The next number in the series 13, 18, 16, 21, 19, is:

Part a: Option c: [tex]3x+90+x-14=180[/tex]

Part b: The value of x is 26

Explanation:

Part a:

Option a: [tex]3x+x-14=180[/tex]

Since, adding all the angles in the straight line results in 180°, and only two of the three angles were added in the equation to find the value of x.

Thus, the equation [tex]3x+x-14=180[/tex] cannot be used to determine the value of x.

Hence, Option a is not the correct answer.

Option b: [tex]3x+90+x-14=90[/tex]

Adding all the angles in the straight line results in 180°.

Thus, adding all the angles does not equals to 90°

Hence, the equation [tex]3x+90+x-14=90[/tex] cannot be used to determine the value of x.

Hence, option b is not the correct answer.

Option c: [tex]3x+90+x-14=180[/tex]

Since, the straight line is 180° and thus adding the angles in this straight line will result in 180°

Thus, the angles in this straight line are 3x, 90° and x-14.

Hence, adding these angles will result in 180°

Thus, the equation becomes

[tex]3x+90+x-14=180[/tex]

Hence, the equation used to determine the value of x is [tex]3x+90+x-14=180[/tex]

Thus, Option c is the correct answer.

Option d: [tex]4x+90=360[/tex]

Adding all the angles in the straight line results in 180°.

Since, not all the three angles were added in this equation and the equation equals to 180°

Hence,  the equation [tex]4x+90=360[/tex] cannot be used to determine the value of x.

Thus, Option d is not the correct answer.

Part b:

To determine the value of x, we shall add all the angles of the equation [tex]3x+90+x-14=180[/tex]

Thus, we get,

[tex]4x+76=180[/tex]

Subtracting both sides by 76,

[tex]4x=104[/tex]

Dividing both sides by 4, we get,

[tex]x=26[/tex]

Thus, the value of x is 26.

Answer:

2, there'd be more, but natural numbers are like, whole numbers, integers basically except they're like non-negative integers. Enough ranting. So 4 and 8 would be the numbers because they are mulitplied by 4,1, and 2.

Since 4 cant go into 10 completely without a decimal, there'd only be 2 multiples.

Confusing explanation, but i think my answer is correct. (or is it, dun dun dun!)

Have a good day~

Answer:

Therefore the cost of each apple is $ 0.50 and each banana is $1.

Step-by-step explanation:

Given , Amanda buys 6 apples and 5 bananas , it will cost $8.00 and if she buys 5 apples and 7 bananas it will cost $9.50.

Let the cost of one apple be =$ x

and the cost of one banana be =$y

According to the problem,

6x+5y=8.........(1)                  5x+7y= 9.50............(2)

Equation (1)×5 - equation (2) × 6

30x +25 y-(30x+42y)= 40-57

⇔30x+25y -30x-42y= -17

⇔-17y =-17

⇔y=1

putting the value of y in equation (1)

6x+5×1=8

⇔6x = 8-5

⇔6x=3

⇔[tex]x =\frac{3}{6}[/tex]

⇔x = 0.50

Therefore the cost of each apple is $ 0.50 and each banana is $1.

Answer:

3.13 * 10^-1

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

Step :1

Given x- 2 y =5 .......(1)

put x=1 and y= -3 on left hand side of given equation

1 - 2 (-3) = 5

1 + 6 = 5

7 ≠ 5

both sides are not equal

so it is false

Answer:

false

Step-by-step explanation:

x - 2y = 5

when x = 1, and y = -3

1 -2(-3) = 5

1 +  6 = 5

7 ≠ 5

Answer:

D, 28, 45, 53

Step-by-step explanation:

A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. ... The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a2 + b2 = c2; thus, Pythagorean triples describe the three integer side lengths of a right triangle.

Answer:

4a+20

Step-by-step explanation:

Answer:4a + 20

Step-by-step explanation:

Answer:

x+3

Step-by-step explanation:

Since the number of cookies in the jar could be anything we'll use a variable to represent it, x.  so three more than x is what?

Well, what's thee more than 5? 8, so you add 3.

So x+3

Answer:

[tex]\large \boxed{\$35.80}[/tex]  

Step-by-step explanation:

Discount = Regular price × % discount

[tex]\text{Discount} = \text{\$179 regular price} \times \dfrac{\text{\$20 }}{\text{\$100 regular price}} = \textbf{\$35.80}\\\text{Selma will save $\large \boxed{\mathbf{\$35.80}}$}[/tex]

Selma will save $35.8 after getting 20% discount on regular price.

" Discount is the deduction amount from the regular price assigned to any product."

Formula used

Discount = Regular Price × discount %

According to the questions,

Regular price = $179

Discount% = 20%

Substitute the value in the formula we get,

Discount = 179 × 20%

               = 179 × (20 / 100)

              = $ 35.8

Hence, Selma will save $35.8 after getting 20% discount on regular price.

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Answer:

18.9 units to 1 decimal Place

Step-by-step explanation:

You need the diameter so do 3 X 2 = 6

Circumference is pi X diameter so

Do 6 X pi = 6pi or 18.9 to 1 dp

Answer: the answer is 6

Step-by-step explanation:

The value of x is 6.

Two triangles are comparable if the measurements of their corresponding sides are proportionate. The same is true if the lengths of two sides in one triangle are proportional to the lengths of the corresponding sides in another triangle and the included angles are congruent.

Given:

As, the rectangles in the figure below are similar.

Using the property of similarity

x/(x+ 4) = 3/5

5x = 3x + 12

5x - 3x = 12

2x = 12

Divide both side by 2

2x /2 = 12/2

x = 6

Hence, the value of x is 6.

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Answer:

Option 4 - The solution of x is [tex]x=4\pm5i[/tex].

Step-by-step explanation:

Given : Equation [tex]x^2-8x+41=0[/tex]

To find : Solve for x in the equation ?

Solution :

Solving a quadratic equation [tex]ax^2+bx+c=0[/tex] solution is given by, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Here, a=1, b=-8 and c=41

[tex]x=\frac{-(-8)\pm\sqrt{(-8)^2-4(1)(41)}}{2(1)}[/tex]

[tex]x=\frac{8\pm\sqrt{-100}}{2}[/tex]

[tex]x=\frac{8\pm10i}{2}[/tex]

[tex]x=4\pm5i[/tex]

Therefore, the solution of x is [tex]x=4\pm5i[/tex].

Answer:

D

Step-by-step explanation:

trust meh

Answer:

  A. just as it leaves the bat

Step-by-step explanation:

It depends on the assumptions you make.

If you assume that the speed is reduced by air resistance, and that the hit is a fly ball, then the speed begins to slow as soon as the ball leaves the bat. Its maximum speed will be just as it leaves the bat.

__

If you assume no air resistance and that the ball takes 1 second to reach the ground, the speed will be a maximum just as the ball hits the ground, a second after it leaves the bat.

__

If you assume no air resistance and that the ball takes 2 seconds to reach the ground, the speed will be a maximum just as the ball hits the ground, two seconds after it leaves the bat.

__

Depending on the nature of the pitch and the hit (and the assumptions you make about energy loss and gain), the maximum speed may be as the ball leaves the pitcher's hand, or just as the ball hits the bat.

__

My guess is that the assumptions listed for the first case are the ones you're most likely expected to use. The answer above reflects that choice.

Answer:

Step-by-step explanation:

Answer 22,16,18,36

Step-by-step explanation:

Second data set 22, 16, 18, 36 is the most spread from its mean

" Mean is defined as the ratio of the sum of the all the numbers of data set to the total numbers of number present in data set."

Formula used

Mean = [tex]\frac{Sum of all the numbers in data set}{Total number of numbers}[/tex]

According to the question,

Given data set,

Mean of first data set,

Substitute the values in the formula we get,

Mean = [tex]\frac{14 +26 + 24 + 28}{4}[/tex]

          [tex]=\frac{92}{4}\\ =23[/tex]

Mean of second data set,

Substitute the values in the formula we get,

Mean = [tex]\frac{22 +16 + 18 + 36}{4}[/tex]

          [tex]=\frac{92}{4}\\ =23[/tex]

Mean of third data set,

Substitute the values in the formula we get,

Mean = [tex]\frac{22 +28 + 20 + 22}{4}[/tex]

          [tex]=\frac{92}{4}\\ =23[/tex]

Mean of fourth data set,

Substitute the values in the formula we get,

Mean = [tex]\frac{21 +19 + 27+ 25}{4}[/tex]

          [tex]=\frac{92}{4}\\ =23[/tex]

Hence, second data set 22, 16, 18, 36 is the most spread from its mean.

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Answer:

the system would have crossed one solution

Answer: x^2-9x+20

Step-by-step explanation:

Answer:

x² - 9x + 20

Step-by-step explanation:

Given

(x - 5)(x - 4)

Each term in the second factor is multiplied by each factor in the first factor, that is

x(x - 4) - 5(x - 4 ) ← distribute both parenthesis

= x² - 4x - 5x + 20 ← collect like terms

= x² - 9x + 20

Answer:

Mean  = 45.178

Standard Deviation = 10.33

Step-by-step explanation:

class                m              frequency, f           m [tex]\times[/tex] f            f [tex]\times[/tex] [tex]m^{2}[/tex]      

25 - 34          29.5                22.1                   651.95         19232.525

35 - 44           39.5                31.5                  1244.25        49147.875

45 - 54           49.5                37.7                  1866.15        92374.425

55 - 64            59.5               25.3                 1505.35        89568.352

                                          116.6                    5267.7           250323.15

mean = [tex]\frac{5267.7}{116.6} = 45.178[/tex]      standard deviation  = [tex]\sqrt{\frac{250323.15 - \frac{(5267.7)^2}{116.6} }{(116.1 - 1)} } = 10.33[/tex]

The mean of a distribution is the average of the distribution ; it is the sum of observation divided by the count of the observation.

Given that:

[tex]\begin{array}{ccccc}{Age}&25-34&35-44&45-45&55-64\\{Number}&22.1&31.5&37.7&25.3\end{array}[/tex]

First, we calculate midpoint of each class.

This is the sum of the class interval divided by 2.

So, we have:

[tex]x_1 = \frac{25+34}{2} = 29.5[/tex]

[tex]x_2 = \frac{35+44}{2} = 39.5[/tex]

And so on...

The table becomes:

[tex]\begin{array}{ccccc}{Age}&25-34&35-44&45-45&55-64&{Number(f)}&22.1&31.5&37.7&25.3&{x}&29.5&39.5&49.5&59.5\end{array}[/tex]

The mean of the distribution is:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

[tex]\bar x = \frac{29.5 \times 22.1 + 39.5 \times 31.5 + 49.5 \times 37.7 +59.5 \times 25.3}{22.1 + 31.5 + 37.7 +25.3}[/tex]

[tex]\bar x = \frac{5267.7}{116.6}[/tex]

[tex]\bar x = 45.18[/tex]

The standard deviation is calculated as follows:

[tex]\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]

[tex]\sigma= \sqrt{\frac{(29.5 - 45.1)^2\times 22.1 + (39.5 - 45.1)^2 \times 31.5 + (49.5 - 45.1)^2 \times 37.7 + (59.5 - 45.1)^2 \times 25.3}{22.1 + 31.5 + 37.7 +25.3}}[/tex]

[tex]\sigma= \sqrt{\frac{12342.176}{116.6}}[/tex]

[tex]\sigma= \sqrt{105.85}[/tex]

[tex]\sigma= 10.29[/tex]

Hence:

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Basically 45% of 360.

45/100 * 360

45/360 * 100

16,200 / 100

162

Answer:

162

Step-by-step explanation:

There are 360 seventh graders and 45% of this 360 ride the school bus

All we need to do is find 45% of 360

we have;

45 / 100 X 360

= 162

Hence 162 seventh graders ride the school bus

Answer:

200

Step-by-step explanation:

Question:

Solve the inequality:

5.1 – r ≥ 5

Answer:

r ≤ 0.1

Solution:

Step 1: Given inequality:

5.1 – r ≥ 5

Step 2: Subtract 5.1 from both sides of the inequality

⇒ 5.1 – r – 5.1 ≥ 5 – 5.1

⇒ – r ≥ – 0.1

Step 3: To reverse the inequality, multiply both sides by –1.

⇒ (–r) × (–1) ≥ – 0.1 × (–1)

Negative × Negative = Positive

⇒ r ≤ 0.1

Hence the solution to the given inequality is r ≤ 0.1.

Fido's dog must lose 1.17 pounds each month to reach healthier weight.

Step-by-step explanation:

Given,

Weight of fido's dog = 35 pounds

Time period = 6 months

Goal weight to reach = 28 or less pounds

Let,

m be the weight to be lose each month.

Weight of dog - Time period * Weight to lose each month ≤ Goal weight

[tex]35-6m\leq 28\\-6m\leq 28-35\\-6m\leq -7[/tex]

Dividing both sides by -6

[tex]\frac{-6m}{-6}\leq \frac{-7}{-6}\\\\m\leq 1.17[/tex]

Fido's dog must lose 1.17 pounds each month to reach healthier weight.

Keywords: division, subtraction

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Answer:

$8.48

Step-by-step explanation:

$8.00 x .06%= $ .48  ---$8.00 + $ .48=$8.48

Answer:

$8.48

Step-by-step explanation:$8.00 x .06%= $ .48  ---$8.00 + $ .48=$8.48

Answer:

The rate at which energy is used is called power.

Step-by-step explanation:

Answer:

Power is the answer

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Given data

(4/5)x = -16

x = -16 (5/4)

x = -20

Now,

-2x-15 = ?

putting the value of x

-2(-20)-15 = 25

The adult weight of puppy B is estimated to be around 11 pounds, as we learned by understanding percentages and using a mathematical formula to determine the total from a known percentage.

The subject is Mathematics and it involves a commonly used concept known as ratios and percentages. From the question, we know that puppy B weighs 8 pounds which is about 75% of its adult weight. This means that the adult weight will be greater than 8 pounds.

To find the adult weight, we know that the puppy's current weight represents 75% of it. So, we use the formula to find the total when we know the percentage:

Therefore, we can estimate that the adult weight of puppy B will be around about 11 pounds.

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The adult weight of Puppy B will be approximately 10.67 pounds.

To find the adult weight of Puppy B, we can set up a simple proportion based on the given information that 8 pounds is 75% of its adult weight. Let's denote the adult weight as A .

We can express the relationship as:

[tex]\[ 8 \text{ pounds} = \frac{75}{100} \times A \][/tex]

To solve for [tex]\( A \)[/tex], we can multiply both sides of the equation by [tex]\( \frac{100}{75} \)[/tex] to isolate [tex]\( A \)[/tex]:

[tex]\[ A = 8 \text{ pounds} \times \frac{100}{75} \][/tex]

Now, we calculate the value of  A:

[tex]\[ A = 8 \times \frac{4}{3} \][/tex]

[tex]\[ A = \frac{32}{3} \][/tex]

[tex]\[ A \approx 10.67 \text{ pounds} \][/tex]

Therefore, the adult weight of Puppy B is approximately 10.67 pounds.

Answer:

[tex]\frac{13}{6}[/tex] or [tex]2\frac{1}{6}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:3/2 x 3= 9/6

2/3 x 2= 4/6

9/6 + 4/6 = 13/6

13/6=2 1/6

Answer:

C

Step-by-step explanation:

Note that (f + g)(x) = f(x) + g(x)

f(x) + g(x)

= 4x + 1 + x² - 5 ← collect like terms

= x² + 4x - 4 → C