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3 years ago

5x+y=23 2x+y=11 in elimination method

1 answer:

3 0

Multiply the 2nd equation by -1 then add equations together
-1(2x+y=11)
-2x - y = -11
(Adding will eliminate the Y)
3x = 12
------------------------------------
Divide each side by 3
3x ÷ 2 = 12 ÷ 3
x = 4
==================================================================
To find Y substitute 4 for x in 5x+y=23
(5)(4)+y=23
y+20=23
-----------------------------
Add -20 on each side
y+20+-20=23+-20
y = 3

Your answers are x = 4 and y = 3

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A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(

gavmur [86]

We have the following function:
f(t) = −16t2 + 34t + 546
By definition, the average rate of change is:
Avr = (f (t2) - f (t1)) / (t2 - t1)
We have then:
For t1 = 5:
f (5) = -16*(5)^2 + 34*(5) + 546
f (5) = 316
For t2 = 5:
f (7) = -16*(7)^2 + 34*(7) + 546
f (7) = 0
Substituting values:
Avr = (0 - 316) / (7 - 5)
Avr = -158
Answer:
The average rate of change of f (t) from t = 5 seconds to t = 7 seconds is -158 feet per second.

6 0

3 years ago

48. Reading Rates The reading speed of sixth-grade students is approximately normal, with a mean speed of 125 words per minute a

son4ous [18]

Answer:

The reading speed of a sixth-grader whose reading speed is at the 90th percentile is 155.72 words per minute.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

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:

$\mu = 125, \sigma = 24$

What is the reading speed of a sixth-grader whose reading speed is at the 90th percentile

This is the value of X when Z has a pvalue of 0.9. So it is X when Z = 1.28.

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

$1.28 = \frac{X - 125}{24}$

$X - 125 = 1.28*24$

$X = 155.72$

The reading speed of a sixth-grader whose reading speed is at the 90th percentile is 155.72 words per minute.

4 0

3 years ago

Read 2 more answers

A department store sold 51 51 shirts one day. All short-sleeved shirts cost $14.00 $ 14.00 each and all long-sleeved shirts cost

Dmitrij [34]

Answer:

28 short-sleeved shirts were sold and 23 long-sleeved shirts were sold.

Step-by-step explanation:

We can solve this question by a system of equations.

I am going to say that:

x is the number of short-sleeved shirts sold.

y is the number of long-sleeved shirts sold.

A department store sold 51 shirts one day.

This means that $x + y = 51$

All short-sleeved shirts cost $14.00 each and all long-sleeved shirts cost $23.00 each. Total receipts for the day were $921.00.

This means that

$14x + 23y = 921$

How many of each kind of shirt were sold?

We have to solve the system of equations.

$x + y = 51$

$x = 51 - y$

--------------

$14x + 23y = 921$

$14(51 - y) + 23y = 921$

$714 - 14y + 23y = 921$

$9y = 207$

$y = \frac{207}{9}$

$y = 23$

--------

$x = 51 - y = 51 - 23 = 28$

28 short-sleeved shirts were sold and 23 long-sleeved shirts were sold.

7 0

3 years ago

What is the value of x? Enter your answer in the box. x =

Karo-lina-s [1.5K]

Answer:

Step-by-step explanation:

you do 180 and subtract both values you already have 102 and 39. you get the answer of 39

4 0

3 years ago

Read 2 more answers

Find the coordinates of P so that partitions ab in the ratio 5:1 with A(2,4) and B(8,10)

julsineya [31]

Answer:

The answer would be (7,9).

Step-by-step explanation:

If you partition that line by 6 you'd get (3,5), (4,6), (5,7), (6,8), and (7,9) in the middle of the two points. And the ratio of 5:1 would be seen at point (7,9).

8 0

2 years ago