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3 years ago

Toby ran 5 miles.Gwen ran twice as far as toby? How fast did Gwen run

Mathematics

2 answers:

Alexxandr [17]3 years ago

4 0

5×2= Gwen
Gwen ran 10 miles

antiseptic1488 [7]3 years ago

4 0

Gwen ran 10 miles
Do you mean how far did she run?

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Solve the system of equations below. A. B. C. D.

timofeeve [1]

Answer:

A. (-7 -2)

Step-by-step explanation:

You can eliminate y by multiplying the first equation by 7 and subtracting 6 times the second equation:

7(-3x +6y) -6(5x +7y) = 7(9) -6(-49)

-21x +42y -30x -42y = 63 +294 . . . . eliminate parentheses

-51x = 357 . . . . . . . . collect terms

x = -7 . . . . . . . divide by -51. This matches answer choice A.

7 0

2 years ago

Katy's favorite rides at the amusement park are the roller coasters and water slide. The wait time for the roller coaster is 25

ioda

Answer:

She went on the slide 8 times and on the roller coaster 4 times

Step-by-step explanation:

We convert each statements to a mathematical equation.

Firstly, let's represent the number of times she went on the coaster with R and the number of times on the slide with S. We know quite well she went on 12 rides. Hence the summation of both number of times yield 12.

Mathematically, R + S = 12. ........(i)

Now we also know her total wait time was 3hours. Since an hour equals 60 minutes, her total wait time would equal 180 minutes.

To get a mathematical representation for the wait time, we multiply the number of roller coaster rides by 25 and that of the slides by 10.

Mathematically, 25R + 10S = 180 .......(ii)

Here we now have two equations that we can solve simultaneously.

From equation 1 we can say R = 12 - S. We can then substitute this into equation 2 to yield the following:

25(12 - s) + 10s = 180

300 - 25s + 10s = 180

300 - 15s = 180

15s = 300 - 180

15s = 120

S = 120/15

S = 8

S = 8 , and R = 12 - S = 12 - 8 = 4

7 0

3 years ago

Use Newton’s Method to find the solution to x^3+1=2x+3 use x_1=2 and find x_4 accurate to six decimal places. Hint use x^3-2x-2=

luda_lava [24]

Let $f(x) = x^3 - 2x - 2$ . Then differentiating, we get

$f'(x) = 3x^2 - 2$

We approximate $f(x)$ at $x_1=2$ with the tangent line,

$f(x) \approx f(x_1) + f'(x_1) (x - x_1) = 10x - 18$

The $x$ -intercept for this approximation will be our next approximation for the root,

$10x - 18 = 0 \implies x_2 = \dfrac95$

Repeat this process. Approximate $f(x)$ at $x_2 = \frac95$ .

$f(x) \approx f(x_2) + f'(x_2) (x-x_2) = \dfrac{193}{25}x - \dfrac{1708}{125}$

Then

$\dfrac{193}{25}x - \dfrac{1708}{125} = 0 \implies x_3 = \dfrac{1708}{965}$

Once more. Approximate $f(x)$ at $x_3$ .

$f(x) \approx f(x_3) + f'(x_3) (x - x_3) = \dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125}$

Then

$\dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125} = 0 \\\\ \implies x_4 = \dfrac{5,881,319,037}{3,324,107,515} \approx 1.769292663 \approx \boxed{1.769293}$

Compare this to the actual root of $f(x)$ , which is approximately 1.769292354, matching up to the first 5 digits after the decimal place.

4 0

1 year ago

How to factorise the difference of perfect squares. for the g on the top and j on the top

Fed [463]

Answer:

see explanation

Step-by-step explanation:

A difference of two squares is factored as

a² - b² = (a - b)(a + b)

(g)

1 - 81y²

= 1² - (9y)²

= (1 - 9y)(1 + 9y)

(j)

64x² - 25y²

= (8x)² - (5y)²

= (8x - 5y)(8x + 5y)

7 0

3 years ago

Use the recursive formula to answer the question.

scZoUnD [109]

You know a1.
So find a2, a3, and so on until a7.

a(1) = 12
a(2) = 16
a(3) = 20
a(4) = 24
a(5) = 28
a(6) = 32
a(7) = 36
Each is 4 more than the previous.

4 0

2 years ago