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slava [35]
3 years ago
7

What is the value of the expression z2+3z-3 when z=6?

Mathematics
1 answer:
oksano4ka [1.4K]3 years ago
8 0

Answer:

51

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Define

z² + 3z - 3

z = 6

Step 2: Substitute and Evaluate

6² + 3(6) - 3

36 + 18 - 3

36 + 15

51

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A circle has a diameter with endpoints at (6, 5) and (8, 5). Write the equation for the circle.
mario62 [17]

Answer:

(x-7)^2+(y-5)^2=1

Step-by-step explanation:

The two things that are required to formulate the equation of the circle is the center coordinate and the radius of the circle!

<u>Center of the circle:</u>

  • The center of the circle always lies at the midpoint of the endpoints of its diameter: Let's call the endpoints A(6,5) and B(8,5).

Using the midpoint formula we'll get:

(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)

(x_m, y_m) = \left(\dfrac{6+8}{2},\dfrac{5+5}{2}\right)

(x_m, y_m) = (7,5)

This is the center coordinate of our circle.

<u>Radius: </u>

The radius of the circle is the distance from the center of the circle to any of the endpoints of the diameter (A or B)

We can use the distance formula:

r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}

r = \sqrt{(x_1-x_m)^2+(y_1-y_m)^2}

r = \sqrt{(6-7)^2+(5-5)^2}

r = \sqrt{1^2}

r = 1

<u>Equation of the circle: </u>

The equation is written as:

(x-a)^2+(y-b)^2=r^2

here, (a,b) are the center points of the circle

in our case this is (a,b)=(x_m,y_m)=(7,5)

and r = 1

(x-7)^2+(y-5)^2=1^2

(x-7)^2+(y-5)^2=1

This is the equation of the circle!

3 0
3 years ago
Stefanie spends entire allowance one month she spends 1/2 of a on new clothes 1/4 on food 1/6 on movies and 1/12 on Music how mu
Komok [63]

Answer:

Option D: 1/3

Step-by-step explanation:

Let

x ------> the entire Stefanie's allowance

we know that

She spends on clothes (1/2)x

She spends on movies (1/6)x

To find out how much more does she spend on clothes that he does on movies, subtract the amount she spends on movies from the amount she spend on clothes

\frac{1}{2}x-\frac{1}{6}x=\frac{2}{6}x

Simplify

\frac{1}{3}x

therefore

She spends 1/3 more on clothes that he does on movies

4 0
2 years ago
If someone average free throw for basketball is 60% how many times in the next 50 tries will she make a free throw. Describe how
Anon25 [30]
So remember that percent means parts out of 100
60%=60/100=6/10
so every 10 throws she makes 6
how many 5 in 50?
50/10=5
answe ris 5
so 5 tens so therefor 5 sixes
5 times 6=30
answer is 30 throws
4 0
3 years ago
Please help me.
ikadub [295]

Answer:

area of square =length × length ×height

=6×6×8

=288

5 0
3 years ago
Read 2 more answers
Please help me my grade is on the line
NemiM [27]
Answer shown and explanation above! Hope this helps!

5 0
3 years ago
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