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3 years ago

In triangle ABC, AB = 5 inches and BC = 3 inches. Which of the choices represents all possible values for AC, inches?

Mathematics

1 answer:

shusha [124]3 years ago

8 0

Answer:

-2 < AC < 8

Step-by-step explanation:

The last side has to be less than the sum of the other 2 sides, or less than 8. The only answer choice with this is the 3rd one.

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Find the simplified form of each expression (2/5n^9)^2 ?

Natali5045456 [20]

${( \frac{2}{5 {n}^{9} } ) }^{2} = \frac{ {2}^{2} }{( {5 {n}^{9} )}^{2} } = \frac{4}{ {5}^{2} {n}^{9 \times 2} } = \frac{4}{25 {n}^{18} }$

3 0

4 years ago

Tobias sent a chain letter to his friends, asking them to forward the letter to more friends. The number of people who receive t

PSYCHO15rus [73]

Answer:

$P(t)=a\cdot 4^{\frac{t}{9.1}}$ , where a is initial value.

Step-by-step explanation:

We have been given that Tobias sent a chain letter to his friends, asking them to forward the letter to more friends. The number of people who receive the email increases by a factor of 4 every 9.1 weeks. We are supposed to write the function to represent the given scenario.

Our function will be in form of $P(t)=a\cdot b^{f(t)}$ , where,

a = Initial value,

b = Factor of increase,

$f(t)$ = Linear function to determine the time.

Since number of people receiving email increase every 9.1 weeks, that is 1 people is 9.1 weeks, so slope of the increase would be $\frac{1}{9.1}$ .

Increase in number of people in t weeks would be $\frac{1}{9.1}(t)=\frac{t}{9.1}$ .

Upon substituting our given values in growth function, we will get:

$P(t)=a\cdot 4^{\frac{t}{9.1}}$

Therefore, our required function would be $P(t)=a\cdot 4^{\frac{t}{9.1}}$ , where a is initial value.

7 0

4 years ago

Read 2 more answers

The 9 officers of the Student Council are going on a trip to an amusement park. Each student must pay an entrance fee plus $5 fo

slava [35]

D) $20 because if you plug it in to the equation it equals $225

5 0

3 years ago

Read 2 more answers

A certain triangle has a perimeter of 3084 mi. The shortest side measures 76 mi less than the middle side, and the longest side

kari74 [83]

shortest side: 851

middle side:927

longest side : 1306

Explanation

Step 1

Let

x represents the shortest side

y represents the middle side

z represents the longest side

so, set the equations

a) the perimeter of a rectangle is the sum of the sides, so

$\begin{gathered} \text{Perimeter= side1+side2+side3} \\ replace \\ 3084=x+y+z \\ x+y+z=3084\Rightarrow\text{ Equation(1)} \end{gathered}$

b) The shortest side measures 76 mi less than the middle side( in other words, you have to subtract 76 from middle side to get the shortest side)

$x=y-76\Rightarrow equation(2)$

c) and the longest side measures 379 mi more than the middle side,( in other words, you have to add 379 to middle side to obtain the longest side)

$z=y+379\Rightarrow equation(3)$

Step 2

solve the equations

a) now, replace the x an z value sfrom equation (2) and (3) into equation(1)

$\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ (y-76)+y+(y+379)=3084 \\ -76+3y+379=3084 \\ 303+3y=3084 \\ 3y=3084-303 \\ \\ 3y=2781 \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{2781}{3} \\ y=927 \end{gathered}$

now, replace the y value in equatino (2) to find x

$\begin{gathered} x=y-76\Rightarrow equation(2) \\ x=927-76 \\ x=851 \end{gathered}$

c) finally, prelace x and y value in equation (1) to find z

$\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ 851+927+z=3084 \\ \text{add like terms} \\ 1778+z=3084 \\ \text{subtract 1778 in both sides} \\ 1778+z-1778=3084-1778 \\ z=1306 \end{gathered}$

shortest side: 851

middle side:927

longest side : 1306

I hope this helps you

4 0

1 year ago

Solve the proportion: |h|/3 = 4/9

Liono4ka [1.6K]

Im assuming thats a modulus sign so
the value of h should be positive only ( i dont see why thats necessary here)

h=4*3/9 or h=4/3

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4 0

3 years ago