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2 years ago

Anna is making a banner out of 4 congruent triangles as shown below. How much blue trim will she need for each side

Mathematics

1 answer:

Ede4ka [16]2 years ago

3 0

Answer:

The length of each blue trim is 17.2 inches

Step-by-step explanation:

Given

See attachment for banner

Required

The length of each blue trim

Since all 4 triangles are equal, then the dimension of 1 triangle is:

$Side\ 1 = 10$

$Side\ 2 = 14$

The hypotenuse (x) of the triangle blue trim is represented by the blue trim

So:

$x^2 = Side\ 1^2 + Side\ 2^2$

This gives

$x^2 = 10^2 + 14^2$

$x^2 = 100 + 196$

$x^2 = 296$

Take square root

$x = \sqrt{296$

$x = 17.2in$

You might be interested in

A basketball has a diameter of 9.5 inches what is the volume of the basketball using 3.14 for pi.

Step2247 [10]

Answer:

448.69 in^3

Step-by-step explanation:

The volume of a sphere is given by the formula ...

V = (4/3)πr^3

We want to use diameter, so we can substitute r = d/2 into the formula:

V = (4/3)π(d/2)^3 = (4/(3·8))πd^3

V = (π/6)d^3

For the given numbers, ...

V = (3.14/6)(9.5^3) ≈ 448.69 in^3 . . . . volume of a basketball

7 0

2 years ago

No work needed! pythagorean theorem.

Ulleksa [173]

2) x = 4

4) x = sqrt(106) = 10.3

7 0

2 years ago

A recursive rule for a sequence is given. Find the first four terms of the sequence.

tigry1 [53]

Answer:

So...

a0 = -2

a1 = (a0)2 - 4 = 4 - 4 = 0

a2 = (a1)2 - 4 = ((a0)2-4)2 - 4 =...= 02 - 4 = -4

For an+1, you may use the previous term (an) if you have just calculated it, rather than calculating it recursively again

a3 = (-4)2 - 4 = 12

The first four terms in the sequence are -2, 0, -4, 12.

Step-by-step explanation:

This recursive sequence is defined as follows:

a0 = -2 [the first term]

an+1 = an2 - 4 [for all other terms, n≥0; note that you cannot find a0 using this line]

Note that this is not "BASE" for a number base, but it is "SUB" for subscript, indicating the term. Sometimes, sequences are written with the first term being a1 and sometimes sequences are written with the first term being a0. This is because there are situations that make one or the other more convenient (for example, starting with elapsed time t=0 makes sense).

To find the value of later terms, a recursive definition requires that you find the value of the previous term, which requires that you find the value of the previous term, which requires that you find the value of the previous term, which requires that you find the value of the previous term, ... which requires that use the value of the first term.

That's why (joke) that the dictionary definition of "recursive" is "see recursive."

4 0

2 years ago

What is the radius of a circle with an area of 9671.99 cm²? Use 3.14 for pi.

Tcecarenko [31]

Answer:

55.5000143456...

Step-by-step explanation:

Use the formula for the area of a circle and solve for r:

$A=\pi r^2\\9671.99=3.14r^2\\3080.25159236...=r^2\\55.5000143456...=r$

6 0

2 years ago

The time rate of change of a rabbit population PP is proportional to the square root of PP. At time t=0t=0 (months) the populati

frosja888 [35]

Answer:

$\frac{dP}{\sqrt{P}} = k dt$

And if we integrate both sides we got:

$2 \sqrt{P} = kt +C$

Where C is a constant., we can rewrite the expression like this:

$\sqrt{P} = \frac{1}{2} (kt +C)$

If we square both sides we got:

$P = \frac{1}{4} (kt +C)^2$

If we use the initial condition we have that:

$P(0) = 100 = \frac{1}{4} (k*0 +C)^2$

And we can solve for C like this:

$400 = C^2$

$C = 20$

And now we can find the derivate of the function and we got:

$P'(t) = 2* \frac{1}{4} (kt + 20) * k$

Using the condition $P'(0) = 10$ we got:

$10 = \frac{1}{2} k (k*0 +20)$

$20 = 20 k$

k= 1

And then the model is defined as:

$P = \frac{1}{4} (t +20)^2$

And for t =12 months we have:

$P(12) = \frac{1}{4} (12 +20)^2 = 256$

Step-by-step explanation:

For this case we cna use the proportional model given by:

$\frac{dP}{dt} = k \sqrt{P}$

Where k is a proportional constant, P the population and the represent the number of months

For this case we know the following initial condition $P(0) =100$ and $P'(0) = 10$

we can rewrite the differential equation like this:

$\frac{dP}{\sqrt{P}} = k dt$

And if we integrate both sides we got:

$2 \sqrt{P} = kt +C$

Where C is a constant., we can rewrite the expression like this:

$\sqrt{P} = \frac{1}{2} (kt +C)$

If we square both sides we got:

$P = \frac{1}{4} (kt +C)^2$

If we use the initial condition we have that:

$P(0) = 100 = \frac{1}{4} (k*0 +C)^2$

And we can solve for C like this:

$400 = C^2$

$C = 20$

And now we can find the derivate of the function and we got:

$P'(t) = 2* \frac{1}{4} (kt + 20) * k$

Using the condition $P'(0) = 10$ we got:

$10 = \frac{1}{2} k (k*0 +20)$

$20 = 20 k$

k= 1

And then the model is defined as:

$P = \frac{1}{4} (t +20)^2$

And for t =12 months we have:

$P(12) = \frac{1}{4} (12 +20)^2 = 256$

6 0

2 years ago