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3 years ago

Which point lies on both y=5x−3 and y=−4x+6 ?

Mathematics

1 answer:

AlladinOne [14]3 years ago

6 0

The answer is (1, 2)

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1546:12 = Please pake cara

defon

Answer:

It is a ratio. Is it?

If so, I think the answer is 773 : 6

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3 years ago

How is 3 millionths written in scientific notation

masya89 [10]

3,000,000 = 3 × 1,000,000 = 3 × 106.

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3 years ago

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Find the length of side x simplest radical form with a rational denominator

Nuetrik [128]

Answer:

The length of x in the simplest radical form with a rational denominator will be:

$x=\frac{5\sqrt{3}}{2}$

Step-by-step explanation:

Given

hypotenuse = 5

angle Ф = 60°

To determine

x = ?

Using the trigonometric ratio

cos Ф = adjacent / hypotenuse

here

Ф = 60°

adjacent of 60° = x

hypotenuse = 5

so substituting Ф = 60°, adjacent = x and hypotenuse = 5 in the equation

cos Ф = adjacent / hypotenuse

$cos\:60^{\circ }\:=\:\frac{x}{5}$

$\frac{\sqrt{3}}{2}=\frac{x}{5}$

switch sides

$\frac{x}{5}=\frac{\sqrt{3}}{2}$

Multiply both sides by 5

$\frac{5x}{5}=\frac{5\sqrt{3}}{2}$

Simplify

$x=\frac{5\sqrt{3}}{2}$

Therefore, the length of x in the simplest radical form with a rational denominator will be:

$x=\frac{5\sqrt{3}}{2}$

5 0

3 years ago

A = ???? 4 −2

irinina [24]

Answer:

1. The matrix A isn't the inverse of matrix B.

2. |B|=12, |A|=12

Step-by-step explanation:

1. We want to know if matrix A is the inverse of matrix B, this means that if you do the product between B and A you have to obtain the identity matrix.

We have:

$A=\left[\begin{array}{cc}4&-2\\-1&3\end{array}\right]$

and

$B=\left[\begin{array}{cc}3&2\\1&4\end{array}\right]$

A and B are 2×2 matrices (2 rows and 2 columns), if you multiply them you have to obtain a 2×2 matrix.

Then if A is the inverse of B:

$B.A=I$

Where,

$I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right]$

Observation:

If you have two matrices:

$A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]\\and\\B=\left[\begin{array}{cc}e&f\\g&h\end{array}\right]\\\\\\A.B=\left[\begin{array}{cc}(a.e+b.g)&(a.f+b.h)\\(c.e+d.g)&(c.f+d.h)\end{array}\right]$

Now:

$B.A=\left[\begin{array}{cc}3&2\\1&4\end{array}\right].\left[\begin{array}{cc}4&-2\\-1&3\end{array}\right]\\\\\\B.A=\left[\begin{array}{cc}4.3+(-2).1&4.2+(-2).4\\(-1).3+3.1&(-1).2+3.4\end{array}\right]\\\\\\B.A=\left[\begin{array}{cc}12-2&8-8\\-3+3&-2+12\end{array}\right]\\\\\\B.A=\left[\begin{array}{cc}10&0\\0&10\end{array}\right]$

$B.A=\left[\begin{array}{cc}10&0\\0&10\end{array}\right]\neq \left[\begin{array}{cc}1&0\\0&1\end{array}\right]=I\\\\\\B.A\neq I$

Then, the matrix A isn't the inverse of matrix B.

2. If you have a matrix A:

$A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]$

The determinant of the matrix is:

$|A|=ad-bc$

Then the determinant of B is:

$B=\left[\begin{array}{cc}3&2\\1&4\end{array}\right]$

$a=3, b=2, c=1, d=4$

$|B|=3.4-2.1\\|B|=12-2=10$

The determinant of A is:

$A=\left[\begin{array}{cc}4&-2\\-1&3\end{array}\right]$

$a=4, b=-2, c=-1, d=3$

$|A|=4.3-(-2).(-1)\\|B|=12-2=10$

6 0

4 years ago

Answer this question. please

dimaraw [331]

Answer:

$\boxed{\textsf{ The total surface area of the cuboid is \textbf{62 cm} $\sf ^2$ .}}$

Step-by-step explanation:

Given that the base area of the cuboid is 7cm² . And it's volume is 21cm³ . We need to find its total surface area . Now here we need to find the height . We can find height as ,

Height :-

$\qquad\boxed{\boxed{\sf Height =\dfrac{ Volume}{Area } }}$

$\sf\implies Height =\dfrac{Volume}{Area} \\\\\sf\implies h =\dfrac{ 21cm^3}{7cm^2}\\\\\implies \boxed{ \pink{\frak { Height = 3 cm.}}}$

$\rule{200}2$

Let's find out the Total surface area .

TSA of cuboid :-

$\qquad\boxed{\boxed{\sf TSA_{(cuboid)} =2(lb + bh + hl ) }}$

Put on the respective values :-

$\sf\implies TSA_{(cuboid)}= 2( lb + bh + hl )\\\\\sf\implies TSA_{(cuboid)}= 2( 7cm\times 1cm + 1cm\times 3cm + 3cm \times 7 cm ) \\\\\sf\implies TSA_{(cuboid)}=2 ( 7cm ^2+3cm^2+21cm^2 ) \\\\\sf\implies TSA_{(cuboid)}= 2\times 31cm^2 \\\\\sf\implies \boxed{\pink{\frak{ TSA_{(cuboid)}= 62 cm^2}}}$

3 0

3 years ago

Read 2 more answers