What is the point-slope form of a line that has a slope of One-half and passes through point (–7, 2)? PLS HELP

Answer:

C. 31 \(\frac{1}{6}\)

Step-by-step explanation:

1. Convert mixed numbers into improper fractions:

\(\frac{29}{4}\) · 2² + ( \(\frac{17}{2}\) - 2) ÷ 3

2. Calculate within the parenthesis:

\(\frac{29}{4}\) · 2² + \(\frac{13}{2}\) ÷ 3

3. Calculate the exponent:

\(\frac{29}{4}\) · 4 + \(\frac{13}{2}\) ÷ 3

4. Multiply and divide (left to right):

29 + \(\frac{13}{2}\) ÷ 3

29 + \(\frac{13}{6}\)

5. Add:

\(\frac{187}{6}\)

6. Convert the improper fraction to a mixed number:

= 31 \(\frac{1}{6}\)

hope this helps!

Answer:

9

Step-by-step explanation:

45 seconds / 2 cars at a time = 22.5

22.5 x 16 carts = 360 seconds or 6 minutes

6 minutes / 2 cars at a time = 3

3 x 3 = 9

(1) The altitude of the triangle is increasing at a rate of 0.4 cm/min when the altitude is 20 cm and the area is 80 cm².

(2) We can solve for (ds/dt), the rate at which the shadow is growing.

(3) We can solve for (dh/dt), the rate at which the height is growing, when h = 3 m.

(1)To find the rate at which the altitude of the triangle is increasing, we can use the formula for the area of a triangle and differentiate it with respect to time.

Let A be the area of the triangle, b be the base, and h be the altitude. We have the formula for the area of a triangle:

A = (1/2) * b * h

Differentiating both sides with respect to time t:

dA/dt = (1/2) * (db/dt) * h + (1/2) * b * (dh/dt)

Given that dA/dt = 4 cm²/min and db/dt = 1 cm/min, we can substitute these values into the equation:

4 = (1/2) * 1 * 20 * (dh/dt)

Simplifying the equation:

4 = 10 * (dh/dt)

Now we can solve for (dh/dt):

dh/dt = 4/10 = 0.4 cm/min

Therefore, the altitude of the triangle is increasing at a rate of 0.4 cm/min when the altitude is 20 cm and the area is 80 cm².

(2) To find the rate at which the man's shadow is growing, we can use similar triangles and differentiate the relationship between the height of the man, the distance between the man and the lamp post, and the length of the shadow.

Let h be the height of the man, d be the distance between the man and the lamp post, and s be the length of the shadow. We have the following similar triangles:

h/s = (h+5)/(s+d)

Differentiating both sides with respect to time t:

(dh/dt)/s = [(dh/dt) + 0]/(s + d) - (h+5)/(s+d)² * (ds/dt)

Given that dh/dt = -1.5 m/s (since the man is getting farther from the lamp post), h = 2 m, d = 10 m, and we want to find (ds/dt), the rate at which the shadow is growing, we can substitute these values into the equation:

(-1.5)/s = (-1.5)/(s+10) - (2+5)/(s+10)² * (ds/dt)

Now, we can solve for (ds/dt), the rate at which the shadow is growing.

(3) To find how fast the height of the pile is growing, we can use related rates and the formula for the volume of a cone.

Let V be the volume of the sand pile, r be the radius of the base, and h be the height of the cone. We have the formula for the volume of a cone:

V = (1/3) * π * r² * h

Differentiating both sides of the equation with respect to time t:

dV/dt = (1/3) * π * (2r * dr/dt * h + r² * dh/dt)

Given that dV/dt = 1.2 m³/min and dh/dt is what we want to find, we can substitute these values into the equation:

1.2 = (1/3) * π * (2r * dr/dt * h + r² * dh/dt)

Since the base diameter and height are always equal, we have r = h/2. Let's substitute this into the equation:

1.2 = (1/3) * π * (2(h/2) * dr/dt * h + (h/2)² * dh/dt)

Simplifying the equation:

1.2 = (1/3) * π * (h * dr/dt * h + (h²/4) * dh/dt)

1.2 = (1/3) * π * (h² * dr/dt + (h²/4) * dh/dt)

Now, we need to find the value of dr/dt, which represents the rate at which the radius of the base is changing. Since the base diameter and height are always equal, when the height is 3 m, the radius is 3/2 = 1.5 m.

Now we can solve for (dh/dt), the rate at which the height is growing, when h = 3 m.

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a. The altitude of the triangle is increasing at a rate of -1.5 cm/min.

b. The man's shadow is increasing at a rate of 1 m/s.

c. The height of the pile is growing at a rate of 0.1698 m/min.

In Mathematics and Geometry, the area of a triangle can be calculated by using the following mathematical equation (formula):

Area of triangle = 1/2 × b × h

Where:

For the base area, we have:

b = 2(80)/20

b = 8 cm.

By taking the first derivative of the triangle's area by using product rule, we have:

dA/dt = 1/2(db/dt)h + 1/2(dh/dt)b

4 = 1/2(20) + 1/2(8)(dh/dt)

(dh/dt) = (4 - 10)/4

(dh/dt) = -1.5 cm/min.

Part B.

Let the variable x represent the distance between the man and the lamp post.

Let the variable y represent the length of the man's shadow.

Based on the basic proportionality theorem, we have:

\(\frac{5}{x+y} =\frac{2}{y}\)

5y = 2x + 2y

3y = 2x

3dy/dt = 2dx/dt

dy/dt = 1/3 × 2dx/dt

dy/dt = 2/3 × 1.5

dy/dt = 1 m/s.

Part C.

In Mathematics and Geometry, the volume of a cone can be calculated by using this formula:

Volume of cone, V = 1/3 × πr²h

Where:

Since the height and base diameter are always equal, we have:

radius = base diameter/2 = h/2

V = 1/3 × π(h/2)²h

V = πh³/12

dV/dt = 3πh²/12dh/dt

1.2 = 3 × 3.142 × (3)²/12dh/dt

dh/dt = 0.1698 m/min.

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The total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards.

Total distance if Pete walks from A to B to C:

= 15 + 25 = 40 yards

As we know in the triangle the sum of the two sides is greater than the third side.

25 + 15 > AC

40 > AC

or

AC < 40

The direct distance from A to C is more than 10(25-15) yards.

The inequality w < 30 represents the distance, w, that Pete might save by taking the direct path.

Thus, the total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

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Answer:

40, 10, 30
see picture

Step-by-step explanation:

The inequality that describes that Trina must spend at least 45 minutes studying for her test at x ≥ 45 min.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance. In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions.

Trina is to spend at least 45 minutes studying for her test which means that she can either spend 45 minutes studying, or more than 45 minutes.

The inequality for this is therefore:

x ≥ 45

Assuming that the minutes she spends studying is x.

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Full question is:

Trina must spend at least 45 minutes studying for her math test. (find the inequality)

The inflection point of f(t) is approximately t = 3.73.

(a) To determine if the function f(t) = -0.425t^3 + 4.758t^2 + 6.741t + 43.7 is increasing or decreasing, we need to find its derivative and examine its sign.

Taking the derivative of f(t), we have:

f'(t) = -1.275t^2 + 9.516t + 6.741

To determine the sign of f'(t), we need to find the critical points. Setting f'(t) = 0 and solving for t, we have:

-1.275t^2 + 9.516t + 6.741 = 0

Using the quadratic formula, we find two possible values for t:

t ≈ 0.94 and t ≈ 6.02

Next, we can test the intervals between these critical points to determine the sign of f'(t) and thus the increasing or decreasing behavior of f(t).

For t < 0.94, choose t = 0:

f'(0) = 6.741 > 0

For 0.94 < t < 6.02, choose t = 1:

f'(1) ≈ 14.982 > 0

For t > 6.02, choose t = 7:

f'(7) ≈ -5.325 < 0

From this analysis, we see that f(t) is increasing on the intervals (0, 0.94) and (6.02, ∞), and decreasing on the interval (0.94, 6.02).

(b) To find the inflection point of f(t), we need to find the points where the concavity changes. This occurs when the second derivative, f''(t), changes sign.

Taking the second derivative of f(t), we have:

f''(t) = -2.55t + 9.516

Setting f''(t) = 0 and solving for t, we find:

-2.55t + 9.516 = 0

t ≈ 3.73

Therefore, The inflection point of f(t) is approximately t = 3.73.

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Write an example from daily life that uses rational numbers .

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Answer:

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

A function would be f(x), a output for each x input.

The slope intercept form is y - mx + b! *keep this in mind*

If you graph this as well, it would be easier to see if its a function too. If the line crosses through it once, it is indeed a function. If it doesn't, it isn't

Hope this helps

Answer:

149

Step-by-step explanation:

The equation of the line with a slope of 1 passing through the point (0, 2) is y = x + 2.

To verify this, we can substitute the coordinates of the given point (0, 2) into the equation y = x + 2:

2 = 0 + 2

This equation holds true, confirming that the line y = x + 2 passes through the point (0, 2) and has a slope of 1.

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Answer:

(A)increasing

Step-by-step explanation:

Given the time and total distance ran by Myra in the table below.

\(\left|\begin{array}{c|c}Time(minutes)&Distance(miles)\\--&--\\0&0.0\\2&0.4\\4&0.8\\6&1.2\\8&1.6\end{array}\right|\)

We observe that as time increases, Myra's distance also increases. It is the speed(0.2 miles per minute) which is constant.

Therefore Option A is the correct option.

Answer:

its a

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

All of the choices of answers are reasons for taking a sample rather than a census. Reasons for taking a sample instead of a census include:

A census is a comprehensive count of a population. It is conducted by national governments to collect demographic, economic, and other types of data about a population.

The data collected in a census can be used to inform public policy, allocate resources, and plan for the future. The US census is conducted every 10 years and is used to determine the number of representatives each state has in the House of Representatives. In addition to the national census, many countries also conduct local censuses. These are typically used to collect data about local populations, such as population density, economic activity, housing, and education.

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The table values using function rule y = -10x - 2 is (8,-2,-12,-52)

Given function

y = -10x - 2

From the table

x = -1 , 0 , 1 , 5

substitute x values in function

if x = -1

y = -10x - 2

= -10(-1) - 2

= 10 - 2

y = 8  

if x = 0

y = -10(0) -2

y = -2

if x = 1

y = -10(1) - 2

y  = -12

if x = 5

y = -10(5) -2

y = -52

y values (8,-2,-12,-52)

Table:

x      y

-1     8

0    -2

1     -12

5    -52

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Answer:

-------------------

Given:

First, convert the two side length as below:

Now find the third side:

Hence the third side is 5√7 feet.

The equation is given as,

Consider the value of 'x' as -3, the corresponding y-coordinate will be,

Consider the value of 'x' as 2, the corresponding y-coordinate will be,

Consider the value of 'x' as 5, the corresponding y-coordinate will be,

Thus, the table will contain (-3,-10), (2,-5) and (5,-2).

The corresponding table is given below,

Answer:

1. -10

2. -5

3. -2

Step-by-step explanation:

1. -3 - 7 = -10

2. 2 - 7 = -5

3. 5 - 7 = -2

Answer:

The same way as the question before.

5 × 2 = 10 which means 10 ÷ 2 = 5

3 × 5 = (3 x 10)÷2

3 x 10 = 30

30 ÷ 2 = 15

3 × 5 = 15

The sum of the angle measures of the polygon is 540°, the value of x is 5.

The sum of the angle measures of the polygon is 540°.

We know that the sum of the interior angles of a polygon of n sides = (n – 2) × 180°. = 3× 180°= 540°

If a polygon has x sides, then the sum of its angle measures can be found using the formula:

Therefore, for a polygon with x sides, the equation becomes:

⇒(x-2) * 180° = 540°

Solving for x, we get:

⇒x = (540° + 360°) / 180° + 2

⇒x = 3 + 2

⇒x = 5

So, the polygon has 5 sides.

Therefore, the value of  x is 5.

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Answer:

x (378) + y (378) =

Step-by-step explanation:

First i split 756.00 in half so basically what ever is multiplied by two to get 756 and i got 378. So since x = 3.00 and y = 2.00, it would come out to this:

3.00 x 378 = x (378) =

2.00 x 378 = y (378) =

So:

x (378) + y (378) =

im sorry if i got it wrong-

We can use Coulomb's law to calculate the magnitude of the electric field at a distance r away from a point charge Q:

E = k * Q / r^2

where k is Coulomb's constant, Q is the charge of the point charge, and r is the distance from the point charge.

In this problem, we have a point charge Q of -10 nC located at (1.2 cm, 0 cm), and we want to find the x-component of the electric field at a distance r = 5.3 cm away at position (-4.1 cm, 0 cm).

To find the x-component of the electric field, we need to use the cosine of the angle between the electric field vector and the x-axis, which is cos(180°) = -1.

So, the x-component of the electric field at position (-4.1 cm, 0 cm) is:

E_x = - E * cos(180°) = - (k * Q / r^2) * (-1)

where k = 9 x 10^9 N*m^2/C^2 is Coulomb's constant.

Substituting the given values, we get:

E_x = - (9 x 10^9 N*m^2/C^2) * (-10 x 10^-9 C) / (0.053 m)^2

E_x ≈ -30,566.04 N/C

Rounding this to two significant figures and including the appropriate units, we get:

The x-component of the electric field is about -3.1 x 10^4 N/C (to the left).

Answer:

23.75

Step-by-step explanation:

IM GANNA HELP FOR THE SECOND ONE CUZ THE FIRST QUESTION DOESNT HAVE SOME VALUES AND THE THIRD IS KINDA HARD

BUT I HOPE I HELPED

the question:

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. At the farmers market, Nathaniel buys two dozen oranges at $3.50 per dozen, four kilograms of apples at $3.25 per kilogram, two kilograms of carrots at $1.90 per kilogram, and one kilogram of potatoes for $1.20. He received a 5% discount off his total bill. How much money did Nathaniel spend on fruits and vegetables at the farmers market? Nathaniel spent $______ at the farmers market.

nathaniel got 2 dozen so 7$ for the oranges

4 kg  so 13$ for apples

2 kg so 3.8$ for carrots

1 kg so 1.2$ for potatoes

LETS ADD IT TOGETHER

25$ TOTAL

DISCOUNT=5%

5% OF 25 IS 1.25

SO 25-1.25=23.75

SO NATHANIEL SPENT 23.75$ IN ALL

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

  ✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                 PEACE!

The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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Answer:

6.08

Step-by-step explanation:

since 2 is lower than 5 we will use two to round it up

the number 7 will be used

making the 2 to be called 1 add it to 7 making it

8

Rounding 6.027 to the nearest hundredth gives us 6.03.

To round 6.027 to the nearest hundredth,

Since we know that,

Changing a number's digits so that it approximates a value is known as rounding.

In other words, when rounding numbers, we substitute an approximated value for the original number, which is a shorter and simpler representation of the original number. Finding the estimated value of the supplied decimal number up to 2 decimal places is known as rounding to the nearest hundredth.

we first need to identify the second digit after the decimal point, which is 2.

If this digit is less than 5, the number rounds down to 6.02.

If it is 5 or greater, the number rounds up to 6.03.

Since 7 is greater than 5, we round down to 6.03.

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The smallest possible inside length of the cubical steel tank that can hold 275 liters of water is approximately 0.640 meters.

The side length of the cube is found by converting the volume of water from liters to cubic meters, as the unit of measurement for the side length is meters.

Given that the volume of water is 275 liters, we convert it to cubic meters by dividing it by 1000 (1 cubic meter = 1000 liters):

275 liters / 1000 = 0.275 cubic meters

Since a cube has equal side lengths, we find the side length by taking the cube root of the volume. In this case, we find the cube root of 0.275 cubic meters:

∛(0.275) ≈ 0.640

Rounded to the nearest 0.001 meters, the smallest possible inside length of the tank is approximately 0.640 meters.

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The area of the rectangle formed by connecting the points A(-4, -1), B(6, -1), C(6, 4), and D(-4, 4) is 50 square units.

Calculate the length of the rectangle by finding the difference between the x-coordinates of points A and B (6 - (-4) = 10 units).

Calculate the width of the rectangle by finding the difference between the y-coordinates of points A and D (4 - (-1) = 5 units).

Calculate the area of the rectangle by multiplying the length and width: Area = length * width = 10 * 5 = 50 square units.

Therefore, the area of the rectangle formed by the points A(-4, -1), B(6, -1), C(6, 4), and D(-4, 4) is 50 square units. So, the correct answer is B. 50 square units.

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Answer:

For Soccer ball:

x = | 12. 05 + 3.55 |

For basketball:

x = | 8.00 + 0.5 |

For volleyball:

x = | 4.44 + 0.18 |

Step-by-step explanation:

Given the following :

Let x = ball's actual air pressure

_________avg Recommended psi ___tolerance

Soccer ball____ 12. 05 ____________+3.55

Basketball _____8. 00_____________+0.5

Volleyball _____ 4.44 _____________ + 0.18

Actual air pressure = | average recommended psi + tolerance |

Hence ;

For Soccer ball:

x = | 12. 05 + 3.55 |

For basketball:

x = | 8.00 + 0.5 |

For volleyball:

x = | 4.44 + 0.18 |

Answer:

D

Step-by-step explanation: