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2 years ago

5

in triangleABC the side lengths are b=13, ac=21 and bc=x. write a compound inequality the represents the range of possible value

s for x

1 answer:

tankabanditka [31]2 years ago

3 0

Answer:

8 < x < 34

Step-by-step explanation:

ab = 13, ac = 21, bc = x

The longest side of a triangle must be less than the sum of the other two sides.

If 21 is the longest side:

21 < 13 + x

8 < x

If x is the longest side:

x < 13 + 21

x < 34

Therefore, 8 < x < 34.

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The Smiths bought new furniture that cost $3,298.00. The store offered them

ad-work [718]

Answer:

10.99%.

Step-by-step explanation:

We have been given that the Smiths bought new furniture that cost $3,298.00. The store offered them an option of putting $600 down and making equal payments of $300 a month for 10 months.

First of all, we will find amount paid by down-payments in 10 months.

$\$300\times 10=\$3,000$

Total amount paid by Smiths: $\$3,000+\$600=\$3,600$ .

Now we will find amount paid in interest by subtracting initial amount from total amount.

$\text{Amount paid in interest}=\$3,600-\$3,298$

$\text{Amount paid in interest}=\$302$

10 months = 10/12 year =5/6 year.

Now, we will use simple interest formula to solve for interest rate.

$I=Prt$

$\$302=\$3,298*r*\frac{5}{6}$

$\$302=r*\frac{\$16,490}{6}$

$\$302*\frac{6}{\$16,490}=r*\frac{\$16,490}{6}*\frac{6}{\$16,490}$

$\frac{1,812}{\$16,490}=r$

$r=\frac{1,812}{\$16,490}$

$r=0.1098847786$

$r=0.1098847786\times 100$

$r=10.98847786\%$

$r\approx 10.99\%$

Therefore, the annual interest rate is 10.99%.

7 0

2 years ago

a phone company offers a monthly data plan at for $10 a month . the plan includes two megabytes of data and charges $0.10 per me

tatuchka [14]

Answer:

$\ m(x) = \{ {{10, if x\leq 2} \atop {0.1x + 9.8, if x>2}} \right.$

Step-by-step explanation:

One off charge = $10
Charge for data over 2 Mb is = $0.10 per MB

<u>The monthly charge for x MB data is:</u>

1 . Data ta used up to 2 Mb

$10

2 . Data used more than 2 Mb

m(x) = 10 + 0.1(x - 2) = 10 + 0.1x - 0.2 = 0.1x + 9.8
m(x) = 0.1x + 9.8

So the function is:

$\ m(x) = \{ {{10, if x\leq 2} \atop {0.1x + 9.8, if x>2}} \right.$

5 0

2 years ago

Find the missing value for the exponential function represented by the table below x -2 -1 0 1 2 y 29 20.3 14.21 6.9629

andre [41]

Answer:

y=4.8710 is the missing value

Step-by-step explanation:

The first step in approaching this question is determining the exponential equation that models the set of data. This can easily be done in Ms.Excel application. We first enter the data into any two adjacent columns of an excel workbook. The next step is to highlight the data, click on the insert tab and select the x,y scatter-plot feature. This creates a scatter-plot for the data.

The next step is to click the Add chart element feature and insert an exponential trend line to the scatter plot ensuring the display equation on chart is checked.

The exponential regression equation for the data set is given as;

$y=12.321e^{-0.464x}$

To find the missing y value, we simply substitute x with 2 in the regression equation obtained;

$y=12.321e^{-0.464(2)}\\\\y=4.8710$

5 0

2 years ago

How many 5-digit numbers are there that are divisible by either 45 or 60 but are not divisible by 90?

o-na [289]

Answer:

2500 numbers

Step-by-step explanation:

Problem;

Solving for the number of 5-digit numbers divisible either by 45 or 60 but not divisible by 90;

Let us approach this in a step wise manner;

5 -digits numbers ranges from 10,000 to 99,999

To solve this problem, let us find the number of digits that are divisible by 45;

the first number divisible by 45 within this range is 10035

the last number divisible by 45 in this range is 99990

increment is 45

The total number in this range is:

$\frac{last number - first number}{increment}$ + 1 = $\frac{99990 - 10035}{45}$ + 1

= 2000 numbers

To solve this problem, let us find the number of digits that are divisible by 60;

the first number divisible by 60 within this range is 10020

the last number divisible by in this range is 99960

increment is 60

$\frac{99990 - 10080 }{90}$

The total number in this range is:

$\frac{last number - first number}{increment}$ + 1 = $\frac{99960 - 10020}{60}$ + 1

= 1500 numbers

To solve this problem, let us find the number of digits that are divisible by 90;

the first number divisible by 90 within this range is 10080

the last number divisible by in this range is 99990

increment is 90

The total number in this range is:

$\frac{last number - first number}{increment}$ + 1 = $\frac{99990 - 10080}{90}$ + 1

= 1000 numbers

Now solution:

Number of 5 digits = number of 45 + number of 60 - number of 90

= 2000 + 1500 - 1000

= 2500 numbers

3 0

2 years ago

Expand the following expression by using the distributive method. 6(3b - 4c)

Kruka [31]

18b - 24c because you multiply the outside with everything inside

8 0

2 years ago