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2 years ago

Easy Question:598-__=78

Mathematics

2 answers:

wel2 years ago

7 0

598- 518= 78
That's the answer

kykrilka [37]2 years ago

4 0

520 this is the answer, You could use a calculator for this as well

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What is the solution to this system of equations?<br>5x + 2y = 29<br> x + 4y = 13

4vir4ik [10]

Answer:It would be 5,2 (Or C)

Step-by-step explanation:

6 0

2 years ago

The temperature, H, in °F, of a cup of coffee t hours after it is set out to cool is given by the following equation. H = 70 + 1

Alex73 [517]

Answer:

The temperature a t = 0 is 190 °F

The temperature a t = 1 is 100 °F

The temperature a t = 2 is 77.5 °F

It takes 1.5 hours to take the coffee to cool down to 85°F

It takes 2.293 hours to take the coffee to cool down to 75°F

Step-by-step explanation:

We know that the temperature in °F, of a cup of coffee t hours after it is set out to cool is given by the following equation:

$H(t)=70+120(\frac{1}{4})^t$

a) To find the temperature a t = 0 you need to replace the time in the equation:

$H(0)=70+120(\frac{1}{4})^0\\H(0)=70+120\cdot 1\\H(0) = 70+120\\H(0)=190 \:\°F$

b) To find the temperature after 1 hour you need to:

$H(1)=70+120(\frac{1}{4})^1\\H(1)=70+120(\frac{1}{4})\\H(1) = 70+30\\H(1)=100 \:\°F$

c) To find the temperature after 2 hours you need to:

$H(2)=70+120(\frac{1}{4})^2\\H(2)=70+120(\frac{1}{16})\\H(2) = 70+\frac{15}{2} \\H(2)=77.5 \:\°F$

d) To find the time to take the coffee to cool down $85 \:\°F$ , you need to:

$85 = 70+120(\frac{1}{4})^t\\70+120\left(\frac{1}{4}\right)^t=85\\70+120\left(\frac{1}{4}\right)^t-70=85-70\\120\left(\frac{1}{4}\right)^t=15\\\frac{120\left(\frac{1}{4}\right)^t}{120}=\frac{15}{120}\\\left(\frac{1}{4}\right)^t=\frac{1}{8}$

$\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)$

$\ln \left(\left(\frac{1}{4}\right)^t\right)=\ln \left(\frac{1}{8}\right)$

$\mathrm{Apply\:log\:rule}=\log _a\left(x^b\right)=b\cdot \log _a\left(x\right)$

$t\ln \left(\frac{1}{4}\right)=\ln \left(\frac{1}{8}\right)$

$t=\frac{\ln \left(\frac{1}{8}\right)}{\ln \left(\frac{1}{4}\right)}\\t=\frac{3}{2} = 1.5 \:hours$

e) To find the time to take the coffee to cool down $75 \:\°F$ , you need to:

$75=70+120\left(\frac{1}{4}\right)^t\\70+120\left(\frac{1}{4}\right)^t=75\\70+120\left(\frac{1}{4}\right)^t-70=75-70\\120\left(\frac{1}{4}\right)^t=5\\\left(\frac{1}{4}\right)^t=\frac{1}{24}$

$\ln \left(\left(\frac{1}{4}\right)^t\right)=\ln \left(\frac{1}{24}\right)\\t\ln \left(\frac{1}{4}\right)=\ln \left(\frac{1}{24}\right)\\t=\frac{\ln \left(24\right)}{2\ln \left(2\right)} \approx = 2.293 \:hours$

3 0

3 years ago

Find the larger of two consecutive integers if the larger is 149 less than twice the smaller.

snow_tiger [21]

Answer:

151

Step-by-step explanation:

Let x = the smaller integer and y = the larger integer.

We have two conditions:

(1) x + 1 = y

(2) y = 2x - 149 Substitute (1) into (2)

x + 1 = 2x - 149 Add 150 to each side

x + 150 = 2x Subtract x from each side

x = 150 Substitute into (1)

150 +1 = y

y = 151

The larger integer is 151.

<em>Check: </em>

(1) 150 + 1 = 151

151 = 151

(2) 151 = 2×150 -149

151 = 300 -149

151 = 151

4 0

3 years ago

Origami is the Japanese art of paper folding. The diagram below represents an unfolded paper kabuto, a samurai warriors helmet.

sasho [114]

Answer:

A, C, and D

Step-by-step explanation:

A. QRC and QRO

C. IRS and MRS

D. CRU and IRU

3 0

2 years ago

Can anyone help me with this question ? 6c + 3 =45

ikadub [295]

Answer:

Ans: 6c+3=45

6c=45-3

6c/6=42/6

C=7

So my correct answer is C=7

7 0

3 years ago

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