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docker41 [41]
3 years ago
6

The graph of a quadratic function has roots at -3 and -7 and a vertex at (-5, 4). What is the equation of the function in vertex

form?
Mathematics
1 answer:
melomori [17]3 years ago
3 0

Answer:

y = -(x + 5)² + 4

Step-by-step explanation:

The roots are -3 and -7, so:

y = a (x + 3) (x + 7)

Distribute and complete the square:

y = a (x² + 10x + 21)

y = a (x² + 10x + 25 − 4)

y = a (x² + 10x + 25) − 4a

y = a (x + 5)² − 4a

The vertex is (-5, 4), so a = -1.

y = -(x + 5)² + 4

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Evaluate: [7(5 – 2) + 42] ÷ 9
Inessa05 [86]

Answer:

7

Step-by-step explanation:

7 0
3 years ago
The two cylinders are similar. If the ratio of their surface areas is 9/1.44, find the volume of each cylinder. Round your answe
WITCHER [35]
R1² π : r2² π = 9 : 1.44
r1 : r 2 = 3 : 1.2
r2 = 1.2 · r1  / 3
r 2 = 0.4 · r1
If the two cylinders are similar than also: h 2 = 0.4 · h 2
V 1 = r1²   · π  · h1
V 2 = ( 0.4 r1)² π · 0.4 · h1 = 0.064 r1² · π · h1
V 2 ( small cylinder )= 0.064 · V 1 ( large cylinder ) 
851.22 m³= 13.300.25 m³ · 0.064
Answer: C )
4 0
3 years ago
Read 2 more answers
Match The Term
GalinKa [24]

Answer:

jyyj    

Step-by-step explanation:

From the figure,

Radius matches with (F) that is a segment between the centre of a circle and a point on the circle.

Arc matches with (D) that is Circle A and the portion of the circle between points B and C is darkened.

Chord matches with (C) Circle A and a line segment connecting points B and C which are on the circle.

Secant matches with (E) that is Circle A and a line segment connecting points B and C which are on the circle.

Tangent matches with (A) that is a line intersects a circle in exactly one point.

Circumference matches (B) that is the distance around a circle.


4 0
3 years ago
Read 2 more answers
Simone invests 1200 into two savings accounts. One account earns 4% annual interest and the other earns 5.9% annual interest. At
Allisa [31]

Answer: He invested $350 at 4% and $850 at 5.9%

Step-by-step explanation:

Let x represent the amount which he invested in the account earning 4% interest.

Let y represent the amount which he invested in the account earning 5.9% interest.

Simone invests 1200 into two savings accounts. One account earns 4% annual interest and the other earns 5.9% annual interest. This means that

x + y = 1200

The formula for determining simple interest is expressed as

I = PRT/100

Considering the account earning 4% interest,

P = $x

T = 1 year

R = 4℅

I = (x × 4 × 1)/100 = 0.04x

Considering the account earning 5.9% interest,

P = $y

T = 1 year

R = 5.9℅

I = (y × 5.9 × 1)/100 = 0.059y

At the end of 1 year, Simon earned 64.15 in interest. it means that

0.04x + 0.059y = 64.15 - - - - - - - - -1

Substituting x = 1200 - y into equation 1, it becomes

0.04(1200 - y) + 0.059y = 64.15

48 - 0.04y + 0.059y = 64.15

- 0.04y + 0.059y = 64.15 - 48

0.019y = 16.15

y = 16.15/0.019

y = 850

x = 1200 - y = 1200 - 850

x = 350

7 0
3 years ago
12, 17, 22, ...<br> Find the 36th term.
pychu [463]

Answer:

187

Step-by-step explanation:

a=12,d=17-12=5

nth term =a+(n-1)d

36th term=12+(36-1)5

=12+(35×5)

12+175

36th term=187

8 0
2 years ago
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