Giovanni was playing with blocks and started with one blue triangular block and kept adding more
blocks to create the following pattern sequence:


See picture


How many blocks would he need on the 12th step of the pattern?
O 34
O 36
O 33
O 37

Answer:

A. true

Step-by-step explanation:

"f(x) = ... " is the classic way of writing a function.

The solution to x^2 - 4x = 5 is x = -1 or 5

The equation is given as:

x^2 - 4x = 5

Take the coefficient of x

k = -4

Divide by 2

k/2 = -2

Square both sides

(k/2)^2 = 4

Add this value to the sides of the equation

x^2 - 4x + 4= 5 + 4

Express as a difference of two squares

(x - 2)^2 = 9

Take the square root of both sides

x - 2 = ±3

Add 2 to both sides

x = 2 ± 3

Evaluate

x = -1 or 5

Hence, the solution to x^2 - 4x = 5 is x = -1 or 5

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Step-by-step explanation:

I hope this helps!!!!!

Answer:

X=60°

Step-by-step explanation:

Because the sum of angle of all side of a triangle is 180°

and

if that goes on

the equation become

x°+75°+45°=180°

x°+120°=180°

x°=180°-120°

x°=60° hence prove

Using it's formula, it is found that the mean of the discrete random variable is given by:

B. 30.47.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

Hence, considering the table, the mean of the discrete distribution is:

E(X) = 23 x 0.16 + 25 x 0.09 + 26 x 0.18 + 31 x 0.12 + 34 x 0.24 + 38 x 0.21 = 30.47.

Hence option B is correct.

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Answer:

51 pounds, 48 pounds, 44 pounds and 40 pounds in that chronological order.

The other root is 1 and the value of the coefficient q is 12.

A quadratic equation is a second-order polynomial equation in a single variable x. ax²+bx+c=0. with a ≠ 0 .

Given:

x²-13x+q=0

when x= 12

So, 12²-13*12+q=0

144-156+q=0

-12+q=0

q=12

Now, x²-13x+12=0

x²-12x-x+12=0

x(x-12) - 1(x-12)=0

(x-1)(x-12)=0

x=1, 12

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Answer: 2556

Step-by-step explanation:

Let the amount of the deposit be x dollars

The amount of simple interest earned can be represented by the formula PRT/100

Where,

P is the amount of deposit

R is the annual rate of interest

T is the time in years

Therefore,

P=x

R=6

T=150/360 = 15/36 = 5/12

So,

Simple interest = x(6)(5)/1200

63.90 = 30x/1200

63.90= x/40

x= 63.90×40

x=2556

Therefore, amount deposited = 2556

The probability that Hope performs any of the activities each day of the week can be expressed in the tree diagram.

A tree diagram is a term for a graphical tool that shows the possible outcomes of an experiment. To build a tree diagram, start by putting a branch for each of the possibilities.

The tree diagram of Hope's activities must include all the days of the week and on each day there must be three branches for each of the possible activities that she is going to do (play tennis, swim or play soccer).

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Answer:

Exact form: -3/2

Decimal Form: -1.5

Step-by-step explanation:

Hello there!

We need to find out the slope of the given two coordinates/points, that are:

Solution:

We'll need to use the formulae that is used to find out the slope,that is:

[tex] \pink{\star}\boxed{\rm \: Slope = \cfrac{y_2 -y_1}{x_2 - x_1}} \pink{\star}[/tex]

According to this question,here:

So substitute them accordingly:

[tex] \rm \: m = \cfrac{ - 6 -( 6)}{8 - 0} [/tex]

Simplify using PEMDAS rule.

[tex] \rm \: m = \cfrac{ - 12}{8} [/tex]

-12/8 could be canceled.

[tex] \rm \: m = \cfrac{ - 6}{4} [/tex]

-6/4 could also be canceled.

[tex] \boxed{ \rm \: m = \cfrac{ - 3}{2} \: or \: - \cfrac{3}{2} }[/tex]

Or it could be represented as decimal:

[tex] \boxed{ \rm \: m = - 1.5}[/tex]

Hence , the slope m will be -3/2 or -1.5

[tex] \rule{225pt}{2pt}[/tex]

Answer: [tex]a+b+\sqrt{a^{2}+b^{2}}[/tex]

Step-by-step explanation:

The distance from (0,b) to (0,0) is b.

The distance from (0,a) to (0,0) is a.

Using the Pythagorean theorem, the distance from (0,b) to (a,0) is [tex]\sqrt{a^{2}+b^{2}}[/tex]

So, the perimeter is [tex]\boxed{a+b+\sqrt{a^{2}+b^{2}}}[/tex]

Answer:

Step-by-step explanation:

(1) The sum of the interior angles of a polygon is [tex]180(n-2)[/tex] degrees, where n is the number of sides. In this case, n=5, so the sum is 180(5-2)=540 degrees, meaning the first statement is false.

(2) Since the angles add to 540 degrees, dividing this amongst the five equal angles, we get that each angle measures 108 degrees, so this statement is true.

(3) By definition, all angles of a regular polygon are congruent.

(4) A hexagon has 6 sides, but this polygon has only 5 sides, so this statement is false.

(5) This is true. (See statement (1)).

Answer:

Options B, C, E

Step-by-step explanation:

(f+g)(x)  

= f(x) + g(x)

= 4x^2 +5x -3 + 4x^3 -3x^2 +5

= 4x^3+x^2+5x+2

Answer:

33 blocks

Step-by-step explanation:

Given the length , breath and height for small block  6cm, 4cm, and 2cm an d for large 2m = 200cm, 4cm and 2cm.

volume is given by  

             V = Length x breath x height

Volume of small block = 6 x 4 x 2 = 48 cm^3

Volume of big block = 200 x 4 x 2 = 1600 cm^

No of blocks = Volume of big block/ volume of small block

                     = 1600/48

                     = 33.33

Therefore no of blocks formed = 33

Since 7y is common to both factors, hence the GCF of the expression is 7y. The factored form will be 7y(3x + 2)

The greatest common factor is the value that will divide an expression without leaving a remainder.

Given the expression 21xy + 14y

Find the factors

21xy = 7 * 3 * x * y

14y = 7 * 2* y

Since 7y is common to both factors, hence the GCF of the expression is 7y. The factored form will be 7y(3x + 2)

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Answer:

He multiplied the denominators incorrectly

Step-by-step explanation:

we know that

The volume of a rectangular prism is given by the formula

V=LWH

we have

L=3/4 ft

W=5/1 ft

H=1/2

substitute

V=(3/4)(5/1)(1/2)= 3x5x1=    15

                           ₋₋₋₋₋₋₋₋    ₋₋₋₋ ft³

                           4x1x2=    8

therefore

He multiplied the denominators incorrectly

Answer: $5.99 is the answer hope this helps!

Answer:

81

Step-by-step explanation:

for example log2 8=3 is the same as 2^3=8, so if you switch around the variables from your question, your able to do 3^4, which is 81

Using the figure given, The one equation that matches with the diagram is 3x=30-6.  The diagram that matches the equation circled is given in the image attached.

From the above, we can see that the equation that matches with the diagram are:

Note that for 3(x+6)=30

3x +  18 = 30

3x = 30-18

3x = 12

x = 12/3

x = 4

Then fixing x into the equation =

3(x+6)=30

3(4+6)=30

Therefore , 12 + 18 will give us 30 and the answer is straight forward. The same applies for 30=3x+6 and 6+3x=30 as the answer is straight forward.

But the one equation that does not matches with the diagram is 3x=30-6 because its output is not straight forward.

3x =30-6

3x = 24

x = 24/3

x = 8

Fixing 8 into the equation

3x = 30-6

3(8) = 24

=24 is the  answer and not 30

Therefore, Using the figure given, The one equation that matches with the diagram is 3x=30-6.

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Answer:

it’s C, 5.2

hope i helped

ur wlcm :)

correct me if im wrong

By finding the minimum of the given function, we conclude that the lowest average temperature that year is 57°F.

We know that the average temperature is given by the equation:

f(x)=31cos(0.0055πx)+88

And it is in Fahrenheit degrees.

To get the lowest average temperature, we just need to find the minimum of the above function.

Remember that the minimum of the cosine function is:

cos(x) = -1

Then the lowest value of the above function is:

f(x₀) = 31*(-1) + 88 = 57

From this, we conclude that the lowest average temperature that year is 57°F, so the correct option is A.

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Answer:

2

Step-by-step explanation:

4 halves=2

1 half=0.5

2 halves=1

3 halves=1.5

4 halves=2

Answer:

b

Step-by-step explanation:

because it is 4 dolls and x is the amount of dollars 1 doll is and 4x dolls are less then 102, the only answer that makes sense is b

The answer is B. I will choose to explain by process of elimination. It is not A because it is not less than or equal to, it is just less than. Therefore, we can also eliminate C. It is not D because it is four dolls that cost the same so it is 4x instead of 4+x. I hope I helped!

Answer:

4/7=12/21

18/20=9/10

6/5=30/25

81/90=9/10

Step-by-step explanation:

12 / 21  will be equal to 4/7 and is denoted in the simplest form.

A fraction that possesses the same value as another fraction regardless of how it's denominators and numeric components could be different is said to be equivalent.

12 / 21 can be simplified with the help of 3. This will result in 4/7.

18/20 can be simplified with the help of 2. This will result in a 9/10.

30/25 can be simplified with the help of 5. This will result in 6/5.

81/90 can be simplified with the help of 9. This will result in a 9/10.

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Answer:

135

Step-by-step explanation:

3b + B = 180

4b = 180. ÷4

b = 45

a = 135