Cora is wrapping a ribbon around a cylinder-shaped gift box. The box has a diameter of 15 inches and the ribbon is 60 inches long. Cora is able to wrap the ribbon all the way around the box once, and then continue so that the second end of the ribbon passes the first end. What is the central angle formed between the ends of the ribbon? Round your answer to the nearest tenth of a degree.

The correct statements regarding the behavior of a quadratic function are:

A quadratic function with roots [tex]x_1[/tex] and [tex]x_2[/tex] is defined by:

[tex]y = a(x - x_1)(x - x_2)[/tex]

In which a is the leading coefficient.

The coefficient influences the behavior, as follows:

In this problem, the function is:

f(x) = -(x + 6)(x + 2).

The roots are x = -6 and x = -2, and the leading coefficient is of a = -1 < 0, hence:

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The height of the mountain from a point a sea level is approximately 1496.650 meters.

First, we construct the geometric diagram of the situation and find all needed angles and sides to determine the height of the mountain. First, we determine the missing side x by the law of sines:

Law of sines

1000 m/sin 3° = x/sin 14.261°

x ≈ 4706.886 m

Now we determine the height of the mountain by trigonometric functions:

h = 100 m + (4706.886 m) · sin 17.261°

h ≈ 1496.650 m

The height of the mountain from a point a sea level is approximately 1496.650 meters.

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I give u the answers of first and second one.

thank you

brainlist please

Answer:

First answer is 9 or 1 . Second answer is 7 or -7.

Step-by-step explanation:

[tex](x-5)^{2} =16[/tex]

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

so [tex]x = 9[/tex] or [tex]x = 1[/tex]

[tex]2x^{2} = 98[/tex]

[tex]x^{2} =49[/tex]

[tex]x=7[/tex] or [tex]x = -7[/tex]

The probability that a random sample of 12 students will have a mean reading rate of more than 95 wpm is 0.0418.

There are several sorts of mean in arithmetic, in particular in statistics. each implies serves to summarize a given institution of information, often to better recognize the general fee of a given record set.

They imply (aka the mathematics mean, extraordinary from the geometric imply) of a dataset is the sum of all values divided with the aid of the entire variety of values. it is the maximum commonly used a degree of crucial tendency and is regularly referred to as the “average.”

Common can truely be described as the sum of all of the numbers divided by means of the entire quantity of values. An average is described as the mathematical common of the set of or more statistics values. common is commonly described as implying or arithmetic mean. mean is really a method of describing the average of the sample.

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Using the mean concept, the ratio of the number of female attendants to the number of male attendants was of 3.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

In this problem:

Hence:

[tex]\frac{1200f + 800m}{f + m} = 900[/tex]

1200f + 800m = 900f + 900m

100m = 300f

[tex]\frac{f}{m} = 3[/tex]

Hence the ratio was of 3.

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Answer:

64

Step-by-step explanation:

if there 2 to begin with and the bacteria dobles every hour and there were 6 hours it would be 2⁶ and when you time 2 to the power of 6 you get 64

Answer:

1. 3 terms; degree 5

2. 2 terms; degree 3

3. 9mn³ + 14mn²

4. 9a^4b^3

Step-by-step explanation:

Problems 1 - 2:

Each product of a number and variables is a term. The number may be 1, so it is not written. Also, a term may not have a variable.

The degree of a term is the sum of the exponents of all the variables of the term. A plain variable, such as x has an exponent of 1 which is not written but must be added to determine the degree.

The degree of the polynomial is the same as the degree of the term with the highest degree.

1.

3 terms

degree 5

2.

2 terms

degree 3

Problems 3 - 4:

Combine like terms. Like terms have the same variables and exponents.

3.

6mn³ - mn² + 3mn³ + 15mn² =

= 6mn³ + 3mn³ - mn² + 15mn²

= 9mn³ + 14mn²

4.

a^4b^3 + 8a^4b^3 =

= 1a^4b^3 + 8a^4b^3

= 9a^4b^3

The rewritten equation for the given equation is [tex]x=\frac{h+g}{-f}[/tex]. So, option C is correct.

A linear equation given in the form ax + b = c can be rewritten to solve for x as below:

ax + b = c

⇒ ax = c - b

∴ x = (c - b)/a

So, here the basic operations such as addition, subtraction, multiplication, and division are used on both sides to rewrite the given equation for solving x.

Given equation is -fx - g = h

Step 1: Adding 'g' on both sides

-fx - g + g = h + g

⇒ -fx = h + g

Step 2: Dividing by '-f' on both sides

-fx = h + g

⇒ -fx/-f = (h + g)/-f

∴ x = (h + g)/-f

Therefore, the rewritten equation to solve for x is x = (h + g)/-f.

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Disclaimer: The given question was incomplete in the portal. Here is the complete question.

Question: Select the correct answer. which equation is correctly rewritten to solve for x?

Equation: -fx = h + g

A. x = (g - h)/f

B. x = (h - g)/-f

C. x = (h + g)/-f

D. x = (h + g)/f

Answer: 1/8

Step-by-step explanation:

Answer:

The correct answer is 15.

Step-by-step explanation:

We are given that the original sides BC is 5.  To find the length of B'C' we take the side of BC and multiply it by the scale factor.

5 (original BC) x 5 (the given scale factor) = 15

Answer:

15

Step-by-step explanation:

correct on edge 2023

[tex]x = y + 5 \\ y = x - 5[/tex]

[tex]x = \frac{3}{8} y \\ y = \frac{8}{3}x [/tex]

[tex]x = - y - 2 \\ y = - 2 - x[/tex]

[tex]x = 6y + 1 \\ 6y = x - 1 \\ y = \frac{x - 1}{6} [/tex]

[tex]x = y - 11 \\ y = x + 11[/tex]

[tex]x = 8y \\ y = \frac{x}{8} [/tex]

[tex]x = \frac{ - 1}{3} y \\ y = - 3x[/tex]

[tex]basically \: flip \: x \: and \: y \: then \: solve \: for \: y[/tex]

Answer:

[tex]\frac{23}{90}[/tex]

Step-by-step explanation:

we require 2 equations with the recurring digit placed after the decimal point.

let x = 0.2555.. ( multiply both sides by 10 and 100 )

10x = 2.555... (1)

100x = 25.555.... (2)

subtract (1) from (2) thus eliminating the recurring digits

90x = 23 ( divide both sides by 90 )

x = [tex]\frac{23}{90}[/tex]

Answer:

[tex]\sf \dfrac{23}{90}[/tex]

Step-by-step explanation:

  x = 0.25555.....  --------------(I)

Number of non-recurring digits is 1. So, multiply equation (I) by 10.

10x = 2.5555.... --------------(II)

Number of recurring digits is 1. So, multiply equation (II) by 10.

 100x = 25.5555...... (III)

Subtract equation (II) from (III)

     100x = 25.5555........

       10x =    2.5555.......

    -             -                      

         90x = 23

             x = 23/90

Answer:

I don't think the answer is in the options.

Answer:

95

Step-by-step explanation:

We know the measure of angle 4 is 85, therefore the measure of angle 2 is also 85.

Measure 2 is equal to measure 6, therefore measure 6 also equals 85, measure 8 equals measure 6 giving it the measure of 85.

Now the sum of angles 5 and 7 must equal 190, given we have two 85 degree angles, and the other two are equal, they must sum to 190, since they are equal we will divide 190 into 2, making angles 5 and 7 have a measure of 95.

Answer: 95°

Step-by-step explanation: With 2 parallel lines cut by a transversal, the following conditions are true.

Alternate interior angles are congruent. <4 and <6 are alternate interior angles, and so are <3 and <5.

Corresponding angles are congruent. Corresponding angles are angles that are in the same position in one line as the other. <1 and <5 are corresponding angles, and <4 and <6 are congruent. <2 and <6 are congruent, and <3 and <7 are congruent.

Vertical angles are congruent. Angles that are directly diagonal on the same line are congruent. <5 and <7, and <6 and <8 are examples of this.

Supplementary angles are, well, supplementary. By definition, two angles that are supplementary add up to 180°. Supplementary angles are angles that are on the same line and transversal, but not vertical angles. Rather, the angles are right next to teach other.

Alternate exterior angles are congruent. Alternate exterior angles are angles that are like alternate interior angles, but both share a position on the outside (and are diagonal.) The alternate exterior angles are <2 and <8, and <1 and <7.

Now that we have all definitions and conditions at hand, this will be easy.

If m<4 is 85°, and we want m<5, then we can see that <4 and <3 are supplementary angles. So by definition, <4 + <3 = 180°. We can substitute in <4 since we know it. We get 85° + <3 = 180°. Subtracting 85° from both sides, we get <3 = 95°.

Now we see <3 and <5 are alternate interior angles. By definition they are congruent. Thus, m<5 is 95° too.

Hope this helped!

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The perimeter of a rectangle is the sum of its side lengths.

A rectangle is special in that sides opposite one another have equal length. So if [tex]x[/tex] is the length of the horizontal sides, the total perimeter of the rectangle is

[tex]4\,\mathrm{cm} + 4\,\mathrm{cm} + x\,\mathrm{cm} + x\,\mathrm{cm} = (8+2x)\,\mathrm{cm}[/tex]

We're given the perimeter is actually 18 cm, so

[tex]8+2x = 18[/tex]

Solve for [tex]x[/tex].

[tex](8 + 2x) - 8 = 18 - 8[/tex]

[tex]2x = 10[/tex]

[tex]\dfrac12 \cdot 2x = \dfrac12 \cdot 10[/tex]

[tex]\boxed{x = 5}[/tex]

Answer: B, D, E

Step-by-step explanation:

Answer:

-6, -15

Step-by-step explanation:

Each term is 9 less than the previous term.

Answer:

? = 4

Step-by-step explanation:

4/5 = 4/1 x 1/5

4/5 = 4/5

Answer:

pretzel: 2

hotdog: 3

Step-by-step explanation:

Let h be the hotdog price and p the pretzel price.

We know that:

h + p = 5

and

2h + 3p = 12

We can solve this system of equations:

h = 5-p

2(5-p) + 3p = 12

So the second eq. becomes:

10 - 2p + 3p = 12

10 + p = 12

p = 2

Sub in the first:

h = 5 - p = 5-2 = 3

So p = 2, h = 3

Answer: $3 / hot dog

Step-by-step explanation:

Given information:

1 hot dog + 1 pretzel = $5

2 hot dogs + 3 pretzels = $12

Set variables:

Let x be the price per hot dog

Let y be the price per pretzel

Set system of equations:

x + y = 5

2x + 3y = 12

Multiply the first equation by 3:

3x + 3y = 15

2x + 3y = 12

Subtract the second equation from the first equation (Elimination):

(3x + 3y) - (2x + 3y) = 15 - 12

3x + 3y - 2x - 3y = 3

(3y - 3y) + 3x - 2x = 3

0 + x = 3

[tex]\boxed{x=3}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Angle CAB and angle CBA are congruent.

Step-by-step explanation:

Isosceles triangles have two sides of equal length as well as two congruent base angles.

Answer:

b

Step-by-step explanation:

Answer:

The plane's resultant vector is 890.3 miles, at an angle of 59.5° west of north.

Step-by-step explanation:

• To find the magnitude of the resultant vector, we have to use Pythagoras's theorem:

[tex]\boxed{a^2 = b^2 + c^2}[/tex]

where:

a ⇒ hypotenuse (= resultant vector = ? mi)

b, c ⇒ the two other sides of the right-angled triangle (= 452 mil North, 767 mi West).

Using the formula:

resultant² = [tex]452^2 + 767^2[/tex]

⇒ resultant =  [tex]\sqrt{452^2 + 767^2}[/tex]

⇒ resultant = 890.3 mi

• To find the direction, we can find the angle (labeled x in diagram) that the resultant makes with the north direction:

[tex]tan (x) =\frac{767}{452}[/tex]

⇒ [tex]x = tan^{-1} (\frac{767}{452} )[/tex]

⇒ [tex]x = \bf{59.5 \textdegree}[/tex]

∴ The plane's resultant vector is 890.3 miles, at an angle of 59.5° west of north .

Answer:

[tex]\displaystyle Approximately\:59°\:at\:a\:magnitude\:of\:approximately\:890\:miles[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:\theta \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:\theta \\ \frac{OPPOCITE}{ADJACENT} = tan\:\theta \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:\theta \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:\theta \\ \frac{ADJACENT}{OPPOCITE} = cot\:\theta[/tex]

We must use trigonometry to help us find the direction of the aeroplane's resultant vector. Do as I do:

[tex]\displaystyle \frac{452}{767} = cot\:x \hookrightarrow cot^{-1}\:\frac{452}{767} = x; 59,488772482...° = x \\ \\ \boxed{59° \approx x}[/tex]

Now, we will use the Pythagorean Theorem to find the magnitude of the aeroplane's resultant vector. Do as I do:

[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 767^2 + 452^2 = c^2 \\ \sqrt{792593} = \sqrt{c^2}; 890,27692321... = c \\ \\ \boxed{890 \approx c}[/tex]

Therefore, the direction and magnitude of the aeroplane's resultant vector are approximately eight hundred ninety miles at an angle of elevation of fifty-nine degrees.

I am joyous to assist you at any time.

The relationship of the data can be classified as a fairly strong positive correlation.

Correlation is a statistical measure used to measure the relationship that exists between two variables.

Positive correlation is when two variables move in the same direction. If one variable increases, the other variable also increases. When there is a positive correlation, the graph of the variables is upward sloping

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Using a proportional relationship, it is found that Sam buys milk at a lower rate, of $3.4 per gallon.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

Researching the problem on the internet, Edwin's graph goes through (2,7), hence the price is:

p = (7/2)g = 3.5g.

3.5 > 3.4, hence Sam buys milk at a lower rate, of $3.4 per gallon.

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Answer:

B.) as x --> -∞, f(x) --> ∞ and x --> ∞, f(x) --> ∞

Step-by-step explanation:

F(x) is another way of representing "y". That being said, the question is asking you the behavior of the graph in terms of the y-axis. On both sides of the function, there is an arrow pointing upwards, towards infinite, positive y-values. Therefore, as "x" approaches -∞ and ∞, f(x) is approaching ∞ (positive infinity).

Answer:

6) Selling price =  ₹ 1608

   Labelled price =  ₹ 2010

7) Profit percentage = 10.5%

Step-by-step explanation:

Finding the selling price:

6) Cost Price =  ₹ 1200

          [tex]\sf Profit = 33\dfrac{1}{3} \% * Cost\ price\\\\[/tex]

                    [tex]\sf = \dfrac{102}{300}*1200\\\\ = 102 * 4\\\\[/tex]

                    =  ₹ 408

Selling price = Cost price + Profit

                     = 1200 + 408

                     =  ₹ 1608

      Let the labelled price = x

             Discount % = 20%

     (100-20)% of x  = 1200 + 408

            80%  of  x  = 1608

                           [tex]\sf x = 1608*\dfrac{100}{80}\\\\[/tex]

                           x = ₹ 2010

Answer: Selling price =  ₹ 1608

             Labelled price =  ₹ 2010

7) Let the Cost price =  ₹ X

Marked price = (100 + 30)% of  Cost price

                       [tex]\sf = \dfrac{130}{100}X\\\\ = 1.3 X[/tex]

Discount% = 15%

Selling price = (100 - 15)% of 1.3X

                     = 85% * 1.3X

                     = 0.85 * 1.3X

                     = 1.105X

[tex]\sf \boxed{\bf Profit \% =\dfrac{Selling \ price - Cost \ Price}{Cost \ price }*100}[/tex]

             [tex]\sf = \dfrac{1.105X - X}{X}*100\\\\ = \dfrac{0.105X}{X}*100\\\\ = 0.105*100\\\\ = 10.5 \%[/tex]

[tex]y = \frac{1}{mx} [/tex]

[tex]11 = \frac{1}{8m} [/tex]

[tex]m = \frac{1}{88} [/tex]

[tex]y = \frac{1}{ \frac{1}{88}x } = \frac{88}{x} [/tex]

[tex]when \: x = 2 \\ y = \frac{88}{2} = 44[/tex]

Answer:

(2x + 20) ft^2.

Step-by-step explanation:

Area  = length * width

         =   2 * (x + 10)

         = (2x + 20) ft^2.