The original cost of a lamp is $18.95. The lamp is on sale for 25% off. How much will you pay?

$9.48

$14.21

$4.74

$1.90

Answer:

B. (0, 3)

Step-by-step explanation:

Trying the offered solutions in the given equations gets you there pretty quickly.

7·(-6) -2(3) ≠ -6 . . . eliminates choice A

__

7·0 -2·3 = -6

8·0 +3 = 3 . . . . . . . choice B is the solution

Answer:

(0,3)

B is correct

Step-by-step explanation:

Given: The system of equation.

[tex]7x-2y=-6[/tex]

[tex]8x+y=3[/tex]

Now, we solve for x and y using elimination method.

Elimination method: In this method to make the coefficient of one variable same and then cancel out by addition of both equation.

Multiply 2nd equation by 2 and we get

[tex]16x+2y=6[/tex]

[tex]7x-2y=-6[/tex]

Add both equation and eliminate y

[tex]23x=0[/tex]

[tex]x=0[/tex]

Put x=0 into 1st equation, 7x-2y=-6

7(0) - 2y = -6

           y = 3

Solution: x = 0 and y = 3

Hence, The solution of the equation would be (0,3)

➷ You have to subtract the values:

38,428 - 21,728 = 16,700

He should have $16,700 (you can change the currency symbol if required)

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

In a system of equations, if the variable x is found to be equal to 2 and y is found to be equal to 4, the value of x - y is -2.

To solve for the values of x and y in this pair of linear equations, we can use a method known as substitution or elimination. However, the question asks for the value of x-y, not for the individual values of x and y.

First, let's multiply the first equation by 2 and the second equation by 3:

4x - 6y = -28 (equation 1)

9x - 6y = -18  (equation 2)

If we subtract Equation 2 from Equation 1, we get -5x = -10. Solving for x, we find that x = 2.

Substituting the value of x into the first equation, we get:

2(2) - 3y = -14

Solving for y, we find that y = 4.

Therefore, x - y = 2 - 4 = -2.

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For the last part, you have to find where [tex]f'(t)[/tex] attains its maximum over [tex]0\le t\le8[/tex]. We have

[tex]f'(t)=-6\sin3t+6\cos2t[/tex]

so that

[tex]f''(t)=-18\cos3t-12\sin2t[/tex]

with critical points at [tex]t[/tex] such that

[tex]-18\cos3t-12\sin2t=0[/tex]

[tex]3\cos3t+2\sin2t=0[/tex]

[tex]3(\cos^3t-3\cos t\sin^2t)+4\sin t\cos t=0[/tex]

[tex]\cos t(3\cos^2t-9\sin^2t+4\sin t)=0[/tex]

[tex]\cos t(12\sin^2t-4\sin t-3)=0[/tex]

So either

[tex]\cos t=0\implies t=\dfrac{(2n+1)\pi}2[/tex]

or

[tex]12\sin^2t-4\sin t-3=0\implies\sin t=\dfrac{1\pm\sqrt{10}}6\implies t=\sin^{-1}\dfrac{1\pm\sqrt{10}}6+2n\pi[/tex]

where [tex]n[/tex] is any integer. We get 8 solutions over the given interval with [tex]n=0,1,2[/tex] from the first set of solutions, [tex]n=0,1[/tex] from the set of solutions where [tex]\sin t=\dfrac{1+\sqrt{10}}6[/tex], and [tex]n=1[/tex] from the set of solutions where [tex]\sin t=\dfrac{1-\sqrt{10}}6[/tex]. They are approximately

[tex]\dfrac\pi2\approx2[/tex]

[tex]\dfrac{3\pi}2\approx5[/tex]

[tex]\dfrac{5\pi}2\approx8[/tex]

[tex]\sin^{-1}\dfrac{1+\sqrt{10}}6\approx1[/tex]

[tex]2\pi+\sin^{-1}\dfrac{1+\sqrt{10}}6\approx7[/tex]

[tex]2\pi+\sin^{-1}\dfrac{1-\sqrt{10}}6\approx6[/tex]

The correct answer for part (d) is: The particle is moving the fastest at [tex]\( t = 4.7 \)[/tex] with a speed of [tex]5[/tex] units per time period.

To find when the particle is moving the fastest, we need to determine the time at which the velocity of the particle is maximized. The velocity of the particle is given by the derivative of the position function with respect to time. The position function is [tex]\( f(t) = 2 \cos(3t) + 3 \sin(2t) \)[/tex]. Differentiating this with respect to [tex]\( t \)[/tex] gives the velocity function:

[tex]\[ v(t) = \frac{d}{dt}(2 \cos(3t) + 3 \sin(2t)) = -6 \sin(3t) + 6 \cos(2t) \][/tex]

To find the maximum velocity, we need to find the critical points of the velocity function by setting its derivative equal to zero:

[tex]\[ \frac{d}{dt}(-6 \sin(3t) + 6 \cos(2t)) = -18 \cos(3t) - 12 \sin(2t) = 0 \][/tex]

Solving for [tex]\( t \)[/tex] in the interval [tex]\( 0 \leq t \leq 8 \)[/tex] will give us the times at which the velocity is maximized or minimized. Let's solve for [tex]\( t \)[/tex]:

[tex]\[ -18 \cos(3t) = 12 \sin(2t) \][/tex]

This is a transcendental equation and cannot be solved algebraically. We would typically use numerical methods or graphing to find the solutions. However, since we are given that the time when the particle is moving the fastest is [tex]\( t = 4.7 \)[/tex], we can assume that this is the time at which the velocity function reaches its maximum value.

Now, to find the speed at which the particle is moving the fastest, we evaluate the velocity function at [tex]\( t = 4.7 \)[/tex]:

[tex]\[ v(4.7) = -6 \sin(3 \cdot 4.7) + 6 \cos(2 \cdot 4.7) \][/tex]

Calculating the sine and cosine values and then substituting them into the equation will give us the maximum velocity. Since we are looking for the speed, which is the absolute value of the velocity, we take the absolute value of the result.

The speed is given by the magnitude of the velocity vector, so we have:

[tex]\[ |v(4.7)| = |-6 \sin(3 \cdot 4.7) + 6 \cos(2 \cdot 4.7)| \][/tex]

Evaluating this expression will give us the speed at which the particle is moving the fastest. The correct answer, rounded to the nearest integer, is [tex]\( 5 \)[/tex] units per time period, not [tex]\( -5 \).[/tex] The negative sign in the velocity does not affect the speed, as speed is a scalar quantity and is always positive.

Therefore, the particle is moving the fastest at [tex]\( t = 4.7 \)[/tex] with a speed of [tex]\( 5 \)[/tex] units per time period.

Answer:

Step-by-step explanation:

3y + 19 = 6y + 1

6y + 1 = 3y + 19

6y - 3y = 19 - 1

3y = 18

y = 6

6y + 1

6.6 + 1

37

The first one

I hope I helped you.

Answer:

Option A. 37

Step-by-step explanation:

We will understand first what is a regular hexagon?

Hexagon is a structure in which number of all the sides are 6 and since its a regular hexagon all the sides will be equal.

Since all the sides are equal and given two sides are (3y + 19) and (6y + 1)

Therefore, by the definition of regular hexagon

3y + 19 = 6y + 1

19 = 6y - 3y + 1

19 - 1 = 6y - 3y

18 = 3y

y = [tex]\frac{18}{3}=6[/tex]

Now we have to calculate the length of both the sides given.

Side ST = 6y + 1 = 6×6 + 1 = 36 + 1 = 37

and QR = 3y + 19 = 3×6 + 19 = 18 + 19 = 37

Therefore, option A. 37 is the correct answer.

➷ There is only one '3' on the cube

Therefore, it would be B. 1/6

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

See the attached picture for the solution:

Answer:

Step-by-step explanation:

1/(1+sinθ) + 1/(1-sinθ)

= (1-sinθ)/[(1+sinθ)(1-sinθ)] + (1+sinθ)/[(1-sinθ)(1+sinθ)]

= [(1-sinθ) + (1+sinθ)] / [(1-sinθ)(1+sinθ)]

= [1 - sinθ + 1 + sinθ] / [1 - sin^2sθ]

= 2 / cos^2θ

Answer:

4/9

Step-by-step explanation:

Given rate is 1/3 acre per 3/4 hours.

To calculate the rate per hour, we have to divide total acres by the fraction of hour

=> [tex]\frac{\frac{1}{3} }{\frac{3}{4} }[/tex]

=> [tex]\frac{4}{3*3}[/tex]

=> 4/9

Answer:

6

Step-by-step explanation:

***If choosing one of each, this is the answer*** This wasn't clearly asked for in the question though

When counting the number of arrangements of multiple choices, multiply the number of choices of each item together.

(3)(2)(1) = 6

Here is them listed..

Green ball 1, red ball 1, white ball

Green ball 1, red ball 2, white ball

Green ball 2, red ball 1, white ball

Green ball 2, red ball 2, white ball

Green ball 3, red ball 1, white ball

Green ball 3, red ball 2, white ball

Answer:

the the third graph

Step-by-step explanation:

this is because the third graph shows a correlation of the time and when the rainfall in a proporational relesho=inshop

Answer:

the third graph :)

Step-by-step explanation:

each hour the rain is increasing by 2 drops.

Answer:

A. quadrilateral, parallelogram, rhombus

Step-by-step explanation:

Parallel sides are equal

Answer:

The answer is ellipse; 30° ⇒ answer (d)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

* 13x² + 6√3xy + 7y² - 16 = 0

∵ A = 13 , B = 6√3 , C = 7

∴ B² - 4 AC = (6√3)² - 4(13)(7) = -256

∴ B² - 4AC < 0

∴ The graph is ellipse or circle

* If A and C are nonzero, have the same sign, and are not

 equal to each other, then the graph is an ellipse.

* If A and C are equal and nonzero and have the same

 sign, then the graph is a circle.

∵ A and C have same signs with different values

∴ It is an ellipse

* To find the angle of rotation use the rule:

- cot(2Ф) = (A - C)/B

∵ A = 13 , B = 6√3 , C = 7

∴ cot(2Ф) = (13 - 7)/6√3 = 6/6√3 = 1/√3

∵ tan(2Ф) = 1/cot(2Ф)

∴ tan(2Ф) = √3 ⇒ 2Ф = [tex]tan^{-1}\sqrt{3}=60[/tex]

∴ 2Ф = 60°

∴ Ф = 30°

* The answer is ellipse; with angle of rotation = 30°

Answer:

The answer is ellipse; 30° ⇒ answer (d)

Step-by-step explanation:

Answer:

1056.25π square units

Step-by-step explanation:

A few formulas an definitions which will help us:

(1) [tex]\pi=\frac{c}{d}[/tex], where c is the circumference of a circle and d is its diameter

(2) [tex]A=\pi r^2[/tex], where A is the area of a circle with radius r. To put it in terms of d, remember that a circle's diameter is simply twice its radius, or mathematically, (3) [tex]d=2r \rightarrow r=\frac{d}{2}[/tex].

We can rearrange equation (1) to put d in terms of π and c, giving us (4) [tex]d = \frac{c}{\pi}[/tex], and we can make a few substitutions in (2) using (3) and (4) to get use the area in terms of the circumference and π:

[tex]A=\pi r^2\\=\pi\left(\frac{d}{2}\right)^2\\=\pi\left(\frac{d^2}{4}\right)\\=\pi\left(\frac{(c/\pi)^2}{4}\right)\\=\pi\left(\frac{c^2/\pi^2}{4}\right)\\=\pi\left(\frac{c^2}{4\pi^2}\right)\\\\=\frac{\pi c^2}{4\pi^2}\\ =\frac{c^2}{4\pi}[/tex]

We can now substitute c for our circumference, 65, to get our answer in terms of π:

[tex]A=\dfrac{65^2}{4\pi}=\dfrac{4225}{4\pi}=1056.25\pi[/tex]

Answer:

Area = 2112.5 / pi

Step-by-step explanation:

They are asking you not to use 3.14 for pi. Just leave it as a symbol.

C = 2*pi*r

C = 65

65 = 2*pi*r

65/(2*pi) = r

The area of a circle is 2*pi * r^2

Area = 2 * pi * (65/2pi)^2

Area = 2 * pi * 65^2/(4*pi^2)           Cancel out one of the pi-s in the denominator

Area = 2 * 65^2 / (4 * Pi)                  Expand the numerator

Area = 8450/(4*pi)                           Divide by 4

Area = 2112.5 / pi

Answer:

A

Step-by-step explanation:

To find the best equation, we simply substitute the values of a, b, and c into the given equations.

a = 21

b = 5

c = 36

[tex]a=\dfrac{7}{10}b\sqrt{c}[/tex]

[tex]21=\dfrac{7}{10}5\sqrt{36}[/tex]

[tex]21=\dfrac{7}{10}5(6)[/tex]

[tex]21=\dfrac{7}{10}30[/tex]

[tex]21=(0.7)30[/tex]

[tex]21=21[/tex]

i think its 5x-15 OR -1x-15

Answer:

b.  (√15)/4

Step-by-step explanation:

Since Sin Ф = (opposite side)/Hypotenuse, we have 2 sides of a right triangle.  

Use Pythagorean theorem to solve for the missing leg (the adjacent side)

 1² + b² = 4²

    1 + b² = 16

            b² = 15

                 b = √15

So the adjacent side is √15, so Cos Ф = (√15)/4

Answer:

b. [tex]\frac{\sqrt{15}}{4}[/tex]

Step-by-step explanation:

Given that [tex]\sin(\theta)=\frac{1}{4}[/tex] where [tex]0\:<\: \theta \:<\:\frac{\pi}{2}[/tex].

Recall and use the Pythagorean Identity;

[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]

This implies that;

[tex](\frac{1}{4})^2+\cos^2(\theta)=1[/tex]

[tex]\frac{1}{16}+\cos^2(\theta)=1[/tex]

[tex]\cos^2(\theta)=1-\frac{1}{16}[/tex]

[tex]\cos^2(\theta)=\frac{15}{16}[/tex]

Take the square root of both sides;

[tex]\cos(\theta)=\pm \sqrt{\frac{15}{16}}[/tex]

[tex]\cos(\theta)=\pm \frac{\sqrt{15}}{4}[/tex]

Since we are in the first quadrant;

[tex]\cos(\theta)=\frac{\sqrt{15}}{4}[/tex]

Parallel lines are lines that do not intersect each other at any point.

The correct definition of parallel lines is option A: 'Parallel lines are lines that do not intersect.' Parallel lines are two lines in a plane that do not intersect each other at any point, no matter how far they are extended.

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The lateral area is the area not including the base.

You have 2 sides that are 6 x 8 = 48 x 2 = 96 square feet.

One side of 4 x 8 = 32 square feet

And the top triangle = 1/2 x 4 x 6 = 12 square feet.

For lateral area you would not include the triangle at the bottom ( base).

Total Lateral area = 96 + 32 + 12 = 140 square feet.

Answer:

  an = 2(−4)^(n − 1); all integers where n ≥ 1

Step-by-step explanation:

The equation has the form ...

  an = a1(r)^(n-1) . . . . . where a1 is the first term and r is the common ratio.

The first term is given as 2, and the ratio will be the ratio of the first two terms:

  r = (-8)/(2) = -4

Terms are numbered starting with n=1, so the formula is ...

  an = 2(-4)^(n-1) for n≥1

You're answer to the following question: "Which Point Must be the Centre of the Circle?" Is C

Answer:

The statement is false.

Step-by-step explanation:

When you are looking at used cars, you should only look at local lots and newspapers - This statement is false.

When you are buying a used car, you should look not only in the local lots and newspapers but also online ans various used cars websites.

You can also personally visit the used car market to get wide range of cars and various comparative prices.

Answer:1/3

Step-by-step explanation:

2/3*1/2=1/3

The area of a parking lot measuring 2/3 km long and 1/2 km wide is 1/3 km². This is found by multiplying the length by the width.

The question is asking for the area of a rectangular parking lot that measures 2/3 km long and 1/2 km wide. The formula for the area of a rectangle is length times width. Applying this formula, we multiply 2/3 km by 1/2 km.

It's important to remember that when multiplying fractions, you just multiply the numerators (top numbers) and the denominators (bottom numbers) separately. So, (2/3) x (1/2) = 2/6 km², which simplifies to 1/3 km².

So, the area of the parking lot is 1/3 km².

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Carol's total earnings can be calculated by adding up her net salary plus her taxes paid.                                              

So, Total earnings of Carol = 642.20 + 115.34 + 62.75 = $820.29

So, her hourly wage = [tex]\frac{820.29}{37} =22.17[/tex]

Hence, Carol's hourly wage is = $22.17                                                        

Answer:

10 1/2

Step-by-step explanation:

Answer:

A) w + w

Step-by-step explanation:

Combine like terms

A)w+w   = 2w

B)2w+w   = 3w

C)2w-w  = w

D) w+2 = w + 2

So answer is A) w + w

Answer:

w+w

Step-by-step explanation:

Answer:

Part B. see the procedure

Part C. see the procedure

Step-by-step explanation:

we have

[tex]f(x)=x^{2}+2x+1[/tex] -----> equation A

[tex]g(x)=3-x-x^{2}[/tex] -----> equation B  

Part B. Solve the system algebraically

equate the equation A and the equation B

[tex]x^{2}+2x+1=3-x-x^{2}[/tex]

[tex]2x^{2}+3x-2=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]2x^{2}+3x-2=0[/tex]

so

[tex]a=2\\b=3\\c=-2[/tex]

substitute in the formula

[tex]x=\frac{-3(+/-)\sqrt{3^{2}-4a(2)(-2)}} {2(2)}[/tex]

[tex]x=\frac{-3(+/-)\sqrt{25}} {4}[/tex]

[tex]x=\frac{-3(+/-)5} {4}[/tex]

[tex]x1=\frac{-3(+)5} {4}=0.5[/tex]

[tex]x2=\frac{-3(-)5} {4}=-2[/tex]

Find the values of y

For x=0.5

[tex]f(0.5)=0.5^{2}+2(0.5)+1=2.25[/tex]

For x=-2

[tex]f(-2)=(-2)^{2}+2(-2)+1=1[/tex]

the solutions are the points

(0.5,2.25) and (-2,1)

Part C. Solve the system by graph

using a graphing tool

we know that

The solution of the non linear system is the intersection point both graphs

The intersection points are (0.5,2.25) and (-2,1)

therefore

The solutions are the points (0.5,2.25) and (-2,1)

see the attached figure

Option: C is the correct answer.

    C.   [tex]f(1)=4\\\\f(n)=5\cdot f(n-1)\ ;\ n\geq 2[/tex]  

Recursive Formula--

It is the formula which is used to represent the nth term of a sequence in terms of (n-1)th term of the sequence.

Here we are given a table of values by:

            n            f(n)

            1              4

            2             20

            3             100  

i.e. when n=1 we have:

[tex]f(1)=4[/tex]

Also,

[tex]f(2)=20\\\\i.e.\\\\f(2)=5\cdot 4\\\\i.e.\\\\f(2)=5\cdot f(1)[/tex]

Also,

[tex]f(3)=100\\\\i.e.\\\\f(3)=5\cdot 20\\\\i.e.\\\\f(3)=5\cdot f(2)[/tex]

Hence, the recursive formula is:

[tex]f(n)=5\cdot f(n-1)\ for\ n\geq 2[/tex]

Answer:

for plato family

f(1)=4

f(n)=5. f(n-1) ,for n [tex]\geq[/tex] 2

Step-by-step explanation:

x3 + 4x2 - 9x - 36

x2 (x + 4) - 9(x + 4)

(x2 - 9) (x + 4)

(x - 3) (x + 3) (x + 4)

Answer:

D) 59.8

Step-by-step explanation:

m<B = 120 deg

Since we know the measure of an angle and the length of the opposite side, we can establish the ratio of the law of sines, so we use the law of sines to find the length of side BA.

[tex] \dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c} [/tex]

[tex] \dfrac{\sin A}{BC} = \dfrac{\sin B}{AC} = \dfrac{\sin C}{AB} [/tex]

[tex] \dfrac{\sin B}{AC} = \dfrac{\sin C}{AB} [/tex]

[tex] \dfrac{\sin 120^\circ}{200} = \dfrac{\sin 15^\circ}{AB} [/tex]

[tex] \dfrac{\sin 120^\circ}{200} = \dfrac{\sin 15^\circ}{AB} [/tex]

[tex] (AB)\sin 120^\circ = 200 \sin 15^\circ [/tex]

[tex] AB = \dfrac{200 \sin 15^\circ}{\sin 120^\circ} [/tex]

[tex] AB = 59.8 [/tex]

Answer:

158 square feet

Step-by-step explanation:

The surface area of a prism is found using the following formula: SA = 2(lh+lb+bh). This formula takes the area of each face (6 in total( and adds them together to find a total sum. Substitute l = 8, b = 3 and h = 5 to solve for the surface area.

SA = 2(lh+lb+bh)

SA = 2(8*5+8*3+3*5)

SA = 2(40 + 24 + 15)

SA = 2(79)

SA = 158