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3 years ago

The table below shows how much money a grocery store receives for selling different amounts of asparagus.

1 answer:

3 0

The answer is C) $30.00. First, find out how much 1lb costs. 1lb would cost 1/4 of 4lb. $10×1/4=$2.50/1lb. So 12 pounds would be 12x the cost of 1lb. $2.50×12 pounds=$30/12lb.

You might be interested in

Solve for y. identify the slope and y-intercept. then graph the equation.<br><br> y=-3x+1

stealth61 [152]

Answer:

the slope -3, slope meaning rate of change and y intercept is 1.

hope that answers your question

(used desmos to graph, good stuff!!!)

4 0

3 years ago

Complete the square and write in standard form. Show all work.What would be the conic section:CircleEllipseHyperbolaParabola

mote1985 [20]

ANSWER

This is an ellipse. The equation is:

$\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1$

EXPLANATION

We have to complete the square for each variable. To do so, we have to take the first two terms and compare them with the perfect binomial squared formula,

$(a+b)^2=a^2+2ab+b^2$

For x we have to take 16x² and -32x. Since the coefficient of x is not 1, first, we have to factor out the coefficient 16,

$16x^2-32x=16(x^2-2x)$

Now, the first term of the expanded binomial would be x and the second term -2x. Thus, the binomial is,

$(x-1)^2=x^2-2x+1$

To maintain the equation, we have to subtract 1,

$16(x^2-2x+1-1)=16((x-1)^2-1)=16(x-1)^2-16$

Now, we replace (16x² - 32x) from the given equation by this equivalent expression,

$16(x-1)^2-16+9y^2+72y+16=0$

The next step is to do the same for y. We have the terms 9y² + 72y. Again, since the coefficient of y² is not 1, we factor out the coefficient 9,

$9y^2+72y=9(y^2+8y)$

Following the same reasoning as before, we have that the perfect binomial squared is,

$(y+4)^2=y^2+8y+16$

Remember to subtract the independent term to maintain the equation,

$9(y^2+8y)=9(y^2+8y+16-16)=9((y+4)^2-16)=9(y+4)^2-144$

And now, as we did for x, replace the two terms (9y² + 72y) with this equivalent expression in the equation,

$16(x-1)^2-16+9(y+4)^2-144+16=0$

Add like terms,

$\begin{gathered} 16(x-1)^2+9(y+4)^2+(-16-144+16)=0 \\ 16(x-1)^2+9(y+4)^2-144=0 \end{gathered}$

Add 144 to both sides,

$\begin{gathered} 16(x-1)^2+9(y+4)^2-144+144=0+144 \\ 16(x-1)^2+9(y+4)^2=144 \end{gathered}$

As we can see, this is the equation of an ellipse. Its standard form is,

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

So the next step is to divide both sides by 144 and also write the coefficients as fractions in the denominator,

$\begin{gathered} \frac{16(x-1)^2}{144}+\frac{9(y+4)^2}{144}=\frac{144}{144} \\ \\ \frac{(x-1)^2}{\frac{144}{16}}+\frac{(y+4)^2}{\frac{144}{9}}=1 \end{gathered}$

Finally, we have to write the denominators as perfect squares, so we identify the values of a and b. 144 is 12², 16 is 4² and 9 is 3²,

$\frac{(x-1)^2}{(\frac{12}{4})^2}+\frac{(y+4)^2}{(\frac{12}{3})^2}=1$

Note that we can simplify a and b,

$\frac{12}{4}=3\text{ and }\frac{12}{3}=4$

Hence, the equation of the ellipse is,

$\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1$

3 0

1 year ago

Determine whether the relationship between the circumfrance of a circle and its diameter is a direct variation. If so, identify

kipiarov [429]

Answer:

The relationship between the circumference of a circle and its diameter represent a direct variation and the constant of proportionality is equal to the constant $\pi$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y=kx$

where K is the constant of proportionality

In this problem we know that

The circumference of a circle is equal to

$C=\pi D$

therefore

the relationship between the circumference of a circle and its diameter is a direct variation and the constant of proportionality is equal to the constant $\pi$

3 0

3 years ago

The price of a cup of coffee has dropped to $2.10 today. Yesterday's price was $2.35 . Find the percentage decrease. Round your

Lady bird [3.3K]

Percent increase/decrease is: (Change/original amount)x100 (.25/2.35)x100= 10.6%

6 0

3 years ago

What is the slope of c=3.95p

Vladimir79 [104]

The answer is m=3.95

8 0

3 years ago