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almond37 [142]
3 years ago
6

Ms.Booth has 16 red buttons and 24 blue buttons.She is making finger puppets. Each puppet has the same number of blue buttons an

d red buttons.How many puppets can she make if she uses all of the buttons
Mathematics
1 answer:
Leya [2.2K]3 years ago
7 0

Answer:

8 finger puppets.

Step-by-step explanation:

If the puppets both have the same number of buttons, you have to find the largest number that will fit into both numbers. In this case that would be 8:

2 red and 3 blue buttons per puppet.

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What is the length of the segment, endpoints of which are intersections of parabolas y=x^2− 11/4 x− 7/4 and y=− 7/8 x^2+x+ 31/8
kobusy [5.1K]

Answer:

The length of line segment is 5

Step-by-step explanation:

we are given equation of parabolas as

y=x^2-\frac{11}{4}x-\frac{7}{4}

y=-\frac{7}{8}x^2+x+\frac{31}{8}

Firstly, we will find intersection points

we can set them equal

and then we can solve for x

x^2-\frac{11}{4}x-\frac{7}{4}=-\frac{7}{8}x^2+x+\frac{31}{8}

Multiply all sides by 8

x^2\cdot \:8-\frac{11}{4}x\cdot \:8-\frac{7}{4}\cdot \:8=-\frac{7}{8}x^2\cdot \:8+x\cdot \:8+\frac{31}{8}\cdot \:8

8x^2-22x-14=-7x^2+8x+31

15x^2-30x-45=0

now, we can factor it

15(x^2-2x-3)=0

15(x-3)(x+1)=0

x=-1,x=3

now, we can find y-values

At x=-1:

y=(-1)^2-\frac{11}{4}(-1)-\frac{7}{4}

y=2

so, we get point as

(-1,2)

At x=3:

y=(3)^2-\frac{11}{4}(3)-\frac{7}{4}

y=-1

so, we get point as

(3,-1)

now, we can find distance between these two points

(-1,2)

x1=-1 , y1=2

(3,-1)

x2=3 , y2=-1

now, we can find distance

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

now, we can plug values

D=\sqrt{(3+1)^2+(-1-2)^2}

D=5

So,

The length of line segment is 5

6 0
3 years ago
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