This is a popular type of problem that appeared in mathematics textbooks in the 1970s and 1980s. can you find the answer? the sum of the digits of a two-digit number is 6. if the digits are reversed, the difference between the new number and the original number is 18. find the original number.

Answers

Answer 1
A digit is a number in one of the places, so for example the number 54 has two digits; a tens place digit (5) and a ones place digit (4).

Say the mystery number is a two digit number = xy
* that's not x times y but two side by side digits.

Info given:
the sum of the digits of a two-digit number is 6
x + y = 6
if the digits are reversed, yx the difference between the new number and the original number is 18.

**To obtain the number from digits you must multiply by the place and add the digits up. (Example: 54 = 10(5) + 1(4))

Original number = 10x + y
Reversed/New number = 10y + x

Difference:
10y + x - (10x + y) = 18
9y - 9x = 18
9(y - x) = 18
y - x = 18/9
y - x = 2

Now we have two equations in two variables
y - x = 2
x + y = 6

Re-write one in terms of one variable for substitution.
y = 2 + x
sub in to the other equation to combine them.
x + (2 + x) = 6
2x + 2 = 6
2x = 6 - 2
2x = 4
x = 2

That's the tens digit for the original number. Plug this value into either of the equations to obtain y, the ones digit.

2 + y = 6
y = 4

number "xy" = 24


Related Questions

how many twelfths are in 3?

Answers

3/ (1/12) = 3(12)=36

there are 36 twelfths in 3

Answer:

36 twelfths.

Step-by-step explanation:

We are asked to find number of twelfths are in 3.

We can write 3 as a fraction as:

[tex]\frac{3}{1}[/tex]

To convert our given number to twelfths, we will multiply numerator and denominator of our fraction by 12 as:

[tex]\frac{3}{1}\times \frac{12}{12}[/tex]

[tex]\frac{3\times 12}{1\times12}[/tex]

[tex]\frac{36}{12}[/tex]

Therefore, there are 36 twelfths in 3.

Given quadrilateral XYWZ determine whether WX and YZ are parallel, perpendicular, or niether. W(0,-3), X(-1,5), Y(2,5), Z(-1,2)

Answers

The slope of both sides is needed in order to determine whether they are parallel, perpendicular or neither.

The slope of a line connecting two points is just the change in y over change in x.

WX
m = (-3 - 5)/(0 - -1)
m = -8/1
m = -8

YZ
m = (5 - 2)/(2- -1)
m = 3/3
m = 1

The sides are neither parallel or perpendicular.

Suppose that in a particular sample, the mean is 70.07 and the standard deviation is 10.27. what is the z score that corresponds to a raw score of 80?

Answers

To find the z score, we need to use the following formula: (raw score - Mean)/ standard deviation. We know that the raw score is 80, the standard deviation is 10.27, and the mean is 70.27, so plugging in those values gives us: (80 - 70.27)/10.27 = 0.9474

The set of possible values of m is {5,7,9}. What is the set of possible values of k if 2k=m+3?

Answers

just plug in the values for m

so the possible values for k are
when m=5
[tex]2k=5+3 \\ k=4[/tex]
when m=7
[tex]2k=7+3 \\ k=5[/tex]
when m=9
[tex]2k=9+3 \\ k=6[/tex]
so the possible values for k are {4,5,6}

Using mental math, the approximate tip to leave for a bill of $81.79, if you tip 15% would be _____..

Answers

About $12.30

($12.27)
81.79 is approximately 80.
10% of 80 is 8
20% of 80 is 16
15% is right in between 10% and 20%, so the tip should be $12 which right in between $8 and $16.

how would a weather reporter say 0.103 meters of snow

Answers

They would say that there is
zero point one-zero-three meters of snow, 
zero point one oh three meters of snow
point one hundred three meters of snow, etc.
I'm not exactly sure what you are looking for, so hopefully one of these works :)

(I personally haven't ever heard a weather reporter say this, as I live in a place without snow. pick the one you think is closest to something they'd say XD)

In a standard normal curve, what percentile corresponds to a z score of 1.0?

Answers

Z score of 1 is .8413

The point (2, -3) lies in quadrant I II III IV

Answers

The point (2, -3) lies in the IV quadrant since its x value is positive, but its y value is negative.

*If possible, please give me brainliest*
It lies in the IV quadrant ....
1st quadrant (+ , +)
2nd ( - , + )
3rd ( - , - )
4th ( + , -)
....
just think u are in the centre and if u go right thats + and if u go up that is also + ... if u go downward and left thats - ....
We go first in x-axis so
For the 1st quadrant to obtain u should go right and up from centre so (+ , + )
And for 4th quadrant u should go right ( 1st x-axis) and then down so (+ and -)

630 meters in 18 seconds write this ratio as a unit rate

Answers

divide 630 by 18

630/18 = 35


so unit rate would be 35 meters per second

write an expression that represents the product the of q and 5 divided by 2

Answers

The expression will be (5q)/2

Dakota runs a half-marathon every 6 weeks, and Madison runs a half-marathon every 15 weeks. If they start now, in how many weeks will they again be running a half marathon at the same time?

Answers

30 weeks. You continue to find the factors of each number and find one that’s the same.

6, 12, 18, 24, 30
15, 30

Both lines have the 30 in common. So it’ll take 30 weeks until they run a half- marathon together

Answer:

30 weeks

Step-by-step explanation:

Given : Dakota runs a half-marathon every 6 weeks,

            Madison runs a half-marathon every 15 weeks

To Find : . If they start now, in how many weeks will they again be running a half marathon at the same time?

Solution :

Since Dakota runs a half-marathon every 6 weeks, Madison runs a half-marathon every 15 weeks

So, to calculate  If they start now, in how many weeks will they again be running a half marathon at the same time

We will take the LCM (lowest common factor) of 6 and 15

3 | 6,15

2 | 2,5

5 | 1,5

  | 1,1

LCM = 3*2*5 =30

The LCM of 6 and 15 is 30

So, If they start now, in 30 weeks they will again be running a half marathon at the same time

y=-3/8x-7 in standard form

Answers

y = -3/8x - 7....add 3/8x from both sides
3/8x + y = -7 ...multiply both sides by 8
3x + 8y = - 56 <==

To convert the slope-intercept form equation y = -3/8x - 7 into standard form, mulitply by 8 to remove the fraction, then rearrange to form 3x + 8y = -56, making sure the 'A' coefficient is positive.

The student's question asks about rewriting the slope-intercept form equation y = -3/8x - 7 into standard form. To do so, we need to rearrange the equation so that all variables and constants are on one side and the equation is set equal to zero. In standard form, the equation should be written as Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Let's convert the given equation to standard form step by step:

Multiply both sides of the equation by 8 to clear the fraction: 8y = -3x - 56.

Move the 'x' term to the left side by adding 3x to both sides: 3x + 8y = -56.The equation now is in standard form; however, typically, we want A to be positive. Since our A is already positive, we are done.
The final standard form of the given equation is 3x + 8y = -56.

A baseball used in major league games weighs at least 5 oz and not more than 5.25 oz.About what is that range measured in grams?Explain your reasoning.

Answers

From 141.748 to 148.835 when you convert them using a conversion chart

The bottom floor of a parking garage has an elevation of -36 feet. The top floor is 124 feet higher. What is the elevation of the top floor

Answers

It should be 88ft because 124-36=88

Convert 95 pints to gallons. Round to one decimal point. Please show your work

Answers

There is 8 pint in 1 gallon, therefore:

95/8 = x gallon

95/8 = 11.875
x = 11.875

There is ~11.875 gallons 

hope this helps
You divide pints by 8 to get gallons

Therefore,

95/8 = 11.875

What's the correct name for the polygon below?

 

       A. Octagon   B. Nonagon   C. Pentagon   D. Heptagon

Answers

Octagon. Cause if you count the sides it is 8 and in math terms octa means eight sided or eight figured.

A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?

Answers

A direct variation has a constant slope, i.e. (y/x)= constant.

Both of the given two points give a slope of (y/x)=14/2=28/4=7, so the equation of the function is
y/x=7, or simply
y=7x

Find the equation, (f(x) = a(x-h)2+ k), for a parabola containing point (-1,0) and having (-3, 4) as a vertex. What is the standard form of the equation?

Answers

Let's begin with  f(x) = a(x-h)^2+ k.  Note that we must use "^" to indicate exponentiation.  Write (x-h)^2, not (x-h)2.

If (-3,4) is the vertex, then the above equation becomes f(x) = a(x-[-3])^2 + 4, or 

f(x) = a(x+3)^2 + 4.  We are told that the graph passes through (-1,0), so must now substitute those coordinates into the above equation:

f(-1) = a([-1]+3)^2 + 4 = 0 (0 is the value of f when x is -1)

Then we have a(2)^2 + 4 =0, or 4a + 4 = 0.  Thus, a = -1.

The equation of this parabola is now f(x) = -(x+3)^2 + 4.

Write it in "standard form:"  f(x) = -(x^2 + 6x + 9) + 4, or 
                                           f(x)  = -x^2 - 6x - 9 + 4, or
       answer =>                   f(x) = -x^2 - 6x - 5 = ax^2 + bx + c

Thus, a=-1, b=-6 and c= -5.

Answer:

D.The vertex form is f(x) = −(x +3)^2 + 4. The standard form is f(x) = −x2−6x−5.  

Step-by-step explanation:

usatestprep

Compare and Contrast: Below are two equations. Solve each equation and compare the two solutions. Choose the statement that is true about each solution. (3 points)

Equation #1
|2x - 3| = -17

Equation #2
|5x + 3| = 12

a-Equation #1 and Equation #2 have the same number of solutions.
b-Equation #1 has more solutions than equation #2.
c-Equation #1 has fewer solutions than equation #2.
d-None of the statements above describe the number of solutions to equations shown.

Answers

Equation #1:
|2x - 3| = 17
The first solution is
2x - 3 = 17
2x = 17 + 3 = 20
x = 10
The second solution is
3 - 2x = 17
-2x = 17 - 3 = 14
x = -7
The solutions are x = 10 or x = -7.

Equation #2:
|5x + 3| = 12
The only solution is
5x + 3 = 12
5x = 12 - 3 = 9
x = 9/5

Let us examine the given answers.
a. Equation #1 and #2 have the same number of solutions.
    FALSE
b. Equation @1 has more solutions than Equation #2.
    TRUE
c. Equation #1 has fewer solutions than equation #2.
    FALSE
d. None of the statements a,b, or c apply.
    FALSE

Answer: b.

Listed below are four different cases in which a comparison of means was conducted. match the case to the appropriate set of equations needed to compare the means.

Answers

Impossible to answer without diagram, please repost with diagram so we can help.
Final answer:

The cases can be categorized by comparing the means as follows: 'B. Two proportions' apply to situations like income bracket and voter likelihood comparison, 'C. Matched pairs, dependent groups' apply to dependent groups like a math test given to third graders, 'D. exclusive groups' represent separate unaffected and experimental groups, and 'A. Two independent means, normal distribution' refers to situations where two separate groups are compared.

Explanation:

From the details given, we can classify the cases by comparing the means as follows:

B. Two proportions: This would apply to the question of politicians comparing the proportion of individuals from different income brackets who might vote for them. It implies two independent groups and hence a comparison of two population proportions. C. Matched pairs, dependent groups: This could describe a scenario like a math exam given to the third-grade children attending ABC school. Two random samples of scores were taken. This represents a dependent groups design in which two means are compared, for instance before and after a treatment. D. exclusive groups: These likely represent two independent means involving separate unaffected (control) groups and experimental groups. An example of this is studies that compare various diet and exercise programs. A. Two independent means, normal distribution: This refers to a situation where two separate groups are compared, such as studies involving independent samples where the sample values selected from one population are not related in any way to the sample values selected from the other population.

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A fair die will be rolled 11 times. what is the probability that 1, 2, or 3 is rolled exactly 4 times? round your answer to four decimal places.

Answers

1/11. Because you divide and then bring to simpilist form

The probability of a 1, 2, or 3 is 3/6 = 1/2. There are C(11,4) = 11!/(4!(11-4)!) = 330 ways the desired outcome can show up in the 11 rolls. The probability is

... 330×(1/2)⁴(1/2)⁷ = 330/2048 ≈ 0.1611

if x -6 is one factor of x^2 - 10x +24, which is the other factor?

Answers

To get the other factor of the expression x² - 10x + 24, we can use long or synthetic division. We are given that the other factor is x - 6, so we can use that as our divisor. Our setup should look something like this:
x² - 10x + 24 ÷ x - 6
Here is the work using polynomial long division:
          x     -4             
x - 6 | x² - 10x + 24
          x² - 6x
          0  - 4x + 24
               -4x - 24
                          0
We can see that our quotient is x - 4, which would be the other factor of x - 6 to get x² - 10x + 24. The answer to your query is x - 4. Hope this helps and have a phenomenal day!

Question 26(multiple choice worth 1 points) (02.02) simplify . −4 4

Answers

cant help you sorry bro this is sad because I usually can help but sorry

Solve the equation.

-3(y - 5) = 24

y = ______?

Answers

[tex]-3(y-5)=24\\\\\frac{-3(y-5)}{-3}=\frac{24}{-3}\\\\(y-5)=-8\\\\y-5+5=-8+5\\\\\\y=-3[/tex]

The value of Equation is y = -3.

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have Equation,

-3(y-5) = 24

Now, solving for y

Divide both side by (-3) we get

-3(y-5) / (-30= 24/ (-3)

y-5 = -8

Add 5 to both side

y- 5 +5 = -8 + 5

y = -3

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Find the critical numbers of the function. (Enter your answers as a comma-separated list.)
f(θ) = 8sec θ + 4tan θ,    0 < θ < 2π

Answers

Critical numbers of the functionF(o) = 8 sec θ + 4 tan θ, 0 < θ <2 π.F(o) = 0 for critical numbersF(o) = 8 sec θ tan θ + 4 sec^2 θ = 0        = 4 sec θ [2 tan θ + 4 sec θ] = 0Sec θ = 0 or 2 tan θ + sec θ = 0Sec θ = 0 is no solution.2 tan θ + sec θ = 0 => (2 sin θ / cos θ) + (1 / cos θ) = 0  (2 sin θ + 1 / cos θ) = 0 => 2 sin θ + 1 = 0 Sin θ = -1/2 Θ = 7π/6 , 11π/6  Therefore, critical number are 7π/6 , 11π/6
Final answer:

The critical numbers of the function f(θ) = 8sec(θ) + 4tan(θ) are where the derivative is undefined, specifically at θ = π/2 and θ = 3π/2.

Explanation:

To find the critical numbers of the function f(θ) = 8sec(θ) + 4tan(θ), we need to take its derivative and set it equal to zero or find where the derivative does not exist. First, we compute the derivative of the function. Recall that the derivative of sec(θ) is sec(θ)tan(θ) and the derivative of tan(θ) is sec2(θ).

Thus, the derivative f'(θ) is 8sec(θ)tan(θ) + 4sec2(θ). We look for where this derivative is undefined or equal to zero. The derivative is undefined when sec(θ) is undefined, which occurs at θ = π/2 and θ = 3π/2. To find where the derivative is zero, we can factor out 4sec(θ):

4sec(θ)(2tan(θ) + sec(θ)) = 0

The second factor will never be zero because sec(θ) and tan(θ) will not be zero for the same θ in the interval given. Therefore, the critical numbers are where the derivative is undefined, which is θ = π/2 and θ = 3π/2.

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In a group of 48 children there are twice as many boys as girls how many girls are they

Answers

Let x =  the number of boys.
Let y =  the number of girls.

There are 48 children, therefore
x + y = 48           (1)

There are twice as many boys as girls, therefore
x = 2y                 (2)

Substitute (2) into (1).
2y + y = 48
3y = 48
y = 48/3 = 16
x = 2y = 2*16 = 32

x=32, y = 16

Answer: 16 girls

How many integers between 14 and 3,452 can be divided by 42 with a remainder of zero?

Answers

      _______
42 I 3,452

82 with a remainder

There are 82 integers between 14 and 2452 that can be divided with a remainder of 0

Which equation correctly applies the distributive property?

A. ​ 2.4⋅(−3.4)⋅(−1.25)=−3.4⋅2.4⋅(−1.25) ​
B.​ −3⋅(6.48)=(−3⋅6)+(−3⋅0.4)+(−3⋅0.08) ​
​C. −2.5⋅(4⋅3.67)=(−2.5⋅4)⋅3.67 ​
D.​ (42⋅3.5)+(42⋅1.3)+(42⋅5.2)=42+(3.5+1.3+5.2)

Answers

distributive property
B.​ −3⋅(6.48)=(−3⋅6)+(−3⋅0.4)+(−3⋅0.08) ​

Answer:

B

Step-by-step explanation:

Find the slope of the line containing the points (3,8) (1,8)

Answers

hi 

slope of a line accordind to two point form is given by

tan∅=y₂-y₁/x₂-x₁

∴ tan∅=8-8/1-3

⇒ tan∅ = 0

∴∅=0°

hence the line lies in the x axis.
The answer is zero. 8-8=0. 3-1=2. 2/0 equals 0

The tax rate is 8.5% what is the tax on $95? Rounded to the nearest hundredth.

Answers

0.085 x 95 = 8.08

answer
sales tax is $8.08 

The tax on $95 will be equal to $8.08 at the rate of 8.5%.

What is the percentage?

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the tax rate is 8.5% the tax on $95 will be calculated as,

Sales tax = 8.5% of 95

Sales tax = 0.085 x 95

Sales tax = $8.08

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