Solve systems of linear equations by elimination.check your solution

Given:

Vertex of a quadratic function is at (3,-10).

The quadratic function passes through the point (0,8).

To find:

The equation of the quadratic function.

Solution:

The vertex form of a quadratic function is:

[tex]y=a(x-h)^2+k[/tex]              ...(i)

Where, (h,k) is vertex and a is a constant.

Vertex of a quadratic function is at (3,-10). So, [tex]h=3,k=-10[/tex].

[tex]y=a(x-3)^2+(-10)[/tex]

[tex]y=a(x-3)^2-10[/tex]              ...(ii)

The quadratic function passes through the point (0,8).

Putting [tex]x=0,y=8[/tex] in (ii), we get

[tex]8=a(0-3)^2-10[/tex]

[tex]8+10=a(-3)^2[/tex]

[tex]18=9a[/tex]

Divide both sides by 9.

[tex]2=a[/tex]

Putting [tex]a=2[/tex] in (ii), we get

[tex]y=2(x-3)^2-10[/tex]

Therefore, the correct option is J.

Answer:

150

Step-by-step explanation:

us I'd send bag I'd send veg svdudhvgdkdbdbdudduddh

Answer:

1/676

Step-by-step explanation:

In a deck of cards there are 2 red 8's ( 8 of diamonds and 8 of hearts)

P( red 8)  = number of red 8's/ total

               = 2/52 = 1/26

Then we put the card back so there are still 52 cards

In a deck of cards there are 2 black 10's ( 10 of spades and 10 of clubs)

P( black)  = number of black 10's/ total

               = 2/52 = 1/26

Multiply the probabilities together

P( red 8, black 10) = 1/26 * 1/26 = 1 /676

Answer:

Step-by-step explanation:

Answer:

200.96

803.84

Step-by-step explanation:

I wasn't sure if 16mm was the radius or diameter. If it's the diameter then use the first answer. If it was the radius then use the second answer.

In order to find the area of a circle use equation

[tex]A=\pi r^2[/tex]

r = radius, which is half of the line along the circle. If you have the diameter simply divide it by two and you have the radius.

Answer:

solution:

[tex] \sqrt{98 \times 2} [/tex]=[tex] \sqrt{196} [/tex]=[tex] \sqrt{14²} [/tex]=±14 is your answer

Answer:

[tex]\sqrt{98\cdot \:2}[/tex]

[tex]=\sqrt{196}[/tex]

[tex]=\sqrt{14^2}[/tex]

[tex]=14[/tex]

OAmalOHopeO

Answer:

Car 1 consumed 15 gallons, and Car 2 consumed 20 gallons.

Step-by-step explanation:

fuel efficiency = distance in miles/gallons of gas

fuel efficiency * gallons of gas = distance in miles

Car 1: 20 mpg

Car 2: 40 mpg

Total miles: 1100

Miles of Car 1: x

Miles of Car 2: 1100 - x

Total gallons: 35

Gallons for Car 1: y

Gallons for Car 2: 35 - y

Car 1:

fuel efficiency * gallons of gas = distance in miles

20 * y = x

Car 2:

fuel efficiency * gallons of gas = distance in miles

40 * (35 - y) = 1100 - x

20y = x

1400 - 40y = 1100 - x

20y = x

x = 40y - 300

40y - 300 = 20y

20y = 300

y = 15

35 - y = 35 - 15 = 20

Car 1 consumed 15 gallons, and Car 2 consumed 20 gallons.

Answer: 100

Hi!

ok so the Pythagorean theorem is

[tex]c=\sqrt{x} a^2+b^2=\sqrt{x} 8^2+6^2=10[/tex]

so the other side is 10.

the square 8 is 8*8

and square 6 is 6*6

so the other square is 10*10=100.

so the area of the blank square is 100.

Step-by-step explanation:

Can I have brainliest?

Thanks!

Have a nice day!

Answer:

The GCF is 12t

Step-by-step explanation:

Here, we want to calculate the greatest common factor of the given polynomials

To do this, we need to write each as the product of its prime factors

We have this as;

48t = 2 * 2 * 2 * 2 * 3 * t

60st = 2 * 2 * 3 * 5 * s * t

we then bring out pairs of similar terms

So the GCF would be;

2 * 2 * 3 * t = 12t

Answer:

La respuesta al ejercicio es:

Step-by-step explanation:

Teniendo en cuenta que el capital inicial es de $9,000.00 y el capital tras un año es de $9,400.00, se identifica en primera instancia que la ganancia gracias al interés anual fue de $400, por lo cual se pueden tener en cuenta las siguientes variables:

Y el siguiente sistema de ecuaciones:

En la segunda ecuación, cambiaremos los porcentajes para facilitar los cálculos posteriores:

   2. x * 0.05 + y * 0.04 = 400

Lo cual también se puede representar como:

   2. 0.05x + 0.04y = 400

Procedemos a despejar una variable, en este caso despejaré la variable y de la primera ecuación:

Y la reemplazaré en la segunda ecuación:

Ahora operamos:

Restamos las variables x:

Y despejamos el valor real de x:

Ya que x es el monto de dinero puesto al 5% anual, ahora sabemos que dicho monto fue $4,000.00, por último, reemplazamos este valor en la primera ecuación para identificar el valor de y:

Por último, sabemos que el monto de dinero puesto al 4% fue $5,000.00.

Answer:

27x30=810

Step-by-step explanation:

Answer: Mr.Smith ordered 810 baseballs

Step-by-step explanation:

To find the answer we need to:

1) Since, we know that Mr.Smith ordered 27 boxes and 30 baseball are in each of them. We need to multiply.

27 x 30 = 810

60+40=x

y=x+9

MInus

x=100

y=109

Diffrence 9

Answer:

x = -20

y = -11

Answer:

150.9 cubic inches

Step-by-step explanation:

volume of he gas = volume of a cone x 3/4

Volume of a cone 1/3(nr^2h)

n = 22/7

r = radius  

h = height

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

8/2 = 4 inches

1/3 (22/7 x 4^2 x 12) = 201.142857 in^3

volume of the gas = 3/4 x 201.142857 in^3 = 150.9 in^3

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

Answer:

u = 2√3 ≈ 3.46410162

Step-by-step explanation:

Because this is a right triangle, you can use the trigonometric formulas:

tangent = opposite side/adjacent side

sine = opposite side/hypotenuse

cosine = adjacent side/hypotenuse

Here, we have the measure of an angle, 60°. Side u is opposite to it and the hypotenuse, 4, is given. We can use these numbers to work with:

sine = opposite side/hypotenuse

sin(60) = u/4

sin(60)/1 = u/4

Cross multiply:

u = 4 (sin(60))

Input into calculator:

u = 2√3 ≈ 3.46410162

Answer: The slope intercept is at (0,5)

Step-by-step explanation: This is because the line intercepts the y-axis at (0.5).

Answer:

f=

1

/4

y+

−1

/2

Step-by-step explanation:

Let's solve for f.

y=5x^0+4x−3

Step 1: Flip the equation.

4x+2=y

Step 2: Add -2 to both sides.

4x+2+−2=y+−2

4x=y−2

Step 3: Divide both sides by 4.

4x

/4

=

y−2

/4

x=

1

/4

y+

−1

/2

=f=

1

/4

y+

−1

/2

Answer:

D.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:5:3

Step-by-step explanation:

Answer:

Mango is the answer

Step-by-step explanation:

The question is incomplete, let's take an hypothetical value for the Area of the circle ;

Let the are aid the circle = x in²

Answer:

Kindly check explanation

Step-by-step explanation:

The scale factor = 5/4

The initial area of square = x in²

The area of the circle after dilation will be :

Scale factor * initial area of circle

5/4 * x in²

Area after dilation = 5/4(x) in²

Just substitute the original value of the square for X in the solution to obtain the exact answer.

Answer: 19 and 1/2 cups

Step-by-step explanation:

write out the problem then do 3/4 then multiply by 13. Next, multiply the answer by 2.

Hope this helps!

Answer:

15

Step-by-step explanation:

Pythagorean theorem: the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

C = the square root of A squared + B squared.

plug in the numbers

C = the square root of 9 squared + 12 squared = 15

Answer:

15

Step-by-step explanation:

[tex] {9}^{2} + {12}^{2} = c ^{2} \\ 81 + 144 = {c}^{2} \\ 225 = {c}^{2} \\ \sqrt{225} = c \\ \sqrt{225} = 15[/tex]

Answer:

the answer is 84 being how you asked the question but I dont think thats what you meant to ask. if thars wrong just tell me and ill answer it the way you need it

Step-by-step explanation:

Answer:

84 miles

Step-by-step explanation:

Answer:

1 hour and 48 minutes

Step-by-step explanation:

270/2 hours = 135 per hour for 3 people

135/3 people = 45, so each person delivers 45 per hour

45 x 5 people =225 per hour

405/225 = 1.8 hours

It will take 1.8 hours for five people to deliver leaflets to 405 houses.

Given that, 3 people take 2 hours to deliver leaflets to 270 houses.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here,

270/2 hours = 135 leaflets per hour for 3 people

135/3 people = 45, so each person delivers 45 leaflets per hour

45 x 5 people =225 per hour

405/225 = 1.8 hours

Hence, it will take 1.8 hours for five people to deliver leaflets to 405 houses.

To learn more about the unitary method visit:

brainly.com/question/22056199.

#SPJ2

Answer:

28

Step-by-step explanation:

Im from the long comment this is the answer

576+b^2=900

b^2=324

√324

b= 18

so 18+10 = 28