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2 years ago

A recipe to make 5 cupcakes calls for 10 tablespoons

Mathematics

1 answer:

arlik [135]2 years ago

3 0

Answer:

10×5

Step-by-step explanation:

put a zero at the end of five and make it 50

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A farmer has 520 feet of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one s

Setler [38]

Answer:

$310\text{ feet and }210\text{ feet}$

Step-by-step explanation:

GIVEN: A farmer has $520 \text{ feet}$ of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one side of the pen. The length of the barn is $310 \text{ feet}$ .

TO FIND: Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions.

SOLUTION:

Let the length of rectangle be $x$ and $y$

perimeter of rectangular pen $=2(x+y)=520\text{ feet}$

$x+y=260$

$y=260-x$

area of rectangular pen $=\text{length}\times\text{width}$

$=xy$

putting value of $y$

$=x(260-x)$

$=260x-x^2$

to maximize $\frac{d \text{(area)}}{dx}=0$

$260-2x=0$

$x=130\text{ feet}$

$y=390\text{ feet}$

but the dimensions must be lesser or equal to than that of barn.

therefore maximum length rectangular pen $=310\text{ feet}$

width of rectangular pen $=210\text{ feet}$

Maximum area of rectangular pen $=310\times210=65100\text{ feet}^2$

Hence maximum area of rectangular pen is $65100\text{ feet}^2$ and dimensions are $310\text{ feet and }210\text{ feet}$

5 0

2 years ago

An athlete knows that when she jogs along her neighborhood greenway, she can complete the route in 10 minutes. It takes 20 minu

IgorLugansk [536]

Answer:

10 miles per hour.

Step-by-step explanation:

Let x represent athlete's walking speed.

We have been given that her jogging rate is 5 mph faster than her walking rate, so athlete's jogging speed would be $x+5$ miles per hour.

$\text{Distance}=\text{Rate}\cdot \text{Time}$

10 minutes = 1/6 hour.

20 minutes = 1/3 hour

While walking, we will get $D_{\text{walking}}=x\frac{\text{miles}}{\text{hour}}\cdot \frac{1}{3}\text{hour}$

$D_{\text{walking}}=\frac{x}{3}$

While jogging, we will get $D_{\text{jogging}}=(x+5)\frac{\text{miles}}{\text{hour}}\cdot \frac{1}{6}\text{hour}$

$D_{\text{jogging}}= \frac{(x+5)}{6}$

Since athlete is covering same distance while walking and jogging, so we can equate both expressions as:

$\frac{x}{3}=\frac{x+5}{6}$

Cross multiply:

$6x=3x+15$

$6x-3x=15$

$3x=15$

$\frac{3x}{3}=\frac{15}{3}\\\\x=5$

Therefore, athlete's walking speed is 5 miles per hour.

Jogging speed: $x+5\Rightarrow 5+5=10$

Therefore, athlete's jogging speed is 10 miles per hour.

3 0

3 years ago

27. In a school of 500 students, 125 like chess and 160 like badminton. 45 students like chess and badminton both. Find how many

ozzi

Answer:

170

Step-by-step explanation:

Add 160 and 45 and 125

Then subtract it to the total number of students

So 500 minus 330

5 0

3 years ago

What is the sum of 1/2 + 1/4? A. 2/8 B. 2/6 C. 4/8 D. 6/8

Pie

3/4 is the total.

See attached image for explanation.

Please consider marking "Brainliest".

Thanks <3

6 0

2 years ago

Which is equivalent to x^3 y^-7

PilotLPTM [1.2K]

For this case we must find an expression equivalent to:

$x ^ 3 * y ^ {- 7}$

By definition of power properties we have to meet:

$a ^ {-1} = \frac {1} {a ^ 1} = \frac {1} {a}$

Then, we can rewrite the expression as:

$x ^ 3 * \frac {1} {y ^ 7} =\\\frac {x ^ 3} {y ^ 7}$

Answer:

$\frac {x ^ 3} {y ^ 7}$

8 0

2 years ago