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3 years ago

5

in order to enter the state fair, there is an admission cost. Each game is $3. Steven went to the state fair, played 4 games and

spent a total of $20 of admissions and games

1 answer:

Gennadij [26K]3 years ago

3 0

Answer:

$8

Step-by-step explanation:

Since he used $20

Each game cost $3 and he played 4 games (So 3 x 4 = 12)

20 - 12 = 8

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A) by completing the square find in the form of the constant p the roots of the equation x^2+px+4=0

iris [78.8K]

Answer:

<em>a) </em>

<em /> $\displaystyle x=-\frac{1}{2}p\pm\sqrt{\frac{1}{4}p^2-4}$ <em />

<em>b) p is in the interval (-4,4)</em>

Step-by-step explanation:

<u>Quadratic Equation</u>

It's given the following quadratic equation:

$x^2+px+4=0$

a)

It's required to complete squares and find the roots. This can be done by recalling the polynomial identity:

$a^2+2ab+b^2=(a+b)^2$

We already have the first term squared, and we need to find the second term. Rewriting the equation:

$\displaystyle x^2+2(\frac{1}{2}px)+4=0$

The second term of the binomial is 1/2p, thus completing the squares with $b^2$ :

$\displaystyle x^2+2(\frac{1}{2}px)+\left(\frac{1}{2}p\right)^2+4-\left(\frac{1}{2}p\right)^2=0$

Factoring:

$\displaystyle \left(x+\frac{1}{2}p\right)^2+4-\frac{1}{4}p^2=0$

Moving the independent term to the right side:

$\displaystyle \left(x+\frac{1}{2}p\right)^2=\frac{1}{4}p^2-4$

Taking the square root:

$\displaystyle x+\frac{1}{2}p=\pm\sqrt{\frac{1}{4}p^2-4}$

Solving for x:

$\displaystyle x=-\frac{1}{2}p\pm\sqrt{\frac{1}{4}p^2-4}$

b) If the equation won't have real roots, then the radicand should be negative:

$\displaystyle \frac{1}{4}p^2-4$

Factoring:

$\displaystyle \left(\frac{1}{2}p-2\right)\left(\frac{1}{2}p+2\right)$

The zeros of the left-side polynomial are:

$\displaystyle \frac{1}{2}p-2=0$

$\displaystyle \frac{1}{2}p=2$

p = 4

$\displaystyle \frac{1}{2}p+2=0$

$\displaystyle \frac{1}{2}p=-2$

p = -4

The inequality:

$\displaystyle \left(\frac{1}{2}p-2\right)\left(\frac{1}{2}p+2\right)$

Is satisfied for values of p in the interval (-4,4)

5 0

3 years ago

5% of 400 grams..........

Elanso [62]

Just do a proportion. 5%= 5/100, 400= x/400, Do 5 x 400= 2000, 2000 divided by 100 is 20. Your answer is 20 grams

7 0

4 years ago

Consider the linear expression and a first step of simplification shown below.

wlad13 [49]

Answer:

Commutative Property

Step-by-step explanation:

From step 1 to step 2, we are changing the order, that means we are using the Commutative Property. The Commutative Property means to move around, or a+b = b+a

6 0

3 years ago

quester [9]

Answer:

1030 Smart TV's are in Picayune this year.

Step-by-step explanation:

25% of 824 is 206

800 ÷4=200

24÷4+6

For 206, then add that to the total, since it is a 25% increase, not just what that 25% is

5 0

3 years ago

Two trains leave the station at the same time, one heading west and the other east. The westbound train travels 20 miles per hou

zavuch27 [327]

2 (x-20)+2x=38
4x-40=380
4x=420
x=150

The train is 130mph.

4 0

4 years ago