5. a. Three metal rods of lengths 234cm, 270cm and 324cm were cut into shorter pieces, all of the same length to make window grills. Calculate the length of the longest piece that can be cut from each of the rods and hence the number of pieces that can be obtained from the rods. ​

A triangle undergoes a sequence of transformations.

First, the triangle is dilated by a scale factor of 1/3 about the origin. Then the triangle is reflected over the x-axis. Finally, the triangle is translated left 3 units and up 2 units.

The family consumes 3 whole pizzas in total. They should order 3 whole pizzas to have enough for everyone.

To find out how many whole pizzas the Hayden family should order, we can calculate the total number of pizzas they need.

Since each person always eats 3/4 of a pizza, the total amount they eat can be calculated as follows:

3/4 + 3/4 + 3/4 + 3/4 = 4 × (3/4) = 3

So, the family consumes 3 whole pizzas in total. Therefore, they should order 3 whole pizzas to have enough for everyone.

As for the picture, imagine a circle representing a whole pizza. Divide it into four equal parts to represent each person's portion (3/4). Repeat this division three times to represent the three pizzas needed.

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Step-by-step explanation:

[tex] = ( {x}^{3} ) { ({x}^{7} )}^{2} [/tex]

[tex] = {x}^{3} \times {x}^{7 \times 2} [/tex]

[tex] = {x}^{3} \times {x}^{14} [/tex]

[tex] = {x}^{3 + 14} [/tex]

[tex] = {x}^{17} [/tex]

The complement of y is 110 - 8x degrees.

Complementary angles are angles that add up to 90 degrees.

Therefore,

y = 8x - 20

The complement of y can be found as follows;

complement of y = 90 - (8x - 20)

complement of y = 90 - 8x + 20

complement of y = 110 - 8x

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Answer:

30 or 120 /4

Step-by-step explanation:

a^p/q here p denotes power raised and q denotes inverse power or root. So, 60^1/2 denotes square root of 60 raised to power 1.

(3(1) + 9)² - 64

(3 + 9)² - 64

(12)² - 64

= 144 - 64

= 80

Answer:

78 m²

Step-by-step explanation:

V = bh

V = 13 m × 6 m

V = 78 m²

Answer:

Step-by-step explanation:

The amount of the temperature decrease will be 332 °C.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The oven temperature was at 325 degrees because my mom just finished baking a pie.

I increased the temperature, 75 degrees, so I could bake a pizza.

Then the temperature will be

⇒ 325 °C + 75 °C

⇒ 400 °C

After the pizza was cooked, I turned off the oven.

The oven cooled to the room temperature of 68 degrees.

Then the amount of the temperature decrease will be

⇒ 400 °C – 68 °C

⇒ 332 °C

The remaining question is given below.

How much did the temperature decrease?

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Answer:

9 students

Step-by-step explanation:

First find the amount of cross-country team students, 4% * 1125 = 45

Then 20% * 45 = 9, so 9 students in the team weigh between 60 and 70 kilos.

Answer:

Birds = 8

Mice = 6

Step-by-step explanation:

Conditions

Let the birds = x

Let the mice = y

Equations

x + y = 14

2x + 4y = 40

Solution

Using the top equation solve for x

x = 14 - y

Use this result to substitue for x

2(14 - y) + 4y = 40                      

Remove the brackets

28 - 2y + 4y = 40

Combine

28 + 2y = 40

Subtract 28 from both sides

28 - 28 + 2y = 40 - 28

2y = 12

Divide by 2 on both sides

2y/2 = 12/2

y = 6

Solve for x

x + y = 14

x + 6 = 14

Subtract 6 from both sides

x + 6 - 6 = 14 - 6

x = 8

Answer:

7 mice and 7 birds

Step-by-step explanation:

14 heads would mean there are 14 animals in total, as each animal has one head.

Birds have two legs, and mice have four.

2+4=6

40/6=6.67 (recurring)

6.67*2=13.3 (recurring)

6.67*4=26.67 (recurring)

Animal legs can't be in decimal numbers, so we can round the numbers.

13.3 becomes 13, 26.67 becomes 27.

13+27=40

Now we can see that there are 13 bird legs and 27 mice legs.

Divide the bird legs by 2 to get 6.5

Divide the mice legs by 4 to get 6.75

Again, we can't have a decimal of an animal, so we can round.

6.5 becomes 7, and 6.75 also becomes 7.

Therefore, there is 7 of each type of animal.

Answer:

3

Step-by-step explanation:

V=⅓b²h

16=⅓*16*h

16=16h/3

h=3cm

Answer:

SOLUTION :-

There is theorem/proof that tells that in these types of figure the other angle is double of the previous one

Means , the required angle will be ( 36 x 2 ) i.e. 72°.

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The attached graph represents the location of the pH values 0 and 1

The given parameters are:

pH value 0 = (1, 0)

pH value 1 = (0.1, 1)

This means that we plot a point at the coordinate (1, 0) and another point at the coordinate (0.1, 1).

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Complete question

The pH value is 0 at (1, 0) and 1 at (0.1, 1).

Using desmos

A. Locate, plot, and label on your graph where the pH value is 0.1

B. Locate, plot, and label on your graph where the pH value is 1.

The correct option is (A). The solution of the equation is x=48.125.

Given an equation [tex]x+\frac{x}{7}+\frac{1}{11}\left(x+\frac{x}{7}\right)=60[/tex].

A statement that uses the equal sign to show that two expressions have the same value is called an equation. The equation is represented as ax+by=c.

Firstly, we will apply the distributive property to the given equation a×(b+c)=ab+ac, we get

[tex]x+\frac{x}{7}+\frac{x}{11}+\frac{x}{77}=60[/tex]

Now, we will simplify the right-hand side equation by taking LCM, we get

[tex]\begin{aligned}\frac{77x+11x+7x+x}{77}&=60\\ \frac{96x}{77}&=60\end[/tex]

Further, we will multiply both sides with 77, we get

77×(96x/77)=77×60

96x=4620

Then, we will divide both sides with 96, we get

96x/96=4620/96

x=48.125

Hence, the solution of the given equation [tex]x+\frac{x}{7}+\frac{x}{11}+\frac{x}{77}=60[/tex] is x=48.125.

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Answer:

The correct option is (A). The solution of the equation is x=48.125.

Given an equation .

A statement that uses the equal sign to show that two expressions have the same value is called an equation. The equation is represented as ax+by=c.

Firstly, we will apply the distributive property to the given equation a×(b+c)=ab+ac, we get

Now, we will simplify the right-hand side equation by taking LCM, we get

Further, we will multiply both sides with 77, we get

77×(96x/77)=77×60

96x=4620

Then, we will divide both sides with 96, we get

96x/96=4620/96

x=48.125

Hence, the solution of the given equation is x=48.125.

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Step-by-step explanation:

Answer:

H (3x,3y)

Step-by-step explanation:

Dilation is a transformation when figure is enlarged or reduced by scale factor. During dilation, every point of preimage is dilated by scale factor, so it means each coordinate of that point must be multiplied by scale factor.

Hence, H(3x,3y) can be the result of dilation with scale factor of 3.

Answer:

Step-by-step explanation:

The solutions for the given quadratic equation are:

[tex]x = 8 \pm i[/tex]

Here we have the quadratic equation:

[tex]x^2 = 16x - 65[/tex]

We can rewrite it as:

[tex]x^2 - 16x + 65 = 0[/tex]

Using Bhaskara's formulas, we get:

[tex]x = \frac{-(-16) \pm \sqrt{(-16)^2 - 4*65} }{2} \\\\x = \frac{16 \pm \sqrt{(-4)} }{2}[/tex]

Now, remember that:

[tex]\sqrt{-1} = i[/tex]

Then we can rewrite:

[tex]x = \frac{16 \pm \sqrt{-1} *\sqrt{4} }{2}\\\\x = 8 \pm i[/tex]

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Going by the rules of the game to pick a random card and then multiply it by a roll of a number cube, we can find that:

If the die is rolled, it will land on a number between 1 and 6 while there are only four cards that can be picked.

The sample space is:

                  Dice             Card            Product        

                      1                 5                         5

                      1                 6                         6

                      1                 7                         7

                      1                 8                         8

                      2                 5                         10

                      2                 6                         12

                      2                 7                         14

                      2                 8                         16  

                      3                 5                         15

                      3                 6                         18

                      3                 7                         21

                      3                 8                         24

                      4                 5                         20

                      4                 6                         24

                      4                 7                         28

                      4                 8                         32

                      5                 5                         25

                      5                 6                         30

                      5                  7                         35

                      5                  8                         40

                      6                 5                         30                        

                      6                 6                         36

                      6                 7                         42

                      6                 8                         48

Based on the products, we can come up with the following frequency table:

                                 Frequency table

                          Product                     Frequency

                              5                                      1

                              6                                      1

                              7                                      1

                              8                                      1

                              10                                      1

                              12                                      1

                              14                                      1

                              16                                      1

                              15                                      1

                              18                                      1

                              21                                      1

                              24                                      2

                              20                                      1

                              28                                      1

                              30                                      2

                              32                                      1

                              25                                      1

                              35                                      1

                              40                                      1

                              36                                      1

                              42                                      1

                              48                                      1

                              Total                                24

The frequency table shows that to get 28 or more, a person will have a relative frequency of:

= 1 + 2 + 1 + 1 + 1 + 1 + 1 + 1

= 9

Probability is:

= 9 / 24

= 3/8

= 37.5%

The number of products required to win 25% of the time is:

= 25% x 24

= 6

To find the winning number, count down from the highest product 6 times to get 32.

The probability of getting 36 or higher is:

= ∑(Probabability of picking 36 and above numbers)

= 1 / 24 + 1/24 + 1/24 + 1/24

= 1 / 6

The probability of repeating this 4 consecutive times is:

= 1 / 6 x 1 / 6 x 1/ 6 x 1 / 6

= 1 / 1,296

= 0.0007716

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The area of the playground of dimensions 18 and 240is 432 [tex]m^{2}[/tex].

Given  If the dimensions of the playground in the layout are given by 180 cm x 240 cm.

The area of rectangle is length *breadth.

The given playground is in the shape of rectangle because there are two sides given and both the sides are different. In a rectangle length of opposite side found to be equal and each side form an angle of 90 degree.

Area=length*breadth

=180*240

=43200 [tex]cm^{2}[/tex]

We have to convert in meters so we have to divide by 100.

Area=43200 [tex]cm^{2}[/tex]

=43200/100

=432 [tex]m^{2}[/tex]

Hence the area of playground having dimensions 180 cm and 240 cm is 432[tex]m^{2}[/tex].

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Answer:

Its a right isosceles triangle

Answer:

right isosceles

Step-by-step explanation:

it has the right at the top

Answer:

[tex]x = \frac{-7 +\sqrt{489} }{2}[/tex]

[tex]x = \frac{-7 - \sqrt{489} }{2}[/tex]

Step-by-step explanation:

2x² +21x-61 = (x+7)²

expand

2x² + 21x - 61 = x² + 14x +49

move everything to one side

x² + 7x - 12 = 0

use quadratic formula

[tex]x = \frac{-b +- \sqrt{b^{2}-4ac } }{2a}[/tex]

plug in the values

[tex]x = \frac{-7 +- \sqrt{7^{2}-4(1)(-110) } }{2(1)}[/tex]

solve

[tex]x = \frac{-7 +- \sqrt{49-4(1)(-110) } }{2}[/tex]

[tex]x = \frac{-7 +- \sqrt{49 + 440 } }{2}[/tex]

[tex]x = \frac{-7 +- \sqrt{489} }{2}[/tex]

Answer:

obtuse because 6^2+10^2<10^2

Step-by-step explanation:

The given triangle whoe sides are 6cm, 10cm, and 12cm is an obtuse triangle and it can be determine by using pythagorian theorem, i.e. 6^2 + 10^2 < 12^2.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a^2 + b^2 = c^2.

here, we have,

Given :

The side lengths of a triangle are: 6cm, 10cm, and 12cm.

Pythagorian theorem can be used to find out that the triangles are acute or obtuse. According to pythagorian theorem, the sum of square of shorter side is equal to the square of the third side of the right angle triangle.

According to pythagorian theorem:.

That is, H^2 = P^2 + B^2.

There are some rules to find the triangle is obtuse or acute:

If  H^2 > P^2 + B^2, than the triangle is obtuse.

If H^2 < P^2 + B^2, than the triangle is acute.

Now, applying pythagorian theorem:

we get,

6^2 + 10^2 = 12^2

136 = 144

Here, it is clearly observe that 136 <  144, i.e. 6^2 + 10^2 < 12^2 therefore, the triangle is obtuse.

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Answer:

x+10

Step-by-step explanation:

x is any number and sum means addition, so x(number) +(sum) 10(10)

The formula to convert degrees Fahrenheit to Celsius is:

[tex]\bf{^{\circ}C=\dfrac{5}{9}(^{\circ}F-32) \ \ \to \ \ \ Formula }[/tex]

Convert 59°F to degrees Celsius.

Add the number 59 in the formula, and solve.

        [tex]\bf{=\dfrac{5}{9}(59-32) }[/tex]

Subtract 32 from 59.

         [tex]\bf{=\dfrac{5}{9}(27) }[/tex]

Multiply 5 x 9 = 135, then divide 135/9 = 15.

         [tex]\bf{=15 \ ^{\circ}C}[/tex]

Therefore 59 °F = 15 °C. The correct option is "D".