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2 years ago

One-half the sum of two consecutive odd integers is −12. Find the smallest integer.

Mathematics

1 answer:

melisa1 [442]2 years ago

3 0

Answer:

Step-by-step explanation:

Let the larger integer = 2x + 1

Let the second integer = 2x - 1

1/2 (2x + 1 + 2x - 1) = - 12 Combine the left

1/2(4x) = - 12 Combine 1/2 (4x)

2x = - 12 Divide by 2

2x/2 = - 12/2

x = - 6

2x + 1 = 2*-6 + 1 = -11

2x - 1 = 2*-6 - 1 = - 13

Check

-11 + - 13 = - 24

1/2(-24) = -12 which checks.

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Evaluate the expression for x = 5, y = 3, and z = 14 . 5x−6y+20z over 4yz Enter your answer in the box.

spin [16.1K]

Hello from MrBillDoesMath!

Answer: 1 17/24

Steps:

Evaluate (5x-6y+20x)/ 4yz when x = 5, y = 3, z = 14

(5(5) - 6(3) + 20(14)) / 4 (3)(14) (Substitute in values)

= (25 - 18 +280) / 4 (3) (14) (Evaluate products)

= (287) / 4 (3) (14) (Evaluate expressions)

= 287/ 168 (4 (3)(14) = 168)

= (168 + 119 ) /168 287 = 168 + 119

= (168)/168 + 119/168

= 1 + 119/168

= 1 119/168

BUT 119 = 17 * 7 (surprise!) and 168 = 12 * 7 * 2 so answer

= 1 (17*7)/(12*7*2)

= 1 (17)/(12*2) (Cancel 7's)

= 1 (17/24)

Regards, MrB

3 0

3 years ago

for the first four weeks of school,the cafeteria either served spaghetti or lasagna on thursday. based on this evidence, liam st

erica [24]

Theorem because it is most likely

7 0

3 years ago

A conical water tank with vertex down has a radius of 13 feet at the top and is 21 feet high. If water flows into the tank at a

VLD [36.1K]

Answer:

$\frac{dh}{dt}\approx0.08622\text{ ft/min}$

Step-by-step explanation:

We know that the conical water tank has a radius of 13 feet and is 21 feet high.

We also know that water is flowing into the tank at a rate of 30ft³/min. In other words, our derivative of the volume with respect to time t is:

$\frac{dV}{dt}=\frac{30\text{ ft}^3}{\text{min}}$

We want to find how fast the depth of the water is increasing when the water is 17 feet deep. So, we want to find dh/dt.

First, remember that the volume for a cone is given by the formula:

$V=\frac{1}{3}\pi r^2h$

We want to find dh/dt. So, let's take the derivative of both sides with respect to the time t. However, first, let's put the equation in terms of h.

We can see that we have two similar triangles. So, we can write the following proportion:

$\frac{r}{h}=\frac{13}{21}$

Multiply both sides by h:

$r=\frac{13}{21}h$

So, let's substitute this in r:

$V=\frac{1}{3}\pi (\frac{13}{21}h)^2h$

Square:

$V=\frac{1}{3}\pi (\frac{169}{441}h^2)h$

Simplify:

$V=\frac{169}{1323}\pi h^3$

Now, let's take the derivative of both sides with respect to t:

$\frac{d}{dt}[V]=\frac{d}{dt}[\frac{169}{1323}\pi h^3}]$

Simplify:

$\frac{dV}{dt}=\frac{169}{1323}\pi \frac{d}{dt}[h^3}]$

Differentiate implicitly. This yields:

$\frac{dV}{dt}=\frac{169}{1323}\pi (3h^2)\frac{dh}{dt}$

We want to find dh/dt when the water is 17 feet deep. So, let's substitute 17 for h. Also, let's substitute 30 for dV/dt. This yields:

$30=\frac{169}{1323}\pi (3(17)^2)\frac{dh}{dt}$

Evaluate:

$30=\frac{146523}{1323}\pi( \frac{dh}{dt})$

Multiply both sides by 1323:

$39690=146523\pi\frac{dh}{dt}$

Solve for dh/dt:

$\frac{dh}{dt}=\frac{39690}{146523}\pi$

Use a calculator. So:

$\frac{dh}{dt}\approx0.08622\text{ ft/min}$

The water is rising at a rate of approximately 0.086 feet per minute.

And we're done!

Edit: Forgot the picture :)

3 0

3 years ago

What is the value of x to the nearest tenth??

Stolb23 [73]

Answer:

$\displaystyle 12,3 ≈ x$

Step-by-step explanation:

We have to determine which trigonometric ratio to use, depending on what is displayed for us, and we will be using the <em>cotangent</em> [or <em>tangent</em>] ratio, this time with two angle measures:

$\displaystyle cot\:39° = \frac{x}{10} → 10cot\:39° ≈ 12,34897157 ≈ 12,3 \\ \\ tan\:39° = \frac{10}{x} → \frac{10}{tan\:39°} ≈ 12,34897157 ≈ 12,3 \\ \\ \\ OR \\ \\ \\ cot\:51° = \frac{10}{x} → \frac{10}{cot\:51°} ≈ 12,34897157 ≈ 12,3 \\ \\ tan\:51° = \frac{x}{10} → 10tan\:51° ≈ 12,34897157 ≈ 12,3$

Extended Information on Trigonometric Ratios

$\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ$

I am joyous to assist you anytime.

3 0

3 years ago

What do I need to know for these and how to do it and answer

Tom [10]

Answer:
i beleavive it would be D) 3/4
Step-by-step explanation:
i dont really know how to explain it sorry but i hope the answer helps and if its not that then its 1/24

4 0

1 year ago