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2 years ago

72 is 25% of students that have a cat, how many total students are there?

Mathematics

1 answer:

Lemur [1.5K]2 years ago

7 0

Answer:

the answer is 288 because 72 would be one fourth or 25% of 288. 72 plus 72 plus 72 plus 72 equals 288 equals 100%

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1+secA/sec A = sin^2 A / 1-cos A

Fofino [41]

Answer: see proof below

<u>Step-by-step explanation:</u>

$\dfrac{1+\sec A}{\sec A}=\dfrac{\sin^2 A}{1-\cos A}$

Use the following Identities:

sec Ф = 1/cos Ф

cos² Ф + sin² Ф = 1

<u>Proof LHS → RHS</u>

$\text{LHS:}\qquad \qquad \dfrac{1+\sec A}{\sec A}$

$\text{Identity:}\qquad \qquad \dfrac{1+\frac{1}{\cos A}}{\frac{1}{\cos A}}$

$\text{Simplify:}\qquad \qquad \dfrac{\frac{\cos A+1}{\cos A}}{\frac{1}{\cos A}}\\\\\\.\qquad \qquad \qquad =\dfrac{1+\cos A}{1}$

$\text{Multiply:}\qquad \qquad \dfrac{1+\cos A}{1}\cdot \bigg(\dfrac{1-\cos A}{1-\cos A}\bigg)\\\\\\.\qquad \qquad \qquad =\dfrac{1-\cos^2 A}{1-\cos A}$

$\text{Identity:}\qquad \qquad \dfrac{\sin^2 A}{1-\cos A}$

$\text{LHS = RHS:}\quad \dfrac{\sin^2 A}{1-\cos A}=\dfrac{\sin^2 A}{1-\cos A}\quad \checkmark$

3 0

3 years ago

Find an equation for the nth term of the arithmetic sequence.

amm1812

Answer:

$a_n=-301 +37(n-1)$

Step-by-step explanation:

arithmetic sequence formula: $a_n=a +(n-1)d$

where $a$ is the first term and $d$ is the common difference

Given:

$a_{10}=32$

⇒ $a +(10-1)d=32$

⇒ $a+9d=32$

Given:

$a_{12}=106$

⇒ $a +(12-1)d=106$

⇒ $a+11d=106$

Rearrange the first equation to make $a$ the subject:

a = 32 - 9d

Now substitute into the second equation and solve for $d$

(32 - 9d) + 11d = 106

⇒ 32 + 2d = 106

⇒ 2d = 106 - 32 = 74

⇒ d = 74 ÷ 2 = 37

Substitute found value of $d$ into the first equation and solve for $a$ :

a + (9 x 37) = 32

a + 333 = 32

a = 32 - 333 = -301

Therefore, the equation is: $a_n=-301 +37(n-1)$

4 0

2 years ago

Solve for p -6p+7=3(2p-3)-4(-10+4p

ozzi

p-6p+7=3(2p-3)-4(-10+4p

We move all terms to the left:

p-6p+7-(3(2p-3)-4(-10+4p)=0

We add all the numbers together, and all the variables

p-6p-(3(2p-3)-4(4p-10)+7=0

We add all the numbers together, and all the variables

-5p-(3(2p-3)-4(4p-10)+7=0

8 0

3 years ago

A large pizza has a circumference of approximately 43.96 inches2. what is the diameter of the pizza? Use 3.14 to approximate Pi.

Nookie1986 [14]

Answer:

d = 14

43.96/3.14 = 14

8 0

2 years ago

Need Help! 10 points!

Dominik [7]

The answer is d because 4+8=12 and they are 4 units away from eachother:)

6 0

2 years ago