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Pavel [41]
3 years ago
15

For his phone service, Ivan pays a monthly fee of $14, and he pays an additional $0.05 per minute of use. The least he has been

charged in a month is $74.75.What are the possible numbers of minutes he has used his phone in a month?
Mathematics
1 answer:
Tomtit [17]3 years ago
8 0

Answer:

1215 minutes are the possible numbers he has used his phone in a month.

Step-by-step explanation:

He has a monthly fee of 14$ then to the least that he has been charged we need to substract the monthly fee as follows:

Monthly charged = 74,75-14

Monthly charged= 60,75$

Then he pays an additional 0,05 $/minute of use, to know the consume:

Minutes= \frac{60,75}{0,05}

Minutes= 1215 possible numbers of minutes he has used his phone.

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Bill and Pete shared 1/2 of a cake. Bill got to eat twice as much cake as Pete. What fraction of the whole cake did Bill eat?
KatRina [158]

Answer:

Step-by-step explanation:

Total cake shared=1/2

Pete share=x

Bill= twice as much as Pete

=2x

Pete's share+ Bill's share=total share

x+2x=1/2

3x=1/2

x=1/2÷3

x=1/2×1/3

=1/6

Pete's share=x=1/6

Bill's share=2x

=2(1/6)

=2/6

=1/3

3 0
3 years ago
How do you prove each of the following theorems using either a two-column, paragraph, or flow chart proof?
lilavasa [31]

All the theorems are proved as follows.

<h3>What is a Triangle ?</h3>

A triangle is a polygon with three sides , three vertices and three angles.

1. The Triangle sum Theorem

According to the Triangle Sum Theorem, the sum of a triangle's angles equals 180 degrees.

To create a triangle ABC, starting at point A, move 180 degrees away from A to arrive at point B.

We turn 180 degrees from B to C and 180 degrees from C to return to A, giving a total turn of 360 degrees to arrive to A.

180° - ∠A + 180° - ∠B + 180° - ∠C = 360°

- ∠A - ∠B  - ∠C = 360° - (180°+ 180°+ 180°) = -180°

∠A + ∠B  + ∠C = 180°

(Hence Proved)

2. Isosceles Triangle Theorem

Considering an isosceles triangle ΔABC

with AB = AC, we have by sine rule;

\rm \dfrac{sinA}{BC} =  \dfrac{sinB}{AC} =  \dfrac{sinC}{AB}\\

as AB = AC

sin B = sin C

angle B = angle C

3.Converse of the Isosceles theorem

Consider an isosceles triangle ΔABC with ∠B= ∠C, we have by sine rule;

\rm \dfrac{sinA}{BC} =  \dfrac{sinB}{AC} =  \dfrac{sinC}{AB}\\

as  ∠B= ∠C ,

AB = AC

4. Midsegment of a triangle theorem

It states that the midsegment of two sides of a triangle is equal to (1/2)of the third side parallel to it.

Given triangle ABC with midsegment at D and F of AB and AC respectively, DF is parallel to BC

In ΔABC and ΔADF

∠A ≅ ∠A

BA = 2 × DA, BC = 2 × FA

Hence;

ΔABC ~ ΔADF (SAS similarity)

BA/DA = BC/FA = DF/AC = 2

Hence AC = 2×DF

5.Concurrency of Medians Theorem

A median of a triangle is a segment whose end points are on vertex of the triangle and the middle point of the side ,the medians of a triangle are concurrent and  the point of intersection is inside the triangle known as Centroid .

Consider a triangle ABC , X,Y and Z are the midpoints of the sides

Since the medians bisect the segment AB into AZ + ZB

BC into BX + XB

AC into AY + YC

Where:

AZ = ZB

BX = XB

AY = YC

AZ/ZB = BX/XB = AY/YC = 1

AZ/ZB × BX/XB × AY/YC = 1 and

the median segments AX, BY, and CZ are concurrent (meet at point within the triangle).

To know more about Triangle

brainly.com/question/2773823

#SPJ1

8 0
1 year ago
1. You have $10 saved. Each week you receive $5 in allowance. Let x represent the number of weeks you
bazaltina [42]
That looks hard sorry I don’t know answer good luck
7 0
3 years ago
Read 2 more answers
58 is the difference of Janelle's height and 24.
abruzzese [7]

Answer:

Janelle's height is 82 units.

Step-by-step explanation:

Let j represent Janelle's height.

It is mentioned that, 58 is the difference between Janelle's height and 24.

Mathematically, we can write it as :

j-24 = 58

We can solve it as follows :

Adding 24 both sides,

j-24+24 = 58+24

j = 82

Hence, Janelle's height is 82 units.

3 0
2 years ago
Nelson decides to invest $1,000,000 in a period annuity that earns 4.8% APR
Lyrx [107]

Answer:

<h2> 21years</h2>

Step-by-step explanation:

Amount invested by Nelson = $1,000,000

Interest rate per month = 4.8%

Simple Interest = Principal * Rate * Time/100

simple Interest = $1,000,000 * 4.8 *(1/12)/100

simple Interest = $1,000,000 * 4.8/1200

simple interest = $4,000/ month

Simple interest for one year = $4,000*12 = $48,000

In order to determine the number of years it will take Nelson to earn back his initial investment, we will divide its initial investment by the interest earned on the investment yearly as shown;

amount of years =  $1,000,000/ $48,000

Amount of years = 20.8years ≈ 21years

6 0
2 years ago
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