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NARA [144]
3 years ago
5

Math help on questions #4 and #5

Mathematics
1 answer:
Vanyuwa [196]3 years ago
7 0
<h3>Answer:</h3>

4. -3

5. 3

<h3>Step-by-step explanation:</h3>

4. For x > -2, the value of a is the slope of the line. The line goes down 3 units for each 1 to the right, so the slope is -3/1 = -3. Then a = -3.

___

5. The ordered pair (h, k) is typically used to name the point to which a function is translated. The vertex of the function f(x) = |x| is (0, 0). When it is translated to (h, k), the function becomes ...

... q(x) = |x -h| +k

If the new vertex is (3, 0), then h = 3 and k = 0. This is consistent with the equation shown. (k = 0 means q(x) = |x -h|.)

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Equations and functions
Brilliant_brown [7]

Answer:

first one

Step-by-step explanation:

Absolute value functions usually have that shape. The only absolute value function  out of all of the answer choices is the first one.

6 0
3 years ago
Read 2 more answers
The growth of a city is described by the population functionwhereis the initial population of the city, t is the time in years,
mamaluj [8]

Complete question:

The growth of a city is described by the population function p(t) = P0e^kt where P0 is the initial population of the city, t is the time in years, and k is a constant. If the population of the city atis 19,000 and the population of the city atis 23,000, which is the nearest approximation to the population of the city at

Answer:

27,800

Step-by-step explanation:

We need to obtain the initial population(P0) and constant value (k)

Population function : p(t) = P0e^kt

At t = 0, population = 19,000

19,000 = P0e^(k*0)

19,000 = P0 * e^0

19000 = P0 * 1

19000 = P0

Hence, initial population = 19,000

At t = 3; population = 23,000

23,000 = 19000e^(k*3)

23000 = 19000 * e^3k

e^3k = 23000/ 19000

e^3k = 1.2105263

Take the ln

3k = ln(1.2105263)

k = 0.1910552 / 3

k = 0.0636850

At t = 6

p(t) = P0e^kt

p(6) = 19000 * e^(0.0636850 * 6)

P(6) = 19000 * e^0.3821104

P(6) = 19000 * 1.4653739

P(6) = 27842.104

27,800 ( nearest whole number)

3 0
3 years ago
What is the algebraic expression for: four less than three times the number of egg orders and six more than two times the number
Ira Lisetskai [31]
3n - 4 + 6 + 2n

I believe that's the answer!
5 0
3 years ago
Solve the following simultaneous linear equations.<br>2x + y = 5<br>4x – 3y = -10​
Jet001 [13]

Answer:

(1/2,4)

Step-by-step explanation:

First, determine y in first equation: 2x+y=5 or  y=5-2x

replace value of y determined in first equation (5-2x) into 2nd equation    

4x-3(5-2x)=-10

4x-15+6x=10

10x=5

x=1/2

put value of x into either equation to solve for y so

2(1/2)+y=5

1+y=5

y=4

answer: x=1/2, y=4

check answer by substituting x and y into either equation:

4x-3y=-10

4(1/2)-3(4)=-10

2-12=-10

-10=-10

or

2x+y=5

2(1/2)+4=5

1+4=5

5=5

7 0
3 years ago
f(x) = 500(1.05)x What was the average rate of change of the value of Sophia's investment from the second year to the fourth yea
hjlf
\bf slope = {{ m}}= \cfrac{rise}{run} \implies &#10;\cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby &#10;\begin{array}{llll}&#10;average\ rate\\&#10;of\ change&#10;\end{array}\\\\&#10;-------------------------------\\\\&#10;f(x)=500(1.05)^x   \qquad &#10;\begin{cases}&#10;x_1=2\\&#10;x_2=4&#10;\end{cases}\implies \cfrac{f(4)-f(2)}{4-2}&#10;\\\\\\&#10;\cfrac{[500(1.05)^4]~-~[500(1.05)^2]}{4-2}\implies \cfrac{56.503125}{2}\implies 28.2515625
6 0
3 years ago
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