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Rudik [331]
3 years ago
14

A farmer has 4 times as many ducks as chickens.There are 72 more chickens than ducks.How many chickens and ducks does the farmer

have altogether?
Mathematics
1 answer:
HACTEHA [7]3 years ago
8 0

Answer: The farmer has 120 birds altogether

Step-by-step explanation:

Now, since the number of chickens us equal to 4 times the number of ducks, it means that if there are 2 ducks, there are (2 × 4) chickens and if there are 5 ducks in the farm, there are (5 × 4) chickens.

Let's then denote the number of ducks by "b". So, if the number of chickens is equal to 4 times the number of ducks, then the total quantity of birds belonging to the farmer

= 4b + b

If there are 72 more chickens than ducks, the quantity of birds is:

4b - b = 72

3b = 72

b = 72/3

b = 24 ducks

Since 4b represents the quantity of chickens and b is equal to 24, then the actual quantity of chickens = 4 × 24 = 96.

Therefore, if there are 96 chickens and 24 ducks in the farm, then the actual sum of the birds belonging to the farmer is:

96 + 24

= 120 birds

The farmer has 120 birds altogether.

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Tresset [83]

The quadratic regression equation for this data set is \rm y=-0.143x^2+0.59x+2.82\\.

<h3>What is the general form of a quadratic equation?</h3>

The general form of the quadratic equation is given by;

\rm ax^2+bx+c=0

Where; a, b, and c are the constants.

x;   0       1         2        3          4         5

y;  2.82  3. 29  3. 46  3. 33   2. 88  2. 24

From the table when the value of x = 0 the value of y is 2.82.

Then,

\rm y=ax^2+bx+c\\\\x=0\\\\2.82=a0^2+b(0)+c\\\\c=2.82

From the table when the value of x = 3 the value of y is 3.33.

\rm y=ax^2+bx+c\\\\x=3\\\\2.82=a(3)^2+b(3)+c\\\\9a+3b+2.82=2.82\\\\9a=-3b\\\\b=-3a\\\\

From the table when the value of x = 5 the value of y is 2.24.

\rm y=ax^2+bx+c\\\\x=3\\\\2.24=a(5)^2+(-3a)(5)+c\\\\25a-15a+2.82=2.24\\\\40a=2.24-2.82\\\\10a=-0.68\\\\a= \dfrac{-0.68}{10}\\\\a=-0.143

And the value of b is;

\rm b=3a\\\\b=3(-0.14)\\\\b=0.59

Therefore,

The quadratic regression equation for this data set is;

\rm y=ax^2+bx+c\\\\y=-0.143x^2+0.59x+2.82\\\\

Hence, the quadratic regression equation for this data set is \rm y=-0.143x^2+0.59x+2.82\\.

To know more about the Quadratic equation click the link given below.

brainly.com/question/14935613

8 0
3 years ago
True or false m angle 5 is greater than m angle 8​
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Answer:

True

Step-by-step explanation:

You can see that Angle 5 is slightly greater than 90°, so it is obtuse

Angle 8 is less than 90°, and is acute

Since obtuse angles are larger than acute angles, Angle 5 is greater than Angle 8.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

3 0
3 years ago
Two shelters offers dog adoption twice a year ruff had 123 dogs adoption in january 196 fogs adoption in July barks had 78 dogs
liq [111]

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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