In triangle ABC, m∠BAC = 50°. If m∠ACB = 30°, then the triangle is triangle. If m∠ABC = 40°, then the triangle is triangle. If triangle ABC is isosceles, and AB = 6 and BC = 4, then AC =

You can't simplify this equation anymore.

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

The correct answer is the third graph, C!

I hope this helped you!

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.

To solve this question, let us take one part at a time.

Part 1 (MHz to GHz)

We know that 1 MHz=0.01 GHz

Therefore, [tex]63.45 MHz=63.45\times 0.001 GHz=0.06345 GHz[/tex]

Thus, for the time being we know that Option A is correct.

Part 2 (MHz to KHz)

We know that 1 MHz=1000 KHz

Therefore, [tex]63.45 MHz=63.45\times 1000 KHz=63450 KHz[/tex]

Thus, Option B too is correct.

Therefore, Both A and B are correct. Thus, out of the given options, Option C is correct.

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.

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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

Carla

Amir

Carlo

Esther

From greatest to least!

Answer:

1. Carla

2. Amir

3. Carlo

4. Esther

the reciprocal of 5 3/5 is 5/28

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

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

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.

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]

So remember the product rule of radicals: √ab = √a × √b

In this case:

√2 × √5 × √11 = √(2 × 5 × 11) = √110

√110 is your final answer.

Algebraic expression:

x-5/5+10

Solution:

                                                                                                 ∴-1 + 10 = 9

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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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.

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]

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:

                       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

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.

Answer:

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

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

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.