HELPPP

Solve for x and graph the solution on the number line below.


-x - 8 ≤ -15 and -18 ≤ -x - 8

Answer: To solve this problem, we can use the equations of motion for projectile motion. Let's calculate the time of flight, horizontal distance, and maximum height of the ball.

Time of Flight:

The time of flight can be determined using the vertical motion equation:

where:

h = initial height = 3 ft

v₀y = initial vertical velocity = v₀ * sin(θ)

v₀ = initial speed = 125 ft/sec

θ = launch angle = 40 degrees

g = acceleration due to gravity = 32.17 ft/sec² (approximate value)

We need to solve this equation for time (t). Rearranging the equation, we get:

Using the quadratic formula, t can be determined as:

where:

Plugging in the values, we have:

Solving the quadratic equation for t, we get:

Therefore, the ball was in the air for approximately 4.86 seconds.

Horizontal Distance:

The horizontal distance traveled by the ball can be calculated using the horizontal motion equation:

where:

Plugging in the values, we have:

d = 95.44 * 4.86

d ≈ 463.59 feet

Therefore, the ball traveled approximately 463.59 feet horizontally.

Maximum Height:

The maximum height reached by the ball can be determined using the vertical motion equation:

Using the previously calculated values:

Plugging in these values, we can calculate the maximum height:

h = 80.21 * 4.86 - (1/2) * 32.17 * (4.86)²

h ≈ 126.98 feet

Therefore, the ball reached a maximum height of approximately 126.98 feet.

Hi there!  

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I believe your answer is:  

O False

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Here’s why:  

⸻⸻⸻⸻

\(\boxed{\text{Simplifying the Equation Given...}}\\\\\frac{1}{4}(12x-16)=4 \\---------------\\\\\rightarrow \left \{ {{\frac{1}{4} * 12 = 3} \atop {\frac{1}{4}*-16 = -4}} \right.\\\\\rightarrow \boxed{3x - 4 = 4}\\\\\\\rightarrow\boxed{3x - 4 = 4\neq 3x - 16 = 4} \leftarrow\\\\\text{The 'simplified' equation is not distributed correctly.}\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer: Two quanties are said to have a proportional relationship if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio. ... inversely proportional: y is inversely proportional to x of y=k/x.

Answer:

10/14

Step-by-step explanation:

See 3 +5+4+2= 14 , if the question would be what's the probability of getting yellow the answer would be 4/14 but it's not, so 14 - 4 which will be 10 so 10 / 14 .

The other way is get the sum of all the marbles except the yellow one, then that no. will be upon the total.

Answer: \(\frac{2}{7}\)or 0.2857142857

Step-by-step explanation:

P(not yellow)=\(\frac{4}{14}\)

P(not yellow)=\(\frac{2}{7}\) or 0.2857142857

By noticing that x grows to the left, we can see that the coordinates of point B are (-3, 0)

The coordinates of a point are written as (x, y), the fisrt value tells us the horizontal position, while the second value gives the vertical position.

For B, we can see that it lies over the x-axis, so its y-value is y = 0.

Now notice that in this particular case, x grows to the left. And B is at 3 units at the right, then the x-value will be x = -3

Finally, the coordinates of point B are (-3, 0).

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The distance bewteen the points (-3,5) and (3,1) in a simple radical form is 2√13.

The distance formula used in finding the distance between two points is expressed as;

d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

From the graph;

Point A: (-3,5)

x₁ = -3

y₁ = 5

Point B: (3,1)

x₂ = 3

y₂ = 1

Plug the given values into the distance formula and simplify.

\(d = \sqrt{( x_2 - x_1)^2 + (y_2 -y_1 )^2} \\\\d = \sqrt{( 3-(-3))^2 + (1 -5)^2} \\\\d = \sqrt{( 3+ 3)^2 + (1 -5)^2} \\\\d = \sqrt{( 6)^2 + (-4)^2} \\\\d = \sqrt{36 + 16} \\\\d = \sqrt{52}\\\\d = 2\sqrt{13}\)

Therefore, the distance between the points is 2√13.

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The function's formula for the ice sheet's thickness is S(t) = 0.2t + 1.02.

Mathematically, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be modeled (represented) by this mathematical expression;

S(t) = mt + b

Where:

After a time of 7 weeks and a rate of decrease of 0.2, the y-intercept or initial amount of ice can be calculated as follows;

S(t) = mt + b

2.42 = 0.2(7) + b

2.42 = 1.4 + b

y-intercept, b = 2.42 - 1.4

y-intercept, b = 1.02.

Therefore, the required linear function is given by S(t) = 0.2t + 1.02.

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Complete Question:

A lake near the Arctic Circle is covered by a thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a rate of 0.2 meters per week. After 7 weeks, the sheet is only 2.42 meters thick.

Let S(t), denote the ice sheet's thickness S (measured in meters) as a function of time t (measured in weeks).

Write the function's formula.

S(t) = ?

The quadratics that would not have 5 and -7 as zeros are (1) and (3)

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

Zeros: 5 and -7

This means that

x = 5 and x = -7

Rewrite as

x - 5 = 0 and x + 7 = 0

Multiply both equation

This gives

(x - 5)(x + 7) = 0

Rewrite as

f(x) = (x - 5)(x + 7)

When expanded, we have

f(x) = x² + 2x - 35

So, we have

(2) f(x) = x² + 2x - 35

(4) f(x) = 2(x + 7)(x - 5)

Hence, the quadratics that would not have 5 and -7 as zeros are (1) and (3)

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Answer:

Option D

Step-by-step explanation:

(x + 8) (2x² - 5x - 3)

=> (2x³ - 5x² - 3x) + (16x² - 40x - 24)

=> 2x³ + 11x² - 43x - 24

Hope this helps!

Answer:

x= -1

Step-by-step explanation:

Since x= 5 is a vertical line, the unknown line would also be a vertical line with an equation of x=___ as they are parallel to each other.

Given that the line passes through (-1, 2), the equation of the line is x= -1.

Parallel lines have the same slope and will never meet.

Answer:

  1994

Step-by-step explanation:

After 1 year, the balance has been multiplied by 1.05. After t years, it has been multiplied by 1.05^t.

You want to find t such that ...

  100(1.05^t) > 520

  1.05^t > 5.20

  t×log(1.05) > log(5.20) . . . . take logarithms

  t > log(5.20)/log(1.05) ≈ 33.8

The account balance will exceed $520 after interest is added in ...

  1960 +34 = 1994

Answer:

252008 miles 405696 km from earth

Step-by-step explanation:

In triangle ABC, we are given that angle C is a right angle, which means it measures 90°. We also know that angle B is 36°12′, and side c has a length of 0.6209 m. Our goal is to find the measures of angle A and the lengths of sides a and b.

Using the fact that the sum of angles in a triangle is 180°, we can find angle A:

A + B + C = 180°

A = 180° - B - C = 180° - 36°12′ - 90° = 53°48′

Now, we can apply the trigonometric ratios in the right-angled triangle ABC. The ratios are defined as follows:

Sine (sin) = Opposite / Hypotenuse

Cosine (cos) = Adjacent / Hypotenuse

Tangent (tan) = Opposite / Adjacent

Using the given values, we can determine the lengths of sides a and b:

Sine ratio:

sin B = a / c

Substituting the known values, we find:

sin 36°12′ = a / 0.6209

a = 0.6209 x sin 36°12′ = 0.3774 m

Cosine ratio:

cos B = b / c

Substituting the known values, we find:

cos 36°12′ = b / 0.6209

b = 0.6209 x cos 36°12′ = 0.5039 m

Tangent ratio:

tan B = a / b

Substituting the values of a and b, we find:

tan 36°12′ = 0.3774 / 0.5039 = 0.7499

Therefore, the lengths of sides a and b are approximately 0.3774 m and 0.5039 m, respectively. Angle A measures 53°48′, angle B measures 36°12′, and angle C is the right angle.

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By 1/2 millimeters of mercury will the normal systolic blood pressure for an adult male increase.

To find by how many millimeters of mercury will the normal systolic blood pressure for an adult male increase:

Therefore, by 1/2 millimeters of mercury will the normal systolic blood pressure for an adult male increase.

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Answer:

mathematics 5 puntosHaso minutos what tienes what aquel 400but when

Answer:

C. right angle

Step-by-step explanation:

I will upload an image of a right angle that perfectly fits the question:

The angles that measure 90° are called right angles, so the correct option is C.

A 90° angle is the one we get when two perpendicular lines intersect (we actually get four of these).

And are the same ones that we can see on squares or rectangles, where the connecting sides are perpendicular between them.

The name of that type of angle, as one could imagine, is Right Angle (for the nature of the intersection that conforms them). So the correct option is C.

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Answer: ($)8.75

Step-by-step explanation:

To calculate the tax, simply do 10%(0.1)*7.95 to get 0.795, rounding up to 0.80(money typically rounds up).

To calculate the total cost, simply do 7.95+0.80 to get 8.75.

Hope it helps <3

Answer:

11.3 (√128)

Step-by-step explanation:

\( \\ {a}^{2} + {b}^{2} = {c}^{2} \)

in this case a is given and c is given

a =side of the triangle

b= side of the triangle

c = hypotenuse or the longest side of the triangle

4^2 + b^2 = 12^2

16+ b^2 = 144

144 - 16 = b^2

128 = b^2

√128 = b

11.3137...= b = 11.3 (rounded to nearest tenth)

Answer: 715*10^7

Step-by-step explanation:

Answer:

Expressed in scientific notation: 7.15 * 10^7 tons

Step-by-step explanation:

Period of the functions: The period of the function f(t) = (7 cos t)² is given by 2π/b where b is the period of cos t.The period of the function f(t) = cos (2φt²/m) is given by T = √(4πm/φ). The period of the function f(t) = (7 cos t)² is given by 2π/b where b is the period of cos t.

We know that cos (t) is periodic and has a period of 2π.∴ b = 2π∴ The period of the function f(t) =

(7 cos t)² = 2π/b = 2π/2π = 1.

The period of the function f(t) = cos (2φt²/m) is given by T = √(4πm/φ) Hence, the period of the function f(t) =

cos (2φt²/m) is √(4πm/φ).

The function f(t) = (7 cos t)² is a trigonometric function and it is periodic. The period of the function is given by 2π/b where b is the period of cos t. As cos (t) is periodic and has a period of 2π, the period of the function f(t) = (7 cos t)² is 2π/2π = 1. Hence, the period of the function f(t) = (7 cos t)² is 1.The function f(t) = cos (2φt²/m) is also a trigonometric function and is periodic. The period of this function is given by T = √(4πm/φ). Therefore, the period of the function f(t) = cos (2φt²/m) is √(4πm/φ).

The period of the function f(t) = (7 cos t)² is 1, and the period of the function f(t) = cos (2φt²/m) is √(4πm/φ).

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The long run behavior of the function f(x)=5(2)x+1 is that it approaches 1 as x approaches negative infinity and it approaches infinity as x approaches positive infinity.

The long-term behavior of the function f(x)=5(2)x+1 can be discovered by examining how the function behaves as x gets closer to negative and positive infinity.

As x→−[infinity], f(x) = 5(2)^ -∞+1 = 5(0)+1 = 1

As x approaches negative infinity, the value of the function approaches 1.

As x→[infinity], f(x) = 5(2)^ ∞+1 = 5(∞)+1 = ∞

As x approaches positive infinity, the value of the function approaches infinity.

As a result, the function f(x)=5(2)x+1 behaves in the long run in such a way that it approaches 1 as x approaches negative infinity and infinity as x approaches positive infinity.

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Answer:

4b=3

b= 3/4

b=0.75

...........................

Answer:

7200

Step-by-step explanation:

Find the exponents first.

10^3 = 1000

10^2 = 100

So..

7 x 1000 + 2 x 100

Do the multiplication first (BEDMAS - Brackets Exponents Division Multiplication Addition Subtraction).

7000 + 200 = 7200

To solve the given differential equation, we will make the substitution x = exp(z).

Let's go through the steps to transform the equation and obtain a second-order ordinary differential equation (ODE) with constant coefficients. Differentiating x = exp(z) with respect to z using the chain rule, we get dx/dz = exp(z) and d^2x/dz^2 = d(exp(z))/dz = exp(z).

Now, let's express the derivatives of y with respect to x in terms of derivatives with respect to z. We have dx/dz = exp(z), so dx = exp(z)dz. By differentiating y with respect to x using the chain rule, we have dy/dx = dy/dz * dz/dx = dy/dz * (dx/dz)^(-1) = dy/dz * exp(-z). Similarly, d^2y/dx^2 = d/dx (dy/dx) = d/dz (dy/dz * exp(-z)) * (dx/dz)^(-1) = [d^2y/dz^2 * exp(-z) - dy/dz * exp(-z)] * exp(-z).

Now, substitute these expressions into the original differential equation. We have (exp(z))^2 * [d^2y/dz^2 * exp(-z) - dy/dz * exp(-z)] * exp(-z) + exp(z) * dy/dz * exp(-z) + y = ln((exp(z))^2) + 1. Simplifying, we get:
exp(z) * [d^2y/dz^2 - dy/dz] + y = 2z + 1.

This is a second-order ODE with constant coefficients. The general solution of this equation can be found by solving the characteristic equation associated with it, which is given by:
r^2 - r + 1 = 0.

The roots of this equation are complex, given by r = (1 ± i√3)/2. Therefore, the general solution of the ODE is:
y = C1 * exp(r1 * z) + C2 * exp(r2 * z), where C1 and C2 are arbitrary constants, and r1 and r2 are the roots of the characteristic equation.

Finally, substituting x = exp(z) back into the equation, the general solution in terms of y and x is:
y = C1 * x^((1 + i√3)/2) + C2 * x^((1 - i√3)/2), where C1 and C2 are arbitrary constants.

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Reflection of point 1 over X axis is (-4, -2)

Reflection of point 2 over Y axis is (2, 3)

Reflection of point 3 over x = 1 is (2, 1)

Reflection of point 4 over y = x is  (2, -1)

What is Reflection of a point?

A reflection point occurs when a figure is constructed around a single point known as the point of reflection or center of the figure. For every point in the figure, another point is found directly opposite to it on the other side.

According to the given question:

1. Reflection of point 1 over X axis (x, -y) ⇔ (x, y)

 ∴ Reflection of (-4, 2) over X axis is (-4, -2)

2. Reflection of point 2 over Y axis (x, y) ⇔ (-x, y)

 ∴ Reflection of (-2, 3) over Y axis is (2, 3)

3. Reflection of point 3 over x = 1

 ∴ Reflection of (-2, 1) over x = 1 axis is (2, 1)

4. Reflection of point 4 over y = x is  (x, y) ⇔ (y, x)

 ∴ Reflection of (-1, 2) over X axis is (2, -1)

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The triple integral using these bounds ∫₀^(π/2) ∫₀^(√(9 - z)) ∫₀^(9 - r^2) (r cosθ + r sinθ + z) r dz dr dθ.

To evaluate the triple integral ∭E (x + y + z) dV in cylindrical coordinates, we first need to express the bounds of the integral and the differential volume element in cylindrical form.

The paraboloid z = 9 - x^2 - y^2 can be rewritten as z = 9 - r^2, where r is the radial distance from the z-axis. In cylindrical coordinates, the solid E in the first octant is defined by the conditions 0 ≤ r ≤ √(9 - z) and 0 ≤ θ ≤ π/2, where θ is the angle measured from the positive x-axis.

Now, let's express the differential volume element dV in cylindrical form. In Cartesian coordinates, dV = dx dy dz, but in cylindrical coordinates, we have dV = r dr dθ dz.

Now we can rewrite the triple integral using cylindrical coordinates:

∭E (x + y + z) dV = ∫∫∫E (r cosθ + r sinθ + z) r dr dθ dz.

The bounds of integration are as follows:

For z: 0 ≤ z ≤ 9 - r^2 (from the equation of the paraboloid)

For r: 0 ≤ r ≤ √(9 - z) (within the first octant)

For θ: 0 ≤ θ ≤ π/2 (within the first octant)

We can now evaluate the triple integral using these bounds:

∫∫∫E (r cosθ + r sinθ + z) r dr dθ dz

= ∫₀^(π/2) ∫₀^(√(9 - z)) ∫₀^(9 - r^2) (r cosθ + r sinθ + z) r dz dr dθ.

Performing the integration in the specified order, we can find the numerical value of the triple integral.

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Answer:

To solve for x in the equation 2(x + 1) = -8, we can use the following steps:

Distribute the 2 on the left side of the equation:

2x + 2 = -8

Subtract 2 from both sides to isolate the x term:

2x = -10

Divide both sides by 2 to solve for x:

x = -5

Therefore, the solution for x is -5.

Answer:

x=-5

Step-by-step explanation:

multiple 2 by x and 1

2x+2

then subtract 2 on both sides

2x=-10

divide 2x from both sides

x=-5

Evaluating this triple integral will give us the volume of the solid bounded below by the cone z and bounded above by the sphere xyz.

To find the volume of the solid bounded below by the cone z and bounded above by the sphere xyz, we can use a triple integral.

First, we need to determine the limits of integration for each variable.

For z, the lower limit is 0 (since the solid is bounded below by the cone z), and the upper limit is the equation of the sphere, which is x^2 + y^2 + z^2 = r^2 (where r is the radius of the sphere). Solving for z, we get z = sqrt(r^2 - x^2 - y^2).

For y, the limits are -sqrt(r^2 - x^2) to sqrt(r^2 - x^2), which represents the cross-section of the sphere at a given value of x.

For x, the limits are -r to r, which represents the entire sphere.

Therefore, the triple integral to find the volume of the solid is:

V = ∭dV = ∫∫∫ dzdydx

Where the limits of integration are:

-∫r^2-x^2-y^2 to ∫sqrt(r^2-x^2-y^2) for z
-∫sqrt(r^2-x^2) to ∫-sqrt(r^2-x^2) for y
-∫-r to ∫r for x

The integrand, dV, represents an infinitesimal volume element in Cartesian coordinates.

Evaluating this triple integral will give us the volume of the solid bounded below by the cone z and bounded above by the sphere xyz.

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The cost of direct labor per unit is $5.628 per apple.

To calculate the cost of direct labor per unit, we need to determine the total labor hours required to produce one unit of output and then multiply it by the wage rate.

Let's denote the labor hours required for the first resource as "L₁" and the labor hours required for the second resource as "L₂".

The first resource has a capacity of 2.1 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the first resource per unit of output are:

L₁ = 1 apple / (2.1 apples/hour) = 0.4762 hours/apple (rounded to 4 decimal places)

The second resource has a capacity of 4.4 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the second resource per unit of output are:

L₂ = 1 apple / (4.4 apples/hour) = 0.2273 hours/apple (rounded to 4 decimal places)

Now, let's calculate the total labor hours required per unit:

Total labor hours per unit = L₁ (first resource) + L₂ (second resource)

= 0.4762 hours/apple + 0.2273 hours/apple

= 0.7035 hours/apple (rounded to 4 decimal places)

Finally, to calculate the cost of direct labor per unit, we multiply the total labor hours per unit by the wage rate:

Cost of direct labor per unit = Total labor hours per unit * Wage rate

= 0.7035 hours/apple * $8/hour

= $5.628 per apple (rounded to 3 decimal places)

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9514 1404 393

Answer:

  25.5 cm

Step-by-step explanation:

If the walk is x meters wide, it adds 2x to the overall length and width. Then the area of the walkway is ...

  (2x +5)(2x +6.25) -(5)(6.25) = 6

  4x^2 +22.5x = 6 . . . . simplify left side

  4x^2 +22.5x -6 = 0 . . . subtract 6 to put into standard form

Using the quadratic formula, the walkway width can be found to be ...

  x = (-22.5 +√(22.5² -4(4)(-6)))/(2(4)) = (-22.5 +√602.25)/8

  x ≈ 0.25510

The border width should be about 25.5 cm.