All categories

3 years ago

If a ⊥ b and b ∥ c, then _____

Mathematics

1 answer:

Tasya [4]3 years ago

3 0

Answer: If a ⊥ b and b ║ c, then a ║c

Step-by-step explanation: I substituted a more legible symbol for parallel. I believe that is what the question means.

a will be perpendicular to any line that is parallel to b.

You might be interested in

John is measuring a piece of glass to fit in a triangular frame. He can only remember

blagie [28]

Answer: (c)

Step-by-step explanation:

Given

length of two sides of a triangle is 6 cm and 11 cm

In a triangle length of the third side lies between the sum and subtraction of the other two sides

Suppose x is the length of the third side so

$11-6$

6 0

3 years ago

The equation y^2+8y−x+18=0 represents a parabola. Drag and drop the expressions into the boxes in the equation to rewrite the eq

mario62 [17]

Answer:

The equation of parabola is standard form is $x=\left(y+4\right)^2+2$

Step-by-step explanation:

Given equation of parabola is,

$y^2+8y-x+18=0$

In order to find the equation of parabola in standard form, eliminate x from left side of equation and use completing square method to find the equation.

First step is to add x on both side of equation.

$y^2+8y-x+18+x=0+x$

$y^2+8y+18=x$

Rewriting,

$x=y^2+8y+18$

Now applying completing square method as follows.

Following are the steps for calculation of this method.

Find the last term of above equation by using below formula,

$Last\:term\:of\:square=\left(\dfrac{coefficient\:of\:y}{2}\right)^{2}$

Now coefficient of y is 8.

$\therefore Last\:term\:of\:square=\left(\dfrac{8}{2}\right)^{2}$

Simplifying,

$Last\:term\:of\:square=\left(4\right)^{2}$

$Last\:term\:of\:square=16$

Second step is to add and subtract the last term.

$x=y^2+8y+18+16-16$

Rewriting,

$x=y^2+8y+16+18-16$

Since $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$

Using above formula,

$x=\left(y+4\right)^{2}+2$

Therefore, the equation of parabola in standard form is $x=\left(y+4\right)^{2}+2$

4 0

3 years ago

Select the quadratic equation that has roots x=8 and x=-5

stellarik [79]

Step-by-step explanation:

Since, x=8 and x=-5 are the roots.

Therefore, (x - 8) & (x - 5) will be factors.

Hence, required quadratic equation can be given as:

$(x - 8)(x - 5) =0 \\ \\ \therefore {x}^{2} + ( - 8 - 5) x+ ( - 8) \times ( - 5) = 0 \\ \\ \therefore {x}^{2} + ( - 13) x+ 40= 0 \\ \\ \huge \red{ \boxed{ \therefore {x}^{2} - 13x+ 40= 0 }} \\ is \: the \: required \: quadratic \: equation.$

5 0

3 years ago

The cosine equation for a function that has a period of 4 straight pi and an amplitude of 8

lara [203]

Answer:

y=4sin[2(x−π2)]−6

Step-by-step explanation:

The standard form of a sine function is

y=asin[b(x−h)]+k

where

•a : is the amplitude,

•2π/b : is the period,

•h : is the phase shift, and

•k : is the vertical displacement.

We start with classic

y=sinx :

graph{(y-sin(x))(x^2+y^2-0.075)=0 [-15, 15, -11, 5]}

(The circle at (0,0) is for a point of reference.)

The amplitude of this function is

a=1 .To make the amplitude 4, we need

a to be 4 times as large, so we set

a=4

Our function is now

y=4sinx ,and looks like:

graph{(y-4sin(x))(x^2+y^2-0.075)=0 [-15, 15, -11, 5]}

The period of this function—the distance between repetitions—right now is

2π , with b=1

.To make the period π , we need to make the repetitions twice as frequent, so we need

b=normal period/desired period

=2π/π=2

Our function is now

y=4sin(2x), and looks like: graph

{(y-4sin(2x))(x^2+y^2-0.075)=0 [-15, 15, -11, 5]}

This function currently has no phase shift, since

h=0

. To induce a phace shift, we need to offset

xby the desired amount, which in this case is

π2 to the right. A phase shift right means a positive

h, so we set

h = π2

Our function is now

y=4sin[2(x−π2)] , and looks like:graph

{(y-4sin(2(x-pi/2)))((x-pi/2)^2+y^2-0.075)=0 [-15, 15, -11, 5]}

Finally, the function currently has no vertical displacement, since

k=0

.To displace the graph 6 units down, we set

k=−6

Our function is now

y=4sin[2(x−π2)]−6, and looks like:graph {(y-4sin(2(x-pi/2))+6)((x-pi/2)^2+(y+6)^2-0.075)=0 [-15, 15, -11, 5]}

6 0

3 years ago

at a summer camp there is one counselor for every 8 campers. write an equation for the number of caper, y, that there are for x

antoniya [11.8K]

campers = y and counselors = x, 1 counselor to 5 campers

6 0

3 years ago