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2 years ago

What is BC ? Enter your answer in the box.

Mathematics

2 answers:

tamaranim1 [39]2 years ago

5 0

Answer-

The length of BC is 8 units.

Solution-

Mid-Point Theorem-

The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

As given,

AD = DB, so D is the mid point of AB

FA = FC, so F is the mid point of AC

Hence, DF is the line segment connecting the midpoints of two sides of a triangle.

Applying the theorem,

BC = 2DF = 2×4 = 8 units

astraxan [27]2 years ago

4 0

Answer: BC= 8 units.

Step-by-step explanation:

In the given figure m, we have a Δ ABC in which point D and F are the mid point of sides AB and AC respectively .

We know that the Mid - segment theorem says that a line segment that connects the midpoints of two sides of a triangle is parallel to the third side and it should be equal to one-half of the third side.

Therefore , For the given situation , we have

$DF=\dfrac{1}{2}BC\\\\\Rightarrow\ BC= 2 DF$

Since DF = 4 units [Given ]

Then, $BC= 2(4)= 8\text{ units}$

Hence, BC= 8 units.

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Find an equation of a line with the x- and y-intercepts below. Use exact fractions when necessary.

tamaranim1 [39]

Answer:

$y=\frac{5}{7}x-5$

Step-by-step explanation:

All lines in the plane are of the form

y = mx+b

The intersection with the Y-axis is obtained by replacing x with 0

The intersection with the X-axis is obtained by replacing y with 0

If we want that the Y-intercept = -5, then

-5 = m(0)+b

So b = -5

Our temporal equation is then

y = mx-5

If we want that the X-intercept = 7, then

0 = m(7)-5

7m = 5

m = 5/7

So our final equation is

$y=\frac{5}{7}x-5$

Attached is the graph of the line

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3 years ago

If 7000 is borrowed at the rate of 5% per annum for 3 years, the simple interest is?

Tcecarenko [31]

7000 • 5 • 3 = 105,000

Hope this helps!

7 0

3 years ago

Indefinite integral need help pleaseeeeeee

tatiyna

Integrate indefinite integral:
$I=\int\frac{dx}{e^{2x}+3e^x+2}dx$

Solution:
1. use substitution $u=e^x$
=>
$du=e^xdx$
=>
$dx=\frac{du}{e^x}$
=>
$dx=\frac{du}{u}$
=>
$I=\int\frac{du}{u(u^2+3u+2)}du$
$=\int\frac{du}{u(u+2)(u+1)}du$
2. decompose into partial fractions
$\frac{1}{u(u+2)(u+1)}$
$=\frac{A}{u}+\frac{B}{u+2}+\frac{C}{u+1}$
where A=1/2, B=1/2, C=-1
$=\frac{1}{2u}+\frac{1}{2(u+2)}-\frac{1}{u+1}$
3. Substitute partial fractions and continue
$I=\int\frac{du}{2u}+\int\frac{du}{2(u+2)}-\int\frac{du}{u+1}$
$=\frac{log(u)}{2}+\frac{log(u+2)}{2}-log(u+1)}$
4. back-substitute u=e^x
$=\frac{log(e^x)}{2}+\frac{log(e^x+2)}{2}-log(e^x+1)}$
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Note: log(x) stands for natural log, and NOT log10(x)

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2 years ago

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?

liq [111]

Answer:

7/3

Step-by-step explanation:

f(x) = 3x^2 + 2x + 1, [0, 2]

f(0)=1

f(2)=17

f'(c)=f(2)-f(0)/2-1

f'(c)=17-1/1=16

f'(c)= 6x+2

6x+2=16

6x=16-2

6x=14

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4 0

3 years ago

Read 2 more answers

Which expression is equivalent to ( 4mn / m^-2n^6)^-2

inn [45]

Here are a few rules with exponents that apply here:

Raising a power to a power: $(x^m)^n=x^{m*n}$
Dividing exponents of the same base: $\frac{x^m}{x^n}=x^{m-n}$
Converting negative exponents to positive ones: $x^{-m}=\frac{1}{x^m}\ \textsf{and}\ \frac{1}{x^{-m}}=x^m$