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3 years ago

15

Dave is helping his grandmother make trail mix. His grandmother asks him to add 1/5 cup of fruit for every 1/3 cup of nuts. To s

atisfy his grandmothers request, Dave must mix _____ cups of fruit for a single cup of nut.

1 answer:

erma4kov [3.2K]3 years ago

3 0

3/5 cup of fruit because 1/3 +1/3 +1/3 = 3/3 or one. 1/5 +1/5 +1/5 = 3/5

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What is the<br> the distance between a point at (-3,4) and a point at (2,-5)

zaharov [31]

<h2><u>Q</u><u>u</u><u>e</u><u>s</u><u>t</u><u>i</u><u>o</u><u>n</u>:-</h2>

What is the distance between a point at (-3,4) and a point at (2,-5) ?

<h2><u>S</u><u>o</u><u>l</u><u>u</u><u>t</u><u>i</u><u>o</u><u>n</u>:-</h2>

Let the two points be A and B .

And, let the distance be P .

Now, the distance P between the point A (-3,4) and the point B (2,-5) is

$\bf P \: = \sqrt{(-3 \: - \: 2)^2 \: + \: (4 \: + \: 5)^2}$

$\implies$ $\bf P \: = \sqrt{(-5)^2 \: + \: (9)^2}$

$\implies$ $\bf P \: = \sqrt{25 \: + \: 81}$

$\implies$ $\bf P \: = \sqrt{106}$

$\implies$ $\bf P \: = \: 10.3$

<h3>The distance between a point at (-3,4) and a point at (2,-5) is <u>1</u><u>0</u><u>.</u><u>3</u> . [Answer]</h3>

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3 years ago

Solve by using substitution. Express your answer as an ordered pair.

Deffense [45]

Answer:

(1, -2)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

<u>Algebra I</u>

Solving systems of equations using substitution/elimination

Step-by-step explanation:

<u>Step 1: Define Systems</u>

4x + y = 2

y = x - 3

<u>Step 2: Solve for </u><em><u>x</u></em>

<em>Substitution</em>

Substitute in <em>y</em>: 4x + (x - 3) = 2
Combine like terms: 5x - 3 = 2
Isolate <em>x</em> term: 5x = 5
Isolate <em>x</em>: x = 1

<u>Step 3: Solve for </u><em><u>y</u></em>

Define equation: y = x - 3
Substitute in <em>x</em>: y = 1 - 3
Subtract: y = -2

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3 years ago

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Volgvan

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3 years ago

find the equation of the perpendicular bisector of segment ab with endpoints a=2,2 and b=-4,6 if the perpendicular bisector inte

aleksklad [387]

Equation of perpendicular bisector is , $y=\frac{3}{2} x+\frac{11}{2}$

Length of both pa and pb are $\sqrt{\frac{65}{4} }$ unit.

Slope of segment ab is, $\frac{6-2}{-4-2} =-\frac{2}{3}$

So, slope of perpendicular bisector will be, negative of reciprocal of slope of segment ab.

Therefore, slope of perpendicular bisector is, $\frac{3}{2}$

Since, perpendicular bisector passes through the mid point of segment ab.

So, coordinate of mid point of segment ab is,

$(\frac{2-4}{2},\frac{2+6}{2} )=(-1,4)$

Thus, perpendicular bisector of ab passing through (- 1, 4) and have slope 3/2.

So, equation of angle bisector is,

$y=\frac{3}{2} x+\frac{11}{2}$

Since, the perpendicular bisector intersects the y-axis at point p

So, coordinate of point p is (0, 11/2)

By applying distance formula,

$pa=\sqrt{(2-0)^{2}+(2-11/2)^{2} }\\\\ =\sqrt{4+\frac{49}{4} }\\\\ =\sqrt{\frac{65}{4} }$

$pb=\sqrt{(-4-0)^{2}+(6-11/2)^{2} }\\\\ =\sqrt{16+\frac{1}{4} }\\\\ =\sqrt{\frac{65}{4} }$

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Answer:

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Step-by-step explanation:

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