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2 years ago

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Zachary’s final project for college course took a semester to write and had 95,234 words.zachary wrote 35,295 words the first mo

nth and 19,240 words the second month.

1 answer:

kap26 [50]2 years ago

5 0

Answer:

40,999

Step-by-step explanation:

95,234-35,295= 59,939 and then 59,939-19,240= 40,999

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Isaac is purchasing two pairs of shoes—one pair for $37.00 and the second pair for $42.00. The state sales tax applied to Isaac’

Nadusha1986 [10]

Answer:

Isaac's total bill is $84.53

Step-by-step explanation:

$37.00 + $42.00 = $79.00 < <em>b</em> (bill)

<em>b</em> + <em>t</em> (sales tax) = <em>c</em> (total cost)

(7%/100 = 0.07)

(0.07 * 79 = 5.53)

(<em>t</em> = $5.53)

$79.00 + $5.53 = $84.53

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1 year ago

The square of a number decreased by 3 times the number 28 find all possible values for the number

stealth61 [152]

Question:

The square of a number decreased by 3 times the number is 28 find all possible values for the number

Answer:

The possible values of number are 7 and -4

Solution:

Given that the square of a number decreased by 3 times the number is 28

To find: all possible values of number

Let "a" be the unknown number

From given information,

square of a number decreased by 3 times the number = 28

$a^2 - 3a = 28$

$a^2 - 3a - 28 = 0$

Let us solve the above quadratic equation

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0$

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Using the above formula,

$\text { For } a^{2}-3 a-28=0 \text { we have } a=1, b=-3, c=-28$

$\begin{aligned}&a=\frac{-(-3) \pm \sqrt{(-3)^{2}-4(1)(-28)}}{2 \times 1}\\\\&a=\frac{3 \pm \sqrt{9+112}}{2}\\\\&a=\frac{3 \pm \sqrt{121}}{2}=\frac{3 \pm 11}{2}\\\\&a=\frac{3+11}{2} \text { or } a=\frac{3-11}{2}\\\\&a=7 \text { or } a=-4\end{aligned}$

Thus the possible values of number are 7 and -4

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2 years ago

What are the factors of the polynomial function? Use the rational root theorem to determine the factors. f(x) = 2x³ + x² - 8x -

fredd [130]

Answer:

( x + 2 ) ( x - 2 ) ( 2x + 1)

Step-by-step explanation:

coefficient of x³ is 2 and denote it with q and denote -4 as p

the set of possible rational roots through rational theorem will be within ± (p/q)

now factors of -4 are ±(1,2,4) and factors of 2 are ± (1,2) the possible rational roots are ± ( 1/1, 1/2, 2/1, 2/2, 4/1, 4/2) which reduces to ± (1, 1/2, 2, 4)

substitute each of the value into the equation

f(x) = 2x³ + x² - 8x - 4 to the root ( that gives f(x) = 0)

the equation can be made easy writing it in reduced form

2x³ + x² - 8x - 4

(2x³ + x²) - (8x + 4)

x² (2x + 1) - 4 (2x + 1)

(x² - 4) (2x + 1)

( x + 2 ) ( x - 2) ( 2x + 1) are the factors which correspond to 2, -2, -1/2 roots

4 0

2 years ago

There are 527 pencils 646 erasers 748 sharpeners there are to be put in seperate packets containing the same number of items fin

blsea [12.9K]

Step 1

<u>Find the Greatest Common Factor (GCF)</u>

the prime factorization of each number is equal to

$527=17*31\\ 646=2*17*19\\ 748=2^{2} *11*17$

The GCF is 17

That means that the maximum number of packets is 17 and the maximum number of the items possible in each packet is

Number of pencils=527/17=31 pencils in each packet

Number of erasers=646/17=38 erasers in each packet

Number of sharpeners=748/17=44 sharpeners in each packet

7 0

2 years ago