Pls if you can answer it :)

Find value of x for 7(3x+4)+2=156

mr_godi [17]

21x + 28 = 156 - 2
21x = 154 - 28
21x/21 = 126/21
X = 6

4 0

3 years ago

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ABCD is a trapezoid. What is the area of trapezoid?

lana [24]

Let h represent the height of the trapezoid, the perpendicular distance between AB and DC. Then the area of the trapezoid is
Area = (1/2)(AB + DC)·h
We are given a relationship between AB and DC, so we can write
Area = (1/2)(AB + AB/4)·h = (5/8)AB·h

The given dimensions let us determine the area of ∆BCE to be
Area ∆BCE = (1/2)(5 cm)(12 cm) = 30 cm²

The total area of the trapezoid is also the sum of the areas ...
Area = Area ∆BCE + Area ∆ABE + Area ∆DCE
Since AE = 1/3(AD), the perpendicular distance from E to AB will be h/3. The areas of the two smaller triangles can be computed as
Area ∆ABE = (1/2)(AB)·h/3 = (1/6)AB·h
Area ∆DCE = (1/2)(DC)·(2/3)h = (1/2)(AB/4)·(2/3)h = (1/12)AB·h

Putting all of the above into the equation for the total area of the trapezoid, we have
Area = (5/8)AB·h = 30 cm² + (1/6)AB·h + (1/12)AB·h
(5/8 -1/6 -1/12)AB·h = 30 cm²
AB·h = (30 cm²)/(3/8) = 80 cm²

Then the area of the trapezoid is
Area = (5/8)AB·h = (5/8)·80 cm² = 50 cm²

6 0

3 years ago

Can someone help me with this in a scientific notation

Leviafan [203]

Answer:

3.762 x 10^-7

Step-by-step explanation:

Alright this has the same exact concept as other scientific notation problems.

First, multiply your first numbers: 4.18 x 9 = 37.62

Next, we add our powers together -4 +-4 = -8 (can also be read as -4 - 4 = -8)

We now have 37.62 x 10^-8

Wait! This isn't in scientific notation.

Taking a closer look at this we see 37.62 x 10^-8 can be adjusted by moving the decimal over to the left. Scientific notation must be in simplest form with only one number on the left of the decimal. This gives up 3.762.

Now we need to adjust our notation. Since we moved the decimal over one we are adding one more power to our problem.

Our current power of -8 is now adding a power due to moving the decimal place over one unit to the left. This is equivalent to saying -8 + 1 which equals -7. Now that we fixed our powers, we can put our equation back together for our final answer

3.762 x 10^-7

6 0

3 years ago

A rectangular poster is to contain 882 square inches of print. The margins at the top and bottom of the poster are to be 2 inche

Zinaida [17]

Answer:

L = 23 in

h = 46 in

Step-by-step explanation:

Let call " x " and " y " dimensions of the print area of the poster then:

882 = x*y and y = 882/x

We also know that dimensions of the poster is:

L = x + 2 in and h = y + 4 in

Therefore area of the poster is:

A(p) = ( x + 2 ) * ( y + 4 ) And area as function of x is:

A(x) = ( x + 2 ) * ( 882/x + 4 )

A(x) = 882 + 4*x + 1764 /x + 8

Taking derivatives on both sides of the equation we have:

A´(x) = 4 - 1764/x²

A´(x) = 0 ⇒ 4 - 1764/x² = 0 ⇒ 4*x² - 1764 = 0

x² = 1764 / 4

x² = 441

x = 21 in and y = 882/x y = 42

The second derivative A´´(x) is > 0 ( the second term changes its sign to +) there is a minimum for the function at the point x = 21

As x and y are dimensions of the printing area of the poster, dimensions of the poster are

L = x + 2 = 21 + 2 = 23 in and

h = y + 4 = 42 + 4 = 46 in

4 0

3 years ago

Which of the following is NOT a rational number?

makvit [3.9K]

Answer:

A rational number is a number that can be expressed as a fraction (the ratio of two integers).

Integer: A whole number that can be positive, negative, or zero.

To calculate if each radical can be expressed as a rational number, convert the decimals into rational numbers, then simplify:

$\sqrt{121}=\sqrt{11^2}=11=\dfrac{11}{1} \quad \leftarrow \textsf{rational}$

$\sqrt{12.1}=\sqrt{\dfrac{1210}{100}}=\dfrac{\sqrt{1210}}{\sqrt{100}}=\dfrac{\sqrt{121\cdot 10}}{10}=\dfrac{\sqrt{121}\sqrt{10}}{10}=\dfrac{11\sqrt{10}}{10} \leftarrow \textsf{not rational}$

$\sqrt{1.21}=\sqrt{\dfrac{121}{100}}=\dfrac{\sqrt{121}}{\sqrt{100}}=\dfrac{\sqrt{11^2}}{\sqrt{10^2}}=\dfrac{11}{10} \leftarrow \textsf{rational}$

$\sqrt{0.0121}=\sqrt{\dfrac{121}{10000}}=\dfrac{\sqrt{121}}{\sqrt{10000}}=\dfrac{\sqrt{11^2}}{\sqrt{100^2}}=\dfrac{11}{100} \leftarrow \textsf{rational}$

Therefore, $\sf \sqrt{12.1}$ is not a rational number.

5 0

2 years ago