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gregori [183]
2 years ago
10

Divide and find quotient and reminder 4x³+6x²+19x-5 by 2x+5​

Mathematics
1 answer:
gayaneshka [121]2 years ago
7 0

Answer:

2x+5 ) 4x³ + 6x² + 19x - 5 (2x²-2x

4x³ +10x²

- -__________

- 4x² + 19x

- 4x² - 10x

+ +_______

29x - 5

Quotient = 2x² - 2x

Remainder = 29x - 5

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If triangle ABC is reflected over the y‐axis, reflected over the x‐axis, and rotated 180 degrees, where will point A' lie?
Ronch [10]

Given that ABC is a triangle and is reflected over the y - axis, reflected over the x - axis and rotated 180°

We need to determine the coordinates of the point A'

<u>Reflection over the y - axis:</u>

The coordinates of the point A is (-2,1)

The transformation rule to reflect across the y - axis is (x,y)\rightarrow (-x,y)

Substituting the point (-2,1) in the rule, we get;

(-2,1)\rightarrow (2,1)

Thus, the coordinates of the point A after reflection over the y - axis is (2,1)

<u>Reflection over the x - axis:</u>

The transformation rule to reflect across the x - axis is (x,y)\rightarrow (x,-y)

Substituting the point (2,1) in the rule, we get;

(2,1)\rightarrow (2,-1)

Thus, the coordinates of the point A after reflection over the x - axis is (2,-1)

<u>Rotation about 180°:</u>

The transformation rule to rotate about 180° is (x,y)\rightarrow (-x,-y)

Substituting the point (2,-1) in the rule, we get;

(2,-1)\rightarrow (-2,1)

Thus, the coordinates of the point A after the rotation about 180° is (-2,1)

Therefore, the coordinates of the point A' is (-2,1)

Hence, Option B is the correct answer.

7 0
3 years ago
10. Three kinds of teas are worth $4.60 per pound, $5.75 per pound, and $6.50 per pound. They are to be
zepelin [54]

Answer:

The mass of the $4.60/lb tea that should be used in the mixture is 10 lb

The mass of the $5.75/lb tea that should be used in the mixture is 8 lb

The mass of the $6.50/lb tea that should be used in the mixture is 2 lb

Step-by-step explanation:

The parameters of the question are;

The worth of the three teas are

Tea A = $4.60/lb

Tea B = $5.75/lb

Tea C = $6.50/lb

The mass of the mixture of the three teas = 20 lb

The worth of the mixture of the three teas = $5.25 per pound = $5.25/lb

The amount of the $4.60 in the mixture = The sum of the amount of the other two teas

Therefore, given that the mass of the mixture = 20 lb, we have in the mixture;

The mass of tea A + The mass of Tea B + The mass of Tea C = 20 lb

The mass of tea A = The mass of Tea B + The mass of Tea C

Therefore;

The mass of tea A + The mass of tea A = 20 lb

2 × The mass of tea A in the mixture = 20 lb

The mass of tea A in the mixture = 20 lb/2 = 10 lb

The mass of tea A in the mixture = 10 lb

The mass of Tea B + The mass of Tea C = The mass of tea A = 10 lb

The mass of Tea B + The mass of Tea C = 10 lb

The mass of Tea B  = 10 lb - The mass of Tea C

Where the mass of Tea C in the mixture = x, we have;

The mass of Tea B in the mixture = 10 lb - x

The cost of the 10 lb of tea A = 10 × $4.60 = $46.0

The worth of the tea mixture = 20 × $5.25 = $105

The worth of the remaining 10 lb of the mixture comprising of tea A and tea B is given as follows;

The worth of Tea B + The worth of Tea C in the mixture = $105.00 - $46.00 = $59.00

Therefore, we have;

x lb × $6.50/lb + (10 - x) lb × $5.75/lb = $59.00

x × $6.50 - x × $5.75 + $57.50 = $59.00

x × $0.75 = $59.00 -  $57.50 = $1.50

x =  $1.50/$0.75 = 2 lb

∴ The mass of Tea C in the mixture = 2 lb

The mass of Tea B in the mixture = 10 lb - x = 10 lb - 2 lb = 8 lb

The mass of Tea B in the mixture = 8 lb

Therefore, since we have;

Tea A = $4.60/lb

Tea B = $5.75/lb

Tea C = $6.50/lb

The mass of tea A in the mixture = 10 lb

The mass of tea B in the mixture = 8 lb

The mass of tea C in the mixture = 2 lb, we find;

The mass of the $4.60/lb tea that should be used in the mixture = 10 lb

The mass of the $5.75/lb tea that should be used in the mixture = 8 lb

The mass of the $6.50/lb tea that should be used in the mixture = 2 lb.

6 0
2 years ago
Using f(x)=2x-3 and g(x)=4x, what is f(2) - g(3)
Rashid [163]
First fine f(2).

f(2) = 2*2 - 3
f(2) = 4 - 3
f(2) = 1

Now g(3).

g(3) = 4*3
g(3) = 12

Now subtract 1 - 12 = -11

-11 is your answer.
6 0
3 years ago
(01.01 MC) Monica earned $60 from a bonus plus $8.50 per hour (h) she worked this week. Which of the following expressions best
Anna11 [10]

Answer:

Option (1)

Step-by-step explanation:

Monica earned a bonus = $60

Per hour earning in addition to bonus = $8.50

Let she worked for 'h' hours this week.

Then total earning from the hourly rate = $8.50h

Total earning for the week = Earning of 'h' hours + Bonus earned

                                             = $(8.50h + 60)

Therefore, Option (1) will represent Monica's earnings for the week.

8 0
3 years ago
Read 2 more answers
Find the distance between line 11x-60y-15=0 and point (2, 1/60)
vovikov84 [41]

Answer:

The answer to your question is: d = 6 / 61 or 0.1 units

Step-by-step explanation:

Data

Line: 11x - 60y - 15 = 0   A = 11; B = -60; C = -15

Point (2, 1/60)                 x = 2    y = 1/60

Formula

d = | Ax + By + C | / √(A² + B²)

Process

d = | (11)(2) + (-60)(1/60) -15 | / √(11² + (-60²)

d = | 22 -1 - 15 | / √ 121 + 3600

d = | 6 | / √3721

d = | 6 | / 61

d = 6 / 61 or 0.1 units

8 0
3 years ago
Read 2 more answers
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