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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:

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

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:

4a+20

Step-by-step explanation:

Answer:4a + 20

Step-by-step explanation:

The answer to (-4.7)⁰ is 1

How to solve the exponent

We have a rule of thumb that Any non-zero number raised to the power of 0 is equal to 1.

This is a fundamental rule in mathematics and is consistent across all real numbers.

So, when you have (-4.7)⁰, you're essentially raising the number -4.7 to the power of 0.

Even though -4.7 is negative, it's still a non-zero number. Therefore, according to the rule, (-4.7)⁰ equals 1.

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: 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:

$15606000

Step-by-step explanation:

17,000,000*.15 (15% off)

$ 2550000 off

17,000,000

-2550000

$14450000 (15% off)

*1.08 (sales tax)

$15606000

sorry if it is incorrect

Answer:

if the sale tax comes first before the 15% off,

Sales Tax: 1360

so the price became 18360

Price Off: 2754

18360 - 2754 = 15606

if the sale tax comes after the 15% off,

Price Off: 2550

17000-2550 = 14450

eight percent of 14450 is 1156

14450+1156 = 15606

anyways, the price is the same no matter if the sales tax comes first or the discount comes first

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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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.

Answer:

Distrbutive Property

Step-by-step explanation:

The equation -4x - 1/4 = 1 illustrates the addition property of equality.

The property illustrated by the equation -4x - 1/4 = 1 is the addition property of equality. According to this property, if you add the same number to both sides of an equation, the equality of the equation is maintained. To isolate the variable, we need to get rid of the constant term (-1/4) on the left side of the equation by adding 1/4 to both sides. This simplifies the equation to -4x = 1 + 1/4. Then, divide both sides by -4 to solve for x.

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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:

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

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: 2.5

Step-by-step explanation:

Mean m = Sum s ÷ no of observation n

m = 2.5, n = 10

2.5 = s ÷ 10

s = 10 × 2.5

s = 25.

If one observation 2.5 is deleted from sum 25, new sum equals 25 — 2.5 = 22.5.

The no of observation becomes 9.

Therefore new mean = 22.5 ÷ 9

m = 2.5.

How this helps?

The question is about calculation of a new mean after deleting an observation from a data group. Despite deleting an observation of 2.5 from a data set with a mean of 2.5, the mean remains the same.

The subject matter is about computing the mean of a data set after a data point has been deleted. Starting off, we know we initially have 10 observations with a mean of 2.5. Therefore, the total sum of the observations can be calculated by multiplying the mean with the number of data points (2.5 * 10) to get 25.

Now, if we are to delete one observation worth 2.5, we have to subtract it from our total of 25 to get a new sum of 22.5. Then, we also decrease the number of data points by 1, which leaves us with 9 data points.

Finally, the new mean can be calculated by dividing the new sum by the new number of data points. In this case, it would be 22.5 divided by 9, which equals 2.5. Thus, the mean remains the same even after deleting the observation of 2.5.

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Answer:

3.13 * 10^-1

Step-by-step explanation:

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:

72 dollars

Step-by-step explanation:

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.

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 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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Solution:

Mike correctly found the slope and y-intercept of the line passing through the points (–5, –2) and (3, 14)

To find:  Equation of the line in slope - intercept form

y = mx + c ------ eqn 1

Where, "m" is the slope of line and "c" is the y intercept

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

From given,

[tex](x_1, y_1) = (-5, -2)\\\\(x_2, y_2) = (3, 14)[/tex]

Therefore,

[tex]m = \frac{14-(-2)}{3-(-5)}\\\\m = \frac{14+2}{3+5}\\\\m = \frac{16}{8}\\\\m = 2[/tex]

Thus slope of line is 2

Substitute m = 2 and (x, y) = (-5, -2) in eqn 1

-2 = 2(-5) + c

-2 = -10 + c

c = -2 + 10

c = 8

Substitute c = 8 and m = 2 in eqn 1

y = 2x + 8

Thus the equation of line is found

Answer:

the answer is y=2x+8

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:

Step-by-step explanation:

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:

3)  A

4)  D

Step-by-step explanation:

3)

Find any four points where y intersects with x on graph A

(-4 , 2)        (-2 , 1)          (4, - 2)           (2 , -1)    

Find the relationship(s) between x and y

(-4 , 2)        (-2 , 1)          (4, - 2)           (2 , -1)    

x = -2y       x = -2y        x = -2y           x = -2y

It is shown that there is a direct proportional relationship between x and y, (x = -2y)

Repeat for graphs B, C, and D

Find any four points where y intersects with x on graph B

(3 , 2)           (5 , 4)          (-3 , -4)              (-4 , -5)

Find the relationship(s) between x and y    

x = 1.5y         x =  1.25y       x =  0.75y       x =  0.8y

As you can see, there is not a constant direct proportional relationship between x and y. B is not the correct answer

Graph C

Find any four points where y intersects with x on graph C

(-5 , -3)         (-1 , -3)      (1 , -3)          (5 , -3)

Find the relationship(s) between x and y    

x = 1.67y    x = 0.3y   x = -0.3y        x = -1.67y

Once again, there is not a constant direct proportional relationship between x and y, so C is not the correct answer

Graph D

Find any four points where y intersects with x on graph D

(2 , 1)      (2 , 2)      (2 , 3)          (2 , 4)

Find the relationship(s) between x and y    

x = 2y    x = y      x = 0.67y     x = .5y

There is no direct constant relationship between x and y in this graph either.

Graph A is the only graph with a direct proportional relationship between x and y.

4) Allison wants to know whom seventh-grade students will vote for in the upcoming class president election.

A) Every member of the student council

Asking every member of the student council who they are voting for will not help Allison, because it is likely that there are multiple grades involved in the student council, when Allison just wants to know the opinions of seventh-graders. The student council also might have a different opinion than the general seventh-graders.

B) All 12 girls in Allison's homeroom class

It is likely that the girls at Allison's school have a very different opinion than the boys at her school, making this a bad data set.

C) Every tenth student who arrives at school on Monday

Allison only want to know the opinions of seventh-graders, not every tenth student at her school, which would consist of more than seventh-graders.

D) Every tenth name on a roster of all of the seventh-graders at the school

This data set would be the most useful to Allison because it is multi-gender, only seventh-grade, and consists of the general seventh-graders (not part of a special group).

D

Hope this helps :)

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:

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:

200

Step-by-step explanation: