129,543 rounded to the nearest ten thousand

Factor completely. 4 - 12x + 9x^2

murzikaleks [220]

$4-12x+9x^{2} \\4-6x-6x+9x^{2} \\2(2-3x)-3x(2-3x)\\(2-3x)(2-3x)\\(2-3x)^2$

7 0

3 years ago

Which statement is true?

Nadusha1986 [10]

The correct statement is D.

Step-by-step explanation:

Given,

For backyard

Length = 5x-2

Width = 2x+4

For house

Length = 5x-2

Width = 4x-12

For driveway

Length = x+10

Width = 4x-12

To find the correct statement.

Formula

The area of a rectangle = Length × Width

So,

The area of the house and the driveway = (5x-2)(4x-12) + (x+10)(4x-12)

= (4x-12)(5x-2+x+10)

= (4x-12)(6x+8)

= $24x^{2} +32x-72x-96$

= $24x^{2} -40x-96$

So, the correct statement is D

You can cross check the other statements.

5 0

3 years ago

A building makes a 90° angle with the ground. A ladder leans against the building, making a 110° exterior angle with the ground.

liberstina [14]

Answer:

A building makes a $90^{\circ}$ angle with the ground .The two interior angles are $70^{\circ}$ and $20^{\circ}$

Solution:

Given, a ladder which is against the building wall makes an exterior angle of $110^{\circ}$

And building makes a $90^{\circ}$ angle with the ground.

So, altogether it makes a right angle triangle with ladder as hypotenuse and ground as base leg and building as another leg.

Now, we know that, sum of exterior angles and interior angles equals to $180^{\circ}$

Here, in the case of ground and ladder, exterior angle is $110^{\circ}$ and interior angle is unknown.

Exterior angle + interior angle = 180

110 + interior angle = 180

Interior angle = 180 – 110

Interior angle = $70^{\circ}$

We have found one of the two interior angles of right angle triangle.

We know that, sum of angles in a triangle is 180 degree

Known Interior angle + unknown interior angle + right angle = 180

70 + unknown interior angle + 90 = 180

Unknown interior angle + 160 = 180

Unknown interior angle = 180 - 160

Unknown interior angle = $20^{\circ}$

Hence the two interior angles are $70^{\circ}$ and $20^{\circ}$

7 0

4 years ago

WHAT IS 18 TONS 42 POUNDS DEVIDED BY 3

Alecsey [184]

A ton is 2,000 pounds so multiply 2,000 x 18

2,000 x 18 = 36,000 pounds, now add the 42 pounds to the 36,000

36,000 + 42 = 36,042 pounds. Now divide 36,042 by 3

36,042 ÷ 3 = 12,014

Your answer is 12,014 pounds

If you need your answer in tons it's 6.007 tons

Calculations for pounds to tons

12,014 ÷ 2,000 = 6.007

Hope this helps. :)

4 0

3 years ago

Read 2 more answers

s(t) = 0.29t2 − t + 25 gallons per year (0 ≤ t ≤ 7), where t is time in years since the start of 2007. Use a Riemann sum with n

Sav [38]

Answer: The answer is 300 gallons.

Step-by-step explanation: Riemann sum is a method of calculating the total area under a curve on a graph, which is also known as Integral.

To calculate that area, we divide it into a number of rectangles with one point touching the curve. The curve has a closed interval [a,b] that can be subdivided into n subintervals, each having a width of Δ $x_{k}$ = $\frac{b-a}{n}$

If a function is defined on the closed interval [a,b] and $c_{k}$ is any point in [ $x_{k-1}$ , $x_{k}$ ], then a Riemann Sum is defined as ∑f( $c_{k}$ )Δ $x_{k}$ .

For this question:

Δ $x_{k}$ = $\frac{7-0}{5}$ = 1.4

Now, we have to find s(t) for each valor on the interval:

s(t) = 0.29 $t^{2}$ - t +25

s(0) = 25

s(1) = 24.29

s(2) = 24.16

s(3) = 24.61

s(4) = 25.64

s(5) = 27.25

s(6) = 29.44

s(7) = 32.21

Now, using the formula:

∑f( $c_{k}$ )Δ $x_{k}$ = 1.4(25+24.29+24.16+24.61+25.64+29.44+32.21)

∑f( $c_{k}$ )Δ $x_{k}$ = 1.4(212.6)

∑f( $c_{k}$ )Δ $x_{k}$ ≅ 300

With Riemann Sum, it is estimated the total country's per capita sales of bottled water is 300 gallons.

3 0

3 years ago