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2 years ago

Help fast worth 10points

Mathematics

1 answer:

Nina [5.8K]2 years ago

7 0

Answer:

30 ( I think so)

Step-by-step explanation:

Well, the total measurement 4 a triangle is 90. So 60 and 60 is 120 so it should be 30. If not I am sorry for being wrong.

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Find the quadratic function that fits the following data. which one function fits.

Oksana_A [137]

Answer:

Step-by-step explanation:

The general rule for the quadratic function is

$y=ax^2+bx+c$

Use the data from the table:

$y(50)=130\Rightarrow 130=a\cdot 50^2+b\cdot 50+c\\ \\y(70)=130\Rightarrow 130=a\cdot 70^2+b\cdot 70+c\\ \\y(90)=200\Rightarrow 200=a\cdot 90^2+b\cdot 90+c$

We get the system of three equations:

$\left\{\begin{array}{l}2500a+50b+c=130\\ \\4900a+70b+c=130\\ \\8100a+90b+c=200\end{array}\right.$

Subtract these equations:

$\left\{\begin{array}{l}4900a+70b+c-2500a-50b-c=130-130\\ \\8100a+90b+c-2500a-50b-c=200-130\end{array}\right.\Rightarrow \left\{\begin{array}{l}2400a+20b=0\\ \\5600a+40b=70\end{array}\right.$

From the first equation

$b=-120a$

Substitute it into the second equation:

$5600a+40\cdot (-120a)=70\Rightarrow 800a=70,\\ \\ a=\dfrac{7}{80},\\ \\ b=-120\cdot \dfrac{7}{80}=-\dfrac{21}{2}=-10.5$

So,

$2500\cdot \dfrac{7}{80}+50\cdot (-10.5)+c=130\Rightarrow 218.75-525+c=130\\ \\c=130-218.75+525=436.25$

The quadratic function is

$y=\dfrac{7}{80}x^2-10.5x+436.25\\ \\y=0.0875x^2-10.5x+436.25$

4 0

3 years ago

Plzz solve in 2 mins

Katen [24]

Answer:

A is the answer

Step-by-step explanation:

3×3 is 9 and 2×3 is 6

4 0

3 years ago

Read 2 more answers

Simplify the equation. x/(x-4 )+ 4/(x-4 )

ANTONII [103]

Answer:

x+4/x-4

Step-by-step explanation:

=x/(x-4)+4/(x-4) [ l.c.m= (x-4)]

=x+4/x-4

6 0

2 years ago

A certain car depreciates such that its value at the end of each year is p % less than its value at the end of the previous year

icang [17]

Answer:

b(b/a)^2

Step-by-step explanation:

Given that the value of the car depreciates such that its value at the end of each year is p % less than its value at the end of the previous year and that car was worth a dollars on December 31, 2010 and was worth b dollars on December 31, 2011, then

b = a - (p% × a) = a(1-p%)

b/a = 1 - p%

p% = 1 - b/a = (a-b)/a

Let the worth of the car on December 31, 2012 be c

then

c = b - (b × p%) = b(1-p%)

Let the worth of the car on December 31, 2013 be d

then

d = c - (c × p%)

d = c(1-p%)

d = b(1-p%)(1-p%)

d = b(1-p%)^2

d = b(1- (a-b)/a)^2

d = b((a-a+b)/a)^2

d = b(b/a)^2 = b^3/a^2

The car's worth on December 31, 2013 = b(b/a)^2 = b^3/a^2

4 0

3 years ago

Write the given linear system in matrix form. Assume X = x y z . dx dt = −8x + 7y − 9z dy dt = 5x − y dz dt = 10x + 7y + 8z

Akimi4 [234]

Answer:

The matrix form of given linear system is

$\begin{bmatrix}x'\\ y'\\ z'\end{bmatrix}=\begin{bmatrix}-8 & 7 &-9\\ 5 & -1 & 0\\ 10 & 7 & 8\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}$

Step-by-step explanation:

Let as assume that

$X=\begin{bmatrix}x\\ y\\ z\end{bmatrix}$

Given differential equations are

$\frac{dx}{dt}=-8x+7y-9z$

$\frac{dy}{dt}=5x-y$

$\frac{dz}{dt}=10x+7y+8z$

We need to find the matrix form of given linear system.

Write the elements of left side in a column matrix.

Write all the coefficients in one matrix first which is called a coefficient matrix. Multiply coefficient matrix with the variables matrix and equate left and right side.

$\begin{bmatrix}\frac{dx}{dt}\\ \frac{dy}{dt}\\ \frac{dz}{dt}\end{bmatrix}=\begin{bmatrix}-8 & 7 &-9\\ 5 & -1 & 0\\ 10 & 7 & 8\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}$

It can be written as

$\begin{bmatrix}x'\\ y'\\ z'\end{bmatrix}=\begin{bmatrix}-8 & 7 &-9\\ 5 & -1 & 0\\ 10 & 7 & 8\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}$

6 0

3 years ago