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3 years ago

Which algebraic expression represents "one-third of the number s, plus t"?

Mathematics

2 answers:

Svetllana [295]3 years ago

7 0

Answer:

The answer is A) s/3 + t

Step-by-step explanation:

The "plus t" portion of the equation is fairly straightforward, and is found in every equation apart from C, immediately ruling it out. Lets assume s=6. Then, one third of 6 would be 2. 2s = 12, and 12 is not equal to 2, so B is not the answer. 1/2 + 6 = 6 1/2, and 6 1/2 is not equal to 2, so D is not the answer. 6/3 = 2, which is one third of 6, so A is the answer.

TiliK225 [7]3 years ago

6 0

Answer:

A) s/3 +t

Step-by-step explanation:

To represent 1/3 of a number, we can simply divide this number by 3, meaning if s is the number, 1/3 of s would be s/3. Now to add t all we have to do is + t, making our answer s/3 + t

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A medical clinic is reducing the number of incoming patients by giving vaccines before flu season. During week 5 of flu season,

8_murik_8 [283]

Answer:

$f(x) = -6x +120$

Step-by-step explanation:

Let's call y the number of patients treated each week

Let's call x the week number.

If the reduction in the number of patients each week is linear then the equation that models this situation will have the following form:

$y = mx + b$

Where m is the slope of the equation and b is the intercept with the x-axis.

If we know two points on the line then we can find the values of m and b.

We know that During week 5 of flu season, the clinic saw 90 patients, then we have the point:

(5, 90)

We know that In week 10 of flu season, the clinic saw 60 patients, then we have the point:

(10, 60).

Then we can find m and b using the followings formulas:

$m=\frac{y_2-y_1}{x_2-x_1}$ and $b=y_1-mx_1$

In this case: $(x_1, y_1) = (5, 90)$ and $(x_2, y_2) = (10, 60)$

Then:

$m=\frac{60-90}{10-5}$

$m=-6$

And

$b=90-(-6)(5)$

$b=120$

Finally the function that shows the number of patients seen each week at the clinic is:

$f(x) = -6x +120$

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3 years ago

Read 2 more answers

24 cooking takes for 384 sprinkles, how many sprinkles would 60 cookies need

alukav5142 [94]

Answer:

960 i think

Step-by-step explanation:

5 0

3 years ago

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The rate of change of the function f(x) = 8 sec(x) + 8 cos(x) is given by the expression 8 sec(x) tan(x) − 8 sin(x). Show that t

liq [111]

Answer:

Shown - See explanation

Step-by-step explanation:

Solution:-

- The given form for rate of change is:

8 sec(x) tan(x) − 8 sin(x).

- The form we need to show:

8 sin(x) tan2(x)

- We will first use reciprocal identities:

$8\frac{sin(x)}{cos^2(x)} - 8sin(x)$

- Now take LCM:

$8\frac{sin(x)- sin(x)*cos^2(x)}{cos^2(x)}$

- Using pythagorean identity , sin^2(x) + cos^2(x) = 1:

$8*sin(x)*\frac{1- cos^2(x)}{cos^2(x)} = 8*sin(x)*\frac{sin^2(x)}{cos^2(x)}$

- Again use pythagorean identity tan(x) = sin(x) / cos(x):

$8*sin(x)*tan^2(x)$

8 0

3 years ago

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Genius question: A long level railway bridge passes over a railroad track, which is 100 feet below it and at right angles to it.

nataly862011 [7]

Answer: <u>110 feet per second</u>

Step-by-step explanation:

In this problem we will assume that the car at 45 miles per hour is moving into the x direction with a high of 100 feet, and the train is going in the y direction, so they trajectories will made an angle of 90º.

Now we can calculate the speed of the trains in feet per second so:

$S1=\frac{45*5280}{3600}=66$

$S2=\frac{60*5280}{3600}=88$

So we can make a right triangle with sides 66 and 88 and the hypotenuse will be the rate that the trains will separate per second so:

$h=\sqrt{66^{2} +88^{2} } =\sqrt{4356+7744}$

$h=\sqrt{12100}=110$

Is important to have in mind that the initial high is not going to change how fast the trains will separate, however, if we are going to calculate the distance we should have it in the calculations.

7 0

3 years ago

Solve each multiplication problem, use the cancellation method if possible, and reduce your answers. a. 39⁄64 × 8⁄13 b. 2⁄3 × 1⁄

blsea [12.9K]

A). 39⁄64 × 8⁄13 ====> 39 / 64 * 8 / 13 ===> 312/832 ==> 3 / 8 (Decimal: 0.375).

B). 2⁄3 × 1⁄5 × 4⁄7 ==> 2/3 * 1/5 * 4/7 ====> 8 / 105 ===> (Decimal: 0.07619)

C). 3⁄5 × 10⁄12 × 1⁄2 ===> 3/5 * 10/12 ===> 30/60 ===> 1/2 ==> 1/2 * 1/2 ===> 1/4 (Decimal: 0.25)

D). 4⁄9 × 54 ===> 4 * 54/ 9.1 ====> 216/9 ===> 24/1 ===> 24

E). 20 × 3 1⁄5 ===> 20 * 16/ 1.5 ====>320/5 ====> 64/1 =====> 64

F). 11 × 2 7⁄11 ====> 319/11 ====> 29/1 ======> 29

G). 5 1⁄3 × 5 1⁄8 ==> 16/3 * 41/8 ==> 656/24 ==> 82/3 ==> 27 1/3 ==> (Decimal: 27.33333)

H). 10 2⁄3 × 1 3⁄8 ===> 32/3 * 11/8 ===> 44 / 3 ===> 14 2/3 ==> (Decimal: 14.666667)

Hope that helps!!!! : )

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3 years ago