A carpenter has 2 pipes which are 60 dm and 72 dm long respectively. he cuts them into equal lengths. what is the greatest possible length of each pipe?

Answer:

10.5:12:13.5

Step-by-step explanation:

The only two values you know and can compare are 8 and 12, so you have to find the relationship between them. 12/8 = 1.5. To get the two unknown values, you multiply 1.5 by the ones you do know.

7 * 1.5 = 10.5

9 * 1.5 = 13.5

So, you get 10.5:12:13.5

Answer:  8

Step-by-step explanation:

5-1

3 out of 4 = 1/4

1. The value of t in the triangle is 50°

2. The value of x in the triangle is 107°

It should be noted that the total sum of the angles that are in a triangle is 180°.

Therefore, the calculation of the angles will be illustrated thus:

1. 2t + 12 + t + 18 = 180°

3t + 30 = 180°

Collect like terms

3t = 180° - 30°

3t = 150°

Divide through by 3

3t/3 = 150° / 3

t = 50°

2. x + 30° + 43° = 180°

x + 73° = 180°

Collect like terms

x = 180° - 73°

x = 107°

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7 × 12 = 72 satisfies the closure property of multiplication, the other integer when the sum is - 38 and one integer is - 22 will be - 16 and the total score for Gopi will be 112 marks.

1)

Closure property of multiplication:

It states that if  two real numbers a and b are multiplied, then the product will be a real number as well.

We have 7 × 12 = 72

7, 12 and 72 all are real numbers.

So, it is a closure property under multiplication.

2)

Sum = - 38

a = - 22

We need to find b

a + b = - 38

- 22 + b = - 38

b = - 38 + 22

b = - 16

3)

1 correct answer = 4 marks

1 incorrect answer = - 2 marks

Number of correct answers = 32

Number of incorrect answers = 8

Total score = 32 × 4 + (- 2) × 8

= 128 - 16

= 112 marks.

Therefore, we get that, 7 × 12 = 72 satisfies the closure property of multiplication, the other integer when the sum is - 38 and one integer is - 22 will be - 16 and the total score for Gopi will be 112 marks.

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The value of a negative number such that the sum of that number and its square is 42 is -7.

Let the negative number be -x.

According to the question, the sum of the negative number and its square is 42.

So, we form an equation

- x + (-x)² = 42

x² - x - 42 = 0

Solving the quadratic equation,

x² - 7x + 6x - 42 = 0

x(x - 7) + 6(x - 7) = 0

(x - 7)(x + 6) = 0

x = -6 and x = 7

We have taken the number -x to be negative.

So, -x = -6 and -x = 7

x = 6 and x = -7

Hence, the value of the negative number is -7.

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The correct question is: "Determine the value of a negative number such that the sum of that number and its square is 42."

               8 square = 64

               5 cube = 125

Step-by-step explanation:

               =8² + 5³

            =64 + 125

                   =189

What are square and cube ?

The square of a number is the multiplication by itself. That means, for any integer, we can obtain the square by multiplying the integer itself. For example, the square of an integer 4 will be: 4 × 4 = 16, i.e., the square of 4 is equal to 16.

The cube of a number is the multiplication by itself thrice. That means, for any integer, we can obtain the cube by multiplying the integer by its square. For example, the cube of an integer 5 will be: 52 × 5 or 5 × 5 × 5, i.e., the cube of 5 is equal to 125.

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Answer:

[tex]{ \tt{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ \\ { \tt{ - 3 = \frac{ - 3 - ( - 6)}{s - 5} }} \\ \\ { \tt{ - 3(s - 5) = 3}} \\ \\ { \tt{s - 5 = - 1}} \\ \\ { \tt{s = 4}}[/tex]

Answer:

1. X+3x8=24
2.X+3x5=15

Step-by-step explanation:

Hello! So...

We are given the following to simplify:

[tex]\frac{(x+3)^8}{(x+3)^5}[/tex]

_______________________________

1. Apply the exponent rule ([tex]a^b^+^c=a^b * a^c[/tex]).

[tex](x+3)^8=(x+3)^5(x+3)^3[/tex]

=[tex]\frac{(x+3)^5(x+3)^3}{(x+3)^5}[/tex]

________________

2. Cancel out the common factor, given us our solution: [tex](x+3)^5[/tex].

________________________________________________________

Hope this helps! If so, please lmk! Thanks and good luck!

<HMN, <HMK, <KMN

using the graph

The special angle pair relationship between the given angles are:

1. Corresponding angles

2. Alternate exterior angles

3. Consecutive

The following are some special angle pair relationships:

1. Angles 1 and 3 form a special angle pair relationship known as: corresponding angles.

2. Angles 8 and 4 form a special angle pair relationship known as: alternate exterior angles.

3. Angles 2 and 3 both lie on the same side of the given transversal, therefore, the special angle pair relationship between angle 2 and angle 3 is: consecutive interior angles.

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By solving using given linear equation f(x)=x2-7 and g(x) = 2x + 9 we get  the desired value as ( g - f )(-2) = 32 .

An equation is deemed to be linear when the maximum power of the variable is consistently 1. It is also known as a one-degree equation. A linear equation with one variable usually has the form Ax + B = 0. In this scenario, the variables x and A are variables, whereas B is a constant.

A linear equation in two variables is of the form Ax + By + C = 0, in which A and B are the coefficients, C is a constant term, and x and y are the two variables, each with a degree of 1.

For example, 7x + 9y + 4 = 0 is a linear equation in two variables. If we consider two such linear equations, they are called simultaneous linear equations.

Simplification:

f(x)  = x2 - 7

g(x) = 2x + 9

( g - f )(-2) = (2x-7-2x -9)(-2)

                = -16 * -2

                = 32 .

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one is the pmf or probability mass function of X = number of children in the family

The Probability Mass Function (PMF) is also called a probability function or frequency function which characterizes the distribution of a discrete random variable.

X takes values: { 3, 4, 5 }

where:  P ( X = 3 ) + P ( X = 4 ) + P ( X = 5 ) = 1

For X = 3 we have : BBB or GGG.

P ( X = 3 ) = ( 1/2 * 1/2 * 1/2 ) * 2 = 1/8 * 2 = 2 / 8 = 1/4

P ( X = 4 ) = ( 1/2 * 1/2 * 1/2 * 1/2 ) * 6 = 6 /16 = 3/8

P ( X = 5 ) = ( 1/2 * 1/2 * 1/2 * 1/2 * 1/2 ) * 12 = 12 / 32 = 3/8

1 / 4 + 3 / 8 + 3 / 8 = 8 / 8 = 1

the complete question is

A family decides to have children until it has three kids of the same gender. Assuming P(B) = P(G) = 0.5, what is the pmf of X = number of children in the family?

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Answer: Multiplicative inverses or reciprocal, is a number that when multiplied by the given number gives the product as 1.

Step-by-step explanation:

1) [tex]\angle A \cong \angle D, \angle C \cong \angle E, \overline{AB} \cong \overline{DF}[/tex] (given)

2) [tex]\triangle ABC \cong \triangle DFE[/tex] (AAS)

3) [tex]\angle ACB \cong \angle DEF[/tex] (CPCTC)

[tex]s=(\frac{1}{2} p)(l)[/tex]

Flip equation:

[tex]\frac{1}{2} lp=s[/tex]

Divide both sides by p/2:

[tex]\frac{1/2lp}{p/2} =\frac{s}{p/2}[/tex]

[tex]l=\frac{2s}{p}[/tex]

The number of trees that would be saved from a stack of newspapers 24 feet high given the by ratio of trees saved from a stack of recyclable newspaper is 8 trees

Convert feet to inches

Quantity of recyclable newspaper needed : number of trees

36 : 1 = 288 : x

36/1 = 288/x

36 × x = 1 × 288

36x = 288

x = 288 / 36

x = 8 trees

In conclusion, the trees that would be saved from a stack of newspapers 24 feet high is 8 trees

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Answer:

B

Step-by-step explanation:

The values of p and q if x-1 is a common factor of f(x)=x⁴-px³ +7qx+1, and g(x)=x²-4x² + px² +qx-3,​are 13/2 and -1/2 respectively.

In Mathematics, factors are positive integers that can divide a number evenly.  Suppose we multiply two numbers to get product. The number that is multiplied are the factors of the product. Each number is factor of itself.  Factors have many real-life examples, such as arranging sweets in box, arranging numbers in pattern, distributing chocolates among children, etc. To find the factors of number, we need to use the multiplication or division method.

Factors are numbers that can divide a number exactly.  Hence, after the division, there is no remainder left. Factors are numbers you multiply together to get the another number. Thus, factor is the divisor of another number.

f(x)=[tex]x^{4}-px^{3}+7qx+1[/tex]

    = 1-p+7q+1

     = p-7q=2---------1

g(x)= [tex]-3x^{2} +px^{2} +qx-3[/tex]

      = -3+p+q-3

      =p+q= 6----------2

p-7q=2

p+q=6

-----------------

By subtracting 2 from 1

-8q=4

q=-1/2

putting value of q in equation 2 we get,

p+(-1/2)=6

p=6+[tex]\frac{1}{2}[/tex]

p=13/2

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a) The problem is in the second step, the square root can't be distributed under sum.

b) 10*√41

a) The incorrect step is the second one, the square root can't be distributed like that.

Here we have the numeric expression:

5*√164

And we want to simplify it.

We can write:

5 = √25

Then:

5*√164 = √25*√164 = √(164*25) = √4,010

Now we can decompose this as a product of square numbers:

4,010 = 4*1,025 = 4*25*41

Then we rewrite:

√4,010 = √4*√25*√41 = 2*5*√41 = 10*√41

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The line that passes through the point -1, four and is parallel to the line 2 X plus Y equals one is y + 2x = 2.

Slope is measure of steepness of a line.

The Equation of line is y = mx + c

where,

m is slope

c is y intercept

To find equation of the parallel line we must first find the slope of the original line

The original line is 2x + y = 1

We must first write equation in the general form above

That's

y = - 2x + 1

Comparing with general equation above

Slope = - 2

Since lines are parallel their slope are also same

Slope of parallel line = - 2

So the equation of line using point

( - 1 , 4) and the slope - 2 is

y-4= -2(x+1)

y-4= 2x-2

y+2x= -2+4

We have final answer as

y + 2x = 2

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The estimate of 24% of 289 is 69.36

From the question, we are to determine the estimate the given rate

The given rate is

24% of 289

This can be expressed as

24% × 289

Now, we will evaluate the percentage

To evaluate the percentage, we will divide the number by 100.

That is,

24% = 24/100

Thus,

The expression can further be expressed as

24/100 × 289

= 0.24 × 289

=  69.36

Hence, the estimate is 69.36

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Answer:

Clearly, the given sequence is an AP with first term a=2, common difference d=5 and n=10.

Now,

s10 = 10/2 (2a + 10-1d)
=5(2x2+9x5)

=245

Step-by-step explanation:

Answer:

S₁₀ = 245

Step-by-step explanation:

the sum to n terms of an AP is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = 2 and d = a₂ - a₁ = 7 - 2 = 5 , then

S₁₀ = [tex]\frac{10}{2}[/tex] [ (2 × 2) + (9 × 5) ]

      = 5(4 + 45)

      = 5 × 49

      = 245

Step-by-step explanation:

Use the Pythagorean Theorem.

a^2+b^2=c^2

a^2 + 5^2 = 16^2

a^2 + 25 = 256

a^2 = 231

a = square root of 231

a= 15.20

Answer:15.20

Step-by-step explanation:

From the word problem given, the number of pizzas each that were delivered are:

Step I

Let a = number of small pizzas delivered

Let b = number of medium pizzas delivered

Let c = number of large pizzas delivered

Step 2 - Creating relevant expressions based on number and type ordered, we have:

a + b + c = 8.............................1

3a + 5b + 11c = 56..................2
4a + 9b + 12C = 4 * 8 + 12.....3a

We can rewrite (3) as
4a + 9b + 12C = 44 ....3b

Step 3

Multiply both sides of (1) by 4

We have

4a +4b +4c = 32

-
4a +4b +4c = 32
5b +8C = 12......................(4)

Multiply both sides of (1) by 3 and subtract from (2), and we have:

3a + 3b + 3c = 24, removing this from (2) we have

3a + 5b + 11c = 56

-
3a + 3b + 3c = 24
2b + 8c = 32.....................(5)

Step 4 - Subtract (4) from (5)

2b + 8c = 32
-
5b + 8c = 12
-3b = 20

b = - 20/3

= - 6.67
Since we cannot have negative values, we work with absolute value to get:

b [tex]\approx[/tex] 7

Since b = 7

2(7) + 8c = 32
8c = 32 - 14
c = 18/8

c [tex]\approx[/tex] 2


Plug in that back into a we have

a + b + c = 8
a + 7 + 2 = 8

a = 8-9
a = -1 (recall we must have absolute values)
a therefore = 1.

Hence the number of pizzas that were ordered are:

1 small
7 medium; and

2 large.

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The number of animals that are on the farm is 48.

A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 2/3.

The first step is to determine the fraction of the animals that are chickens.

Fraction that are chickens = 1 -  fraction that are pigs and horses.

[tex]\frac{1}{8} + \frac{2}{3}[/tex]

[tex]\frac{3 + 16}{24}[/tex] = [tex]\frac{19}{24}[/tex]

Fraction that are chickens = 1 - 19/24 = 5/24

The next step is to divide the number of chickens by the fraction of the chickens.

Number of animals = number of chickens ÷ fraction of chickens

10 ÷ 5/24

10 x 24/ 5 = 48

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Answer:

False.

Step-by-step explanation:

That answer would be true if, it was 54 ÷ 9 = 6

54 ÷ 0.9 = 60.

Hope this helps!

Answer:

False

Step-by-step explanation:

hope it helps and have a nice day! :)

Write an algebraic expression to represent each statement.

the number, b, divided by thirty-six

b/36

Answer:

71

Step-by-step explanation:

Mean is Average

You can Find the Mean of a set of numbers by adding them all up and then dividing that number by the amount of numbers in the set.

72 + 75 + 68 + 84 = 231

231 / 4 = 57.75

This is his current mean.

Let's add his next score.

72 + 75 + 68 + 84 + 71 = 370
Divide by 5 instead of 4 because we added another number to the data set.

370 / 5 = 74