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2 years ago

Calculate AD and hence BD.

Mathematics

1 answer:

Vilka [71]2 years ago

7 0

Answer:

AD = 15 cm , BD = 3 cm

Step-by-step explanation:

Δ ABC is similar to Δ ADE ( by the AA postulate )

then the ratios of corresponding sides are in proportion, that is

$\frac{AD}{AB}$ = $\frac{DE}{BC}$ ( substitute values )

$\frac{AD}{12}$ = $\frac{10}{8}$ ( cross- multiply )

8 × AD = 12 × 10 = 120 ( divide both sides by 8 )

AD = 15 cm

AB + BD = AD , that is

12 + BD = 15 ( subtract 12 from both sides )

BD = 3 cm

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Find two positive numbers satisfying the given requirements. The product is 216 and the sum is a minimum. (No Response) (smaller

fgiga [73]

Answer:

$x1=\sqrt{216} \ and \ y1=\ \sqrt{216}$

Step-by-step explanation:

Let the first number is x1 and other number is y1 then

$x1 * y1 =216$

Therefore

$y1=$ $\frac{216}{x1}$

also there sum is

$s1 =x1+y1$ ....Eq(1)

Putting the value of y1 in the previous equation

$s1\ =x1 + \frac{216}{x1}$ ........Eq(2)

Differentiate the the Eq(2) with respect to x1 we get

$\frac{ds1}{dx1} \ =\ 1+216*\frac{1}{-x1^{2} }$

$\frac{ds1}{dx1} \ =\ 1-\frac{216}{x1^{2} }\ =\ 0$

${x1^{2} }\ =\ 216\\ x1=\sqrt{216}$

Putting the value of X1 in Eq(1) we get

$y1=\frac{216}{\sqrt{216} } \\y1=\frac{216*\sqrt{216} }{216} \\y1=\ \sqrt{216}$

So $x1=\sqrt{216} \ and \ y1=\ \sqrt{216}$

6 0

4 years ago

Reid ate 1/4 if pie, joe ate 1/3 of pie. How much was left after they both ate their pieces

Sindrei [870]

Considering Reid ate 1/4 of the pie and Joe ate 1/3 of the pie, we have to bring this to their common denominator. In this case that is 12.

1/4 + 1/3 = ?

(1 * 3)/12 + (1*4)/12 =
3/12 + 4/12 =
(3 + 4)/12 =
7/12

But this is the amount of the pie that both Reid and Joe ate.

To calculate the remaining amount we have to imagine our pie was still whole (12/12)
and substract what they both ate (7/12):

12/12 - 7/12 = 5/12

Only 5/12 of the pie was left, a little less than half of it :)

4 0

4 years ago

I got this wrong a million times, and I just want to know what the answer is.

KATRIN_1 [288]

Answer:

The cost to make one sandwich: S

Number of sandwiches the band sold: 73

The amount of money the band receives for making one sandwich: S+0.2S

The profit the band earns from selling one sandwich: 0.2S

Step-by-step explanation:

In the word problem, it says that it takes S dollars to make one sandwich.

In the word problem, it states that the band sells each sandwich for 20%(.2) more than it costs to make. This can be described as 0.2S

S+0.2S can describe how much profit the band makes.

73 represents how many sandwiches the band sold.

5 0

3 years ago

What are the coordinates of the point on the directed line segment from (-8, -1)(−8,−1) to (6, -8)(6,−8) that partitions the seg

VladimirAG [237]

Answer:

8/5=3.6

2*3.6=7.2

3*3.6=10.8

Step-by-step explanation:

8 0

3 years ago

Simplify the expression to one number using order of operations:

geniusboy [140]

<h2><u>COMBINED OPERATIONS</u></h2><h3>Exercise</h3>

First, let's solve the subtraction (in parentheses):

$\mathsf{\dfrac{-8\left(2-6\right)}{2}}$

$\mathsf{\dfrac{-8(-4)}{2}}$

Now, let's solve the multiplication. Remember: in multiplication, two negative numbers will give a positive number:

$\mathsf{\dfrac{-8(-4)}{2}}$

$\mathsf{\dfrac{32}{2}}$

Finally, let's solve the division:

$\mathsf{\dfrac{32}{2} = 16}$

<h3><u>Answer</u>: 16</h3>

5 0

3 years ago