Step by step solution thank you much appreciated

First, remember that:

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this problem, notice that:

2 + 3 is not greater than 5.

3 + 5 is not greater than 2.

2 + 5 is not greater than 3.

So, the statement is false. A triangle can't have sides 2

Step-by-step explanation:

im still working on the 2nd part

The amount of each loan are $2,100 and $1,400.

What is mean by Simple interest?

The simple interest is defined as;

Simple interest = P r t

Where, P is principal amount.

r is rate and t is time period.

Given that;

Student take 2 loans for pay the college.

One loan at 8% interest and the other at 9% interest.

And, The total borrowed amount = $3,500

and, The interest loan = $294

Let The first amount of loan = x

And, The other amount of loan = y

So, We can formulate;

x + y = $3,500  ..... (i)

And, The interest loan = $294

So, We can formulate;

8x/100 + 9y/100 = $294  

8x + 9y = 29400  ... (ii)

Solve equation (i) and (ii) , we get;

Multiply by 8 in equation (i) and subtract from (ii), we get;

y = $1400

Hence,

x + y = $3,500

x + 1400 = 3500

x = 3500 - 1400

x = $2,100

Therefore, The amount of each loan are $2,100 and $1,400.

Learn more about the simple interest visit:

https://brainly.com/question/28350221

#SPJ1

802/198​ is equal to 4.0505

 Polynomial equations are those created using exponents, coefficients, and variables. It may have several exponents, with the higher one being referred to as the equation's degree.

Polynomial equation illustration

     Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. The original equations' answers are the solutions to the derived equations. Factoring cannot always be used to solve polynomial equations.

6h²(5 + 9h)(5 - 9h)

6h²(9h + 5)(5 - 9h)

6h²(9h + 5)(-9h + 5)

6h²(9h + 5)(-9h + 5)

54(-9h +5)h³ + 30(-9h + 5)h²

(-486h)4 + 270h³+30(-9h+5)h²

(-486h)4 + 270h³-270h³+150h²

(-486h)4 + 150h²

(-486h)4 + 150h²

To Learn more About polynomial equation, Refer:

https://brainly.com/question/2833285

#SPJ13

The area of a rectangle is given by the formula

So, you have

Therefore, the area of this rectangle is 16.25 square feet.

The composition of two functions is defined as follows:

Use the given rules of correspondence of h and g to find the composition of those two functions. Then, evaluate the composition at -9:

Then:

Evaluate the composition of h and g at a=-9:

Therefore:

Given data:

The given point is (a,b)=(-5,1).

The given line is 2y=2x-4.

The given line can be written as,

2y=2(x-2)

y=x-2

The standard equation of the line is,

y=mx+c

comapre the given line with the standard form.

m=1

The slope of two parallel lines are always equal.

m'=m

=1

The expression of the line which is parallel to the given line is,

y-b=m'(x-a)

Substitue the given values in the expression.

y-1=1(x-(-5))

y-1=x+5

y=x+6.

Thus, the equation of the line parallel to the given line is y=x+6.

We need to calculate 1/5 + 1/2:

H = 1/5 + 1/2

Then: H = 7/10

ANSWER:

5

STEP-BY-STEP EXPLANATION:

We have the following expression:

We substitute the value of w, when it is equal to 3, just like this:

The value of the expression is equal to 5

The Solution:

Given:

Lella deposited $600 into an account that pays 2% simple interest per year.

Required:

To find the interest Lella will get in the first 3 years.

To find the interest, we shall use the formula below:

In this case,

Substituting these values in the above formula, we get

Thus, the interest she will be paid in 3 years is $36.00

Therefore, the correct answer is $36.00

This is a problem based on permutations. We must select four jobs among ten jobs and see how many arrangments can be made.

The formula for the number of permutations is:

Where:

• n = total number of jobs = 10,

• r = number of jobs to be selected = 4.

Replacing these data in the formula above, we get:

5040

Problem

Solution

We have the following sequence of terms 34,25,16,7,....

Part a

The common difference for this case would be:

25-34= -9

16-25=-9

7-16= -9

Then the answer for part a would be -9

Part b

We want to write the following form:

an = a1 + (n-1) d

For this case d=-9, a1= 34

And then we can write the genral expression like this:

an = 34 + (n-1 ) (-9)

With n = 1,2,3,4....

Part c

In order to find the 20 th term we can replace n =20 and we got:

a20= 34 + (20-1) (-9) = 34-171= -137

b. You have to consider year 2000 as the initial year, i.e. as x=0.

To predict the percent of adults with diabetes in 2014, first, you have to calculate the difference between this year and the initial year to determine which value of x you need to use:

The value of x you have to use is x=14

Replace this value into the linear model calculated in item a to predict the percentage of adults with diabetes (y)

In the year 2014, the predicted percentage of adults with diabetes is 17.8%

c. You have to determine the year in which the model predicts the percent to be 27.96%.

To determine this year, you have to equal the linear model to 27.96% and calculate for x:

-Subtract 10.692 from both sides of the equal sign

-Divide both sides by 0.508

Next, add x=34 to the initial year:

The model predicts the percentage to be 27.96% for the year 2034

The values of the functions are:

1. f(2/3) = 2/9

2. f(1/4) = -21/4

If we are given the a function to find the value for which x assumes a given value, substitute the given value of x into the function and solve.

1. To find the value of f(2/3), substitute x = 2/3 into the function f(x) = 2x² - 4x + 2.

f(2/3) = 2(2/3)² - 4(2/3) + 2

f(2/3) = 2(4/9) - 8/3 + 2

f(2/3) = 8/9 - 8/3 + 2

f(2/3) = (8 - 24 + 18)/9

f(2/3) = 2/9

2. To find the value of f(1/4), substitute x = 1/4 into the function f(x) = 4x² + 2x - 6.

f(1/4) = 4(1/4)² + 2(1/4) - 6

f(1/4) = 4(1/16) + 1/2 - 6

f(1/4) = 1/4 + 1/2 - 6

f(1/4) = (1 + 2 - 24)/4

f(1/4) = -21/4

Learn more about function on:

https://brainly.com/question/2284360

#SPJ1

First, plot the points on a graph and form the triangle:

By looking at the triangle we can see that:

Base: 2

Height: 4

Area : 1/2 x 2 x 4 = 4 units2

In this problem, we must solve some linear equations.

1)

2)

3)

4)

Answers

• a = 2

• k = 4

• e = 2

• c = 7

Explanation:

Area of the rectangular rug = length × width

dimension of rug = 9'×12'

length = 12', width = 9'

Area = 12 × 9

Area = 18

The length of the trail is equal to 3mi and the selling price of the item is equal to $120.

In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14.

In this question, we have to use the ratio given to determine the length of the trail.

Given that the ratio is 5in : 2mi, we have to convert the values to uniform units.

[tex]1mi = 63360in\\2mi = x\\x = 126720[/tex]

The ratio is now 5in : 126720in

Given that on the map, the length is 7.5in

[tex]5 = 126720\\7.5 = x\\x = 190080in[/tex]

Let's convert this into mi.

[tex]190080in = 3mi[/tex]

The actual length of the trail is 3in.

b)

To find the selling price of the item, let's use the percentage given to do that.

We can find 40% of 200 and then subtract the value from 200.

[tex]40\% of 200 = 0.4 * 200 = 80[/tex]

The discount price is $80 and we can find the selling price here.

[tex]selling price = actual price - discount price\\selling price = 200 - 80\\selling price = 120[/tex]

The selling price of the item is $120

Learn more on ratio and percentages here;

https://brainly.com/question/2784798

#SPJ1

The given system of equations are

y=-3x/2 + 6

y=5x - 7

We would substitute values for x into the equations and find the corresponding y values. These values would be plotted on a graph. Where the lines of both equations meet would represent the solution of the system of equations.

For the first equation,

y = - 3x/2 + 6

if x = 0, y = 3 * 0/2 + 6 = 6

If x = 1, y = - 3 * 1/2 + 6 = 4.5

if x = 2, y = - 3 * 2/2 + 6 = 3

We would plot these values on the graph

For the second equation,

y = 5x - 7

if x = 0, y = 5 * 0 - 7 = - 7

If x = 1, y = 5 * 1 - 7 = - 2

if x = 2, y = 5 * 2 - 7 = 3

We would plot these values on the graph

The diagram of the graph is shown below

Looking at the graph, at the point where both lines meet,

x = 2, y = 3

Thus, the solution is (2,3)

Let h be the number of hours that the customer rented the van, then we can set the following equation:

Subtracting 17.99 from the above equation we get:

Dividing by 19.99 we get:

Answer: 2 hours.

The positive numbers that the difference is 14 and the product is 1976 are 38 and 52.

The difference of the positive numbers is 14 and the products of the positive numbers is 1976.

The positive numbers are the numbers that are greater than zero.

Positive numbers includes fractions, In general, positive numbers are natural counting numbers.

Therefore,

let the numbers be x and y

Hence, the difference of the positive numbers is 14.

x - y = 14

The product of the positive numbers is 1976. Therefore,

xy = 1976

Make x the subject of the formula in equation(ii)

x = 1976 / y

Substitute the value of x in equation(i)

1976 / y - y = 14

14y = 1976 - y²

solve the quadratic equation formed.

y² + 14y - 1976 = 0

Hence,

y² - 38y + 52y - 1976

y(y - 38) + 52(y - 38)

(y - 38)(y + 52)

Therefore,

y = 38 and y = -52

The number is positive .

Therefore, we can only use 38.

y = 38

Substitute the value of y in equation(i)

x - 38 = 14

x = 14 + 38

x = 52

Therefore, the positive numbers are 38 and 52.

learn more on positive numbers here: https://brainly.com/question/22696821

#SPJ1

answer: D. x = 4

Given:

a. The amount of flour that the bakery used this month was a 50% increase relative to last month.

So, we will draw a diagram that represents the situation

As shown, for last month, we have drawn a rectangle divided into two equal areas, each one represents 50%

this month was a 50% increase, so, we have drawn 3 areas which represent 50% increase

b. The amount of milk that the bakery used this month was a 75% decrease relative to last month.

As shown, for last month, we have drawn a rectangle with four equal areas

75% decrease, so, we have to remove 3 areas to make the remaining = 25%

So, the difference will give a 75% decrease

Answer:

√52

Step-by-step explanation:

[tex] \sqrt{ {(4 - ( - 2))}^{2} + {(1 - ( - 3))}^{2} } [/tex]

[tex] \sqrt{ {6}^{2} + {4}^{2} } = \sqrt{36 + 16} = \sqrt{52} [/tex]

Zale's percent mark up is 37.5 percent.

Mark up percentage is calculated by dividing the gross profit of a unit by the cost of that unit.

In other words, Mark-up percentage is the difference between a product's selling price and cost as a percentage of the cost.

Therefore, Zale's sells diamonds for $1,100 that cost $800.

Hence,

mark up = 1100 - 800

mark up = $300

percentage mark up = 300 / 800 × 100

percentage mark up = 30000 / 800

Therefore,

percentage mark up = 37.5%

learn more on percent mark up here: https://brainly.com/question/12284542

#SPJ1

The answer is 7/24

The running trail is 3.826 miles long. If we add 2.46 miles, the new length will be:

which gives 6.286 miles. Then, the new lenght will be 6.286 miles long.

Diammeter = 4.2 inch

Radius = diammeter/2 = 4.2/2 =2.1 inch

We are given the information that Bailey reads 2 and a half books in 3 and a third weeks.

2 and a half books can be seen as 5/2 books, just as follows

On the other hand, 3 and a third weeks can be seen as 10/ weeks, just as follows:

Next, we just have to use a rule of three, its as follows: "if Bailey read 5/ books in 10/3 weeks, how many books does she reads per week?"

With that, we proceed with the division:

That means that Bailey reads 3/4 books per week