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3 years ago

12

Line p passes through (8, -6) and is perpendicular to the line 2x + y = -7. The slope of line p is . The equation of line p is y

= 1/2x + ?.

1 answer:

Bingel [31]3 years ago

3 0

Answer:

y = (1/2) x -10

Step-by-step explanation:

Perpendicular lines are lines make right angles. The slopes of perpendicular lines are opposite reciprocals !

2x + y = -7 rewrite in form y=

y = -7 -2x

slope of this line is -2

perpendicular lines are opposite reciprocals so the line p has a slope = 1/2

line p passes through (8, -6) so plug in point into equation of p and get ?

y = 1/2 x +?

-6 =1/2(8) +?

-6 =4 + ? subtract 4 from both sides

-6-4 = ?

-10 = ?

y = (1/2) x -10

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9. Triangle Construction pays Square Insurance $5,980

xxTIMURxx [149]

The triangle pay $32 more for that day than it paid per day during the first period of time.

Step-by-step explanation:

The given is,

Triangle Construction pays Square Insurance $5,980

To insure a construction site for 92 days

To extend the insurance beyond the 92 days costs $97 per day

Triangle extends the insurance by 1 day

Step:1

Insurance per day from the 92 days period,

$= \frac{Total insuratio for 92 days}{Period}$

Where, Total insurance for 92 days = $ 5,980

Period = 92 days

From the values, equation becomes,

$=\frac{5980}{92}$

= $ 65 per day

Step:2

Insurance per day after the 92 days,

= $ 97

Amount Pay for that day than it paid per day during the first period of time,

$=(97-65)$

= $32

Result:

The triangle pay $32 more for that day than it paid per day during the first period of time, if the Triangle Construction pays Square Insurance $5,980 to insure a construction site for 92 days and to extend the insurance beyond the 92 days costs $97 per day.

8 0

3 years ago

What value of b will cause the system to have an infinite number of solutions?

irga5000 [103]

b must be equal to -6 for infinitely many solutions for system of equations $y = 6x + b$ and $-3 x+\frac{1}{2} y=-3$

<u>Solution: </u>

Need to calculate value of b so that given system of equations have an infinite number of solutions

$\begin{array}{l}{y=6 x+b} \\\\ {-3 x+\frac{1}{2} y=-3}\end{array}$

Let us bring the equations in same form for sake of simplicity in comparison

$\begin{array}{l}{y=6 x+b} \\\\ {\Rightarrow-6 x+y-b=0 \Rightarrow (1)} \\\\ {\Rightarrow-3 x+\frac{1}{2} y=-3} \\\\ {\Rightarrow -6 x+y=-6} \\\\ {\Rightarrow -6 x+y+6=0 \Rightarrow(2)}\end{array}$

Now we have two equations

$\begin{array}{l}{-6 x+y-b=0\Rightarrow(1)} \\\\ {-6 x+y+6=0\Rightarrow(2)}\end{array}$

Let us first see what is requirement for system of equations have an infinite number of solutions

If $a_{1} x+b_{1} y+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0$ are two equation

$\Rightarrow \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$ then the given system of equation has no infinitely many solutions.

In our case,

$\begin{array}{l}{a_{1}=-6, \mathrm{b}_{1}=1 \text { and } c_{1}=-\mathrm{b}} \\\\ {a_{2}=-6, \mathrm{b}_{2}=1 \text { and } c_{2}=6} \\\\ {\frac{a_{1}}{a_{2}}=\frac{-6}{-6}=1} \\\\ {\frac{b_{1}}{b_{2}}=\frac{1}{1}=1} \\\\ {\frac{c_{1}}{c_{2}}=\frac{-b}{6}}\end{array}$

As for infinitely many solutions $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

$\begin{array}{l}{\Rightarrow 1=1=\frac{-b}{6}} \\\\ {\Rightarrow6=-b} \\\\ {\Rightarrow b=-6}\end{array}$

Hence b must be equal to -6 for infinitely many solutions for system of equations $y = 6x + b$ and $-3 x+\frac{1}{2} y=-3$

8 0

3 years ago

PLEASE HELP ME 16 POINTS PLEASE HELP

lorasvet [3.4K]

Answer:

A.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A rectangular field has an area 28800 sq.meter.its length is twice as long as its width.what is the length of its sides?

AVprozaik [17]

Let
x---------> the length side of rectangle
y---------> the width side of rectangle

we know that
x=2y-----> equation 1
area=x*y-------> 28800=x*y------> equation 2
substitute 1 in 2

28800=[2y]*y-----> 28800=2y²-------> y²=14400------> y=120 m
x=2*y----> x=2*120------> x=240 m

the answer is
the length side of rectangle is 240 m
the width side of rectangle is 120 m

5 0

3 years ago

Six pyramids are shown inside of a cube. The height of the cube is h units. Six identical square pyramids can fill the same volu

Amiraneli [1.4K]

The height of squared pyramid is $\frac{1}{3}h$ unit.

<h3>What is the volume of a cube?</h3>

A cube is a solid three-dimensional object with six square faces or sides, three of which meet at each vertex. One of the five Platonic solids, the cube is the only regular hexahedron. It contains 8 vertices, 6 faces, and 12 edges.

Volume of cube $= (side)^3 \ unit^3$

Given the height of cube is $h$ unit.

Volume of cube is $h^3 \ unit^3$

Let the height of squared pyramid is $x$ unit

Volume of squared pyramid is $\frac{1}{3} h^{2} \times x \ unit^3$

According to the question, we have

Volume of cube = $6 \times$ volume of squared pyramid

$\Rightarrow h^3=6 \times \frac{1}{3}h^2 \times x\\\Rightarrow h^3=2 \ h^2 \times x\\\Rightarrow h=2x\\\Rightarrow x= \frac{1}{2}h$

Therefore, the height of squared pyramid is $\frac{1}{3}h$ unit.

To learn more about squared pyramid from the given link

brainly.com/question/27476449

#SPJ4

8 0

2 years ago