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BabaBlast [244]
3 years ago
9

Triangle DEF is similar to triangle PQR. Side DE measures 3, side EF measures 7 and side FD measures 9. Side PQ measures 5x – 25

and side QR measures 6x + 4. Find the value of x
Mathematics
1 answer:
White raven [17]3 years ago
7 0
For this problem, we can set up a proportion using similarity ratios. We know that triangle DEF is similar to triangle PQR, so we know that DE/PQ = EF/QR = FD/RP:

DE/PQ = EF/QR

3/(5x - 25) = 7/(6x + 4)

Cross multiplying, we get:

7(5x - 25) = 3(6x + 4)

35x - 175 = 18x + 12

Now, we can solve for x:

35x - 18x = 12 + 175

17x = 187

x = 11

So, x is 11. 
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What is the recursive rule for the sequence 2, -1, 1/2 , -1/4
Helga [31]

Answer:

a_n=\frac{-1}{2}a_{n-1}

a_1=2

Step-by-step explanation:

The recursive rule is a term defined in terms of other terms in the sequence.

The is a geometric sequence because it has a common ratio.

The common ratio can be found by dividing a term by previous term.

For example, all of these are equal:

\frac{-1}{2}

\frac{\frac{1}{2}}{-1}

\frac{\frac{-1}{4}}{\frac{1}{2}}

They are all equal to \frac{-1}{2}.

So we are saying:

\frac{\text{term}}{\text{previous term}}}=\frac{-1}{2}

More formally:

\frac{a_n}{a_{n-1}}=\frac{-1}{2}.

Multiply both sides by a_{n-1}:

a_n=\frac{-1}{2}a_{n-1}

When doing recursive form, you need to state a term of the sequence (or more depending on the recursive form you have).

So the first term is 2.

So the full thing for the answer is:

a_n=\frac{-1}{2}a_{n-1}

a_1=2

8 0
3 years ago
Find the GCF of the following monomials.<br> -50m⁴ n⁷ and 40m² n¹⁰
babunello [35]
Greetings!

We can factor this expression/ the GCF is:
-10m^2n^7

(-10m^2n^7)(5m^2-4n^3)

Hope this helps.
-Benjamin
8 0
3 years ago
Read 2 more answers
Need help with this question regarding functions. :)
Tanzania [10]

The Y-intercept is found when X is equal to 0.

In the table, when X is 0, f(x) is 1.


On the graph, when X is 0 the line crosses at Y = 1.


This means that they are equal.


The answer would be equal to.

4 0
4 years ago
which linear system has been correctly solved for one of the variables from the following system? 2x - y = -1 2x y = -7 2x - y =
mr Goodwill [35]
If you would like to solve the system of linear equations, you can do this using the following steps:

2x - y = -1 ... y = 2x + 1
2x + y = -7 ... y = -7 - 2x

The correct result would be: y = 2x + 1, <span>2x + y = -7.</span>
4 0
3 years ago
Solve for x. <br> 35x = 21
emmasim [6.3K]
X = 21/35

x = 3/5 

Explanation: divide both sides by 35 and reduce the fraction 21/35 to get 3/5.

7 0
3 years ago
Read 2 more answers
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