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3 years ago

I need help with this question

Mathematics

1 answer:

AVprozaik [17]3 years ago

5 0

Step-by-step explanation:

Angle formed at the circumference of the circle is half of the angle formed at the center of the same circle.

Hence,

$m\angle ADC = \frac{1}{2} \times m\angle ABC \\ \\ \therefore \: m\angle ADC = \frac{1}{2} \times 40 \degree \\ \\ \therefore \:m\angle ADC = 20 \degree \\ \\$

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Which package has the lowest cost per ounce of rice ( 12, 18, 7)

Katarina [22]

The package with the most low cost is 7.

4 0

3 years ago

Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to p

zalisa [80]

General Idea:

(i) Assign variable for the unknown that we need to find

(ii) Sketch a diagram to help us visualize the problem

(iii) Write the mathematical equation representing the description given.

(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE

Applying the concept:

Given: x represents the length of the pen and y represents the area of the doghouse

Statement 1: "The pen is 3 feet wider than it is long"

$Length \; of\; the \; pen = x\\ Width \; of\; the\; pen=x+3$

------

Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"

$Area \; of\; the\; Dog \; house=y\\ Perimeter \; of\; Dog\; house=y$

------

Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."

$Area \; of \; the\; Pen - Area \;of \;the\;Dog \;House=\;Space\;inside\;Pen\\ \\ x \cdot (x+3)-y=178\\ Distributing \;x\;in\;the\;left\;side\;of\;the\;equation\\ \\ x^2+3x-y=178\Rightarrow\; 1^{st}\; Equation\\$

------

Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."

$Perimeter\; of\; the\; Pen=3\; \cdot \; Perimeter\; of\; the\; Dog\; House\\ \\ 2(x \; + \; x+3)=3 \cdot y\\ Combine\; like\; terms\; inside\; the\; parenthesis\\ \\ 2(2x+3)=3y\\ Distribute\; 2\; in\; the\; left\; side\; of\; the\; equation\\ \\ 4x+6=3y\\ Subtract \; 6\; and \; 3y\; on\; both\; sides\; of\; the\; equation\\ \\ 4x+6-3y-6=3y-3y-6\\ Combine\; like\; terms\\ \\ 4x-3y=-6 \Rightarrow \; \; 2^{nd}\; Equation\\$

Conclusion:

The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.

$178=x^2+3x-y\\ \\ -6=4x-3y$

8 0

3 years ago

Read 2 more answers

A gas grill originally priced at 399 is on sale for 30% off

DanielleElmas [232]

Answer:

Step-by-step explanation:

a = -32

2. x=−3/2 ( which also equals -1.5)

7 0

3 years ago

Joe bought a box of laundry detergent that contains 195 scoops.

7nadin3 [17]

Answer:

78 laundries

$0.25

Step-by-step explanation:

If the box contains 195 scoops and at once he uses 2 1/2 you have to divide 195 by 2 1/2 and you get 78.

How much is he paying for each load? you have to find the unit rate. The box costs $19.99 he can do 78 laundries at once so you divide the money by the quantity or in other words $19.99 by 78 and get 0.2562820512820513, since we are talking about money we use only the firs two decimals, so he pays $0.25 per load of laundry.

8 0

2 years ago

the scale map says that 10cm represents 2km what distance on the map in centimeters represent an actual distance of 15 kilometer

Leno4ka [110]

Answer:

75cm

Step-by-step explanation:

Well, I can't see a photo, so I'll have to assume that the description provides enough info.

10cm/2km = x/15km,

where x is the distance on the map (in centimeters) of a real-life distance of 15 kilometers.

10cm/2km = x/15km

10/2 = 5/1

This means we have to multiply 5 by 15 to find x.

x = 5 · 15

x = 75

Let's plug the new value back in...

10cm/2km = x/15km

10cm/2km = (75cm)/15km

(Simplify each side to its simplest form)

10cm/2km = 75cm/15km

5/1 = 5/1

It works! So x = 75cm.

Hope this helps! :)

8 0

3 years ago