One tossed coin landing heads and the next landing tails

Answer:

x = - 2

Step-by-step explanation:

f(x) + g(x) = x² - 2x + 6x + 4 = x² + 4x + 4, hence

x² + 4x + 4 = 0 ← This is a perfect square in the form

(x + a)² = x² + 2ax + a²

Hence 2a = 4 ⇒ a = 2, thus

(x + 2)² = 0

x+ 2 = 0 ⇒ x = - 2 ( 2 equal roots )

Value of x = - 2

Answer:

x = - 2

Step-by-step explanation:

mn - mk + xk - xn

mn - xn - mk + xk

n(m - x) - k(m - x)

(n - k) (m - x)

//Hope it helps.

Answer: (n-k)(m-x)

Step-by-step explanation:

mn - mk + xk - xn

mn - xn - mk + xk

n(m - x) - k(m - x)

(n - k) (m - x)

Answer:

See below.

Step-by-step explanation:

I will assume that 3n is the last term.

First let  n = k, then:

Sum ( k terms) =  7k^2 + 3k

Now, the sum of k+1 terms  = 7k^2 + 3k + (k+1) th term

=  7k^2 + 3k + 14(k + 1) - 4

=   7k^2 + 17k + 10

Now 7(k + 1)^2 = 7k^2 +14 k + 7 so

7k^2 + 17k + 10

=  7(k + 1)^2  + 3k  + 3

= 7(k + 1)^2 + 3(k + 1)

Which is the  formula for the Sum of k terms with the k replaced by k + 1.

Therefore we can say if the sum formula is true for k terms then it is also true for (k + 1) terms.

But the formula is true for 1 term because  7(1)^2 + 3(1) = 10 .

So it must also be true for all subsequent( 2,3 etc) terms.

This completes the proof.

Inductive reasoning can include making generalizations based on specific instances, such as predicting that water freezes at 32°F based on past observations. The binomial theorem, a series expansion, is an example that can be proven using mathematical induction.

Understanding Inductive Reasoning

Inductive reasoning is a method of reasoning in which the premises seek to supply strong evidence for the truth of the conclusion.

While the conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument is probable, based upon the evidence given.

This form of reasoning allows us to create generalizations based on observations or patterns we have seen.

For instance, when we see that water freezes at 32° Fahrenheit, and we observe a temperature drop to 30°F at night, we can induce that there will be ice in the morning.

Mathematical Induction

Mathematical induction is a specific type of inductive reasoning that is used for proving that a statement is true for all natural numbers. It is a two-step process where we first prove that a base case is true, typically for n=1.

Then, we show that if the statement is true for an arbitrary positive integer n, this implies that it's also true for n+1.

This creates a domino effect, proving the initial statement for all natural numbers.

The binomial theorem is a classic example of series expansion that can be proven using mathematical induction.

The theorem expands powers of binomials in a form that involves summation of terms, and each term is a product of binomial coefficients and the variables raised to appropriate powers.

Series Expansions and Inductive Inferences

Series expansions in mathematics, such as the binomial theorem, are formulated based on patterns observed in specific instances.

These patterns are then generalized to hold for all numbers within the constraints of the theorem. In contrast, weak inductive inferences are those which cannot firmly establish a conclusion due to insufficient or irrelevant evidence.

Two angles on a straight line will always equal 180 when combined.

180 - 45 = x

X = 135

Answer:

135°

Step-by-step explanation:

These two angles, 45° and x, are "supplementary," which means that they add up to 180°.

Thus, x = 180° - 45° = 135°

Answer:

you have the rounded part already rounded how it should be. for the mad I need a list of numbers. sorry!!

Answer:

it is a for addend

Step-by-step explanation:

Answer:

D) GCD

D) 9(7 + 9)

Step-by-step explanation:

Given in the question an expression

44  + 12

4(11 + 3)

2 |  44, 12

2 | 22 , 6

  |  11 , 3

D) GCF = 2x2 = 4

C) LCM = 2x2x11x 3

        = 132

B) The difference between each number in an arithmetic sequence is called common difference.

A) A number which is added to another is called addend.

63 + 81

3  | 63 , 81

3  | 21 , 27

   |  7 , 9

GCF = 3x3

        =  9

Distributive property = 9(7 , 9)

Answer:

12

Step-by-step explanation:

Answer:

Cars in one hour: 40 cars

Step-by-step explanation:

30 cars ---> 45 min

Xc ----------> 60 min

Xc = [(60min)*(30 cars)]/45 min

Xc = 40

Best regards

Answer:

∠QRS = 114°

Step-by-step explanation:

Note that the external angle ∠QRS is equal to the sum of the 2 opposite interior angles, hence

∠QRS = ∠PQR + ∠QPR = 52° + 62° = 114°

The measure of angle QRS in a triangle depends on the properties of the triangle and measurements of other angles. Without additional information, it's impossible to provide a definitive measure for angle QRS. A triangle's total angles are always 180 degrees.

In order to answer your question about the measure of ∠QRS, we first need information about the other angles in the triangle or the property that defines this triangle. For instance, if we know that this is a right-angle triangle and we have the measure of one of the other angles, we can easily find ∠QRS as a triangle's total angles are always 180 degrees. Alternatively, if this is an equilateral triangle, then all angles measure 60 degrees. Without more specific information, it is impossible to definitively state the measure of ∠QRS.

https://brainly.com/question/32829977

#SPJ2

Answer:

B

Step-by-step explanation:

Angles g and h are supplementary, which means they add up to 180 degrees.

So the equation would go g + h = 180.

Substitute 117 for g to get

117 + h = 180

Subtract 117 from each side.

h = 63.

The answer is B

Don’t trust me on it because I sorta use google

Answer:

Step-by-step explanation:

To figure out the unit rate, divide 5.12 by 128. You should get 0.04, which is the unit rate or cost per ounce. To figure out how much the 96 oz can should be, multiply $0.04 times 96.

Your answer should be $3.84.

Final answer:

To maintain the same unit rate as the 128 ounce container of orange juice that costs $5.12, the supermarket should price the 96 ounce container at $3.84.

Explanation:

The student is asking how to calculate the price for a 96 ounce container of orange juice, given that a 128 ounce container costs $5.12, with the condition that the unit rate remains the same. First, we need to determine the unit rate for the orange juice in the 128 ounce container. To do that, divide the total cost by the number of ounces to find the cost per ounce:

$5.12 \/ 128  ext{ounces} = $0.04  ext{per ounce}

Now that we have the unit rate ($0.04 per ounce), we can calculate the cost for a 96 ounce container by multiplying the unit rate by the number of ounces:

96  ext{ounces} \times $0.04  ext{per ounce} = $3.84

Therefore, the supermarket should sell the 96 ounce container of orange juice for $3.84 to keep the unit rate the same as the 128 ounce container.

Answer:

circumference of any circle to the diameter of that circle.

-3 < 0  Because -3 is less than 0.

Hope this helps ;P

Answer:

-3 > 3

Step-by-step explanation:

If you look at the number line, a negative number is just the positive number upside down. But a negative number is always greater than the positive number for your number line.

Answer:

[tex]W>20[/tex]

Step-by-step explanation:

Let

L-----> the length of a rectangle

W---> the width of a rectangle

we know that

[tex]L=W+9[/tex] -----> equation A

[tex]W>20[/tex] -----> inequality B

The inequality B represent the equation that could be used to find the possible values of the width

The solution for the width of the rectangle  is all real numbers greater than 20 units

Answer:

Go to brainfuse.com

Step-by-step explanation:

This website will give you one on one tutoring for free (they won't see your face!)

Answer: C.  [tex]\dfrac{1}{6}[/tex]

Step-by-step explanation:

Given: A spinner has 6 equal sectors labeled A, B, C, D, E and F on it. The spinner is spun twice.

If it is given that the  spinner shows B on the first spin, then the total outcomes will be{ (B,A), (B,B), (B,C), (B,D), (B,E), (B,F)}=6

The number of favorable outcome = 1

Now, the probability of spinning B and then E, given that the spinner shows B on the first spin=[tex]\dfrac{1}{6}[/tex]

Answer: C. 1/6

Step-by-step explanation:

The answer and work is the attached sheet!

Hope I helped~! :)

Answer:

3w - 4 1/2

Step-by-step explanation:

Expand the brackets.

6*1/2w - 6*3/4

6/2w - 18/4

3w - 18/4

3w - 4 1/2

Answer:

The answers are C, D, and E.

Step-by-step explanation:

10% of 33 is 10%×33

10% = [tex]\frac{10}{100}[/tex] = [tex]\frac{1}{10}[/tex] = 0.1

You can plug in [tex]\frac{10}{100}[/tex], [tex]\frac{1}{10}[/tex], and 0.1 into 10%×33 for 10%.

[tex]\frac{10}{100}[/tex]×33 = E

[tex]\frac{1}{10}[/tex]×33 = C

0.1×33 = D

The answers are C, D, and E.

Answer:

THE FIRST ONE!! HOPE THIS HELPS!

Step-by-step explanation:

Answer:

Step-by-step explanation:

18% of 50 people said they liked strawberry. The word 'of' in math means multiply, so 18%•50 or .18•50. Multiply them together: .18•50=9.00 or just 9. 9 people like strawberry ice cream :)

Answer:

96

Step-by-step explanation:

Total number of people attending the history museum is 200

Surveyed people are 25

Out of the 25, 12 people said yes

Therefore; the fraction which said yes = 12/25

To find the total number of people expected to say yes out of those that attended the history museum;

Fraction of the sampled that said yes × total number of people that attended.

= 12/25 × 200

=  96

Answer:

[tex]z=10[/tex]

Step-by-step explanation:

we have

[tex]\frac{1}{z}=\frac{(4/5)}{8}[/tex]

solve for z

[tex]z(\frac{4}{5})=8[/tex]

[tex]z=8*5/4[/tex]

[tex]z=10[/tex]

Answer:

Area=25 inches

Step-by-step explanation:

Formula for area of triangle is BxH/2 (base times height divided by two.)

So 5x10=50, 50/2=25

just 25in2 I just passed this question

The easiest way to do this is to plot the points. I used the pythagorean theorem for this one, too. Add the side lengths to get the perimeter: 5 + 5 + 5 + 3 + √40 = 24.32455532 units or just 24 units.

Answer:

a=16

Step-by-step explanation:

We want to take the 6 on the left side of the equal sign and do the equation in the reverse.

First since we are adding 2, we want to substract 2 away from 6.

6-2 = 4

Then, since we are dividing by 4, we want to multiply by 4.

4*4 = 16

We can check this to make sure it's correct by replacing a with 16:

16/4 = 4

4+2 = 6

The solution of the expression is,

⇒ a = 16

We have to given that;

Expression is,

⇒ 6 = 2 + a/4

Now, WE can simplify as;

⇒ 6 = 2 + a/4

⇒ 6 - 2 = a/4

⇒ 4 = a/4

⇒ a / 4 = 4

⇒ a = 4 × 4

⇒ a = 16

Thus, The solution of the expression is,

⇒ a = 16

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ6

Answer:

circumference of the circle [tex]=18.8m[/tex]

Step-by-step explanation:

Given radius = r = 3m {From comment section}

We need to find the circumference of the circle to the nearest tenth. Question also says to use 3.14 for pi.

Apply formula of circumference of the circle.

circumference of the circle [tex]=2\pi r[/tex]

circumference of the circle [tex]=2(3.14)(3m)[/tex]

circumference of the circle [tex]=18.84m[/tex]

Rounding that to nearest tenth, we get:

circumference of the circle [tex]=18.8m[/tex]

Answer:

Step-by-step explanation:

If W is the midpoint of VX then VW = WX. Therefore we have the equation:

2x + 5 = 4x - 3          subtract 5 from both sides

2x = 4x - 8       subtract 4x from both sides

-2x = -8        divide both sides by (-2)

x = 4

VX = VW + WX

VX = 2x + 5 + 4x - 3 = (2x + 4x) + (5 - 3) = 6x + 2

Put the value of x = 4 to 6x + 2:

VX = 6(4) + 2 = 24 + 2 = 26

The length of line segment VX, given W is the midpoint and the lengths of VW and WX are represented by 2x+5 and 4x-3 respectively, is 26 units.

In the given problem, W is the midpoint of VX. This indicates that VW is equal to WX. So, we can set up an equation using the given expressions for VW (2x+5) and WX (4x-3).

We have:
2x+5 = 4x-3

By rearranging the terms, we can find the value of x:
2x-4x = -3-5
-2x=-8
x = 4

Substitute x=4 in either VW or WX to find the length of half of VX: 2x+5 = 2*4+5 = 13.

Since W is the midpoint, VW = WX, so VX = VW + WX = 13 + 13 = 26.

https://brainly.com/question/33812804

#SPJ2

Answer:

It could not have gone anywhere. It is impossible to travel negative miles per hour.

However if it was traveling 34 mph for 0.75 miles then it would go 25.5 miles

Answer:

I'm pretty sure a set a decimal fractions is {1/4, 1/2, 3/4}

I think a set of whole numbers is {3, 4, 5.}

A set of integers might be {-2, -1, 0, +1.}

I'm am sure a set of natural numbers is {1, 2, 3.}

The set if rational numbers is {0.1, 0.2, 0.3} I think.

I am not that sure if my answers are right or not so sorry if this is incorrect.

Answer:

1-e

2-b

3-c

4-q

5-d    

Step-by-step explanation:

In this question, we have to match the left hand side to corresponding right hand side. On the right side we are given

a){3,4,5}

b){0,1,2,3}

c){-2,-1,0,1}

d){[tex]\frac{1}{4}[/tex], [tex]\frac{1}{2}[/tex], [tex]\frac{3}{4}[/tex]}

e){0.1, 0.2, 0.3}

1) a set of decimal numbers:

It is clear the the set of decimal numbers is e) {0.1, 0.2, 0.3}

2) a set of whole numbers is b) {0,1,2,3}

3) a set of integers is c)  {-2,-1,0,1}

4)  a set of natural numbers is a) {3,4,5}

5) a set of rational numbers is d) {[tex]\frac{1}{4}[/tex], [tex]\frac{1}{2}[/tex], [tex]\frac{3}{4}[/tex]}