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Yanka [14]
3 years ago
10

A partial factorization of x2-3x-10 is modeled with algebra tiles

Mathematics
1 answer:
Allushta [10]3 years ago
5 0

X² - 3x - 10


x² = x * x

10 can be factored:

1 x 10 ⇒⇒⇒ difference between factors = 9

2 x 5   ⇒⇒⇒ difference between factors = 3  ⇒ (The correct pair)


(x-5)(x+2) = x(x+2) - 5(x+2)

                = x² + 2x - 5x - 10

                = x² - 3x - 10



∴ x - 5 = 0  ⇒⇒⇒ x = 5

  x + 2 = 0  ⇒⇒⇒ x = -2

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According to company records, 128 of 460 employees purchase health insurance through the company. The chief human resources offi
Doss [256]

Answer:

\dfrac{128}{460}\times 100 \approx \bold{27.83\%}

Step-by-step explanation:

Given that:

Number of employees who purchased health insurance through the company = 128

Total number of employees = 460

To find:

Expression to find out the percentage of employees that purchase health insurance through the company ?

Solution:

Percentage of employees that purchase health insurance through the company:

\dfrac{\text{Number of employees that purchase health insurance through the company}}{\text{Total number of employees}}\times 100

= \dfrac{128}{460}\times 100 \approx \bold{27.83\%}

4 0
3 years ago
Bob and James are finishing the roof of a house. Working alone, Bob can shingle the roof in 14 hours. James can shingle the same
Snowcat [4.5K]

we know that Bob can do the whole job in 14 hours, how much of the work has he done in 1 hour only?  well since he can do the whole lot in 14 hours in 1 hour he has only done 1/14 th of the job.

we know that James can do it in 18 hours, a bit slower, so in 1 hour he has done only 1/18 th of the job.

let's say it takes both of them working together say "t" hours, so in 1 hour Bob has done (1/14) of the work whilst James has done (1/18) of the work, the whole work being t/t or 1 whole, so for just one hour that'd 1/t done by both Bob and James.

\bf \stackrel{Bob}{\cfrac{1}{14}}~~+~~\stackrel{James}{\cfrac{1}{18}}~~=~~\stackrel{total~for~1~hour}{\cfrac{1}{t}} \\\\\\ \stackrel{\textit{using an LCD of 126}}{\cfrac{9+7}{126}=\cfrac{1}{t}}\implies \cfrac{16}{126}=\cfrac{1}{t}\implies 16t=126\implies t=\cfrac{126}{16} \\\\\\ \stackrel{\textit{7 hrs, 52 minutes and 30 seconds}}{t=\cfrac{63}{8}\implies t=7\frac{7}{8}}\implies \stackrel{\textit{rounded up}}{t=7.88}

7 0
3 years ago
Solve the equation, and check the solutions 2(√x+3)=6.
zhannawk [14.2K]

Answer:

x = 0

Step-by-step explanation:

2(\sqrt{x}+3)=6

Expanding the left hand side we get

\Rightarrow 2\sqrt{x}+6=6

Taking 6 from left hand side to right hand side

\Rightarrow 2\sqrt{x}=6-6\\\Rightarrow 2\sqrt{x}=0

Dividing both sides by 2

\Rightarrow \sqrt{x}=\frac{0}{2}\\\Rightarrow \sqrt{x}=0\\\Rightarrow x=0

So, x = 0

4 0
3 years ago
The amount c in grams of a 100 gram sample of carbon-14 remaining after t years is represented by the equation c= 100 (0.99988)t
tigry1 [53]

Answer: The amount of carbon-14 remaining after 4 years is 99.95 grams.

Step-by-step explanation:

Hi, to answer this question we simply have to substitute t=4 in the equation given and solve for c.

c= 100 (0.99988)^t

c =100 (0.99988)^4

c = 100 x 0.999520086

c= 99.95200864 ≅99.95 grams (rounded)

The amount of carbon-14 remaining after 4 years is 99.95 grams.

Feel free to ask for more if needed or if you did not understand something.

8 0
3 years ago
Which is f(-3) for the quadratic function graphed?<br> -9<br> -3<br> 0<br> 9
KATRIN_1 [288]

Answer:

9

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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