what is the difference between slope intercept and point slope form?

George's kitten is approximately 15.23 yards away from its bed

What is distance?

Distance is a measure of the length or spatial separation between two points. It is a scalar quantity, which means it has magnitude but not direction. In physics, distance is often measured in units such as meters (m), feet (ft), kilometers (km), or miles (mi).

We can use the Law of Cosines to solve this problem. Let's call the distance from the kitten's final position to the bed "d". Then, we have:

d² = 23² + 14² - 2(23)(14)cos(140°)

d² = 529 + 196 + 644cos(140°)

d² = 529 + 196 - 644(0.766)

d² = 529 + 196 - 493.304

d² = 231.696

d = sqrt(231.696)

d ≈ 15.23

Therefore, George's kitten is approximately 15.23 yards away from its bed

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A stationary point at x = 3 means the derivative dy/dx = 0 at that point. Differentiating, we have

dy/dx = 6x ² + 2ax + b

and so when x = 3,

0 = 54 + 6a + b

or

6a + b = -54 … … … [eq1]

The curve passes through the point (4, 2), which is to say y = 2 when x = 4. So we also have

2 = 128 + 16a + 4b - 30

or

16a + 4b = -96

4a + b = -24 … … … [eq2]

Eliminate b by subtracting [eq2] from [eq1] and solve for a, then for b :

(6a + b) - (4a + b) = -54 - (-24)

2a = -30

a = -15   ===>   b = 96

To determine the function that models the data, we need to analyze the relationship between the cost per photo and the number of photos a customer buys. From the given information, we can observe that the cost per photo varies inversely with the number of photos. This implies that as the number of photos increases, the cost per photo decreases, and vice versa.

To model this relationship, we can use the inverse variation equation, which can be expressed as:

y = k/x

Here, y represents the cost per photo, x represents the number of photos, and k is the constant of variation.

Let's examine the data given in the table to find the value of k:

Number of Photos (x) Cost per Photo (y)

10 10

25 4

50 2

100 1

We can see that as the number of photos increases, the cost per photo decreases. We can use any pair of values from the table to solve for k. Let's choose the pair (50, 2):

2 = k/50

Solving for k:

k = 2 * 50 = 100

Now that we have the value of k, we can write the function that models the data:

y = 100/x

Therefore, the function that models the data is y = 100/x, where y represents the cost per photo and x represents the number of photos a customer buys.

Answer:

★ 40 over 17 is roughly 2.35294, which can be rounded to the nearest hundredth as 2.35

Step-by-step explanation:

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Answer:

where?

Step-by-step explanation:

maybe I can help to your question

The value of the expression which shows the amount he paid for lunch is 7 dollars.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and divisions.

Given that Frankie orders two hamburgers and a soda for lunch. A hamburger is $3 and a soda is $1.00.

Now here is the expression-

1+(2x3)= 2 x 3 = $6

Cost of lunch = ($3 / hamburger) (2) + ($1 / soda) (1)

Cost of lunch = $6 + $1

Cost of Frankie's  lunch = $7

Therefore, the value of the expression which shows the amount he paid for lunch is 7 dollars.

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The probability that the random sample of 100 male students has a mean gpa greater than 3. 42 is 0.9452.

A statistic known as the standard deviation is used to describe how volatile or dispersed a group of numerical values is. While a big standard deviation denotes that the values are scattered across a wider range, a low standard deviation indicates that the values tend to be close to the set mean.

From the given information, a scores random sample of 100 male students is selected and the GPA for each student is calculated which follows approximately normal with a mean of 3.5 and standard deviation of 0.5. That is,

µ = 3. 5 and σ = 0. 5

and the random sample of 100 male students has a mean GPA 3.42 is considered.

The z-score value is,

Z=( 3.42-3.5)/ (0.5/√100)

Z= -0.08/0.05

Z=-1.6

The value of z-score is obtained by taking the difference of x and µ. Then the resulting value is divided with the standard deviation by sample size.

The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is obtained below:

The required probability is,

P(X>3.42)=P(z>-1.6)

= 1- P(Z≤-1.6)

From the “standard normal table”, the area to the left of Z=-1.6 is 0.0548.

P(X>3.42)= 1- P(Z≤-1.6)

=1-0.0548

=0.9452

The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is 0.9452.

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Value of an exterior angle of a triangle is equal to the sum of values of two opposite interior angles of a triangle.

\(\qquad\displaystyle \tt \dashrightarrow \: 5x + 10 = 40 + 70\)

\(\qquad\displaystyle \tt \dashrightarrow \: 5x = 110 - 10\)

\(\qquad\displaystyle \tt \dashrightarrow \: 5x = 100\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 100 \div 5\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 20\)

Value of x = 20°

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Answer:

Step-by-step explanation:

In this question we are given with two interior angles of the triangle that are 40° and 70° , also we are given an exterior angle that is (5x + 10)°. And we are asked to find the value of angle x.

Solution :-

For finding the value of angle x , we have to use exterior angle property of triangle which states that sum of opposite interior angles of triangle is equal to the given exterior angle. So :

Step 1: Making equation :

\( \longmapsto \: \sf{40 {}^{°} + 70 {}^{°} = (5x + 10) {}^{°} }\)

Solving :

\( \longmapsto \: \sf{110 {}{°} = (5x) {}^{°} +10 {}^{°} }\)

Step 2: Subtracting 10 on both sides :

\( \longmapsto \sf{ 110 {}^{°} - 10 {}^{°} = 5x + \cancel{10 {}^{°}} - \cancel{10 {}^{°} } }\)

We get ,

\( \longmapsto \sf{(5x ){}^{°} = 100 {}^{°} }\)

Step 3: Dividing both sides by 5 :

\( \longmapsto \dfrac{ \cancel{5}x {}^{°} }{ \cancel{5}} = \dfrac{ \: \: \: \: \cancel{ 100} {°}^{} }{ \cancel{5} }\)

On cancelling , we get :

\( \longmapsto \underline{\boxed{\red{\sf{ \bold{ x = 20 {}^{°} }}}}} \: \: \bigstar\)

Verification :-

For verifying sum of both the interior angles is equal to given exterior angles. As we get the value of x as 20 we need to substitute it's value in place x and then L.H.S must be equal to R.H.S :

Therefore , our answer is correct .

Answer:

q = -15

Step-by-step explanation:

5q = -75

Divide both sides by 5 : q = -15

Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. The weight per carton is 55 pounds.

Given that twenty standard cartons of octal boxes weigh a total of 1,100 pounds. We need to find the weight per carton.

How to find the weight per carton? To find the weight per carton, we need to divide the total weight of twenty standard cartons of octal boxes by 20.Let's assume the weight of each carton be x.

Therefore, the equation can be formed asx * 20 = 1,100 Solving the above equation for x, x = 1,100/20 Therefore, the weight per carton is 55 pounds. So, twenty standard cartons of octal boxes weigh a total of 1,100 pounds.

The weight per carton is 55 pounds.

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Answer:

x=3

Step-by-step explanation:

\(-15x+32=13\\-15x=13-32\\-15x=-45\\x=-45/-15\\x=3\)

Step-by-step explanation:

To Solve This Equation You will need to

Original Equation;

-15x+32=-13

•(Firstly you will Group Like Terms)

-15x=-13-32

•(After Grouping you will go ahead and simplify)

-15x=-13-32

(You will have to add the two negative numbers and note that negative plus negative is still negative even though there is no addition sign there but you'll add them because when there is two negatives without a multiplication or division or any other sign you have to add)

-15x=-13-32

-15x=-45

(Then you proceed to divide both sides by -15)

x=3

This is because -45 divided by -15 is positive 3

Positive 3 because the negative signs cancel each other out.

Formula for slant height:

\(l = \sqrt{ {r}^{2} + {h}^{2} } \)

We dont have height so we will find it with the help of area

\( \sf \: area = \pi {r}^{2} + \sqrt{ {r}^{2} + {h}^{2} } \)

\( \sf \: 31.4 = 3.14 \times {2}^{2} + \sqrt{ {2}^{2} + {h}^{2} } \)

\( \sf \: 31.4 = 3.14 \times 4 + \sqrt{ 4 + {h}^{2} } \)

\( \sf \: 31.4 =12.56 + \sqrt{ 4 + {h}^{2} } \)

\( \sf \: 31.4 - 12 .56 = \sqrt{ 4 + {h}^{2} } \)

\( \sf \: 18.84 = \sqrt{ 4 + {h}^{2} } \)

\( \sf \: 18.84 ^{2} = 4 + {h}^{2} \)

\( \sf \: 354.9456 - 4 = {h}^{2} \)

\( \sf \: 350.9456 = {h}^{2} \)

\( \sf \: h = \sqrt{ 350.9456}\)

\( \sf \: h = 18.73\)

Now put this in the first formula to find slant height (l)

\( \tt \: l = \sqrt{ {r}^{2} + {h}^{2} } \)

\( \tt \: l = \sqrt{ {2}^{2} + {18.73}^{2} } \)

\( \tt \: l = \sqrt{ 4 + 350.8129 } \)

\( \tt \: l = \sqrt{ 354.8129 } \)

\( \tt \: l = 18.83\)

Answer:

c

Step-by-step explanation:

Its C the answer is c

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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The general solution for the equation 5tan(θ) - 6cos(θ) = 0 is:

θ = sin⁻¹(2/3) + nπ, where n is an integer.

To determine the general solution of the trigonometric equation 5tan(θ) - 6cos(θ) = 0, we can use algebraic manipulation and trigonometric identities to simplify and solve for θ.

Starting with the given equation:

5tan(θ) - 6cos(θ) = 0

First, we can rewrite the tangent function in terms of sine and cosine:

5(sin(θ)/cos(θ)) - 6cos(θ) = 0

Next, multiply through by cos(θ) to eliminate the denominator:

5sin(θ) - 6cos²(θ) = 0

Using the identity sin²(θ) + cos²(θ) = 1, we can express cos²(θ) as 1 - sin²(θ):

5sin(θ) - 6(1 - sin²(θ)) = 0

Expanding and rearranging terms:

5sin(θ) - 6 + 6sin²(θ) = 0

Rearranging the equation:

6sin²(θ) + 5sin(θ) - 6 = 0

Now, we have a quadratic equation in terms of sin(θ).

We can solve this quadratic equation by factoring or using the quadratic formula.

However, since this equation is not easily factorable, we will use the quadratic formula:

sin(θ) = (-b ± √(b² - 4ac)) / 2a

For our equation:

a = 6, b = 5, c = -6

Plugging these values into the quadratic formula and simplifying, we get:

sin(θ) = (-5 ± √(5² - 4(6)(-6))) / (2(6))

sin(θ) = (-5 ± √(25 + 144)) / 12

sin(θ) = (-5 ± √169) / 12

sin(θ) = (-5 ± 13) / 12.

This gives us two possible solutions for sin(θ):

sin(θ) = (13 - 5) / 12 = 8/12 = 2/3

sin(θ) = (-13 - 5) / 12 = -18/12 = -3/2

Since the range of the sine function is -1 to 1, the second solution (-3/2) is not valid.

Now, to find the values of θ, we can use the inverse sine function (sin⁻¹) to solve for θ:

θ = sin⁻¹(2/3)

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Answer:

4.28%

Step-by-step explanation:

We Know

Last year you earned $72,400

This year you earned $75,500

What was the rate of change in your earnings since last year?

We Take

(75,500 ÷ 72,400) x 100 ≈ 104.28%

Then We Take

104.28 - 100 = 4.28%

So, the earning increased by about 4.28%.

Answer:

S

ThenSn=n(a1+an)2Sn=n(a1 + an)2 , where nn is the number of terms, a1a1 is the first term and anan is the last term. The sum of the first nn terms of an arithmetic sequence is called an arithmetic series .

Step-by-step explanation:

Responder: 36.9

explicación paso a paso:

1771.2 / 48 = 36.9

Answer:

a = 7.9

Step-by-step explanation:

a^2 + b^2 = c^2

9^2 + 12^2 = a

9 x 9 = 81

12 x 12 = 144

144 - 81 = 63

Square root of 63 is about 7.9

Answer:

1:4

Step-by-step explanation:

To represent 14:56 as a simplified ratio, we need to reduce it by finding the GCF (greatest common factor) and dividing it by both terms.

The GCF of 14 & 56 is 14.

14 / 14 = 1

56 / 14 = 4

Thus we are left with our new simplified ratio, 1:4.

Answer:

3.999 millimeters.

Step-by-step explanation:

To find the height of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the radius (r) of the cylinder is 4 millimeters and the volume (V) is 200.96 cubic millimeters, we can substitute these values into the formula and solve for the height (h).

200.96 = π(4²)h

200.96 = 16πh

To solve for h, we can divide both sides of the equation by 16π:

200.96 / (16π) = h

Using a calculator, we can calculate the approximate value of h:

h ≈ 200.96 / (16 × 3.14159)

h ≈ 3.999

Therefore, the height of the cylinder is approximately 3.999 millimeters.

The possible score for the third test for his average to be 80 or greater is: x ≥ 91.

The average of a set of data can be described as the sum total of all the data values in the data set divided by the number of data set.

Let x represent be the third score Jim needs to score for his average to be 80 or greater.

His first two scores are, 72 and 77.

Thus, the inequality for this would be written as:

(72 + 77 + x)/3 ≥ 80

72 + 77 + x ≥ 3(80)

149 + x ≥ 240

x ≥ 240 - 149

x ≥ 91

Thus, the possible score for the third test for his average to be 80 or greater is: x ≥ 91.

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In the equation of the parabola, the value for p represents the distance between the vertex and the focus. To find it, use the formula to find the distance between 2 points:

It means that the value of p is 1/16, in decimal form, 0.0625.

The value of h is the x coordinate of the vertex, which is -2.

The value of k is the y coordinate of the vertex, which is 2.

Answer:

Natasha can wrap 128 gifts in total

Step-by-step explanation:

Let us use the ratio method to solve the question

∵ Natasha has 240 square feet of wrapping paper

∵ Natasha can wrap 8 gifts with 15 square feet

→ By using the ratio method

→  Gift  :  square feet

→   8     :  15

→   x      :  240

→ By using cross multiplication

∵ x × 15 = 8 × 240

∴ 15x = 1920

→ Divide both sides by 15

∵ x = 128

∵ x represents the number of gifts

∴ Natasha can wrap 128 gifts in total

9514 1404 393

Answer:

  +12,008,304

Step-by-step explanation:

Your calculator can tell you the product is positive. (Any product involving an even number of minus signs will be positive.)

  (-38)(378)(-836) = (38)(378)(836) = 12,008,304 . . . a positive answer

Using the concept of perimeter of polygon, the perimeter of figure C is 27cm shorter than total perimeter of A and B

To solve this problem, we have to know the perimeter of the polygon C.

The perimeter of a polygon is the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The perimeter of the figures are;

Using the concept of perimeter of a rectangle;

a. figure A = 2(4 + 11) = 30cm

b. figure B = 2(8 + 4) = 24cm

c figure C = 11 + 4 + 8 + 4 = 27cm

Now, we can add A and B and then subtract c from it.

30 + 24 - 27 = 27cm

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