What is the values of x and y? (5x) + (9y)

Choose the phrase that best describes the matrix

lions [1.4K]

Answer:

coefficent matrix

Step-by-step explanation:

P. 366

"If the column of constant terms is not included, the matrix reduces to that of the coefficent matrix of the system"

-1 -3 -1

9 -9 -1

-1 -3 4

7 0

3 years ago

Read 2 more answers

Find the solution of the given initial value problem in explicit form. y′=(1−5x)y2, y(0)=−12 Enclose numerators and denominators

Nata [24]

Answer:

The solution is $y=-\frac{12}{12x-30x^2+1}$ .

Step-by-step explanation:

A first order differential equation $y'=f(x,y)$ is called a separable equation if the function $f(x,y)$ can be factored into the product of two functions of $x$ and $y$ :

$f(x,y)=p(x)h(y)$

where $p(x)$ and $h(y)$ are continuous functions.

We have the following differential equation

$y'=(1-5x)y^2, \quad y(0)=-12$

In the given case $p(x)=1-5x$ and $h(y)=y^2$ .

We divide the equation by $h(y)$ and move $dx$ to the right side:

$\frac{1}{y^2}dy\:=(1-5x)dx$

Next, integrate both sides:

$\int \frac{1}{y^2}dy\:=\int(1-5x)dx\\\\-\frac{1}{y}=x-\frac{5x^2}{2}+C$

Now, we solve for $y$

$-\frac{1}{y}=x-\frac{5x^2}{2}+C\\-\frac{1}{y}\cdot \:2y=x\cdot \:2y-\frac{5x^2}{2}\cdot \:2y+C\cdot \:2y\\-2=2yx-5yx^2+2Cy\\y\left(2x-5x^2+2C\right)=-2\\\\y=-\frac{2}{2x-5x^2+2C}$

We use the initial condition $y(0)=-12$ to find the value of C.

$-12=-\frac{2}{2\left(0\right)-5\left(0\right)^2+2C}\\-12=-\frac{1}{c}\\c=\frac{1}{12}$

Therefore,

$y=-\frac{2}{2x-5x^2+2(\frac{1}{12})}\\y=-\frac{12}{12x-30x^2+1}$

4 0

3 years ago

Choose the congruence theorem that you would use to prove the triangles congruent.

Elena L [17]

Answer:

SAS

Explanation:

Before solving the problem, let's define each of the given theorems:

1- SSS (side-side-side): This theorem is valid when the three sides of the first triangle are congruent to the corresponding three sides in the second triangle

2- SAS (side-angle-side): This theorem is valid when two sides and the included angle between them in the first triangle are congruent to the corresponding two sides and the included angle between them in the second triangle

3- ASA (angle-side-angle): This theorem is valid when two angles and the included side between them in the first triangle are congruent to the corresponding two angles and the included side between them in the second triangle

4- AAS (angle-angle-side): This theorem is valid when two angles and a side that is not included between them in the first triangle are congruent to the corresponding two angles and a side that is not included between them in the second triangle

Now, let's check the given triangles:

We can note that the two sides and the included angle between them in the first triangle are congruent to the corresponding two sides and the included angle between them in the second triangle

This means that the two triangles are congruent by SAS theorem

Hope this helps :)

5 0

3 years ago

Read 2 more answers

D3 Find two numbers between 100 and 150 that have a HCF of 22.

vesna_86 [32]

The first two numbers between 100 and 150 that have a HCF of 22 are 110 and 132

<h3>Highest common factors</h3>

The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

According to the question, we are to find two numbers between 100 and

150 that have a HCF of 22.

In order to do that we will multiply 22 by the values 5 and 6

First number = 22 * 5 = 10

Second number = 22 * 6 = 132

Hence the first two numbers between 100 and 150 that have a HCF of 22 are 110 and 132

Learn more on HCF here; brainly.com/question/21504246

#SPJ1

4 0

1 year ago

How many corners does a cube have? how many faces does a cube have? how many other cubes would share a given corner atom or face

andreev551 [17]

How many corners does a cube have?
A cube is a 3-dimensional solid figure made by square faces. It would have 8 corners which connects the faces of the cube.

how many faces does a cube have?
There would be 6 faces in a cube

how many other cubes would share a given corner atom or face atom if several cubes were stacked side-to-side, front-to-back, and top-to-bottom?

If several of these cubes are being stacked side-to-side, front-to-back, and top-to-bottom, each corner would share a total of eight cubes. All of the corners would share a different cube. We have eight corners thus eight cubes.

7 0

3 years ago