the line x transforms from the point with coordinates (5,3) into the point with coordinates (1,-1). What is the equation of line x?

The baker needs to use 100/3 pounds of 90% chocolate to make the cake.

An equation is an expression used to show the relationship between two or more numbers and variables.

Let x represent the amount of 90% chocolate. Using equation:

100 * 70% + x * 90% = (x + 100) * 75%

100 * 0.7 + 0.9 * x = (x + 100) * 0.75

70 + 0.9x = 0.75x + 75

x = 100/3

The baker needs to use 100/3 pounds of 90% chocolate to make the cake.

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Answer:

100/3 pounds

Step-by-step explanation:

Answer:

x = 2, y = 2

Step-by-step explanation:

Equating the x and y coordinates , that is

2x + 3 = 7 ( subtract 3 from both sides )

2x = 4 ( divide both sides by 2 )

x = 2

and

7 = 3y + 1 ( subtract 1 from both sides )

6 = 3y ( divide both sides by 3 )

2 = y

Answer:

question 6 is false. 2/5 does not equal 24/144

Step-by-step explanation:

2/5 x 12/12 = 24/60, not 24/144

Answer:

2m−7n

Step-by-step explanation:

Let's simplify step-by-step.

6(m−2n)−(4m−5n)

Distribute the Negative Sign:

=6(m−2n)+−1(4m−5n)

=6(m−2n)+−1(4m)+−1(−5n)

=6(m−2n)+−4m+5n

Distribute:

=(6)(m)+(6)(−2n)+−4m+5n

=6m+−12n+−4m+5n

Combine Like Terms:

=6m+−12n+−4m+5n

=(6m+−4m)+(−12n+5n)

=2m+−7n

Answer:

72 males

Step-by-step explanation:

female=1/4

male=4/4-1/4=3/4

       =3/4 of 96

       =72 males

OR

Females=1/4 of 96=24

males=96-24=72

Answer:

They are both correct.

Step-by-step explanation:

6c=72

We can divide by 6 on both sides and get

c=72/6

Answer:

both lori and jayden are correct

Step-by-step explanation:

first solve 72/6, you should get 12. Therefore c should be 12 since to get the number of cards in a pack you divide the total number of cards by the number of packs.
plug in 12 for the equation 6c=72

6x12 = 72 (6 being the number of packs and twelve the number of cards per pack).

Answer:

Step-by-step explanation:

We know that:

Solution:

Hence, Gregg cut 4 sections of pizza dough.

Answer:

117

Step-by-step explanation:

4 : 9 = 52 : 117

Since

4 : 9 = 52 : X

Then we know

9/4 = X/52

Multiplying both sides by 52 cancels on the right

52 × (9/4) = (X/52) × 52

52 × (9/4) = X

Then solving for X

X = 52 × (9/4)

X = 117

Therefore

4 : 9 = 52 : 117

Answer:

Step-by-step explanation:

Start with the distance formula:

√[(x2-x1)2+(y2-y1)2]

Plugging your x and y values in you get:

√[(-8.3-2.8)2+(9.6-(-1.8))2]

Simplify inside before you square:

√[(-11.1)2+(11.4)2]

√(123.21)+(129.96)

√(253.17)

15.911

The total area of the walls is 140 m²

Since the room is in the shape of a cuboid, and we require the area of the walls of the room, the walls of the cuboid are the walls of the room.

So, the total surface area of a cuboid is A = 2(lb + lh + bh) where

Since we require the total area of the walls, lb which is the area of the floor is removed from the equation.

So, the area of the walls is A' = 2(lh + bh)

= 2h(l + b)

Since the dimensions of the floor are 4 meters by 6 meters and the height of the basement is 7 m. So,

So, substituting the values of the variables into the equation, we have

A' = 2h(l + b)

A' = 2 × 7 m × (4 m + 6 m)

A' = 14 m × 10 m

A' = 140 m²

So, the total area of the walls is 140 m²

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Answer:

x=14

Step-by-step explanation:

The interior angles of a regular decagon are the same and add up to 1440.

10(10x+4)=1440

Answer:

(x-6)

Step-by-step explanation:

There are many ways to divide this, one of them is done below.

(x^2-11x+30)/(x-5)

Factorize (x^2-11x+30),

(x^2-6x-5x+30)
(x(x-6)-5(x-6))
(x-5)(x-6)

We have,

(x^2-11x+30)/(x-5)
(x-5)(x-6)/(x-5)

(x-5) cancel each other,

(x-6)

You can also use synthetic division, traditional division or other methods of division.

Answer:

Height = 5

Step-by-step explanation:

[tex]Solution,\\Volume(V)=45\pi \\Radius(r)=3\\Height(h)=?\\As,\\V=\pi r^{2} h\\45\pi =\pi (3)^{2} h\\\frac{45\pi }{9\pi } =h\\h=5[/tex]

Answer:

beto and mark

Step-by-step explanation:

beto

3m = 3m+5

solving it we get

5=0

mark

6-n = -n+2

solving it

4=0

Answer:

4m

Step-by-step explanation:

3m is the side length touching both triangles in the right picture, or the line directly left of the red line

4m is the side going up from the right angle, and the red line

5m is the diagonal line, which would be two lines to the left of the red line

6m is the height of the prism, or the line perpendicular to the red line

You can use the fact that the middle area can be found by subtracting internal area from the total area.
The amount of wood(in area, assuming almost flat) needed by the carpenter to build the frame is given by

Option A: 5.5π + 106 sq. inches.

The middle area can be found by subtracting internal area from the total area.
For example, if you've got a big circle, and a small circle inside that big circle, and you want the remaining area in the big circle not occupied by smaller circle, then we have

Remaining area = Area of bigger circle - Area of smaller circle

The diagram is attached below.

The wooden region between those two semicircles in the top is of this below area

Area of bigger semicircle - Area of smaller semicircle.

Since bigger semicircle has 6 inch radius and smaller has 1 inch less(since width of the wood is 1 inch everywhere) which is 5 inch radius, thus,

As area of semicircle with radius r units is [tex]\dfrac{\pi r^2}{2} \: \rm unit^2[/tex]

Thus,

Area of wood between two semicircles = [tex]\pi \times 6^2/2 - \pi \times 5^2/2 = \pi \times 11/2 = 5.5\pi \rm \: \: inch^2[/tex]

Area of the wood in the bottom of the window = area of rectangle GLMH

Since |GL| = |HM| = 1 inch and |LM| = 12 inches, thus, as

Area of rectangle = length times width

thus,

Area of GLMH = [tex]1 \times 12 = 12 \rm \: inch^2[/tex]

Remaining wood is as rectangle ABGE and CDFH

Since we have |AL| = 48 inches but |GL| = 1 inch, thus, |AG| = 47 inches(1 less than |AL|

Also, since |GE| = 1 inch wide, thus,

Area ABGE = [tex]1 \times 47 = 47 \: \rm inch^2[/tex]

Similar to above case, we have

Since we have |DM| = 48 inches but |HM| = 1 inch, thus, |DH| = 47 inches(1 less than |DM|

Also, since |FH| = 1 inch wide, thus,

Area CDFH = [tex]1 \times 47 = 47 \: \rm inch^2[/tex]

Thus, total wood used(in terms of area) = Area CDFG + Area ABCD + Area of bottom rectangle GLHM + Area of the internal of two semicircles on top ADCB(thick arc like shape)

or

Total area of wood = 47 + 47 + 12 + 5.5π = 5.5π + 106 sq. inches.

Thus,

The amount of wood(in area, assuming almost flat) needed by the carpenter to build the frame is given by

Option A: 5.5π + 106 sq. inches.

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Answer:

-5 or 5

Step-by-step explanation:

Because when it is absolute value, all real numbers result in positive numbers.

Answer:

C

Step-by-step explanation:

In a Pythagorean triple the square on the longest side is equal to the sum of the squares on the other 2 sides.

A

longest side = 10 ⇒ 10² = 100

6² + 8² = 36 + 64 = 100

A is a Pythagorean triple

B

longest side = 17 ⇒ 17² = 289

8² + 15² = 64 + 225 = 289

B is a Pythagorean triple

C

longest side = 9 ⇒ 9² = 81

5² + 8² = 25 + 64 = 89

89 ≠ 81

C is not a Pythagorean triple

D

longest side = 13 ⇒ 13² = 169

5² + 12² = 25 + 144 = 169

D is a Pythagorean triple

Answer:

(e+8)°+(3e-4)°=180°

4e+4=180

4e=180-4

4e=176

e=176/4

e= 44°

e+8=44+8=52

===================================================

Explanation:

Rule: The diagonals of any rectangle are the same length.

Because of that rule, we can say

NQ = PR

(NK) + (KQ) = (PK) + (PR)

(x+4) + (2y+5) = (2x+1) + (4y+3)

x+2y+9 = 2x+4y+4

x+2y-2x-4y = 4-9

-x-2y = -5

x+2y = 5

------------------

Rule: The diagonals of any rectangle cut each other in half (aka bisect each other)

So the pieces NK and KQ are the same length.

NK = KQ

x+4 = 2y+5

x = 2y+5-4

x = 2y+1

Plug this into the previous equation we found. Solve for y.

x+2y = 5

(2y+1) + 2y = 5

4y+1 = 5

4y = 5-1

4y = 4

y = 4/4

y = 1

Then use this to find x

x = 2y+1

x = 2*1+1

x = 3

---------------

We now have enough info to find the length of each segment.

Furthermore,

We get identical segment lengths, which helps confirm the correct answer.

Answer:

1

Step-by-step explanation:

1 to any power is itself

Step-by-step explanation:

A rectangle: P=2l+2w or P=2(l+w) (same formula written differently)

50=2x17+2w

50=34+2w

2w=50-34

2w=16

w=16÷2=8

Since it says twice as wide then we will multiply w with 2

2xW

2x8=16 which is the width of the 2nd rectangle

Hope this helps :)

Answer:

8. ∠1=118° ∠2=118°

9. ∠1=72° ∠2=108°

10. ∠1=127° ∠2=127°

Step-by-step explanation:

8. In this problem, 118° is corresponding to ∠1, meaning they are congruent. ∠2 is supplementary with ∠1, meaning that together, they equal 180°. So, to get ∠2, you must subtract 118° from 180°

9. In this problem, 72° is same side interior with ∠1, meaning they are congruent. ∠2 is supplementary with ∠1, so you do 180°-72°=  108°

10. In this problem, ∠1 is vertical angles with 127°, making them equal to each other. ∠2 is corresponding with 127°, making them also equal.

Answer:

327 children and 318 adults

Step-by-step explanation:

The x be the amount of children and y be the amount of adults that were at the swimming pool. We can use this to set up a system of equations:

x+y=645

1.75x+2.50y=1367.25

Move y to the other side in the first equation to isolate x and solve the system using substitution:

x=645-y

  1.75(645-y)+2.50y=1367.25

Distribute

1128.75-1.75y+2.50y=1367.25

         1128.75+0.75y=1367.25

Subtract 1128.75 from both sides

                        0.75y=238.5

Divide both sides by 0.75

                                y=318

x=645-y

x=645-318

x=327

327 children and 318 adults swam at the pool that day

[tex]\qquad \qquad\huge \underline{\boxed{\sf ᴀɴsweʀ}}[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: x {}^{3} - 3 {x}^{2} y + 9[/tex]

Now, use the given values :

[tex]\qquad \sf  \dashrightarrow \: ( - 1) {}^{3} - (3 \times ( - 1) {}^{2} \times 2) + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 1 - ( 3\times 1 \times 2) + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 1 - 6 + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 7 + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2[/tex]

Answer: Ez Neither

Step-by-step explanation: