Check the box labeled Show Segment Parallel to BC. Notice that DE intersects two sides of triangle ABC creating a smaller triangle, triangle ADE. How is triangle ADE related triangle ABC to ? How do you know?

Answer:

y=-3x+5

Step-by-step explanation:

y=mx+b

m=(-4-2)/(3-1)=-3

b=y-mx

b =-4 - (3)(-3)

b=-4+9

b=5

Answer:

Is this slope?

Step-by-step explanation:

Answer:

y = 3x - 5

Step-by-step explanation:

Let the equation be y = mx + c

Since the equation is parallel to y = 3x + 6, gradients of the two eqns are the same

therefore, m = 3

sub (4, 7):

7 = 3(4) + c

c = -5

therefore, equation of the line is y = 3x - 5

Answer:

3

Step-by-step explanation:

Factor the numerator and denominator and cancel the common factors.

Answer:

2.25 or fraction 9/4

Step-by-step explanation:

A is the correct answer

Answer:

h = 12

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define equation

0.75h + 3 = 12

Step 2: Solve for h

Step 3: Check

Plug in h into the original equation to verify it's a solution.

Here we see that 12 does indeed equal 12.

∴ h = 12 is a solution of the equation.

Answer:

h = 12

Step-by-step explanation:

Given

0.75h + 3 = 12 ( subtract 3 from both sides )

0.75h = 9 ( isolate h by dividing both sides by 0.75 )

h = 12

Answer:

Step-by-step explanation:

If Angela bought gift for her friend and each gift costs 10$. This means that the more the number of her friends, the more the money she will pay and vice versa. This is known as a direct relationship.

Let y represent the total cost and

x represent the number of gifts

According to direct variation]

y ∝ x

y = kx

k is the constant of proportionality

If each gift item cost $10, x gift will cost 10x. The constant of proportionality in this case will be 10. Substituting, the equation will become;

y = 10x

Hence the required relationship is y = 10x

Answer:

0.947

Step-by-step explanation:

We are told that the true probability of a baby being a girl is 0.479.

This means that probability of a baby being a boy is;

p = 1 - 0.479

p = 0.521

Now,using binomial probability distribution formula we can solve this problem.

P(X=x) = C(n, x) × p^(x) × (1 - p)^(n - x)

We are told that a mound the next four randomly selected births in the country, what is the probability that at least one of them is a boy.

This is;

P(X ≥ 1) = P(1) + P(2) + P(3) + P(4)

P(1) = C(4, 1) × 0.521^(1) × (1 - 0.521)^(4 - 1)

P(1) = 0.229

P(2) = C(4, 2) × 0.521^(2) × (1 - 0.521)^(4 - 2)

P(2) = 0.3737

P(3) = C(4, 3) × 0.521^(3) × (1 - 0.521)^(4 - 3)

P(3) = 0.27096

P(4) = C(4, 4) × 0.521^(4) × (1 - 0.521)^(4 - 4)

P(4) = 0.0737

Thus;

P(X ≥ 1) = 0.229 + 0.3737 + 0.27096 + 0.0737

P(X ≥ 1) = 0.94736

P(X ≥ 1) ≈ 0.947

Answer:

Step-by-step explanation:

Step one:

Let A be the altitude of the plane

Hence we can define a function that represents this scenario.

the rate at which the plane's altitude decreases is

=33000-17000/8

= 16000/8

=2000

The rate of decrease is 2000 ft per minute.

Thus for anytime "t" the expression for the altitude is

S=33000-2000t-------where t is the time in minute.

say we want to find altitude after 12 minutes

then t=12

substitute  in the expression we have

S=33000-2000(12)

S=33000-24000

S=9000ft

Answer:

Part 1)  Descending Rate = -2,000 ft/min

Part 2)  Starting altitude value is 33,000 ft

Part 3)  The linear equation for the plane's altitude (y) as a function of time (x) is:  

Part 4)  The information not used for the equation is that the plane was travelling for 4 hours to cover 1800 miles before starting the descent

Step-by-step explanation:

Part 1)

The rate at which the airplane descends is given by the difference between final and initial altitude (17,000 ft-33,000 ft) divided the elapsed time (8 minutes):

Part 2)

When graphing the descent (that is the plane's altitude as a function of time), the starting value for the altitude should be 33,000 ft

Part 3)

We can build the equation of the plane's altitude as a function of time in slope y-intercept form y = m x + b

by noticing that the slope "m" stands for the rate of descent that we found in part 1), and then using the information that at time zero (when the plane starts its descent), its altitude is 33000 ft:

with this information about the intercept "b", we can write the final expression for the plane's altitude as a function of time during its descent as:

Part 4)

The information that was not used to write the descent equation was the initial details about how long the plane traveled (4 hours) and for 1800 miles.

Step-by-step explanation:

Answer:

the first one is. hope helps

Answer:

o

Step-by-step explanation:

Answer:

59.3sq ft

Step-by-step explanation:

it would be -4 i think

come back and tell me if im wrong

Answer:

6x^2+10x-6=0

Step-by-step explanation:

First, you need to add all like terms:

6x^2+8x-6=-2x

Now move the -2x to the other side:

6x^2+10x-6=0

Answer:

x =(-5+√61)/6= 0.468

or:

x =(-5-√61)/6=-2.135

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    6*x^2+8*x-6-(2-2*x-2)=0  

Step by step solution :

STEP 1 :

The Equation at the end of step 1

 (((2•3x2) +  8x) -  6) -  -2x  = 0  

STEP 2 :

STEP 3 :

Pulling out like terms

3.1     Pull out like factors :

  6x2 + 10x - 6  =   2 • (3x2 + 5x - 3)  

Trying to factor by splitting the middle term

3.2     Factoring  3x2 + 5x - 3  

The first term is,  3x2  its coefficient is  3.

The middle term is,  +5x  its coefficient is  5.

The last term, "the constant", is  -3  

Step-1: Multiply the coefficient of the first term by the constant   3 • -3 = -9  

Step-2: Find two factors of  -9  whose sum equals the coefficient of the middle term, which is   5.

     -9    +    1    =    -8  

     -3    +    3    =    0  

     -1    +    9    =    8  

Observation: No two such factors can be found !!

Conclusion: Trinomial can not be factored

The Equation at the end of step 3 :

 2 • (3x2 + 5x - 3)  = 0  

STEP 4 :

Equations which are never true:

4.1      Solve :    2   =  0

This equation has no solution.

A non-zero constant never equals zero.

Parabola, Finding the Vertex:

4.2      Find the Vertex of y = 3x2+5x-3

Parabolas have the highest or lowest point called the Vertex.   Our parabola opens up and accordingly has the lowest point (AKA absolute minimum).   We know this even before plotting  "y"  because the coefficient of the first term, 3, is positive (greater than zero).  

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x-intercepts (roots or solutions) of the parabola. That is if the parabola has indeed two real solutions.  

Parabolas can model many real-life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that an object, thrown upwards, can reach. For this reason, we want to be able to find the coordinates of the vertex.  

For any parabola, Ax2+Bx+C, the x -coordinate of the vertex is given by  -B/(2A). In our case, the  x  coordinate is  -0.8333  

Plugging into the parabola formula  -0.8333  for  x  we can calculate the  y -coordinate :  

 y = 3.0 * -0.83 * -0.83 + 5.0 * -0.83 - 3.0

or   y = -5.083

Parabola, Graphing Vertex, and X-Intercepts :

Root plot for :  y = 3x2+5x-3

Axis of Symmetry (dashed)  {x}={-0.83}  

Vertex at  {x,y} = {-0.83,-5.08}  

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-2.14, 0.00}  

Root 2 at  {x,y} = { 0.47, 0.00}  

Solve Quadratic Equation by Completing The Square

4.3     Solving   3x2+5x-3 = 0 by Completing The Square.

Divide both sides of the equation by  3  to have 1 as the coefficient of the first term :

  x2+(5/3)x-1 = 0

Add  1  to both side of the equation :

  x2+(5/3)x = 1

Now the clever bit: Take the coefficient of  x, which is  5/3, divide by two, giving  5/6, and finally square it giving  25/36  

Add  25/36  to both sides of the equation :

 On the right-hand side we have :

  1  +  25/36    or,  (1/1)+(25/36)  

 The common denominator of the two fractions is  36   Adding  (36/36)+(25/36)  gives  61/36  

 So adding to both sides we finally get :

  x2+(5/3)x+(25/36) = 61/36

Adding  25/36  has completed the left-hand side into a perfect square :

  x2+(5/3)x+(25/36)  =

  (x+(5/6)) • (x+(5/6))  =

 (x+(5/6))2

Things which are equal to the same thing are also equal to one another. Since

  x2+(5/3)x+(25/36) = 61/36 and

  x2+(5/3)x+(25/36) = (x+(5/6))2

then, according to the law of transitivity,

  (x+(5/6))2 = 61/36

We'll refer to this Equation as  Eq. #4.3.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x+(5/6))2   is

  (x+(5/6))2/2 =

 (x+(5/6))1 =

  x+(5/6)

Now, applying the Square Root Principle to  Eq. #4.3.1  we get:

  x+(5/6) = √ 61/36

Subtract  5/6  from both sides to obtain:

  x = -5/6 + √ 61/36

Since a square root has two values, one positive and the other negative

  x2 + (5/3)x - 1 = 0

  has two solutions:

 x = -5/6 + √ 61/36

  or

 x = -5/6 - √ 61/36

Note that  √ 61/36 can be written as

 √ 61  / √ 36   which is √ 61  / 6

Solve Quadratic Equation using the Quadratic Formula

4.4     Solving    3x2+5x-3 = 0 by the Quadratic Formula.

According to the Quadratic Formula,  x, the solution for   Ax2+Bx+C  = 0, where  A, B,  and  C are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     3

                     B   =    5

                     C   =   -3

Accordingly,  B2  -  4AC   =

                    25 - (-36) =

                    61

Applying the quadratic formula :

              -5 ± √ 61

  x  =    —————

                   6

 √ 61, rounded to 4 decimal digits, is   7.8102

So now we are looking at:

          x  =  ( -5 ±  7.810 ) / 6

Two real solutions:

x =(-5+√61)/6= 0.468

or:

x =(-5-√61)/6=-2.135

HOPE THIS HELPS!

PLEASE MARK BRAINLIEST IF THIS HELPED YOU LEARN! :)

Number of student lunch today is 450 students

Given:

Fraction of student lunch today = 5/8

Total number student = 720 students

Find:

Number of student lunch today

Computation:

Number of student lunch today = Fraction of student lunch today × Total number student

Number of student lunch today = (5/8) × (720)

Number of student lunch today = (5) × (90)

Number of student lunch today = 450 students

Learn more:

https://brainly.com/question/12816397?referrer=searchResults

Answer: at least 19

Step-by-step explanation:

Since there were at least 224 pieces of pie sold. We would divide the amount of slices of pie sold (224) by the amount of slices in each pie (8). Which would be (28) pies sold and then we would subtract the (9) pies that the school gave us, and we would end up with (19) pies.

I hope that can help you

Answer:

9

Step-by-step explanation:

because area = length times with so it also means area divided by with with = length

Answer:

The answer to the cost for each toffee is given below:

Step-by-step explanation:

The computation of the cost for each toffee is shown below:

Given that

There are a total 180 candies hat includes three types  in a ratio of 4:2:3

Gobs = 4 ÷ 9 × 180 = 80

Blobs = 2 ÷ 9 × 180 = 40

Toffees = 3 ÷ 9 × 180 = 60

Now the total cost of all the candies shipment is $430

So,

The equation would be

80 × $1.50 + 40 × $2.50 + 60 × per cost = $430

120 + 150 + 60 × per cost = $430

60 × per cost = $430 - $120 - $150

60 × per cost = $160

Per cost is $2.67

So for toffees it would be 160

Answer:

y= x + 2

Step-by-step explanation:

Answer:

18 deg

Step-by-step explanation:

pi in radians = 180 deg

180/10 would be 18

hope that helps

Complete question is;

A 21 ft ladder is leaning against a tall wall with the foot of the ladder placed at 7 feet from the base of the wall and the angle of elevation is?

Answer:

θ = 70.5°

Step-by-step explanation:

The angle of elevation simply means the angle that the ladder makes with the ground. Let's call this angle θ.

I've attached a diagram showing the triangle made by this ladder and the wall.

From the attached diagram, we can see the triangle formed by the ladder and the wall.

We can find the angle of elevation θ from trigonometric ratios.

Thus;

7/21 = cos θ

cos θ = 0.3333

θ = cos^(-1) 0.3333

θ = 70.5°

Answer:

The number was 20

Step-by-step explanation:

As the average is 11 and the numbers are 4, so the total sum of numbers will be 11X4=44. now the sum of three numbers are (20+8+4)=24. So the last number will be= (44-24)=20. :)

Answer:

20, 12,8,4 average out to 11

Step-by-step explanation:

omni average calculator on google will help :)

Answer:

1) -6·n - (-4·n) = -10·n (The double negative should change to positive  + sign here)

-6·n - (-4·n) = -6·n + 4·n = -2·n

The correct solution is;

n = 4

2)  y = 23.2 - 11.6 = 11.6, y = 11.6 (Seraphina's mistake is that subtraction was done rather than the division as shown here)

The correct solution is;

y = 2

Step-by-step explanation:

The given parameters are

-6·n + 22 = -4·n + 14

22 -  14= 6·n - 4·n = 2·n

8 = 2·n

n = 8/2 = 4

Cullen's mistake is as follows;

-6·n + 22 = -4·n + 14

-6·n - (-4·n)   =  -22 + 14

-6·n + 4·n   =  -22 + 14 (The double negative should change to positive  + sign here)

-2·n   =  -8

n = -8/(-2) = 4

n = 4

2) 8.4·y - 6.8 = -3.2·y + 16.4

8.4·y - (-3.2·y) = -(- 6.8) + 16.4

11.6·y = 23.2 → y = 23.2 - 11.6 = 11.6, y = 11.6 (Seraphina's mistake is that subtraction was done rather than the division as shown here)

y = 23.2/11.6 = 2

y = 2

3) The last equation has parts missing

Answer:

the answer is y=3.88894

Step-by-step explanation:

Answer:10

Step-by-step explanation: 5 + x is 10 because x is a verable

Answer:

6

Step-by-step explanation:

Solve x then y after..

Answer:

4

Step-by-step explanation:

Define coefficient:

a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4xy).

Hope this helped.

Answer:

5cm

Step-by-step explanation:

Given parameters:

Volume = 45cm³

Radius  = 3cm

Unknown:

Height of the cone  = ?

Solution:

Volume of cone is given as ;

  V = [tex]\frac{1}{3} \pi[/tex] r² h

r is the radius

h is the height

      45  =  [tex]\frac{1}{3} \pi[/tex]x 3² x h

      45  = 3π x h

       h  = [tex]\frac{45}{3 x3.142}[/tex]   = 4.77cm

5cm is the closest answer choice

Answer:

x=10

Step-by-step explanation:

first substitute y with the value (-5)

2x+5(-5)=-5 which is simplified to 2x+-25=-5

add 25 to -5 which gives you 2x=20

then divide 20 by 2 which makes x=10