MATHEMATICS HIGH SCHOOL

Given right triangle DEF, what is the value of tan(F)?

Answers

Answer 1

Answer:

we know that

In the right triangle DEF

the tangent of the angle F is equal to

$tan(F)=(opposite\ side\ angle\ F)/(adjacent\ side\ angle\ F)=(DE)/(EF)$

substitute the values

$tan(F)=(40)/(9)$

therefore

the answer is the option

$(40)/(9)$

Answer 2

Answer:

Answer: $(40)/(9)$

Step-by-step explanation:

We know that for any angle x in a triangle ,

$\tan x=\frac{\text{side opposite to x}}{\text{side adjacent to x}}$

Now, for the given triangle DEF, the value of tan(F) is given by :-

$\tan F=\frac{\text{side opposite to F}}{\text{side adjacent to F}}\n\n\Rightarrow\ \tan F=(40)/(9)$

Hence, the value of tan(F) = $=(40)/(9)$

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Reggie can line a football field in 120 minutes. Rosalinda can line a football field in 80 minutes. If they work together, how many minutes does it take them to line a football field?a. 40 minutes
b. 80 minutes
c. 200 minutes
d. 240 minutes HELP?!

Answers

Answer:

If they work together, they take 48 minutes to line the football field.

Step-by-step explanation:

Given: Reggie can line a football field in 120 minutes. Rosalinda can line a football field in 80 minutes.

To find : If they work together, how many minutes does it take them to line a football field?

Solution :

If they work together,

Let the number of minutes(x) they take to line the foot ball field.

According to question,

$(1)/(x)=(1)/(120)+(1)/(80)$

$(1)/(x)=(80+120)/(120* 80)$

$(1)/(x)=(200)/(120* 80)$

Cross multiply,

$x=(120* 80)/(200)$

$x=12* 4$

$x=48$

Therefore, If they work together, they take 48 minutes to line the football field.

Answer: If they work together, they can line a football field in 48 minutes.

Step-by-step explanation: Given that Reggie can line a football field in 120 minutes and Rosalinda can line a football field in 80 minutes.

We are to find the number of minutes does it take them to line a football field if they work together.

We have

Time taken by Reggie to line a football field = 120 minutes.

So, in 1 minute, Reggie can line $(1)/(120)$ part of the field.

Time taken by Rosalinda to line a football field = 80 minutes.

So, in 1 minute, Rosalinda can line $(1)/(80)$ part of the field.

Therefore, if they work together, the portion of the football field that they can lie in 1 minute is given by

$(1)/(120)+(1)/(80)\n\n\n=(2+3)/(240)\n\n\n=(5)/(240)\n\n\n=(1)/(48)$

Thus, if they work together, they can line a football field in 48 minutes.

You have 160 boxes of cookies. In each case you can pack 8 boxes of cookies. How many cases would be filled from these boxes of cookies ?

Answers

160 boxes of cookies / 8 boxes per case = 20 cases that can be filled.

you divide 160 by 8 and you get 20. 20 cases will be filled

find the volume of a can of chicken broth that had a diameter of 7.5cm and a height of 11cm. round 5o the neatest tenth

Answers

cans are normally cylinders
Vcylinder=hpir^2

h=11

d/2=r
7.5/2=3.75=r

V=11pi3.75^2
V=11pi14.0625
V=154.6875pi
aprox pi=3.141592 and multiply
V=485.96
round tenth
486.0 cm^3

The total number of fungal spores can be found using an infinite geometric series where a1 = 8 and the common ratio is 4. Find the sum of this infinite series that will be the upper limit of the fungal spores.

Answers

The formula for infinite geometric series is equal to a1 / (1-r) where in this problem a1 is equal to 8 and r is equal to 4. In this case, r is not equal to less than 1. This means the sum should be infinity and cannot be determined definitely.

Answer:

This infinite geometric series is divergent and thus we cannot find the sum. The sum is infinity.

Step-by-step explanation:

There are two types of geometric series: convergent and divergent.

The sum of an infinite geometric sequence is given by the formula:

Sum = $(a)/(1-r)$

Where,

r is the common ratio and

$|r|<1$

If absolute value of r is NOT less than 1, then the series is divergent and sum cannot be found.

For our given problem, $r=4$ , clearly $|4|=4$ , which is NOT less than 1, so the series is divergent and sum cannot be found.

Find the product of the complex number and its conjugate. 3 + 3i

Answers

First, we are going to find the conjugate of our complex number. Remember that to find the conjugate of a complex number we just need to keep the real part and change the sing of the imaginary part.

We can infer from our problem that the real part of our complex number is 3 and its imaginary part is $3i$ . We are going to keep the real part 3 and change the imaginary part from positive to negative, so our conjugate is $3-3i$ .

Next, we are gong to multiply both the complex number and its conjugate using the distributive property:

$(3+3i)(3-3i)=(3*3)-(3*3i)+(3*3i)-(3i*3i)=9-9i+9i-9i^2=9-9i^2$

Remember that $i^2=√(-1)^(2) =-1$ , so:

$9-9i^2=9-9(-1)=9+9=18$

We can conclude that the product of the multiplication of the complex number 3+3i and its conjugate, 3-3i, is 18.

Product of complex number and its conjugate will be 18 .

Complex number : x ± iy

Given , 3 + 3i

Conjugate pair of complex number = x ± iy

So, the complex conjugate pair are :

3 + 3i and 3 - 3i

Product of complex conjugate pair,

(3 + 3i) (3 - 3i)

Open the brackets,

= 9 - 9i + 9i - 9i²

Here, i = √-1 ; i² = -1

Substitute the value of iota(i),

= 9 -9i + 9i +9

= 18

Thus the product value is 18.

Know more about complex numbers,

brainly.com/question/20566728

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Let y be a function of x such that 2x-3y=6. What is the rate if change of y with respect to x?

Answers

2x - 3y = 6
first, isolate y:
-3y = -2x + 6
y = (2/3)x - 2
This is a linear function in standard form, so we know that the slope (in this case the rate of change of y in respect to x) is 2/3

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