3x + ky = 8
X – 2ky = 5
are simultaneous equations where k is a constant.
a) Show that x = 3.
b) Given that y = 1/2 determine the value of k.

Answer:

gradient = slope = 1

Y =1X +1  is the equation

Step-by-step explanation:

x1 y1  x2 y2

4 5  1 2

(Y2-Y1) (2)-(5)=   -3  ΔY -3

(X2-X1) (1)-(4)=    -3  ΔX -3

slope= 1          

B= 1          

Y =1X +1    

Given:

The skateboard Rita would like to buy costs $ 6 less than 3 times the amount she saved.

The skateboard costs $69.

To find:

The saved amount.

Solution:

Let x be the saved amount.

The skateboard Rita would like to buy costs $ 6 less than 3 times the amount she saved. So, the cost of the skateboard is [tex]3x-6[/tex].

The skateboard costs $69.

[tex]3x-6=69[/tex]

[tex]3x=69+6[/tex]

[tex]3x=75[/tex]

Divide both sides by 3.

[tex]x=\dfrac{75}{3}[/tex]

[tex]x=25[/tex]

Therefore, Rita saved $25.

Answer:

hello,

Step-by-step explanation:

n+2*(2n-5)=20

5n-10=20

5n=30

n=6

Answer:

k = 11

Step-by-step explanation:

What the factor theorem is telling us is that if x + 1 is a factor of 2x - kx²-8x + 5 then when x = - 1 is put into the equation, the result will be 0. That's because x +1 = 0 when x  = - 1

f(-1) = 2(-1) - k(-1)^2 - 8(-1) + 5

f(-1) = -2 - k(1) + 8 + 5 = 0

-k*(1) + 11 = 0

-k = -11

k = 11

Answer:

12 minutes

Step-by-step explanation:

We can use the formula

1/a+ 1/b = 1/c  where a and b are the times alone and c is the time together

1/20 + 1/30 = 1/c

Multiply by the common denominator to clear the fractions

60c(1/20 + 1/30 = 1/c)

3c +2c = 60)

5c = 60

Divide by 5

5c/5 = 60/5

c = 12

12 minutes

Answer: 12 minutes

Step-by-step explanation: To solve this kind of a problem, which is called a work problem, it's important to understand the following idea:

Since Barry can eat a bag of popcorn in 30 minutes, we know that in 1 minute, Barry can eat 1/30 of the bag of popcorn and in 2 minutes, Barry can eat 2/30 of the bag of popcorn. Therefore, in t minutes, Barry can eat t/30 of the bag of popcorn. The same thing applies for Andrea. In t minutes, Andrea can eat t/20 of the bag of popcorn.

Now to solve the problem, we use the following formula:

Part of Job done by Barry + Part of Job done by Andrea = 1 job done

The part of job done by Barry is t/30 and the part

of the job done by Andrea is t/20.

So we have t/30 + t/20 = 1.

To solve for t, multiply both sides by the common denominator of 60.

So we get 2t + 3t = 60 or 5t = 60 so t = 12.

So Barry and Andrea can eat 1 bag together in 12 minutes.

Answer:

There is an asymptote at x = 0

There is an asymptote at y = 23

Step-by-step explanation:

Given the function:

(23x+14)/x

Vertical asymptote is gotten by equating the denominator to zero

Since the denominator is x, hence the vertical asymptote is at x = 0. This shows that there is an asymptote at x = 0

Also for the horizontal asymptote, we will take the ratio of the coefficient of the variables in the numerator and denominator

Coefficient of  x at the numerator = 23

Coefficient of x at the denominator = 1

Ratio = 23/1 = 23

This means that there is an asymptote at y = 23

Answer:

3136 = 2^6 × 7^2

2744 = 2^3 x 7^3

✓3136/3✓2744​ = ✓(2^6 × 7^2)/3✓(2^3 x 7^3) = (2^3 x 7)/3 x 14(✓14) = 56/42✓14 =4/3✓14

supplementary angles = the sum of those angles will equal to 180 degrees

so,

2x + 3 + 3x + 2 = 180

5x + 5 = 180

5x = 175

x = 35

angle 1 -> 2x + 3 = 70 + 3 = 73

angle 2 -> 3x + 2 = 105 + 2 = 107

if you want to check, 107 + 73 = 180

hope it helps :)

Answer:

180 degrees

Step-by-step explanation:

ABCD is now opposite where it started, so it was rotated 180 degrees

I hope this helps!

Answer:

180 degrees

Step-by-step explanation:

Answer:

SP is Rs 800.

Step-by-step explanation:

MP = Rs 875

Discount = Rs 75

so

SP = MP - discount

= Rs 875 - Rs 75

= Rs 800

Answer:

75.7

Step-by-step explanation:

Area of the sector,

17²×π×30/360

= 289π/12

= 75.7 (rounded to the nearest tenth)

Answered by GAUTHMATH

Answer:

35

Step-by-step explanation:

6:5

 We need to get the first number to 43

6*7 = 42

Multiply each term by 7

6*7 : 5*7

42  : 35

Answer:

Step-by-step explanation:

[tex]in~the~expansion~of~(x+a)^n\\T_{r+1}=ncr x^{n-r}a^r\\r+1=3\\r=3-1=2\\n=4\\4c2=\frac{4 \times 3}{2 \times 1} =6\\T_{2}=4(x^2)^{4-2}(2)^2\\=16(x^2)^2\\=16x^4[/tex]

the third term is: 24*x^4

We want to find the third term of the equation:

(x^2 + 2)^4

So we need to expand that.

Remember the rule:

(a + b)^2 = a^2 + 2*a*b + b^2

(a + b + c)^2 = a^2 + b^2 + c^2 + 2*a*b + 2*b*c + 2*c*a

Then we can write:

(x^2 + 2)^4 = (x^2 + 2)^2*(x^2 + 2)^2

and we have:

(x^2 + 2)^2 = (x^4 + 2*2*x^2 + 2^2) = (x^4 + 4*x^2 + 4)

Then we have:

(x^2 + 2)^4 = (x^2 + 2)^2*(x^2 + 2)^2

(x^2 + 2)^4 = (x^4 + 4*x^2 + 4)^2

And we can expand this as:

(x^4)^2 + (4*x^2)^2 + 4^2 + 2*(x^4)*(4*x^2) + 2*(4*x^2)*(4) + 2*(x^4)*(4)

now we have this expanded, so we need to simplify this:

x^8 + 16*x^4 + 16 + 8*x^6 + 32*x^2 + 8*x^4

Putting the terms in order (larger degrees go in the left) we get:

x^8 + 8*x^6 + 16*x^4 + 8*x^4 + 32*x^2 + 16

x^8 + 8*x^6 + (16 + 8)*x^4 + 32*x^2 + 16

x^8 + 8*x^6 + 24*x^4 + 32*x^2 + 16

So the third term would be the third counting from the left, which is:

24*x^4

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Answer:

Gray Widow made $111,357,284.5 in theaters on opening weekend.

Step-by-step explanation:

75% more revenue in theaters than it did via streaming video.

The sum of the revenues is 100%.

So the theaters were responsible for the following percentage:

[tex]P = 50 + \frac{75}{2} = 50 + 37.5 = 87.5[/tex]

How much money did Gray Widow make in theaters on opening weekend?

87.5% of the total revenue, that is, 0.875 out of $127,265,468.

0.875*127,265,468 = $111,357,284.5

Gray Widow made $111,357,284.5 in theaters on opening weekend.

Answer:

[tex]Max\ z = 1[/tex]

[tex]Min\ z = -9[/tex]

Step-by-step explanation:

Given

[tex]z = 4x + 5y[/tex]

[tex]x \ge -1[/tex]

[tex]y \le 2x +3[/tex]

[tex]y \le -1[/tex]

Required

The maximum and minimum of z

To do this, we make use of the graphical method

See attachment for graphs of

[tex]x \ge -1[/tex]

[tex]y \le 2x +3[/tex]

[tex]y \le -1[/tex]

The corner points of the function are:

[tex](x,y) = (-1,1)[/tex]

[tex](x,y) = (-1,0)[/tex]

[tex](x,y) = (-1,-1)[/tex]

We have:

[tex]z = 4x + 5y[/tex]

Calculate z with  the above values

[tex]z = 4(-1) + 5(1) = 1[/tex]

[tex]z = 4(-1) + 5(0) = -4[/tex]

[tex]z = 4(-1) + 5(-1) = -9[/tex]

So, we have:

[tex]Max\ z = 1[/tex]

[tex]Min\ z = -9[/tex]

Hi there!  

»»————-　★　————-««

I believe your answer is:  

The soccer ball.  

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'c'...}}\\\\15.32 + c = 29.00\\-----------\\\rightarrow 15.32 - 15.32 = 29.00 - 15.32\\\\\rightarrow \boxed{13.68}[/tex]

⸻⸻⸻⸻

She would have $13.68 dollars left. Her second item should be the soccer ball.

»»————-　★　————-««  

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

Answer:

3:15 hours

Step-by-step explanation:

i don't know I just took the test

Answer:

4.75 or 4 3/4

Step-by-step explanation:

rate = distance/time

Multiply both sides by time:

time * rate = distance

Divide both sides by rate:

time = distance/rate

We are given:

distance = 76 km

rate = 16 km/h

time = ?

time = distance/rate

time = 76 km/(16 km/h)

time = 4.75 h = 4 3/4 h

Answer:

60

Step-by-step explanation:

b = the hypotenuse of a right angle triangle

a = the adjacent side.

R is being defined by the cosine

cos(R) = adjacent /  hypotenuse

adjacent = 16* sqrt(2)

hypotenuse = 32*sqrt(2)

Cos(R) = 16*sqrt(2) / 32*sqrt(2)      sqrt(2) cancels.

cos(R) = 1/2

R = cos-1(1/2)

R = 60 degrees.

Answer:

157

hope it help

...

....

.....

......

.......

Answer:

(-1/3, 2) and (2, 3)

Step-by-step explanation:

Answer:

x is approximately 226.3 feet

y is approximately 308.6 feet

z is approximately 226.3 feet

Step-by-step explanation:

The given parameters of the walls are;

The angle of elevation from the top of the shorter wall to the top of the opposing wall, θ₁ = 20°

From the diagram, the angle of depression from the top of the shorter wall to the bottom of the opposing wall, θ₂ = 45°

The distance from the bottom of the shorter wall to the base of the opposing wall, l = 320 feet

x = The height of the shorter wall = l × sin(θ₂)

∴ x = 320 feet × sin(45°) = 320 feet × (√2)/2 = 160·√2 feet ≈ 226.3 feet

∴ x ≈ 226.3 feet

By observation, we have;

y = x + z × tan(θ₁)

Where;

z = l × cos(θ₂)

∴ y = 160·√2 + 320 × cos(45°) × tan(20°) ≈ 308.6

y ≈ 308.6 feet

z =  l × cos(θ₂)

∴  z = 320 × cos(45°) = 160·√2 ≈ 226.3

z ≈ 226.3 feet.

Answer:

-8

Step-by-step explanation:

Solve the brackets first

4/2x+28=12

then group the like terms

2x=12-28

2x/2=-16/2

x= -8

i hope this helps

Answer:

1/2x + 7=12/4=3

1/2x = 3-7=-4

x=-4/0.5

x=-8

Answer:

Step-by-step explanation:

This requires some serious work before we even begin. First off, we will convert the km to meters:

32 km = .032 m

46 km = .046 m

And then we have to deal with the angle given as 40 degrees west of north. An angle 40 degrees west of north "starts" at the north end of the compass and moves towards the west (towards the left in a counterclockwise manner) 40 degrees. That means that the angle that is made with the negative x axis is a 50 degree angle. BUT the way angles are measured in standard form are from the positive x-axis, therefore:

40 degrees west of north = 50 degrees with the negative x axis = 130 degrees with the positive x axis. 130 is the angle measure we use. Phew! Now we're ready to start. Adding vectors requires us to use the x and y components of vectors in order to add them.

[tex]A_x=.032cos90.0[/tex] so

[tex]A_x=0[/tex] (the 90 degrees comes from "due north")

[tex]B_x=.046cos130[/tex] so

[tex]B_x=-.030[/tex] and if we add those to get the x component of the resultant vector, C:

[tex]C_x=-.030[/tex]   And onto the y components:

[tex]A_y=.032sin90.0[/tex] so

[tex]A_y=.032[/tex]

[tex]B_y=.046sin130[/tex] so

[tex]B_y=.035[/tex] and if we add those together to get the y component of the resultant vector, C:

[tex]C_y=.067[/tex]  Note that since [tex]C_x[/tex] is negative and [tex]C_y[/tex] is positive, the resultant angle (the direction) will put us into QII.

We find the magnitude of C:

[tex]C_{mag}=\sqrt{(-.030)^2+(.067)^2}[/tex]

We will round this after we take the square root to the thousandths place.

[tex]C_{mag}=.073m[/tex] and now for the angle:

[tex]\theta=tan^{-1}(\frac{.067}{-.030})[/tex] which gives us an angle measure of -67, but since we are in QII, we add 180 to that to get that, in sum:

The magnitude of the resultant vector is .073 m at 113°

Answer:

j' = (1,-2)   k'=(3,-1) L' = (3,-3)

Step-by-step explanation:

I think that you just multiply all the x,y values for the three points by 1/5?

5 1

-10 -2

j' = (1,-2)

~~~~~~~~~~~~~~~~~~  

15 3

-5 -1

k'=(3,-1)

~~~~~~~~~~~~~~~

15 3

-15 -3

l' = (3,-3)

Answer:

Hence the mean of the sampling distribution of proportion is,  

[tex]\mu\hat p = p = 0.37[/tex].

Step-by-step explanation:

Here the given details are,  

p = 0.37  

1 - p = 1 - 0.37 = 0.63  

n = 144  

The mean of the sampling distribution of proportion is,  

[tex]\mu\hat p = p = 0.37[/tex]

Step-by-step explanation:

the answer of the following is in the figure

Answer:

Mutal fund because its a formerly greatest instruments

The name of an investment that pools money from many investors in order to acquire a large variety of stocks, bonds, and other investments is Mutual fund.

Investment is traditionally defined as the "commitment of resources to achieve later benefits

A mutual fund is a type of investment vehicle that pools money from multiple investors to invest in a diversified portfolio of stocks, bonds, and other securities.

Mutual funds are managed by professional fund managers who use the pooled funds to purchase a range of investments, with the goal of generating a return for the investors.

Investors in mutual funds own shares in the fund, and the value of their investment is based on the performance of the underlying securities held by the fund.

Mutual funds offer investors the benefits of diversification, professional management, and ease of investment, as well as the ability to invest in a variety of asset classes with relatively low minimum investment requirements.

Hence, the name of an investment that pools money from many investors in order to acquire a large variety of stocks, bonds, and other investments is Mutual fund.

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