MATHEMATICS HIGH SCHOOL

Write an equation of the parabola in vertex form.

Answers

Answer 1

Answer:

Answer:

$y= -\frac19(x-3)^2+1$

Step-by-step explanation:

the x-3 is to shift a normal parabola 3 to the right

the +1 is to lift the top up by one

the -1/9 is to compress and swapt it around

Answer 2

Answer:

Answer:

y =- $(1)/(9)$ (x - 3)² + 1

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (3, 1) , thus

y = a(x - 3)² + 1

To find a substitute another point on the graph into the equation

Substitute (1, $(5)/(9)$ ) into the equation

$(5)/(9)$ = a(1 - 3)² + 1 ( subtract 1 from both sides )

- $(4)/(9)$ = 4a ( divide both sides by 4 )

a = - $(1)/(9)$

y = - $(1)/(9)$ (x - 3)² + 1 ← equation of parabola in vertex form

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the length of a tennis court is 78 feet. this is 3 less than 3 times the width of the court. what is the width of the court

Answers

$length:l=78ft.\n\nw-width\n\nl=3w+3\n\n3w+3=78\ \ \ \ /-3\n\n3w=75\ \ \ \ /:3\n\nw=25\ (ft.)\leftarrow answer$

An infant is 32.625 inches (in) long. Write this as a common fraction.

Answers

the fraction will be 261/8

32.625 is written as a common fraction is 261/8

Three multiplied by the sum of 4 and a number is the same as 18 more than the number. Find the number.. . If n is \"the number,\" which equation could be used to solve for the number?. . . 3n + 4 = n + 18. 4(3 + n) =n + 18. 3(4 + n) =n + 18. 3(4 + n) + 18 > n

Answers

Answer:

3(n+4)=n+18

The value of n is 3

Step-by-step explanation:

Let n be the required number.

Sum of 4 and the number n is (n +4)

Three multiplied by the sum of 4 and the number= 3(n +4)

Now, 18 more than the number = (n + 18)

From, the given directions, we can write the equation

$3(n+4)=n+18$

Now, we solve this equation for n

Distribute 3 over the parenthesis

$3n+12=n+18$

Subtract n to both sides

$2n+12=18$

Subtract 12 to both sides

$2n=6$

Divide both sides by 2

$n=3$

Therefore, the required equation is

3(n+4)=n+18

The value of n is 3

Translate the statement to algebraic language:1) Call x the unknown number2) The sum of 4 and a number = 4 + x3) Three multiplied by the sum of 4 and a number = 3(4 + x)4) Is the same as 18 more than the number: 3( 4 + x) = 18 + xSolve the equation:3*4 + 3x = 18 + x3x - x = 18 - 122x = 6x = 6/3x = 2.The number is 2.

What is the greatest common factor of 2 and 2.5

Answers

The GCF of 2 and 2.5 would be 2

What is the answer to this ‘???

Answers

Because trying to move the 14x and 23 to each side with just cancel themselves out and youll get 0=0

The two legs (shorter sides ) if a right angle triangle have lengths of 15 cm and 8 cm respectively. Determine the length of the largest third side (to the nearest cm).

Answers

By Pythagoras theorem,
h^2=a^2+o^2
Longest side is the same as the hypotenuse (h)
h^2=8^2+15^2
h^2=64+225
h^2=289
Square root both sides
h=17 cm

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