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3 years ago

Simplify the expression

Mathematics

2 answers:

sasho [114]3 years ago

7 0

Answer:

$\frac{(x+1)}{5x}$

Expression:

$\frac{x^{2}-8x-9 }{5x^{2} -45x}$

Factorise the expression:

Numerator:

x^2 - 8 - 9

Find a pair of factors of c, that summed, make b. And decide whether the numbers are positive or negative.

1 * 9 = 9

-1 * 9 = -9

1 * -9 = -9

-1 * -9 = 9

1 + 9 = 10

1 - 9 = -8

-1 + 9 = 8

-1 - 9 = -10

The factors are

(x+1) and (x-9)

Denominator

5x^2 - 45x

Remove the factor here is visible - 5x.

Divide the expression by 5x.

5x(x - 9)

Both expressions have a common factor - (x - 9). This will cancel out.

Now you're left with:

(x+1)/5x

$\frac{(x+1)}{5x}$

mars1129 [50]3 years ago

4 0

Answer:

B but - is missing in the answer

Step-by-step explanation:

x² - 8x - 9

5x² - 45x

express

x × x - 8 × x - 9

5 × x × x - 45 × x

-8 - 9

5 - 45

18 -9 = 1 and 5 - 45 = -40

-1/40

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2 years ago

Drag each object to show whether cost is proportional to area in the situation represented.

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Answer:

see the explanation

Step-by-step explanation:

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A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Verify each case

case 1) Sod that is quoted at a set price per square yard plus a labor fee

The Cost is NOT proportional to Area, because the line don't pass though the origin (the equation has an y-intercept equal to the labor fee)

case 2) Pavers that cost a set amount per square foot

The Cost is Proportional to Area

In this problem the constant of proportionality k is equal to the set amount per square feet

case 3) Hardwood flooring that cost $16 for every 2 square feet

The Cost is Proportional to Area

The constant of proportionality k is equal to

$k=\frac{y}{x}$ ----> $k=\frac{16}{2}=\$8\ per square\ foot$

The linear equation is $y=8x$

case 4) The given graph

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The Cost is Proportional to Area

case 5) The given table

Find the constant of proportionality k for each ordered pair

If all values of k are the same, then the cost is proportional to area

For x=2, y=3,000 -> $k=\frac{y}{x}$ --> $k=\frac{3,000}{2}=1,500$

For x=4, y=4,000 -> $k=\frac{y}{x}$ --> $k=\frac{4,000}{4}=1,000$

For x=6, y=6,000 -> $k=\frac{y}{x}$ --> $k=\frac{6,000}{6}=1,000$

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3 years ago

What substation should be used to rewrite 4x^4-21z^2+20=0

elena-s [515]

\left[x _{4}\right] = \left[ \frac{ - \left( -1\right) ^{\frac{3}{4}}\,\sqrt[4]{\left( 20 - 21\,z^{2}\right) }}{\sqrt[4]{4}}\right][x4]=[4√4−(−1)434√(20−21z2)]
I hope helping with u

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3 years ago

2. A right triangle has a hypotenuse of 15 cm. What are possible lengths for the two legs of the triangle? Explain your reasonin

dolphi86 [110]

Answer:

Two possible lengths for the legs A and B are:

B = 1cm

A = 14.97cm

Or:

B = 9cm

A = 12cm

Step-by-step explanation:

For a triangle rectangle, Pythagorean's theorem says that the sum of the squares of the cathetus is equal to the hypotenuse squared.

Then if the two legs of the triangle are A and B, and the hypotenuse is H, we have:

A^2 + B^2 = H^2

If we know that H = 15cm, then:

A^2 + B^2 = (15cm)^2

Now, let's isolate one of the legs:

A = √( (15cm)^2 - B^2)

Now we can just input different values of B there, and then solve the value for the other leg.

Then if we have:

B = 1cm

A = √( (15cm)^2 - (1cm)^2) = 14.97

Then we could have:

B = 1cm

A = 14.97cm

Now let's try with another value of B:

if B = 9cm, then:

A = √( (15cm)^2 - (9cm)^2) = 12 cm

Then we could have:

B = 9cm

A = 12cm

So we just found two possible lengths for the two legs of the triangle.

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$(x-4) \times\left(x^{2}-7\right)=0$

We know the formula, $a^{2}-b^{2}=(a+b)(a-b)$ , make use of this, we get

$(x-4) \times(x-\sqrt{7}) \times(x+\sqrt{7})=0$

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2 years ago