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Lesechka [4]
3 years ago
10

for the equation 2x(3x+5)+3(3x+5)=ax^2+bx+c , if this equation is true for all values of x,what is the value of b if a,b,and c a

re constants
Mathematics
1 answer:
guapka [62]3 years ago
6 0

Answer:

b=19

Step-by-step explanation:

2x(3x+5)+3(3x+5)=ax2 +bx+c

by expansion,

6x2 +10x +9x+15=6x2 +19x +15

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Para decorar una pared se disponen de tiras de papel azules de 15 cm, verdes de 20 cm, y rojas de 25 cm. En la pared se quiere a
den301095 [7]

Answer:

a) Smallest line that can be made with each color = 300 cm

b) Total strips should be used = 47 strips

c) Total strips used of blue color = 20

  Total strips used of green color = 15

  Total strips used of red color = 12

Step-by-step explanation:

Given - To decorate a wall, there are 15 cm blue, 20 cm green, and 25 cm red strips of paper. On the wall you want to build three lines of the same size, one of each color and without cutting any strip.

To find - a) How long is the smallest line that can be made with each color?

              b) How many strips should be used?

              c) How many of each color?

Proof -

a)

For the smallest line that can be made with each color, we just have to find the lcm (least common multiple) of the 3 srtips.

Firstly,

Decompose the 3 strips to its prime factors , we get

15 = 3×5

20 = 2²×5

25 = 5²

So,

The Lcm(15, 20, 25) = 3×2²×5² = 3×4×25 = 300

∴ we get

Smallest line that can be made with each color = 300 cm

b)

Now,

Total strips used = 300 cm

Strips used by 15 cm blue = \frac{300}{15} = 20 strips

Strips used by 20 cm green = \frac{300}{20} = 15 strips

Strips used by 25 cm red = \frac{300}{25} = 12 strips

So,

Total strips should be used = 20 + 15 + 12 = 47 strips

c)

Total strips used of blue color = 20

Total strips used of green color = 15

Total strips used of red color = 12

6 0
3 years ago
Write a real world problem where the Unit rate is 6 miles per hr
Galina-37 [17]
This is just an example i came up with randomly:

Emma is going somewhere for vacation. Emma has been traveling for 6 hours and in those 6 hours, she has travelled 36 miles. How many miles did she travel in one hour?
8 0
2 years ago
Austin keeps a right conical basin for the birds in his garden as represented in the diagram. The basin is 40 centimeters deep,
Lina20 [59]

The shortest distance between the tip of the cone and its rim exits 51.11cm.

<h3>What is the shortest distance between the tip of the cone and its rim?​</h3>

If you draw a line along the middle of the cone, you'd finish up with two right triangles and the line even bisects the angle between the sloping sides. The shortest distance between the tip of the cone and its rim exists in the hypotenuse of a right triangle with one angle calculating 38.5°. So, utilizing trigonometry and allowing x as the measurement of the shortest distance between the tip of the cone and its rim.

Cos 38.5 = 40 / x

Solving the value of x, we get

Multiply both sides by x

$\cos \left(38.5^{\circ}\right) x=\frac{40}{x} x

$\cos \left(38.5^{\circ}\right) x=40

Divide both sides by $\cos \left(38.5^{\circ}\right)$

$\frac{\cos \left(38.5^{\circ}\right) x}{\cos \left(38.5^{\circ}\right)}=\frac{40}{\cos \left(38.5^{\circ}\right)}

simplifying the above equation, we get

$x=\frac{40}{\cos \left(38.5^{\circ}\right)}

x = 51.11cm

The shortest distance between the tip of the cone and its rim exits 51.11cm.

To learn more about right triangles refer to:

brainly.com/question/12111621

#SPJ9

7 0
1 year ago
Read 2 more answers
Write the letters of the expressions that are equivalent to the given expression.
Tresset [83]

Answer: A.) 10x + 15

Step-by-step explanation:

You would distribute (multiply) the 5 to the 2x which would then make it 10x and you would distribute (multiply) the 5 to the 3 which would then make it 15. Because the 5 is a positive number the sign stays the same.

Therefore, 10x + 15 is your answer.

3 0
2 years ago
As an estimation we are told 5 miles is 8 km.
melamori03 [73]

Answer:

Step-by-step explanation:

52.5 mi(8 km/5mi) = 84 km

3 0
3 years ago
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