Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2

Answer:

Step-by-step explanation:

EB/BC=15/12=5/4

ED/AC=X+5/Y=5/4

5y=4x+20

y=0.8x+4

Answer:

Step-by-step explanation:

75%

In a case whereby two planes, which are 2235 miles apart, fly toward each other. Their speeds differ by 45 mph. If they pass each other in 3 hours, the speed of slower is 350mph and faster is 395mph.

The concept here is simplification.

Let represent the speed of the slower plane using the( x),

Let us represent the speed of the faster to be ( x + 45)

The distance traveled  that can be associated to the slower plane ( 3x).

then the distance that can be attributed toi that of the faster plane = 3(x + 45).

given that the  total distance=(2235 miles).

[3x + 3(x + 45) ]= 2235

3x + 3x + 135= 2235

[6x ]= 2235-135

6x = 2100

x=350

hence,  the speed of the slower plane is 350

the speed of the faster= x + 45 = 350+45= 395

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The speed of first plane is 350 miles/hour and the speed of second plane is 395 miles/hour .

Given, Distance between the planes = 2235 miles

Let, the speed of the first plane be 'x' miles/hour.

Let, the speed of the second plane be 'x+45' miles/hour.

Since, they are flying towards each other, their speed will get added.

The collective speed of both the planes = (2x + 45) m/h.

A/Q, they pass each other in 3 hours, i.e. they collectively covers the distance of 2235 miles in 3 hours.

We know Distance = Speed × Time

Given, Distance = 2235 miles , Time = 3 hours , Speed = (2x + 45) m/h

                      2235 = 3  × (2x + 45)

                       745 = 2x + 45

                        x = 350 miles/hour.

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The coordinates of A' in triangle A'B'C' which was produced after reflection with condition y =x is equal to option d. ( 1, 2).

Graph is attached.

Triangle A'B'C' is produced after reflection of the triangle ABC over the line y = x.

From the graph we have ,

Coordinates of A is ( 2 , 1)

Coordinates of B is (-1, 4)

Coordinates of C is ( 0, -2)

Condition of reflection of triangle ABC over the line y = x.

x-coordinates replace by y and y replace by x.

Coordinates of triangle A'B'C' are

Coordinates of A' is ( 1, 2)

Coordinates of B' is (4, -1 )

Coordinates of C' is ( -2, 0 )

Therefore, if the coordinates of point A in triangle ABC are (2, 1), the coordinates of point A' in triangle A'B'C' would be option d. (1, 2).

The above question is not complete , the complete question is:

Triangle ABC is reflected over the line y = x to produce triangle A'B'C'. What will be the coordinates of A'? Graph is attached.

a.  (2,−1)            b.  (−2,−1)                 c.  (2,1)                d.  (1,2)

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The rational roots of the polynomial P(x) = x^3 + 3x^2 + x - 1 can be found using the Rational Root Theorem.

The Rational Root Theorem states that if a polynomial has a rational root, it will be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. In this case, the constant term is -1 and the leading coefficient is 1. The factors of -1 are -1 and 1, and the factors of 1 are 1. Therefore, the possible rational roots of this polynomial are -1/1, 1/1, or -1 and 1.

We can test these possible roots by plugging them into the polynomial and seeing if the result is 0.

P(-1) = (-1)^3 + 3(-1)^2 + (-1) - 1 = -1 + 3 - 1 - 1 = 0
P(1) = (1)^3 + 3(1)^2 + (1) - 1 = 1 + 3 + 1 - 1 = 4

Therefore, the only rational root of this polynomial is -1.

So, the rational roots of the polynomial P(x) = x^3 + 3x^2 + x - 1 are -1.

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The solution to the simultaneous equation given is (3, 4)

Given the system of equation below

2x+y=10

3x-y=5

From equation 2, the value of y is expressed as:

y = 3x - 5

Substitute the result into equation to have:

2x + 3x - 5 = 10

5x - 5 = 10

5x = 15

x = 3

Since y = 3x - 5

y = 3(3) - 5

y = 4

Hence the solution to the system of equation is (3, 4)

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The value of x for the given circle is 115°.

Geometry is a branch of mathematics that deals with the study of shapes, sizes, positions, and properties of objects in space. It includes the study of points, lines, planes, angles, curves, surfaces, and solids.

Using the Angles of Intersecting Chords Theorem,

When two chords cross inside of a circle, the resulting angle's measure is equal to the product of the lengths of the arcs it intercepts and its vertical angle, divided by two.

So, angle x = (190° + 40°)/2  = 115°

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Answer:

1. S = 20w + 100

2. M = -400w + 3,500

Step-by-step explanation:

1. Since Mateo is starting with a balance of $100, we can set this as our constant term (the 'b' in y = mx + b). Every week, he earns $20, so we can set this as the coefficient on the variable w (which represents how many weeks have passed).

2. Emily is spending money in this situation, so the coefficient on w is negative, as the amount of money she has left is getting smaller. The exact amount that she spends each week is $400, so the negative of that is going to be the coefficient of w in the equation. We can set the constant term in this equation to $3500, as Emily starts with that much money when no weeks have passed (when w = 0).

The dimensions of the rectangular pool are (2x − 1) and (3x − 3). The length of the pool is 3x − 3 and the width of the pool is 2x − 1.

The area of Rectangle is length times of width.

Area of rectangular pool = 6x² − 11x + 3

To factor the trinomial, we need to find two binomials that multiply together to give the trinomial 6x² − 11x + 3.

We use product-sum method of factoring to find the two binomials.

We need to find two numbers that multiply to 6 (the coefficient of the x² term) and add to -11 (the coefficient of the x term).

6x² − 11x + 3

6x² −2x-9x + 3

(2x − 1)(3x − 3)

Hence, the dimensions of the rectangular pool are (2x − 1) and (3x − 3). The length of the pool is 3x − 3 and the width of the pool is 2x − 1.

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Answer:

7/10

Step-by-step explanation:

Here ya go!

An ice cube with a lower volume will melt faster than an ice cube with a higher volume. This is because there is the less mass and surface area for the heat to transfer through, causing the ice cube to melt at a quicker rate.

For example, imagine two ice cubes, one with a volume of 2 cubic centimeters and another with a volume of 4 cubic centimeters. The ice cube with the lower volume (2 cubic centimeters) will melt faster than the ice cube with the higher volume (4 cubic centimeters) because there is less mass for the heat to transfer through.  In conclusion, an ice cube with a lower volume will melt faster than an ice cube with a higher volume. This is due to the fact that there is the less mass and surface area for the heat to transfer through, causing the ice cube to melt at a quicker rate.

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The volume of the prism is 105 cm³.

Volume of a three dimensional shape is the space occupied by the shape.

Given is a rectangular prism.

Volume of a rectangular prism = l × w × h

Here, l is the length, w is the width and h is the height.

Given that,

l = 7 cm, w = 3 cm and h = 5 cm

Substituting,

V = 7 × 3 × 5

   = 105 cm³

Hence the volume of the given rectangular prism is 105 cm³.

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The length of the slide shown is 15 feet

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let l represent the length of the slide, hence:

sin(53) = 12/l

l = 12/sin(53)

l = 15 feet

The length is 15 feet

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Answer:no

Step-by-step explanation:

if it was then it supposed to be like 4*20=5*15 which is not right equation

The value of the length, x is 5√3

From the question, we have the following parameters that can be used in our computation:

Rise = 11

Length = x

Hypotenuse = 14

The value of the length , x is calculated as

x^2 = Hypotenuse^2 - Rise^2

Substitute the known values in the above equation, so, we have the following representation

x^2 = 14^2 - 11^2

So, we have

x^2 = 75

Take the square root of bpth sides and evaluate

x = 5√3

Hence, the value of x is 5√3

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Answer:

Step-by-step explanation:

your going to have to show anwser choices

The weighted average of the numbers is 0.1.

The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average.

Given that, average of the numbers -3 and 5 with 3/5

The weight of first number and 2/5 of second number.

Here, -3(3/5)+5(2/5)/2

= (-1.8+2)/2

= 0.2/2

= 0.1

Therefore, the weighted average of the numbers is 0.1.

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From the sum of the interior angles, it is possible to find x=70°.

There are different quadrilaterals, for example square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example,  in a square, all angles are 90° and all sides present the same value.

The sum of the interior angles of a quadrilateral is equal to 360°.

The question gives a trapezoid and its respective angles. Thus,

x+85+150+55= 360

x+140+150=360

x+290=360

x=360-290

x=70°

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Answer:

b) 70°

Step-by-step explanation:

We know that,

→ The sum of all interior angles in a quadrilateral is 360°.

Now we have to,

→ Find the required value of x.

Forming the equation,

→ 85° + 150° + 55° + x = 360°

Then the value of x will be,

→ 85° + 150° + 55° + x = 360°

→ 290° + x = 360°

→ x = 360° - 290°

→ [ x = 70° ]

Hence, the value of x is 70°.

Answer:

180 - 119.4 = 60.6

So the answer is 60.6

Answer:

60.6°

Step-by-step explanation:

Supplementary angles equal 180 degrees. So we can show this with the following equation:

119.4 + x = 180

where x is the measure of the other supplementary angle.

If we subtract 119.4 from both sides, we get the the value of x, which is 60.6.

x' is the mean of all the x-values,  y' is the mean of all the y-values, and n is the number of pairs in the data set.

[tex]y=b_1x+b_0[/tex]

There is always one straight line that fits the data more accurately than any other, in the sense of minimizing the total of the squared errors, given any set of integers in pairs (apart from the case when all the x-values are the same). The least squares regression line is what it is known as. Additionally, its slope and y-intercept have formulae.

Given a collection of pairs (x,y) of numbers, there is a line [tex]y=b_1x+b_0[/tex] that best fits the data in the sense of the least squares regression line, its slope is b1 and the y-intercept is b0.

[tex]b_1=\frac{SS_{xy}}{SS{_xx}}}\\\\and\\\\b_0=y-b_1x\\\\SS_{xx}=\sumx^2-1/n[\sum x]^2\\\\SS_{xy}=\sum{xy}-1/n(\sum x)(\sum y)[/tex]

x' is the mean of all the x-values,  y' is the mean of all the y-values, and n is the number of pairs in the data set.

[tex]y=b_1x+b_0[/tex]

specifying the least squares regression line is called the least squares regression equation.

Example,

Find the least squares regression line for the five-point data set

x = 2  2  6  8  10  

y=  0  1   2  3  3.

compute the table,

x   y     x2         xy

2  0     4           0

2  1      4            2

6   2   36       12

8   3   64        24

10  3   100    30

28  9   208    68   (sum)

[tex]S_{xx}=208-(1/5)(28)^2=51.2\\\\SS_{xy}=68-(1/5)(28)(9)=17.6\\\\x'=\frac{28}{5}=5.6\\\\y'=1.8\\\\b_1=17.6/51.2=0.34375\\\\b_0=y-b_1(x)=1.8-(0.34375)(5.6)= -0.125[/tex]

The regression line is y=0.34375x-0.125

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The equation which is perpendicular to the equation of line passing through the points (-4, 7) (1, 3):

 y = 5/4x + 8.

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

To find the equation of a line that is perpendicular to another line, we need to know the slope of the original line.

The slope of the line passing through (-4,7) and (1,3) is:

m = (3 - 7) / (1 - (-4)) = -4/5

The slope of any line perpendicular to this line would be the negative reciprocal of -4/5, which is 5/4.

Therefore, the equation of a line that is perpendicular to the line passing through (-4,7) and (1,3) would be of the form:

y = 5/4 x + b

where b is the y-intercept.

Among the given options, the equation that matches this form is:

A. y = 5/4 x + 8

So the answer is (A) y = 5/4x + 8.

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The Credit Score is 4274274274274274.

A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts.

A phrase is used to describe each number in the series.

Given:

The sum of any three adjacent digits is 13.

The  second digit is 2 and the tenth digit is 4.

So, _2_ _ _ _ _ _ _ 4 _ _ _ _.

Now, the 2nd, 5th, 8th, 11th, 14th digits are equal and so are the 3rd, 6th, 9th, 12th, 15th.

So, the credit card number is 4274274274274274 and the last three digits are 274 which shows the sum is 13.

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A pharmacist wants to mixture of 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution. He used 85 ml of 40% saline solution and 34 ml of 12% saline solution.

Mixture word problems require you to combine two or more separate items, and then calculate some quantity of the resulting mixture (such as a percentage, price, or number of liters, for example). There will always be some type of "rate," like miles per hour or price per pound. Mixtures are substances that contain two or more distinct substance categories. To separate them, utilize physical tools. Examples include air, different gases, a mixture of sugar and water, a solution of salt and water, and so on.

here, we have,

Given,

A pharmacist wants to mixture of 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution.

Equation:

X + y = 119

y = 119 - x

0.40x + 0.12y = 119 of 0.32

0.40x + 0.12y = 38.08

Using y = 119 -x

0.40x + 0.12(119 - x) = 38.08

0.40x + 14.28 - 0.12x = 3808  Eq(2)

0.28x = 23.8

x = 85

and,

y = 119 - 85

y = 119 - 85

y = 34

Equating values in equation (2),

=0.40(85) + 0.12(34)

=34 + 4.08

=38.08

A pharmacist wants to mix a 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution. He used 85 ml of 40% saline solution and 34 ml of 12% saline solution.

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Answer:

Area = 452 cm²

Step-by-step explanation:

[tex] = \frac{\pi }{4} {d}^{2} [/tex]

[tex] = \frac{\pi}{4} {(24)}^{2} = 452.39 \: cm²[/tex]

The solution is, B = 245, is a Reflex Angle., when it is given that A=65.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

We know that, a ray is a line that continues on forever inn one direction with a point at it's start.

here, we have,

A = 65°

now,  B is a Reflex Angle ,

so, we know that Reflex Angle means the angle with value >180 to <270.

now, we get,

B = 180 + 65

  = 245

Hence, The solution is, B = 245, is a Reflex Angle.

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Answer:

We can use the triangle inequality theorem to determine the possible lengths of the third side of the triangle. According to the theorem, the length of any side of a triangle must be less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.

So, for a triangle with sides of length 16 and 17, the length of the third side must satisfy the following inequality:

17 - 16 < third side < 17 + 16

1 < third side < 33

Therefore, the length of the third side must be described by the expression:

1 < third side < 33

Step-by-step explanation:

skiing for 5 hours will make the cost of skiing at both ski resorts equal.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given, Bunny Hill Ski Resort charges $50 for ski rentals and $5 per hour of skiing, while Black Diamond Ski Resort charges $25 for rentals and $10 per hour of skiing.

Let's define:

x as the number of hours of skiing

C₁ as the total cost of skiing at Black Diamond ski resort

C₂ as the total cost of skiing at Bunny Hill ski resort

At Black Diamond ski resort, the total cost of skiing is the sum of the cost of rental and the cost of skiing per hour:

C1 = 25 + 10x

At Bunny Hill ski resort, the total cost of skiing is the sum of the cost of rental and the cost of skiing per hour:

C₂ = 50 + 5x

We want to find at what point C₁ = C₂, so we set the two equations equal to each other:

25 + 10x = 50 + 5x

Simplifying the equation, we get:

5x = 25

Dividing both sides by 5, we get:

x = 5

Therefore, skiing for 5 hours will make the cost of skiing at both ski resorts equal.

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60 kilometers per hour (kph) is equal to  roughly 37.28  long hauls (miles) per hour( mph).

To convert kilometers per hour to long hauls per hour, you can use the following conversion formula:

long hauls per hour =  kilometers per hour x0.621371.

Plugging in 60 kilometers per hour, we get,

long hauls per hour =  60 x0.621371  

long hauls per hour ≈37.28.  

Thus, 60 kilometers per hour is roughly 37.28 long hauls per hour.  

A kilometer (km) is a unit of length or distance used in the metric system. It is roughly original to 0.621  long hauls.

Mile is a unit of length or distance used in the customary system of dimension, primarily in the United States and United Kingdom. One afar is original to 280 bases or 760 yards, which is  roughly 1.609 kilometers in the metric system.

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Answer:

It is B: A180 mm side length