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2 years ago

5

If ad=30 and dc=30 what is the length of bd

1 answer:

DerKrebs [107]2 years ago

7 0

BD =√30 +√30

BD = 2√30

Here you go

You might be interested in

To get a 100 kilograms of a 48% fat content chocolate how many kilograms of a 30% and 50% mix should be used

wlad13 [49]

A kilogram %30 chocolate,
b kilogram %50 chocolate,
a+b = 100 kilogram chocolate,

48.(a+b) = 30.a + 50.b
48a + 48b = 30a + 50b
18a = 2b
b = 9a

a+b = a + 9a = 10a = 100 kg
a = 10 kg
b = 9.a = 90 kg

You should use,

10 kg %30 chocolate,
90 kg %50 chocolate

8 0

3 years ago

Help find zeros for 9 and 10

Bingel [31]

<span><span> x4-10x2+9=0</span> </span>Four solutions were found :<span> x = 3 x = -3 x = 1 x = -1</span>

Step by step solution :<span>Step 1 :</span>Skip Ad
<span>Equation at the end of step 1 :</span><span> ((x4) - (2•5x2)) + 9 = 0 </span><span>Step 2 :</span>Trying to factor by splitting the middle term

<span> 2.1 </span>    Factoring <span> x4-10x2+9</span>

The first term is, <span> <span>x4</span> </span> its coefficient is <span> 1 </span>.
The middle term is, <span> <span>-10x2</span> </span> its coefficient is <span> -10 </span>.
The last term, "the constant", is  <span> +9 </span>

Step-1 : Multiply the coefficient of the first term by the constant <span> <span> 1</span> • 9 = 9</span>

Step-2 : Find two factors of   9  whose sum equals the coefficient of the middle term, which is <span> -10 </span>.

<span> -9 + -1 = -10 That's it</span>

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  -1
                     <span>x4 - 9x2</span> - <span>1x2 - 9</span>

Step-4 : Add up the first 2 terms, pulling out like factors :
                    <span>x2 • (x2-9)</span>
              Add up the last 2 terms, pulling out common factors :
                     1 • <span>(x2-9)</span>
Step-5 : Add up the four terms of step 4 :
                    <span>(x2-1)  •  (x2-9)</span>
             Which is the desired factorization

<span>Trying to factor as a Difference of Squares : </span>

<span> 2.2 </span>     Factoring: <span> x2-1</span>

Theory : A difference of two perfect squares, <span> A2 - B2  </span>can be factored into <span> (A+B) • (A-B)

</span>Proof :<span>  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 <span>- AB + AB </span>- B2 =
        <span> A2 - B2</span>

</span>Note : <span> <span>AB = BA </span></span>is the commutative property of multiplication.

Note : <span> <span>- AB + AB </span></span>equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1
Check : <span> x2  </span>is the square of  <span> x1 </span>

Factorization is :       (x + 1)  •  (x - 1)

<span>Trying to factor as a Difference of Squares : </span>

<span> 2.3 </span>     Factoring: <span> x2 - 9</span>

Check : 9 is the square of 3
Check : <span> x2  </span>is the square of  <span> x1 </span>

Factorization is :       (x + 3)  •  (x - 3)

<span>Equation at the end of step 2 :</span> (x + 1) • (x - 1) • (x + 3) • (x - 3) = 0 <span>Step 3 :</span>Theory - Roots of a product :

<span> 3.1 </span> A product of several terms equals zero.<span>

</span>When a product of two or more terms equals zero, then at least one of the terms must be zero.<span>

</span>We shall now solve each term = 0 separately<span>

</span>In other words, we are going to solve as many equations as there are terms in the product<span>

</span>Any solution of term = 0 solves product = 0 as well.

<span>Solving a Single Variable Equation : </span>

<span> 3.2 </span>     Solve  :    x+1 = 0<span>

</span>Subtract  1 from both sides of the equation :<span>
</span>                     x = -1

<span>Solving a Single Variable Equation : </span>

<span> 3.3 </span>     Solve  :    x-1 = 0<span>

</span>Add  1 to both sides of the equation :<span>
</span>                     x = 1

<span>Solving a Single Variable Equation : </span>

<span> 3.4 </span>     Solve  :    x+3 = 0<span>

</span>Subtract  3 from both sides of the equation :<span>
</span>                     x = -3

<span>Solving a Single Variable Equation : </span>

<span> 3.5 </span>     Solve  :    x-3 = 0<span>

</span>Add  3 to both sides of the equation :<span>
</span>                     x = 3

Supplement : Solving Quadratic Equation Directly<span>Solving <span> x4-10x2+9</span> = 0 directly </span>

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

<span>Solving a Single Variable Equation : </span>

Equations which are reducible to quadratic :

<span> 4.1 </span>    Solve  <span> x4-10x2+9 = 0</span>

This equation is reducible to quadratic. What this means is that using a new variable, we can rewrite this equation as a quadratic equation Using  w , such that <span> w = x2</span> transforms the equation into :
<span> w2-10w+9 = 0</span>

Solving this new equation using the quadratic formula we get two real solutions :
   9.0000  or   1.0000

Now that we know the value(s) of <span> w</span> , we can calculate <span> x</span> since <span> x</span> <span> is  </span><span> √<span> w </span></span>

Doing just this we discover that the solutions of
  <span> x4-10x2+9 = 0</span>
  are either :
  x =√<span> 9.000 </span>= 3.00000 or :
  x =√<span> 9.000 </span>= -3.00000 or :
  x =√<span> 1.000 </span>= 1.00000 or :
  x =√<span> 1.000 </span>= -1.00000

Four solutions were found :<span> x = 3 x = -3 x = 1 x = -1</span>

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Processing ends successfully</span>

5 0

2 years ago

A 60 by 80-foot rectangular walk in a park surrounds a flower bed. If the walk is of uniform width and its area is equal to the

alekssr [168]

Answer: 17.14 ft

<u>Step-by-step explanation:</u>

The area of the flower bed is 60 ft x 80 ft = 4800 ft²

The perimeter of the sidewalk that surrounds the flower bed is:

2(60 ft) + 2(80 ft)
= 120 ft + 160 ft
= 280 ft

The area of the sidewalk is:

perimeter x width
= 280w

area of sidewalk = area of flower bed

280w = 4800

$\text{w}=\dfrac{4800}{280}$

$=\dfrac{120}{7}$

≈ 17.14

8 0

2 years ago

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round y

tino4ka555 [31]

Answer:

0.8762 or 87.62%

Step-by-step explanation:

Since our mean is μ=14.3 and our standard deviation is σ=3.7. If we're trying to figure out what percentage is P(10 ≤ x ≤ 26) equal to we must first calculate our z values as such:

$z=\frac{x-\mu}{\sigma}$

Our x value ranges from 10 to 26 therefore let x=10 and we obtain:

$z=\frac{10-14.3}{3.7} =-1.16\\$

If we look at our z-table we find that the probability associated with a z value of -1.16 is 0.1230 meaning 12.30%.

Now let's calculate the z value when x = 26 and so:

$z=\frac{26-14.3}{3.7}=3.16\\$

Similarly, we use the z-table again and find that the probability associated with a z value of 3.16 is 0.9992 meaning 99.92%.

Now we want to find the probability in between 10 and 26 so we will now subtract the upper limit minus the lower limit in P(10 ≤ x ≤ 26) therefore:

0.9992 - 0.1230 = 0.8762

or 87.62%

7 0

3 years ago

Round 5,439 to the nearest thousand

Murrr4er [49]

Answer:

5,000

Step-by-step explanation:

4 is less than 5 and more so, it will leave the 5 alone

It will also turn everything else into 0's. Making it:

-------------------------------------------------------------------------------

5,000

7 0

3 years ago