Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.Match each approximate volume of a half sphere to the approximate area of the largest cross section of the sphere. Use . 2,789 cubic units 1,796 cubic units 1,287 cubic units 884 cubic units 349 cubic units 575 cubic units 284 square units arrowRight 177 square units arrowRight 380 square units arrowRight 95 square units arrowRight

Answer:

106°

Step-by-step explanation:

180-74=106°

Answer:

106

Step-by-step explanation:

supplementary means 2 angles = 180

so..

180-74=106

By interpretating the graph of a quadratic equation, the initial height of the ball is equal to 5 feet above ground.

In this problem we must determine the initial height of the ball according to a graph, whose form resembles quadratic equations. Graphically speaking, the initial height is the y-coordinate of the y-intercept. First, the coordinates of the y-intercept of the equation are:

(t, h) = (0 s, 5 ft)

Second, the final height of the ball is equal to:

h = 5 ft

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The expression that does not represent the same function as y = 2x + 4 is B, which is y = 2x - 4.

A. y = 2(x + 2)

With x = 1, we obtain y = 2(1 + 2) = 6.

The resultant value of y is 6, which corresponds to the value of y when x = 1 for the formula y = 2x + 4. As a result, y = 2x + 4 is represented by the same function as this expression.

B. y = 2x - 4

With x = 1, we obtain y = 2(1) - 4 = -2.

When y = 2x + 4 and x = 1, the value of y obtained is -2, which is not identical to the value of y when x = 1. The function represented by this statement is therefore distinct from that of y = 2x + 4.

C. y = 2(x + 4) - 8

With x = 1, we obtain y = 2(1 + 4) - 8 = 2.

The obtained value of y is 2, which differs from the value of y when

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The function f(x) = sin⁻¹x, x ≠ π/4 and sinx, x = π/4 is continuous on[-1, π/4) ∪ (π/4, 1]. There is a removable discontinuity at x = π/4

A function is said to be continuous if there are no breaks or jumps in the functions

Conditions for continuity of a function

Now, for the given function f(x) = sin⁻¹x, x ≠ π/4 and sinx, x = π/4

We need to determine the interval of continuity, We proceed as follows.

Since f(x) = sin⁻¹x, x ≠ π/4 , we know that the minimum value of x is - 1 and its maximum value is 1.

So, x must lie in the interval (-1, 1) for x ≠ π/4,

Now, when x = π/4 f(x) = sinx. We know that x = π/4 lies in the interval (-1, 1).

But we know that f(x) = sinx at x = π/4. So, there is a removable discontinuity at x = π/4.

So, from the left, f(x) is continuous on the interval [-1, π/4) and  from the right, f(x) is continuous on the interval (π/4, 1]

So, combining both intervals, we have f(x) is continous on the interval [-1, π/4) ∪ (π/4, 1] and since f(x) = sinx at x = π/4, there is a removable discontinuity at x = π/4

So, the function f(x) is continuous on[-1, π/4) ∪ (π/4, 1]. There is a removable discontinuity at x = π/4

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Answer:

\(n = 4\)

\(x = 2\)

\(p = 38\%\)

\(q = 62\%\)

Step-by-step explanation:

Required

Find n, x, p and q

n always represent the population surveyed;

So:

\(n = 4\)

x represents the sample from the population

So:

\(x = 2\)

p always represents the given proportion

\(p = 38\%\)

Solving for q

\(p + q = 1\)

\(q = 1 - p\)

\(q = 1 - 38\%\)

\(q = 62\%\)

The directed distance from point A to the curve at the angle theta = 5\(\pi\)/6 is:

\(\sqrt(192 + 48\sqrt(3))\)

To find the directed distance from point A to the curve at the angle theta = 5\(\pi\)/6, we first need to find the equation of the tangent line to the curve at point A.

To do this, we can take the derivative of the curve equation with respect to x:

\(2x + 2y * dy/dx + 8 = 0\)

Solving for dy/dx, we get:

\(dy/dx = -x / (y + 4)\)

At point A, we have x = -4 and y = 4, so:

\(dy/dx = -(-4) / (4 + 4) = 1/2\)

Therefore, the equation of the tangent line to the curve at point A is:

\(y - 4 = (1/2) * (x + 4)\)

Simplifying, we get:

\(y = (1/2) * x + 6\)

Now we can find the intersection point of the tangent line with the line passing through point A and making an angle of 5π/6 with the positive x-axis.

The line passing through point A with angle 5π/6 has slope:

\(tan(5\pi /6) = -\sqrt(3)\)

So the equation of this line is:

\(y - 4 = -\sqrt(3) * (x + 4)\)

Simplifying, we get:

\(y = -\sqrt(3) * x + 4\sqrt(3) + 4\)

Now we can solve for the intersection point of the two lines. Setting the equations for y equal to each other, we get:

\((1/2) * x + 6 = -\sqrt(3) * x + 4\sqrt(3) + 4\)

Solving for x, we get:

\(x = -8 / (2 + \sqrt(3))\)

Now we can find the corresponding value of y using either equation for the tangent line or the line with angle 5π/6. Using the equation for the tangent line, we get:

\(y = (1/2) * (-8 / (2 + \sqrt(3))) + 6 = 11 - 4\sqrt(3) / (2 + \sqrt(3))\)

The directed distance from point A to this intersection point is the distance between these two points along the line with angle 5π/6. This distance can be found using the distance formula:

\(d = \sqrt((x2 - x1)^2 + (y2 - y1)^2)\)

Plugging in the values, we get:

\(d = \sqrt((-4 - (-8 / (2 + \sqrt(3))))^2 + (4 - (11 - 4\sqrt(3) / (2 + \sqrt(3))))^2)\)

Simplifying, we get:

\(d = \sqrt(192 + 48\sqrt(3))\)

Therefore, the directed distance from point A to the curve at the angle theta = 5π/6 is:

\(\sqrt(192 + 48\sqrt(3))\)

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The directed distance from point A to the point on the curve corresponding to θ = 5π/6 is 4 units.

What is curve?

In mathematics, a curve refers to a continuous and smooth line that has no corners or edges. Curves can be described using equations or parametric equations, and they can be represented in a two-dimensional or three-dimensional space.

To find the directed distance when θ = 5π/6, we first need to find the corresponding point on the curve.

The equation \(x^2 + y^2 + 8x = 0\) can be rewritten as \((x + 4)^2 + y^2 = 16\), completing the square. This is the equation of a circle with center (-4, 0) and radius 4.

To find the point on the circle corresponding to θ = 5π/6, we can use polar coordinates. Let r be the radius of the circle (r = 4), and let θ be the angle from the positive x-axis to the point we want to find. Then we have:

x = r cos(θ) = 4 cos(5π/6) = -2√3

y = r sin(θ) = 4 sin(5π/6) = 2

So the point on the curve corresponding to θ = 5π/6 is (-2√3, 2).

To find the directed distance from point A (-4, 4) to this point, we can use the distance formula:

distance = √[\((x2 - x1)^2 + (y2 - y1)^2\)]

= √[\((-2\sqrt3 - (-4))^2 + (2 - 4)^2\)]

= √[12 + 4]

= 2√4

= 4

Therefore, the directed distance from point A to the point on the curve corresponding to θ = 5π/6 is 4 units.

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Answer: c

This system has no solutions.

Step-by-step explanation:

Solve by substitution:

1) Solve \(y=-x+8\) for y:

\(y=-x+8\)

2) Substitute \(-x+8\) for \(y\) in \(x+y=7\):

\(x+y=7\)

\(x+-x+8=7\)

3) Simplify both sides of the equation:

\(8=7\)

4) Add -8 to both sides of the equation:

\(8+-8=7+-8\)

5) Simplify both sides of the equation:

\(0=-1\)

Therefore, There are no solutions to the system of equations.

Solve by elimination:

You can't solve the system of equations by elimination.

Solve by graphing:

The lines are parallel to each other, Therefore they never cross, so, The system of equations has no solutions.

Answer:

-Equations:

AA=75+2x

AA=75+2x

-Company A would be cheaper.

Step-by-step explanation:

-Company A: The equation would indicate that the amount the company would charge is equal to the initial fee for the rental plus the cost per mile driven for the number of miles driven:

AA=75+2x

AA=75+2(45)

AA=75+90

AA=165

-Company B: The equation would indicate that the amount the company would charge is equal to the initial fee for the rental plus the cost per mile driven for the number of miles driven:

BB=35+3x

BB=35+3(45)

BB=35+135

BB=170

According to this, if Brandon needs to drive 45 miles with the rented truck, Company A would charge $165 and Company B would charge $170 which means that Company A would be cheaper.

Answer:

88%

Step-by-step explanation:

No Johnny boy did not

\(\begin{array}{ccll} pens&\$\\ \cline{1-2} 10 & 8\\ 2& x \end{array} \implies \cfrac{10}{2}=\cfrac{8}{x}\implies 5=\cfrac{8}{x}\implies 5x=8\implies x=\cfrac{8}{5}\implies x=1.6\)

The value of sin (α + β) is,

⇒ sin (α + β) = - 135/377

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Angle α in quadrant 3:

y = opposite = 21 and x = adjacent = 20

Then, hypotenuse = √( 21² + 20²)

                            = √ ( 441 + 400)

                            = sqrt( 881)

So, sin α = 21/√881

              = 21 × sqrt(881)/881

And, cos α = 20/sqrt(881) = 20sqrt(881) / 881

Since, Angle β in Quadrant 2:

Hence,  adjacent = -5 and hypotenuse = 13

Then, by Pythagorean,

y = opposite = 12

So, sin β = 12/13, cos β = -5/13

as given,

And, tan β = -13/12

Since, We know that;

sin (α + β) = sin α cos β + cos α sin β

               = 21/√881 × - 5/13 + 20/√881 × 12/13

               = 1/√881 (- 105/13 + 240/13)

               = - 1/√881 (135/13)

              = - 135/377

Hence, The value of sin (α + β) is,

sin (α + β) = - 135/377

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the answer is D

The figure can be divided into a rectangle and 2 triangles

Answer:

Step-by-step explanation:

add all the three.

Answer:

60

Step-by-step explanation:

AD= AB+BC+CD

=22+29+9

=60 cm

Answer:

not unless you want them to have it :)

Step-by-step explanation:

Answer:

Point A will be 2 times it's original value, because the original scale is 3, and the new scale is 6. Therefore using a times 2 rule. So point A will be plotted at (8, 16)

Answer:

Step-by-step explanation:

\( \frac{y}{2} - \frac{1}{5} = 2 - \frac{y}{3} \)

First multiply through by the LCM to eliminate the fractions

The LCM of 2 , 5 and 3 is 30

We have

\(30 \times \frac{y}{2} - 30 \times \frac{1}{5} = 2(30) - 30 \times \frac{y}{3} \\ 15y - 6 = 60 - 10y\)

Add 10y to both sides of the equation

\(15y + 10y - 6 = 60 + 10y - 10y \\ 25y - 6 = 60\)

Add 6 to both sides of the equation

\(25y + 6 - 6 = 60 + 6 \\ 25y = 66\)

Divide both sides by 25

\( \frac{25y}{25} = \frac{66}{25} \)

We have the final answer as

\(y = \frac{66}{25} \)

Hope this helps you

i) 4 more gallons of petrol will be needed to complete the journey.

ii) The cost of the petrol for the 420 km journey is GH¢55.00.

i) To determine the number of gallons of petrol needed to complete the journey, we can calculate the total distance that can be covered with the available petrol and then subtract it from the total distance of the journey.

Given that the car consumes 1 gallon of petrol for every 30 km, we can calculate the distance that can be covered with 10 gallons of petrol by multiplying 10 (gallons) by 30 (km/gallon):

Distance covered with 10 gallons = 10 * 30 = 300 km

To find the remaining distance that needs to be covered, we subtract the distance covered with the available petrol from the total distance of the journey:

Remaining distance = Total distance - Distance covered with available petrol

Remaining distance = 420 km - 300 km = 120 km

Since the car consumes 1 gallon of petrol for every 30 km, we can determine the additional gallons of petrol needed by dividing the remaining distance by 30:

Additional gallons needed = Remaining distance / 30 = 120 km / 30 km/gallon = 4 gallons

Therefore, the driver will need 4 more gallons of petrol to complete the journey.

ii) To calculate the cost of the petrol for the journey of 420 km, we need to multiply the total number of gallons used for the journey by the cost per gallon.

Given that a gallon of petrol costs GH¢5.50, and the total number of gallons used for the journey is 10 (given in the problem), we can calculate the cost using the formula:

Cost of petrol = Total gallons used * Cost per gallon

Cost of petrol = 10 gallons * GH¢5.50/gallon = GH¢55.00

Therefore, the cost of the petrol for the journey of 420 km is GH¢55.00.

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Rewrite the limit as

\(\displaystyle \lim_{x\to0} \frac{x\cos(5x)}{\sin(5x)} = \lim_{x\to0} \frac{5x}{\sin(5x)} \cdot \lim_{x\to0} \frac{\cos(5x)}5\)

Then using the known limit,

\(\displaystyle \lim_{x\to0} \frac{\sin(x)}x = 1 \implies \frac1{\lim\limits_{x\to0}\frac{\sin(x)}x} = \lim_{x\to0}\frac x{\sin(x)}=1\)

it follows that

\(\displaystyle \lim_{x\to0} \frac{x\cos(5x)}{\sin(5x)} = 1 \cdot \frac{\cos(0)}5 = \boxed{\frac15}\)

Answer:

The y-intercept in this situation means that when the cab travels 0 miles, the total fee will be $14.00. This indicates that the cab service charges a flat fee of $14.00, regardless of the number of miles traveled.

Step-by-step explanation:

The y-intercept in this situation represents the base fee that the cab service charges regardless of distance traveled. In this case, when the cab travels 0 miles, the total fee is $14.00.

In this context, the y-intercept represents the base fee that the cab service charges, regardless of distance traveled. This is the amount you would pay for a cab ride of 0 miles. From the given table, we can't directly see the y-intercept, but we can infer it using the rate of change or slope, which represents the fee per mile. The amount increases by $1.50 for every additional mile (difference in y divided by difference in x), so to find the y-intercept, we back-calculate from one of the given points, like (2, 17). Subtracting 2 miles' worth of fees from $17 gives a y-intercept of $14. Therefore, when the cab travels 0 miles, the total fee is $14.00, which likely represents a starting charge or a minimum fare.

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Answer: X = -3

Step-by-step explanation:

Answer:

The product of given binomial and trinomial is:

\(8x^3-34x^2-27x-9\)

Step-by-step explanation:

A binomial is a polynomial with 2 terms and trinomial is a term with 3 terms.

Given

\((4x+3)\\and\\(2x^2-5x-3)\)

Distributive property can be used to find the result.

Writing mathematically

\((4x+3)(2x^2-5x-3)\\= 4x(2x^2-5x-3)+3(2x^2-5x-3)\\= 8x^3-40x^2-12x+6x^2-15x-9\)

Combining alike terms

\(= 8x^3-40x^2+6x^2-12x-15x-9\\= 8x^2-34x^2-27x-9\)

Hence,

The product of given binomial and trinomial is:

\(8x^3-34x^2-27x-9\)

Answer:

You: Your welcome❤

Answer:

-48.015

Step-by-step explanation

The solution to the system of equations is x = -3 and y = -4.

To solve the system of equations:

Equation 1: 2x - y = -10

Equation 2: 3x + 2y = -1

We can use the method of substitution or elimination to find the values of x and y.

Let's use the method of elimination:

Multiply Equation 1 by 2 to make the coefficients of y in both equations equal:

2(2x - y) = 2(-10)

4x - 2y = -20

Now, we can eliminate y by adding Equation 2 and the modified Equation 1:

(3x + 2y) + (4x - 2y) = -1 + (-20)

7x = -21

x = -3

Substitute the value of x into Equation 1 to solve for y:

2(-3) - y = -10

-6 - y = -10

y = -10 + 6

y = -4

Therefore, the solution to the system of equations is x = -3 and y = -4.

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The distance from the pole at which the cable is anchored is about 25 feet from the pole .

Given that a 35-foot cable is run from the top of the pole and anchored to the ground at a distance from the pole. The problem is to determine about how far away from the pole would it be anchored.

Let AB be the pole of length 40 feet, and CD be the 35-foot long cable anchored to the ground at D and attached to the top of the pole at C. Let E be the point on the ground at which the cable is taut and is anchored. The distance ED is to be determined.

we can see that ∆CDE is a right-angled triangle with ∠CED = 90°.

Using Pythagoras Theorem, we have:CD² = CE² + DE²35² = (40 - ED)² + DE² .

Simplifying the above equation

1225 = 1600 - 80ED + ED²

1225 - 1600 + 80ED - ED² = 0ED² - 80ED + 375 = 0

Factorizing the above quadratic equation

ED² - 25ED - 15ED + 375 = 0ED(ED - 25) - 15(ED - 25)

  = 0(ED - 15)(ED - 25) = 0So, ED = 15 ft or ED = 25 ft.

The negative value of ED is extraneous since it represents a point below the ground, which is not possible. Therefore, the distance from the pole at which the cable is anchored is about 25 feet from the pole.

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Answer:

Emily is now 12.

Jacob is now 16.

Step-by-step explanation:

since Emily is 4yrs younger than Jacob, let Jacob be x and Emily be (x - 4) yrs.

eight yrs ago: Emily is ( x-4-8) = ( x - 12)

Jacob is ( x - 8)

Emily was half Jacob's age: so, we have to balance the ages by either multiplying Emily's age by 2 or dividing Jacob's age by 2. ( I multiplied by 2)

2( x - 12) = x - 8

2x - 24 = x - 8............ Bring the like terms together and solve for x

x = 16, which is Jacob's current age

Emily ( x - 4) = 12 yrs

Classification:

Monomial: One term

Mono = One

Polynomial: Multiple terms e.g. (2,3,4 and so on)

Poly: Many

Binomial: Two terms

Bi = Two

Trinomial: Three terms

Tri = Three  

The expression of "mx + b" would be classified as a monomial due to it having only one exponent.