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3 years ago

Ezra enjoys gardening.

Mathematics

1 answer:

svlad2 [7]3 years ago

7 0

Answer:

Ezra can plant 8 sunflowers

Step-by-step explanation:

0.7S + 0.5L < 11

0.7S + 0.5(10) < 11

0.7S + 5 < 11

0.7S < 6

6 ÷ 0.7 = 8.5

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a concession stand is selling hot dogs and hamburgers during a game. at halftime they sold a total of 78 hot dogs and hamburgers

lara31 [8.8K]

Let x=number of hamburgers sold and y=number of hot dogs sold.
Step 1)
cost of burgers X # of burgers + cost of hotdogs X # of hotdogs=$ collected 1.5x + 1.25y=105.5

step 2)
# of burgers sold + number of hot dogs sold = total number of items sold
x + y = 78

step 3) solve for y in the second equation
y = 78 - x

step 4) substitute y = 78 - x in the first equation for the value of y and solve for x
1.5x + 1.25(78 - x)=105.50
1.5 x + 97.5 - 1.25x=105.50
.25x = 8
x = 32

step 5) plug in our value for x in the second equation and solve for y
x+y=78
32+y=78
y=46

answer 32 hamburgers and 46 hot dogs

3 0

3 years ago

**Spam answers will not be tolerated**

Morgarella [4.7K]

Answer:

$f'(x)=-\frac{2}{x^\frac{3}{2}}$

Step-by-step explanation:

So we have the function:

$f(x)=\frac{4}{\sqrt x}$

And we want to find the derivative using the limit process.

The definition of a derivative as a limit is:

$\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Therefore, our derivative would be:

$\lim_{h \to 0}\frac{\frac{4}{\sqrt{x+h}}-\frac{4}{\sqrt x}}{h}$

First of all, let's factor out a 4 from the numerator and place it in front of our limit:

$=\lim_{h \to 0}\frac{4(\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x})}{h}$

Place the 4 in front:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}$

Now, let's multiply everything by (√(x+h)(√(x))) to get rid of the fractions in the denominator. Therefore:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}(\frac{\sqrt{x+h}\sqrt x}{\sqrt{x+h}\sqrt x})$

Distribute:

$=4\lim_{h \to 0}\frac{({\sqrt{x+h}\sqrt x})\frac{1}{\sqrt{x+h}}-(\sqrt{x+h}\sqrt x)\frac{1}{\sqrt x}}{h({\sqrt{x+h}\sqrt x})}$

Simplify: For the first term on the left, the √(x+h) cancels. For the term on the right, the (√(x)) cancel. Thus:

$=4 \lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }$

Now, multiply both sides by the conjugate of the numerator. In other words, multiply by (√x + √(x+h)). Thus:

$= 4\lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }(\frac{\sqrt x +\sqrt{x+h})}{\sqrt x +\sqrt{x+h})}$

The numerator will use the difference of two squares. Thus:

$=4 \lim_{h \to 0} \frac{x-(x+h)}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Simplify the numerator:

$=4 \lim_{h \to 0} \frac{x-x-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}\\=4 \lim_{h \to 0} \frac{-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Both the numerator and denominator have a h. Cancel them:

$=4 \lim_{h \to 0} \frac{-1}{(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Now, substitute 0 for h. So:

$=4 ( \frac{-1}{(\sqrt{x+0}\sqrt x)(\sqrt x+\sqrt{x+0})})$

Simplify:

$=4( \frac{-1}{(\sqrt{x}\sqrt x)(\sqrt x+\sqrt{x})})$

(√x)(√x) is just x. (√x)+(√x) is just 2(√x). Therefore:

$=4( \frac{-1}{(x)(2\sqrt{x})})$

Multiply across:

$= \frac{-4}{(2x\sqrt{x})}$

Reduce. Change √x to x^(1/2). So:

$=-\frac{2}{x(x^{\frac{1}{2}})}$

Add the exponents:

$=-\frac{2}{x^\frac{3}{2}}$

And we're done!

$f(x)=\frac{4}{\sqrt x}\\f'(x)=-\frac{2}{x^\frac{3}{2}}$

5 0

2 years ago

Using technology or by hand, make a dot plot representing the data shown in the table. Make sure to label your plot appropriatel

Alchen [17]

Second one should be wright 86%

5 0

2 years ago

A) Work out the size of angle x.

Andru [333]

Answer:

100°= angle b(VERTICAL OPPOSITE ANGLE)

100°+x°=180°[co interior angle]

x=180°-100°

x=80°

7 0

3 years ago

David earns $8 per hour he works 40 hours each week how much does he earn in 6 weeks

dem82 [27]

Answer:

$1920

Step-by-step explanation:

First, find out how much he earns in one week-so $8 times 40 = 320. Then multiply 320 by 6 to get how much earns in 6 weeks which is $1920.

(hope this helps :P)

5 0

3 years ago

Read 2 more answers