find three consecutive integers such that the sum of the first and twice the second is 98 minus three times the third

Answers

Answer 1

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let the numbers be : x, x + 1 and x + 2 ~

now, according to given condition :

[tex]\qquad \sf  \dashrightarrow \: x + 2(x + 1) = 98 - 3(x + 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: x + 2x + 2 = 98 - 3x - 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: x + 2x + 3x = 98 - 6 - 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: 6x = 90[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 90 \div 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 15[/tex]

So, tge required numbers are : 15, 16 and 17


Related Questions

Which is a solution of 2x+6>12? x>0 x>3 x>−1 x>5

Answers

Answer:

x>3

Step-by-step explanation:

2x+6-6 > 12-6    ditch the 6

2x/2 > 6/2          divide by 2

x>3

Simplify the radical √54​

Answers

Answer: 3√6

Step-by-step explanation:

√54​=

√(9*6)=3√6

Michael drove from point A to point B at 15 miles
per hour and immediately returned by the same
route at 30 miles per hour. What was his average
speed, in miles per hour, for the entire trip?
E. 20
F. 22.5
G. 24
H.25

Answers

Answer:

E

Step-by-step explanation:

Say the distance is 'd'

time for going  =  d/15

time for returning  = d/30

average speed =  total distance / ( total time)

                           =  2d / ( d/15 + d/30 )  

                                 solve for average speed  = 20 mi/hr

I wish I can help you out to this work

(Scientific Notation LC)

WILL MARK BRAINLEIST ONLY IF CORECCT!
!Rewrite 2,290,000 in scientific notation.

2.29 x 10−6
2.29 x 10−4
2.29 x 104
2.29 x 106

Answers

2,290,000 in scientific notation is 2.29 x 10⁶.

What is scientific notation?

Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form in the United Kingdom. This base ten notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations.

Converting a number in these cases means to either convert the number into scientific notation form, convert it back into decimal form or to change the exponent part of the equation.

Now the given number is,

2,290,000

To convert 2,290,000 into scientific notation, 2,290,000 must be converted into into decimal and multiples of 10.

So, factorizing 2,290,000 we get,

2,290,000 = 229 x 10,000

Now converting 10,000 into multiples of 10

Since, 10,000 = 10 x 10 x 10 x 10

So, 2,290,000 can be written as,

2,290,000 = 229 x 10 x 10 x 10 x 10

Multiplying and divide 229 by 100 we get,

2,290,000 = (229 x 100 x 10 x 10 x 10 x 10) / 100

Rearranging we get,

2,290,000 = (229 x 100) / 100 x (10 x 10 x 10 x 10)

Since, (229 x 100) / 100 = 2.29 x 100

2,290,000 = (2.29 x 100) x (10 x 10 x 10 x 10)

And 100 = 10 x 10

Therefore we get,

2,290,000 = 2.29 x 10 x 10 x 10 x 10 x 10 x 10

Since 10 x 10 x 10 x 10 x 10 x 10 = 10⁶

Therefore we get,

⇒ 2,290,000 = 2.29 x 10⁶

this is the required scientific notation of 2,290,000 .

Thus, 2,290,000 in scientific notation is 2.29 x 10⁶.

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the quotient of 10 and a number in math terms

Answers

The answer
N= number
The quotient means you would take 10 and divide it by n.

Answer—> 10/n

A traffic cone with a height of 20 in. is ideal for traffic control. Find the lateral area of a cone with a height of 20 in. and a diameter of 12 in. Round the answer to the nearest whole number.​ (Hint: The height given is not the slant​ height.)

Answers

The lateral area of the cone is 394 square inches

How to determine the value

The formula for lateral area of a cone is expressed as;

Lateral area = πr √h² + r²

Given that;

height = 20 inDiameter = 12 in, radius = 12/ 2 = 6 in

Substitute the values into the formula

Lateral area = 3. 142(6) √20² + 6²

Lateral area = 18. 85 √436

Lateral area = 18. 85 × 20. 8

Lateral area = 394 square inches

Thus, the lateral area of the cone is 394 square inches

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Helpppp meeeee!!!! Ayudaaamee

Answers












It’s q 7 becaues if you add x and 6 it’s be 7 and q is the main one

Hello! I need help with #2 and #3 please!

Answers

The banker should invest $ 30,000 at 6 % interest rate to earn an interest of 3800 per year from both the investments.

Principal 1 = $ 50,000

Rate 1 = 4 %

Let principal 2 be x

Rate = 6 %

Time = 1 year

Interest = 3800

Using simple interest, we get that:

SI = p × r × t

3800 = ( 50,000 × 0.04 × 1) + ( x × 0.06 × 1)

3800 = 2000 + 0.06 x

0.06 x = 3800 - 2000

0.06 x = 1800

6 x = 180000

x = 180000 / 6

x = 30,000

Therefore, we get that, the banker should invest $ 30,000 at 6 % interest rate to earn an interest of 3800 per year from both the investments.

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true or false???????

Answers

Answer:

False

Step-by-step explanation:

3 x 1/3

3/1 x 1/3 = 1

Answer:false

Step-by-step explanation: i did the test

Express 55 mph in kilometers per hour. Round to the nearest hundredth.

Answers

Answer:
55mph -> 88.51 kilometers per hour.

Explanation:
Multiply the speed value by 1.609. 88.514 rounded up to the nearest hundredth is 88.51 kilometers per hour.

The perimeter of the figure below is 110 cm. Find the length of the missing side.

Answers

Answer:

  6.1 cm

Step-by-step explanation:

You want to know the remaining side of the irregular figure such that the perimeter is 110 cm.

Perimeter

The perimeter of a plane figure is the sum of the lengths of the sides. Working clockwise from the upper left corner, we have ...

  34.6 +8.6 +17.3 +11.6 +? +11.6 +11.6 +8.6 = 110

  103.9 +? = 110 . . . . collect terms

  ? = 6.1 . . . . . . . . . subtract 103.9

The length of the missing side is 6.1 cm.

__

Additional comment

If the angles that appear to be right angles actually were right angles, the perimeter would be 109.6 cm. The perimeter is longer than this, so at least three of the angles are not right angles.

2 m - 54 cm equals????????

Answers

Answer:

146 centimeters or 1.46 meters.

Step-by-step explanation:

1m = 100cm

2m = 200cm

200 - 54 =146

Hope this helps!

What is your average speed in miles per hour and in feet per second if you travel a mile in 21 ​minutes?

Answers

Answers:  

2.857142 mph

4.190476 ft per second

Both values are approximate

=======================================================

Work Shown:

21 min = 21/60 = 0.35 hrs which is exact

distance = rate*time

rate = distance/time

rate = (1 mile)/(0.35 hrs)

rate = (1/0.35) mph

rate = 2.857142 mph which is approximate

------------------

21 min = 21*60 = 1260 seconds

1 mile = 5280 ft

rate = distance/time

rate = (5280 ft)/(1260 seconds)

rate = (5280/1260) ft per second

rate = 4.190476 ft per second approximately

Answer: 2.857 miles/hr

4.19 ft/sec

Step-by-step explanation:

60 min=1 hr.

1 mi/21 min*60 min=

60 min*1 mi/21 min=2.857 miles/hr

60 sec=1 min

60*60 sec=1 hr

1 hr=3600 sec

2.857 miles/hr=

2.857/3600 miles/sec=0.00079 miles/sec

1 mile=5280 ft

0.00079 miles/sec=

0.00079*5280 ft/sec=4.19 ft/sec


Find the greatest common factor of the expressions.
12y1329, -16y6z9

Answers

Answer:

2 and 3 and y

Step-by-step explanation:

2x2x4x y x 1x2x3x3x3

-2x7x y x 2x3x z x3x3

XZ is the perpendicular bisector of segment WY. Solve for k. Enter a NUMBER only.

Answers

Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 4.

What is the numerical value of K?

A bisector divides an angle or segment into two equal halves.

Given the data in the question;

XZ is the perpendicular bisector of segment WYSegment WX = 6k + 8Segment XY = 11k - 12Value of k = ?

Since XZ is a  perpendicular bisector of segment WY,

Segment WX is equal to Segment XY

Segment WX = Segment XY

Plug in the given values and solve for k.

6k + 8 = 11k - 12

Collect like terms

6k - 11k = -12 - 8

-5k = -20

Divide both sides by the coefficient of k

-5k/-5 = -20/-5

k = 4

Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 4.

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A group of people were asked if they had run a red light in the last year. The number of people that
responded yes is 397 and no is 159. Find the probability that if a person is chosen at random, he/she has
run a red light in the last year. Round to two decimal places.
Question Help:

Answers

If a person is chosen at random, there is a 71% probability that he or she has run a red light in the last year.

What do we mean by probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

So, to find the probability:

P = number of favorable terms/number of total termsFavorable terms = 397Total number of terms = 397 + 159 = 556

Apply values in the formula:

P = 397/556P = 0.714028On rounding off, P = 71%.

Therefore, if a person is chosen at random, there is a 71% probability that he or she has run a red light in the last year.

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I have 6 quarts of paint. How many shelves can be painted if each one takes one third of a quart.

Answers

6 divided by 1/3 =
6 multiplied by 3 =
28 shelves

How do you express without exponents [tex](3a^3)^2[/tex]

Answers

__________________________________________________________

Hello! In this question, we were given an expression and would have to express it without the use of exponents.

__________________________________________________________

Explanation:

In the question, we were given:

(3a³)²

In order to express the expression without the exponents, we would have to first simplify it and then expand the expression.

__________________________________________________________

Solve:

[tex](3a^3)^2[/tex]

Simplify by "squaring" the variable inside the parenthesis, in which in this case we would multiply the "2" to the "3".

[tex]3a^6[/tex]

Now in this step, we would have to expand the expression in a different form to get rid of the exponent.

To get rid of the exponent, we would expand the " [tex]a^6[/tex] " term.

Note that the term [tex]a^6[/tex] is the same thing as a · a · a · a · a · a, it is just the expanded version of the exponent.

This means that our expressed expression without exponents, including our constant "3" would be:

3 · a · a · a · a · a · a

__________________________________________________________

Answer:

3 · a · a · a · a · a · a

__________________________________________________________

Additional Info:

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__________________________________________________________

In the following triangle, what is the value of n?

Answers

Given that the triangle is a right triangle, the value of sin (n) is √5/5.

Hence, option D)√5/5 is the correct answer.

What is the value of sin(n) in the triangle?

Trigonometry is simply a branch in mathematics that looks into the relationships between angles and side lengths of a triangle.

Given the data in the question;

Hypotenuse = 2√5Opposite of angle n = 2Adjacent of angle n = 4

To determine the value of sine n, we will use one of six functions of an angle commonly used in trigonometry.

Sine of angle n = Opposite of angle n / Hypotenuse

sin(n) = Opposite / Hypotenuse

Plug in the given values and simplify

sin(n) = Opposite / Hypotenuse

sin (n) = 2 / 2√5

Next, rationalize the denominator.

Cancel out the common factor 2.

sin (n) = 2 / 2√5

sin (n) = 1 /√5

Multiply both the numerator and the denominator by √5.

sin (n)  = (1×√5) / (√5 × √5)

sin (n)  = √5/5

Given that the triangle is a right triangle, the value of sin (n) is √5/5.

Hence, option D)√5/5 is the correct answer.

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How would this graph look please help

Answers

The inequality graph of the system of inequalities is graph (a)

What are inequality expressions?

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

How to determine how the inequality graph would look like?

The system of inequalities is given as

-2x + 3y < 9

x^2 - y <= 10

4x + y > 3

In the above system of inequalities, there are two linear inequalities and a parabola inequality

The inequality symbols in the linear inequalities are opposite

This means that the region between both lines would be shaded

Also, for the parabola; the upper part would be shaded.

This is so because when y is made the subject of the formula, the symbol  becomes >=

Using the above as a guide, the inequality graph of the system of inequalities is graph (a)

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How can u do the 5th problem

Answers

Answer:

3/4 of 5. It equals 3 3/4.

Step-by-step explanation:

The question asks for 3/4 of 5 cups of milk.

Find the quotient. Do not round your answer 58.543/10,000

Answers

Answer:

0.0058543

Step-by-step explanation:

58.543/10,000 = 58.543 divide 10,000

1-7: MathXL for School: Practice & Problem Solving
Challenge You buy 3.18 pounds of apples, 1.45 pounds of peaches, and 1.71 pounds of pears. What is your total bill?
Grocery Store Prices
Item
Apples
Peaches
Pears
Cost
$0.99 per pound
$1.09 per pound
$1.19 per pound
Your total bill is:
(Round to the nearest cent as needed.)

Answers

The total bill for 3.18 pounds of apples, 1.45 pounds of peaches, and 1.71 pounds of pears is $6.78  .

In the given question

The price of 1 pound apple = $0.99

The price of 1 pound Peaches = $1.09

The price of 1 pound Pears = $1.19

Total pounds of apples bought = 3.18 pounds

price of 3.18 pounds of apple = ( pounds of apple bought)*(price of 1 pound apple)

=3.18*0.99

=$3.15    ...(i)

Total pounds of Peaches bought = 1.45 pounds

price of 1.45 pounds of peaches = 1.45*1.09

                                                 = $1.59    ...(ii)

Total pounds of Pears bought = 1.71 pounds

price of 1.71 pounds of pears = 1.71*1.19

                                                = $2.04     ...(iii)

Total bill = price of 3.18 pounds of apple + price of 1.45 pounds of peaches + price of 1.71 pounds of pears.

Substituting the values from equation (i),(ii)and (iii) we get ,

Total bill = $3.15 + $1.59 + $2.04  

= $6.78

Therefore , the total bill for 3.18 pounds of apples, 1.45 pounds of peaches, and 1.71 pounds of pears is $6.78  .

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Absolute value of 4 is

Answers

Answer: -4

Step-by-step explanation:

it is -4 because we are looking for like the opposite so the opposite of 4 is -4

Answer:

Absolute value of |4| = 4

Step-by-step explanation:

The absolute value of a number is always positive

Question
The following data set represents the dollar amounts of donations collected at the entrance to a free museum during one hour.

Donation Amount ($) Frequency
1 1
5 5
10 3
15 1
600 1


Is the median a reasonably good measure of central tendency for this data set? What if the outlier were removed from consideration?

Select the correct answer below:


The median is a good measure regardless of whether the outlier is included.

The median is a very poor measure regardless of whether the outlier is included.

The median is a good measure when the outlier is included, but it would be a very poor measure if the outlier were removed from consideration.

The median is a very poor measure when the outlier is included, but it would be a good measure if the outlier were removed from consideration.

Answers

In the given situation (A) the median is a good measure regardless of whether the outlier is included.

What do we mean by media?The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution in statistics and probability theory. It is sometimes referred to as "the middle" value in a data set. The basic difference between the median and the mean in describing data is that the median is not skewed by a small proportion of extremely large or small values, and thus provides a better representation of a "typical" value.

To find the median:

1, 5, 5, 5, 5, 5, 10, 10, 10, 15, 600The number of terms is 11, so the middle number will be the 5th term from both ends.The 5th term is 5.So, regardless of whether the outlier is included, the median is a good measure in the given situation.

Therefore, in the given situation (A) the median is a good measure regardless of whether the outlier is included.

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The correct question is given below:

The following dataset represents the dollar amounts of donations collected at the entrance to a free museum for one hour.

(Refer to the table given below)

Is the median a reasonably good measure of central tendency for this dataset? What if the outlier were removed from consideration?

Select the correct answer below:

(A) The median is a good measure regardless of whether the outlier is included.

(B) The median is a very poor measure regardless of whether the outlier is included.

(C) The median is a good measure when the outlier is included, but it would be a very poor measure if the outlier were removed from consideration.

(D) The median is a very poor measure when the outlier is included, but it would be a good measure if the outlier were removed from consideration.

P₁ 1:23:55 AM
Jatch help video
an is preheating his oven before using it to bake. Fabian wants to predict the final
perature after a minutes. He wrote the equation y 50x+78, where y
resents the final temperature in degrees Fahrenheit. What could the number 50 in
bian's equation represent?
-

Answers

Number 50 in the Jack's equation represents the rate of change in the oven's temperature over time (per minute) or with respect to time by using the slope form concept.

As per the question statement, Jack is preheating his oven before using it to bake. He wants to predict the final temperature after [tex]x[/tex] minutes.

He wrote the equation [tex]y =50x+78[/tex] , where [tex]y[/tex]  represents the final temperature in [tex]fahrenheit[/tex]. We are supposed to tell the significance of number 50 in the given equation.

As we know that the equation which is in the form of [tex]y=mx+c[/tex], or the slop form equation, m is called the slope or the rate of change of value of [tex]y[/tex] with respect to value of [tex]x[/tex].

And the given equation [tex]y =50x+78[/tex] is also of the form of [tex]y=mx+c[/tex] hence we conclude that 50 is the slope or the  rate of change of value of [tex]y[/tex] with respect to value of [tex]x[/tex].

As y is the temperature in Fahrenheit therefore x is the time hence "50 Degrees Fahrenheit change of temperature per unit minute" is the significance of 50.

Slop Form Equation: [tex]y=mx+c[/tex] where m is the slope and c is called as the intercept of the line

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Steve and Jenna go door-to-door selling chocolate bars. Steve sells 23 chocolate
bars and Jenna sells 12 chocolate bars. Together they collect $210. How should
they divide the money so that each person gets a fair share?

Answers

Answer:

Steve: $138.00

Jenna: $72.00

Step-by-step explanation:

Steve:

[tex]\frac{23}{35}[/tex] x 210 = 138

Jenna:

[tex]\frac{12}{35}[/tex] x 210 = 72

I'm not really sure what this means, but i'll do what i think is right!

Answer:

Steve: $138

Jenna: $72

Step-by-step explanation:

If you're doing it so they each get what they sold, you would have to first add the total number of chocolate bars, giving you 35. To see how much each bar costs, you just have to divide $210 ÷ 35, giving you $6 per chocolate bar.

To give each what they gained, you multiply $6 by whichever amount you chose, 23 or 12, which will give you that person's amount. Steve will get $138 and Jenna will get $72.

hope this helps!

The graph below defines a function f (x). Find f (2).
3
N
7
s
4
m
14
-2 +
771 ?
1
2345

Answers

N is the answer pls pls help pls pls please pls help me to get some more points

Solve
31320= x + (.08x)

Answers

Answer:

Step-by-step explanation:

31320=x+0.08x

31320=1.08x

swap the sides

1.08x=31320

Divide by 1.08

x=29000

Are these fractions equivalent or
nonequivalent?

Answers

The two fractions are equivalent.

When two fractions have the same value, they are said to be equivalent, meaning that even though the numbers in the two fractions are different, their overall value is the same.

Fractions that are not equal to one another are referred to as nonequivalent fractions. The same cross multiplication procedure must be used to determine whether two fractions are comparable or not.

Consider these two fractions,

x = ( m / 4n ) and y = ( 2m / 8n )

Now when the fraction x is multiplying and dividing by 2.

We get,

x = ( m / 4n ) × ( 2 / 2 )

x = 2m / 8n

Therefore, x = y

Hence, the fractions are equivalent.

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