Which represents a quadratic function?

Manuel bought 2kg of jelly beans and 2kg of gummy worms for a total of $26. Danny bought 2kg of jelly beans and 3kg of gummy wor

charle [14.2K]

Answer:

Jelly beans: $6 for 1 kg

Gummy worms: $7 for 1 kg

Step-by-step explanation:

In this question, we need to find the cost of 1kg of jelly beans and gummy worms.

To do this, make equations for both scenarios and solve:

2j + 2g = 26

2j + 3g = 33

Turn the bottom equation negative, as we will first solve for gummy worms (g).

2j + 2g = 26

-2j - 3g = -33

Solve:

-g = -7

Divide both sides by -1.

g = 7

We now know that gummy worms cost $7 for 1 kg

To solve for jellybeans (j), plug in 7 to g in one of the equations and solve:

2j + 2(7) = 26

2j + 14 = 26

Subtract 14 from both sides.

2j = 12

Divide both sides by 2.

j = 6

Jellybeans cost $6 for 1 kg.

Check answer by plugging in values to one of the equations:

2(6) + 2(7) = 26

12 + 14 = 26

26 = 26

3 0

3 years ago

Triangle P Q R is shown. Angle Q R P is a right angle. Angle R P Q is 30 degrees and angle P Q R is 60 degrees. Given right tria

mote1985 [20]

Answer:

The correct option is option (c).

$Sin \ P= \frac {RQ}{PQ}$

Step-by-step explanation:

Right angled triangle:

One angle must be 90° and other two angles are acute angle.
The hypotenuses is the longest side of the triangle and opposite right angle.
It follows the Pythagorean Theorem.

Given that,

∠QRP= 90°, ∠RPQ= 30°, ∠PQR = 60°

we know that,

$sin \theta =\frac{Opposite }{Hypotenuse}$

for sin P , the opposite is QR.

The hypotenuse is PQ.

Therefore,

$Sin \ P= \frac {RQ}{PQ}$

5 0

3 years ago

Read 2 more answers

Which phrase best describes the translation from the graph y=(x-5)^2+7 to the graph of y=(x+1)^2-2

Helga [31]

Start from the parent function $f(x)=x^2$

In the first case, you are computing

$f(x-5)+7$

In the second case, you are computing

$f(x+1)-2 /tex] There are two translation going on: when you transform [tex] f(x) \to f(x+k)$ , you translate the function horizontally, $k$ units left if $k>0$ and $k$ units right if $k$ .

On the other hand, when you transform $f(x) \to f(x)+k$ , you translate the function vertically, $k$ units up if $k>0$ and $k$ units down if $k$ .

So, the first function is the "original" parabola $f(x)=x^2$ , translated $5$ units right and $7$ units up. Likewise, the second function is the "original" parabola $f(x)=x^2$ , translated $1$ units left and $2$ units down.

So, the transformation from $(x-5)^2+7$ to $(x+1)^2-2$ is: go $6$ units to the left and $2$ units down

8 0

3 years ago

Read 2 more answers

Line segment WX is the radius of circle X, and line segment ZY is the radius of circle Y. Points W, X, C, Y, and Z are all on li

Andrews [41]

Point D is the midpoint of the outer circle that we aim to find the area of

The circle has a diameter of WZ and radii of WC and CZ

We know that YZ=YD=10 cm

Let DC be $x$ and CY be $10-x$

The radius of the outer circle can be written as $8+8+x$ or $10+10-x$ which we can equate to find the value of $x$

$8+8+x=10+10-x$
$16+x=20-x$
$2x=4$
$x=2$

Therefore, the radius of the circle is $8+8+2=18$

And hence the area of the circle is $\pi (18^{2})$ =324 $\pi$

4 0

3 years ago

Read 2 more answers

What is the surface area of this right rectangular prism? Enter your answer as a

mixas84 [53]

You will find all of the surface area of all of the sides and add them together to find the surface area of the retangular prisim. So, what I would do is the front and back are both 54, so 108. The sides are 27, so 54. The top and bottom are 18, so 36. Add them together, and you will get 198. I hope this helps.

6 0

3 years ago