinates are A(1, -2), B(4, -2), C(4, -4), and D(3, 1), option c is accurate (1,-4)

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The 52nd term of the arithmetic sequence -24, -7, 10, ..... is equal to 843.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = -7 - (-24)

Common difference, d = -7 + 24

Common difference, d = 17

Substituting the given parameters into the formula, the 52nd term of this arithmetic sequence is given by;

a₅₂ = a₁ + (52 - 1)d

a₅₂ = -24 + (51)(17)

a₅₂ = -24 + 867

a₅₂ = 843.

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Since lines mn are parallel lines, the value of x is equal to 32°.

In Mathematics, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.

In Mathematics, the Linear Pair Postulate states that the measure of two (2) angles would add up to 180° provided that they both form a linear pair.

By applying the Linear Pair Postulate to the two (2) angles on the straight lines cut by a transversal, we have the following:

x + 148° = 180°

x + 148° = 180°

x = 180° - 148°

x = 32°.

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The probability that they are both blue given that they are the same color is 7/22.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Total socks = 5 + 7 = 12

So, Probability of a blue socks = 7/12

and, the Probability of the second blue socks = 6/11

So, the probability of the 2 blue socks in a row

= 7 /12 x 6/11

= 7/22

Hence, the probability is 7/22.

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Answer:

$11,500 per year or $958.33 per monthThe amount of money you will have in your account in 30 years would be $1,311,715.94The total money you will put into the account is $3,465,000The total growth/interest you should expect to earn is $946,315.94If you manage to save an additional $100 each month, you will have $1,385,719.71 in the account after 30 years.

Step-by-step explanation:

Answer:

[tex]\boxed{\sf x\le \cfrac{15}{2}}[/tex]

[tex]\boxed{\sf x\le \:7.5}[/tex]

Step-by-step explanation:

[tex]\sf 6x-18\le \:27[/tex]

Add 18 to both sides.

[tex]\sf 6x\le \:45[/tex]

Divide  both sides by 6:-

[tex]\sf \cfrac{6x}{6}\le \cfrac{45}{6}[/tex]

[tex]\sf x\le \cfrac{15}{2}[/tex]

or

[tex]\sf x\le \:7.5[/tex]

__________________

-Hope this helps!

Answer:

10.58

Step-by-step explanation:

We are here given a right angled triangle in which two of the sides are 16 and 12 and we are interested in finding the third side x . We will use Pythagoras theorem here according to which the sum of squares of base and perpendicular is equal to the square of hypotenuse. so that,

[tex]\longrightarrow\sf h^2 = p^2+b^2\\ [/tex]

[tex]\longrightarrow\sf x^2 + 12^2 = 16^2\\ [/tex]

[tex]\longrightarrow\sf x^2 = 256 - 144\\ [/tex]

[tex]\longrightarrow\sf x =\sqrt{ 112}=\boxed{10.58} [/tex]

and we are done!

-Rishabh

Answer:

[tex]x=4\sqrt{7}=10.6\; \sf (nearest\;tenth)[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

From inspection of the given right triangle:

Substitute the given values into Pythagoras Theorem formula and solve for x:

[tex]\implies x^2+12^2=16^2[/tex]

[tex]\implies x^2+144=256[/tex]

[tex]\implies x^2=112[/tex]

[tex]\implies x=\sqrt{112}[/tex]

[tex]\implies x=\sqrt{16 \cdot 7}[/tex]

[tex]\implies x=\sqrt{16} \sqrt{7}[/tex]

[tex]\implies x=4\sqrt{7}[/tex]

[tex]\implies x=10.6\; \sf (nearest\;tenth)[/tex]

The colors and fonts on a website are created with CSS.

rgb: #FFC0CB in pink (255,192,203)

Rgb: #EE82EE Violet (238,130,238)

rgb, built-in color #FF0000 for red (255,0,0)

Rgb green #008000 (0,128,0) (0,128,0)

Orange in RGB. #FFA500 (255,165,0) (255,165,0)

Rgb, #FFFF00, Yellow (255,255,0)

Rgb, blue #0000FF (0,0,255) (0,0,255)

a visual representation of CSS colors

In CSS, hex values (or decimal digits) are most frequently used to represent color. Hex values are actually merely another method for expressing RGB values. Instead of three values ranging from 0 and 255, six hexadecimal numbers are used. Hex numbers run from 0 to 9 and from A to F.

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We can write the complete table as -

x {table}           y {guests}

    1                          2

    2                         4

    3                         6

    4                         8

Given is that Ashley is having a party she’ll have 4 tables for every 8 guest.

It is given that -

there are 4 tables for every 8 guest.

then on 1 table there would be (8/4) = 2 guests.

The linear equation guarding the table would be -

y = 2x

We can write the table as -

x {table}           y {guests}

    1                          2

    2                         4

    3                         6

    4                         8

Therefore, we can write the complete table as -

x {table}           y {guests}

    1                          2

    2                         4

    3                         6

    4                         8

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Answer:

4!/(1! 1! 1! 1!) = 24

Step-by-step explanation:

None of your answers are correct!

Using sine function: sin =opposite/hypotenuse

sin =opposite/hypotenuse

step1

example;

sin(60)=2.4/[tex]x[/tex]

[tex]x[/tex]=2.4/sin(60)

[tex]x[/tex]≈2.8

answer is 2.8

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The square root of 3/10 is 0. 55

The square root of a number is simply the the inverse operation of squaring that number. It is the value obtained with multiplying the number by itself.

It is determined by finding a number that when it is squared, gives the original number.

The square root of a number is also referred to as that factor of a number that when multiplied by itself gives the original number.

They are special exponents with squares.

Example:

If the square root of x is y, then x × x = y

It is represented with the symbol, √.

We have to calculate;

[tex]\sqrt{\frac{3}{10} }[/tex]

= √0. 3

= 0. 55

Hence, the value is 0. 55

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Answer:

slope is -1/4

Step-by-step explanation:

We are given the points (-5,2) and (7,-1)

the slope formula is [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

y₂ = -1

y₁ = 2

x₂ = 7

x₁ = -5

[tex]m=\frac{(-1)-2}{7-(-5)}[/tex]

[tex]m=\frac{-3}{12}[/tex]

[tex]m=-\frac{1}{4}[/tex]

The average speed of the racoon is given by 1.28 m per second

Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route. In other words, velocity is a vector, whereas speed is a scalar number.

The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance traveled between them are not the same. The length of the entire journey taken to go from one point to another is the distance traveled.

The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.

Total distance travelled = 15 + 45 m = 60 m

Total time of travel = 12 + 15 + 20 = 47 sec

Avewrage speed = Total distance / total time = 60/ 47 = 1.28 m/sec

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Regardless of the type of triangle, all triangles have internal angles that sum up to 180°. An isosceles triangle will have two equal-sized angles.

The hypotenuse, or side across from the right angle, has a square whose length is equal to the sum of the squares of the other two sides in a right triangle, according to the Pythagorean theorem. In other words, if the hypotenuse's length is c and the lengths of the other two sides are a and b, then c2 = a2 + b2.

Whatever the type of triangle, all triangles have internal angles which sum to 180°. The two angles of an isosceles triangle will be equal in size. Every angle of an equilateral triangle is 60 degrees. The other two angles in a right-angled triangle will add up to 90° because the triangle has one angle that is 90°.

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