Mathematics High School

The sum of three consecutive even integers is 72. Let x represent the first integer, x + 2 represent the second integer, and x + 4 represent the third integer.

Which equation can be used to find the first integer?



3x + 72 = 2x + 6

2x + 64 = 72

3x = 2x + 6

3x + 6 = 72

Answers

Answer 1
3x+6=72 is the right one

Answer 2

The equation 3 x + 6 = 72 be used to find the first integer.

Option 4 is true.

Here,

The sum of three consecutive even integers is 72.

Let x represent the first integer, x + 2 represent the second integer, and x + 4 represent the third integer.

We have to find equation which can be used to find the first integer.

What is Integers?

An integer is a whole number (not a fractional number) that can be positive, negative, or zero.

Now,

The sum of three consecutive even integers is 72.

So,

x + ( x + 2 ) + ( x+ 4 ) = 72

x + x + 2 + x+ 4 = 72

3x + 6 = 72

Hence, The equation 3 x + 6 = 72 be used to find the first integer.

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Related Questions

Which age group is appropriate to receive the 2-dose hpv9 vaccine series?

Answers

2-Dose hpv9 vaccine can be given to the kids started at the age of 9 to 14. It can be given to the girl or boy 6 months once is perfect. Before 15th birthday the 2 doses good to the kids.
Final answer:

The 2-dose HPV9 vaccine series is appropriate for individuals between the ages of 9 and 14, according to the CDC.

Explanation:

The 2-dose HPV9 vaccine series is appropriate for individuals between the ages of 9 and 14 years old, according to the Centers for Disease Control and Prevention (CDC).

It is recommended to receive the first dose at the age of 11 or 12, and the second dose 6 to 12 months after the first dose.

If the vaccine series is started after the age of 14, three doses are required for full protection.

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Let −→ ab= h2, −3, −1i. if the coordinates of a are (2, −1, 5), what are the coordinates of the point b?

Answers

the answer to that is -2 and -3

The number of roses (r) in a garden increases when the number of weeds (w) decreases. Write the correct equation for this scenario, and solve for the number of roses when there are 5 weeds. Weeds Roses 10 20 20 10

Answers

Hello,

[tex]r= \dfrac{k}{w} \\ \textrm{if w=10 then r=20} ==\ \textgreater \ 20= \dfrac{k}{10} ==\ \textgreater \ k=200\\\\ \textrm{if w=5 then }\\\\ r= \dfrac{200}{5} =\boxed{40}[/tex]

At the city museum, child admission is $5.20 and adult admission is $8.50 . on friday, three times as many adult tickets as child tickets were sold, for a total sales of $1074.50 . how many child tickets were sold that day?

Answers

202 child tickets were sold.

write an equasion in slope-intercept form. What are the slope and y intercept? -2x - 11y = 5

Answers

Slope intercept form : y = mx+b

You are solving for y ...

- 2 x - 11 y = 5
+2x              +2x

- 11 y = 2x + 5   ...... Divide both sides by -11

y = -2/11 x -5/11

EQUATION : y = -2/11 x -5/11

SLOPE = -2/11 

Y INTERCEPT = -5/11

y=-2/11x-5/11 is the required slope intercept form

Slope is -2/11

y intercept is -5/11

The given equation is -2x-11y=5, We need to find the slope intercept equation, slope and y intercept.

What is slope intercept form of a line?

y=mx+c

m is the slope of the line

c is the y intercept of line

The given equation is -2x-11y=5

We need to separate the y variable to find the slope intercept form

-11y=5+2x

To convert the above equation to slope intercept form, we need to divide both sides by -11.

y=-5/11-2/11x

Therefore y=-2/11x-5/11 is the required slope intercept form for -2x - 11y = 5

Slope is -2/11

y intercept is -5/11

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Add.

(6x3+3x2−2)+(x3−5x2−3)
pleaseeeeeee answer in standard form!!!!

Answers

I believe the answer is
7x^3-2x^2-5

Using graphite furnace atomic absorption spectrometry, the mean cadmium (cd2 ) content value in a homogenized sample of 40 zebra mussles was found to be 7.50 ppb cd2 with a standard deviation (s) of 0.52 ppb cd2 (assume that s is a good approximation of σ). calculate the 90% and 95% confidence intervals (ci) for: (a) two analyses and (b) five analyses of this homogenized sample.

Answers

Part A1:

Given that the mean cadmium (cd2 ) content value in a homogenized sample of 40 zebra mussles was found to be 7.50 ppb cd2 with a standard deviation (s) of 0.52 ppb cd2

The 90% confidence interval for a sample of size n, with sample mean [tex](\bar{x})[/tex] and a standard deviation of s is given by:

[tex]90\%\ C.I.=\bar{x}\pm1.645\left( \frac{s}{ \sqrt{n} } \right)[/tex]

Thus, the 90% confidence intervals (ci) for two analyses is given by:

[tex]7.50\pm1.645\left( \frac{0.52}{ \sqrt{2} } \right)=7.50\pm1.645(0.3677) \\ \\ =7.50\pm0.6049=(6.90, \ 8.1)[/tex]


Part A2:

Given that the mean cadmium (cd2 ) content value in a homogenized sample of 40 zebra mussles was found to be 7.50 ppb cd2 with a standard deviation (s) of 0.52 ppb cd2

The 95% confidence interval for a sample of size n, with sample mean [tex](\bar{x})[/tex] and a standard deviation of s is given by:

[tex]95\%\ C.I.=\bar{x}\pm1.96\left( \frac{s}{ \sqrt{n} } \right)[/tex]

Thus, the 95% confidence intervals (ci) for two analyses is given by:

[tex]7.50\pm1.96\left( \frac{0.52}{ \sqrt{2} } \right)=7.50\pm1.96(0.3677) \\ \\ =7.50\pm0.7207=(6.78, \ 8.22)[/tex]



Part B1:

Given that the mean cadmium (cd2 ) content value in a homogenized sample of 40 zebra mussles was found to be 7.50 ppb cd2 with a standard deviation (s) of 0.52 ppb cd2

The 90% confidence interval for a sample of size n, with sample mean [tex](\bar{x})[/tex] and a standard deviation of s is given by:

[tex]90\%\ C.I.=\bar{x}\pm1.645\left( \frac{s}{ \sqrt{n} } \right)[/tex]

Thus, the 90% confidence intervals (ci) for five analyses is given by:

[tex]7.50\pm1.645\left( \frac{0.52}{ \sqrt{5} } \right)=7.50\pm1.645(0.2326) \\ \\ =7.50\pm0.3825=(7.12, \ 7.88)[/tex]



Part B2:

Given that the mean cadmium (cd2 ) content value in a homogenized sample of 40 zebra mussles was found to be 7.50 ppb cd2 with a standard deviation (s) of 0.52 ppb cd2

The 95% confidence interval for a sample of size n, with sample mean [tex](\bar{x})[/tex] and a standard deviation of s is given by:

[tex]95\%\ C.I.=\bar{x}\pm1.96\left( \frac{s}{ \sqrt{n} } \right)[/tex]

Thus, the 95% confidence intervals (ci) for five analyses is given by:

[tex]7.50\pm1.96\left( \frac{0.52}{ \sqrt{5} } \right)=7.50\pm1.96(0.2326) \\ \\ =7.50\pm0.4559=(7.04, \ 7.96)[/tex]

Which represents a rational Number and how can you tell?[tex] \sqrt{17} \sqrt{36} \sqrt{50} \sqrt{101} [/tex]

Answers

[tex]\bf \begin{array}{llll} \sqrt{17}\\\\ \sqrt{101} \end{array}\impliedby \textit{17 and 10 are both prime numbers} \\\\\\ \sqrt{36}\implies \sqrt{6^2}\implies \pm 6 \\\\\\ \sqrt{50}\implies \sqrt{25\cdot 2}\implies \sqrt{5^2\cdot 2}\implies 5\sqrt{2}\impliedby \textit{2 is a prime number}[/tex]

if a number is a prime number, it has no two equal factors that can produce a product of such a number, and therefore such value is an irrational number.

now, the last one, 5 is being multiplied by an irrational, and therefore the product will yield the same irrational, just a bit larger.

so, the only rational there is the ±6 really.

Question 3(Multiple Choice Worth 5 points) (01.06) Jack and Jill had 5 pails of water. Each trip up the hill, Jack and Jill obtained 2 more buckets of water. Which of the graphs below represents Jack and Jill's number of pails over time? graph of line going through 1, 7 and 2, 12 graph of line going through 1, 7 and 3, 11 graph of line going through 2, 6 and 4, 7 graph of line going through 0, 2 and 6, 3

Answers

It's B 1,7 and 3,11 hops this helped
Answer:

The graph which represents Jack and Jill's number of pails over time is:

   graph of line going through (1,7) and (3,11) Step-by-step explanation:

It is given that:

Jack and Jill had 5 pails of water. Each trip up the hill, Jack and Jill obtained 2 more buckets of water.

Let x be the number of hills they tripped.

and y denote the number of buckets of water they have.

Then the equation which represent the relationship between y and x is:

             [tex]y=5+2x[/tex]

On making  a table for x and y:

        x             y

        1              7

        2             9

        3             11

        4             13

        5             15

        6             17

Hence, the graph will pass through the points (1,7) (2,9) (3,11) (4,13) (5,15) (6,17) and many more.

70 is 20% of what number

Answers

350 is the answer to the question
x*0.20= 70
x=70/0.20
x=350

make sense?

what is the solution of 1/3b = -3

Answers

simplify 1/3b to b/3

b/3 = -3


multiply both sides by 3

b = -3 * 3

multiply 3 * 3 so it can = 9

Answer: b = -9
The answer would be b= -9. To do so you need to multiply the equation by 3 so you can get rid of the fraction. You then end up with 1b= -9. Then you divide both sides by 1 and there you go. I hope this helps love! :)

Dos angulos consecutivos de un paralelogramo estan e la relacion de 2 a 7. calcula el mayor angulo del paralelogramo

Answers

Can you translate to English?

A picture is enlarged by keeping its width the same and increasing its length. The scatter plot shows the perimeter of the picture (y) for different lengths (x):

Answers

Since you have not included the plot, I'll just tell you how to find the function of the graph that you are looking for.
Function of the straight line has the general formula: y = mx + c
where: 
m is the slope of the line and c is the y-intercept

So first we will need to find the slope (m):
Taking two points from the graph (x1,y1) and (x2,y2), the slope can be calculated as follows:
m = (y2-y2) / (x2-x2)

Then, we will need to find the y intercept.
we have the equation y = mx + c and we have m calculated
Take any point that belongs to the line and substitute with the values of x,y and m and then calculate c.

Now you have both m and c calculated, just substitute with the values in the formula.

Answer: This is the CORRECT answer ----> y = 2x + 20

Step-by-step explanation: slope, y2 - y1/x2 - x1

replace it with these numbers 120 - 60/50 - 20=60/30

than,simplified it we get 2/1. so, now we  have the slope of our equation

y = 2x + b. but we still have b (or where the y intersects.) now are slope we have to change it to 1/2 because we are going backwards. So multiply 60 by .5, Thus will give us 30

Now we have y = 2x + 30, But that's not one of your answer,

So y = 2x + 20 cant be -20 because this is a positive y intersect and We know it is a slope of 2.

Therefore the answer is : y = 2x + 20

ALSO I know it's correct because I got it right on the test!! Hoped I helped :))

List in order the specific operations that you would use to isolate X in the following equation show the step that corresponds to each operation

7 + 3 (2 - 3x) = 67

Answers

7 + 3.(2 - 3x) = 67
3 brackets are distributed

7+6-9x = 67
13-9x = 67
-9x = 67
x = 67/-9

The total cost CC (in dollars) to participate in a ski club is given by the literal equation C=85x+60C=85x+60, where xx is the number of ski trips you take
How many ski trips do you take if you spend a total of $315? $485?

Answers

First of all why is there 2 similar equation connected to one another?

Second in order to solve this all you need to do is plug in the number and solve for x

For 485

85x+60=485
85x=420
X=5

Do the same thing and you get 3

Answer:

The total cost C (in dollars) to participate in a ski club is given by the literal equation :

[tex]C=85x+60[/tex]

Where x is the number of ski trips you take.

1. When C = 315 ;substituting the value of C in the above equation.

[tex]315=85x+60[/tex]

=> [tex]85x=315-60[/tex]

=> [tex]85x=255[/tex]

x = 3 trips.

2. When C = 485

[tex]485=85x+60[/tex]

=> [tex]85x=485-60[/tex]

=> [tex]85x=425[/tex]

x = 5 trips.

Each marble bag sold by jenny's marble company contains 3 yellow marbles for every 5 orange marbles. if a bag has 15 yellow marbles, how many orange marbles does it contain?

Answers

it would contain 25 Orange marbles

if <PQR measures 75°, what is the measure of <SQR?

Answers

To f ind this subtract PQS from PQR:

75-22

53 

Hope this helps!
The answer is to this question is: 53°

There is 6/8 of a birthday cake leftover after a birthday party. How many 1/4 pieces can be made from the leftover cake?

Answers

divide both 6 & 8 by 2 6/2 = 3

8/2 = 4

so 6/8  = 3/4

 there is 3 pieces


Elton pours 41 1/4 ounces of water from a large pitcher into a bottle. That amount is 2/5 of the water that was in the pitcher. There were _____ ounces of water in the pitcher.

Write your answer as a mixed number in lower terms.

Answers

Okay. 41 1/4 is 2/5 if what was previously in the pitcher. In this case, we have to divide to see how much was previously in the pitcher. We convert 41 1/4 to an improper fraction, which is 165/4. Then we must keep that fraction the same, change the sign to a multiplication sign, and flip the second fraction over. So turn 2/5 into 5/2. 165/4 * 5/2. When you do that, you should get 825/8 or 103 1/8 when simplifies. There were 103 1/8 ounces of water in the pitcher.

geometry help me please

Answers

First Answer: Transitive property of Equality

Explanation: If x = y and z = y, then x = z. This is the basic template. In this case, both left side expressions of the problem are equal to 180, so they must be equal

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

Second Answer: Alternate Interior Angles Theorem

Explanation: These angles are on the inside of the parallel line train tracks (hence the "interior") and they are on opposite sides of the transversal line (hence the "alternate"). Alternate interior angles are congruent if the lines are parallel, which they are in this case.

if a=b then ac=bc. this called the of quality.(2words)

Answers

I'm not sure how this is 2 words, as the answer is the Multiplication Property of Equality.

Hope this helps!

Round 90608.5881594 to 1 decimal place

Answers

90608.6 is the answer

 Remember if the number after this line is less than 5 round down, or round up if the number is 5 or above.

Answer:

90608.6

Step-by-step explanation:

Round 90608.5881594 to 1 decimal place

To round the answer to 1 decimal place , we round the answer to nearest tenth.

In the given number , 5 after decimal point is in tenths place

8 is in hundredths place

Here 8 in hundredths place is greater than 5. If it is greater than 5 then we add 1 in tenths place

So 5 in tenths place becomes 6

90608.5881594 to 1 decimal place is 90608.6

It takes the earth 24 hours to complete a full rotation. It takes mercury approximately 58 days, 15 hours, and 30 minutes to complete a full rotation. How many hours does it take mercury to complete a full rotation?

Answers


To answer this question you need to convert the mercury rotation time from 58 days, 15 hours, and 30 minutes into hours. 
First, try to convert the days into hours. The calculation would be=
58 days x 24 hours/day= 1392 hours.
Then convert the 30 minutes into the hours. 
30 minutes / (60 minutes/hour)= 0.5 hours

After that you just need to add them all, then hours need for mercury to complete a full rotation: 1392 hours + 15 hours+ 0.5 hours= 1407.5 hours.
Final answer:

Mercury takes approximately 1407.5 hours to complete a full rotation, calculated by converting 58 days, 15 hours, and 30 minutes entirely into hours.

Explanation:

To calculate how many hours it takes for Mercury to complete a full rotation, we need to convert the given time of approximately 58 days, 15 hours, and 30 minutes into hours. Here are the step-by-step calculations:

First, convert the days into hours. Since there are 24 hours in a day, we multiply 58 days by 24 hours per day.58 days × 24 hours/day = 1392 hoursNext, add the additional hours to the total from the days.1392 hours + 15 hours = 1407 hoursFinally, convert the minutes to hours. There are 60 minutes in an hour, so we divide 30 minutes by 60.30 minutes ÷ 60 minutes/hour = 0.5 hoursAdd this to the total number of hours.1407 hours + 0.5 hours = 1407.5 hours

Therefore, it takes Mercury approximately 1407.5 hours to complete a full rotation.

Solve for a. 15(25−5a)=4−a
A- 0
B-−1
C-all real numbers
D- no solution

Answers

the answer is d- no solutions

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

[tex]\dfrac{1}{5}(25-5a)=4-a[/tex]

We need to find the value of 'a'.

First we simplify the brackets :

[tex]\dfrac{1}{5}(25-5a)=4-a\\\\25-5a=5(4-a)\\\\25-5a=20-5a\\\\25-20=-5a+5a\\\\5=0[/tex]

which is wrong.

Hence, there is no solution.

Therefore, Option 'D' is correct.

simplify
14+4(12−34)2

Answers

The answer for that is -162

Answer:  The required simplified answer is 1950.

Step-by-step explanation:  We are given to simplify the following algebraic expression :

[tex]E=14+4(12-34)^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To simplify the given expression, first we evaluate the square term, multiply it by 4 and add the result to 14.

From expression (i), we get

[tex]E\\\\=14+4(12-34)^2\\\\=14+4(-22)^2\\\\=14+4\times484\\\\=14+1936\\\\=1950.[/tex]

Thus, the required simplified answer is 1950.

How do u graph linear equations like this where it's just y=-5x ?Plz explain

Answers

Calculate the y value for a bunch of x values.

E.g. x=0: y=-5*0 = 0, plot the point (0,0)
x=1: y=-5*1=-5, plot the point (1,-5)

repeat the process until you are confident to draw a smooth line through it. For straight lines two points suffice. In this example I'd choose them sufficiently far apart, like x=-4 and x=+4.

If x represent a number , then write an expression for one half the sum of x and 7

Answers

Hello there!

It would be (x + 7) / 2

Hope This Helps You!
Good Luck :)

the sum of x and 7 would be x+7

 then to get half of that you would divide by 2

 so equation is (x+7)/2

What expression completes the equation 30/2+10

A. 3(2+3)
B. 7(2+1)
C. 6(3+7)
D. 5(4+1)

Answers

30/2 = 15

30/2 + 10 = 15 +10 = 25

5(4+1) = 5 x 5 = 25

Your answer is D

how do you write the decimal 0.7 as a fraction in simplest form

Answers

0.7 is 7/10 in fraction form

It is also already in simplest form

7/10 is your answer

hope this helps

Which word describes the slope of the line?

positive
negative
zero
undefined

Answers

Since the line, from left to right, is going upward, the slope is positive.

Answer:

positive

Step-by-step explanation:

The slope is the inclination of the line with respect to the x-axis.  It is denoted by the letter [tex]m[/tex]. In mathematical language, the slope [tex]m[/tex] of the line is defined as the difference on the y-axis divided by the difference on the x-axis for two different points [tex]P_1(x_1,y_1)[/tex] and [tex]P_2(x_2,y_2)[/tex] on the line:

[tex]m=\frac{\Delta y}{\Delta x} =\frac{y_2-y_1}{x_2-x_1}[/tex]

If:

[tex]m>0[/tex] The slope is positive and the line is increasing from left to right

[tex]m<0[/tex] The slope is negative and the line is decreasing from left to right

If a line is vertical the slope is undefined

[tex]m=0[/tex]   is a constant function.

Since the graph of the linear function shown is increasing from left to right, we can conclude that the slope is positive.

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