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Nookie1986 [14]
2 years ago
7

Exit Ticket: At noon, a tank has a water depth of 9 in. After 3 hours, the depth was 8 inches. At 6pm, the depth was 7 inches. W

hat is the initial value for the function? help will be appreciated.
Mathematics
1 answer:
OLEGan [10]2 years ago
4 0

Answer:

Step-by-step explanation:

The  straight line equation is:

y = m*x  + b     Where m is the slope of the line and b the intercept with   y-axis, in our case y is the depth of the tank and x (time in lapsus of 3 hours).

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

We have point  A ( 3 , 8 )  and point  B ( 6 , 7 )

m  = ( 6 - 3 ) / (7 - 8 )  m = -3

We see that  each 3 hours time-depth decreases  1 in.

Then   to find the depth at the beginning of x-axis

At  noon     12   tank was  9 inches, three hours before at 9 in the morning the depth was 10 inches and:

9  in the morning   10

6  in the morning   11

3  in the midnight   12

12 in the night         13

Then 13 is the intercept with y-axis

then the equation is:

h = - 3*x + 13

Note x is time in lapsus  of 3 hours

You might be interested in
What is the slope of o line that passes through (-4,-14) and (19,11)?
DerKrebs [107]

Answer:

D, see description below.

There is a possible typo in the problem since these points have slope 25/23.

Step-by-step explanation:

To find the slope of a line, calculate the distance between points with a ratio of vertical to horizontal distance. This is done using the formula:

m=\frac{y_2-y_1}{x_2-x_1}

Here the points are (-4,-14) and (19,11). Substitute and simplify.

m=\frac{11--14}{19--4}=\frac{11+14}{19+4}=\frac{25}{23}

I think there is a typo in your points (-4,-14) and (19,11) because the answer doesn't align to the answer choices. But based on them, I would answer D or 24/23 since it's the closest value.

6 0
3 years ago
In a G.P the 3rd term is 4 times the 1st term and the sum of the 2nd term and the 4th term is 30.find the common ratio,find the
STALIN [3.7K]

Answer:

the common ratio is either 2 or -2.

the sum of the first 7 terms is then either 765 or 255

Step-by-step explanation:

a geometric sequence or series of progression (these are the most common names for the same thing) means that every new term of the sequence is created by multiplying the previous term by a constant factor which is called the common ratio.

so,

a1

a2 = a1×f

a3 = a2×f = a1×f²

a4 = a3×f = a1×f³

the problem description here tells us

a3 = 4×a1

and from above we know a3 = a1×f².

so, f² = 4

and therefore the common ratio = f = 2 or -2 (we need to keep that in mind).

again, the problem description tells us

a2 + a4 = 30

a1×f + a1×f³ = 30

for f = 2

a1×2 + a1×2³ = 30

2a1 + 8a1 = 30

10a1 = 30

a1 = 3

for f = -2

a1×-2 + a1×(-2)³ = 30

-10a1 = 30

a1 = -3

the sum of the first n terms of a geometric sequence is

sn = a1×(1 - f^(n+1))/(1-f) for f <>1

so, for f = 2

s7 = 3×(1 - 2⁸)/(1-2) = 3×-255/-1 = 3×255 = 765

for f = -2

s7 = -3×(1 - (-2)⁸)/(1 - -2) = -3×(1-256)/3 = -3×-255/3 =

= -1×-255 = 255

4 0
2 years ago
Alex is trying to run a certain number of miles by the end of the month Alex is 40% of the way to achieving her goal and she alr
docker41 [41]

Answer:

30 miles

Step-by-step explanation:

Given that:

Alex has some target to run a certain number of miles by the end of the month.

Goal already achieved = 40% of the total goal

Number of miles already run by Alex = 12 miles

To find:

Number of miles that Alex is trying to run by the end of month?

Solution:

We have to find nothing but the goal of Alex here.

Let the number of miles that Alex is trying to run by the end of the month = x miles

As per question statement:

40% of total number of miles to be run = 12 miles

OR

\dfrac{40}{100}\times x = 12\\\Rightarrow 40x=12\times 100\\\Rightarrow x = \dfrac{1200}{40}\\\Rightarrow \bold{x = 30\ miles}

Total number of miles that Alex is trying to run by the end of the month = <em>30 miles</em>

4 0
3 years ago
Divide 33 into 2 groups so the ratio can be 4 to 7
svet-max [94.6K]
To do this task the best way is always add both "sides" of ratio and divide whole group by this sum.sum=4+7=1133:11=3Now we know how much is 1 and we can multiply by 4 and by 7 to find the answer.3*4=12 - first group3*7=21 - second group
Your result is ok.
7 0
2 years ago
Read 2 more answers
Solve for x.
S_A_V [24]

Answer:

x = {-2, 2/3}

Step-by-step explanation:

2x = -4

x = -2

3x = 2

x = 2/3

x = {-2, 2/3}

3 0
2 years ago
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