The product of two numbers is 32. The first number, x, is one-half of the second number, y. Which system of equations can be used to find the two numbers? A system of equations. x y equals 32. x equals StartFraction one-half EndFraction y. A system of equations. x y equals 32. x equals y minus StartFraction one-half EndFraction. A system of equations. x plus y equals 32. x equals y minus StartFraction one-half EndFraction. A system of equations. x plus y equals 32. x equals StartFraction one-half EndFraction y.

Answer:

Step-by-step explanation:

Let x be the height of the box . x will be cut at four corners .

each side of the box = 6 - 2x

volume of box V = ( 6 - 2 x )² x

V = ( 36 + 4 x² - 24 x ) x

V = 4x³ - 24 x ² + 36 x

For maximum volume

dV / dx = 12 x² - 48 x + 36 = 0

x² - 4 x + 3 = 0

( x - 3 ) ( x - 1 ) = 0

x = 1 , x = 3 ( not possible )

Possible solution x = 1

Volume  , for x = 1

V = V = ( 6 - 2 x )² x

V = 4² x 1

= 16 m³.

Answer:  B) as x → -5  from the left, y → -∞

                    as x → -5 from the right, y → +∞

Step-by-step explanation:

[tex]g(x) =\dfrac{x^2+15x+56}{x+5}\quad =\dfrac{(x+7)(x+8)}{x+5}\\\\\\\text{Evaluate from the left. Let x = -6}\rightarrow \dfrac{(-)(-)}{(-)}=-\\\\\\\text{Evaluate from the right. Let x = -4}\rightarrow \dfrac{(-)(-)}{(+)}=+[/tex]

Refer to the graph which confirms that

Answer:

Step-by-step explanation:

cosФ=0 then the angle=π/2=90 degrees

sinФ==1     sin 90=1

12) the original price of the console  that Amanda bought :

240+(240*50%)=360 dollars

the price before the tariffs:

360-(360*50^)=180 dollars

Answer:

(-4, -8)

Step-by-step explanation:

Let the coordinates of common point of the given lines are (x, y),

Thus, the slope of the line passes through the points (a, b) and R(4,2) is,

       2 - b

m1 = ------

        4 - a

Again, the slope of the line passes through two points P(-6,4) and Q(4,-4),

      -4 - 4          -8           -8          -4

m2 = ------  =   --------- = --------- = ---------

        4- (-6)       4 + 6         10        5

= m1 * m2 = -1

  2 - b      -4

= -------   x ---- =  -1

   4 - a      5

        8 - 4b

=     -----------   = 1

        20 - 5a

= 8 - 4b  = 20 - 5a

= 5a - 4b = 12 --------- equation 1

For a = -6   and b = -10

5 x -6  - 4  x  10 = -70 ≠ 12

For a = -4   and b = -8

5 x -4  - 4  x  - 8  = 12 = 12

For a = 0  and b = -1

5 x 0 - 4 x -1 = 4 ≠ 12

For a = 2 and b = 4

5 x 2 - 4 x 4 = -6 ≠ 12

therefore Second is correct

hope it helps and i get the brainliest.

The point lies on the line that passes through point R and is perpendicular to line PQ will be (-4, -8). Then the correct option is B.

If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The points are P(-6, 4), Q(4, -4), and R(4, 2). Then the slope of the line PQ is calculated as,

m = (4 + 4) / (-6 - 4)

m = - 4/5

The slope of the perpendicular line is calculated as,

⇒ -1/m

⇒ -1/(-4/5)

⇒ 5/4

The equation of the perpendicular line is written as,

y - 2 = (5/4)(x - 4)

y - 2 = (5/4)x - 5

y = (5/4)x - 3

Let's check which option satisfies the equation. Then we have

a) For, x = -6 and y = 10, then we have

10 = (5/4) (-6) - 3

10 ≠ - 10.5

b) For, x = -4 and y = -8,

-8 = (5/4) (-4) - 3

-8 = -8

c) For, x = 0 and y = -1,

-1 = (5/4) (0) - 3

-1 ≠ - 3

d) For, x = 2 and y = 4,

4 = (5/4) (2) - 3

4 ≠ - 0.5

The point lies on the line that passes through point R and is perpendicular to line PQ will be (-4, -8). Then the correct option is B.

More about the equation of a perpendicular line link is given below.

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Answer:

Step-by-step explanation:

Step one:

Applying the SOH CAH TOA principle

assuming all dimensions are in cm

Step two:

Given data

opposite= 1 cm

hypotenuse= 2 cm

Sin(θ)= opp/hyp

Sin(θ)= 1/2

Sin(θ)= 0.5

θ= sin-1 0.5

θ= 30°

hence  from tables cos 30°= 0.866

Answer:

2065.5

Step-by-step explanation:

You have to approximate the following calculation 3.5^6

The binomial theorem is given by:

[tex](a+b)^n=\Sigma_{k=0}^{k=n}\left[\begin{array}{c}n&k\end{array}\right] a^{n-k}b^k[/tex]      (1)

You can express the number 3as follow:

[tex]3.5^6=(3+0.5)^6=(3+\frac{1}{2})^6[/tex]          (2)

by comparing the equation (1) with the equation (2) you have

a = 3

b = 1/2

To calculate the first three terms of the binomial theorem you use k=3. You replace the values of a, b, n and k in the equation (1):

[tex](3+\frac{1}{2})^6=\Sigma_{k=0}^{k=6}\left[\begin{array}{c}6&k\end{array}\right] (3)^{6-k}b^k[/tex]

You only take the first three terms:

[tex](3+\frac{1}{2}^6)\approx(1)(3)^6(\frac{1}{2})^0+(6)(3)^5(\frac{1}{2})^1+\frac{6\cdot 5}{1\cdot 2}(3)^4(\frac{1}{2})^2\\\\(3+\frac{1}{2}^6)\approx729+729+\frac{1215}{2}=2065.5[/tex]

By using the first three terms of bynomial theorem you obtain 2065.5

Answer:

200°

Step-by-step explanation:

<2 = 90° (right angle)

<3 = 70° (vertically opposite angles)

<4 + <3 = 180° ( angles on a straight line)

<4 + 70 = 180°

<4 = 180° - 70°

<4 = 110°

<2 + < 4

= 90 ° + 110° = 200°

Answer: Center D I think

Step-by-step explanation:

Answer:

A. The domain is (1,∞), and the range is (-7,∞)

Step-by-step explanation:

Well lets graph it first,

Look at the image below ↓

By looking at the image we move it 3 units right and 3 units down.

Then it will be located at the point (1,-7).

Meaning for the domain it starts at 1 and goes on for infinity.

And For the range it starts down at -7 and goes down for infinity.

Thus,

the correct answer is choice A.

Hope this helps :)

Answer:

A

Step-by-step explanation:

Solution:-

- First we will go through the guidelines that are followed when a given function [ f ( x ) ] is translated in a cartesian coordinate system domain.

Horizontal shifts:

Where, the constant ( a ) denotes the magnitude of shift  

Vertical shifts:

Where, the constant ( b ) denotes the magnitude of shift  

- The generalized form of a translated function is defined by the combination of both horizontal and vertical shifts as follows:

                    General: f ( x ) -> f ( x ± a ) ± b

Where, (a) and (b) are constants of respective translation shifts.

- We are given a function H ( x ) is to be translated 3 units to right and 3 units down. Use the above guidelines to determine the translated function H* ( x ) as follows:

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

- Substitute ( x - 3 ) in place of all ( x ) in the given function H ( x ) and subtract ( 3 ) from H ( x ) as follows:

                   [tex]H^* ( x ) = \sqrt{x-3 + 2} -4 - 3\\\\H^* ( x ) = \sqrt{x-1} -7\\[/tex]

- Now we will look for any transcendental functions in the translated function H*(x). These are " Radicals, fractions, Logs, trigonometric ratios "

- We have a radical - > " square root " in H* ( x ). To find the domain of H*(x) we need to determine for what real values of x is the function H*(x) is defined.

- The square root exist for all only positive numbers. So the terms under the square root must be positive; hence,

                     [tex]x - 1 \geq 0\\\\x \geq 1[/tex]

- Since the square root is the only transcendental in the given function H*(x) we have a one sided closed interval for the domain of the translated function.

                    Domain: [ 1 , ∞ )       ... Answer  

- The range of the function is the corresponding output of function H*(x) for the domain established above. We can determine this by plugging in the end-points of the defined domain in the translated function H*(x) as follows:

                    [tex]H^* ( 1 ) = \sqrt{1 - 1} - 7 = -7\\\\H^* ( inf ) = \sqrt{inf - 1} - 7 = inf - 7 = inf\\\\[/tex]

Therefore the range of the function is also a one sided closed interval bounded by x = 1.

                    Range: [-7 , ∞ )       ... Answer

Answer:

If it is warm outside, then it is summer

Step-by-step explanation:

To find the converse, interchange the hypothesis and the conclusion

"If it is summer, then it is warm outside"

If it is warm outside, then it is summer

Answer:

A. If it is warm outside, then it is summer

Step-by-step explanation:

statement "If it is summer, then it is warm outside" : warm=summer

A. If it is warm outside, then it is summer. : warm = summer ✓

B. If it is not warm outside, then it is summer. : not warm = summer x

C. If it is warm outside, then it is not summer. : warm =not  summer x

D. If it is not warm outside, then it is not summer. : not warm = not summer x

Answer:

158.73 yd

Step-by-step explanation:

A picture of the situation is needed, investigating I could find a related one, in the same way the important thing is the solution, the data can be exchanged. I attach the drawing.

Let use the formula of the law of cosine:

c ^ 2 = a ^ 2 + b ^ 2 - 2 * a * b * cos C, to solve the problem

Let the third side be c, we replace:

c ^ 2 = 375 ^ 2 + 240 ^ 2 - 2 * 375 * 240 * cos 16 °

c ^ 2 = 198225 - 173027.10

c ^ 2 = 25197.9

c = 158.73

So the distance is 158.73 yd

Answer: the right answer is 195.4

Step-by-step explanation: this guy does not what's happening

Answer:

The term inside the box should be 3 x.

Step-by-step explanation:

Given the equation:

- (x - 1) + 5 = 2 (x + 3) - T

(where T is the missing term in Leonardo's equation)

we can work with the given terms and accumulate all of them on one side of the equal sign (let's pick the right side for that, and move the tremt T to the left):

- x + 1 + 5 = 2 x + 6 - T

- x + 6 = 2 x + 6 - T

0 = 3 x - T

T = 3 x

For such equation to render infinite number of solutions, the term T on the left must equal "3 x". that way, the equation would be verified for any possible value x.

Answer:

3x

Step-by-step explanation:

i did the test and got it right, hope this helps!

Answer: d. 0.0047

Step-by-step explanation: The p-value is the calculated value used to compare to the significance level to determine if you reject or fail to reject the null hypothesis.

To find p-value, first find the z-score:

z = [tex]\frac{x-\mu}{SE}[/tex]

x is sample mean

μ is population mean

SE is standard error calculated by [tex]\frac{s}{\sqrt{n} }[/tex]

SE = [tex]\frac{10}{\sqrt{50} }[/tex]

SE = 1.414

z = [tex]\frac{24-28}{1.414}[/tex]

z = - 2.83

The hypotheses ([tex]H_{0}, H_{a}[/tex]) are if sample mean is equal or different from the average given, so, p-value will be the value of z from z-table multiplied by 2:

p-value = 0.00233*2

p-value = 0.0047

The p-value for this test is 0.0047

The answers are did not make, and both the slope and the y-intercept match if the line of the best fit is represented by the equation y = 0.77x + 1.34

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

We have a line of best fit:

y = 0.77x + 1.34

Here the slope of the line is 0.77 and y-intercept is 1.34

From the graph and line of best fit, we can say heather did not make an error when writing the equation of the line in her notebook because both the slope and the y-intercept match the slope and the y-intercept of the equation she recorded

Thus, the answers are did not make, and both the slope and the y-intercept match if the line of the best fit is represented by the equation y = 0.77x + 1.34

Learn more about the line of best fit here:

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Answer:

Heather likely did not make an error when writing the equation of the line in her notebook because both the slope and the y-intercept match the slope and the y-intercept of the equation she recorded.

Answer:

Everything but B

Step-by-step explanation:

When solving you can not have the degrees on the top

Answer:

work is shown and pictured

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

- 3y + 4x = 9

3y = 4x - 9

Divide both sides by 3

y = 4/3x - 3

Comparing with the above formula

Slope / m = 4/3

Since the lines are parallel their slope are also the same

So slope of the parallel line l is also 4/3

Equation of the line using point (-12 , 6) is

y - 6 = 4/3(x + 12)

Multiply through by 3

That's

3y - 18 = 4(x + 12)

3y - 18 = 4x + 48

We have the final answer as

Hope this helps you

Answer:

88 inches

Step-by-step explanation:

We are finding the perimeter of the stop sign, therefor we have to either multiply or add the value of 11. Since this sign is an octagon we will have to multiply by eight or add 11 eight times. This will give you an answer of 88 inches.

Answer:

88 inches

Step-by-step explanation:

The stop sign is in the shape of an octagon. An octogon has 8 sides. If each side is 11 inches you multiply 11 * 8 which is 88.

Answer:

El reloj está marcando:

las 4:00 horas

Step-by-step explanation:

El reloj avanzó a su mismo ritmo pero en sentido contrario a partir de las 6:45

si ahora son las 9:30 el reloj marca:

9:30 = 9horas 30minutos = 9h 30'

6:45 = 6horas 45minutos = 6h 45´

1 hora = 60'

9h 30' = 8h + 60' + 30' = 8h + 90' = 8h 90'

entonces:

 8h 90'

- 6h 45'

= 2h 45

entonces el reloj está marcando 2h 45' menos que la hora en que se dañó.

por tanto:

 6h 45'

- 2h 45'

= 4h 00'

El reloj ahora está marcando las

4 horas en punto.

Answer:

The divisor and dividend have the same signs.

Step-by-step explanation:

Let's look at all of the possible outcomes of dividing with different signs.

Positive / positive = positive

Positive / negative = negative

Negative / positive = negative

Negative / negative = positive

We can see that whenever the signs are the same, the quotient is positive.

Answer:

[tex]\boxed{\frac{25\pi }{36}}[/tex]

Step-by-step explanation:

Use the formula to convert from degrees to radians: [tex]x * \frac{\pi }{180}[/tex], where x is the value in degrees.

[tex]125 * \frac{\pi }{180}[/tex] = [tex]\frac{125\pi }{180}[/tex]

Then, simplify your fraction ⇒ [tex]\frac{125\pi }{180} = \boxed{\frac{25\pi}{36} }[/tex]

119°

Step-by-step explanation:

for this angle A has to be found for that you can use the theorem that states sum of interior angles is equal to the sum of opp exterior angle

51 + A = 112

A = 112 - 51

A = 61°

THEN WE CAN FIND THE B angle

they are angles on a straight line

so 61 + B = 180

B = 119°

Answer:

2

Step-by-step explanation:

|a+x|/2-|a-x|/2

Plug in the values.

|-2+-6|/2-|-2- -6|/2

Evaluate.

|-8|/2-|4|/2

Apply rule : |-a| = a

8/2 - 4/2

4 - 2

Subtract.

= 2

Answer:

9 cm.

Step-by-step explanation:

Let the height of the pyramid be h cm, then the height of the cuboid is (15 - h) cm.

Volume of the pyramid:

= 1/3 * h * s^2      where s is the length of a side of the square base.

= hs^2/3 cm^3

Volume of the cuboid:

= s^2(15 - h).

So we have:

hs^2/ 3 = 300.......................(1)

s^2(15 - h) = 600..................(2)

From  equation (1) :

h s^2 = 900

s^2 = 900/h

Now substitute for s^2 in  equation (2) :

(900/h)(15 - h) = 600

Multiply through by h:

900(15 - h) = 600h

13500 - 900h = 600h

1500h = 13500

h = 9 cm (answer).

If the total height of the solid is 15 cm. If the volume of the pyramid and cuboid are 300 cm and 600 cm respectively, then height of pyramid is 9cm.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Let the height of the pyramid be h cm, then the height of the cuboid is (15 - h) cm.

Volume of the pyramid:

300= 1/3 ×h×s²  

300= hs²/3

hs²=900

Volume of the cuboid:

600= s² (15 - h).

600=15s²-hs²

600=15s²-900

600+900=15s²

1500=15s²

100=s²

s=10

Now substitute s value in hs²=900

h(100)=900

Divide both sides by 100

h=9cm

Hence height of the pyramid is 9cm.

To learn more on Three dimensional figure click:

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Answer:

The radius of the circle is 40.44 cm

Step-by-step explanation:

We can use the formula for the arc of a circle of radius R and central angle [tex]\theta[/tex], where [tex]\theta[/tex] is given in radians (we therefore convert [tex]17^o[/tex] into radians with [tex]17^o\,\pi/180^o=0.2967[/tex] radians)

[tex]arc=R\,\theta\\12\,cm= R\,\theta\\12\,cm=R\,(0.2967)\\R=\frac{12}{0.2967} \,cm\\R=40.44\,cm[/tex]

Answer:

The amount in 2001 is 8400

Step-by-step explanation:

Let x be the amount in 2001

There is an increase of 25% to get to the amount in 2002

x+ .25x = 1.25 x

1.25x = 10500

Divide each side by 1.25

1.25x / 1.25 = 10500/1.25

x =8400

The amount in 2001 is 8400

Answer:

36 ft.

Step-by-step explanation:

11+11+7+7=

22+14= 36

Answer:

36 ft

Step-by-step explanation:

The rectangle's sides lengths are 7 ft and 11 ft, wich are the width and the length.

The formula of the perimeter is:

P= 2w+2L with w the width and L the length

P= 2*7+2*11

P= 14+22

P= 36 ft

The perileter is 36 ft

Answer:

its simplest form for the question is 2:1

Answer:

19

Step-by-step explanation: