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Romashka [77]
3 years ago
7

Find the vertex for the parabola given by the function ƒ(x) = −3x2 − 6x.

Mathematics
1 answer:
Digiron [165]3 years ago
6 0

do you like jazz in terms of music??

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The product of the length of 2 unequal poles before cutting 2 cm from each was 285 cm. Their present sum after cutting 2cm from
labwork [276]

Answer:

15 cm

Step-by-step explanation:

The length of the shorter pole can be found by forming and subsequently solving 2 equations.

Start by defining the variables that are going to be used in the working.

Let the original length of the shorter pole be a cm and that of the longer pole be b cm.

'Product' refers to the multiplication operation.

ab= 285 -----(1)

On the other hand, 'sum' refers to the addition operation.

Length of shorter pole after cutting= a -2

Length of longer pole after cutting= b -2

(a -2) +(b-2)= 30

a +b -4= 30

Adding 4 to both sides:

a +b= 30 +4

a +b= 34 -----(2)

From (2):

a= 34 -b -----(3)

Let's solve by substitution:

Substitute (3) into (1):

b(34 -b)= 285

Expand:

34b -b²= 285

b² -34b +285= 0

Factorise:

(b -15)(b -19)= 0

b -15= 0       or       b -19= 0

b= 15            or             b= 19

Substitute into (1):

a(15)= 285       or       a(19)= 285

a= 285 ÷15      or             a= 285 ÷19

a= 19                or             a= 15

Since a <b, a= 15 and b= 19.

Thus, the length of the shorter pole is 15 cm.

8 0
2 years ago
The perimeter of the triangle is 42. Find the length of all the sides.
iragen [17]
<h3>Given :-</h3>

  • Perimeter of triangle = 42

  • Side 1 of triangle = (x + 4)

  • Side 2 of triangle = (3x + 8)

  • Side 3 of triangle = (5x + 6)

<h3>To find:-</h3>

  • Length of sides

<h3>Explanation:</h3>

So to find length of sides we have to find the value of x.We can find value of x , by this formula:

\\  \\

\bigstar \boxed{ \rm perimeter \: of \triangle \:  = side_1 + side_2 + side_3}

\\  \\

So:-

\\

\dashrightarrow \tt perimeter \: of \triangle \:  = side_1 + side_2 + side_3 \\

\\  \\

\dashrightarrow \tt 42  = (x + 4) + (3x + 8)+( 5x + 6) \\

\\  \\

\dashrightarrow \tt 42  = x + 4+ 3x + 8+5x + 6 \\

\\  \\

\dashrightarrow \tt 42  = x + 3x+5x+ 4 + 8 + 6 \\

\\  \\

\dashrightarrow \tt 42  = 9x+ 4 + 8 + 6 \\

\\  \\

\dashrightarrow \tt 42  = 9x+ 18\\

\\  \\

\dashrightarrow \tt 42  - 18 = 9x \\

\\  \\

\dashrightarrow \tt 24 = 9x \\

\\  \\

\dashrightarrow \tt  9x = 24 \\

\\  \\

\dashrightarrow \tt  x = \dfrac{24}{9}  \\

\\  \\

\dashrightarrow \bf  x =2.67 \{approx \}\\

\\  \\

  • Side 1 of triangle = (x + 4)
  • Side 1 of triangle =2.67 + 4
  • Side 1 of triangle = 6.67

  • Side 2 of triangle = 3x + 8
  • Side 2 of triangle = 3 × 6.67 + 8
  • Side 2 of triangle = 20.01 + 8
  • Side 2 of triangle = 28.01

  • Side 3 of triangle = 5x + 6
  • Side 3 of triangle = 5 × 2.67 + 6
  • Side 3 of triangle = 13.35 + 6
  • Side 3 of triangle = 19.35

━━━━━━━━━━━━━━━━

~WindyMint

3 0
2 years ago
What is the slope of the line that contains the points (-3, -2) and (4, -2)?
schepotkina [342]
You have to use the formule: y2-y1/x2-x1
-2-(-2)/4-(-3)=0/7
6 0
3 years ago
Read 2 more answers
Find the standard form of the equation of the circle with endpoints of a diameter at the points (3,8) and (-7,2)
poizon [28]

(x+2)^{2}+(y-5)^{2}= 34

The equation of a circle in standard form is

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

where (a , b) are the coordinates of the centre and r is the radius

The centre is at the midpoint of the endpoints and the radius is the distance from the centre to either of the 2 endpoints

Using the midpoint formula

midpoint = [\frac{1}{2}(xx_{1}+x_{2}, \frac{1}{2}(y_{1}+y_{2}

where (x_{1},y_{1}=(3,8) and (x_{2},y_{2}=(-7,2)

centre = (\frac{1}{2}(3-7),\frac{1}{2}(8+2)) = (-2,5)

Calculate r using the distance formula

r = √(x_{2}-x_{1})²+(y_{2}-y_{1})²)

= √((3+2)²+(8-5)²) = √(25+9) = √34 ⇒ r² =(√34)² = 34

equation of circle is : (x+2)²+(y-5)² = 34


8 0
3 years ago
Oscar wants to put $1000 in a bank account that
Feliz [49]

Answer:

he would end up with 3000$ in 10 years with simple interest

Step-by-step explanation:

8 0
3 years ago
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