All categories

2 years ago

Question 1

Mathematics

2 answers:

aksik [14]2 years ago

6 0

The number of ounces of jam that each jar can hold is 4 large jars and 2 small jars.

<h3>What is Matrix?</h3>

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

Here, from the given matrix by comparing the equations, we have:

l + 2s = 8 ...........(i)

l - s = 2 .............(ii)

Subtract the second equation from the first, to eliminate l

3s = 6

s = 2

Substitute 2 for s in l - s = 2

l - 2 = 2

Add 2 to both sides

l = 4

Thus, the number of ounces of jam that each jar can hold is 4 large jars and 2 small jars.

Learn more about matrix from:

brainly.com/question/11989522

#SPJ1

olga2289 [7]2 years ago

6 0

The number of ounces of jam that each jar can hold is 4 large jars and 2 small jars

<h3>How to solve for the variables?</h3>

The matrix is given as:

$\left[\begin{array}{cc}1&2&1&-1\end{array}\right] \left[\begin{array}{c}l&s\end{array}\right] = \left[\begin{array}{c}8&2\end{array}\right]$

Evaluate the product of the matrices

$\left[\begin{array}{c}l+ 2s&l -s\end{array}\right] = \left[\begin{array}{c}8&2\end{array}\right]$

By comparing the equations, we have:

l + 2s = 8

l - s = 2

Subtract the second equation from the first, to eliminate l

3s = 6

Divide both sides by 3

s = 2

Substitute 2 for s in l - s = 2

l - 2 = 2

Add 2 to both sides

l = 4

Hence, the number of ounces of jam that each jar can hold is 4 large jars and 2 small jars

You might be interested in

A pig wights 9.8 pounds convert the pigs wight to ounces

Elodia [21]

9.8 pounds in ounces is 156.8
Hope this helped!!

5 0

3 years ago

You are a member of your local movie theater’s club. Every time you see a movie at the theater, you earn 2 advantage points. Whe

Snowcat [4.5K]

You have to watch 30 movies to earn a free movie pass.

Step-by-step explanation:

Given,

Points earned for each movie = 2 points

Current points = 40 points

Free movie pass = 100 points

Let,

x be the number of movies you have to watch.

2*number of movies + current points = 100

$2x+40=100$

Subtracting 40 from both sides

$2x+40-40=100-40\\2x=60$

Dividing both sides by 2

$\frac{2x}{2}=\frac{60}{2}\\x=30$

You have to watch 30 movies to earn a free movie pass.

Keywords: linear equation, division

Learn more about division at:

#LearnwithBrainly

5 0

3 years ago

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

4 years ago

Without solving determine the character of the solutions of the equation x^2+2x+5=0

Sav [38]

★ QUADRATIC RESOLUTION ★

Roots of the given equation will be imaginary because it's discriminant is less than 0 and hence it'll yield imaginary solutions

D < 0

b² - 4ac < 0

4² - 4 ( 5 ) < 0

16 - 20 < 0

-4 < 0

Hence it's character is stated above

★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★

8 0

3 years ago

Read 2 more answers

An interior painter is painting a wall that is 8 feet by 14 feet. He needs to determine how much paint he will need for the job.

dsp73

So if you do 8x14=112 is the area. So 112 divided by 40= 2.8. He will need 2.8 pints of paint.

7 0

4 years ago