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NARA [144]
3 years ago
10

Construct a triangle with sides congruent to given line segments. Does a solution always exist? How many congruent solutions are

there for this problem?

Mathematics
1 answer:
Alik [6]3 years ago
8 0

Answer:

ii. Yes, a solution always exists.

iii. There is only one congruent solution to the problem.

Step-by-step explanation:

Two or more lines are said to be congruent is they have the same length. These lines could be at certain angles to each other, which can be constructed to produce a triangle.

Given line segments, constructing a triangle with sides congruent to the line would produce only one triangle.

See the attachment for an example of the construction.

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R^3 +4r^2-25r-100<br><br> Help
Marina86 [1]

Answer:

The zeroes in this equation are -5, -4, and 5

Step-by-step explanation:

In order to find these, you need to factor by splitting. For this, we separate out the two halves of the equation and pull out the greatest common factor of each. Let's start with the front end.

r^3 + 4r^2

r^2(r + 4)

Now the second half.

-25r - 100

-25(r + 4)

Since what is left in the parenthesis are exactly the same, we can use that parenthesis next to one with what we pulled out.

(r^2 - 25)(r + 4)

And we can further factor the first parenthesis using the difference of two squares

(r^2 - 25)(r + 4)

(r + 5)(r - 5)(r + 4)

Now that we are fully factored, set each parenthesis equal to 0 and solve for x.

r + 5 = 0

r = -5

r - 5 = 0

r = 5

r + 4 = 0

r = -4

7 0
3 years ago
Solve for x: −2x − 4 &gt; 8<br><br> x &lt; −6<br> x &gt; −6<br> x &lt; −2<br> x &gt; −2
Yuki888 [10]

Answer:

x > -6

Step-by-step explanation:

-2x - 4 > 8

collect like terms

-2x > 8 + 4

-2x > 12

Divide both sides by -2, we will have

x > 12/-2

x > -6

8 0
4 years ago
Read 2 more answers
Nina opened a savings account and deposited $300.00. The account earns 4% interest, compounded monthly. If she wants to use the
mylen [45]

Answer:

up to $338.18

Step-by-step explanation:

Use the compound amount formula:

A = P(1 + r/n)^(n*t), where r is the interest rate as a decimal fraction and n is the number of compounding periods per year.

Here, A = $300(1 + 0.04/12)^(12*3), or

          A = $300(1.0033333)^*36, or

          A = $300(1.127) = $338.18

Nina will be able to spend up to $338.18 on a new bike.

5 0
3 years ago
Read 2 more answers
Please help with is !!!!!!!!
kirill115 [55]
Answer is X=16. Y=16
5 0
3 years ago
Which graph represents an exponential function?
geniusboy [140]

Answer:The function that represents an exponential function is the 4th graph and it can be modeled as y = aeᵇˣ.

What are exponential functions?

The exponential functions are written in the form of y = aeᵇˣ, where the output y increases exponentially for the input x.

In order to find the graph that represents an exponential function, we will discuss each of the following graphs,

For the 1st graph, (Black),

In the first graph, the graph is of a parabola, and the function which represents this kind of graph is a quadratic equation, therefore, this graph represents a parabolic equation. It is given by the function,

y=ax²+bx+c or y=a(x-h)²+k

For the 2nd graph, (Red),

In the second graph, the graph represented is the graph of a reciprocal function, the function that can be represented by the graph,

y=a/x + b

For the 3rd graph, (Blue),

In the third graph, the graph represented is the graph of root function, it can be modeled as,

y = a+√(x+b)

For the 4th graph, (Green),

In the fourth graph, the graph represented is the graph of an exponential function, and it can be modeled as,

y = aeᵇˣ

Hence, the function that represents an exponential function is the 4th graph and it can be modeled as y = aeᵇˣ.

Step-by-step explanation:

7 0
2 years ago
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