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3 years ago

Patricia needs to save $20 for a new backpack. She has $5 saved in her bank.

Mathematics

2 answers:

Misha Larkins [42]3 years ago

5 0

(2-0.50)•X=20-5
1.50•X=15
X=15/1.50
X=10

Ivanshal [37]3 years ago

3 0

Answer:

y=1.5x+5

Step-by-step explanation:

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If a polynomial function f(x) has roots 3+root5 and -6, what must be a factor of f(x)? (X+(3-root5) (x-(3-root5)) (x+(5+root3))

belka [17]

Answer:

$(x-(3+\sqrt5))$ or $(x-3-\sqrt5)$ is a factor of the given polynomial.

Step-by-step explanation:

Let us learn the concept with an example first.

Let the polynomial be a quadratic function $g(x)$ .

$g(x) = x^{2} -5x+6$

The roots of $g(x)$ are 2 and 3.

Putting $x= 2\ in \ g(x)$

$2^2-5\times 2+6 = 4-10+6 =0$

Putting $x= 3\ in \ g(x)$

$3^2-5\times 3+6 = 9-15+6 =0$

Putting x = 2 or x = 3, g(x) = 0 $\therefore$ The roots of equation g(x) are 2 and 3.

Now, let us try to factorize g(x):

$x^{2} -2x-3x+6\\\Rightarrow x(x -2)-3(x-2)\\\Rightarrow (x-3)(x-2)$

so, the equation can be written as:

$g(x) = x^{2} -5x+6=(x-3)(x-2)$ where 3 and 2 are the roots of equation.

The factors are (x-3) and (x-2).

$\therefore$ for the polynomial f(x) which has roots $3+\sqrt5\ and\ -6$ will have a factor:

$(x-(3+\sqrt5))$ or $(x-3-\sqrt5)$

8 0

3 years ago

"Find the point at which the line touches the circle" I really need help no one helped last time...

Troyanec [42]

The solution for a system of equations will be when the graphs touch each other, or intersect, and that happens when both equations equate each other, so, let's do so,

$\bf \begin{cases}
\boxed{y}=3x+10\\
-------\\
x^2+y^2=10\\
y^2=10-x^2\\
y=\sqrt{10-x^2}
\end{cases}\qquad \qquad \boxed{3x+10}=\sqrt{10-x^2}
\\\\\\
\textit{now we square both sides}\qquad (3x+10)^2=(\sqrt{10-x^2})^2
\\\\\\
(3x+10)^2=10-x^2\implies 9x^2+60x+100=10-x^2
\\\\\\
10x^2+60x-90=0\implies x^2+6x-9=0\implies (x+3)(x+3)=0
\\\\\\
x=
\begin{cases}
-3\\
-3
\end{cases}\qquad thus\qquad \boxed{x=-3}$

$\bf -------------------------------\\\\
\textit{now, when x = -3, what is \underline{y}?}\qquad y=3x+10\implies y=3(-3)+10
\\\\\\
y=-9+10\implies \boxed{y=1}\qquad \qquad therefore\qquad (\stackrel{x}{-3}~,~\stackrel{y}{1})$

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3 years ago

Tomorrow, Mrs. Wendel's class will be using toothpicks for a science project. Each student must use at least 5 toothpicks for th

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3 years ago

Find the area to the right of the z-score 1.39 and to the left of the z-score 1.53 under the standard normal curve.1.2 1.3 1.4 0

svetoff [14.1K]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The value is $P( 1.39 < z < 1.53 ) = 0.0193$

Step-by-step explanation:

From the question we are told to obtain the area to the of the z-score 1.39 and to the left of the z-score 1.53, this is mathematically represented as

$P( 1.39 < z < 1.53 ) = P( z < 1.53 ) - P( z < 1.39 )$