what is the vertex of the parabola using this equation y=-x^2+4x+5

Answers

Answer 1

Answer:

             (2, 9)

Step-by-step explanation:

[tex]y=-x^2+4x+5\quad \implies\quad a=-1\,,\ b=4\,,\ c=5\\\\h=\dfrac{-b}{2a}=\dfrac{-4}{2(-1)}=2\\\\k=c-\dfrac{b^2}{4a}=5-\dfrac{4^2}{4(-1)}=5-\dfrac{16}{-4}=5+4=9[/tex]

Or by completing the square:

[tex]y=-x^2+4x+5\\\\y=-(x^2-4x)+5\\\\y=-(\underline{x^2-2\cdot x\cdot 2+2^2}-2^2)+5\\\\y=-\left((x-2)^2-4\right)+5\\\\y=-(x-2)^2+4+5\\\\y=-(x-2)^2+9\quad\implies\quad h=2\,,\ k=9[/tex]


Related Questions

Help me with this plz!

Answers

Answer:

y=2x-2

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=2x-2

i'll mark you has brainliest​

Answers

Answer:

x-1=y

Step-by-step explanation:

Is this what you need?

Find the measure of the numbered angles.

9. m<1

10. m<2

11. m<3

12. m<4

13. m<5

14. m<6​

Answers

Answer:

the complementary angles and the supplementary angles

Step-by-step explanation:

m<1=60

m<2=120

m<3=60

m<4=120

m<5=30

m<6=30

simplify the number using the imaginary unit i square root of -98

Answers

Answer:

[tex]\sqrt{-98}=7i\sqrt{2}[/tex]

Step-by-step explanation:

We wish to simplify:

[tex]\sqrt{-98}[/tex]

We can rewrite it as such:

[tex]=\sqrt{-1\cdot 98} =\sqrt{-1\cdot 49\cdot2}=\sqrt{-1}\cdot\sqrt{49}\cdot\sqrt{2}[/tex]

Hence:

[tex]=i(7)\sqrt{2}[/tex]

Therefore:

[tex]\sqrt{-98}=7i\sqrt{2}[/tex]

Is this expression true or false?

Answers

Answer:

False

Step-by-step explanation:

THE ANSWER IS FALSE.

What is the simplest form of the expression (-12.7 - 3.1x) + 5.9y - (4.2y + x)

Answers

Answer:

Step-by-step explanation:

(-12.7-3.1x)+5.9y-(4.2y+x) combine terms

-4.1x+1.7y-12.7

55% of 120 children at the theatre were boys. How many were boys?

Answers

There were 66 boys.

2x - y = 9
x + 3y = -6

Answers

Answer: Your answer should be {x,y}={3,−3}

Step-by-step explanation: Hoped this helped!!!!

2c+3d+2c+6d get it correct mark brainliest

Answers

Answer:

4c+9d

Step-by-step explanation:

group together the twos to get four and the 3 and the 6 to get 9.

A rubber bouncy ball is bouncing up and down such that the ball's distance, d, in feet above the ground is given by the inequality

Which of the following graphs shows all the possible distances?

Answers

Answer: Option D.

Step-by-step explanation:

We have the inequality:

Id - 3.5I ≤ 1.5

remember that : IxI < d means that:

-d < x  < d

Now let's find the possible values of d, breaking the absolute value we have that:

-1.5 ≤ d - 3.5 ≤ 1.5

adding 3.5 in each part, we have:

-1.5 + 3.5 ≤ d - 3.5 + 3.5 ≤ 1.5 + 3.5

2 ≤ d ≤ 5

Then d can be any value in the set [2, 5]

Then the correct graph is D, because the purple line starts at 2, and ends at 5.

A pizza shop sells pizzas that are 10 inches (in diameter) or larger. A 10-inch cheese pizza costs $1.50, and each additional topping costs $0.75.

Write an equation that represents the cost of a pizza. Be sure to specify what the variables represent.

Answers

Answer:

A pizza shop sells pizzas that are 10 inches orr larger. A 10-inch cheese pizza costs $8 and each additional costs $1.50 and each additional topping costs $0.75.

The equation that represents the cost of a pizza is:

P = $10 + $1.50a + $0.75b

Where 'a' represents the number additional inches and 'b' represents the number of additional toppings.

Step-by-step explanation:

what would the slope intercept form be?​

Answers

Answer:

y=-2x

Step-by-step explanation:

Lines a and d are
A. non-coplanar.
B. parallel.
C. perpendicular.
D. skew.

Answers

c. perpendicular
they make right angles so they would be perpendicular
The answer would be C

a cuboid with a volume of 374cm^3 has dimensions

Answers

Answer:

2 x 11  x 17  = L x W x H

Step-by-step explanation:

x² + 12 (8) - 160 = 0

8(8) + 96 -160 = 0

8(8) + 96 -160  

160 -160 = 0

x² + 12x -160 = 0  

x² + 8 × - 20 = 0  

(x +8) (x-20)

2( x+3 ) × (x+9) = 374

(x+3) × (x+9) = 374 ÷ 2

(x+3)× (x+ 9) = 187

x² = 184 - 9

x² = 175

x = 175/25

x = 8

Formula of Volume of Cuboid  

V = L ×W × H

V = 2 × (x+3) × (x+9)

2 ( 8+3 ) × ( 8+ 9)

2 (11) × (17)

x + 3 = 11

x + 9 = 17

Volume L × W × H

2 × 11 × 17 = 374cm³

satisfies the equation

dimensions of the cuboid

2  11  and  17  

PLS HELP MATH HURRY WILL GIVE BRAINLIEST

Answers

Answer:

B

Step-by-step explanation:

It’s B

ABD=CBD=1/2 ABC

Answer: D.

Step-by-step explanation:

reasoning is because if you were take the measure of CBD and divide it by 2 then you would get the measure of ABD.

(a) In 2008 the total number of tickets sold for an athletics meeting was 3136.
The ratio child tickets sold : adult tickets sold = 17:32.
(i) How many child tickets were sold?

Answers

It’s child TO adult. So 17 child tickets were sold

Un introductor de carne de res en canal compró mil piezas a 200 pesos cada. Vendió 600 de ellas obteniendo una ganancia del 25 %. ¿A qué precio deberá vender las piezas restantes si la utilidad promedio del lote completo (de las mil piezas) debe ser del 30 %? ¿Cuál es su utilidad por la venta de las mil piezas?

Answers

Responder:

275 pesos

60.000 pesos

Explicación paso a paso:

Dado que :

Número de piezas = 1000

Precio por pieza = 200

600 piezas vendidas con un beneficio del 25%

(100 + 25)% = 125% de 200

1,25 * 200 = 250 cada uno

Precio de 600:

(600 * 250) = 150 000

Para un beneficio del 30% de todo el lote:

(100 + 30)% = 130% * 200 = 260

(1000 * 260) = 260 000

Precio de los 400 restantes:

(260.000 - 150.000) / 400 = 110.000 / 400 = 275 peso

Beneficio de la venta:

Precio de venta:

(150.000 + 110000) = 260000 pesos

Precio de compra :

(1000 * 200) = 200.000 pesos

260.000 - 200.000 = 60.000 pesos

help me with this please it’s 3 grade

Answers

Answer:

10 more hotdogs were sold on Friday than Monday.

Step-by-step explanation:

On Monday the graph says that there were 10 hotdogs sold, on Friday it says that there were 20 sold

20-10=10, so 10 hotdogs more were sold

Answer:10

Step-by-step explanation: there was 20 hot dogs sold on saturday and on monday there was 10.  20-10=10

At the bowling alley ethans family spent $4 to rent shoes plus $8 for each game that they bowled if they spent $36 total how many games did they bowl

Answers

Answer:

4

Step-by-step explanation:

If they spent 36 dollars

and the shoes were 4 dollars,

36-4=32 dollars left for the games

32/8=4 games

**ANSWER FAST!!**

h(1)=

Evaluate functions from their graph

Answers

-2 is the correct answer, because h(1) is the input and on the graph h(1) is the x-value so your y- value is -2 and it is the output

Answer:

Evaluate functions from their graph h(1)= -2

Step-by-step explanation:

See attached!

I'm sorry, I am struggling with this Question. Can anyone help me with the toxicity of this Question. ​

Answers

Answer:

I could be wrong but I don't think they're congruent.

Step-by-step explanation:

What is the value of x?
2x-5/3=11

Answers

Answer:

19/3

Step-by-step explanation: 19/3=6.33


The sum of two numbers is 72. The greater number is 8 more than the smaller number. Which equation can be used to
solve for the smaller number?
O x-(X + 8) = 72
O x + (x + 8) = 72
O X(X + 8) = 72
O x(x - 8) = 72

Answers

B. X+(x+8)=72 is the answer

The value of y varies directly with x. When y = 75, 7 = 1. What is the value of y when x is 272

Answers

I’m assuming that 7 means x, and honestly all you have to do is multiply. x= 1 , y= 75.. so just multiply 75 and 272. The answer is 20,400.

Please help me......❕

Answers

Answer:

Mia is right

Step-by-step explanation:

the red graph is a negative slope. y=4+6x is a positive slope.

Answer:

Mia

Step-by-step explanation:

If you plot in any number (say 1) for x, then y will equal 10 (4+6(1)). The blue dotted line shows that as it approaches 1 on the x axis, it approaches 10 on the y axis. However, the red line shows that when x=1, y is about 3.5

Thus Mia is correct

Mike wants to fence in part of his backyard. He wants the length of the fenced-in area to be at least 20 feet long, l ≥ 20. He has 200 feet of fencing. The inequality that models the possible perimeter of the yard is 2l + 2w ≤ 200.

Which are possible dimensions for Mike’s backyard? Check all that apply.

Answers

w = 10 ft; l = 50 ft is Correct

w = 90 ft; l = 30 ft is Correct

w = 50 ft; l = 40 ft is Correct

answers in order are 2 3 5

Find the slope of the line that passes through the points (4, 3) and (2, 7).

Answers

Answer: -2/1

Step-by-step explanation:

Slope = Change in y/Change in x

Equation:

(7-3)/(2-4)

Evaluate:

4/-2

Simplify:

-2/1

A store sells $5000 worth of running shoes on Monday. On Tuesday, it sells $6250 worth of running shoes. What is the percent increase in sales between Monday and Tuesday?

Answers

Answer:6300

Step-by-step explanation:

Using synthetic division, what is the width of the rectangle? Brainliest!! 5 stars, thanks.

Answers

Hi there!

[tex]\large\boxed{5x^{2} + 4x - 6}[/tex]

**Work pictured below**

Since x + 3 is one of the factors, set it equal to zero to find the root:

x + 3 = 0

x = -3

Use -3 in the synthetic division process to solve for the width.

Use the coefficients of 5x³ + 19x² + 6x - 18 to do synthetic division:

5, 19, 6, -18

To do synthetic division, arrange the numbers in the polynomial as shown with the root outside of the diagram.

1. Bring down the first number

2. Multiply by the root and add that number to the next number. Bring the sum down to the bottom.

3. Repeat until finished with all numbers. If a number is a perfect root, it will have a remainder of 0 at the last number.

In this instance, doing so produced the numbers 5, 4 and -6. There was also no remainder as the last number produced 0. Therefore, the width of the rectangle is:

5x² + 4x - 6 **First term is always one degree LESS than you started with**

Answer:

5x^2 + 4x - 6

Step-by-step explanation:

(5x^3 + 19x^2 + 6x - 18)/(x + 3)

   

-3  |   5   19   6   -18

            -15  -12  18

         5   4   -6     0

(5x^3 + 19x^2 + 6x - 18)/(x + 3) = 5x^2 + 4x - 6

Given f(x)=5x+4 solve for "x" when f(x)=24.

Answers

Answer:

x=4

Step-by-step explanation:

f(x)=5x+4

By given,

f(x)=24

5x+4=24

5x=20

x=4

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