Write an equation for each line in slope-intercept form.

The linear equation in slope-intercept form for the velocity of sound as a function of temperature is v = 0.068T + 293.2, where v is the velocity of sound and T is the temperature in degrees Celsius. Using this equation, the velocity of sound at 60°C is 339.6 m/s.

The velocity of sound in dry air increases as the temperature increases. At 40°C, sound travels at a rate of about 355 m/s, and at 49°C, it travels at a rate of about 360 m/s. To write a linear equation in slope-intercept form for the velocity of sound as a function of the temperature, first calculate the slope of the line by finding the difference in velocity divided by the difference in temperature: (360 - 355) / (49 - 40) = 0.068. This slope can be written as the coefficient of the T-term in the equation. To find the y-intercept, plug in the temperature at which the velocity was measured (40°C) and the corresponding velocity (355 m/s) into the equation of the form v = mT + b. Solving for b yields 293.2. Therefore, the linear equation in slope-intercept form is v = 0.068T + 293.2. To find the velocity of sound at 60°C, plug in 60 for T in the equation and solve for v, which yields 339.6 m/s.

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Answer:

x = 3

Step-by-step explanation:

Jacob has 1/2 of a container of trail mix.

He is filling snack packs that each use about 1/6 of a container

We need to find the number of snack packs can Jacob make. Let he can make x snack packs.

\(\dfrac{1}{6}x=\dfrac{1}{2}\\\\x=3\)

Hence, he can make 3 snack packs.

9514 1404 393

Answer:

   2/3x -1/4

Step-by-step explanation:

It might be easier to start off by multiplying the expression by 12.

  p = 5/6x-5/12x-1/3+1/4x+1/12  . . . . . . . we have named the expression "p"

  12p = 10x -5x -4 +3x +1 . . . . . . . . clear fractions

  12p = x(10 -5 +3) +(-4 +1) . . . . collect terms

  12p = 8x -3

Now, we can divide by 12 and reduce the fractions.

  p = 8/12x -3/12 = 2/3x -1/4

Answer:

The answer is 13x2 + 10x - 11

Step-by-step explanation:

if you find the area of each square/rectangle and add them together, you get that answer

Answer:

D is the answer.

Step-by-step explanation:

area of a rectangle : length * breadth

here first rectangle has breath: 5x+3 and length 2x-1

                       : 10x²-5x+6x-3

                       : 10x²+x-3

here 2nd rectangle has breath: (3x-2) and length: (x+4)

                                    : 3x²-2x+12x-8

                                    : 3x²+10x-8

                                 : 13x²+11x-11

Therefore D is correct answer.

Answer:

x=11

Step-by-step explanation:

51-x-5*19= -5x

51-5*19= -4x

4x=5*19-51

4x=95-51

4x=44

x=11

Step-by-step explanation:

let x year ago son age was 5 time his father age.

age of son before x year = 19-x

age of father before x year = 51-x

NOW

according to the question

5(19-x) =51-x

95-5x =51-x

95-51 = -X-5x

44 = 4x

x=11

so your ans is 11years ago

Answer:

8,874%

Step-by-step explanation:

Find percent of change by finding the differnce between the original price and new price. You can then use a proportion "change/original = percent/100"

Answer:

10 units

Step-by-step explanation:

1. Do the square in the middle

2 x 2 = 4

2. Do the triangle on the left

2 x 2 divided by 2 = 2

3. Do the triangle on the right

4 x 2 divided by 2 = 4

4. Add them all up

4 + 2 + 4 = 10

The scale of the diagram as described in the task content is; 1: 8 where k= 8.

It follows from the task content that the original length of the room in discuss is 8cm. It therefore follows that the length of the room in the scale diagram is 1cm. On this note, the scale of the diagram in discuss is; 1 : 8 as 1cm on the diagram corresponds to 8cm actual length.

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The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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Answer:

Step-by-step explanation:

357

987

457

hope that help

mark me brill !!

Answer: -70

Step-by-step explanation:

1. You subtract 5-7 because of PEMDAS and you get -2

2. multiply  5x7=35

3. Multiply 35x-2=-70

Parentheses/brackets

Exponents

Multiplication

Division

Addition

Subtraction

Answer:

D

Step-by-step explanation:

from the question;

we to find |x| when x = 15 and when x = -15

by definition of absolute value we have

Thats for every value of x, the absolute value is always positive

Hence,

Also

Therefore the correct answer is

Both values are 15

option B

The break - even point is 5.

C=15x + 150

R=45x

Here, C = R

15x + 150 = 45x

30x = 150

x = 5

The break - even point is 5

                                                 = 225

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Answer:

yes beacuse he have nice grapics and u can play with your friends.

Step-by-step explanation:

Answer: Yes it is very good i recommend getting it, but it takes a ton of time to get use to it.

Step-by-step explanation:

Answer:

a) Malvern - Sheridan - Pine Bluff

b) Camden - Fordyce - Pine Bluff

c) Benton - Malvern - Sharidan - Arkadepia

d) Benton - Malvern - Sharidan - Arkadepia - Gurden - Camden - Fordyce

e) Benton - Malvern - Sharidan - Arkadepia - Gurden - Camden

Step-by-step explanation:

P.S - The exact question is -

Given - According to a map of Arkansas, a number of good roads connect

some of the towns south of Little Rock. The road between

Malvern and Benton is 23 miles long, and between Benton and Pine

Bluff is 62 miles long. The road between Malvern and Sheridan is

28 miles long, and then from Sheridan to Pine Bluff is 22 miles

long. Arkadelphia is connected to two towns: it is 12 miles from

Gurden and 21 miles from Sheridan. Fordyce has three roads to

these towns: 45 miles to Pine Bluff, 39 miles to Sheridan, and 27

miles to Camden. The road from Gurden to Camden is 38 miles.

To find - Unfortunately, the road from Fordyce to Sheridan is closed due to

dangerous road conditions caused by the recent bad weather. Find

the shortest route between each pair of towns:

a) Malvern and Pine Bluff

b) Camden and Pine Bluff

c) Benton and Arkadelphia

d) Fordyce and Malvern

e) Benton and Camden

Proof -

The figure is as follows :

a)

Shortest route between Malvern and Pine Bluff :

Firstly, put all the vertices to  ∞

Start from Malvern ,

Check the shortest distance from the corresponding vertices of Malvern.

Shortest Distance = min { Malvern - Benton, Malvern -Sheridan }

                              = min { 23, 28 } = 23

⇒Shortest distance is 23 ( Malvern -Benton )

Now,

Check shortest distance from Benton and Malvern

Shortest Distance = min { Benton - Pine Bluff, Malvern -Sheridan }

                              = min { 62, 28 } = 28

⇒Shortest distance is 28 ( Malvern -Sheridan )

Now,

Check shortest distance from Benton and Sheridan

Shortest Distance = min { Benton - Pine Bluff, Sheridan - Pine-Bluff}

                              = min { 85, 50 } = 50

⇒Shortest distance is 50 ( Sheridan - Pine-Bluff )

So,

By back tracking , we get

Shortest Route be -

Malvern - Sheridan - Pine Bluff

And the Shortest distance be = 50 miles

b)

Shortest Route between Camden and Pine Bluff

From Camden -

Shortest Distance = min {Camden-Fordyce, Camden-Gurden }

                              = min { 27, 38 } = 27

⇒Shortest Distance = 27 (Camden-Fordyce )

Now,

Check Shortest distance from Camden and Fordyce

Shortest Distance = min { Camden-Gurden, Fordyce-Pine Bluff }

                              = min { 38, 72 } = 38

⇒Shortest Distance = 38 ( Camden-Gurden )

Now,

Check Shortest Distance from Gurden and Fordyce

Shortest Distance = min { Gurden-Arkadepia, Fordyce-Pine Bluff }

                              = min { 50, 72 } = 50

⇒Shortest Distance = 50 ( Gurden-Arkadepia )

Now,

Check Shortest Distance from Arkadepia and Fordyce

Shortest Distance = min { Arkadepia - Sharidan, Fordyce-Pine Bluff }

                              = min { 71, 72 } = 71

⇒Shortest Distance = 71 ( Arkadepia - Sharidan )

Now,

Check Shortest Distance from Sharidan and Fordyce

Shortest Distance = min { Sharidan - Pine Bluff , Fordyce-Pine Bluff }

                              = min { 93, 72 } = 72

⇒Shortest Distance = 72 ( Fordyce-Pine Bluff )

So, By Back tracking , we get

Shortest route be

Camden - Fordyce - Pine Bluff

Shortest Distance be 72 miles

c)

Shortest route between  Benton and Arkadelphia

By applying the same method ,

If we start from Benton and by using Pine bluff lane, distance be 62 + 45 + 27 + 38 + 12 = 184 miles

And

If we start from Benton and by using Malvern lane, distance be 23 + 28 + 21 = 72 miles

So,

Shortest Route be -

Benton - Malvern - Sharidan - Arkadepia

Shortest distance be 72 miles

d)

Shortest route between  Fordyce and Malvern

By applying the same method ,

If we start from Malvern and by using Benton lane, distance be 23 + 62 + 45 = 130 miles

And

If we start from Malvern and by using Sharidan lane, distance be 28 + 21 + 12 + 38 + 27 = 126 miles

So,

Shortest Route be -

Benton - Malvern - Sharidan - Arkadepia - Gurden - Camden - Fordyce

Shortest distance be 126 miles

e)

Shortest route between Benton and Camden

By applying the same method ,

If we start from Benton and by using Pine Bluff lane, distance be 62 + 45 + 27 = 134 miles

And

If we start from Benton and by using Malvern lane, distance be 23 + 28 + 21 + 12 + 38 = 122 miles

So,

Shortest Route be -

Benton - Malvern - Sharidan - Arkadepia - Gurden - Camden

Shortest distance be 122 miles

Answer:

Step-by-step explanation:

Since two angles of △ABC are congruent to two angles of △PQR, the third pair of angles must also be congruent, so ∠C≅∠R, and △ABC≅△PQR by ASA. The corresponding congruent angles are: ∠A≅∠P, ∠B≅∠Q, ∠C≅∠R. The corresponding congruent sides are: AB ≅ PQ, BC ≅ QR, AC ≅ PR.

The two options that could result from combining two linear functions with addition are "16x – 12" and "17x – 12". The r to your question is:

To combine two linear functions with addition, you simply add the coefficients of the same variables. For example, if you have the functions 3x + 4 and 2x - 5, when you combine them with addition, you add the coefficients of x and the constant terms. So, 3x + 4 + 2x - 5 becomes (3 + 2)x + (4 - 5) = 5x - 1.

To combine two linear functions with multiplication, you multiply the coefficients of the same variables. For example, if you have the functions 3x + 4 and 2x - 5, when you combine them with multiplication, you multiply the coefficients of x and the constant terms. So, (3x + 4)(2x - 5) becomes

(3 * 2)x^2 + (3 * -5)x + (4 * 2x) + (4 * -5)

= 6x^2 - 15x + 8x - 20

= 6x^2 - 7x - 20.

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Answer:

A. ∠A is acute.

Step-by-step explanation:

An acute angle is any angle < 90°

===========================================================

Explanation:

12.32 rounds to 12.3 when rounding to the nearest tenth (aka one decimal place). The digit in the tenths place stays the same because the next digit over is not 5 or larger.

7.636 rounds to 7.6 when following the same rule

Adding those two rounded values gets us 12.3+7.6 = 19.9

The absolute value of the test statistic is 2.18. In hypothesis testing, we compare the test statistic to critical values to determine if we can reject the null hypothesis.

To test the claim that the proportion of women who voted for the proposition is greater than the proportion of men who voted for the proposition, we can use a two-sample z-test for proportions.

First, we calculate the sample proportions for women and men. For women, the sample proportion is 22/42 = 0.52, and for men, the sample proportion is 11/70 = 0.157.

Next, we calculate the standard error of the difference in proportions. Using the formula:

SE = sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))

where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes, we get:

SE = sqrt((0.52 * (1 - 0.52) / 42) + (0.157 * (1 - 0.157) / 70)) = 0.094

Now, we calculate the test statistic using the formula:

test statistic = (p1 - p2) / SE

Substituting the values, we have:

test statistic = (0.52 - 0.157) / 0.094 ≈ 2.18

The absolute value of the test statistic is 2.18. In hypothesis testing, we compare the test statistic to critical values to determine if we can reject the null hypothesis. If the absolute value of the test statistic is greater than the critical value, we have evidence to support the claim. In this case, if the critical value corresponds to a desired level of significance, and it is less than 2.18, we would reject the null hypothesis and conclude that the proportion of women who voted for the proposition is indeed greater than the proportion of men who voted for the proposition.

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Notice that the given equations are lines in slope-intercept form.

The slope of both equations is 5, but its y-intercepts are different, therefore the graphs of the given equations are different parallel lines, therefore, they have no common points.

Since the graphs of the equations have no common points the system of equations has no solutions.

Answer: No solution.

The probability that a single randomly selected value from a population with a normal distribution, where the mean (μ) is 189.2 and the standard deviation (σ) is 83.2, falls between 195.2 and 214.1 is approximately 0.1632.

To find the probability, we can standardize the values using the z-score formula: z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.

For 195.2:

z1 = (195.2 - 189.2) / 83.2 = 0.0721

For 214.1:

z2 = (214.1 - 189.2) / 83.2 = 0.2983

Using a standard normal distribution table or a calculator, we can find the area under the curve between these z-scores, which represents the probability:

P(195.2 < x < 214.1) = P(0.0721 < z < 0.2983) ≈ 0.1632

Therefore, the probability that a single randomly selected value falls between 195.2 and 214.1 is approximately 0.1632.

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Complete question is in the image attached below

528 burgers and 322 orders of fries were sold on Saturday.

At Shake Shack in Center City, the delivery truck was unable to drop off the usual order. The restaurant was stuck selling ONLY burgers and fries all Saturday long. 850 items were sold on Saturday. Each burger was $5.79 and each order of fries was $2.99 for a grand total of $4,019.90 revenue on Saturday. How many burgers and how many orders of fries were sold?

:The number of burgers and orders of fries sold can be calculated using the following algebraic equation:

5.79B + 2.99F = 4019.90

where B is the number of burgers sold and F is the number of orders of fries sold. To solve for B and F, we need to use the fact that a total of 850 items were sold on Saturday.B + F = 850F = 850 - BSubstitute 850 - B for F in the first equation:

5.79B + 2.99(850 - B) = 4019.905.79B + 2541.50 - 2.99B

= 4019.902.80B = 1478.40B

= 528.71 burgers were sold on Saturday.

To find out how many orders of fries were sold, substitute this value for B in the equation

F = 850 - B:F = 850 - 528F

= 322

Therefore, 528 burgers and 322 orders of fries were sold on Saturday.

:Thus, it can be concluded that 528 burgers and 322 orders of fries were sold on Saturday.

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Answer:

Blank above the 3: 9

Blanks underneath the 593: 540

Blanks underneath the line: 53

Blank by the "R": 53

Step-by-step explanation:

Simply divide.

It is true that the existence of two local maxima does not guarantee the presence of a local minimum. It is possible for a function to have multiple local maxima and no local minimum.

For example, consider the function f(x,y) = x^4 - 4x^2 + y^2. This function has two local maxima at (2,0) and (-2,0), but no local minimum. Therefore, the statement "if f(x,y) has two local maximal, then f must have a local minimum" is false. The presence or absence of local maxima and minima depends on the behavior of the function in the immediate vicinity of a point, and cannot be determined solely based on the number of local maxima. It is possible for a function to have an infinite number of local maxima and minima, or none at all. Therefore, it is important to carefully analyze the behavior of a function in order to determine the presence or absence of local extrema.

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The area of the given trapezoidal site is 250,000 sq. ft.

The area of the trapezoidal with the dimensions of both bases and the height is given by the formula,

Area = 1/2 × height × (base1 + base2)

Units: square units

The given trapezoidal site has a base of 150 feet, i.e., base1 = 150 ft; a height of 2000 ft, i.e., height = 2000 ft and a parallel base of 100 feet, i.e., base2 = 100 ft.

Then, the area of the trapezoidal is

= 1/2 × 2000 × (150 + 100)

= 1/2 × 2000 × 250

= 250,000 sq. ft

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Since you have the hypotenuse and the adjacent length, you have to use the trigonometric ratio cosine to

solve for x. Formulating the equation we have: