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Dimas [21]
2 years ago
10

Kurt, Sophia, and Franco had a paper airplane throwing contest after school. Kurt's airplane flew 8.6 yards. Sophia's airplane f

lew 2.2 yards farther than Kurt's airplane. Franco threw his airplane 1.5 times as far as Sophia's airplane. How far did Franco's paper airplane fly?
Mathematics
2 answers:
Mila [183]2 years ago
8 0

Answer: 16.2

Step-by-step explanation:

8.6 + 2.2 = 10.8

10.8 x 1.2 = 16.2

horsena [70]2 years ago
5 0

Answer:

16.2

Step-by-step explanation:

You might be interested in
Mary was told that a line goes through the points (1, 3) and (6, -2) and has a slope of 3.
ki77a [65]

Answer:

a. The slope is incorrect

b. y = 3x, ( 0 , 0 )

c) y = 4 - x

Step-by-step explanation:

Given:-

The slope between two points (1, 3) and (6, -2) is 3.

a. Explain why the information Mary was given cannot be correct.

- The slope between two arbitrary points, ( x1 , y1 ) and  (x2 , y2) is given by the following relationship:

                         slope = ( y2 - y1 ) / ( x2 - x1)

- Use the given points (1, 3) and (6, -2) and determine the slope:

                        slope = ( -2 - 3 ) / ( 6 - 1 )

                        slope = ( -5 ) / ( 5 )

                        slope = -1

- Yes, the given slope is incorrect it should be = -1

b.If the given point (1, 3) and the given slope are correct, what is the equation for the line? Give the  coordinates of another point on the line

- We will assume the point (1,3) lies on line with a slope = 3.

- We will use the slope-intercept equation of line:

                              y = slope*x + c

Where,      m : Slope

                 c : y-intercept

                             y = 3x + c

Using the given correct point to evaluate the y-intercept (c):

                             3 = 3*1 + c

                             c = 0

- The equation of line is,

                            y = 3x

- The origin (0,0) lies on the line y = 3x.

c. If the given points are correct for the line, what is the slope? Write an equation for the line

- We will assume the points (1, 3) and (6, -2) lies on line with a slope calculated in part (a) to be = -1.

- We will use the slope-intercept equation of line:

                              y = slope*x + c

Where,      m : Slope

                 c : y-intercept

                             y = -x + c

Using the given points to evaluate the y-intercept (c):

                             3 = -1 + c

                             c = 4

- The equation of line is,

                            y = -x + 4

4 0
2 years ago
For the binomial expansion of (x + y)^10, the value of k in the term 210x 6y k is a) 6 b) 4 c) 5 d) 7
Sloan [31]

Answer:

a) 6

Step-by-step explanation:

Expanding the polynomial using the formula:

$(x+y)^n=\sum_{k=0}^n \binom{n}{k} x^{n-k} y^k $

Also

$\binom{n}{k}=\frac{n!}{(n-k)!k!}$

I think you mean 210x^6y^4

We can deduce that this term will be located somewhere in the middle. So I will calculate k= 5; k=6 \text{ and } k =7.

For k=5

$\binom{10}{5} (y)^{10-5} (x)^{5}=\frac{10!}{(10-5)! 5!}(y)^{5} (x)^{5}= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5! }{5! \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } \\ =\frac{30240}{120} =252 x^{5} y^{5}$

Note that we actually don't need to do all this process. There's no necessity to calculate the binomial, just x^{n-k} y^k

For k=6

$\binom{10}{6} \left(y\right)^{10-6} \left(x\right)^{6}=\frac{10!}{(10-6)! 6!}\left(y\right)^{4} \left(x\right)^{6}=210 x^{6} y^{4}$

5 0
2 years ago
From class we learned that in 2010 the federal debt (in millions) was $13,561,623 and the population of the U.S. was 309 million
NemiM [27]
Question A: The per capita debt would be $43,888.75. 

Per capita means the amount per person. To find this amount, we need to take the total debt and divide it by the number of people.

13,561,623 divided by 309 = 43,888.75

For Question B, you will need to have the other CPI value from the table.
7 0
2 years ago
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, 1) and (0, 3). Everything to th
Allushta [10]

Answer:

y>\frac{2}{3}x+3

Step-by-step explanation:

step 1

Determine the slope of the dashed line

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

we have

(-3,1) and (0,3)

substitute

m=\frac{3-1}{0+3}

m=\frac{2}{3}

step 2

Find the equation of the dashed line in slope intercept form

y=mx+b

we have

m=\frac{2}{3}

b=3 ---> given problem

substitute

y=\frac{2}{3}x+3

step 3

Find the equation of the inequality

we know that

Is a dashed line and everything to the left of the line is shaded

so

y>\frac{2}{3}x+3

see the attached figure to better understand the problem

8 0
1 year ago
Read 2 more answers
Alice has seven times the amount of pens that Maurice has. Paul has two-thirds of the amount of pens as Alice and Suzy have comb
zepelin [54]

Answer:

Dawn has 32 pens.

Step-by-step explanation:

  • Let No. of pens Alice has = A
  • Let No. of pens Maurice has = M
  • Let no of pens Paul has = P
  • Let no. of pens Suzy has = S
  • Let no of pens Dawn has = D

Given :

  • A = 7M
  • P = 2/3 (A + S)  
  • D = P + 12
  • S = 1/2 M
  • If S = 2 {Given}
  • M = 4    [∵ S = 1/2 M → M = 2S = 2X(2) ]
  • A = 28  [ ∵ A = 7M → A = 7 x 4 ]
  • P = 20  [∵ P = 2/3 (A+S) → P = 2/3 (28 + 2) = 2/3 (30) ]
  • D = 32  [ ∵ D = P + 12 → D = 20 + 12 ]

5 0
1 year ago
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