All categories

3 years ago

Can someone please help?

Mathematics

2 answers:

Travka [436]3 years ago

3 0

Answer:

The answer is in the explaination

Step-by-step explanation:

A + B = 180 degrees

14x - 72 = 180

14x = 108

x = 8

A = 5 times 8 plus 20

A = 60

Ira Lisetskai [31]3 years ago

3 0

Answer:

110 degrees.

Step-by-step explanation:

Angle A + Angle B = 180 degrees.

Therefore, 5x+20+9x-92=180

When you solve you get 14x=252 or x=18

When you plug that into A you get 5(18)+20=110

Therefore, A=110 degrees

You might be interested in

John, Sally, and Natalie would all like to save some money. John decides that it

brilliants [131]

Answer:

Part 1) John’s situation is modeled by a linear equation (see the explanation)

Part 2) $y=100x+300$

Part 3) $\$12,300$

Part 4) $\$2,700$

Part 5) Is a exponential growth function

Part 6) $A=6,000(1.07)^{t}$

Part 7) $\$11,802.91$

Part 8) $\$6,869.40$

Part 9) Is a exponential growth function

Part 10) $A=5,000(e)^{0.10t}$ or $A=5,000(1.1052)^{t}$

Part 11) $\$13,591.41$

Part 12) $\$6,107.01$

Part 13) Natalie has the most money after 10 years

Part 14) Sally has the most money after 2 years

Step-by-step explanation:

Part 1) What type of equation models John’s situation?

Let

y ----> the total money saved in a jar

x ---> the time in months

The linear equation in slope intercept form

y=mx+b

The slope is equal to

$m=\$100\ per\ month$

The y-intercept or initial value is

$b=\$300$

$y=100x+300$

therefore

John’s situation is modeled by a linear equation

Part 2) Write the model equation for John’s situation

see part 1)

Part 3) How much money will John have after 10 years?

Remember that

1 year is equal to 12 months

$10\ years=10(12)=120 months$

For x=120 months

substitute in the linear equation

$y=100(120)+300=\$12,300$

Part 4) How much money will John have after 2 years?

Remember that

1 year is equal to 12 months

$2\ years=2(12)=24\ months$

For x=24 months

substitute in the linear equation

$y=100(24)+300=\$2,700$

Part 5) What type of exponential model is Sally’s situation?

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$P=\$6,000\\ r=7\%=0.07\\n=1$

substitute in the formula above

$A=6,000(1+\frac{0.07}{1})^{1*t}\\ A=6,000(1.07)^{t}$

therefore

Is a exponential growth function

Part 6) Write the model equation for Sally’s situation

see the Part 5)

Part 7) How much money will Sally have after 10 years?

For t=10 years

substitute the value of t in the exponential growth function

$A=6,000(1.07)^{10}=\$11,802.91$

Part 8) How much money will Sally have after 2 years?

For t=2 years

substitute the value of t in the exponential growth function

$A=6,000(1.07)^{2}=\$6,869.40$

Part 9) What type of exponential model is Natalie’s situation?

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$P=\$5,000\\r=10\%=0.10$

substitute in the formula above

$A=5,000(e)^{0.10t}$

Applying property of exponents

$A=5,000(1.1052)^{t}$

therefore

Is a exponential growth function

Part 10) Write the model equation for Natalie’s situation

$A=5,000(e)^{0.10t}$ or $A=5,000(1.1052)^{t}$

see Part 9)

Part 11) How much money will Natalie have after 10 years?

For t=10 years

substitute

$A=5,000(e)^{0.10*10}=\$13,591.41$

Part 12) How much money will Natalie have after 2 years?

For t=2 years

substitute

$A=5,000(e)^{0.10*2}=\$6,107.01$

Part 13) Who will have the most money after 10 years?

Compare the final investment after 10 years of John, Sally, and Natalie

Natalie has the most money after 10 years

Part 14) Who will have the most money after 2 years?

Compare the final investment after 2 years of John, Sally, and Natalie

Sally has the most money after 2 years

3 0

3 years ago

Angles R and S are complementary. If angle R is = 4x - 20 and angle S = 6x - 7, then angle R measures ___ degrees.

Shalnov [3]

Answer:

26.8°

Step-by-step explanation:

4x - 20 + 6x - 7 = 90

10x -27 =90

10x = 90+27

10x= 117

x = 11.7

so, the angle R = 4x-20 =4(11.7)-20

= 46.8-20 = 26.8°

6 0

2 years ago

Please help explanation if possible

Eva8 [605]

Answer:

612 adults

361 students

Step-by-step explanation:

To solve this question, set two equations:

Let x be number of adults and y be number of students.

As there are in total 937 people, the equation would be the sum of both adults and children:

$x+y=937$

$x=937-y$ ...... ( 1 )

As the total sale amount is $1109, the equation would be to add up the ticket fee:

$2x+0.75y=1,109$ ...... ( 2 )

Put ( 1 ) into ( 2 ):

$2(937-y)+0.75y=1,109$

$1874-2y+0.75y=1,109$

$-1.25y=-765$

$y=763/1.25$

$y=612$

Put y into ( 1 ):

$x=973-612$

$x=361$

Therefore there are 612 adults and 361 students.

5 0

2 years ago

URGENT

nadya68 [22]

Answer:

Scalene, Acute

Step-by-step explanation:

Scalene because each side has a different length

obtuse because one angle is more than 90°

6 0

3 years ago

A store that sells skis boys them from a manufacturer at a wholesale price of $57. The

Over [174]

Answer:

50 = 2

Step-by-step explanation:

which by definition equates to 68+1

3 0

3 years ago