Which expression shows the first step in simplifying 2x – 3(x + 2y) – 5(y – 7x)? 2x – 8(x + 2y) + (y – 7x) 2x – 3 – 5(3y – 6x) 2x – 3x – 6y – 5y + 35x 2x + 3x + 6y + 5y – 35x

Answer:

Option (C)

Step-by-step explanation:

Domain of any graph is defined by the x-values or the input values of a function.

Similarly, y-values on the graph of a function define the Range.

In the graph attached, x-values varies from (-∞) to (+∞).

Therefore, Domain of the graphed function will be (-∞, ∞)

Or -∞ < x < ∞

Similarly, y-values of the graph varies from (-∞) to (1)

Therefore, range of the graphed function will be (-∞, 1).

Or -∞ < y < 1

Option (C) will be the answer.

Answer:

All the points change, there are no invariant points

Step-by-step explanation:

The given parameters are

To translate the square OABC by the vector  [tex]\dbinom{1}{3}[/tex], we have;

The coordinates of the point O is (0, 0)

The coordinates of the point A is (3, 0)

The coordinates of the point B is (3, 3)

The coordinates of the point C is (0. 3)

The translation is by moving 1 step right and three steps up to give;

O' is (0+1, 0+3) which is (1, 3)

A' is (3+1, 0+3) which is (4, 3)

B' is (3+1, 3+3) which gives (4, 6)

C' is (0+1, 3+3) which gives (1, 6)

As all the points change, there are no invariant points and the number of invariant points is zero.

Answer:

x=70

Step-by-step explanation:

the angles opposite 3.5 equal 55 degrees

180-55-55=70

Answer:

70°

Step-by-step explanation:

since the both size are equal which is 3.5,it is equal length, so the other angle should be 55 also. Just use the triangle =180° ，180-55-55=70°

Answer:

We accept H₀, with CI = 90 %, porcentage of O blood type in college students does not differ from the world population porcentage

Step-by-step explanation:

The test is a proportion  two-tail test ( note: differs)

p₀ = 45 %      or  p₀ = 0,45

n = 1000

p =  47 %        or  p  = 0,47

Test Hypothesis

Null hypothesis                                H₀                   p  =  p₀

Alternative hypothesis                    Hₐ                   p  ≠ p₀

CI  we assume 90 %  then  α = 10 %    α  =  0,1    α/2  = 0,05

z score  from z-table   z(c) = 1,64

To calculate z(s) = ( p - p₀ ) / √ p₀q₀/ n

z(s)  = ( 0,47  -  0,45 )/ √( 0,45)*(0,55)/1000

z(s)  =  0,02/√( 0,2475)/1000

z(s)  =  0,02/0,01573

z(s) = 1,2714

Now we compare z(s) and z(c)

z(s) < z(c)      1,2714 < 1,64

Then z(s) is in the acceptance region we accept H₀

Answer:

This is simple! (Kind of)

Step-by-step explanation:

First, notice how HJ is tangent. HG is a radius intersecting HJ at H.

This means, (According to some theorem that I forgot the name of) that GHJ is a right angle.

Thus, we can use the 180* in a triangle theorem.

[tex]180=90+54+6x+6[/tex]

So, let's solve!

[tex]30=6x\\5=x[/tex]

So, there you go! Nice and simple!

Hope this helps!

Stay Safe!

Step-by-step explanation:

hope it helps yoy..........

Answer:

-1/3

Step-by-step explanation:

The slope of the line can be found by

m = (y2-y1)/(x2-x1)

    = ( 7-8)/(5-2)

    = -1/3

Answer:

-1/3.

Step-by-step explanation:

The slope can be found by doing the rise over the run.

In this case, the rise is 8 - 7 = 1.

The run is 2 - 5 = -3.

So, the slope is 1 / -3 = -1/3.

Hope this helps!

Answer:

Width = [tex] \frac{7}{2} ft[/tex]

Step-by-step explanation:

Given,

Area of rectangle = [tex]42 \: {ft}^{2} [/tex]

Width = X

Length = 2x + 5

Now,

[tex]x(2x + 5) = 42[/tex]

[tex]2 {x}^{2} + 5x = 42[/tex]

[tex]2 {x}^{2} + 5x - 42 = 0[/tex]

[tex]2 {x}^{2} + 12x - 7x - 42 = 0[/tex]

[tex]2x(x + 6) - 7(x + 6) = 0[/tex]

[tex](2x - 7)(x + 6) = 0[/tex]

Either

[tex]2x - 7 = 0[/tex]

[tex]2x = 0 + 7[/tex]

[tex]2x = 7[/tex]

[tex]x = \frac{7}{2} [/tex]

Or,

[tex]x + 6 = 0[/tex]

[tex]x = 0 - 6[/tex]

[tex]x = - 6[/tex]

Negative value can't be taken.

So, width = [tex] \frac{7}{2} ft[/tex]

Again,

Finding the value of length,

Length = [tex]2x + 5[/tex]

[tex]2 \times \frac{7}{2} + 5[/tex]

[tex]7 + 5[/tex]

[tex]12[/tex]

Length = 12 ft

Answer:

length = 12 ft, width = 3.5 ft

Step-by-step explanation:

w = width

l = length = 2w + 5

A = wl = w(2w + 5) = 42

2w² + 5w - 42 = 0

(w + 6)(2w - 7) = 0

w + 6 = 0, w = -6 (dimension cannot be negative)

2w - 7 = 0, w = 3.5

l = 2(3.5) + 5 = 12

Answer:

14.42 units

Step-by-step explanation:

Assuming that this is a right triangle (i.e ∠ACB = 90°), we can use the Pythagorean formula to solve this:

AB² = AC² + BC²

AB² = 12² + 8²

AB = √(12² + 8²)

AB = 14.42 units

Answer:

Shape - Cube

Area= 864

Step-by-step explanation:

The shape folds to become a cube and all the edges are the same size.

Area of a cube is Length * Width * Height = Area

12*12*12= 864

Answer:

Shape - Cube

Area= 864

Step-by-step explanation:

The shape folds to become a cube and all the edges are the same size.

Area of a cube is Length * Width * Height = Area

12*12*12= 864

Answer:

B. The student incorrectly calculated the scale factor to be –2

Step-by-step explanation:

Given that :

After a dilation with a center of (0, 0), a point was mapped as (4, –6) → (12, y).

The student determined y to be -2

If a figure dilated with a center of (0, 0) and scale factor k, then

(x , y) → (kx , ky)

(4, -6) → (12, y)

[tex]k = \dfrac{x'}{x}[/tex]

[tex]k = \dfrac{12}{4}[/tex]

k = 3

Thus; the scale factor is 3

Now; the y-coordinate can now be calculated as;

ky = (3 × -6)

ky = -18

Therefore; the value of y = -18 and the student incorrectly calculated the scale factor to be -2.

Answer:

2.5 m/s^2

Step-by-step explanation:

Answer:

2.5 m/s²

Step-by-step explanation:

First, convert to SI units.

90 km/h × (1000 m/km) × (1 h / 3600 s) = 25 m/s

a = Δv / Δt

a = (25 m/s − 0 m/s) / 10 s

a = 2.5 m/s²

Answer:

140/221.

Step-by-step explanation:

For the triangle containing  angle α:

The adjacent side is -√(13^2-5^2) = -12.

For the triangle containing angle β:

Hypotenuse = √(-8)^2 + (15)^2) =  17.

cos(α - β) = cos α  cos β   + sin α   sin β

= ((-12/13) * (-15/17) + (-5/13)* (8/17)

= 180/221 + - 40/221

= 140/221.

Answer: the correct answer is D.

Step-by-step explanation:

Since we are given the values of angle B and side(a) we can set up an equation cos43.2=3.2/x

we will get 4.4 so c=4.4

using the paythagorion theorm (4.4)^2=x^2+(3.2)^2

we will get an approximate value of 3 so b=3

and for the finding the third angle x+43.2+90=180

x=46.8 degrees

Answer D

Answer:

The answer is option D

Step-by-step explanation:

32m + 56mp

First factor out the HCF out

The HCF of 32and 56 is 8

So we have

8 ( 4m + 7mp)

next factor m out

We have the final answer as

Hope this helps you

Answer:

z = 8.5

Step-by-step explanation:

Let O be the center of the circle, and A, B, C are three points on the circle.

Draw OA and OC are shown in the figure. To make the central angle.

In the figure the measure of arc AC is 118 degrees. measure of central angle and subtrahend arc is same. So, central angle is

[tex]\angle AOC=118^{\circ}[/tex]

Subtended angle on arc AC is  

[tex]\angle ABC=(6z+8)^{\circ}[/tex]

According to central angle theorem of circle, central angle is twice of angle subtended by the arc.

[tex]\angle AOC=2\times \angle ABC[/tex]

[tex]118^{\circ}=2\times (6z+8)^{\circ}[/tex]

[tex]118=12z+16[/tex]

[tex]118-16=12z[/tex]

[tex]102=12z[/tex]

[tex]\dfrac{102}{12}=z[/tex]

[tex]8.5=z[/tex]

Therefore, the value of z is 8.5.

Answer:

3

Step-by-step explanation:

the line crosses the y-axis at (0,3)

Answer:

3

Step-by-step explanation:

The y intercept is where the graph crosses the y axis  ( where x =0)

The lines crosses at y=3

Y intercept is 3

Answer:

Step-by-step explanation:

Use F.O.I.L

F - First

O- Outside

I- Inside

L- Last

First multiply the ds from both to get [tex]d^{2}[/tex], next multiply the first d and the -4 and get -4d, then the 8 and the second d = 8d, and finally the 8 and -4 to get -32

you get [tex]d^{2}[/tex]-4d + 8d - 32

Answer:

45

Step-by-step explanation:

The final had an extra credit as 25, so without it it would be 135. Then, you would divide by three to find that the first test had 45 points.

Answer:

45

Step-by-step explanation:

The final had an extra credit as 25, so without it it would be 135. Then, you would divide by three to find that the first test had 45 points.

Answer:

(g + f) (x) = (2^x + x – 3)^1/2

Step-by-step explanation:

The following data were obtained from the question:

f(x) = 2^x/2

g(x) = √(x – 3)

(g + f) (x) =..?

(g + f) (x) can be obtained as follow:

(g + f) (x) = √(x – 3) + 2^x/2

(g + f) (x) = (x – 3)^1/2 + 2^x/2

(g + f) (x) = (x – 3)^1/2 + (2^x)^1/2

(g + f) (x) = (x – 3 + 2^x)^1/2

Rearrange

(g + f) (x) = (2^x + x – 3)^1/2

Answer:

45

Step-by-step explanation:

Given the legs of the right triangle.

Then using Pythagoras' identity

The square oh the hypotenuse h is equal to the sum of the squares on the other 2 sides, that is

h² = 36² + 27² = 1296 + 729 = 2025 ( take the square root of both sides )

h = [tex]\sqrt{2025}[/tex] = 45

Answer:

45

Step-by-step explanation:

When you are given the opposite and adjacent sides of a triangle, the easiest way to find the hypotenuse is through the Pythagorean theorem!

The formula is a^2 + b^2= c^2

Plugging in the values, your formula would now look like 36^2 + 27^2= c^2

Once you do square your values and add them up, the result would end up being 2025, but since that is squared, to find the actual value of c you have to take the square root of this number, this will result in 45.

Answer:

[tex] C = 28.9 [/tex]

Step-by-step explanation:

Given the right angled triangle, ∆BCD, you are required to find the measure of angle C.

Apply the trigonometric ratio formula to find m < C.

Adjacent side = 7

Hypotenuse = 8

Trigonometric ratio formula to apply would be:

[tex] cos(C) = \frac{7}{8} [/tex]

[tex] cos(C) = 0.875 [/tex]

[tex] C = cos^{-1}(0.875) [/tex]

[tex] C = 28.9 [/tex]

(To nearest tenth)

Let d equal the final amount it depreciates.

Let m equal the number of months.

Since d is the final amount, we put this at the very end of the equation.

Since it depreciates $25 every month, this number is going to be subtracted from the total price of the tablet ($650).

The final equation comes out too: d = 650 - 25m

Best of Luck!

Answer:

x = -2 and y = 3

Step-by-step explanation:

In linear combination method we try one of the variables from bopth of equations by

first making the variable equal in vlaue

then either subtracting or adding the two equation as required to eliminate the variable.

_____________________________________________

7x-2y=-20   equation 1

and 9x+4y=-6   equation 2

we see that y has

has value -2 and +4

4 = 2*2

thus, if we multiply equation1 with 2 we will give value for variable y as 4y and hence y can be eliminated easily.

7x-2y=-20  

multiplying the LHS and RHS with 2

2(7x-2y)=-20 *2

=> 14x - 4y = -40   eqaution 3

now that we have got 4y

lets add equation 2 and equation 3

  9x +4y=   -6

+14x - 4y = -40

________________________________

=> 23x + 0 =  -46

x = -46/23 = -2

Thus, x = -2

substituitinng x = -2 in 7x-2y=-20

7*-2 -2y=-20

=> -14 -2y = -20

=> -2y = -20+14 = -6

=> y = -6/-2 = 3

Thus, y = 3

solution is x = -2 and y = 3

Answer:

b) P(more than 10) = 2/9

c) P(less than 7) = 2/9

Step-by-step explanation:

a) Yaniq spins both spinners and then adds up the results together.

The results are as follow:

5

7

9

6

8

10

7

9

10

These are a total of 9 outcomes.

b) What is the probability that Yaniq gets a total of more than 9?

The probability is given by

P = Number of favorable outcomes/Total number of outcomes

For this case, the favorable outcomes are all those outcomes where the total score is more than 9.

Count the number of times Yaniq got a score of more than 9.

Yes right!

2 times (10 and 10)

P(more than 10) = 2/9

c) What is the probability that Yaniq gets a total of less than 7?

For this case, the favorable outcomes are all those outcomes where the total score is less than 7.

Count the number of times Yaniq got a score of less than 7.

Yes right!

2 times (5 and 6)

P(less than 7) = 2/9

Answer:

11.7

Step-by-step explanation:

Let H be the heipotenys of the big triangle:

H= 28.04

Let's calculate the third side using the pythagorian theorem:

H²= 26²+ d²(the third side)

d² = 28.04²-26²= 110.24

d= 10.49

let's calculate x now

x= 11.65 ≈ 11.7

Answer: 1/5 , 1/2, and 5/6

Step-by-step explanation:

given;

probability that the cube shows a three (3) or five (5).

probability that it stops on yellow.

1. the probability p of the spinner stopping on yello  

= 1/5 times

a cube has 6 sides

2. probability that it shows a 3

this is going to be 3 divided by the total sides on the cube which is 6

P = ( 3 ) = 3/6

Divide both side by 3

= 1/2.

3. probability that it shows a 5,

this is going to be 5 divided by the total sides on the cube which is 6

P = ( 5 )

  = 5/6.

Answer:

Step-by-step explanation:

The given equation is expressed as

(x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12

Simplifying the right hand side of the equation, it becomes

[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)

x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)

(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)

4x/(x - 1)(x + 1)

Therefore,

4x/(x - 1)(x + 1) = 7/12

Cross multiplying, it becomes

4x × 12 = 7(x - 1)(x + 1)

48x = 7(x² + x - x - 1)

48x = 7x² - 7

7x² - 48x - 7 = 0

Applying the quadratic formula,

x = - b ± √(b² - 4ac)]/2a

from our equation,

b = - 48

a = 7

c = - 7

Therefore

x = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)

x = [48 ± √(2304 + 196]/14

x = (48 ± √2500)/14

x = (48 ± 50)/14

x = (48 + 50)/14 or x = (48 - 50)/14

x = 98/14 or x = - 2/14

x = 7 or x = - 1/7

Answer: The given equation is expressed as (x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12Simplifying the right hand side of the equation, it becomes[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)4x/(x - 1)(x + 1)Therefore, 4x/(x - 1)(x + 1) = 7/12Cross multiplying, it becomes4x × 12 = 7(x - 1)(x + 1)48x = 7(x² + x - x - 1)48x = 7x² - 77x² - 48x - 7 = 0Applying the quadratic formula,x = - b ± √(b² - 4ac)]/2a from our equation, b = - 48a = 7c = - 7Thereforex = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)x = [48 ± √(2304 + 196]/14x = (48 ± √2500)/14x = (48 ± 50)/14x = (48 + 50)/14 or x = (48 - 50)/14x = 98/14 or x = - 2/14x = 7 or x = - 1/7

Step-by-step explanation:

Answer:

x(x-3) ( x+4)

Step-by-step explanation:

  2               5

---------- + ------------

x^2 -3x     x^2 + x - 12

Factor the denominator

  2               5

---------- + ------------

x(x -3)     (x-3) (x+4)

The common denominator is

x(x-3) ( x+4)

Answer:

d. 20

Step-by-step explanation:

To answer the question given, we will follow the steps below:

we need to first find p(3)

p(x) = x+ 7/ x-1

we will replace all x by 3 in the equation above

p(3) = 3+7 / 3-1

p(3) = 10/2

p(3) = 5

Similarly to find q(2)

q (x) = x^2 + x - 2,

we will replace x by 2 in the equation above

q (2) = 2^2 + 2 - 2

q (2) = 4 + 0

q (2) = 4

The product of p(3) and q(2)   =   5 × 4   = 20

Answer:

The correct option is;

A.) A dilation by a scale factor of two-fifths and then a translation of 3 units up

Step-by-step explanation:

The given information are;

Square S undergoes transformation into square S'

From the figure, the dimension of S' = 2/5 dimension of S

Therefore, the scale factor of the dilation is two-fifths

The center of dilation = The origin

Therefore, given that the top right edge of S is at the center of dilation, the initial location of the dilated figure will be (0, 0), (2, 0), (2, -2), and (0, -2)

Given that the lowermost coordinates of S' are (0, 1) and (2, 1), and the lowermost coordinates of the initial dilation are (0, -2) and (2, -2), we have that the translation to S' from the initial dilation is T (0 - 0, 1 - (-2)) = T(0, 3) which is 3 units up.

Answer:

A

Step-by-step explanation: