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Fiesta28 [93]
3 years ago
11

Algebraic Representation (

Mathematics
1 answer:
Komok [63]3 years ago
6 0

Answer:

sdfm8

Step-by-step explanation:

du9sufmfhmh

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What is the constant of proportionality in the equation y=1/2x<br> constant of proportionality =?
klasskru [66]

Answer:

1/2

Step-by-step explanation:

In the straight line form...

y=mx+b

m is the constant of proportionality or the "K"

7 0
3 years ago
Read 2 more answers
Divide the rational expressions and express in simplest form. When typing your answer for the numerator and denominator be sure
Veseljchak [2.6K]

Dividing by a fraction is equivalent to multiply by its reciprocal, then:

\begin{gathered} \frac{3y^2-7y-6}{2y^2-3y-9}\div\frac{y^2+y-2}{2y^2+y-3^{}}= \\ =\frac{3y^2-7y-6}{2y^2-3y-9}\cdot\frac{2y^2+y-3}{y^2+y-2}= \\ =\frac{(3y^2-7y-6)(2y^2+y-3)}{(2y^2-3y-9)(y^2+y-2)} \end{gathered}

Now, we need to express the quadratic polynomials using their roots, as follows:

ay^2+by+c=a(y-y_1)(y-y_2)

where y1 and y2 are the roots.

Applying the quadratic formula to the first polynomial:

\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{7\pm\sqrt[]{(-7)^2-4\cdot3\cdot(-6)}}{2\cdot3} \\ y_{1,2}=\frac{7\pm\sqrt[]{121}}{6} \\ y_1=\frac{7+11}{6}=3 \\ y_2=\frac{7-11}{6}=-\frac{2}{3} \end{gathered}

Applying the quadratic formula to the second polynomial:

\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{-1\pm\sqrt[]{1^2-4\cdot2\cdot(-3)}}{2\cdot2} \\ y_{1,2}=\frac{-1\pm\sqrt[]{25}}{4} \\ y_1=\frac{-1+5}{4}=1 \\ y_2=\frac{-1-5}{4}=-\frac{3}{2} \end{gathered}

Applying the quadratic formula to the third polynomial:

\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{3\pm\sqrt[]{(-3)^2-4\cdot2\cdot(-9)}}{2\cdot2} \\ y_{1,2}=\frac{3\pm\sqrt[]{81}}{4} \\ y_1=\frac{3+9}{4}=3 \\ y_2=\frac{3-9}{4}=-\frac{3}{2} \end{gathered}

Applying the quadratic formula to the fourth polynomial:

\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{-1\pm\sqrt[]{1^2-4\cdot1\cdot(-2)}}{2\cdot1} \\ y_{1,2}=\frac{-1\pm\sqrt[]{9}}{2} \\ y_1=\frac{-1+3}{2}=1 \\ y_2=\frac{-1-3}{2}=-2 \end{gathered}

Substituting into the rational expression and simplifying:

\begin{gathered} \frac{3(y-3)(y+\frac{2}{3})2(y-1)(y+\frac{3}{2})}{2(y-3)(y+\frac{3}{2})(y-1)(y+2)}= \\ =\frac{3(y+\frac{2}{3})}{2(y+2)}= \\ =\frac{3y+2}{2y+4} \end{gathered}

8 0
1 year ago
Find two consecutive positive integers such that the sum of their squares is 421 .
maria [59]
We assume the two numbers are x and (x+1)
so x^2+(x+1)^2=421
x^2+(x^2+2x+1)=421
2x^2+2x-420=0
According to the formula of quadratic 
x=14 or-15
cuz we know the two numbers are integers
so x=14
therefore the other number is 15
To make sure that's correct
14^2+15^2=421

Hope that helps you!!


4 0
3 years ago
The cost of one pound of bananas is greater than $0.41 and less than $0.50. Sarah pays $3.40 for x pounds of bananas. Which ineq
vredina [299]

Answer:

0.41<3.40/x<0.50

Step-by-step explanation:

Given that the cost of one pound of bananas is greater than $0.41 and less than $0.50. That is,

If the cost of one banana is P, then, the inequality will be

0.41 < P < 0.50

Sarah pays $3.40 for x pounds of bananas. The inequality that represents the range of possible pounds purchased will be achieved by below

3.40/0.41 = 8.29

3.40/0.50 = 6.8

Therefore, the inequality that represents the range of possible pounds purchased is

6 < x < 9 this is the same as 0.41<3.40/x<0.50

6 0
3 years ago
In this assignment, you will explore how the volume is changed when you adjust the height or radius of a cylinder. You will drag
lesantik [10]

The volume of a cylinder changes when you adjust the height or radius as the volume either increases or reduces.

<h3>How to illustrate the volume?</h3>

Let's assume that the height and radius are 14cm and 7cm. The volume will be:

= πr²h

= 3.14 × 7² × 14

= 2154.04cm³

When the radius and height are reduced to 5cm and 9cm, the volume will be:

= πr²h

= 3.14 × 5² × 9

= 706.5cm³

This illustrates that the volume reduces when the height and radius reduces.

Learn more about volume on:

brainly.com/question/1972490

#SPJ1

8 0
2 years ago
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