Which of the following statements are correct?

Answer:

[tex]\mathsf{x=\dfrac{35}{2}}[/tex]  or  [tex]\mathsf{x=17.5}[/tex]

Step-by-step explanation:

Given:

Let x = number of hours worked

⇒ 6.5x = 113.75

[tex]\implies \mathsf{x=\dfrac{113.75}{6.5}}[/tex]

[tex]\implies \mathsf{x=\dfrac{35}{2}}[/tex]

[tex]\implies \mathsf{x=17.5}[/tex]

Answer:

Oliver pays $6.30

Step-by-step explanation:

Selling price = $15

At discount of 40%, Jinkie's Jumpin' Junkfood's sells for;

[tex]15-(15~x~0.4)=15-6[/tex]

[tex]15-(15~x~0.4)=9[/tex]

But Oliver also has a coupon worth 30% discount off the same price at register;

[tex]9-(9~x~0.3)=9-2.7[/tex]

[tex]9-(9~x~0.3)=6.3[/tex]

Thus, Oliver pays $6.30

Answer:

62°=y

62°=x......

......

......

The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.

y² = x

Take the derivative of both sides with respect to x, assuming y = y(x) :

2y dy/dx = 1

dy/dx = 1/(2y)

Solve for y when dy/dx = 1 :

1 = 1/(2y)

2y = 1

y = 1/2

When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.

This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :

x = y²   ⇒   y = y² + 3   ⇒   y² - y + 3 = 0

has no real solution for y.

The given height of the cylinder of 1.5 m, and radius of 1 m, and the rate

of dripping of 110 cm³/s gives the following values.

1) The rate of change of the oil's radius when the radius is 0.5 m is r' ≈ 9.34 × 10⁻⁵ m/s

2) The rate of change of the oil's height when the height is 20 cm is h' ≈ 1.97 × 10⁻³ m/s

3) The rate the oil radius is changing when the radius is 10 cm is approximately 0.175 m/s

The given parameters are;

Height of the tank, h = 1.5 m

Radius of the tank, r = 1 m

Rate at which the oil is dripping from the tank = 110 cm³/s = 0.00011 m³/s

[tex]1) \hspace{0.15 cm}V = \frac{1}{3} \cdot \pi \cdot r^2 \cdot h[/tex]

From the shape of the tank, we have;

[tex]\dfrac{h}{r} = \dfrac{1.5}{1}[/tex]

Which gives;

h = 1.5·r

[tex]V = \mathbf{\frac{1}{3} \cdot \pi \cdot r^2 \cdot (1.5 \cdot r)}[/tex]

[tex]\dfrac{d}{dr} V =\dfrac{d}{dr} \left( \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot (1.5 \cdot r)\right) = \dfrac{3}{2} \cdot \pi \cdot r^2[/tex]

[tex]\dfrac{dV}{dt} = \dfrac{dV}{dr} \times \dfrac{dr}{dt}[/tex]

[tex]\dfrac{dr}{dt} = \mathbf{\dfrac{\dfrac{dV}{dt} }{\dfrac{dV}{dr} }}[/tex]

[tex]\dfrac{dV}{dt} = 0.00011[/tex]

Which gives;

[tex]\dfrac{dr}{dt} = \mathbf{ \dfrac{0.00011 }{\dfrac{3}{2} \cdot \pi \cdot r^2}}[/tex]

When r = 0.5 m, we have;

[tex]\dfrac{dr}{dt} = \dfrac{0.00011 }{\dfrac{3}{2} \times\pi \times 0.5^2} \approx 9.34 \times 10^{-5}[/tex]

The rate of change of the oil's radius when the radius is 0.5 m is r' ≈ 9.34 × 10⁻⁵ m/s

2) When the height is 20 cm, we have;

h = 1.5·r

[tex]r = \dfrac{h}{1.5}[/tex]

[tex]V = \mathbf{\frac{1}{3} \cdot \pi \cdot \left(\dfrac{h}{1.5} \right) ^2 \cdot h}[/tex]

r = 20 cm ÷ 1.5 = [tex]13.\overline3[/tex] cm = [tex]0.1\overline3[/tex] m

Which gives;

[tex]\dfrac{dr}{dt} = \dfrac{0.00011 }{\dfrac{3}{2} \times\pi \times 0.1 \overline{3}^2} \approx \mathbf{1.313 \times 10^{-3}}[/tex]

[tex]\dfrac{d}{dh} V = \dfrac{d}{dh} \left(\dfrac{4}{27} \cdot \pi \cdot h^3 \right) = \dfrac{4 \cdot \pi \cdot h^2}{9}[/tex]

[tex]\dfrac{dV}{dt} = \dfrac{dV}{dh} \times \dfrac{dh}{dt}[/tex]

[tex]\dfrac{dh}{dt} = \dfrac{\dfrac{dV}{dt} }{\dfrac{dV}{dh} }[/tex]

[tex]\dfrac{dh}{dt} = \mathbf{\dfrac{0.00011}{\dfrac{4 \cdot \pi \cdot h^2}{9}}}[/tex]

When the height is 20 cm = 0.2 m, we have;

[tex]\dfrac{dh}{dt} = \dfrac{0.00011}{\dfrac{4 \times \pi \times 0.2^2}{9}} \approx \mathbf{1.97 \times 10^{-3}}[/tex]

The rate of change of the oil's height when the height is 20 cm is h' ≈ 1.97 × 10⁻³ m/s

3) The volume of the slick, V = π·r²·h

Where;

h = The height of the slick = 0.1 cm = 0.001 m

Therefore;

V = 0.001·π·r²

[tex]\dfrac{dV}{dr} = \mathbf{ 0.002 \cdot \pi \cdot r}[/tex]

[tex]\dfrac{dr}{dt} = \mathbf{\dfrac{0.00011 }{0.002 \cdot \pi \cdot r}}[/tex]

When the radius is 10 cm = 0.1 m, we have;

[tex]\dfrac{dr}{dt} = \dfrac{0.00011 }{0.002 \times \pi \times 0.1} \approx \mathbf{0.175}[/tex]

The rate the oil radius is changing when the radius is 10 cm is approximately 0.175 m

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Answer:

59m

Step-by-step explanation:

280 =81+81 +w + w

280=162+2w

2w =280-162

w=118/2

w=59m

Answer:

21-9 = 12

Step-by-step explanation:

I don't know if this is the correct sentence you are looking for though but i hope it helps

Answer:

d) A ball is thrown directly upward from an initial height of 7 feet, will reach a maximum height of 19.3 ft in 0.9 s, and finally will hit the ground in 2 s.

Step-by-step explanation:

The y-intercept of the curve is at (0, 7) so when t = 0, the ball is 7 ft above the ground.  Therefore, the ball is thrown from an initial height of 7 feet.

The maximum point of the curve is (0.9, 19.3) which means the maximum height is 19.3 feet is reached after 0.9 seconds.

Finally, the curve intercepts the x-axis at t = 2, which means at 2 s the ball's height is zero, i.e. it hits the ground at 2 s.

Answer:

x > -2

Step-by-step explanation:

x+8+3x>2x+6

4x+8>2x+6

4x-2x>6-8

2x> -2

x > -2

[tex] \sf \frac{8 {x}^{2} }{12 {x}^{4} } [/tex]

Reduce the like terms with a common factor 2

[tex] \sf \frac{8}{12 {x}^{2} } [/tex]

Reduce the fraction with 4

[tex] \sf \frac{2}{3 {x}^{2} } [/tex]

1.) We cannot construct a triangle if two of its angles are of measures

We cannot construct such angle because when one angle is 90°, others cannot be close to it because it will form a right angle triangle and we know that it has 3 angles. Also if the angle will 95°, it will be wrong since the sum of all angles must be 180°...

Answer:

95,90

Step-by-step explanation:

According to angle sum property the sum of angles of a triangle is 180°

So here that be x

Angle can't be negative

Answer:

Translations reflections, and rotations

are

Step-by-step explanation:

Hope this helps

Question 1 : Translations Reflections, And Rotations

Question 2 : And

◊ YusuCr ◊

Answer:

[tex]y=-3x+-5[/tex]

Step-by-step explanation:

Given the following question:

Point A = (-3, 4) = (x1, y1)
Point B = (0, -5) = (x2, y2)

To find the slope intercept of a line we must first find the slope, using the formula for slope or rise over run.

[tex]m=\frac{y2-y1}{x2-x1}[/tex]
[tex]m=\frac{-5-4}{0--3} =\frac{-9}{3}[/tex]
[tex]\frac{-9}{3} \div3=\frac{-3}{1} =-3[/tex]
[tex]m=-3[/tex]

Now to find the slope intercept of a line, we must use the formula to find the slope intercept and solve for b.

[tex]y=mx+b[/tex]
[tex]m=-3[/tex]
[tex]y=4[/tex]
[tex]x=-3[/tex]
[tex]4=-3(-3)+b[/tex]

Solve for b:
[tex]4=-3(-3)+b[/tex]
[tex]-3\times-3=9[/tex]
[tex]4=9+b[/tex]
[tex]9-9=0[/tex]
[tex]4-9=-5[/tex]
[tex]b=-5[/tex]
[tex]y=-3x+-5[/tex]

The slope intercept of the line is "y = -3x +-5."

Hope this helps.

Answer:

13 inches and 10 inches

Step-by-step explanation:

First, let's find the factor pairs that make up the area of 130 square inches.

Next, let's see the factor pairs that make a perimeter of 46 inches by using the formula 2(l + w).

Therefore, the dimensions of the folder are 13 inches and 10 inches.

Answer:

B) Least 10 hours, greatest 14 hours

Step-by-step explanation:

The range of sin(x) is -1 ≤ sin(x) ≤ 1

Therefore, the range of  [tex]\sin(\frac{\pi }{6}t)[/tex]  is  [tex]-1\leq \sin(\frac{\pi }{6}t)\leq 1[/tex]

Therefore, the range of  [tex]2 \sin(\frac{\pi }{6}t)[/tex]  is  [tex]-2\leq 2 \sin(\frac{\pi }{6}t)\leq 2[/tex]

This means the range of  [tex]2 \sin(\frac{\pi }{6}t)+12[/tex]  is  [tex]10\leq 2 \sin(\frac{\pi }{6}t)+12\leq 14[/tex]

Answer:

201

Step-by-step explanation:

108/360 x 100% = 30%

So, how far is the car from where it was at t = 0 is 40 m

Since the location x of the car in meters is given by the function x = 30t - 5t² where t is in seconds, we need to find the time at which its velocity is 10 m/s in the negative direction by differentiating x with respect to t to find its velocity, v.

So, v = dx/dt

= d(30t - 5t²)/dt

= d30t/dt - d5t²/dt

= 30 - 10t

When v is 10 m/s in the negative direction, v = -10 m/s.

So, v = 30 - 10t

-10 = 30 - 10t

-10 - 30 = -10t

-40 = -10t

t = -40/-10

t = 4 s

Since at t = 4 s, its velocity is -10 m/s and x = 30t - 5t² is the car's location. The car's distance from t = 0 after its velocity is -10 m/s is

x(4) - x(0) = 30(4) - 5(4)² - [30(0) - 5(0)²]

= 120 - 5(16) - [0 - 0]

= 120 - 80 - 0

= 40 m

So, how far is the car from where it was at t = 0 is 40 m

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answer:

3/11

step-by-step explanation:

— since they have the same denominator you just have to subtract the numerator

8 / 11 - 5 / 11 = it would be just subtracting 8 - 5, which is 3

— so, 3/11

Hey there!

8/11 - 5/11

= 8 - 5 / 11 - 0

= 3 / 11

Therefore, your answer is: 3/11

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Parrelelogram

Step-by-step explanation:

Conggruent means sam angle but diiferent length and a parrelelogram has s standardized size deviation where the symmetry monsizes the ooppiosite size

Answer:

a₂₀ = 60

Step-by-step explanation:

Given :-

a₃ = 9

a₈ = 24

To find :-

a₂₀

Solving :-

Expand the given values.

a + 2d = 9 -(1)

a + 7d = 24 -(2)

Now subtract (1) from (2).

=> 5d = 15

=> d = 3

a = 9 - 2d

a = 9 - 6

a = 3

Final answer :-

a₂₀

= a + 19d

= 3 + 19(3)

= 3+ 57

= 60

a₂₀ = 60

Answer:

-3

Step-by-step explanation:

The line crosses at -3 on the x axis

Answer:

what you are looking? if you need a answer I think it is 24t^7 but tell me what are you looking

Answer:

see explanation

Step-by-step explanation:

given 2 sides of a triangle then the third side x is in the range

difference of 2 sides < x < sum of 2 sides , that is

22 - 18 < x < 22 + 18

4 < x < 40

3rd side can be any value from 5 to 39

Answer:

1) x = 40 B = 10

2) y = 50 U = 60

3) y = 7 x = 13

4) y = 77 k = 13

5) x = 9 A = 35

Step-by-step explanation:

Couple of things to remember:

1. The sum of all angles in a triangle equal 180

2. The letters in the congruent statements correspond to which angles are congruent to each other.

In the first problem, the statement has C and F in the same position. Both are the last letter of each triangle. Therefore, they are congruent and should be set equal to each other

2x = 80 (Solve by dividing both sides by 2)

x = 40

This strategy can be used to solve the others.

Answer:

200ft²

Step-by-step explanation:

1x2=2

10x20=200

So hence, you need 200ft² of flooring for a rom that is 10 feet wide and 20 feet long.

Thanks!