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NikAS [45]
3 years ago
5

Use the fuction h(x)=5x-2 and t(x) =4x+6 to complete the fuction operations listed below

Mathematics
1 answer:
Pavlova-9 [17]3 years ago
8 0
Part A
(h + t)(x)
(5x - 2 + 4x + 6)(x)   First plug in the numbers
(9x + 4)(x)   Add h(x) and t(x)
(9x² + 4x)   Then multiply it by x
x(9x + 4)   Lastly, simplify x out (I'm including both answers because I don't know whether your questions will ask for either one)
Unsimplified Answer: 9x² + 4x      Simplified Answer: x(9x + 4)

Part B
(h x t)(x)
(5x - 2)(4x + 6)(x)    First step is to of cource, plug in the numbers
(20x² + 30x -8x -12)(x)   Next we multiply h(x) and t(x)
(20x² + 22x -12)(x)     Simplify it a little
(20x³ + 22x² - 12x)    After that, multiply the whole thing by x
(2x)(10x² + 11x - 6)     Simplify 2x out of the equation
(2x)(5x - 2)(2x + 3)    Lastly, simplify the rest
Unsimplified Answer: (20x³ + 22x² -12x)    Simplified Answer: (2x)(5x - 2)(2x + 3)

Part C
h[t(x)]
(5x - 2) [(4x + 6)(x)]    Plug in the numbers
(5x - 2)(4x² + 6x)       Multiply t(x) and x
(20x³ + 30x² - 8x² -12x)    Multiply that by h(x)
(20x³ + 22x² -12x)     Simplify a little... Wait! That looks like the answer to Part B! Perhaps we did something wrong, let's go back and alter the third step
(5x -2)(2x)(2x + 3)     This time, simplify before multiplying oh wait, that's part B's simplified answer, isn't it.
Well, there's a good explanation for this: Part B and Part C are essentially the same equations, just in slightly different orders!
So, it will have the same answers and Part B! (At least, in theory, I'd recommend checking this for yourself too!)
Unsimplified Answer: (20x³ + 22x² - 12x)   Simplified Answer: (2x)(5x-2)(2x+3)

Well, that's a wrap, Parts A, B, and, C with work and explanations; if you find that I made a mistake or did something wrong let me know. I hope this helped, and good luck!
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A classroom had 8 rows of desks with 6 desks in each row. Four desks were removed from the room. How many desks were left?
Oduvanchick [21]
Answer: 44 desks.

First of all, you need to find how many desks there are in total. To find it, you need to multiply 8 with 6.

8 x 6 = 48

Next, it says that four desks were removed. All you need to do is subtract 4 from 48.

48 - 4 = 44.
5 0
3 years ago
A line passes through the point (–6, –2), and its y-intercept is (0, 1). What is the equation of the line that is perpendicular
Anna11 [10]

Answer:

Step-by-step explanation:

A line passes through the point (–6, –2), and its y-intercept is (0, 1). What is the equation of the line that is perpendicular to this line and passes through the point (2, 3)?

7 0
2 years ago
Suppose triangle TIP and triangle TOP are isosceles triangles. Also suppose that TI=5, PI=7, and PO=11. What are all the possibl
taurus [48]
<h3>Two answers: 5, 7</h3>

====================================================

Explanation:

A drawing may be helpful to see what's going on. Check out the diagram below. This is one way of drawing out the two triangles. The locations of the points don't really matter, and neither does the the orientation of how you rotate things. What does matter is we have the right points connected to form the segments mentioned.

----------

For now, focus on triangle TIP only. In order to have this be isosceles, we must make TP = 5 or TP = 7.

If TP = 5, then it's the same length as TI.

If TP = 7, then it's the same length as PI.

In either case, we have exactly two sides the same length (the other side different) which is what it means for a triangle to be isosceles.

----------

Let's consider triangle TOP. For it to be isosceles, we must have two sides the same length. We already locked in TP to be either 5 or 7 in the previous section above. So there's no way that TP could be 11 units long to match up with PO = 11.

If TP = 5, then OT must also be 5 units long so that triangle TOP is isosceles.

If TP = 7, then OT = 7 for similar reasoning.

Either way, TP only has two choices on what it could be.

----------

In short, we basically just write the first two values given to us to get the two triangles to be isosceles. We can't use TP = 11 as it would make triangle TIP to be scalene (all sides are different lengths).

5 0
3 years ago
. What's the common difference of the sequence 0, 5, 10, 15, 20, . . . ?
vichka [17]

Answer:

D. d = 5

Step-by-step explanation:

d = d² - d¹

= 5 - 0

= 5

d = d³ - d⁴

= 10 - 5

= 5

d = dⁿ - dⁿ-¹

6 0
3 years ago
Apples are sold in bags of four that cost $5, or bags of six that costs $7 per bag. What is the smallest cost at which you can b
babunello [35]
STEP 1:
BAGS OF FOUR
find number of bags needed to total 74 apples

= 74 ÷ 4 apples/bag
= 18.5 bags

*must round up to 19 bags because we cannot buy a partial bag

STEP 2:
BAGS OF FOUR
calculate price of 19 bags of 4 apples per bag

= 19 bags * $5/bag
= $95 for 19 bags of 4 apples/bag

STEP 3:
BAGS OF SIX
find number of bags needed to total 74 apples

= 74 ÷ 6 apples per bag
= 12.3333 bags needed

*must round up to 13 bags because we cannot buy a partial bag

STEP 4:
BAGS OF SIX

calculate price of 13 bags of 6 apples per bag

= 13 bags * $7 per bag
= $91 for 13 bags of 6 apples/bag


ANSWER: The smallest cost to buy 74 apples is $91.

Hope this helps! :)
3 0
3 years ago
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