Mr. Rijo bought 49 bags of soil one week and 28 bags of soil the next week. Which expression correctly applies the
distributive property to show equivalent expressions for the number of bags of soll he bought?
49 + 28 = 4(7 + 7)
59 + 28 - (7)(7) + (14)(2))
19 + 28 - (7)(14) + (7)(7)
49 + 28 - 7(7+ 4)

An equation is formed when two equal expressions are equated together. The value of x in the equation [√(x+7)]-11=2 is 162.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution for x in the equation [√(x+7)]-11=2 can be solved as,

[tex]\sqrt{x+7}-11=2\\[/tex]

Using the addition property of equality,

[tex]\sqrt{x+7} -11+11= 2+11\\\\\\\sqrt{x+7} = 13[/tex]

Squaring both the sides of the equation,

x + 7 = 169

Using the subtraction property of equality,

x + 7 - 7 = 169 - 7

x = 162

Hence, the value of x in the equation [√(x+7)]-11=2 is 162.

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Answer:

D. Sqroot6

Step-by-step explanation:

6 is not a perfect square. So it is a non-repeating decimal that never ends

sqroot6 ~=

2.4494897428...

this is an irrational number.

The rest on the numbers can be written as a ratio:

0.45=45/100=9/20

0.63636363

= 63/99 = 7/11

sqrt25 = 5 = 5/1

that means they are rational.

The y-coordinate of the other endpoint is 10 units.

The given coordinates are H (-5, 2) and G (–9, –6).

We need to find the y-coordinate of the other endpoint.

The mid-point formula is  [tex](x, y)=(\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2})[/tex]

Now, [tex](-5, 2)=(\frac{x_{1} +(-9)}{2} , \frac{y_{1} +(-6)}{2})[/tex]

⇒[tex]2=\frac{y_{1}-6 }{2}[/tex]

⇒[tex]4=y_{1}-6[/tex]

⇒[tex]y_{1}=10[/tex]

Therefore, the y-coordinate of the other endpoint is 10 units.

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Answer:

3qr - 6q²

Step-by-step explanation:

3q(r - 2q) ← multiply each term inside the parenthesis by 3q

= 3qr - 6q²

Answer:

3qr – 6q²

Step-by-step explanation:

3q(r – 2q)

E X P A N D I N G :-

3qr – 6q²

The three consecutive integers are 15 16 and 17.

Step 1:

Let  X be the first integer. Since they are consecutive, it means that the second number will be X + 1 and the third number will be X + 2 and sum of the first and the third should add up to 32. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) be the three consecutive integers.

Step 2:

The sum of the first and the third should add up to 32.

X + ( X + 2 )= 32

2X + 2= 32

2X = 32 - 2

2X = 30

X = 30/2

X=15

Hence the first number is 15, the second number is 15 + 1, and the third number is 15 + 2.

Therefore, three consecutive integers in which the sum of the first and the third is 32 are 15 16, and 17.

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Answer:

1491 girls (99.4 percent)

Step-by-step explanation:

explanation is in the attached picture

The quotient [tex]\frac{x^2 - 49}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex] is [tex]\frac{3(x +7)}{(x -7)}[/tex]

The expression is given as:

[tex]\frac{x^2 - 49}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex]

Express x^2 - 49 as difference of two squares

[tex]\frac{(x + 7)(x- 7)}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex]

Factorize other expressions

[tex]\frac{(x + 7)(x- 7)}{x + 2} \div \frac{(x -7)(x-7)}{3(x + 2)}[/tex]

Express as product

[tex]\frac{(x + 7)(x- 7)}{x + 2} \times\frac{3(x + 2)}{(x -7)(x-7)}[/tex]

Cancel the common factors

[tex]\frac{(x + 7)}{1} \times\frac{3}{(x -7)}[/tex]

Evaluate the product

[tex]\frac{3(x +7)}{(x -7)}[/tex]

Hence, the quotient [tex]\frac{x^2 - 49}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex] is [tex]\frac{3(x +7)}{(x -7)}[/tex]

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Step-by-step explanation:

I'm going to assume you meant to write [tex]\sqrt{r+1}[/tex] in the equation as +1 - 1 wouldn't make much sense since they would just cancel out.

a. [tex]f(-1) = \sqrt{-1 + 1} - 1\\ f(-1) = \sqrt{0} - 1\\f(-1) = 0-1\\f(-1) = -1[/tex]

b. [tex]f(24) = \sqrt{24 + 1} - 1\\ f(24) = \sqrt{25} - 1\\f(24) = 5 - 1\\f(24) = 4[/tex]

c. [tex]f(x-1) = \sqrt{(x-1)+1} -1\\f(x-1) = \sqrt{x} - 1[/tex]

The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula [tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex], equivalent to the recurrence formula [tex]a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}[/tex].

A sequence is a set of elements which observes at least a defined rule. In this question we see a sequence which follows this rule:

[tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex]      (1)

Now we prove that given expression contains the pattern:

n = 0

7

n = 1

7 + (- 1)² · 2² = 7 + 4 = 11

n = 2

7 + (- 1)² · 2² + (- 1)³ · 3² = 11 - 9 = 2

n = 3

7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² = 2 + 16 = 18

n = 4

7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² + (- 1)⁵ · 5² = 18 - 25 = - 7

The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula [tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex], equivalent to the recurrence formula [tex]a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}[/tex].

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Answer:

Anita= 25 years old

Sumbo= 10 years old

Step-by-step explanation:

Start by forming 2 equations that represent the given information.

Let Anu's and Sumbo's ages be A and S respectively.

A= S +15 -----(1)

A² +S²= 725 -----(2)

Now, solve for A and S by substitution.

Substitute (1) into (2):

(S +15)² +S²= 725

Expand:

S² +2(S)(15) +15² +S²= 725

2S² +30S +225= 725

-725 on both sides:

2S² +30S -500= 0

Divide both sides by 2:

S² +15S -250= 0

Factorise:

(S +25)(S -10)= 0

S +25= 0             or            S -10= 0

S= -25 (reject)     or            S= 10

Sumbo's age cannot be a negative value hence -25 is rejected.

Substitute S= 10 into (1):

A= S +15

A= 10 +15

A= 25

Answer:

the answer is B. 140 units²

Answer:

2 erasers cost $1.20

Step-by-step explanation:

Nigel bought 10 pencils and 5 erasers for $8.

We can write this algebraically:

10p + 5e = 8

We know that the price of 2 pencils is $1. That is $0.50/Pencil.

So, p = $0.50. Now we can plug that into out equation and find the price of one eraser:

10(0.50) + 5e = 8

5 + 5e = 8

5e = 3

e = $0.60

Now, we have the price of one eraser, $0.60, and we can multiply this by 2 to find the price of 2 erasers, which equates to $1.20.

The proportion of sides of the triangle which is not true are 13.5/21 = 9/14, 9/13.5 = 6/21 and 14/6 = 21/9

The three sides of each of the rectangles should be proportional to each other

Triangle A : Triangle B

9 cm : 13.5 cm

= 9/13.5

14 cm : 21 cm

= 14 cm / 21 cm

6 cm : 9 cm

= 6 cm / 9 cm

Therefore, the proportion of sides of the triangle which is not true are 13.5/21 = 9/14, 9/13.5 = 6/21 and 14/6 = 21/9

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Answer: [tex]\left(\frac{1}{2}, 1 \right), (1, 2)[/tex]

Step-by-step explanation:

We have [tex]y=2x^{2}[/tex] and [tex]y=3x-1[/tex].

Since both of the equations are set equal to y, we can conclude that:

[tex]2x^2 = 3x-1\\\\2x^{2}-3x+1=0\\\\(2x-1)(x-1)=0\\\\x=\frac{1}{2}, 1[/tex]

If [tex]x=\frac{1}{2}[/tex], then [tex]y=3\left(\frac{1}{2} \right)-1=1[/tex]

If [tex]x=1[/tex], then [tex]y=3-1=2[/tex]

Therefore, the solutions are [tex]\left(\frac{1}{2}, 1 \right), (1, 2)[/tex]

Answer:

[tex] \frac{?}{?} [/tex]

Answer:

3x^2 + 3xz

Step-by-step explanation:

Under the assumption that I need to distribute,

(x + z)(x + 2x)

(x + 2x) is (3x)

3x(x + z) becomes 3x*x and 3x*z

3x*x = 3x^2

3x*z = 3xz

combine, 3x^2 + 3xz

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The number of the meals possible is 350.

The complete question is given below:-

A menu has 5 choices of appetizers, ten main courses, and seven desserts. How many meals are possible?

The arrangement of the different things or numbers in a number of ways is called the combination.

Given that:-

The number of the combination of the meals will be calculated as:-

N = 5 x 10 x 7

N = 350

Therefore the number of the meals possible is 350.

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There are 210 different three-digit whole numbers that can be formed with the digits 2, 3, 4, 5, 6, 7, 8 if the digits cannot be repeated.

To calculate how many different three-digit whole numbers can be formed with the digits 2, 3, 4, 5, 6, 7, 8 if the digits cannot be repeated, we need to use the permutation formula.

The number of permutations of n objects taken r at a time, where order matters and objects cannot be repeated, is given by:

P(n,r) = n! / (n-r)!

In this case, we have 7 digits to choose from, and we want to form a three-digit number, so r = 3. Therefore, the number of different three-digit whole numbers that can be formed is:

P(7,3) = 7! / (7-3)! = 7! / 4! = 7 x 6 x 5 = 210

Each of these numbers will be unique, as we are not allowed to repeat any of the digits.

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Answer:

-7 is -7 units away from zero. Its opposite is 7 from zero.

Step-by-step explanation: Count from 0 how many digits away it is

Answer: 180 degrees

Step-by-step explanation:

The measure of the arc of a semicircle is 180 degrees.

Answer:

C   34  cm

Step-by-step explanation:

Area = L x W

  72  = 8 x W     then W = 9

Perimeter = 2 ( L+W) = 2 ( 8+ 9) = 34  cm

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{Area of rectangle: A = wl; whereas \boxed{\textsf a} is \underline{area}, \boxed{\textsf w} is \underline{width}, \& \boxed{\textsf{l}} is}\\\large\text{\underline{length}.}[/tex]

[tex]\large\text{a = wl}\\\\\large\text{wl = a}\\\\\large\text{w(8) = 72}\\\\\large\text{8w = 72}\\\\\large\textsf{DIVIDE 8 to BOTH SIDES}\\\\\rm{\dfrac{8w}{8} = \dfrac{72}{8}}\\\\\large\text{SIMPLIFY IT!}\\\\\rm{w = \dfrac{72}{8}}\\\\\rm{w = 9}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{width = \bf 9}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

[tex]x = \frac{25}{13} [/tex]

Step-by-step explanation:

Given:

[tex] \frac{2}{5} x - \frac{1}{2} = \frac{1}{3} + \frac{5}{6} x[/tex]

Combine like terms:

[tex] \frac{2}{5} x - \frac{5}{6} x = \frac{1}{3} + \frac{1}{2} [/tex]

Find GCF :

[tex] \frac{12}{30} x - \frac{25}{30} = \frac{2}{6} + \frac{3}{6} [/tex]

Subtraction and Addition :

[tex] \frac{13}{30} x = \frac{5}{6} [/tex]

Divide both sides by 13/30 :

[tex] \frac{ \frac{13}{30} }{ \frac{13}{30} } x = \frac{ \frac{5}{6} }{ \frac{13}{30} } [/tex]

Simplify :

Multiplication (Reciprocal) :

[tex]x = \frac{5}{6} \times \frac{30}{13} [/tex]

[tex]x = \frac{150}{78} [/tex]

[tex]x = \frac{25}{13} [/tex]

Answer :

[tex]x = \frac{25}{13} [/tex]

Hope it helps

(a) [tex]\{x: x > -4 \}[/tex]

(b) [tex](-4, \infty)[/tex]

Answer:

20

Step-by-step explanation:

492/99x100=21.43

nearest tenth percentage is 20

The expression written in equivalent form with a common denominator is -1/6

Fractions are written as ratio of two integers. For instance a/b is a fraction.

Given the sum of the fractions shown;

-3/4 and 5/8

Sum = -3/4 + 5/8

Sum = 5/8 - 3/4

Sum = 5-6/8

Sum  = -1/8

Hence the sum of the given fraction -1/3 and 5/8 is -1/6

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Answer:

1188

Step-by-step explanation:

√121 (3^2)(2(6)) = 1188

Answer:

264

Step-by-step explanation:

√(121m^2 n^6)   =   11 m n^3

  sub in the values given for m and n

                       11 (3)(2^3) = 11 * 3 * 8 = 264

Answer:

48 cm²

Explanation:

Let the breadth be b, then the length is 3b

P = 2(Length + Breadth)

32 = 2(3b + b)

32 = 2(4b)

8b = 32

b = 4

Breadth is 4 cm

Length: 3b = 3(4) = 12 cm

Area of rectangle:

Length × Breadth

12 × 4

48 cm²

Given :-

To Find :-

Solution :-

Using formula;

Where;

We have;

By putting all values in formula we get;

→ 2(3x + x) = 32

→ 2(4x) = 32

→ 2 × 4x = 32

→ 8x = 32

→ x = 32/8

After dividing 32 with 8, we get;

→ x = 4

Hence;

Now, using formula;

Where;

We have;

By putting all values in formula we get;

→ Area of rectangle = 12 × 4

By multiplying 12 with 4, we get;

→ Area of rectangle = 48 cm²

Answer:

eyyyyyyyyyy wassupppppppp

Answer:

240%

Step-by-step explanation:

Volume of a prism is Bh (area of the base * height)

Let's start with the small prism.

B=125

h=12

Volume = 125*12 = 1500 cubic cm

Bigger prism base are is 160% of 125. 1.6 * 125 = 200

Height is 6 cm more = 12+6 = 18

V = 200 * 18 = 3600

To find the percentage, divide 3600 by 1500. You get 2.4, which is 240%