If [tex]\frac{AD}{DB}=\frac{AE}{EC}\\[/tex], then line segment (BLANK 1) is parallel to line segment (BLANK 2) (View image below)


answer choices for blank 1 are-

A) AD

B) DE


answer choices for blank 2 are-

A)FG

B)BC

Answer:

  1. (-10x -5) -(-7x -4)

  2. (-10x -5) -(-3x -1)

Step-by-step explanation:

The process of simplifying an expression generally involves eliminating parentheses, collecting terms, simplifying fractions, rationalizing denominators, removing appropriate factors from under radicals, and generally putting expressions into general form.

So, to accomplish what the problem is asking, you can create an expression that requires you accomplish as many or as few of these steps as you may like.

In general, you will want to both "do" and "undo" whatever operation(s) you may choose. For example, consider a couple of expressions "a" and "b". For this example, we want our final result to simplify to "a".

If we choose to add "b", we might have ...

  (a+b) -b . . . . . we have both added and subtracted b, so the simplified result is "a"

If we choose to multiply by "b", we might have ...

  (ab)/b . . . . . . we have both multiplied by b and divided by b, so the simplified result is again "a"

_____

We can solve both these problems at once by using ...

If we choose the first approach, we want an expression that is (a+b). That will be ...

  a+b = (-3x -1) +(-7x -4) = -10x -5

By subtracting "b" from this expression, we get "a"--and vice versa. That is ...

_____

Alternate solution to 2

Suppose we choose to multiply instead. Let "b" be -3x+2. Then, using the template for multiplication above, we can write the expression

  (-7x -4)(-3x +2)/(-3x +2) = (21x^2 -2x -8)/(-3x +2)

and we know this rational expression simplifies to -7x -4.

_____

Of course, we can be as elaborate as we might like in modifying the original expression. Whatever we do, we must also include the "undo" so the original expression is recovered when we simplify. To illustrate the point, we can add and subtract 2x from the above rational expression.

  ((21x^2 -2x -8)/(-3x +2) + 2x) - 2x = (21x^2 -2x -8 +2x(-3x +2))/(-3x +2) - 2x

  = (21x^2 -2x -8 -6x^2 +4x)/(-3x +2) -2x

  = (15x^2 +2x -8)/(-3x +2) -2x . . . . . . another alternate solution to #2.

If we're not careful, we can create an expression that is extremely difficult to simplify. The one we have here can be factored to be ...

  (-5x -4)(-3x +2)/(-3x +2) -2x = -5x -4 -2x = -7x -4 . . . our original #2 expression

Knowing that it can be factored is a big help.

Answer:

  d.  1/4

Step-by-step explanation:

The common ratio will be the ratio of any two adjacent terms:

  (3/12)/(3/3) = (1/4)/1 = 1/4

Answer:

d

Step-by-step explanation:

If the sequence is geometric then a common ratio r will exist between consecutive terms.

[tex]\frac{3}{12}[/tex] ÷ 1 = [tex]\frac{3}{12}[/tex] = [tex]\frac{1}{4}[/tex]

[tex]\frac{3}{48}[/tex] ÷ [tex]\frac{3}{12}[/tex] = [tex]\frac{1}{4}[/tex]

[tex]\frac{3}{192}[/tex]  ÷ [tex]\frac{3}{48}[/tex] = [tex]\frac{1}{4}[/tex]

[tex]\frac{3}{768}[/tex] ÷ [tex]\frac{3}{192}[/tex] = [tex]\frac{1}{4}[/tex]

A common ratio of r = [tex]\frac{1}{4}[/tex]

Hence sequence is geometric

ANSWER

a=3, b=5

EXPLANATION

The given equation is

[tex] \frac{3}{x} + \frac{5}{ {x}^{2} } = \frac{ax + b}{ {x}^{2} } [/tex]

We simplify the left hand side.

We collect LCD to obtain:

[tex] \frac{3x + 5}{ {x}^{2} } = \frac{ax + b}{ {x}^{2} } [/tex]

Both sides of the equation are now the same.

By comparing the coefficients of x, we have

[tex]a = 3[/tex]

By comparing the constant terms

[tex]b = 5[/tex]

Answer:

For the first part

A=3

B=5

For the second part

M=3

N=14

P=2

Step-by-step explanation:

Right on edge 2020

Answer:

C:  (x + 4)(x - 1)

Step-by-step explanation:

Please use " ^ " to indicate exponentiation.  Thanks.

x2 + 3x – 4 →  x^2 + 3x - 4 = (x + 4)(x - 1)      This matches Answer C.

Answer:

n = 29

Step-by-step explanation:

We need to find an equation that represents the following statement: "Thirteen less than a number is sixteen" which is the same as: "A number minus thirteen equals sixteen"

In that sense, the equation that represents that statement is: n - 13 = 16

Now, the solution is:  n - 13 = 16 → n = 29

Answer:

n = 29

Step-by-step explanation:

Answer:

1/36

Step-by-step explanation:

Bonnie uses 12×6" = 72" of wire to make her cube.

Roark uses 12×1" = 12" of wire to make each of his cubes. He must make 6³ = 216 cubes to match the volume of Bonnie's cube.

The ratio of wire lengths is then ...

72/(12×216) = 6/6³ = 1/6² = 1/36

Answer:

Since we know that ABCD is an isosceles trapezoid, we can also asume that its diagonals have the same length, which means:

AC = BD

=> 7x - 21 = 5x + 13

=> 7x - 5x = 21 + 13

=> 2x        = 34

=> x           = 34/2 = 17

So the answer is C.

Since we know that ABCD is an isosceles trapezoid, the value of Option C. x= 17

we can also assume that its diagonals have the same length, which means:

AC = BD

=> 7x - 21 = 5x + 13

=> 7x - 5x = 21 + 13

=> 2x        = 34

=> x          = 34/2 = 17

So the answer is C.

An isosceles trapezoid is a trapezoid with congruent base angles and congruent non-parallel sides. A trapezoid is a quadrilateral with only one of its sides parallel. An isosceles trapezoid has many interesting properties that make it unique and help us differentiate it from the other quadrilaterals

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Answer:

The dimensions are 16 meters by 18 meters

Step-by-step explanation:

P = 2(l+w)

is the formula for the perimeter of a rectangle.

We know the length is 2 more than the width ( consecutive even integers)

l = w+2

P = 2 (w+2+w)

P = 2(2w+2)

68 = 2 (2w+2)

Divide each side by 2

34 = 2w+2

Subtract 2

34-2 = 2w+2-2

32 = 2w

Divide by 2

32/2 = 2w/2

16 =w

l = w+2

l =16+2

l = 18

The dimensions are 16 meters by 18 meters

the width of the rectangle is 16 meters and the length is 18 meters.

To find the length and width of a rectangle when given that the length and width are consecutive even integers and the perimeter is 68 meters, we first need to express the length and width in algebraic terms. Let's call the width 'w' and since the length is the next consecutive even integer, it can be expressed as 'w + 2'. The formula for the perimeter (P) of a rectangle is P = 2l + 2w, where 'l' is the length and 'w' is the width. In this case, since width is 'w' and length is 'w + 2', the perimeter formula becomes P = 2(w+2) + 2w.

Let's solve for 'w':
68 = 2(w + 2) + 2w
68 = 2w + 4 + 2w
68 = 4w + 4
64 = 4w
w = 16
Now that we have the width, we can easily find the length:
l = w + 2
l = 16 + 2
l = 18

Therefore, the width of the rectangle is 16 meters and the length is 18 meters.

Answer:

A 2sqrt(7)

Step-by-step explanation:

Use similar triangles and ratios of lengths of corresponding sides.

2/x = x/14

x^2 = 28

x = 2sqrt(7)

Answer:

The answer is the 2nd one

Step-by-step explanation:

A dilation is a transformation in which the lines connecting every point P with its image P' all intersect at a point C.

C is called the center of dilation, and CP'/CP is the same for every point P.

The only picture where the objects are similar and the image has not been rotated or reflected is

It is also seen from the picture that all the faces of the first figure appears to be parallel to all the faces of the second figure. Thus, CP'/CP is the same for every point P.

Therefore, the transformation in the picture above appears to be a dilation.

The transformation in the picture above appears to be a dilation is option 2nd.

Dilation of a figure will leave its sides get scaled (multiplied) by same number. That number is called the scale factor of that dilation.

Its also called scaling of a figure, but due the involvement of coordinates, it involves a center of a dilation, which is like a pinned point which stays at same place after dilation.

Its like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1).

C is called the center of dilation, and CP'/CP is the same for every point P.

It is also seen from the picture that all the faces of the first figure appear to be parallel to all the faces of the second figure.

Thus, CP'/CP is the same for every point P.

Therefore, the transformation in the picture above appears to be a dilation is option 2nd.

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Answer:

20 seconds

Step-by-step explanation:

We just need the x-coordinate of the vertex...so find -b/(2a) and we are done:

-b/(2a)=-640/(2*-16)=-640/-32=20

20 second

Answer:

[tex]\boxed{\text{20 s}}[/tex]

Step-by-step explanation:

The standard form of a quadratic function is  

y = ax² + bx + c

Your function is

h(t) = -16t²+ 640t

a = -16; b = 640; c = 0

a is negative, so you have a downward-opening parabola.

The vertex form of a parabola is

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

h = -b/(2a) and k = f(h)

Your parabola opens downward, so the vertex is a maximum.

Calculate h

[tex]h = \dfrac{640}{-2(-16)}} = \dfrac{640}{32} = 20\\\text{The projectile reaches maximum height }\boxed{\textbf{20 s}} \text{after it is thrown}\\[/tex]

The figure below shows the graph of h(t).

Answer:

the first one is 350 inches (350 in) and the second on is 350 square inches (350 in2)

Step-by-step explanation:

Answer:

Output = 8- input

Step-by-step explanation:

The first point is  (1,7)

The input is 1 and the output is 7

The lines goes down, so we know that this is subtraction

Output = 8- input

7 = 8-1

Lets check another point

(5,3)

3 = 8-5

This checks

Answer:

Value of log625^5 is 13.95

Step-by-step explanation:

We need to find the value of log625^5

Using log rule log a^n = nloga

log625^5

= 5log625

=5(2.79)

=13.95

So, value of log625^5 is 13.95

Answer with explanation:

We have to find the value of :

  [tex]\rightarrow\log 625^5\\\\\rightarrow 5 \log625\\\\\rightarrow 5 \log 5^4\\\\\rightarrow 4 \times 5 \log 5\\\\ \rightarrow 20 \log 5\\\\\rightarrow 20 \times 0.69897\\\\ \rightarrow 13.9794\\\\=13.98\\\\ \text{Used following properties of log}\\\\ \log a^b=b \log a[/tex]  

Answer:

B

Step-by-step explanation:

The area of the shaded sector Rounded to the nearest tenth, is 22.5

Sector of a circle is like slice of a circular pizza. Its two straight edge's having an angle, and edge's length(the radius of the circle) are two needed factors for finding the area of that sector.

If the entire circle was shaded the radius sweeping out the circle would go through 360 degrees.

Too solve this problem is to multiply the entire area of the circle by (81/360)

Area of the sector = (81/360) x  π x r^2

π = 3.14

r = cm

Area of the sector = (81/360) x 3.14 x 8.91^2

Area of the sector = 22.5

The area is 22.5 m2

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Answer:

B.

Step-by-step explanation:

The function is positive when it is above the x-axis

The following x values are where the function has positive y coordinates:

(-2,0)

(4,inf)

The function is negative when it is below the x-axis

The following x values are where the function has negative y coordinates:

(-inf,-2)

(0,4)

So you should see all of these intervals listed in choice B

Answer:

B

Step-by-step explanation:

Answer:

[tex](f+g)(x)=6x^2+13x+14[/tex]

Step-by-step explanation:

(f+g)(x) simply means that you are adding f(x) to g(x) to get a new equation that is the sum of them.

[tex]6x^2+9x+8+4x+6[/tex]

simplifies down to, by combining like terms,

[tex]6x^2+13x+14[/tex]

Expressions do not have an equal sign (although they can have operators such as plus or minus).

[tex]2x+1[/tex] is an expression.

[tex]2x+1=1[/tex] is an equation since it has an equal sign.

Answer:

1.25.

Step-by-step explanation:

The common ratio r  is 1/5 and the first term a1 = (1/5)^(1-1) = 1.

Sum to infinity =  a1 / (1 - r)

=  1 / (1 - 1/5)

= 1 / 4/5

= 5/4

= 1.25 (answer)

Answer:

Step-by-step explanation:

1.25

Answer: [tex]15.57\°[/tex]

In order to understand better this problem, we can use the figure attached, in which we have a right triangle (with a 90 degree angle), where [tex]c[/tex] is its hypotenuse, [tex]a[/tex] is the adjacent side to the angle of elevation [tex]\theta[/tex] from the boat to the top of the lighthouse and [tex]b[/tex] is the opposite side to [tex]\theta[/tex].

Knowing this, we will use the tangent trigonometric function to find [tex]\theta[/tex]:

[tex]tan\theta=\frac{oppositeside}{adjacentside}=\frac{b}{a}[/tex]   (1)

[tex]tan\theta=\frac{34m}{122m}[/tex]   (2)

[tex]tan\theta=0.278[/tex]   (3)

[tex]\theta={tan}^{-1} (0.278)[/tex]   (4)

Finally:

[tex]\theta=15.572\°[/tex]  

Answer:

16

Step-by-step explanation:

A boat is 122 meters from the base of a lighthouse that is 34 meters above sea level. What is the angle of elevation from the boat to the top of the lighthouse? Round to the nearest degree.

Answer:

B-10=N

Step-by-step explanation:

N is the lesser number. So if B is the greater number & there is a difference of 10 this would be your expression

Answer:

5 year  = $2,400

20 year = $18,560

Step-by-step explanation:

Firstly,

You have to identify the cash value per unit. so It 'll be  5 years = 30 dollars per unit.

Secondly,

Now, take the face value of the policy divided by 1000, to find how many units the person has. 80,000 divided by 1000 is 80. Now take the # of units time the cash value it has. so It'll be 80 times 30 is $2,400

Answer: $2,400

Now,

Just like the previous one identify the cash value per unit. so It'll be 20 years= 232 dollars per unit.

Next,

take the face value of the policy divided by 1000, to find how many units the person has. 80,000 divided by 1000 is 80. Now take the # of units time the cash value it has. 80 times 232 is $18,560

Answer:  $18,560

Answer: D

Step-by-step explanation:

Answer:  The correct option is

(D) x represents the number of level 1 tickets; y represents the number of level 2 tickets

Step-by-step explanation:  Given that a sports team came to town. The stadium filled all 10,000 seats at two-level pricing. Level 1 tickets are $50 each, and level 2 tickets are $150 each. The stadium made $75,000 in ticket sales.

The system of equations that models this scenario is:

x + y = 10,000

50x + 150y = 75,000

We are to find the terms that x and y represents.

Since the total number of seats is 10000 and it is given that x + y = 10000, so x and y represents the number of tickets.

Also, since the price of one level 1 tickets is $50 and that of one level 2 ticket is $150 and 50x + 150y = 75000, so

x represents the number of level 1 tickets; y represents the number of level 2 tickets.

Thus, (D) is the correct option.

Answer:

  180 minutes

Step-by-step explanation:

Starting with the distance formula ...

  d = rt

dividing by the coefficient of t will give an equation for t:

  t = d/r

Ryan's rate of 4 miles per hour can be expressed in minutes as 4 miles per 60 minutes. The Ryan's time is ...

  t = (12 mi)/(4 mi/60 min) = 12·60/4 min = 180 min

Ryan's time is 180 minutes.

Answer:

180 MINUTES

Step-by-step explanation:

I TOOKTHE TEST ON FLVS

Answer:

  x = 8

Step-by-step explanation:

The 12 on the right is 1/3 the number 36 on the segment above. The value of x will have the same proportion to the segment above it, so will be 1/3 of 24, or 8.

  x = 8

Answer:

-1/10, -1/5 , -2/5 or -2/5, -1/5 , -1/10

Step-by-step explanation:

let a/r, a, ar  be the first 3 terms of the geometric series

their product would be equal to a^3

a^3=-1/125

a=-1/5

Substitute a=-1/5 into the first 3 terms

-1/5r + -1/5+-r/5=-7/10

Multiply the terms such that they have a common denominator:

-1/5r +-r/5r + -r^2/5r = -3.5r/5r

Multiply both sides by 5r

-r^2-r-1=-3.5r

Add 3.5r to both sides and multiply the equation by 2

-2r^2 + 5r -2=0

Factorize the equation

(2r-1)(r-2)=0

r=0.5 or r-2

For the first three terms where r=0.5

-2/5, -1/5 , -1/10

For the first three terms where r=2

-1/10, -1/5 , -2/5

Answer:

I think is a for the answer

the simplified value of the given expression 2y (x+z) = w for z will be z = (w- 2xy)/2y.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, an expression 2y (x+z) = w

Simplifying the given expression for z

=> 2y (x+z) = w

divide by 2y into both sides

=> x + z = w/2y

subtract by x into both sides

=> z = w/2y - x

=> z = w-2xy /2y

thus,

z = (w- 2xy)/2y

therefore, the simplified value of the given expression 2y (x+z) = w for z will be z = (w- 2xy)/2y.

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Answer:

  x = 24.10

Step-by-step explanation:

The given sides of the triangle are the hypotenuse (x) and a side of length 20 that is adjacent to the 34° angle and opposite the 56° angle.

The mnemonic SOH CAH TOA reminds you of relationships between the hypotenuse and adjacent or opposite sides:

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

If we want to use the "adjacent" side, we would choose ...

  cos(34°) = 20/x

  x = 20/cos(34°) ≈ 20/0.83 ≈ 24.10 . . . . . rounding according to instructions

__

If we want to use the "opposite" side, we would choose ...

  sin(56°) = 20/x

  x = 20/sin(56°) ≈ 20/0.83 ≈ 24.10 . . . . . rounding according to instructions

_____

Comment on rounding

If you round correctly (only at the last step), the proper answer is 24.12.

Answer:

1/6

Step-by-step explanation:

5/10(3/3)=15/30

2/6(5/5)=10/30

15/30 - 10/30= 5/30 = 1/6

Answer: 1/6

Step-by-step explanation:

Hello There!

Divide by 3 each time

so

#1 is 9, because 27/3 = 9

#2 is 3, because 9/3 = 3

#3 is 1, because 3/3 = 1

So your answer is 9, 3, 1