(2x^2+3x^3-16-8x) / (x-2)

Find the value tan 32 degrees 24’ to four places

Zina [86]

Answer:

8.3

Step-by-step explanation:

7 0

3 years ago

ON THE SMARTBOARD, THE

RideAnS [48]

The length of rectangle is 105 cm and width is 98 cm.

Step-by-step explanation:

Given,

Perimeter of rectangle = 406 cm

Let,

w be the width of rectangle

Length of rectangle = w+7

We know that

Perimeter of rectangle = 2(Length + Width)

$406 = 2(w+7+w)\\406 = 2(2w+7)\\406 = 4w+14\\406-14 = 4w\\392=4w\\4w=392$

Dividing both sides by 4

$\frac{4w}{4}=\frac{392}{4}\\w=98$

Width of rectangle = 98 cm

Length of rectangle = 98+7 = 105 cm

The length of rectangle is 105 cm and width is 98 cm.

4 0

3 years ago

An arithmetic series begins 29+25+21+... find the maximum value that the series could have

Fittoniya [83]

The series' value is maximized if the sum only consists of positive terms. Notice that each term in the sum takes the form 4n + 1 for integer n. This means the smallest positive integer that the sum can involve is 1, so the maximum value is

S = 29 + 25 + 21 + … + 9 + 5 + 1

Reversing the order of terms gives the same sum,

S = 1 + 5 + 9 + … + 21 + 25 + 29

Adding terms in the same positions gives us twice this sum,

2S = (29 + 1) + (25 + 5) + (21 + 9) + … + (1 + 29)

Notice how each grouped sum adds to 30. There are 8 terms in the sum, since 4n + 1 = 29 when n = 8. So

2S = 8 × 30 = 240 ===> S = 120

5 0

3 years ago

John the car salesman makes a commission on selling cars, as a percentage of the price, which

Bess [88]

Answer:

John's commission percentage on new cars is x and his commission percentage on used cars is 1.5x, therefore, John's commission percentage on new cars is 2% and his commission percentage on used cars is 3%.

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

John's commission percentage on new cars = x

John's commission percentage on used cars = x + 50%x (His commission on used cars is 50% more than on new cars)

Sales on new cars = $80,000

Sales on used cars = $50,000

John's commission check = $3,100

2. If x represents the commission percentage on new cars, express the commission percentage on used cars in terms of x.

John's commission percentage on new cars = x

John's commission percentage on used cars = x + 50%x = 1.5x

Now we can solve for x, this way:

80,000x + 50,000 * 1.5x = 3,100

80,000x + 75,000x = 3,100

155,000x = 3,100

x = 3,100/155,000

x = 0.02 = 2% ⇒ 1.5x = 3%

John's commission percentage on new cars is 2% and his commission percentage on used cars is 3%

3 0

3 years ago

Given: △ABC, E∈ AB m∠ABC=m∠ACE AB=34, AC=20 Find: AE

LenaWriter [7]

Answer:

AE = 11.76 units

Step-by-step explanation:

For better understanding of the solution, see the attached figure :

Given : E ∈ AB, m∠ABC = m∠ACE, AB = 34 and AC = 20

To find AE :

In ΔABC and ΔACE,

m∠ABC = m∠ACE ( Given )

∠A = ∠A ( Common angle for both the triangles )

By AA postulate of similarity of triangles, ΔABC ~ ΔACE

So, proportion of the corresponding will be equal.

$\implies \frac{AC}{AB}=\frac{CE}{BC}=\frac{AE}{AC}\\\\\implies\frac{AC}{AB}=\frac{AE}{AC}\\\\\implies\frac{20}{34}=\frac{AE}{20}\\\\\implies AE=\frac{20\times 20}{34}\approx 11.76$

Hence, AE = 11.76 units

4 0

3 years ago