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The length of the line segment that connects points at (5, 4) and (−3, −1) is found to be 9.43 units.

Using the formula obtained from Pythagoras' theorem, distance can be computed.

The distance formula in coordinate geometry is:

(P, Q) = √ (x2 – x1)² + (y2 – y1)².

Given points: (5, 4) and (−3, −1)

d = √ (-3 - 5)² + (4 + 1)²

d = √ 64 + 25

d = √ 89

d = 9.43

Thus, the length of the line segment that connects points at (5, 4) and (−3, −1) is found to be 9.43 units.

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Answer:

Step-by-step explanation:

We can use the distributive property and basic algebraic operations to multiply the given expression:

(2x+3)(x^2 - 6x - 2)

= 2x(x^2 - 6x - 2) + 3(x^2 - 6x - 2) // Distribute 2x and 3

= 2x^3 - 12x^2 - 4x + 3x^2 - 18x - 6 // Multiply each term

= 2x^3 - 9x^2 - 22x - 6 // Combine like terms

Therefore, (2x+3)(x^2 - 6x - 2) simplifies to 2x^3 - 9x^2 - 22x - 6.

The maximum height of the ball is given as follows:

92 feet.

The quadratic function modelling the height of the ball is given as follows:

h(t) = -16t² + v(0)t + h(0).

In which:

The parameters for this problem are given as follows:

v(0) = 75, h(0) = 4.

Hence the equation is:

h(t) = -16t² + 75t + 4.

The coefficients are given as follows:

a = -16, b = 75, c = 4.

As the quadratic equation is concave down, the maximum height is at the vertex.

The t-coordinate of the vertex is given as follows:

t = -b/2a

b = -75/-32

b = 2.34375s.

Hence the maximum height is of:

h(2.34375) = -16(2.34375)² + 75(2.34375) + 4.

h(2.34375) = 92 feet.

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Answer:

The percent of Dan's average did he score during this game is 11.11%

What percent of Dan's average did he score during this game?

Dan's score in the high school basketball team during last game= 18 points

Dan's score in the high school basketball team during this season = 20 points

Percent of Dan's score during this game = (20 - 18) / 18 × 100

= 2/18 × 100

= 11.11%

In conclusion, Dan scored an average percentage of 11.11% during this game.

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Answer: 32 presents can be wrapped with 8 yards of ribbon

Step-by-step explanation:

Convert yards to inches

1 yard = 36 inches

8 yards = 288 inches

Divide 288 inches by 9 inches

288/9 = 32

Answer: You can wrap 32 presents with 8 yards.

Step-by-step explanation:

So, first, you need to know how many inches are in a yard. There are 36 inches in 1 yard.

Then, do 36 inches times 8 yards to figure out how many yards are in 8 yards. So in 8 yards, there are 288 inches.

Finally, do 288 divided by 9 to figure out how many present you can wrap with 8 yards (288 inches).

You can wrap 32 presents with 8 yards.

I hope this helped!

The measure of side AC of the right triangle is 7.2 units.

The figure in the image is the of a right triangle.

To solve for the measure of side AC, we use trigonometric ratio.

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Tangent = Opposite / Adjacent

tan( A ) = BC / AC

Plug in the values and solve for side AC.

tan( 51° ) = 8.9 / AC

AC = 8.9 / tan( 51° )

AC = 8.9 / 1.234897

AC = 7.2

Therefore, side AC has a value of 7.2 units.

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The number of men needed to complete the same job in 16 days working 6 hours a day is given as follows:

28 men.

The number of men is obtained applying the proportions in the context of the problem.

The rule of three is given as follows:

n/48 = 8/6 x 7/16.

(the time is inverse proportional to the number of men, hence the fractions are inverted).

Thus:

n/48 = 56/96

Applying cross multiplication, the number of men is obtained as follows:

96n = 48 x 56

n = 48 x 56/96

n = 28 men.

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a. A ⋁ G: Elvis is alive or Elvis gained weight.

b. ~(A ⋀ G): Elvis is not both alive and gained weight.

c. G → ~A: If Elvis gained weight, then Elvis is not alive.

d. A ↔ ~G: Elvis is alive if and only if Elvis did not gain weight.

When given the area of a rectangle, and one of the sides, the unknown measure of the rectangle would be 40 meters

To find the area of a rectangle, you can use the formula:

A = l x w

where A is the area of the rectangle, l is the length of the rectangle, and w is the width of the rectangle.

Seeing as you were given the area to be 2, 800 square meters and one of the sides measures 70 meters, the unknown measure of the rectangle would be:

70x Unknown = 2, 800

Unknown = 2, 800 / 70

Unknown measure = 40 meters

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Full question is:

Area = 2,800 square meters

Side A = 70 meters

Find the unknown measure of the rectangle

Answer:360

Step-by-step explanation:

Answer:

[tex]y = 4d + 8\\[/tex]

Step-by-step explanation:

Since d is the number of large drinks, and there is always a constant of 1 large popcorn, we go to (0, 8). This concludes that since we start off with the cost of 8 dollars with no large drink but a large popcorn, the popcorn will stay a constant cost of $8. (the equation for this scenario is as shown):

y = md + 8

y (total cost)

m (coefficient - in this sense the cost of the drinks.)

d (amount of drinks)

8 (the constant of 8 represents the cost of one large popcorn consistently)

Now, lets find the cost of the dink.

Go to (1, 12).

$12 dollars is the total cost, with one drink and one large popcorn bought.

We have already discussed that we will have a constant of 8 because no matter the amount of drinks we will get, we would have bought 1 large popcorn at $8.

Therefore, we must subtract 8 dollars from 12.

12 - 8 = 4

From the total cost of everything we bought (2 things) and subtracting it with the cost one of the things we bought, we get the cost of the other thing.

each drink will cost $4.

Therefore, with all the variables and their listed meanings, this will be our given equation:

y = 4d + 8

9. The discriminant is 33. And the roots are real and distinct.

10. The discriminant is 4. And the roots are real and distinct.

11. The discriminant is -23. And the roots are imaginary roots.

12. The discriminant is -4. And the roots are imaginary roots.

What is the discriminant?

The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,

D = b² - 4ac

9. 2x² + 3x - 3 = 0, the discriminant is given as,

D = 3² - 4 × 2 × (-3)

D = 33

Roots are real and distinct.

10. 4x² - 6x + 2 = y, the discriminant is given as,

D = (-6)² - 4 × 4 × (2)

D = 4

Roots are real and distinct.

11. 0 = x² - 3x + 8, the discriminant is given as,

D = (-3)² - 4 × 1 × (8)

D = - 23

Roots are imaginary.

12. y = 5x² + 4x + 1​, the discriminant is given as,

D = (4)² - 4 × 5 × (1)

D = -4

Roots are imaginary.

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Answer:

x - 5

Step-by-step explanation:

Okay to write this problem as an expression it would be x -5. x represents James and -5 represents less than.

Answer:

x-5

Step-by-step explanation:

we don't know how much James has but we know it is $5 less so what ever the original amount is we are putting as x for now and we will subtract 5 because it is $5 less making our x-5.

According to the Cartesian plane graph, it can be inferred that the circle was rotated and translated (option B).

To identify the movements that were made to circle 1 to become 2 we must carefully observe the graph. Once we have analyzed this graph we can infer the movements that were made to the circle. In this case, the rotation was performed because it can be seen that it was rotated having the coordinate (-1.5, 0.5) as a reference or point of rotation.

However, it was also translated because it was shifted a bit down and to the left. So the correct answer would be option B.

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Answer: rotation and translation

Step-by-step explanation: I took the quiz

As an example, the 78-mph speed limit in the United States is equivalent to the 130 km/h restriction in Germany.

How quick is that speed?

A connection with a speed of 100 Mbps or higher is considered fast internet. Broadband internet speed is defined by the federal communications regulator (FCC) as 25 Mbps for downloading and 3 Mbps for upload.

We can increase each number by 0.6 to convert overall speed limitations from kilometers per hour into miles per hour. Here is the revised table:

Country Speed Limit (km/h)  Speed Limit (mph)

Germany         130                    78

France             110                     66

Italy                 150                     90

Japan              100                      60

Australia          110                       66

United Kingdom 113              67.8

Hence, Because one kilometer is equivalent to 0.6 miles, it is evident that speed limits in the form of miles per hour were lower than those in kilometers per hour.

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The Panther I traveled approximately 2413 miles before reaching a speed of 130 mph.

A trapezoid is a quadrilateral having two parallel bases and one set of other sides called legs.

To estimate the distance traveled by the Panther I, we need to approximate the area under the velocity curve between 0 and 25.7 seconds. We can divide the area into trapezoids using the data given in the table.

The first trapezoid has a height of 30 mph and a base of 1.8 seconds. The second trapezoid has a height of 40 mph and a base of 1.3 seconds (the difference between 3.1 and 1.8).

Continuing in this way, we get the following table:

Speed       Height

Range    (mph) Base (s)  Area (mph * s)

0-30  30           1.8               54

30-40 40           1.3               52

40-50 50           1.1            55

50-60 60           1.3              78

60-70 70           1.9            133

70-80 80           1.8             144

80-90 90            2.3            207

90-100 100           3.1            310

100-120 120          6.3            756

120-130 130           4.8            624

To find the total area, we add up the areas of all the trapezoids:

54 + 52 + 55 + 78 + 133 + 144 + 207 + 310 + 756 + 624 = 2413

Therefore, the Panther I traveled approximately 2413 miles before reaching a speed of 130 mph.

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The time spent on country driving is 25/44 hour

From the question, we have the following parameters that can be used in our computation:

Total time = 3/4

City driving = 2/11

Given that 2/11 hour was spent on city driving, we can find the time spent on country driving as follows:

Time spent on country driving = Total driving time - Time spent on city driving

Time spent on country driving = 3/4 hour - 2/11 hour

So, we have

Time spent on country driving = 25/44

Hence, the time spent is 25/44

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Answer:

9 54 divided by 9 = 6  72 - 18 = 54

Step-by-step explanation:

Answer:

A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required.

Answer:

Its answer number 4

Step-by-step explanation:

According to the information we can infer that sentence is completed with the words mathematical procedure.

To complete the sentence we must identify the central idea and establish the right words to complete it. In this case, it is referring to a mathematical procedure then we could infer that these are the words that complete the sentence. Then the complete sentence would be like this:

Note: This question is incomplete. Here is the complete information:

Complementary information:

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The x-intercepts and y-intercepts of the graph include the following:

x-intercept: B. -1.

y-intercept: D. none.

The equations for all vertical and horizontal asymptotes are as follows;

Vertical asymptote: x = 1.

Horizontal asymptote: y = 4.

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch. Additionally, the vertical asymptote of a function simply refers to the value of x which makes its denominator equal to zero (0).

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Answer:

↓ ↓ ↓

Step-by-step explanation:

Given: f(x)= x² -4x + 3

Find :-

a) f(1)

f(x)= x² -4x + 3

→ Substitute x with with 1:-

[tex]\tt f(1)=\left(1\right)^2-4\left(1\right)+3[/tex]

[tex]\tt f(1)=1-4\cdot \:1+3[/tex]

[tex]\tt f(1)=1-4+3[/tex]

[tex]\boxed{\tt f(1)=0}[/tex]

_______________________

b) f(3)

f(x)= x² -4x + 3

→ Substitute x with with 3:-

[tex]\tt f(3)=\left(3\right)^2-4\left(3\right)+3[/tex]

[tex]\tt f(3)=\left(3\right)^2-4\left(3\right)+3[/tex]

[tex]\tt f(3)=3^2-4\cdot \:3+3[/tex]

[tex]\tt f(3)=3^2-12+3[/tex]

[tex]\tt f(3)=3^2-9[/tex]

[tex]\tt f(3)=9-9[/tex]

[tex]\boxed{\tt f(3)=0}[/tex]

_______________________

c) f(-1)

f(x)= x² -4x + 3

→ Substitute x with with -1:-

[tex]\tt f(-1)=\left(-1\right)^2-4\left(-1\right)+3[/tex]

[tex]\tt f(-1)=\left(-1\right)^2+4\cdot \:1+3[/tex]

[tex]\tt f(-1)=1+4+3[/tex]

[tex]\boxed{\tt f(-1)=8}[/tex]

_______________________

d) -f(1)

f(x)= x² -4x + 3

→ -f(1)

[tex]\tt -f(1)=\left(1\right)^2-4\left(1\right)+3[/tex]

[tex]\tt -f(1)=1-4\cdot \:1+3[/tex]

[tex]\tt -f(1)=1-4+3[/tex]

[tex]\boxed{\tt -f(1)=0}[/tex]

_____________________

Hope this helps! :)

Answer: $41.62

Step-by-step explanation:

let the price of the jacket be X

then the price of belt will be X-8.61

according to question

X + X-8.61 = 91.85

2X - 8.61 = 91.85

2X = 91.85 + 8.61

2X = 100.46

X = $50.23

cost of jacket = $ 50.23

cost of belt = $ 41.62

Hope this helps!!!

Answer: $41.62

Step-by-step explanation:

*j = jacket*  *b = belt*
belt + jacket = 91.85 (the total cost of the belt and jacket)
belt = jacket - 8.61 (the price of the belt is $8.61 less than the jacket)

We can use substitution to solve for the value of b.
Substitute the second equation into the first equation:
(j - 8.61) + j = 91.85

Simplify by combining like terms:
2j - 8.61 = 91.85
Add 8.61 to both sides:
2j = 100.46
Divide both sides by 2:
jacket = 50.23

b = j - 8.61

b = 50.23 - 8.61

b = 41.62

Answer:

67.97%

Step-by-step explanation:

Answer:

67.97%

Step-by-step explanation:

The function g(x) is translation of f(x) 9 units up. The solution has been obtained by using transformation.

An operation known as a transformation involves moving a polygon or other two-dimensional object on a plane or coordinate system.

We are given that the function g(x) is a translation of the function

f(x) = x².

In the graph, we can see that the vertex of the parabola is at (0, 9).

This means that the function g(x) is 9 units up from the function f(x).

So, g(x) = x² + 9

Hence, the function g(x) is translation of f(x) 9 units up.

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Given:-

To find:-

Answer:-

The given figure is made up of a cone and a hemisphere , so to find the total volume , we would find the volume of cone and hemisphere individually and add them up to find the net volume.

Finding volume of cone:

The data we have is ,

As we know that the volume of cone is given by,

[tex]\implies V =\dfrac{1}{3}\pi r^2 h \\[/tex]

on substituting the respective values,we have;

[tex]\implies V =\dfrac{1}{3}\times 3.14 \times (9in.)^2 \times 14in .\\[/tex]

[tex]\implies V = \dfrac{1}{3}\times 3.14 \times 81in.^2\times 14in. \\[/tex]

[tex]\implies V = 1186.92 \ in.^3 \\[/tex]

Finding the volume of hemisphere:

As we know that the volume of hemisphere is given by;

[tex]\implies V =\dfrac{2}{3}\pi r^3 \\[/tex]

And here ,

So that;

[tex]\implies V =\dfrac{2}{3}\times 3.14\times (9\ in.)^3 \\[/tex]

[tex]\implies V =\dfrac{2}{3}\times 3.14\times 729\ in.^3 \\[/tex]

[tex]\implies V = 1526.04 \ in.^3 \\[/tex]

Hence the total volume will be ,

[tex]\implies V_{prop} = (1526.04 + 1186.92 )in.^3\\[/tex]

[tex]\implies V = 2712.96 \ in.^3 \\[/tex]

[tex]\implies \underline{\underline{ V_{prop}= 2713\ in.^3 }} \\[/tex]

Hence the volume of prop is 2713 in.³

and we are done!

Answer:

2713.0 in³  (nearest tenth)

Step-by-step explanation:

To calculate the volume of the prop, sum the volume of the cone and the volume of the half-sphere.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]     [tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a half-sphere}\\\\$V=\dfrac{2}{3} \pi r^3$ \\\\ where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\\end{minipage}}[/tex]

Therefore, the equation for the volume of the prop is:

[tex]V_{\sf prop}=\dfrac{1}{3} \pi r^2 h+\dfrac{2}{3} \pi r^3[/tex]

From inspection of the given diagram:

Substitute the values of r, h and π into the equation and solve for V:

[tex]\begin{aligned}\implies V_{\sf prop}&=\dfrac{1}{3} \pi r^2 h+\dfrac{2}{3} \pi r^3\\\\&=\dfrac{1}{3} (9)^2 (14)+\dfrac{2}{3} \pi (9)^3\\\\ &=\dfrac{1}{3} \pi (81) (14)+\dfrac{2}{3} \pi (729)\\\\ &=378 \pi+486 \pi\\\\ &=864 \pi\\\\&=864 \cdot 3.14\\\\&=2712.96\\\\&=2713.0\;\sf in^3\;\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the volume of the prop is 2,713.0 in³ to the nearest tenth.