Write an equation of the line in slope-intercept form.
Ay
4
y =
(0, 2)
2
(3, 3)
4
AX

Answer:

[tex]\left.\dfrac{\text{d}x}{\text{d}t}\right|_{h=2}\approx0.184\; \sf m/s[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

Given variables:

Given a = 8.9, use Pythagoras Theorem to create an equation for x² in terms of h²:

[tex]\implies x^2+h^2=a^2[/tex]

[tex]\implies x^2+h^2=8.9^2[/tex]

[tex]\implies x^2+h^2=79.21[/tex]

[tex]\implies x^2=79.21-h^2[/tex]

Differentiate with respect to h:

[tex]\implies 2x\dfrac{\text{d}x}{\text{d}h}=0-2h[/tex]

[tex]\implies \dfrac{\text{d}x}{\text{d}h}=-\dfrac{2h}{2x}[/tex]

[tex]\implies \dfrac{\text{d}x}{\text{d}h}=-\dfrac{h}{x}[/tex]

Given:

[tex]\dfrac{\text{d}h}{\text{d}t}=-0.8\; \sf m/s[/tex]

Therefore:

[tex]\begin{aligned} \dfrac{\text{d}x}{\text{d}t}&=\dfrac{\text{d}x}{\text{d}h}\times \dfrac{\text{d}h}{\text{d}t}}\\\\ \implies &=-\dfrac{h}{x} \times -0.8\\\\ &=\dfrac{0.8h}{x} \end{aligned}[/tex]

Calculate x when h = 2:

[tex]\implies x^2=79.21-2^2[/tex]

[tex]\implies x^2=79.21-4[/tex]

[tex]\implies x^2=75.21[/tex]

[tex]\implies x=\sqrt{75.21}[/tex]

Substitute the values of h and x into the equation for dx/dt:

[tex]\implies \dfrac{\text{d}x}{\text{d}t}=\dfrac{0.8 \times 2}{\sqrt{75.21}}=0.1844939751[/tex]

Therefore, the rate of the ladder's distance from the wall is 0.184 m/s (3 d.p.)

The property justified by step 4 is after substitution in the equation you get the desired result.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the data in the question,

In step 3 substitution of value is taking place.

In step 4 when values are substituted the final result is obtained, so step 4 is the result step.

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BC is the common side of both the triangles.

Answer:

BC

Step-by-step explanation:

Common side in both triangles is BC

    Sides of ΔABC,

                   AB ;  BC  and AC

   Sides of ΔDCB,

                  DC, BC and DB

Answer:

Step-by-step explanation:

A formula is a method that has been proven to work when solving specific types of problems.

Let’s explore some of those familiar formulas by looking at rectangles, squares, area and perimeter.

The perimeter of a figure is the distance around the figure. Perimeter is the sum of all of the sides in a square or rectangle. Since a rectangle has two sets of parallel sides, the formula for determining perimeter  of a rectangle is:

and

Let’s look at an example.

[Figure 2]

The rectangle above shows its dimensions. Find the perimeter.

First, substitute the values for the width  and the length  into the perimeter formula.

Next, complete the multiplication and addition to find the perimeter.

The answer is 42.

The perimeter of the rectangle is 42 inches.

Area is the amount of square units inside the figure. Area is found by multiplying the . The formula for finding the area of a rectangle is:

You can use the dimensions from the rectangle above to find the area of this rectangle.

First, fill the values for  and  into the formula for area.

Next, solve for the area by multiplying.

The answer is 108.

The area of the rectangle is .

Notice that the unit of measurement for area is squared. That is because you multiplied a unit measure times itself: . Area is always written in square units.

You can also find the perimeter and area of a square. Remember that a square has four equal sides given the symbol . You can use the following formula for finding the perimeter of a square:

Let’s look at an example.

A rectangle has a length of 12 feet and a perimeter of 72 feet. Write and solve an equation to determine the width of the rectangle.

First, substitute the values for the perimeter  and the length  into the perimeter formula.

Next, complete the multiplication.

Then, subtract 24 from both sides to get your variable alone on the right side.

Then, multiply both sides by the reciprocal of 2 to isolate your variable.

The answer is 24.

The width of the rectangle is 24 feet.

Examples

Example 1

Earlier, you were given a problem about Raj and his garden fence.

He knows that the area of the land is 240 square feet, the length of one side is 15 feet, and needs to know the width of the land.

First, substitute the values for the area and the side length into the area formula.

Next, multiply both sides by the reciprocal of 15 in order to isolate the variable .

The answer is 16.

The width of Raj’s garden is 16 ft. Therefore the dimensions of the garden are 16 ft by 15 ft.

Example 2

A square has a perimeter of 196 inches. Determine the length of one side of the square.

First, substitute the value for the perimeter  into the perimeter formula.

Next, multiply both sides by the reciprocal of 4 to isolate your variable.

The answer is 49.

Example 3

Find the perimeter of the following square if the side length is 4.5 inches.

First, substitute the value for the side length into the perimeter formula.

Next, multiply by 4 to solve for the perimeter.

The answer is 18.

Example 4

Can you find the area of the square in Example 1?

First, substitute the value for the side length into the area formula.

Next, multiply to solve for the area.

The answer is 20.25.

The area of the square is .

Example 5

A square has an area of 144 sq. meters. What is the side length?

First, substitute the value for the area into the area formula.

Next, take the square root of the area to isolate . Remember that the opposite of square is square root.

The answer is 12.

By using the property of similar triangles, it can be obtained that

Value of x is 7.2

What are similar triangles?

Two triangles are said to be similar if the corrosponding angles are equal and the corrosponding sides are similar.

The different axioms of similarity are-

SAS axiom, AA axiom, SSS axiom

By the property of similar triangles,

[tex]\frac{9}{9 + 6} = \frac{x}{12}\\x = \frac{9}{15} \times 12\\x = 7.2[/tex]

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The equation of the line that passes through the points (-6 , 2) and (-4 , -1) is 3x + 2y = -14 .

In the question ,

two points are given as  (-6 , 2) and (-4 , -1) .

we need to find the equation of the line passing through the given points .

to find the equation First we need to find the slope  ,

slope = (-1-2)/(-4-(-6))

slope = -3/(-4 + 6)

slope = -3/2

So , the equation of the line passing through the point (-6 , 2) with slope -3/2 is  

(y - 2) = (-3/2)(x - (-6))

y - 2 = (-3/2)(x + 6)

y - 2 = (-3/2)x - 9

y = (-3/2)x - 9 + 2

y = (-3/2)x - 7

2y = -3x - 14

3x + 2y = -14

Therefore , The equation of the line that passes through the points (-6 , 2) and (-4 , -1) is 3x + 2y = -14 .

The given question is incomplete , the complete question is

Write the equation for the line that passes through the point (-6, 2) and (-4,-1) , write the answer in fully reduced form .

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Answer:

[tex]x=\dfrac{\pi }{3}+2\pi n, \quad x=\dfrac{5\pi }{3}+2\pi n,\quad x=2\pi n,\quad x=\pi+2\pi n[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Trigonometric Double Angle Identities}\\\\$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B$\\\\$\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B$\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]

Given equation:

[tex]\tan (x + \pi) + \sin(x + \pi) + \sin(x - \pi)=0[/tex]

Simplify using the double angle identities:

[tex]\implies \dfrac{\tan x + \tan \pi}{1 -\tan x \tan \pi} + \sin x \cos \pi+\cos x \sin \pi + \sin x \cos \pi -\cos x \sin \pi=0[/tex]

[tex]\implies \dfrac{\tan x + 0}{1 -\tan x(0)} + \sin x (-1)+\cos x (0) + \sin x(-1) -\cos x (0)=0[/tex]

[tex]\implies \dfrac{\tan x}{1} -\sin x - \sin x=0[/tex]

[tex]\implies \tan x-2\sin x =0[/tex]

Use the tan identity to rewrite tan(x) in terms of sin(x) and cos(x):

[tex]\implies \dfrac{\sin x}{ \cos x}-2\sin x=0[/tex]

Multiply both sides by cos(x):

[tex]\implies \dfrac{\sin x\cos x}{ \cos x}-2\sin x\cos x=0(\cos x)[/tex]

[tex]\implies \sin x-2\sin x \cos x=0[/tex]

Factor out sin(x) from the left side of the equation:

[tex]\implies \sin x(1-2 \cos x)=0[/tex]

Apply the zero-product property.

Case 1

[tex]\implies \sin x=0[/tex]

[tex]\implies x=\sin^{-1}(0)[/tex]

[tex]\implies x=2\pi n, \; \pi+2\pi n[/tex]

Case 2

[tex]\implies 1-2 \cos x=0[/tex]

[tex]\implies 1=2 \cos x[/tex]

[tex]\implies \cos x=\dfrac{1}{2}[/tex]

[tex]\implies x= \cos ^{-1} \left(\dfrac{1}{2}\right)[/tex]

[tex]\implies x=\dfrac{\pi }{3}+2\pi n, \;\dfrac{5\pi }{3}+2\pi n[/tex]

Solution

[tex]x=\dfrac{\pi }{3}+2\pi n, \quad x=\dfrac{5\pi }{3}+2\pi n,\quad x=2\pi n,\quad x=\pi+2\pi n[/tex]

Answer:

They all come out to be infinity

The equation of the graph in the figure is f(x) = |x - 3| + 5

Given that the graph is an absolute value graph

We start by calculating the vertex of the graph

In this case, the graph has it minimum point located at the coordinate (3, 5)

This coordinate can then be interpreted as

(h, k) = (3, 5)

As a general rule, the general representation of the equation of an absolute value function is f(x) = |x - h| + k

Substitute the known values in the above equation

So, we have the following equation

f(x) = |x - 3| + 5

Hence, the equation of the graph is f(x) = |x - 3| + 5

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Answer:

The answer should be -5/2

Step-by-step explanation:

To find the slope take two plots from the table:

(-2,6) and (0,1)

M= y2-y1 / x2-x1

M= 1-6 / 0--2=-5/2

Ruth must have an initial deposit of $12000 in order to have the same simple interest at the same rate within the same time as Carter

Simple Interest (S.I) is the method of calculating the interest amount for some principal amount of money. Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

The formula of simple interest is given as

S.I = PRT

We can set up equivalent equations since both interest are equal.

S.I = P(1 + RT)

S.I = 12000(1 + 0.019 * 1)

S.I = 12228

But since they earned the same interest at the same rate within the same period, their principal or initial amount invested must be equal

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Answer:

99/6=16.5 per pizza

have u good day

Answer:

16 and a half, ($16.50)

Step-by-step explanation:

99 / 6 = 16.5

Answer:

g(x)=(-5x+2)+5

Step-by-step explanation:

For each of the arithmetic sequences, we have that:

a)

b)

c)

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the following rule:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term of the sequence.

For the sequences in this problem, we have that:

Then the general rule is applied to find the nth term of the sequence, while the next two terms are found adding the common ratio.

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Answer:

you have to add x outside of the parentheses

Step-by-step explanation: hope this helps

The graph shown has two straight lines and the correct equation is

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

y = output variable

m = slope

x = input variable

c = y intercept

interpretation of the equations

4x + y = 6 ⇒ y = -4x + 6

m = -4

c = 6

from the graph only one the lines has the y intercept as 6, also the slope is negative. the line shown by at option (c) the intercept is 6/4 and the slope is positive

−2x + y = −5 ⇒ y = 2x - 5

m = 2x

c = -5

The c is not showing here but it is moving towards negative. the x intercept is showing and we can use it to confirm

y = 2x - 5

0 = 2x - 5

2x = 5

x = 2.5

this coincides with the point on the graph (2.5, 0)

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For all samples of 5, there is a 0.05 probability that the sample mean would be higher than 22 pounds.

The assortment of bags weighs 19.7 pounds on average.

3.1 pounds is the standard deviation.

The sampling distribution theorem and the normal probability density function were both utilized.

The z-score formula is used to address problems involving samples with regularly distributed data.

Mean standard deviation, the z-score of a measure X is given by:

z = (x - μ) ÷ σ

The Z-score computes the number of standard deviations. The metric used is the average.

After calculating the Z-score, we look at the p-value associated with it in the z-score table.

This p-value represents the probability that the measure's value is smaller than X, or the percentage of X.

By taking away 1, we can determine the chance that the measure surpasses X.

If n is at least 30, the Central Limitation Theorem can also be applied to variables that are skewed.

No of the sample size, the sample mean will always be the same.

However, the standard error will change.

P(a > 22) denotes the likelihood that the sample means will be greater than 22.

The likelihood that they give it a chance will weigh more than 22 pounds is around 0.05 for all sampling of size 5.

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The probability that a young adult chosen at random will achieve an IQ between 85 and 160 is 0.8185.

The problem states that;

A typical IQ test result for individuals between the ages of 20 and 34 has a mean of 110 and a standard deviation of 25, and the values are regularly distributed.

To get the probability that a randomly selected young adult will score between 85 and 160 on this IQ test.

Let,

P(85 < x < 160) = P[ (85 - 110)/ 25) < (x - μ) / σ < (160 - 110) / 25) ]

                        = P(-1 < z < 2)

                        = P(z < 2) - P(z < -1)

                        = 0.9772 - 0.1587

                        = 0.8185

Therefore, the probability that a randomly selected young adult will score between 85 and 160 on this IQ test is 0.8185.

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Answer:

Step-by-step explanation:

5/6 is closest to 1 and 2/5 is closest to 1/2 so the difference is closest to 1/2.

The percentage statement 28 is 35% of 80 is written in the form

a/b = p/100 as 28/80 = 35/100.

For the given question.

The statement defining the percentage is ;

28 is 35% of 80.

This can be written as;

35% of 80 = 28

Solve percentage.

35×80/100 = 28

35/100 = 28/80

Or,

28/80 = 35/100

This is the form

a/b = p/100

a = 28

b = 80

p = 35

Thus, the percentage statement 28 is 35% of 80 is written in the form

a/b = p/100 as 28/80 = 35/100.

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The probability that the price of the used car is less than $65 is 0.55962.

Here it is given that the price of the used car has a mean of $50 and a variance of $100.

Since it follows normal distribution X~N(μ, σ²)

where,

μ = 50

σ = 100

Here we need to find the probability P(X < 65)
To find this we need to convert the distribution to the standard normal form, N~(0, 1)

We know,

P(X < (x - μ)/ σ) = Φ(Z)

Therefore we get

P(X < (65 - 50)/ 100)

Solving this we get the Z value

= Φ(0.15)

From the Z table, we can get our p-value.

= 0.55962

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Answer:

first and third

Step-by-step explanation:

the equation representing direct proportion is

y = kx ← k is the constant of proportion

y = - 4x is in this form with k = - 4

y = 7x is in this form with k = 7

The simple regression line is used to estimate the population regression line.

We are asked about, the simple regression line

We have options:

a. is estimated by the population regression line.

b. maximizes the sum of the squared differences between the data points in a sample and the sample regression line.

c. shows the actual (or true) relation between the dependent and independent variables.

d. is used to estimate the population regression line.

e. connects the data points in a sample.

From the above options, Option (d) is the correct one i.e. is used to estimate the population regression line.

The simple regression line is used to estimate the population regression line.

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The scale that Wyatt has made use of based on the figures in the question is 1 inch to 0.36 yards.

Building construction would be extremely challenging without a blueprint. You'd be lost without a map! Large objects, such as roads and buildings, can be easily visualized on paper using scale drawings. Scale drawings are even used by a GPS

The scale that Wyatt has used for this drawing is given as:

84 / 231 = 0.36

We would say that for every 1 inch, Wyatt made use of 0.36yards.

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The 25 Kg weight will stretch the spring 120.84 cm .

In the question ,

it is given that

the distance(D) that spring  stretches by hanging objects vary directly to the weight(W) of the object .

which means

D ∝ W

to remove the proportionality sign , we write the constant k

So, D = k × W  ,

where k is the constant of proportionality

given that 6 Kg weight stretches the spring 29 cm

So,

29 = k * 6

k = 29/6

to find the stretch for 25 Kg weight

D = (29/6)*25

D = 120.84 cm

Therefore ,The 25 Kg weight will stretch the spring 120.84 cm .

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Answer: 2 + 0.3 +  0.05 + 0.006

Step-by-step explanation: You just have to technically un add the stuff of you understand it that way.

Hope i helped you

Have a great day Darling

The domain and the range of the function are the sets X = {- 9, - 7, - 5, - 3, - 1, 1, 3} and Y = {- 5, - 3, - 1, 1, 3, 5, 7}.

Herein we need to determine the domain and the range of a function, functions are relations such that every element of the domain is related only to one element of the range.

Graphically speaking, the domain of a function are represented by the set of x-coordinates and the range by a set of y-coordinates. The picture shows a discrete function, that is, a function with a finite set of points. Then, the domain and range are listed by the following sets:

Domain

X = {- 9, - 7, - 5, - 3, - 1, 1, 3}

Range

Y = {- 5, - 3, - 1, 1, 3, 5, 7}

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The inequality that needs to be solved is:

3t +270/ 6 ≥ 90.

let we consider that Heidi has 6 subjects in her school.

Therefore, She needs to average at least 90 on her three remaining tests to have at least a 90 overall average for all 6 tests.

Now,

To obtain an average first add up all the scores of the tests and then divide by the number of tests.

So far Heidi has taken 3 tests and we know the total number of tests will be 6 so we will be dividing by 6 to get the average of all the score.

If we let each of the three remaining tests each be represent by t, then the sum of all the tests would be:

95 + 92 + 86 + t + t + t

or

273 + 3t

The average of these 6 tests can then be represented by:

3t + 273 / 6

And for her average to be at least 90 then she can get a 90 or more which is the same as ≥ 90

So the inequality that needs to be solved is:

 [tex]\frac{3t + 273}{6}[/tex] ≥ 90

or, [tex]\frac{3 ( t + 91)}{6} \geq 90[/tex]

or, [tex]\frac{t + 91}{2} \geq 90[/tex]

Now, Heidi has to score :

t/2 ≥ 91

or, t/2 ≥ 90

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