All categories

3 years ago

Can someone please help me with these! I don’t understand them

Mathematics

1 answer:

Vera_Pavlovna [14]3 years ago

5 0

Answer:

Question #1

m∠4 + m∠7 = 180° - Given.

∠4 and ∠7 are supplementary angles - Definition of supplementary angles.

∠7 and ∠2 form a linear pair - Definition of linear pair.

∠7 and ∠2 are supplementary angles - Definition of linear pair.

m∠7 + m∠2 = 180° - Definition of supplementary angles.

m∠2 = m∠4 - Substitution property.

c ║ d - Converse of corresponding angles postulate.

Question #2

m∠3 = m∠8 - Given.

∠8 and ∠6 form a linear pair - Definition of linear pair.

∠8 and ∠6 are supplementary angles - Definition of linear pair.

m∠8 + m∠6 = 180° - Definition of supplementary angles.

∠3 and ∠6 are supplementary angles - Substitution property.

m∠3 + m∠6 = 180° - Definition of supplementary angles.

Question #3

p ║ q - Given.

∠1 ≅ ∠5 - Given.

∠1 ≅ ∠2 - Alternate interior angle theorem.

∠2 ≅ ∠5 - Substitution property.

~Hope this helps!~

You might be interested in

2.The number of grams A of a certain radioactive substance present at time, in yearsfrom the present, t is given by the formulaA

professor190 [17]

Answer:

Given that,

The number of grams A of a certain radioactive substance present at time, in years

from the present, t is given by the formula

$A=45e^{-0.0045(t)}$

a) To find the initial amount of this substance

At t=0, we get

$A=45e^{-0.0045(0)}$ $A=45e^0$

We know that e^0=1 ( anything to the power zero is 1)

we get,

$A=45$

The initial amount of the substance is 45 grams

b)To find thehalf-life of this substance

To find t when the substance becames half the amount.

A=45/2

Substitute this we get,

$\frac{45}{2}=45e^{-0.0045(t)}$

$\frac{1}{2}=e^{-0.0045(t)}$

Taking natural logarithm on both sides we get,

$\ln (\frac{1}{2})=-0.0045(t)^{}$ $(-1)\ln (\frac{1}{2})=0.0045(t)$ $\ln (\frac{1}{2})^{-1}=0.0045(t)$ $\ln (2)=0.0045(t)$ $0.6931=0.0045(t)$ $t=\frac{0.6931}{0.0045}$ $t=154.02$

Half-life of this substance is 154.02

c) To find the amount of substance will be present around in 2500 years

Put t=2500

we get,

$A=45e^{-0.0045(2500)}$ $A=45e^{-11.25}$ $A=45\times0.000013=0.000585$ $A=0.000585$

The amount of substance will be present around in 2500 years is 0.000585 grams

4 0

10 months ago

What is the volume of aa circle with the radius of 1?

patriot [66]

Answer:

3.14159 (pi)

Step-by-step explanation:

1^1=1*3.14=3.14

7 0

3 years ago

Installments

ioda

Answer:

$ 338.70

Step-by-step explanation:

https://www.calculatorsoup.com/calculators/financial/loan-calculator-simple.php?pv=15%2C000.00&ratepercent=4&t=48&time_t=month&given_data_last=find_pmt&action=solve

6 0

3 years ago

State the radius of the circle of the equation

Eva8 [605]

Answer:

radius = √5 = 2.24 to nearest hundredth.

Step-by-step explanation:

(x + 3)^2 + (y + 3)^2 = 5 comparing with the standard form

(x - h)^2 + (y - k)^2 = r^2

-h = 2 so h = -3, -k = 3 so k = -3.

r^2 = 5 so r = √5.

5 0

2 years ago

Naomi pays $1.50 each time she rides the city bus. She has already ridden the bus 18 times so far this year. The expression repr

klio [65]

Answer:

$27

Step-by-step explanation:

18 times $1.50 = 27 dollars a year

5 0

3 years ago