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3 years ago

6x+3<7-2x I’m not sure if I’m doing it right so an explanation would be nice

Mathematics

1 answer:

enot [183]3 years ago

7 0

Answer:

x<0.5

Step-by-step explanation:

this is just like simplifiying equations if you've done that before

first you want to isolate the variable, so you want to combine the values of x (in this case it's 6x and the -2x)

so you can either add 2x to both sides or you can subtract 6x on both sides, in this case ill just add 2x to both sides.

Then you subtract 3 from both sides to get 8x<4

after you get that, you want to divide both sides by 8, and you generally want to do that step last, it makes it easier, and you get x<1/2 or 0.5

just a reminder that with working with inequalities, you want to remember to flip the direction the inequality is whenever you divide by a negative number

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Solve the inequality 4t^2 ≤ 9t-2 please show steps and interval notation. thank you!

Misha Larkins [42]

Answer:

[0.25, 2]

Step-by-step explanation:

We have

4t² ≤ 9t-2

subtract 9t-2 from both sides to make this a quadratic

4t²-9t+2 ≤ 0

To solve this, we can solve for 4t²-9t+2=0 and do some guess and check to find which values result in the function being less than 0.

4t²-9t+2=0

We can see that -8 and -1 add up to -9, the coefficient of t, and 4 (the coefficient of t²) and 2 multiply to 8, which is also equal to -8 * -1. Therefore, we can write this as

4t²-8t-t+2=0

4t(t-2)-1(t-2)=0

(4t-1)(t-2)=0

Our zeros are thus t=2 and t = 1/4. Using these zeros, we can set up three zones: t < 1/4, 1/4<t<2, and t>2. We can take one random value from each of these zones and see if it fits the criteria of

4t²-9t+2 ≤ 0

For t<1/4, we can plug in 0. 4(0)²-9(0) + 2 = 2 >0 , so this is not correct

For 1/4<t<2, we can plug 1 in. 4(1)²-9(1) +2 = -3 <0, so this is correct

For t > 2, we can plug 5 in. 4(5)²-9(5) + 2 = 57 > 0, so this is not correct.

Therefore, for 4t^2 ≤ 9t-2 , which can also be written as 4t²-9t+2 ≤ 0, when t is between 1/4 and 2, the inequality is correct. Furthermore, as the sides are equal when t= 1/4 and t=2, this can be written as [0.25, 2]

8 0

3 years ago

7. A number of minor automobile accidents occur at various high-risk intersections in Teton County despite traffic lights. The T

Anit [1.1K]

Answer:

Modification has not reduced the number of accidents.

Step-by-step explanation:

$H_0: \mu\geq0\\H_a:\mu$

A B C D E F G H

Before modification 5 7 6 4 8 9 8 10

After modification 3 7 7 0 4 6 8 2

Difference -2 0 1 -4 -4 -3 0 -8

Mean of differences $M_d = \frac{sum}{8}=\frac{2+0-1+4+4+3-0+8}{8}=2.5$

Standard deviation of differences = $\sqrt{\frac{\sum(x-\bar{x})^2}{n}}=2.9277$

Formula of paired t test :

$t=\frac{M_d}{\frac{s}{\sqrt{n}}}\\t=\frac{2.5}{\frac{2.9277}{\sqrt{8}}}\\t = 2.4152$

Df = n-1 = 8-1 =7

$t critical = t_{(df, \alpha)}=t_{7,0.01}=2.998$

t critical> t calculated

So, We failed to reject null hypothesis

Hence modification has not reduced the number of accidents.

6 0

3 years ago

Find FL if H is the circumcenter of EFG,

Zanzabum

The artistic crop isn't helpful; it cuts off some vertex names.

The circumcenter H is the meet of the perpendicular bisectors of the sides, helpfully drawn. We have right triangle ELH, right angle L, so

EH² = HL² + EL²

EL = √(EH² - HL²) = √(5.06²-2.74²) ≈ 4.2539393507665339

Since HL is a perpendicular bisector of EF, we get congruent segments FL=EL.

Answer: 4.25

8 0

3 years ago

Are carpet coast $15 per square metre. The total delivery charge is $21 Peter buys N squared metres of carpet what is the expres

postnew [5]

Answer:

15N + 21

Step-by-step explanation:

We are given that,

Amount of carpet bought by Peter = N meter²

The cost per meter square of the carpet = $15

So, the cost of 'N' meter square of carpet = 15N dollars.

Also, the delivery charge for the carpet = $21

Thus, the total cost of the carpet is given by,

Total cost = Cost per square meter + Delivery charge

i.e. Total cost = 15N + 21 (in dollars).

Hence, the expression representing the cost in dollars is '15N + 21'.

8 0

3 years ago

I cant work this one out, help please

Mashutka [201]

Answer:

a = 8 2/3.

Step-by-step explanation:

The y coordinate of the point is 5, andthe x coordinate is a so substituting for these in the given equation:

3a - 4(5) = 6

3a - 20 = 6

3a = 26

a = 26/3

= 8 2/3

8 0

2 years ago

Read 2 more answers