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3 years ago

Macy estimated a product to be 800. The actual product is 768. Her estimate was an

Mathematics

1 answer:

Vladimir79 [104]3 years ago

6 0

Answer:

Overestimate

Step-by-step explanation:

it would be an underestimate if the number was lower than the actual number but since its larger than it is an overestimation.

hope this helps

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An object is launched upward at 64 ft/sec from a platform that is 80 feet high. What is the objects maximum height if the equati

Free_Kalibri [48]

Max height is the vertex
convert to vertex form (y=a(x-h)^2+k) by completeing the square

h(t)=-16(t²-4t)+80
h(t)=-16(t²-4t+4-4)+80
h(t)=-16((t-2)²-4)+80
h(t)=-16(t-2)²+64+80
h(t)=-16(t-2)²+144

vertex is (2,144)
at t=2, the height is 144

max height is 144ft

4 0

2 years ago

Choose the correct simplification of the expression ( 4x/y)^2.

erik [133]

$\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{4x}{y}\right)^{2} \end{gathered}$}$

To raise 4x/y to a power, raise the numerator and denominator to the power, and then divide.

$\large\displaystyle\text{$\begin{gathered}\sf \frac{(4x)^{2} }{y^{2} } \end{gathered}$}$

Expand (4x)².

$\large\displaystyle\text{$\begin{gathered}\sf \frac{4^{2} x^{2} }{y^{2} } \end{gathered}$}$

Calculates 4 to the power of 2 and gets 16.

$\boxed{\large\displaystyle\text{$\begin{gathered}\sf \frac{16x^{2} }{y^{2} } \end{gathered}$} }$

6 0

1 year ago

The equation 2x2 − 12x + 1 = 0 is being rewritten in vertex form. Fill in the missing step. Given 2x2 − 12x + 1 = 0 Step 1 2(x2

Bezzdna [24]

Answer:

Part 1) $2(x-3)^{2}-17=0$ (the missing steps in the explanation)

Part 3) (8, 4); The vertex represents the maximum profit

Part 4) x = 3.58, 0.42

Part 5) x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made

Part 6) 2(x − 7)2 + 118; x = $7

Part 7) The maximum height of the puck is 4 feet. −(x − 4)^2 + 6

Part 8) (x + 3)^2 − 4

Part 9) 2(x − 1)^2 = 4

Part 10) 8(x − 4)^2 + 592

Step-by-step explanation:

Part 1) we have

$2x^{2} -12x+1=0$

Convert to vertex form

step 1

Factor the leading coefficient and complete the square

$2(x^{2} -6x)+1=0$

$2(x^{2} -6x+9)+1-18=0$

step 2

$2(x^{2} -6x+9)+1-18=0$

$2(x^{2} -6x+9)-17=0$

step 3

Rewrite as perfect squares

$2(x-3)^{2}-17=0$

Part 3) we have

$f(x)=-x^{2}+16x-60$

we know that

This is the equation of a vertical parabola open downward

The vertex is a maximum

Convert to vertex form

$f(x)+60=-x^{2}+16x$

Factor the leading coefficient

$f(x)+60=-(x^{2}-16x)$

Complete the squares

$f(x)+60-64=-(x^{2}-16x+64)$

$f(x)-4=-(x^{2}-16x+64)$

Rewrite as perfect squares

$f(x)-4=-(x-8)^{2}$

$f(x)=-(x-8)^{2}+4$

The vertex is the point (8,4)

The vertex represent the maximum profit

Part 4) Solve for x

we have

$-2(x-2)^{2}+5=0$

$-2(x-2)^{2}=-5$

$(x-2)^{2}=2.5$

square root both sides

$(x-2)=(+/-)1.58$

$x=2(+/-)1.58$

$x=2(+)1.58=3.58$

$x=2(-)1.58=0.42$

Part 5) we have

$f(x)=-x^{2}+50x-264$

we know that

The zeros or x-intercepts are the value of x when the value of the function is equal to zero

In this context the zeros represent the number of monthly memberships where no profit is made

To find the zeros equate the function to zero

$-x^{2}+50x-264=0$

$-x^{2}+50x=264$

Factor -1 of the leading coefficient

$-(x^{2}-50x)=264$

Complete the squares

$-(x^{2}-50x+625)=264-625$

$-(x^{2}-50x+625)=-361$

$(x^{2}-50x+625)=361$

Rewrite as perfect squares

$(x-25)^{2}=361$

square root both sides

$(x-25)=(+/-)19$

$x=25(+/-)19$

$x=25(+)19=44$

$x=25(-)19=6$

Part 6) we have

$-2x^{2}+28x+20$

This is a vertical parabola open downward

The vertex is a maximum

Convert the equation into vertex form

Factor the leading coefficient

$-2(x^{2}-14x)+20$

Complete the square

$-2(x^{2}-14x+49)+20+98$

$-2(x^{2}-14x+49)+118$

Rewrite as perfect square

$-2(x-7)^{2}+118$

The vertex is the point (7,118)

therefore

The video game price that produces the highest weekly profit is x=$7

Part 7) we have

$f(x)=-x^{2}+8x-10$

Convert to vertex form

$f(x)+10=-x^{2}+8x$

Factor -1 the leading coefficient

$f(x)+10=-(x^{2}-8x)$

Complete the square

$f(x)+10-16=-(x^{2}-8x+16)$

$f(x)-6=-(x^{2}-8x+16)$

Rewrite as perfect square

$f(x)-6=-(x-4)^{2}$

$f(x)=-(x-4)^{2}+6$

The vertex is the point (4,6)

therefore

The maximum height of the puck is 4 feet.

Part 8) we have

$x^{2}+6x+5$

Convert to vertex form

Group terms

$(x^{2}+6x)+5$

Complete the square

$(x^{2}+6x+9)+5-9$

$(x^{2}+6x+9)-4$

Rewrite as perfect squares

$(x+3)^{2}-4$

Part 9) we have

$2x^{2}-4x-2=0$

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert to vertex form

Factor 2 the leading coefficient

$2(x^{2}-2x)-2=0$

Complete the square

$2(x^{2}-2x+1)-2-2=0$

$2(x^{2}-2x+1)-4=0$

Rewrite as perfect squares

$2(x-1)^{2}-4=0$

$2(x-1)^{2}=4$

The vertex is the point (1,-4)

Part 10) we have

$8x^{2}-64x+720$

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert to vertex form

Factor 8 the leading coefficient

$8(x^{2}-8x)+720$

Complete the square

$8(x^{2}-8x+16)+720-128$

$8(x^{2}-8x+16)+592$

Rewrite as perfect squares

$8(x-4)^{2}+592$

the vertex is the point (4,592)

The population has a minimum at x=4 years ( that is after 4 years since 1998 )

6 0

2 years ago

Someone please do this one for me !!!!

oee [108]

Answer:

Plot the points in black and connect them.

Plot the point in blue and count up 3 and to the right 1. Plot and connect the points.

Step-by-step explanation:

Using your cursor/mouse, you will first choose the color black. Then you will plot the points given to you (2,2) and (5,8) by first finding the x-coordinate of (x,y). Start at 2 on the x-axis. Follow the grid line up two units so you will also be at the 2 on the y-axis. Plot or draw a dot/circle on this grid line. Go back to the x-axis and start again at 5 on the x-axis. Follow the grid line up eight units so you will also be at the 8 on the y-axis. Plot or draw a dot/circle on this grid line. Connect the dots for your line.

Using your cursor/mouse, you will choose the color blue. Then you will plot the point given to you (10,5) by first finding the x-coordinate of (x,y). Start at 10 on the x-axis. Follow the grid line up five units so you will also be at the 5 on the y-axis. Plot or draw a dot/circle on this grid line. Instead of plotting another point. This time you will count from the blue point up three units and over to the right one. Mark this grid line as a point. Now connect them.

6 0

3 years ago

Which of the following expressions represents the LCM of 91 x^2y and 104 xy^3 ?

Allushta [10]

728x^2y^3 hope this helps

6 0

3 years ago