4x – 7y + 3z - 10<br><br> What's the coefficient of the 2nd term?

A rectangle is formed by placing two identical squares side by side

julsineya [31]

Answer:

200

Step-by-step explanation:

If there are 2 squares next to eachother with the same area, then their perimeter is 6*sidelength.

60 = 6*sidelength

10 = sidelength

Square the sidelength to find the area of the square. 10^2 = 100

Multiply that by 2 to find the area of the rectangle. 100*2 =

200

4 0

3 years ago

To solve y and x, I am adding a picture

Viktor [21]

Answer:

$x =\sqrt 5$

$y = \sqrt{5$

Step-by-step explanation:

Given

The attached triangle

Required

Solve for x

Considering angle 45 degrees, we have:

$\cos(45) = \frac{y}{\sqrt{10}}$ --- cosine formula i.e. adj/hyp

Solve for y

$y = \sqrt{10} * \cos(45)$

In radical form, we have:

$y = \sqrt{10} * \frac{1}{\sqrt 2}$

$y = \sqrt{10/2}$

$y = \sqrt{5$

To solve for x, we make use of Pythagoras theorem

$x^2 + y^2 = (\sqrt{10})^2$

$x^2 + y^2 =10$

Substitute for y

$x^2 + (\sqrt 5)^2 =10$

$x^2 + 5 =10$

Collect like terms

$x^2 =10-5$

$x^2= 5$

Solve for x

$x =\sqrt 5$

4 0

3 years ago

(2tens1one) times 10

Elodia [21]

Answer:

210

Step-by-step explanation:

10+10+1=21

21 x 10=210

6 0

3 years ago

What is the circumference of a circle that's radius is 6.3

77julia77 [94]

39.58 and this is because the radius is half of the diameter so the diameter can be though of as 2r. The formula is C= 2pi r

7 0

2 years ago

Read 2 more answers

Simplify this please

Ugo [173]

Answer:

$\frac{12q^{\frac{7}{3}}}{p^{3}}$

Step-by-step explanation:

Here are some rules you need to simplify this expression:

Distribute exponents: When you raise an exponent to another exponent, you multiply the exponents together. This includes exponents that are fractions. $(a^{x})^{n} = a^{xn}$

Negative exponent rule: When an exponent is negative, you can make it positive by making the base a fraction. When the number is apart of a bigger fraction, you can move it to the other side (top/bottom). $a^{-x} = \frac{1}{a^{x}}$ , and to help with this question: $\frac{a^{-x}b}{1} = \frac{b}{a^{x}}$ .

Multiplying exponents with same base: When exponential numbers have the same base, you can combine them by adding their exponents together. $(a^{x})(a^{y}) = a^{x+y}$

Dividing exponents with same base: When exponential numbers have the same base, you can combine them by subtracting the exponents. $\frac{a^{x}}{a^{y}} = a^{x-y}$

Fractional exponents as a radical: When a number has an exponent that is a fraction, the numerator can remain the exponent, and the denominator becomes the index (example, index here ∛ is 3). $a^{\frac{m}{n}} = \sqrt[n]{a^{m}} = (\sqrt[n]{a})^{m}$

$\frac{(8p^{-6} q^{3})^{2/3}}{(27p^{3}q)^{-1/3}}$ Distribute exponent

$=\frac{8^{(2/3)}p^{(-6*2/3)}q^{(3*2/3)}}{27^{(-1/3)}p^{(3*-1/3)}q^{(-1/3)}}$ Simplify each exponent by multiplying

$=\frac{8^{(2/3)}p^{(-4)}q^{(2)}}{27^{(-1/3)}p^{(-1)}q^{(-1/3)}}$ Negative exponent rule

$=\frac{8^{(2/3)}q^{(2)}27^{(1/3)}p^{(1)}q^{(1/3)}}{p^{(4)}}$ Combine the like terms in the numerator with the base "q"

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)}q^{(1/3)}}{p^{(4)}}$ Rearranged for you to see the like terms

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)+(1/3)}}{p^{(4)}}$ Multiplying exponents with same base

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(7/3)}}{p^{(4)}}$ 2 + 1/3 = 7/3

$=\frac{\sqrt[3]{8^{2}}\sqrt[3]{27}p\sqrt[3]{q^{7}}}{p^{4}}$ Fractional exponents as radical form

$=\frac{(\sqrt[3]{64})(3)(p)(q^{\frac{7}{3}})}{p^{4}}$ Simplified cubes. Wrote brackets to lessen confusion. Notice the radical of a variable can't be simplified.