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Lisa [10]
3 years ago
6

8/10 = z/30 what does z equal

Mathematics
1 answer:
sweet-ann [11.9K]3 years ago
8 0

8×30=10×z

10z=240

z=24

Hence the value of z is 24

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a train makes a trip at 65 mi/h. A plane traveling 130 mi/h makes the same trip in 3 fewer hours. Write and solve an equation to
Rudik [331]

The formula used for calculating the time is:

t = d / v

where t is time, d is distance and v is velocity

 

We know that the difference in the two times is 3 hours, therefore:

d / 65 – d / 130 = 3

 

Calculating for d:

d = 30 / (1/65 – 1/130)

<span>d = 3900 miles</span>

8 0
3 years ago
The graph h = −16t^2 + 25t + 5 models the height and time of a ball that was thrown off of a building where h is the height in f
Thepotemich [5.8K]

Answer:

part 1) 0.78 seconds

part 2) 1.74 seconds

Step-by-step explanation:

step 1

At about what time did the ball reach the maximum?

Let

h ----> the height of a ball in feet

t ---> the time in seconds

we have

h(t)=-16t^{2}+25t+5

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

so

The x-coordinate of the vertex represent the time when the ball reach the maximum

Find the vertex

Convert the equation in vertex form

Factor -16

h(t)=-16(t^{2}-\frac{25}{16}t)+5

Complete the square

h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+5+\frac{625}{64}

h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}\\h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}

Rewrite as perfect squares

h(t)=-16(t-\frac{25}{32})^{2}+\frac{945}{64}

The vertex is the point (\frac{25}{32},\frac{945}{64})

therefore

The time when the ball reach the maximum is 25/32 sec or 0.78 sec

step 2

At about what time did the ball reach the minimum?

we know that

The ball reach the minimum when the the ball reach the ground (h=0)

For h=0

0=-16(t-\frac{25}{32})^{2}+\frac{945}{64}

16(t-\frac{25}{32})^{2}=\frac{945}{64}

(t-\frac{25}{32})^{2}=\frac{945}{1,024}

square root both sides

(t-\frac{25}{32})=\pm\frac{\sqrt{945}}{32}

t=\pm\frac{\sqrt{945}}{32}+\frac{25}{32}

the positive value is

t=\frac{\sqrt{945}}{32}+\frac{25}{32}=1.74\ sec

8 0
3 years ago
If 1 cm represents 30 km on a map and colorado is shown by a 20cm by 15 cm rectangle on the map, what is the approximate actual
zubka84 [21]

Answer:

20*30km = 600km

15*30km = 450km

600km * 450km = 270000 km^2

Step-by-step explanation:

assuming 1cm --- 30km causes that 2cm --- 60km, 3cm --- 90km, 4cm --- 120km etc. Notice that number of km's is 30 times greater than the number of cm's on a map

using this logic, you calculate both real dimensions of Colorado by multiplying 20*30 = 600 km and 15*30 = 450km

Then we use a formula of an area of a rectangle A=a\cdot b assuming a=600km, \ b=450km and get A=600\cdot 450=270000km^2 which is an actual area of Colorado

3 0
2 years ago
4 is the square root of which number ?
Tom [10]
Your answer would be two
6 0
3 years ago
A sapling, or young tree, is planted in a garden. After 3 years, it is 180 cm tall. After 7 years, it is 368 cm tall. What is th
Mashcka [7]
The function modelled by the height (x) of the tree is as follows:
y - 180 = (368 - 180)/(7 - 3) (x - 3)
y - 180 = 47(x - 3) = 47x - 141
y = 47x - 141 + 180 = 47x + 39

Therefore, after 10 years, the tree will be 47(10) + 39 = 470 + 39 = 509 cm tall
8 0
3 years ago
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