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3 years ago

What additional information would you need to prove that ΔABC ≅ ΔDEF by ASA

1 answer:

3 0

What do you mean? You just need to prove there are two angles and the side between these two angles are the same in each triangle. One of the possible combinations could be ∠BAC=∠FDE, ∠ABC= ∠DEF, and AB=DE.

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The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to rep

Alchen [17]

Ooh, fun

geometric sequences can be represented as
$a_n=a(r)^{n-1}$
so the first 3 terms are
$a_1=a$
$a_2=a(r)$
$a_2=a(r)^2$

the sum is -7/10
$\frac{-7}{10}=a+ar+ar^2$
and their product is -1/125
$\frac{-1}{125}=(a)(ar)(ar^2)=a^3r^3=(ar)^3$

from the 2nd equation we can take the cube root of both sides to get
$\frac{-1}{5}=ar$
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
$\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r$
subsituting -1/5 for ar
$\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r$
which simplifies to
$\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}$
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for $ax^2+bx+c=0$
$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$
so
for 2r²-5r+2=0
a=2
b=-5
c=2

$r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}$
$r=\frac{5 \pm \sqrt{25-16}}{4}$
$r=\frac{5 \pm \sqrt{9}}{4}$
$r=\frac{5 \pm 3}{4}$
so
$r=\frac{5+3}{4}=\frac{8}{4}=2$ or $r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}$

use them to solve for the value of a
$\frac{-1}{5}=ar$
$\frac{-1}{5r}=a$
try for r=2 and 1/2
$a=\frac{-1}{10}$ or $a=\frac{-2}{5}$

test each
for a=-1/10 and r=2
a+ar+ar²= $\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}$
it works

for a=-2/5 and r=1/2
a+ar+ar²= $\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}$
it works

both have the same terms but one is simplified

the 3 numbers are $\frac{-2}{5}$ , $\frac{-1}{5}$ , and $\frac{-1}{10}$

6 0

3 years ago

−10=2y Hello Help Me

marin [14]

The answer is -5

Explanation: Divide 2 to get rid of the top number. It looks like this

-10. 2y
___. ___

2. 2

What this does is remove the two from the Y and sets it by itself. Then you divide the -10, and the answer is -5

7 0

3 years ago

Multiply your answer should be in a monomial standard form (7h^3)(3h^7)

KonstantinChe [14]

Answer:

21 h^10

Step-by-step explanation:

(7h^3)(3h^7)

Lets multiply

7*3 h^3 h^7

When the bases are the same , we add the exponents (x^a * x^b) = x ^ (a+b)

21 h^(3+7)

21 h^10

5 0

3 years ago

Read 2 more answers

Help me with this question plz

Alik [6]

Answer:

i dont what it could be but my uncle said it was 32 but i dont know if its correct

Step-by-step explanation:

8 0

3 years ago

Write a power represented with a positive base and a positive exponent whose value is less then the base

sasho [114]

Answer:

The question is open ended as i suppose since there are infinitely many possibilities. one possible form of the solution can be $5^{2}$

Step-by-step explanation:

The base in this case is 5 while the exponent is simply the power to which the base is raised in which case it would be 2. Both values are positive and the exponent is less than the base.

6 0

3 years ago