David travelled 4/5 of his trip by bicycle and the rest of the distance by foot. if the whole trip was 160 km, how many kilometers did he travel by foot?

Answer:

Either -8b - 24 or b = 3

Step-by-step explanation:

Answer: - 8b - 24

Distributive property

Answer: Aiza have left from her lifeguarding job = $ 700

Step-by-step explanation:

Given that,

Aiza made $55 a day lifeguarding in the summer.

She worked six days a week for five weeks.

For two weeks of the summer she went on vacation.

She spent approximately $68 a day each for two weeks.

Aiza earning per day = $55

Aiza worked for six days in a week.

Aiza worked for five weeks.

Total earning for weeks

                          = $ 55(6)

                          = $ 330 / week

Total earning for 5 weeks

                           = $ 330(5)

                           = $ 1650

Aiza spent per day for vacation = $ 68

Aiza was an vacation for two weeks.

Total expenditure for two weeks,

Number of days in each week = 7 days

                                                   = 2(7)($ 68)

                                                   = $ 952

Aiza have left with = Total earning - Total expenditure

                               = $ 1650 - $ 952

                               = $ 700

Therefore, Aiza have left from her lifeguarding job = $ 700

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The formula 3x-y=5 is a linear function.

We must first examine the slope of the original function in order to determine the equation of parallel lines. We are also given the other function's intercept in this issue.

The function's slope-intercept form is y=3x-5.

In order to locate the parallel line that corresponds to the point (0,-7)

Parallel lines are those that share the same slope but have different y-intercepts, as you may have seen.

As a result, we must put in the point to solve for the y-intercept.

Thus,

y = 3x + b

-7 = 3(0) + b

-7 = b

b = -7

Thus the equation of a parallel line is y = 3x - 7

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The sum of the three numbers 7531, 5252 and 6375 is 19158

The numbers are given as

7531, 5252, 6375

Express the numbers as a summation expression

So, we have

Sum = 7531 + 5252 + 6375

Evaluate the sum

So, we have

Sum = 19158

Hence, the sum of the three numbers 7531, 5252 and 6375 is 19158

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The solution of given system of equations is 6 and 7.

To solve the system of equations using elimination, we will equate any one variable. In this case, we will be equating variable y.

Rewriting the equations -

-6x - 6y = −42 : equation 1

-x + 2y = 8 : equation 2

Multiplying equation 2 with 3

-3x + 6y = 24 : equation 3

Adding equation 1 and equation 3 to solve the given system of equations

-6x - 6y = −42

3x + 6y = 24

We get the answer :

-3x = -18

Negative sign will be cancelled and performing division

x = 6

Keep the value of x in equation 2

-6 + 2y = 8

2y = 8 + 6

2y = 14

y = 14 ÷ 2

y = 7

Therefore, the value of x and y is 6 and 7 in given system of equations.

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The unit rate is $26.98

Unit rate can be described as the price of a single item. From the question, we are required to find the unit rate of 1 penguin

The unit rate can be calculated as follows

7 penguins = 188.88

1 Penguin= x

Cross multiply both sides

7x= 188.88

x= 188.88/7

x= 26.98

Hence the unit rate is $26.98

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We have proved below that d( k+1) is only true when d(k) is true , also d(1) should also be true using Mathematical Induction.

Mathematical Induction : For each and every natural number n, mathematical induction is a method of demonstrating a statement, theorem, or formula that is presumed to be true.

It is given that the statement is true for n = k

Explanation:

According to the principle of Mathematical Induction,

Let d(n) be a statement involving Natural Number n such that

d(1) is true

d(m) is true

d(m+1) is true

So ,  the statement d(n) is true for all the n natural numbers.

According to the second principle of Mathematical Induction

Let d(n) be a statement involving Natural number n such that

d(1) is true

d(m) is true when d(n) is true for all n where 1 ≤ n ≤m .

Then the statement d(n) is true for all the values of n ( natural number)

Therefore , we have proved below that d( k+1) is only true when d(k) is true , also d(1) should also be true using Mathematical Induction.

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The values of "x" and "y" in the given matrix equation is 5 and 3 respectively.

A matrix equation is an equation in which a matrix acts as a variable.

The given system of equation;

x + 2y = 11

x + 4y = 17

[1    2 ] =  [11]

[1   4  ]  =  [17]

determinate of the equation, Δ

Δ = [1    2 ]

      [1   4  ]  

Δ = (4 x 1) - (2 x 1) = 2

Δx =  [11    2 ]

        [17   4  ]  

Δx  = (4 x 11) - (17 x 2) = 10

Δy =  [1    11 ]

        [1   17  ]  

Δy = (17 x 1) - (11 x 1) = 6

x = Δx/Δ

x = 10/2 = 5

y = Δy/Δ

y = 6/2 = 3

Thus, the values of "x" and "y" in the given matrix equation is 5 and 3 respectively.

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The marginal distribution of males is 13 %

A two-way frequency table shows the frequencies (or "counts") of two categorical variables.

For example, the following two-way table displays the results of a study in which 100 participants were asked which sport they preferred: baseball, basketball, or football.

The rows represent the respondent's gender, while the columns show which sport they chose:

There are two variables in this example: Sports and Gender.

A marginal distribution is simply the sum of the distributions of these separate variables. The marginal distributions in a two-way table are shown in the table margins: Marginal distributions are valuable because, while we frequently collect data for two variables (such as Sports and Gender), we may have particular questions regarding only one variable.

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Answer: Be careful. There is a slight difference in the order of the questions

Answer:

the answer is the 20⁰ ok that

The algebraic expression become 3n-16<8.

According to the statement

We have to find that the numerical expression.

So, For this purpose, we know that the

Algebraic expression is an expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.

From the given information:

the difference between three times a number and 16 is at least 8

Then

From 1st statement it become 3n -16

And with other statement and combining

Then  the equation become

3n-16<8

Now solve the expression for the value of the n

then it becomes

3n<24

n<8.

The value becomes is 8.

So, The algebraic expression become 3n-16<8.

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Answer: D

Step-by-step explanation:

:)

[tex]4\frac{6}{12}[/tex] hours play speed, what is the total running time of the video.

What does "speed" mean in mathematics?

Running time of cassettes

at standard speed = 1 hr

at standard speed = 4 hr

at standard speed = 4 hr

given the 1/4 part of tape is recorded at standard speed, 1/3 at long-play speed , 5/12 at super long-play speed,

so the running time of standard speed = 1/4 * 1 = 1/4

at long play speed

1/3 * 4 = 4/3 hours

and at super long-play speed,

5/12 * 7 = 35/12 hours

so, the total running time of the video

1/4 + 4/3 + 35/12 = 54/12 = [tex]4\frac{6}{12}[/tex] hours

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Answer:

1.5 meters per second

Step-by-step explanation:

90 meters divided by 60 seconds is 1.5

His final payment will be $271.66464 at the end of the third year.

The term "compound interest" refers to interest that is added back to the principal amount during each compounding period.

Compound interest is calculated using the formula

A = P(1+r )ⁿ,  where

P = principal balance,

r = interest rate,

n =  number of periods.

Given that a man borrows $760 at 4% and of the first year he pays back $270.

Amount owned by him at the end of the first year after repaying $270 =  (1+4%)760 - 270

= 1.04×760 - 270

= $520.4

Amount owned by him at the end of the second year after repaying $280 =  (1+4%)520.4 - 280

= 1.04×520.4 - 280

= 541.216 - 280

= $261.216

Let his final payment be x.

So, the amount owned by him at the end of the third year will be 0.

⇒ (1+4%)261.216 - x = 0

⇒ 1.04×261.216 - x = 0

⇒ 271.66464 = x

Therefore, his final payment will be $271.66464.

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Answer:

subtract 6

Step-by-step explanation:

note there is a common difference between consecutive terms, that is

45 - 51 = - 6

39 - 45 = - 6

33 - 39 = - 6

27 - 33 = - 6

21 - 27 = - 6

the rule being used to make the pattern is subtract 6

this is an arithmetic sequence for which an nth term rule can be found

Answer:

subtract 6

Step-by-step explanation:

the pattern is made by subtracting 6 from the previous number

Answer:

Cube = 8 vertices

Pyramid=5 vertices

Step-by-step explanation:

Cube = 8 vertices

Pyramid=5 vertices

The equation of the line for the  point (-1, 2) is [tex]y=x+3[/tex]

It is given that line is parallel to the line y = x + 4 .    ....(2)

On comparing equation (2) with the slope intercept form which is  y = mx +c , we get  m = 1 . For parallel lines slope is same .

It is given that line passes through the point (-1, 2).

Putting [tex]y_1=2,\ x_1=-1[/tex] and m = 1 in equation (1) , we get

     [tex]y-2=1(x-(-1))\\y-2=x+1\\y=x+3[/tex]

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2y+x/3=-6  is a linear equation.

An equation is written to equate two or more unknown variables and formulating a relation between them.

Equations are of various types such as:

The given equation is 2y+x/3=-6.

Here the power of both the variables is 1. Hence it can be classified as a linear equation in two variables.

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Answer:

a) 10n -6

b) -5n +105

c) 7f + 1

d) -11n +48

Step-by-step explanation:

for an example let's take a) 4, 14, 24, 34

term value:

14 - 4 = 10 (coefficient)

term number:

4 = 34

4×10=40

34 - 40 = -6

coefficient and constant

therefore v = 10n -6

lol are you a Bhutanese?

the expression that models the situation of the total cost of a diner, less a $10 coupon divided by 4 is (x - $10)÷4

Here we have the total cost of a dinner, less a $10 coupon, divided by 4 people.

If the total cost is x, then the total cost less a $10 coupon is:

x - $10.

Now, taking the quotient (dividing the above amount by 4) we will get:

(x - $10)÷4

This is the expression that models the situation of the total cost of a dinner, less a $10 coupon divided by 4.

So the correct option is the first one.

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a) The line segment PQ has a length of √85 (approx. 9.219).

b) The coordinates of the midpoint of the line segment PQ is (4, 0.5).

Herein we find a line segment whose endpoints are known: P(x, y) = (3, 5), Q(x, y) = (5, - 4), and we are asked to determine the length of the line segment and the coordinates of the midpoint as well. a) First, we determine the vector between the points P and Q by sum of vectors:

PQ = Q(x, y) - P(x, y)

PQ = (5, - 4) - (3, 5)

PQ = (2, - 9)

And its magnitude is determined by using the Pythagorean theorem:

PQ = √[2² + (- 9)²]

PQ = √85

b) The coordinates of the midpoint is found by using the following formula:

M(x, y) = 0.5 · P(x, y) + 0.5 · Q(x, y)

M(x, y) = 0.5 · (3, 5) + 0.5 · (5, - 4)

M(x, y) = (1.5, 2.5) + (2.5, - 2)

M(x, y) = (4, 0.5)

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There is No Extraneous solution to the equation

The equation is

[tex]\sqrt{3x - 2}[/tex] - [tex]\sqrt{2x - 7}[/tex] = 0

We need to find the value of x,

[tex]\sqrt{3x + 2}[/tex] = [tex]\sqrt{2x + 7}[/tex]

Squaring both sides of the equation

[tex](\sqrt{3x + 2} )^{2}[/tex] = [tex](\sqrt{2x + 7} )^{2}[/tex]

3x + 2 = 2x + 7

x = 5

Now we need to put the value of x in the equation to know whether it is an extraneous solution or not.

[tex]\sqrt{(3 * 5 ) + 2}[/tex] - [tex]\sqrt{(2 * 5 ) + 7}[/tex] = 0

[tex]\sqrt{17}[/tex] - [tex]\sqrt{17}[/tex] = 0

0 = 0

Therefore we get to know that the equation has no extraneous solution.

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Answer:

Rise/Run

or

[tex]\frac{rise}{run}[/tex]

Step-by-step explanation:

The formula for slope is referred to rise over run,

Because the fraction consists of the rise (the change in y, going up or down) divided by the run (the change in x, going from left to the right).

A rise over run equation would be formatted like this:

Rise/Run

or

[tex]\frac{rise}{run}[/tex]

(i used to struggle with slopes, and i understand how much of a pain they are)

Answer: h=1

Step-by-step explanation:

multiple 5h and -4 by 7

35h-28-1=14-8h

35h-29=14-8h

add 29 to both sides

35h=43-8h

43h=43

i think this is right...

The given equation is,

→ 7(5h - 4) - 1 = 14 - 8h

Now the required value of h will be,

→ 7(5h - 4) - 1 = 14 - 8h

→ 35h - 28 - 1 = 14 - 8h

→ 35h - 29 = 14 - 8h

→ 35h + 8h = 14 + 29

→ 43h = 43

→ h = 43/43

→ [ h = 1 ]

Hence, the value of h is 1.