A table decreased in price by 3/5. After the reduction it was priced at 40. What was the original price of the table

A kite is designed on a rectangular grid with squares that measure 1cm by 1 cm. A hexagonal piece within the kite will be reserv

Nata [24]

Answer:

The answer is the first answer

P = 8 + 4√13 cm

A = 36 cm²

Step-by-step explanation:

* Lets study the figure

- Its a kite with two diagonals

- The shortest one is 12 cm

- The longest one is 26 ⇒ axis of symmetry of the kite

- the shortest diagonal divides the longest into two parts

- The smallest part is 8 cm and the largest one is 18 cm

* To find the area reserved for the logo divide

the hexagonal piece into two congruent trapezium

- The length of the two parallel bases are 4 cm and 8 cm and

its height is 3 cm

- The length of non-parallel bases can calculated by Pythagoras rule

∵ The lengths of the two perpendicular sides are 2 cm and 3 cm

- 3 cm is the height of the trapezium

- 2 cm its the difference between the 2 parallel bases ÷ 2

(8 - 4)/2 = 4/2 = 2 cm

∴ The length of the non-parallel base = √(2² + 3²) = √13

* Now we can find the area of the space reserved for the logo

- The area of the trapezium = (1/2)(b1 + b2) × h

∴ The area = (1/2)(4 + 8) × 3 = (1/2)(12)(3) = 18 cm²

∵ The space reserved for the logo are 2 trapezium

∴ The area reserved for the logo = 2 × 18 = 36 cm²

* The area of the reserved space for the logo = 36 cm²

* The perimeter of the reserved space for the logo is the

perimeter of the hexagon

∵ The lengths of the sides of the hexagon are:

4 cm , 4 cm , √13 cm , √13 cm , √13 cm , √13 cm

∴ The perimeter = 2(4) + 4(√13) = 8 + 4√13 cm

* The perimeter of the reserved space for the logo = 8 + 4√13 cm

4 0

2 years ago

QUICK PLEASE !!!!!

Leni [432]

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

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

From the table we have :

x = 1 → y = 6

x = 2 → y = 9

x = 3 → y = 12

x = 4 → y = 15

Calculate the slope (choice any two pairs, and calculate the slope):

(1, 6), (2, 9)

$m=\dfrac{9-6}{2-1}=\dfrac{3}{1}=3$

We have the equation:

$y=3x+b$

Put the coordinates of the point (1, 6) to the equation, and solve it for b:

$6=3(1)+b$

$6=3+b$ <em>subtract 3 from both sides</em>

$3=b\to b=3$

Finally:

$y=3x+3$

3 0

2 years ago

Solving 8 problems per minute, Fast Finn can finish his test in time. He was however, working faster, solving 10 problems per mi

mrs_skeptik [129]

Answer:

Number of problems = 240

Step-by-step explanation:

Let x be the number of questions and t be the time.

Given:

Average rate = 8 problems per minute

Fast Finn rate = 10 problems per minute

Fast Finn taken time = t - 6

We need to find the number of problems on the test paper.

Solution:

Average rate to solve test paper.

$Average\ rate =\frac{Number\ of\ questions}{time}$

$8 =\frac{x}{t}$

$t =\frac{x}{8}$ --------------(1)

Fast Finn rate to solve the test paper.

$Average\ rate =\frac{Number\ of\ questions}{time}$

$10 =\frac{x}{t-6}$

Using cross multiplication rule.

$x=10(t-6)$

$x=10t-60$

substitute $t =\frac{x}{8}$ from equation 1.

$x=10(\frac{x}{8}) -60$

Rearrange the equation as:

$x - \frac{5}{4}x = -60$

$\frac{4x-5x}{4}=-60$

$-\frac{x}{4} = -60$

Using cross multiplication rule.

$x = 60\times 4$

x = 240 problems.

Therefore, 240 problems were on the test.

4 0

3 years ago

If you're creative, I need help. I am doing a math project where I need to define 20 words and include a picture and some facts

valentinak56 [21]

Answer:

Powerpoint

Step-by-step explanation:

I think that a powerpoint presentation would be best. With the first slide, put the picture and a title. With each slide, put more than one word and maybe an example. Make it colorful and maybe put some math puns in some of them.

Hope this helps.

6 0

3 years ago

PLEASE HELPPPPP MATH

Stels [109]

Answer:

Use the equation 250+25w=400+20w

Step-by-step explanation:

Replace w with one of the answers until you get the right one.

pretty sure its 35 but I don't have a calculator with me so double check

6 0

3 years ago

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