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1 year ago

The line AB is shown on the grid.

Mathematics

1 answer:

Aleksandr [31]1 year ago

6 0

a) The gradient of a line perpendicular to AB is -2.

b) equation of line is y=-2x+6

<h3>What is gradient?</h3>

The gradient is the measure of the steepness of a straight line.

a)The gradient of line is

=(-2-2)/(7+1)

=-4/8

=-1/2

So, gradient of a line perpendicular to AB is -2

b)The coordinates of mid point (3, 0)

m = -2

So,

0= -6+ b

b= 6

So, equation of line is y=-2x+6

Learn more about this concept here:

brainly.com/question/19465597

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Tammy bought a nightstand that was marked down 60% from an original price of $50. If she paid 10% sales tax, what was the total

AURORKA [14]

Answer: the total cost of the nightstand is $22

Step-by-step explanation:

The original price of the night stand is $50. If the original price of the night stand was marked down by 60%, it means that the amount of money by which it was reduced would be

60/100 × 50 = 0.6 × 50 = 30

The new selling price would be

50 - 30 = $20

If she paid 10% sales tax,the amount of tax paid would be

10/100 × 20 = 0.1 × 20 = 2

Therefore, the total cost of the nightstand would be

20 + 2 = $22

7 0

2 years ago

The graph of the equation below is a circle. What is the length of the radius of the circle? (x - 4)^2 + (y + 12)^2 = 17^2

djverab [1.8K]

The correct answer is: [D]: "17" .
______________________________________________________
The radius is: " 17" .
______________________________________________________
Note:
______________________________________________________
The formula/equation for the graph of a circle is:
______________________________________________________
(x − h)² +<span> </span> (y − k)² = r² ;

in which:

" (h, k) " ; are the coordinate of the point of the center of the circle;

"r" is the length of the "radius" ; for which we want to determine;
_______________________________________________________
We are given the following equation of the graph of a particular circle:
_______________________________________________________

→ (x − 4)² +  (y + 12)² = 17² ;

which is in the correct form:

→ " (x − h)² +  (y − k)² = r² " ;

in which: " h = 4 " ;

" k = -12" ;

"r = 17 " ; which is the "radius" ; which is our answer.

→ { Note that: "k = NEGATIVE 12" } ;

→ Since the equation <u>for this particular circle</u> contains the expression: _________________________________________________________
→ "...(y + k)² ..." ;

[as opposed to the standard form: "...(y − k)² ..." ] ;
_________________________________________________________
→ And since the coordinates of the center of a circle are represented by:
" (h, k) " ;

→ which are: " (4, -12) " ; (<u>for this particular circle</u>) ;
_________________________________________________________
→ And since: " k = -12 " ; (<u>for this particular circle</u>) ;
_________________________________________________________
then:

" [y − k ] ² = [ y − (k) ] ² = " [ y − (-12) ] ² " ;

= " ( y + 12)² " ;

{NOTE: Since: "subtracting a negative" is the same as "adding a positive" ;

→ So; " [ y − (-12 ] " = " [ y + (⁺ 12) ] " = " (y + 12) "
___________________________________________________
Note: The above explanation is relevant to confirm that the equation is, in fact, in "proper form"; to ensure that the: radius, "r" ; is: "17" .
___________________________________________________
→ Since: "r = 17 " ;

→ The radius is: " 17 " ;

which is: Answer choice: [D]: "17" .
___________________________________________________

8 0

2 years ago

Read 2 more answers

A gallery has 25 paintings in its permanent collection, with display space for 10 at one time. How many different collections ca

Anastaziya [24]

You need to know in how many ways you can choose 10 out of 25 items when order does not matter. This is a combination problem.

$_{n}C_{r} = \dfrac{n!}{(n - r)!r!}$

$_{25}C_{10} = \dfrac{25!}{(25 - 10)!10!}$

$_{25}C_{10} = \dfrac{25 \times 24 \times 23 \times 22 \times 21 \times 20 \times 19 \times 18 \times 17 \times 16 \times 15!}{15! \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}$

$_{25}C_{10} = \dfrac{25 \times 24 \times 23 \times 22 \times 21 
\times 20 \times 19 \times 18 \times 17 \times 16}{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 
\times 2 \times 1}$

$_{25}C_{10} = \dfrac{23 \times 11 \times 20 \times 19 \times 2 \times 17}{1}$

$_{25}C_{10} = 23 \times 11 \times 20 \times 19 \times 2 \times 17$

$_{25}C_{10} = 3,268,760$

6 0

3 years ago

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Heather finished the 12-kilometer race in 2 hours. If Heather kept her pace constant, what was her rate? A. 24 km/hr. B. 14 km/h

andriy [413]

Answer: D, 6km/hr.

Step-by-step explanation:

Heather can finish a 12-kilometer race in 2 hours, and now we have to find how many kilometers she can ride/run at in 1 hour.

How many hours can Heather run in 1 hour? To solve that, we can use the equation 12 ÷ 2.

12 ÷ 2 = 6.

Therefore, if Heather keeps her pace constant, then her rate will be 6km/hr, or D.

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