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Phantasy [73]
3 years ago
14

The length of a rectangle is 15 ft greater than its width. If each dimension is decreased by 2 ft, the area will be decreased by

106 ft2. Find the dimensions. please explain the formula
Mathematics
1 answer:
padilas [110]3 years ago
6 0

Answer:

length = 35ft, width = 20ft

Step-by-step explanation:

We are working with length (L), width (W), and area (A). We are asked to find the 2 dimensions. The question tells us that L = W + 15, so we can express L in terms of W. However, we still don't know what A is. Since we have 2 unknowns, we somehow need to develop 2 equations to get a solvable system.

We can set up the first equation using the relationship between L and W:

W(W+15)=A

We can set up the second equation using the information in the second sentence:

(W-2)(W+13)=A-106

Now we can plug the first equation, already isolated for A, into the second equation and solve for W:

(W-2)(W+13)=W(W+15)-106\\W^2+11W-26=W^2+15W-106\\4W=80\\W=20

A pretty nasty-looking equation actually becomes pretty easy to solve. We know the length is 15ft greater than the width, so if W=20, L=35.

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natta225 [31]

Answer:

1/3

Step-by-step explanation:

4 0
1 year ago
Slove the following <br>equation without with out transporting I)5y +10=4y-10​
Katen [24]
The answer is y= -20
7 0
3 years ago
Consider a value to be significantly low if its z score less than or equal to minus−2 or consider a value to be significantly hi
den301095 [7]

Answer:

Test scores of 10.2 or lower are significantly low.

Test scores of 31 or higher are significantly high

Step-by-step explanation:

Z-score:

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 20.6, \sigma = 5.2

Significantly low:

Z-scores of -2 or lower

So scores of X when Z = -2 or lower

Z = \frac{X - \mu}{\sigma}

-2 = \frac{X - 20.6}{5.2}

X - 20.6 = -2*5.2

X = 10.2

Test scores of 10.2 or lower are significantly low.

Significantly high:

Z-scores of 2 or higher

So scores of X when Z = 2 or higher

Z = \frac{X - \mu}{\sigma}

2 = \frac{X - 20.6}{5.2}

X - 20.6 = 2*5.2

X = 31

Test scores of 31 or higher are significantly high

6 0
3 years ago
What's the next number 2 7 8 3 12 9
puteri [66]

The <em>correct answer</em> is:

4.

Explanation:

Taking these numbers as groups of three, we have 2, 7, 8; 3, 12, 9.

In the first group, we can see that we first add 5 and then add 1.

The next group seems to start from the next consecutive number. That is, the first group starts with 2, and the next group starts with 3. The next terms in the second group are found by adding 5 to the second term of the first group (12 = 7+5) and then adding 1 to the third term of the first group (9=8+1); this is because we added 5 and added 1 previously.

Following this pattern, the next group of three would start from the next consecutive number up, 4. The next two terms would be 17 (12+5=17) and 10 (9+1=10).

7 0
3 years ago
Read 2 more answers
The equation $y=-4.9t^2+3.5t+5$ describes the height (in meters) of a ball thrown upward at $3.5$ meters per second from $5$ met
Georgia [21]

Answer:

Step-by-step explanation:

The position function is

s(t)=-4.9t^2+3.5t+5 and if we are looking for the time t it takes for the ball to hit the ground, we are looking for the height of the ball when it is on the ground. Of course the height of anything on the ground is 0, so if we set s(t) = 0 and solve for t, we will find our answer.

0=-4.9t^2+3.5t+5 and factor that however you are currently factoring in class to get that

t = -.71428 seconds or

t = 1.42857 seconds (neither one of those is rational so they can't be expressed as fractions).

We all know that time will never be a negative value, so the time it takes this ball to hit the ground is

1.42857 seconds (round how you need to).

4 0
2 years ago
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