All categories

2 years ago

Which option shows the graph of 2y-10 < 3x?

Mathematics

1 answer:

Alex2 years ago

6 0

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

$2y-10 < 3x$

isolate the variable y

Adds 10 both sides

$2y < 3x+10$

Divide by 2 both sides

$y < 1.5x+5$

The solution of the inequality is the shaded area below the dashed line $y=1.5x+5$

The slope of the dashed line is positive

The y-intercept of the dashed line is (0,5) (value of y when the value of x is equal to zero)

The x-intercept of the dashed line is (-3.33,0) (value of x when the value of y is equal to zero)

using a graphing tool

The graph in the attached figure

You might be interested in

It is 4 : 12 p.M. 4:12 p.M.4, colon, 12, start text, space, p, point, m, point, end text Emma's mom will be home from work in 70

Vaselesa [24]

Answer:

40 Minutes.

Step-by-step explanation:

The current time = 4:12 p.M.

Emma's mom will be home from work in 70 minutes.

70 minutes = 1 hour 10 Minutes= 1: 10 Hours

$\left\begin{array}{ccccc}&4&:&12 &p.m.\\+&1&:&10&\\--&--&--&--&--\\&5&:&22&p.m\end{array}\right$

Therefore, Emma's Mom will get home by 5: 22 p.m.

Emma has gymnastics lessons at 6 : 00 p.M.

To determine how much time Emma will have between the time that her mom gets home from work and the beginning of gymnastics lessons, we simply subtract 5:22 from 6.

$\left\begin{array}{ccccc}&6&:&00 &p.m.\\-&5&:&22&\\--&--&--&--&--\\&00&:&40&\end{array}\right$

Emma will have 40 Minutes.

5 0

2 years ago

In January of 2003(group 1), 1188 out of 1500 spots were bare ground (no vegetation). Find the sample proportion of bare ground

Nikitich [7]

Answer:

$n= 1500$ represent the random sample selected

$X= 1188$ represent the number of pots that were bare ground (no vegetation

$\hat p=\frac{X}{n}$

And replacing we got:

$\hat p=\frac{1188}{1500}= 0.792$

So then the sample proportion of bare ground spots is 0.792 for this sample

Step-by-step explanation:

We have the following info given from the problem:

$n= 1500$ represent the random sample selected

$X= 1188$ represent the number of pots that were bare ground (no vegetation)

And for this case if we want to find the sample proportion of bare ground spots we can use this formula:

$\hat p=\frac{X}{n}$

And replacing we got:

$\hat p=\frac{1188}{1500}= 0.792$

So then the sample proportion of bare ground spots is 0.792 for this sample

7 0

2 years ago

Write three numerical expressions that are equivalent to (0.0004) . (0.005)

yKpoI14uk [10]

The three equivalent numerical expressions are:

$(0.0004) . (0.005) = (\frac{4}{10000}).(\frac{5}{1000})$

$(0.0004) . (0.005)= (\frac{1}{2500}).(\frac{1}{200})$

$(0.0004) . (0.005) = (4 \times 10^{-4}).(5 \times 10^{-3})$

Solution:

We have to write three numerical expressions that are equivalent to (0.0004) . (0.005)

Given expression is:

(0.0004) . (0.005)

First numerical expression:

We know that 0.0004 can be written in fraction as:

$0.0004 = \frac{0.0004 \times 10000}{10000} = \frac{4}{10000}$

Similarly,

$0.005 = \frac{0.005 \times 1000}{1000} = \frac{5}{1000}$

Therefore,

$(0.0004) . (0.005) = (\frac{4}{10000}).(\frac{5}{1000})$

Second numerical expression:

The first numerical expression can be simplified to get second numerical expression

$(\frac{4}{10000}).(\frac{5}{1000}) = (\frac{1}{2500}).(\frac{1}{200})$

Third numerical expression:

The given expression can be expressed in scientific notation:

Steps for converting to scientific notation:

Move the decimal point in your number until there is only one non-zero digit to the left of the decimal point. The resulting decimal number is a.

Count how many places you moved the decimal point. This number is b.

If you moved the decimal to the left b is positive.

If you moved the decimal to the right b is negative.

If you did not need to move the decimal b = 0.

Write your scientific notation number as a x 10^b and read it as "a times 10 to the power of b."

Remove trailing 0's only if they were originally to the left of the decimal point.

$0.0004 = 4 \times 10^{-4}\\\\0.005 = 5 \times 10^{-3}$

Therefore, third equivalent numerical expression is:

$(0.0004) . (0.005) = (4 \times 10^{-4}).(5 \times 10^{-3})$

8 0

2 years ago

A dime has the same value as 10 pennies. Marley brought 290 pennies to the bank. How many dimes did Narley get?

Oxana [17]

The answer is simply 290 pennies divided by 10 pennies per dime. The answer is 29 dimes.

5 0

2 years ago

What is the ninth term in the binomial expansion of (X-2y)^13?

vlada-n [284]

Answer:

$329472\cdot x^5\cdot y^8$

Explanation:

Binomial expansion is:

$(a+b)^n=a^n+n\cdot a^{n-1}{\cdot b}+\frac{n(n-1)}{2}\cdot a^{n-2}\cdot b^2+------+b^n$

Here in given expression we have a=x , b=-2y and n = 13

general formula for binomial expansion is:

$T_{r+1} =^nC_r\cdot a^{n-r}\cdot b^r$

Since, $T_{r+1}$

r should be one number less than the term we need to find so it will become the number we need to find like here we have to find 9th term so, r=8

substituting the values in the genral formula we will get

$^13C_8\cdot x^{13-8}\cdot (-2y)^8$

After substituting the values we will get

$\frac{13!}{8!\cdot 5!}\cdot x^5\cdot (-2y)^8}$

After simplification we will get

$329472\cdot x^5\cdot y^8$ which will be the 9th term of the expansion

5 0

2 years ago

Read 2 more answers