The locations of a house, market, and library from a right triangle as shown in the diagram

The next fraction in this sequence 4/5, 13/20, 1/2, 7/20,.... is; 1/5

Arithmetic sequence are sequence that are separated by a common difference.

We are given the sequence as;

4/5, 13/20, 1/2, 7/20,....

The fractions expressed as percentage is given as:

80%, 65%, 50%, 35%...

The general formula for the nth term of the sequence is;

Tₙ = a + (n - 1)d

where;

a is first term

d is common difference

n is position of term

Thus, the fifth term is;

T₅  =  80 + (5 - 1)(-15)

T₅ = 80 + (4)(-15)

T₅ = 80 - 60

T₅ = 20

Expressing 20% as a fraction gives us;

20% = 20/100 = 1/5

Thus the next fraction in the given sequence is 1/5

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Answer: 8 and a half vehicles (if no halves are allowed just 8)

Step-by-step explanation:

We divide 68 vehicles by 8 hours bringing us to 8 and a half vehicles an hour

Answer:

x= 7

Step-by-step explanation:

 3 × 7 =21

[Mathematical Solutions]

1.) [tex]\frac{2}{7} + \frac{1}{4} = \frac{15}{28}[/tex]

2.) [tex]\frac{5}{9} +\frac{3}{8} = \frac{67}{72}[/tex]

3.) [tex]3\frac{5}{6} - 2\frac{7}{15} =\frac{41}{30}[/tex] as the Exact Form, or [tex]1\frac{11}{30}[/tex] as the Mixed Number Form.

Hope this helps!

The substitution property of equality is the property used in 7+(4+6)=7+n

The substitution property of equality refers to when a value is replaced in an equation with another value that are same or equal to the first. say AA is being used in an equation and another value say BB, replaces  AA in the equation. In this case we say that AA is being substituted for BB in the equation

The equation here can be compared to see that n and ( 4 + 6 ) are the pairs that are substituted so we can say that the property used here is the substitution property of equality

Given data

7+(4+6)=7+n

n = ( 4 + 6 )

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The inverse of the function f( x ) = 5x³ + 1 is y = ∛ [ ( x - 1) / 5 ].

A statement, rule, or regulation that establishes the relationship between an independent variable and a dependent variable is known as a function.

A function that can reverse into another function is known as an inverse function or anti-function.

Consider the function,

f(x) = 5 x³ + 1

Now, let y = 5 x³ + 1

Now, swapping the variables x, y we get;

x = 5 y³ + 1

Subtracting 1 from each side of the equation,

5 y³ + 1 - 1 = x - 1

5 y³ = x - 1

Dividing both sides by 5,

5 y³ / 5 = ( x - 1) / 5

y³ = ( x - 1) / 5

Now, take cube root on both sides of the equation,

∛ (y³) = ∛ [ ( x - 1) / 5 ]

y = ∛ [ ( x - 1) / 5 ]

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Answer:

y=-42 or f(x)=-42

Step-by-step explanation:

1. Substitute x for -6. Equation: f(x)=6(-6) + -6

2. Turn f(x) into y. Equation: y=6(-6) + -6

3. Multiply 6 and -6. Equation: y=-36 + -6

4. Add -36 and -6. Equation: y=-42 or f(x)=-42

It should be noted that rewriting the equation y=3(x-5)² +1 in another form is y = 3x² - 30x + 76.

It should be noted that the information is that we should rewrite the equation y=3(x-5)² +1 in another form.

This will be illustrated as:

y = 3(x-5)² + 1.

It should be noted that (x - 5)² will be:

= (x - 5)(x - 5)

= x² - 5x - 5x + 25

= x² - 10x + 25

y = 3(x-5)² + 1.

y = 3(x² - 10x + 25) + 1

y = 3x² - 30x + 75 + 1

y = 3x² - 30x + 76

In conclusion, it should be noted that rewriting the equation y=3(x-5)² +1 in another form is y = 3x² - 30x + 76.

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Answer:

ecdqwef

Step-by-step explanation:

Answer:

Step-by-step explanation:

2.10$

your answer is 2.10$

The given information about the graphs of the given relationship are two points that are not intercepts.

Intercepts of a function are the points on the x-axis or y-axis where the graph of an curve or function intersects the axes.

X intercepts are the points where the graph crosses the x-axis or where y=0

Y intercepts are the points where the graph crosses the y- axis or where

x= 0

Given that Apolline is mowing lawns and her fee for a 5 hour job is $42 and her fee for a 3 hour job is $28.

Let y represents Apolline fee in dollars for a single job that took z hours for her to complete and it is given that when z = 5 hour  then y =$42 and when z= 3 hour then y= $28

Therefore these are two point (y, z) = (42,5 ) and (28, 3 ) where none of the coordinates are zero which means that none of them is intercept.

Thus, the given information about the graph of the relationship are two points (42,5 ),  (28, 3 ) which are not intercepts.

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Answer:

trust me a shoe box or a board game box or a small container

log ( 3x + 1 ) = 2 => x = 33, by properties of logarithm.

Given: log (3x + 1) = 2

Raising both the sides by 10, in order to remove the logarithm:

=> [tex]10^{log_{10}(3x+1)} = 10^{2}[/tex]

=> 3x + 1 = 100 (as [tex]a^{log_a(x)} = x[/tex])

=> 3x = 99

=> x = 33

Hence, log ( 3x + 1 ) = 2 => x = 33, by properties of logarithm.

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We get that when the expression ∛ 54 x³ - ∛ 16 x³ is simplified using subtraction, we get the result as ∛ 2 x.

We are given the expression:

∛ 54 x³ - ∛ 16 x³

We need to subtract to simplify the expression.

First, we know that:

54 = 2 × 3 × 3 × 3

16 = 2 × 2 × 2 × 2

So,

∛ 54 x³ = 3 ∛2 x

∛ 16 x³ = 2 ∛2 x

So, we get the expression as:

3 ∛ 2 x - 2 ∛ 2 x

Combining the like terms, we get that:

= ∛ 2 x

Therefore, we get that when the expression ∛ 54 x³ - ∛ 16 x³ is simplified using subtraction, we get the result as ∛ 2 x.

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Answer:

a. zero point zero zero 5

b. eleven point zero three seven

c. four hundred and three point six zero eight.

I really hope this helps you!!! Have a great day :).

Answer: 1st and 3rd

Step-by-step explanation:

Answer:

A) True, B) False, C) True, D) False.

Step-by-step explanation:

A) True. Every graph on a plane is the set of solutions to the equation that defines it.

B) False. Refer to the answer for question A.

C) To know whether this is true, we should substitute [tex]x = 1[/tex] to the function's equation. If we get that [tex]y = 2[/tex], then (1, 2) lies on the graph as its a solution of the equation.

[tex]y = -2(1) + 4 \to -2 + 4 \to 2[/tex]

y = 2, therefore, (1, 2) lies on the graph. True.

D) Same here as C. Now, we should substitute [tex]x = 0[/tex] instead.

[tex]y = -2(0) + 4 \to 0 + 4 \to 4[/tex]

y = 4, therefore, (0, 2) does not lie on the graph. False.

The probability that at least one of them is defective if three units are picked at random is 0.8560.

We would define Ai as the event that the i th chosen unit is not defective, for I = 1, 2, 3. We are interested in P (A1 ∩ A2 ∩ A3). Note that

P(A1) = 95/100  

Given that the first chosen item was good, the second item will be chosen from 94 good units and 5 defective units, thus

P (A2 ∣ A1) = 94/99

Given that the first and second chosen items were okay, the third item will be chosen from 93 good units and 5 defective units, thus

P (A3∣ A2, A1) = 93/98

Thus, we have

P(A1∩ A2 ∩ A3) =  P(A1) P(A2∣ A1) P(A3∣ A2, A1)

=95/100*94/99*93/98

=0.8560

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I think B.9 is correct

1*3*5=15

1+3+5=9

Answer: 5x

Step-by-step explanation:

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (9 - 2x)⁵ is expanded as 59049 − 65610x + 29160x² − 6480x³ + 720x⁴ − 32x⁵.

The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.

The total number of terms in the expansion of (x+y)ⁿ are (n+1).

The sum of exponents of x and y is always n.

nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ

The binomial coefficients which are equidistant from the beginning and from the ending are equal.

i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.

Let the function be (9 - 2x)⁵

By using binomial expansion theorem, we get

(9 - 2x)⁵ = 59049 − 65610x + 29160x² − 6480x³ + 720x⁴ − 32x⁵.

(9 - 2x)⁵ is expanded as 59049 − 65610x + 29160x² − 6480x³ + 720x⁴ − 32x⁵.

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Let's solve the problem,

→ [(2 + 2) - (6 - 2)] ÷ 2

→ (4 - 4) ÷ 2

→ 0 ÷ 2 = 0

Thus, the answer is 0.

Solving for B in the equation gives B = 5( h - m) / r

A subject of formula can be defined as a variable that is expressed in terms of other variables in an equation or expression.

It is also known as the variable that is being worked out in an equation or given expression.

From the information given, we have the equation;

h = m + 1/5rB

To make 'B' the subject of formula, we have to take the following crucial steps;

Take 'm' over the equality sign

h - m = rB/ 5

Now, cross multiply

5( h - m) = rB

To make 'B' stand alone, divide both sides by r

B = 5( h - m) / r

Thus, solving for B in the equation gives B = 5( h - m) / r

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The decimal number 0.142857 is a rational .

A rational number is defined as a number which can be written in the form p/q such that p and q are co-prime.

The decimal number given is 0.142857 . This number can be written in the form of a fraction of 142857/1000000 .

Now the prime factorization of 142857 gives 3³ x 11 x 13 x 37 and the Prime factorization of 1000000 is given by 2⁶ × 5⁶

So we can see that there are no common factors between the two numbers. Hence they are co-prime.

∴ 0.142857 is a rational number as it can be written in the form p/q.

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From the given situation involving two parallel lines cut by transversal, we have that:

1) The value of x is of x = 20º.

2) Jenna is correct, because 3x and 120º are alternate interior angles.

We have to consider two things, as follows:

Thus:

5x + 35 + m<6 = 180º

5x + 80 = 180

5x = 100

x = 100/5

x = 20º.

The value of x is of x = 20º.

To solve item 2, we have to consider that 3x and 120º are alternate interior angles, hence they are congruent, and:

3x = 120º

x = 120/3

x = 40º.

Hence:

Jenna is correct, because 3x and 120º are alternate interior angles.

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Answer:

your answer would be b ( 6 )

Step-by-step explanation:

Answer:

B) 6

Step-by-step explanation:

[tex]{ \tt{ {(k - 2)x}^{2} - 6x + 12 = 0}} \\ \\ { \tt{ {x}^{2} - \: ( \frac{6}{k - 2})x \: + \: \frac{12}{k - 2} = 0 }}[/tex]

Product of roots: 12/(k-2)

[tex]{ \tt{ \frac{12}{k - 2} = 3 }} \\ \\ { \tt{3(k - 2) = 12}} \\ \\ { \tt{ \frac{3(k - 2)}{3} = \frac{12}{3} }} \\ \\ { \tt{k - 2 = 4}} \\ \\ { \tt{k = 6}}[/tex]

The variable terms in all four expression indicates that the item was on 25% off.

The expressions with more terms indicate a different sale price than the expressions with fewer terms.

The constant term in each expression indicates the original price of the item Mrs. Brady purchased.

The constant term in each expression indicates that the sale price is not dependent on the original price of the item.

The constant term in each expression indicates the amount deducted when the gift card was applied to the purchase.

The variable terms in all four expressions indicate that the item was on sale of 25 percent off.

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