John is 24 years old. Two years ago, he was twice Shane's age at that time. How old is Shane now?

the answer you are looking for is not c or b or a the answer is 4/11 you can not simplify it any lower.

Answer:

de=11

Step-by-step explanation:

We are given that b is the midpoint of ac

ac=cd, ab=3x+4,ac=11x-17 and ce=49

We have to find the value of de

b is the midpoint of ac therefore we have

ab=bc

ac=ab+bc=ab+ab=2ab

[tex]11x-17=2(3x+4)[/tex]

[tex]11x-17=6x+8[/tex]

[tex]11x-6x=8+17=25[/tex]

[tex]5x=25[/tex]

[tex]x=\frac{25}{5}=5[/tex]

Then , substitute the value of x

[tex]ab=3(5)+4=19[/tex]

ac=[tex]11(5)-17=55-17=38=cd[/tex]

ce=cd+de

49=38+de

[tex]de=49-38[/tex]

de=11

The measure of segment DE is 11.

Given:

[tex]AB = 3x+4\\AC = 11x-17\\CE=49[/tex]

See image in the attachment below showing the information given in the question.

Since B is the midpoint of AC, therefore:

[tex]AB = AC[/tex]

[tex]2(AB) = AC[/tex]

Substitute

[tex]2(3x+4)=11x-17[/tex]

Solve for x

[tex]6x +8=11x-17\\17 + 8 = 11x-6x\\25 = 5x\\[/tex]

Divide both sides by 5

[tex]5 = x\\x=5[/tex]

Find DE:

[tex]DE = CE - CD[/tex] (Segment Addition Postulate)

[tex]AC = CD = 11x-17[/tex]

Plug in the value of x

[tex]CD = 11(5) -17 = 38[/tex]

[tex]CE = 49 (given)[/tex]

Substitute

[tex]DE = 49 - 38\\DE = 11[/tex]

Therefore the length of DE = 11.

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First of all, let's get rid of the absolute values. If the number inside is positive, don't do anything. If it's negative, switch the sign. So, the expression becomes

[tex] 6 + 3\cdot 4 + 5 - 0 \cdot 6 [/tex]

We have to perform multiplications first:

[tex] 6 + 12 + 5 - 0 [/tex]

The last subtraction by 0 doesn't affect the number in any way, so we can ignore it:

[tex] 6 + 12 + 5 [/tex]

Now you can perform the sums just as they appear:

[tex] 6 + 12 + 5 = 18 + 5 = 23 [/tex]

|-6| + 3|4| + |-5| - 0 * 6    

Note: absolute value makes the number positive

 6  + 3(4) +  5   - 0 * 6      

Now, use the order of operations (multiply first)

 6   + 12  + 5   -   0        

Next, add and subtract

     18      + 5   -   0

            23      -   0

                    23

Answer: 23

Answer:

m∠SVT= 79

Step-by-step explanation:

8y-33= 5y+9

Subtract 5y from both sides

8y-33= 5y+9

8y-33= 5y +9

-5y     -5y

3y - 33= 9

Then add 33 to the other side

3y-33 = 9

   +33  +33

= 3y= 42

Side by Side need to divide (divide by 3 on each side)

3y= 42

/3    /3

y= 143

m∠SVT = 5y + 9

m∠SVT = 5(14) + 9

m∠SVT = 70 + 9

m∠SVT =  79

Algebraic expression:

x-5/5+10

Solution:

                                                                                                 ∴-1 + 10 = 9

An expression involving a variable is a way to express an idea, rather than a specific number. So, writing [tex] 5x-7 [/tex] means that there is a certain quantity, x, and you want to multiply it by 5, and then subtract 7.

Note that we don't want to know the value of x, we're only saying that we will multiply it by 5 and then subtract 7.

So, if we know that x=9, we will multiply it by 5 and then subtract 7:

[tex] 5x-7 = 5\cdot 9 - 7 = 45-7 = 38 [/tex]

The correct answer is the third graph, C!

I hope this helped you!

The distance traveled by Davis family = 35 miles

Time taken to cover the distance = [tex]\frac{1}{2}[/tex] hour

Speed = Distance [tex]\div[/tex] Time

Speed = [tex]35 \div \frac{1}{2}[/tex]

Speed = [tex]35 \times 2[/tex]

So, speed = 70 miles/hour.

At 2:00 pm, the family destination was 245 miles away.

So, the number of hours, when the family was 245 miles away = [tex]245 \div 70[/tex]

=  3.5 hours

So, after 3.5 hours,  that is at 5:30 pm, the Davis family will be 245 miles away.

To find the Davis family's arrival time, you calculate the average speed, find the time needed for the remaining distance, and then add it to the current time of 2:00pm. Their arrival time is calculated to be 5:30pm.

The student asked: The Davis family traveled 35 miles in 1/2 hour. If it is currently 2:00pm and the family destination is 245 miles away, at what time will they arrive? To solve this, we need to calculate the total travel time based on their average speed and the remaining distance to the destination.

First, we find their speed by dividing the distance traveled by the time taken: 35 miles / 0.5 hours = 70 miles per hour. Next, we calculate the remaining distance to travel, which is 245 miles.

To find the time needed to cover the remaining distance, we divide the distance by the speed: 245 miles / 70 miles per hour = 3.5 hours.

Now, we add the travel time to the current time. Since it's 2:00pm, adding 3.5 hours gives us 5:30pm, which is the arrival time.

Hello,

Please, see the attached files.

Thanks.

28 miles

increasing by 40% = original + increase = 100 + 40 = 140% = 1.4

multiplying 20 by 1.4 gives total he will run

miles run = 1.4 × 20 = 28

Answer:

28 miles

Step-by-step explanation:

Just multiply (20 miles per week) by 1.40:    1.40(20 mpw) = 28 miles

                       Qty                    %                       Qty * %

Solution 1:        x                 6% = 0.06        =      0.06x

Solution 2:    392 - x         2% = 0.02        =      0.02(392 - x)  = 7.84 - 0.02x

Mixture:          392              5% = 0.05        =     0.06x + 7.84 - 0.02x

                                                 392(0.05)   =    0.08x + 7.84

                                                           19.6   =    0.08x + 7.84

                                                          11.76   =    0.08x

                                                            147    =      x

Solution 2:  392 - x    = 392 - (147)   = 245

Answer: 147 gallons 6% and 245 gallons of 2%

{x*0.02+0.06y=392*0.05

{x+y=392, x=392-y

0.04y=11.76, y=294; x=392-294=98

There is need 98 gallons of milk with 2% butterfat and 294 gallons of milk with 6% butterfat

Divide total students by the size of the group:

35 / 5 = 7 groups.

Do 35 divided by 5 and it will give you 7. So Mr. Brown will have 7 teams of 5.

2c + 4d = 92

substitute the given values into the expression and evaluate

2c + 4d = (2 × 30) + (4 × 8) = 60 + 32 = 92

The answer is 92. First substitute in 30 for c and multiply it by 2, and you get 60. Then, substitute in 8 for d and multiply it by 4 to get 32. Add 60 + 32 and it equals 92.

Answer: The 3,8,13,18 and 23 the actual common difference of this sequence.

Explanation:

The given terms of the sequence are 3,8,13,18 and 23.

Where first term is 3, second is 8, thirst term is 18, fourth term is 18 and fifth term is 23.

The difference between second and third term is 5.

[tex]8-3=5[/tex]

The difference between third and fourth term is 5.

[tex]13-8=5[/tex]

So, the common difference of the sequence is 5. Since the difference between terms are same, therefore it is an arithmetic progression.

The formula to find the nth term is ,

[tex]a_n=a+(n-1)d[/tex]

Where a is the first term and d is the common difference.

Given

A triangle.

with vertices at (−2, 1) , (2, 1) , and ​ (3, 4) ​

Find out  the area of a triangle.

To proof

Formula

[tex]Area\ of\ triangle = \frac{1}{2}[ x_{1} (y_{2} -y_{3} ) + x_{2} (y_{3} - y_{1})+x_{3}(y_{1}-y_{2})[/tex]

As given the vertices at (−2, 1) , (2, 1) , and ​ (3, 4)

put in the above equation

we get

[tex]= \frac{1}{2} [-2(1-4)+ 2 (4-1) + 3 ( 1-1) ][/tex]

solving

[tex]= \frac{1}{2} [6 + 6][/tex]

thus

[tex]=\frac{1}{2} [12][/tex]

area of the triangle is 6 units².

Hence proved

The area of a triangle with vertices at (−2, 1) , (2, 1) , and (3, 4) is; Area = 6 units²

The formula for the area of a triangle when given the 3 vertices is;

Area = ½[Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)]

In this question, the vertices coordinates are; A(−2, 1), B(2, 1), and C(3, 4)

Thus;

Ax = -2

Bx = 2

Cx = 3

Ay = 1

By = 1

Cy = 4

Plugging in the relevant values into the area equation gives;

Area = ½[-2(1 - 4) + 2(4 - 1) + 3(1 - 1)]

Area = ½(6 + 6 + 0)

Area = ½ × 12

Area = 6 units²

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The numbers -9 and -3 are 3 units from −6 on this number line.

In mathematics, a number line is a straight line containing numbers arranged at equal segments or periods throughout its duration.

In another word, a number line is basically a line in which infinite numbers have been written in ascending order or increasing order.

A horizontal number line is the most common representation and can be extended infinitely in any direction.

Given a number line,

The 3 units left to the -6 is ⇒ -6 - 3 = -9

The 3 units right to the -6 ⇒ -6 + 3 = -3

Hence "The numbers -9 and -3 are 3 units from −6 on this number line".

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The numbers that are 3 units from -6 on the number line are determined as: -9 and -3.

What is a number line?

A number line is a visual tool that displays numbers in a linear sequence, extending endlessly in both positive and negative directions, illustrating their comparative sizes and positions.

To find numbers that are 3 units from -6 on the number line, you need to consider both numbers that are 3 units to the right and 3 units to the left of -6.

To the right of -6: -6 + 3 = -3

To the left of -6: -6 - 3 = -9

So, the correct numbers are:

D. -3

B. -9

Place them on the number line accordingly.

Carla

Amir

Carlo

Esther

From greatest to least!

Answer:

1. Carla

2. Amir

3. Carlo

4. Esther

Answer:

In this case, the answer is $88.00. Have a nice day! <3

Step-by-step explanation:

You can't simplify this equation anymore.

Isaiah would have to put 10 one-hundred gram weights to balance it out because there are 1000 grams in a kilogram.

the reciprocal of 5 3/5 is 5/28

From the graph, we know the y-intercepts (look at the picture).

y = 2 → y = 3x + 2

y = 3 → y = -1/3x + 3

We have

y ≥ 3x + 2 (shadow up of a line)

y ≤ -1/3x + 3 (shadows down of a line)

the common region is D.

Answer:

Option (a) and (d) are correct.

region A and region D satisfies the given inequality y ≥ 3x + 2.

Step-by-step explanation:

Given :  The graph of the system of inequalities y ≥ 3x + 2.

We have to determine which region contains the solution to the system.

We will chose a test point in each region and  see which point satisfies the given inequality.

For region A)

(0,6) is in region A

Put x = 0 and y = 6 in given inequality

We get,

6 ≥ 3(0) + 2.

6 ≥  2 (True)

For region B)

(4,6) is in region B

Put x = 4 and y = 6 in given inequality

We get,

6 ≥ 3(4) + 2.

6 ≥  12 + 2 = 14 (False)

For region C)

(0,0) is in region C

Put x = 0 and y = 0 in given inequality

We get,

0 ≥ 3(0) + 2.

0 ≥  2 (False)

For region D)

(-2,2) is in region A

Put x = -2 and y = 2 in given inequality

We get,

2 ≥ -3(2) + 2.

2 ≥ -6+ 2 = -4  (True)

Thus, region A and region D satisfies the given inequality

Thus, Option (a) and (d) are correct.

The third side is 9 cm long

Let [tex]x[/tex] represent one of the equal sides. Then the` other side will be [tex]2x-5[/tex].

Adding all the length of the sides should give 23. Thus,

[tex]x+x+2x-5=23[/tex]

This implies that,

[tex]4x-5=23[/tex]

We group like terms and simplify to obtain.

[tex]4x=23+5[/tex]

[tex]4x=28[/tex]

Divide through by 4 to get

[tex]x=7[/tex]

Hence the length of the other side is

[tex]2(7)-5=9[/tex]

The example is 1 x (9 x 5) = 45

Using the associative property of multiplication, we basically rearrange the parenthesis to group the first two terms like so: (1 x 9) x 5

So this is why choice D (1 x 9) x 5 = 45 is the answer

This means that 1 x (9x 5) = (1 x 9) x 5 is a true equation

Total = 21 feet

if each is 3 feet

21/3 = 7

Therefore, there are 7 sections

Mathematics defines division as breaking into parts a larger unit to make several smaller units.

Division of 21 feet wallpaper into 3 feet section will give 7 small parts of the wallpaper.

To reach above answer, following calculation was made:

[tex]\begin{aligned} \rm Total\: length\:of \: the \:wallpaper &= 21\rm \:centimetres\\Length \:of\:each\:section &= 3\: \rm centimetres\end[/tex]

Therefore, number of sections will be the division of total length to length of each section.

[tex]\rm \begin{aligned} Number \:of \:sections &= \dfrac{\rmTotal\: length}{\rmLength\:of\:each\:section}\\ \\&= \dfrac{\rm 21\:centimetres}{\rm 3\:centimetres}\\\\&= \rm 7 \:sections \end[/tex]

Hence, 21 centimetres long wallpaper can be divided into 7 sections that are 3 centimetres long.

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Answer:

19.57

Step-by-step explanation:

100% of 19 is 19.

In order to find out what 1% of 19, move the decimal point two place to the left. 1% of 19= 0.19. To find 3% of 19, multiply .19 x 3. add 0.19 x 3 to 19, aka add 0.57 to 19 to get 19.57= 103% of 19

Answer:

19.57 is the answer

Step-by-step explanation:

Answer:

Variance of the given data = 31.143

Explanation:

  Variance, [tex]\sigma^2=\frac{1}{n} \sum_{i=1}^{n}(x_i-\mu)^2[/tex], where n is the number of observations, μ is the mean and [tex]x_i[/tex] is the observations made.

   Number of observations, n = 7

   Mean, μ = [tex]\frac{10+19+21+28+12+20+16}{7} = 18[/tex]

   [tex]\sum_{i=1}^{n}(x_i-\mu)^2=(10-18)^2+(19-18)^2+(21-18)^2+(28-18)^2+(12-18)^2+(20-18)^2+(16-18)^2\\ \\ \sum_{i=1}^{n}(x_i-\mu)^2=64+1+9+100+36+4+4=218[/tex]

  [tex]\sigma^2=\frac{1}{n} \sum_{i=1}^{n}(x_i-\mu)^2=\frac{218}{7} =31.143[/tex]

  So variance of the given data = 31.143

Final answer:

The variance of the given data set {10, 19, 21, 28, 12, 20, 16} is calculated by finding the mean, squaring the deviations from the mean, summing these squares, and dividing by the number of data points minus one, resulting in a variance of approximately 36.33.

Explanation:

Calculating Variance of a Data Set

To calculate the variance, we first need to find the mean (average) of the data set. Then, we subtract the mean from each data point (deviation), square each deviation, sum them all up, and finally, divide by the total number of data points minus one to account for sample variance.

The given data set is {10, 19, 21, 28, 12, 20, 16}. Let's calculate the mean:

Mean = (10 + 19 + 21 + 28 + 12 + 20 + 16) / 7 = 126 / 7 = 18

Next, calculate each deviation from the mean, square it, and sum these squared deviations:

(10 - 18)² = 64

(19 - 18)² = 1

(21 - 18)² = 9

(28 - 18)² = 100

(12 - 18)² = 36

(20 - 18)² = 4

(16 - 18)² = 4

Sum of squared deviations = 64 + 1 + 9 + 100 + 36 + 4 + 4 = 218

The variance is then the sum of the squared deviations divided by n - 1 (where n is the number of data points in our sample):

Variance = 218 / (7 - 1) = 218 / 6 ≈ 36.33