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2 years ago

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Ashad is rewriting the expression 28 a + 36 a b as a product. Which statements about the expression are accurate and relevant to

his rewriting the expression? Select three options. The GCF of the numbers in each term in the expression is 2. The GCF of the numbers in each term in the expression is 4. The GCF of the variables in each term in the expression is a. The factored form of the expression is 2 a (14 a + 18 a b). The factored form of the expression is 4 a (7 + 9 b)

1 answer:

Gala2k [10]2 years ago

8 0

Answer:

(B)The GCF of the numbers(28 and 36) in each term in the expression is 4.

(C)The GCF of the variables(a and ab) in each term in the expression is a.

(E)The factored form of the expression is 4a(7+9b)

Step-by-step explanation:

Given the expression: $28a+36ab$

If we write it as a product, we obtain:

$28a+36ab=4a(7+9b)$

We can see the following

The GCF of the numbers(28 and 36) in each term in the expression is 4.
The GCF of the variables(a and ab) in each term in the expression is a.
The factored form of the expression is 4a(7+9b)

The correct options are B, C, and E.

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Two forces, F1 and F2, are represented by vectors with initial points that are at the origin. The first force has a magnitude of

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Answer:

Step-by-step explanation:

The two force F1 and F2 are represented by vectors with initial points that are at the origin.

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Therefore, the direction of the vector force is

$v_1=(1-0)\hat i+(1-0)\hat j +(0-0)\hat k\\\\=1\hat i+1\hat j+0\hat k\\\\=\hat i + \hat j$

The unit vector in the direction of force will be

$\frac{v_1}{|v_1|} =\frac{\hat i+ \hat j}{\sqrt{1^2+1^2+0^2} } \\\\=\frac{1}{\sqrt{2} (\hat i +\hat j)}$

The magnitude of the force is 40lb, so the force will be

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The terminal point of its vector is point Q(0, 1, 1)

Therefore, the direction of the vector force is

$v_2=(0-0)\hat i+(1-0)\hat j +(1-0)\hat k\\\\=0\hat i+1\hat j+1\hat k\\\\=\hat j + \hat k$

$\frac{v_2}{|v_2|} =\frac{\hat j+ \hat k}{\sqrt{0^2+1^2+1^2} } \\\\=\frac{1}{\sqrt{2} (\hat j +\hat k)}$

The magnitude of the force is 60lb, so the force will be

$F_2=60\times \frac{1}{\sqrt{2} } (\hat j+\hat k)\\\\=30\sqrt{2} (\hat j+\hat k)$

The resultant of the two forces is

$F=F_1+F_2\\\\=[20\sqrt{2} (\hat i+\hat j)]+[30\sqrt{2} (\hat j +\hat k)]\\\\=20\sqrt{2} \hat i+20\sqrt{2} \hat j +30\sqrt{2} \hat j+30\sqrt{2} \hat k\\\\=20\sqrt{2} \hat i+50\sqrt{2} \hat j+30\sqrt{2} \hat k$

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$|F|=\sqrt{(20\sqrt{2} )^2+(50\sqrt{2} )^2+(30\sqrt{2} )^2} \\\\=\sqrt{800+5000+1800} \\\\=\sqrt{3100} \\\\=55.68$

to (1 decimal place)=55.7lb

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$\alpha=\cos^{-1}(\frac{20\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.5080)\\\\=59.469$

The angle formed by F and y axis

$\alpha=\cos^{-1}(\frac{50\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(1.270)\\\\=$

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1 year ago

Jalen inherited a collection of vintage comic books. An appraiser separated the comic

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Jalen has total 63 comic books.

Step-by-step explanation:

Given,

Total value of comic books = $3135

Let,

Number of $45 comic books = x

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According to given statement;

45x+65y=3135 Eqn 1

x=y+33 Eqn 2

Putting value of x from Eqn 2 in Eqn 1

$45(y+33)+65y=3135\\45y+1485+65y=3135\\110y=3135-1485\\110y=1650\\$

Dividing both sides by 110

$\frac{110y}{110}=\frac{1650}{110}\\y=15$

Putting y=15 in Eqn 2

$x=15+33\\x=48$

Total comic books = x+y

Total comic books = 48+15 = 63

Jalen has total 63 comic books.

Keywords: addition, elimination method

Learn more about elimination method at:

#LearnwithBrainly

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1 year ago

A hospital bill is estimated to be $462.00. It ends up actually costing the patient $525.00. What is the percent error in the bi

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In order to find the percent error, we need to first find the difference between what was expected and what is actually costed. We do this by subtracting:

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So now we know that the expected amount was off by $63. To find the percent error, we need to take this $63, and divide it by the amount that was estimated. Let's do that now:

$\frac{63}{462}=0.1364$

However this is in decimal form. We need to multiply by 100 in order to get it in a percent:

$0.1364*100=13.64%$

Now we know that the percent error of the hospital bill estimate is 13.64%.

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1 year ago

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Place value is the value each digit has in its position: in order from higher to lower value, there is thousands, hundreds, tens, and ones.
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1 year ago

A researcher evaluates the significance of a multiple-regression equation and obtains an F-ratio with df = 2,24. How many partic

alisha [4.7K]

Answer:

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Step-by-step explanation:

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If we assume that we have $k$ independent variables and we have $j=1,\dots,j$ individuals, we can define the following formulas of variation:

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And we have this property

$SST=SS_{regression}+SS_{error}$

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And the total degrees of freedom would be $df=N-1=27 -1 =26$

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1 year ago