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m_a_m_a [10]
3 years ago
15

(05.01)Dawn is making an abstract painting with two triangles. The dimensions of the painting are shown below: Two triangles sha

re the same height of 8 inches. One triangle has a base of 6 inches and the other is 10 inches. The total area of the two triangles is _____ square inches. Numerical Answers Expected! Answer for Blank 1:
Mathematics
2 answers:
Vlad1618 [11]3 years ago
5 0
Multiply the height by the base to get the area. 8 x 6 = 48. The area of the first triangle is 48 square inches. 8 x 10 = 80. The area of the second triangle is 80 square inches.
mrs_skeptik [129]3 years ago
4 0

Answer:

64

Step-by-step explanation:

The area of a triangle is found using the formula

A = 1/2bh

For the first triangle, the base is 6 and the height is 8:

A = 1/2(6)(8) = 3(8) = 24 sq. in.

For the second triangle, the base is 10 and the height is 8:

A = 1/2(10)(8) = 5(8) = 40 sq. in.

The total area will be the sum of these two areas:

24+40 = 64 sq. in.

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The equation p(t) = 1.e represents a
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Answer:

(b), (d) and (e)

Step-by-step explanation:

Given

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See attachment for y = p(t)

Required

Select true statements from the given options

(a) \ln(30) = days the bacteria reaches 30000

We have:

p(t) = 1 * e^t

In this case:

t = \ln(30) and p(t) = 30000

So, we have:

30000 = 1 * e^{\ln(30)}

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Using a calculator, we have:

e^{\ln(30)} = 30

So:

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The above equation is false.

(a) is not true

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p(t) = 1 * e^t

Let t = 3

So;

p(3) = 1 * e^3

From the graph, p(3) = 20

So:

20 = 1 * e^3

20 = e^3

Take natural logarithm of both sides

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This gives:

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(b) is true

(c) \ln(t) = y is the logarithm form of y = e^t

We have:

y = e^t

Take natural logarithm of both sides

\ln(y) = \ln(e^t)

This gives:

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(c) is false

(d) e^4 > 50 and  \ln(50) < 4

From the graph, we have:

e^4 = 54 --- rough readings

This implies that:

e^4 > 50 is true

Because 54 > 50

Take natural logarithm of both sides

\ln(54) > \ln(50)

Rewrite as:

\ln(50) < \ln(54)

We have:

e^4 = 54

Take natural logarithm of both sides

\ln(e^4) = \ln(54)

4 = \ln(54)

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Substitute \ln(54) = 4 in \ln(50) < \ln(54)

\ln(50) < 4

(d) is true

(e) The graph shows that 10 \approx \ln(2.3)

We have:

p(t) = 1 * e^t

Let t = 2.3

So;

p(2.3) = 1 * e^{2.3}

From the graph,

p(2.3) = 10 ---- rough readings

So:

10 = 1 * e^{2.3}

10 = e^{2.3}

Take natural logarithm of both sides

\ln(10) = \ln(e^{2.3})

This gives:

\ln(10) = 2.3

(e) is true

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