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3 years ago

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Johnny and Cage are working together to mold figurines for a craft fair. They already have 8 figurines which were left from the

last craft fair. Johnny and Cage can mold 3 figurines every hour. Explain the reasons why this situation is linear.

2 answers:

alukav5142 [94]3 years ago

8 0

Answer:

See Explanation

Step-by-step explanation:

Given

$Initial = 8$

$Increment = 3$ (every hour)

Required

Explain why it is linear

First, we need to determine the equation that represents the scenario

Let x be the number of hours worked and y be the number of figurines at x hours.

The equation is determined as follows:

$y = Initial\ Figurines + Increment * x$

This gives:

$y = 8 + 3 * x$

$y = 8 + 3x$

Reorder

$y = 3x + 8$

A linear equation is of the form

$y = mx + b$

By comparison,

$y = mx + b$ is equivalent to $y = 3x + 8$

<em>Hence, we can conclude that the situation is linear</em>

stealth61 [152]3 years ago

3 0

Answer:

The situation can be described using the equation y = 3x + 8

The rate of change is not constant.

Step-by-step explanation:

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A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 166 feet and a maximum height of 40 feet. Find

scoray [572]

Answer:

38.27775 feet

Step-by-step explanation:

The bridge has been shown in the figure.

Let the highest point of the parabolic bridge (i.e. vertex of the parabola) be at the origin, $O(0,0)$ in the cartesian coordinate system.

As the bridge have the shape of an inverted parabola, so the standard equation, which describes the shape of the bridge is

$x^2=4ay\;\cdots(i)$

where $a$ is an arbitrary constant (distance between focus and vertex of the parabola).

The span of the bridge = 166 feet and

Maximum height of the bridge= 40 feet.

The coordinate where the bridge meets the base is $A(83, -40)$ and $B(-83, -40).$

There is only one constant in the equation of the parabola, so, use either of one point to find the value of $a$ .

Putting $A(83,-40)$ in the equation (i) we have

$83^2=4a(-40)$

$\Rightarrow a=-43.05625$

So, on putting the value of $a$ in the equation (i), the equation of bridge is

$x^2=-172.225y$

From the figure, the distance from the center is measured along the x-axis, x coordinate at the distance of 10 feet is, $x=\pm 10$ feet, put this value in equation (i) to get the value of y.

$(\pm10)^2=-172.225y$

$\Rightarrow y=-1.72225$ feet.

The point $P_1(10,-1.72225)$ and $P_2(-10,-1.72225)$ represent the point on the bridge at a distance of 10 feet from its center.

The distance of these points from the x-axis is $d=1.72225$ feet and the distance of the base of the bridge from the x-axis is $h=40$ feet.

Hence, height from the base of the bridge at 10 feet from its center

$= h-d$

$=40-1.72225=38.27775$ feet.

8 0

3 years ago

A bag contains 50 tokens: 20 pink ,13 blue and 17 purble.if a person selects one token, replaces it,and then selects a second to

stiv31 [10]

Answer:

Step-by-step explanation:

this is independent

20/50= 2/5= 40% of getting pink, probability of getting 2= 20%

13/50=0.26= 26% of getting blue, probability of getting 2= 13%

17/50=0.34=34% of getting purple, probability of getting 2 = 17%

70%

5 0

2 years ago

Complete the proofs using the most appropriate method. may require CPCTC.

n200080 [17]

For the first one, you did good. I will just suggest a couple things.

Statement Reason

JK ≅ LM Given

<JKM ≅ < LMK Given (You did both of these steps so well done.)

MK ≅ MK Reflexive Property (Your angle pair is congruent but isn't one of the interior angle of the triangles you are trying to prove.)

ΔJMK ≅ ΔLKM SAS

Problem 2: (You also have a lot of great stuff here.)

Statement Reason

DE ║ FG Given

DE ≅ FG Given

<DEF≅<FGH Given

<EDF≅<GFH Corresponding Angles (You don't need to know that F is the midpoint but you got corresponding angle pair which is correct.)

ΔEDF≅ΔGFH ASA

<DFE≅<FHG CPCTC

3 0

3 years ago

-18xy3 (9xy – 2y4 + 10x)

satela [25.4K]

The Answer Is -54xy(9xy-2y^4+10x)

7 0

3 years ago

What is the area of the figure?

Mrrafil [7]

Answer:

The shape has a total area of 14.96cm²

Step-by-step explanation:

To solve this all you need to do is take the area of the outer rectangle, and subtract the area of the inner rectangle.

The outer rectangle is 5.6 by 6.4 cm. To get its area, just multiply those dimensions. When you do so you get the area 35.84cm².

Next the inner rectangle needs to be subtracted. First though, we need its width, which we're not directly given.

We do however know the width of the entire shape, and the width of segments left after cutting out the inner rectangle. All we need to do then is subtract the later from the former to the the inner rectangle's width:

5.6cm - 1.2cm - 0.8cm = 3.6cm

Great! The inner rectangle has an area of 3.6cm × 5.8cm. That gives us 20.88cm².

The final step is to subtract that 20.88 square cm from the 35.84 that we already have. Doing so gives us a result of 14.96cm², and that is the final answer.

5 0

3 years ago

Read 2 more answers