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3 years ago

Solve the inequality for x. - 2 x - 10 ≥ 4

Mathematics

1 answer:

Inga [223]3 years ago

6 0

Answer:

x ≤ -7

Step-by-step explanation

<em>the steps to solve this are:</em>

1. Add 10 to both sides to get the x value and constant isolated on both sides.

-2x ≥ 14

2. Divide both sides by -2 to get the x value

x ≥ -7

3. Flip the inequality sign since you divided by a negative x-value.

x ≤ -7

Hope i could help! :)

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3 years ago

You order seventeen burritos to go from a Mexican restaurant, seven with hot peppers and ten without. However, the restaurant fo

Kisachek [45]

Answer:

$P=0.369$

Step-by-step explanation:

In this binomial probability case, the success is to pick a burrito with hot peppers, there are 7 out of 17, the probability is p=7/17=0.4118. The formula is

$P=_nC_kp^k(1-p)^{n-k}$

Where n is the number of burritos taken at random, k is the number of success (burrito with hot peppers), p is the probability of success. $_nC_k$ denotes the number of combinations and its formula is:

$_nC_k=\frac{n!}{k!(n-k)!}$

At least two burritos have hot peppers means having two or three burritos, these two cases are calculated and sum to get the probability of at least two burritos that have hot peppers.

$P=_nC_kp^k(1-p)^{n-k}=\frac{n!}{k!(n-k)!}p^k(1-p)^{n-k}$

$P_2=\frac{3!}{2!(3-2)!}(0.4118)^2(1-0.4118)^{3-2}=\frac{3\times2!}{2!1!} (0.1696)(0.5882)^1\\P_2=3 (0.1696)(0.5882)=0.2993$

$P_2=\frac{3!}{3!(3-3)!}(0.4118)^3(1-0.4118)^{3-3}=\frac{1}{0!} (0.0698)(0.5882)^0\\P_2=1 (0.0698)(1)=0.0698$

$P=P_2+P_3=0.2993+0.0698=0.3691$

Round to three decimal places: P=0.369

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4 years ago

Using interval notation , identify the domain for the function!!! Math 3 - 10 points. Help needed

In-s [12.5K]

Answer:

The domain by the interval notation is (-∞ , 3)∪(3 , 4)∪(4 , ∞) ⇒ 3rd answer

Step-by-step explanation:

* Lets revise how to find the domain of the function

- The domain is all values of x that make the expression defined

- To find where the expression is undefined put the denominator

equal 0, to get the values of x which make denominator equal to 0

- The domain will be all the real number except those values

* Now lets solve the problem

∵ f(x) = (x² - 9)/(x² - 7x + 12)

- Let the denominator x² − 7x + 12 equal to 0

∵ x² − 7x + 12 = 0 ⇒ factorize it

- Consider the form x² + bx + c

- Find a pair of integers whose product is c and whose sum is b

- In this case, whose product is 12 and whose sum is −7

- They are -3 and -4

- Write the factored form using these integers.

∴ (x -3)(x - 4) = 0 ⇒ put each bracket = 0

∴ x - 3 = 0 or x - 4 = 0

∵ x - 3 = 0 ⇒ add 3 to both sides

∴ x = 3

∵ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

∴ The domain of f(x) is all real number except 3 and 4

* The domain by the interval notation is

(-∞ , 3)∪(3 , 4)∪(4 , ∞)

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3 years ago

The height of a triangle is 4 inches. Greater than twice it's base. The area of the triangle is no more than 168 in.². Which any

mestny [16]

Step-by-step explanation:

this problem seeks to test our knowledge on word problems and algebra

<u>Solution</u>

let the base be x, and

the height h = 2x+4

We know that area of a triangle is given as

$A= \frac{1}{2} b*h$

substituting our given values we have

$168= \frac{1}{2} x*(2x+4)\\\\168= \frac{2x^2+4x}{2} \\\\168= x^2+2x\\\\$

re-arranging we have

$x^2+2x-168=0\\\\$

we can now find two factors that will add up to give 2 and multiply to give -168

they are 14 and -12

$x^2-14x+12x-168=0\\\\x(x-14)+12(x- 14)=0\\\\x+12=0\\\\x=-12\\\\x-14=0\\\\x=14$

The possible base of the triangle is 14 in

and the height is

$h= 2x+4\\\\h=2(14)+4\\\\h= 28+4\\\\\h= 32 in$

7 0

3 years ago