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3 years ago

11

Mathematics

1 answer:

Andrew [12]3 years ago

8 0

Answer:

Given the initial population of termites = 60

After 7 days the population of termites = 225

Step-by-step explanation:

We have given the initial termites and the population of termites after 7 days. Now we are required to find the exponential growth model that will help to predict the future population of termites.

We have, Y = Ca^x

When the value of x is zero then population (Y) is 60 termites.

Y = Ca^x

60 = Ca^x

Now, Y = 60a^x

At x = 7 days

Y = 225

225 = 60 a^7

a^7 = 225/60

a = 1.2078

Thus, final population will be, Y = 60(1.2078)^x

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Complete the proof....

abruzzese [7]

Answer:

The correct options are;

1. Definition of supplementary angles

2. m∠1 + m∠2 = m∠1 + m∠3

3. m∠2 = m∠3

4. Definition of Congruent Angles

Step-by-step explanation:

The two column proof is presented as follows;

Statement ${}$ Reason

1. ∠1 and ∠2 are supplementary ${}$ Given

${}$ ∠1 and ∠3 are supplementary

2. m∠1 + m∠2 = 180° ${}$ Definition of supplementary angles

${}$ m∠1 + m∠3 = 180°

3. m∠1 + m∠2 = m∠1 + m∠3 ${}$ Transitive Property

4. m∠2 = m∠3 ${}$ Subtraction Property of Equality

5. ∠2 ≅ ∠3 ${}$ Definition of Congruent Angles

Given that angles ∠1 and ∠2 are supplementary angles and angles ∠1 and ∠3 are are also supplementary angles, then the sums of m∠1 + m∠2 and m∠1 + m∠3 are equal, therefore, ∠2 and ∠3 have equal quantitative value and therefore ∠2 = ∠3 and by definition, ∠2 ≅ ∠3.

3 0

3 years ago

If each quadrilateral below is a parallelogram,find the missing measures.

zhenek [66]

Answer:

Part 1) $MN=31\ units$

Part 2) $KN=45\ units$

Part 3) m∠K=61°

Part 4) m∠L=119°

Part 5) m∠M=61°

Step-by-step explanation:

we know that

In a parallelogram opposite angles and opposite sides are congruent and consecutive angles are supplementary

Part 1) Find the side MN

we know that

MN≅KL ----> by opposite sides

we have

$KL=31\ units$

therefore

$MN=31\ units$

Part 2) Find the side KN

we know that

KN≅LM ----> by opposite sides

we have

$LM=45\ units$

therefore

$KN=45\ units$

Part 3) Find the measure of angle K

we know that

m∠K+m∠N=180° ----> by consecutive interior angles

we have

m∠N=119°

substitute

m∠K+119°=180°

m∠K=180°-119°

m∠K=61°

Part 4) Find the measure of angle L

we know that

m∠L≅m∠N ----> by opposite angles

we have

m∠N=119°

therefore

m∠L=119°

Part 5) Find the measure of angle M

we know that

m∠M≅m∠K ----> by opposite angles

we have

m∠K=61°

therefore

m∠M=61°

7 0

3 years ago

A radio station broadcasts a signal over qn area with a radius of 50 miles. The station can relay the signal and broadcast over

denpristay [2]

A = pi * r^2
A = 3.14 * 50^2 
A = 7,850 square miles (area of the 50 mile broadcast signal)

A = pi * r^2
A = 3.14 * 75^2
A = 17,662.5 = 17,663 square miles (area of the 75 mile relayed signal)

Now we just need to subtract the 50 mile signal from the 75 mile signal, so:

17,663 - 7,850 = 9,813 square miles greater

Hope this helps :)

7 0

3 years ago

Two-thirds a number plus 4 is 7

ICE Princess25 [194]

The equation (form) is: $\frac{2}{3}x + 4 = 7$