A Chemistry book is moved 2 meters to the left and then 1 meter to the right. What is its displacement?

Answer:

[tex]A) \ \{ \dfrac{-3 + \sqrt{29} }{2}, \dfrac{-3 - \sqrt{29} }{2} \}[/tex]

Step-by-step explanation:

The quadratic equation to be solved is presented here as follows;

x² + 3·x - 5 = 0

The quadratic formula for a quadratic equation of the form, a·x²+b·x + c = 0, where 'a', 'b', and 'c' are constants and 'x' is unknown, is given as follows;

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4 \cdot a \cdot c} }{2 \cdot a}[/tex]

By comparison with the given equation, we have;

a = 1, b = 3, and c = -5

By plugging in the values, we get;

[tex]x = \dfrac{-3 \pm \sqrt{3^2 - 4 \times 1 \times (-5)} }{2 \times 1}[/tex]

Therefore;

[tex]x = \{\dfrac{-3 + \sqrt{9 + 20} }{2}, \dfrac{-3 - \sqrt{9 + 20} }{2}\} = \{\dfrac{-3 + \sqrt{29} }{2}, \dfrac{-3 - \sqrt{29} }{2}\}[/tex]

[tex]x= \{\dfrac{-3 + \sqrt{29} }{2}, \dfrac{-3 - \sqrt{29} }{2}\}[/tex]

The value of 'y' in the isosceles trapezoid ABCD is 14 and this can be determined by using the properties of isosceles trapezoid.

What is Triangle ?

Triangle can be defined as which contains three sides, three angles and the sum of the angles is 180 degrees.

Given ,

ABCD is an isosceles trapezoid with legs AB and CD and base BC.

If the length of AB is (7y - 4),

the length of BC s (4y - 6),

and the length of CD is (8y - 18).

The two legs are of equal length In any isosceles trapezoid that means:

7y - 4 = 8y - 18

Add 18 on both sides in the above equation.

7y - 4 + 18 = 8y - 18 + 18

7y + 14 = 8y

Now, subtract 7y on both sides in the above equation.

7y + 14 - 7y = 8y - 7y

Simplify the above expression in order to get the value of 'y'.

y = 14

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Answer:

  y = -x +3

Step-by-step explanation:

You want the equation of the line through the points (-3, 6) and (5, -2) in slope-intercept form.

The slope can be found using the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (-2 -6)/(5 -(-3)) = -8/8 = -1

The y-intercept can be be found using the formula ...

  b = y -mx

  b = 6 -(-1)(-3) = 3

The equation in slope-intercept form is ...

  y = mx +b

Using the found values, the equation is...

  y = -x +3

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Answer:

x = 24

y = 26

Step-by-step explanation:

The triangle are similar because,

Each corresponding angles in the triangles are equal (AAA).

From the diagram,

5/10 = 12/x

Solving for x

x = (10×12)/5

x = 24

Also applying pythagoras theorem to get the hypotenuse of the larger side in the biggerr triangle.

y² = √(10²+24²)

a = √(100+576)

a = √(676)

a = 26.

Answer:

Step-by-step explanation:

y = a * x(x - 3)(x + 1)^2

2,12 is used to find the value of a

y = a (2)(2 - 3)(2 + 1)^2

12 = a (2)(-1)(3)^2

12 = a (2) (-1) (9)

12 = - 18*a

12/-18 = a

a = - 2/3

y = (-2/3)*x*(x - 3)(x + 1)^2

Answer:

i believe it is B (๑ↀᆺↀ๑)

Answer:

-3x3x-3x-3

Get yourself some braincells in the future, please.

Answer:

Step-by-step explanation:

The y intercept is (0,5)

The slope is found from choosing 2 points on the line. My choice is (4,13) and (0,5)

x2 = 4

x1 = 0

y2 = 13

y1 = 5

slope = (y2 - y1)/(x2 - x1)

slope = (13 - 5)/(4 - 0) = 8/2 = 4

If I'm right answers A and D are both wrong. We don't know exactly what the 5 represents. I would say it is the beginning number of songs she knows when she starts graphing. In any event, B is not the answer.

That leaves C.

y = 2x + 5

x = 20

y = 2*20 + 5

y = 45

(20,45) is on the line

Answer:

oki! Mizuki here to help! 12 will be your answer!

Step-by-step explanation:

Soo... The ratio of blue to green is 4:3 right?

and there are 21 balloons!

4 + 3 is 7! So we divide 21 by 7 and get 3!

Then we multiply 3 by the number of blue balloons(aka 4) and get 12!

Answer:

C. 267.9^3

Step-by-step explanation:

so if you use actual pi you get 268.08^3 since I use calculators... and since were using 3.14 instead of actual pi, it makes it so the answer has to be the third option.

I hope this helps :))

The line parallel to 6y = -36x -3 will have the same slope which will be -6.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

The equation of the line is

6y = -36x -3

⇒y = -6x - 1/2

From slope intercept form of the equation we know that

equation of the line is y = mx + c

where m is the slope.

Therefore,

slope the line is -6

The line parallel to 6y = -36x -3 will have the same slope which will be -6.

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Answer:

The slope of line t is -4/5.

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(14-10)/(2-7)

m=4/-5

Parallel lines have same slopes.

For the given Augmented Matrix ,the correct option is :

A) The solution set has exactly one element.

The exact solution is x = -25 , y = 2 and z = 2.

Augmented Matrix:

An augmented matrix is ​​a means of solving simple linear equations. Coefficients and constant values ​​of linear equations are represented as matrices called augmented matrices. Simply put, an augmented matrix is ​​a combination of two simple matrices along columns. If the first matrix has m columns and the second matrix has n columns, then the augmented matrix has m + n columns.

Now, as given the Augmented matrix:

[1 7 3 -5]

[0 0 0 3]

[0 0 1 2]

[0 1 -1 4]

From this system we get:

y - z = 4       --------------------------- (1)

    z = 2

and, z = 3

and, x + 7y + 3z =-5   ---------------- (2)

Now, Solving the equation with z = 2,

    y - 2 = 4

⇒ y = 6

and, putting y = 6 and z = 2

   x + 7× 6 + 3×2 = -5

⇒ x + 42 + 6 = -5

⇒ x +48 = -5

⇒ x = -53

Therefore, x = -53, y=6 and z =2

Now, for z = 3 in equation (1)

   y - 3= 4

⇒ y = 7

Putting y =7  and z =3, we get:

   x + 7 × 7 + 3×3 = -5

⇒ x + 49 + 9 =-5

⇒ x + 58 = -5

⇒ x = -63

Therefore, x = -63, y =7 and z =3

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Lia gave away 3/5 of the trail mix, which is equal to 2 2/5 pounds.

Lia bought 4 3/5 pounds of trail mix. She gave 3/5 of it to her iter.Since Lia bought 4 3/5 pounds of trail mix, we can express this as 4 + 3/5 pounds, or 9/5 pounds.

To find out how much trail mix Lia gave away, we can multiply 9/5 by 3/5.

3. 3/5 multiplied by 9/5 is equal to 27/25.

To simplify this fraction, we can divide both the numerator and denominator by 3.

27/25 can be simplified to 9/5 or 2 2/5 pounds.

Therefore, Lia gave away 2 2/5 pounds of the trail mix.

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Answer:

+6/27=?/?

Step-by-step explanation:

+6/27=?/? will be the next number as the patter keeps increasing the numerator by 1 and denominator by 9

Answer:

Is this what you wanted

Step-by-step explanation:

Answer:

ansfhbshajsnshafakdkidbsbaga abfjdb

Answer:

26

Step-by-step explanation:

Answer:

QR = 30

Step-by-step explanation:

GHI ~ PQR means that PQR is the same shape and length ratios as GHI but is a different size.

All of the leg lengths of GHI are multiplied by something to get the leg lengths of PQR.

You're given the leg lengths 12 and 20. So you need to find out what 12 is multiplied by to get to 20. 12 * 5/3 = 20.

So multiply 5/3 by the other leg length 18.

18 * 5/3 = 30

So QR = 30

Trigonometric identities are categorized as various identities out of which 11 are ,

Trigonometric Identities are used when trigonometric functions are given in an expression. Geometrically, these identities include one or more trigonometric functions

These are the sine , cosine or the tangent functions.

There are numerous trigonometric identities relating the side length and angle of a triangle. Only the right-angle triangle has the trigonometric identities.

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Answer:

It is A) No, There is no fixed number of baby carrots.

edge 100%

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

See the attached image:  the outer numbers count girls clockwise, showing Antonia at point J.  The inner numbers show counting anticlockwise, showing Antonia as number 8, then continuing the count past her.

Aha!  The inner and outer numbers always sum to 13.

But anticlockwise #12 really counted herself as #1 (she's being counted twice), so there aren't 12 girls, there are 11.

If you're not convinced, draw a picture with, say,  5 girls in it, number them counting both ways.

Answer:

(A.) would be the answer.

Answer:

(A.)Absolute value of (-75) meaning that Richard has a debt of 75 dollars

Step-by-step explanation:

Meaning of the △ is: the given symbol is the representation of the geometrical figure triangle.

Therefore, the meaning of the given symbol △ is the representation of the triangle.

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The value of x will be;

⇒ x = 35

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

In Rectangle RSTW;

⇒ RZ = 3x + 6

⇒ SW = 7x - 23

Since, By the figure we conclude that;

⇒ 2 RZ = SW

Substitute the given values, we get;

⇒ 2 RZ = SW

⇒ 2 (3x + 6) = 7x - 23

⇒ 6x + 12 = 7x - 23

⇒ 12 + 23 = 7x - 6x

⇒ 35 = x

⇒  x= 35

Thus, The value of x = 35

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Answer:

C And D

Step-by-step explanation:

94 Inches Is 7.8 Feet Tall & 79 Inches is 6.5 Feet Tall

Answer:

C and D

Step-by-step explanation:

You should start by changing the inches to feet

(there are 12 inches in foot [ 12 inch = 1 foot ])

A. 9 foot

B. 9.5

C. about 7 feet

D. about 6 feet

C and D are correct. Hope this helps!

Answer:

d

Step-by-step explanation:

Answer: 18pi + 36 + (36-4.5pi)+4.5pi= 22.5pi + 36 + (36-4.5pi)

Step-by-step explanation:

CDEF is a square so all sides of CDEF are 6cm.

This tells us the area of CDEF which is 36cm squared

This tells us the radius of AE which is the side FE which we know is 6cm.

Area of a half circle= pi x r squared/2

Area of AE= pi x 36/2= 18pi

Now, look at the square with the half circle inside ABCF. If the half circle was part of the shaded square, the area would be 36cm squared. But since it isn't we need to minus the area of the half circle from 36cm square (area of ABCF)

Area of half circle BC= pi x 3 squared/2= pi x 9/2= 4.5pi.

So the area of ABCF is 36-4.5pi.

CD would also have an area of 4.5pi as it is the exact same half circle.

Area of AE=18pi cm squared

Area of CDEF= 36cm squared

Area of ABCF= 36-4.5pi

Area of CD= 4.5pi

18pi+36+(36-4.5pi)+4.5pi

simplified to:

22.5pi + 36 + (36-4.5pi)

The factors for the Polynomial are (x+1) and (x+2).

According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0.

Given:

f(x) = 2x³ + 9x² + 13x + 6

Now, first (x+1) =0

x= -1

put x= -1 in f(x) as

f(-1) = 2(-1) + 9(1) + 13(-1) + 6

      = -2 + 9 - 13 + 6

      = 0

So, (x+1) is factor of f(x).

Now, second (x-1)= 0

x= 1

put x= 1 in f(x) as

f(1) = 2(1) + 9(1) + 13(1) + 6

      = 2 + 9 + 13 + 6

      = 31

So, (x-1) is not a factor of f(x).

Now, second (x+2)= 0

x= -2

put x= -2 in f(x) as

f(1) = 2(-2)³ + 9(-2)² + 13(-2) + 6

      = -16 + 36 - 26 + 6

      = 0

So, (x+2) is factor of f(x).

Now, second (x-2)= 0

x= 2

put x= 2 in f(x) as

f(1) = 2(2)³ + 9(2)² + 13(2) + 6

      = 16 + 36 + 26 + 6

      = 84

So, (x-2) is not a factor of f(x).

Now, second (x+3)= 0

x= -3

put x= -3 in f(x) as

f(1) = 2(-3)³ + 9(-3)² + 13(-3) + 6

      = -54 + 81 - 39 + 6

      = -6

So, (x+3) is not a factor of f(x).

Now, second (x-3)= 0

x= 3

put x= 3 in f(x) as

f(1) = 2(3)³ + 9(3)² + 13(3) + 6

      = 54 + 81 + 39 + 6

      = 180

So, (x-3) is not a factor of f(x).

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Answer:

Step-by-step explanation: