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3 years ago

The midpoint of RS has cordon ages (6,8). Points S has coordinates (6,7)...

Mathematics

1 answer:

postnew [5]3 years ago

3 0

The coordinates of R are (6,9)

Step-by-step explanation:

Given

S(6,7) = (x2,y2)

R = (x1,y1)

M = (6,8)

The formula for mid-point is:

$M = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})$

Putting values

$(6,8) = (\frac{x_1+6}{2} , \frac{x_2+7}{2})$

Putting respective coordinates equal

$6 = \frac{x_1+6}{2}\\6*2 = x_1+6\\12 = x_1+6\\x_1 = 12-6\\x_1 =6\\AND\\8 = \frac{y_1+7}{2}\\8*2 = y_1+7\\16 = y_1+7\\16-7 = y_1\\y_1 = 9$

Hence,

The coordinates of R are (6,9)

Keywords: Coordinate geometry

Learn more about coordinate geometry at:

#LearnwithBrainly

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A manufacturer cuts squares from the corners of a rectangular plece of sheet metal that measures 2 inches by 7 inches (see Figur

Vladimir79 [104]

Answer:

The value of x that maximizes the volume enclosed by this box is 0.46 inches

The maximum volume is 3.02 cubic inches

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The volume of the open-topped box is equal to

$V=LWH$

where

$L=(7-2x)\ in\\W=(2-2x)\ in\\H=x\ in$

substitute

$V=(7-2x)(2-2x)x$

Convert to expanded form

$V=(7-2x)(2-2x)x\\V=(14-14x-4x+4x^{2})x\\V=14x-14x^2-4x^2+4x^{3}\\V=4x^{3}-18x^{2} +14x$

using a graphing tool

Graph the cubic equation

Remember that

The domain for x is the interval -----> (0,1)

Because

If x>1

then

the width is negative (W=2-2x)

The maximum is the point (0.46,3.02)

see the attached figure

therefore

The value of x that maximizes the volume enclosed by this box is 0.46 inches

The maximum volume is 3.02 cubic inches

8 0

3 years ago

The nurse needs to mix 2% solution with 10% solution to get 10 ml of the prescribed 6% solution. What amount of each solution do

xenn [34]

<em>Volumes of 2% Solution = </em><em>5 ml</em>

<em>Volumes of 10% Solution = </em><em>5 ml</em>

$\texttt{ }$

<h3>Further explanation</h3>

Simultaneous Linear Equations could be solved by using several methods such as :

<em>Elimination Method</em>
<em>Substitution Method</em>
<em>Graph Method</em>

If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.

Let us tackle the problem!

$\texttt{ }$

<em>Volumes of 2% Solution = x</em>

<em>Volumes of 10% Solution = y</em>

$\texttt{ }$

<em>Total Volume = 10 ml</em>

$\boxed{x + y = 10}$ → <em>Equation 1</em>

$\texttt{ }$

<em>The nurse needs to mix 2% solution with 10% solution to get 10 ml of the prescribed 6% solution</em>.

$2 \% x + 10 \% y = 6 \% (10)$

$2x + 10y = 6(10)$

$\boxed{x + 5y = 30}$ → <em>Equation 2</em>

$\texttt{ }$

<em>Equation 1 - Equation 2:</em>

$( x + y ) - ( x + 5y ) = 10 - 30$

$-4y = -20$

$y = -20 \div -4$

$y = 5 \texttt{ ml}$

$\texttt{ }$

$x + y = 10$

$x + 5 = 10$

$x = 5 \texttt{ ml}$

$\texttt{ }$

<h2>Conclusion:</h2>

<em>Volumes of 2% Solution = </em><em>5 ml</em>

<em>Volumes of 10% Solution = </em><em>5 ml</em>

$\texttt{ }$

<h3>Learn more</h3>

Perimeter of Rectangle : brainly.com/question/12826246
Elimination Method : brainly.com/question/11233927
Sum of The Ages : brainly.com/question/11240586

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations

6 0

2 years ago

Someone help me please

Gemiola [76]

Answer:

$x=2\sqrt{6}$

Step-by-step explanation:

Use the Pythagorean theorem:

$a^2+b^2=c^2$

a and b are the legs and c is the hypotenuse. Insert the values:

$\sqrt{10}^2+\sqrt{14}^2=x^2$

Simplify exponents using the rule $\sqrt{x}^2=x$ :

$10+14=x^2$

Simplify addition:

$24=x^2\\x^2=24$

Find the square root:

$\sqrt{x^2}=\sqrt{24}\\ x=\sqrt{24}$

Simplify in radical form: Find a common factor of 24 that is a perfect square:

$\sqrt{24}=\sqrt{4*6}$

Separate:

$\sqrt{4}*\sqrt{6}$

Simplify:

$2*\sqrt{6}\\x=2\sqrt{6}$

Finito.

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3 years ago

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Step-by-step explanation:

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2 years ago

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emmainna [20.7K]

Answer:

a. The amplitude should be 2.

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Step-by-step explanation:

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2 years ago