Ana saved $3.40 on her grocery bill. This was 10% of her bill. How much was Ana's grocery bill?

Answer:

i. - 3a² + 2ab + b²

ii. 2c² + - 2cd + - 4d²

Step-by-step explanation:

i. First things first, you remove the parenthesis in both expressions to look like this:

a² − 3ab + 2b² - 4a² + 5ab − b²

Next, you add like terms.

(a² + - 4a²) + (- 3ab² + 5ab) + (2b² + - b²)

After adding these like terms, your answer would be:

- 3a² + 2ab + b²

ii. This one is pretty simply. But first, lets simplify by first removing the parenthesis to look like this:

c² - 6d² + c² - 2cd + 2d²

Then, combine like terms

(c² + c²) + (- 2cd) + (-6cd² + 2d²)

After that, your sum would be:

2c² + - 2cd + - 4d²

Hope this helps!

Answer:

see explanation

Step-by-step explanation:

i

(a² - 3ab + 2b²) + (- 4a² + 5ab - b²) ← remove parenthesis

= a² - 3ab + 2b² - 4a² + 5ab - b² ← collect like terms

= - 3a² + 2ab + b²

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

ii

(c² - 6d²) + (c² - 2cd + 2d²) ← remove parenthesis

= c² - 6d² + c² - 2cd + 2d² ← collect like terms

= 2c² - 2cd - 4d²

Answer:

C

Step-by-step explanation:

Use Δ ABC to find AB then Δ ABD to find DB

Δ ABC  is isosceles since ∠ CAB = ∠ CBA = 45° , then CB = CA = 2

Using Pythagoras' identity in Δ ABC , then

AB² = 2² + 2² = 4 + 4 = 8 ( take square root of both sides )

AB = [tex]\sqrt{8}[/tex] = 2[tex]\sqrt{2}[/tex]

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

Using the sine ratio in Δ ABD with the exact value

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{DB}[/tex] = [tex]\frac{2\sqrt{2} }{DB}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

[tex]\sqrt{3}[/tex] × DB = 4[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )

DB = [tex]\frac{4\sqrt{2} }{\sqrt{3} }[/tex] ( multiply numerator/ denominator by [tex]\sqrt{3}[/tex] to rationalise denominator )

     = [tex]\frac{4\sqrt{2} }{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]

     = [tex]\frac{4\sqrt{6} }{3}[/tex] → C

Answer:

A2: 55

A1: 99-55+x:180

X:26

Answer:

6,12

Step-by-step explanation:

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Answer:

Using the graph, just look at the exact spot where the lines are intersecting and that point is the solution.

The solution is: (1.2, -1.6)

Step-by-step explanation:

You can also test this by plugging the values of the point into both equations.

Answer:

top graph

Step-by-step explanation:

The graph of a proportional relationship is a straight line passing through the origin.

The only straight line graph passing through the origin is the top one

The graph on option A displays a proportional relationship.

Option A is the correct answer.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of the line on the graph is given as:

y = mx + c ____(1)

The graph on option A.

If the equation of a line is y = mx and the slope is a unit rate the graph shows proportional relationships.

We will select two points on the graph.

i.e

(2, 2) = (a, b) and (3.3) = (c, d)

Slope:

m = (d - b) / (c - a) = 3 - 2 / 3 - 2 = 1 / 1 = 1

Let (2, 2) = (x, y) and putting in (1) we get,

2 = 1 x 2 + c

2 = 2 + c

c = 2 - 2 = 0

c = 0

The slope of the line is 1

The equation of the line is y = x

Thus,

The graph displays a proportional relationship.

Option A is the correct answer.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ2

Answer:

so the zero is (20,0) but just so you know you can go to desmos and it will answer all of your graphing questions.

Step-by-step explanation:

can you please give me brainliest? I would appreciate it soooo much! I just need one more!

Answer:

angle A is congruent to angle R

Step-by-step explanation:

when it gets rotated counterclockwise around point X that is how the triangles end up matching up

Answer:

The answer is 1. ∠A ≅ ∠R

Step-by-step explaation:

Looking at the triangles when they're in their alphabetical order, ΔABC and ΔRST, since they are congruent, that means that if you were to pick an angle in one triangle, it would be equal to the angle in the same place of the other triangle. So if we were to take the first letter from ΔABC it'd be A, and the first letter in ΔRST is R, so that means angles ∠A and ∠R should be congruent.

Answer:

The equation for the proportional relationship is y = 2.8x. If the relationship between two quantities is a proportional relationship, this relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate.

Step-by-step explanation:

Answer:

Where's the equation

Answer:

D. 104º

Step-by-step explanation:

So the inside of a triangle is equal to 180º and we already know two of the angles.

D = 47º

C = 57º

47 + 57 = 104

To solve angles A and B, we know that a straight line is 180º and we can figure out the angle of B because now all we have to do is subtract 104 from 180.

180 - 104 = 76, B = 76º

Because we know that a straight line is 180º and we already have the measure of angle B, all we have to do now is subtract 76 from 180.

180 - 76 = 104º

Answer:

the slope is -1

the y-intercept is 5

equation: -x+5

Step-by-step explanation:

rise/run = slope

the point that goes through the y-axis is ur y-intercept

9514 1404 393

Answer:

  1 < 15 -2a < 7

Step-by-step explanation:

There are a couple of ways you can do this.

1) Put the minimum and maximum values of a into the expression to see what its corresponding values are:

  15-2a for a=4:

     15-2(4) = 7

  15-2a for a=7:

     15-2(7) = 1

Then ...

  1 < 15-2a < 7

__

2) Solve for a in terms of the value of 15-2a, then impose the limits on a.

  x = 15 -2a

  2a = 15 -x

  a = (15 -x)/2

Now, impose the given limits:

  4 < (15 -x)/2 < 7

  8 < 15 -x < 14 . . . multiply by 2

  -7 < -x < -1 . . . . . . subtract 15

  7 > x > 1 . . . . . . . . multiply by -1

  1 < 15-2a < 7 . . . . . use x=15-2a

_____

The vertical extent of the attached graph is the range of possible values of 15-2a. It goes from 1 to 7.

Given:

A dilation centered at the origin with a scale factor of 2 can be denoted

with the following notation:

[tex]D_2(x,y)=(2x,2y)[/tex].

To find:

The [tex]D_4[/tex] for point  A (-2, 3).

Solution:

If [tex]D_2(x,y)=(2x,2y)[/tex], then

[tex]D_4(x,y)=(4x,4y)[/tex]

Substitute x=-2 and y=3 in the above rule to find [tex]D_4[/tex] for point  A (-2, 3).

[tex]D_4(-2,3)=(4(-2),4(3))[/tex]

[tex]D_4(-2,3)=(-8,12)[/tex]

Therefore, [tex]D_4[/tex] for point  A (-2, 3) is (-8,12).

Answer:

y= 1/4x-2

Step-by-step explanation:

Let's use the two points we have to find the equation.

y = mx + b

-2 = m(0) + b

So b = -2

-1 = 4m - 2

4m = 1

m = 1/4

Answer:

TRUE

Step-by-step explanation:

GIVE ME BRAINLIEST

Answer:

2 dollars

72 dollars

Step-by-step explanation:

im not completely sure

Answer:

Arianna paid $2.75 for each photo coaster. If she purchased three dozen photo coasters, how much did she spend? $99.00

Step-by-step explanation:

Answer:

because every point on the perpendicular bisector of a line is equidistant from the ends of that segment => AP = PC = 8cm

Step-by-step explanation:

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

Explanation:

Let's label (0,7) as point C.

Plot points A and C on the same coordinate system.

Note that to go from A to C, we must do two things (in either order)

These two items will be replicated in either order to go from point C to point B.

The translation rule we follow is [tex](x,y) \to (x+6, y+1)[/tex] which is a mathematical way of saying "go right 6 and up 1". If we plug in x = -6 from point A we get to x = 0 which is the x coordinate of point C. Repeating this leads to x = 6, which is the x coordinate of point B.

Through similar arguments, we go from y = 6, to y = 7, to y = 8, when we hop from points A, to C, to B in that exact order.

Put everything together and we see that B is located at (6,8)

The diagram below provides a visual summary.

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

Extra info:

If we draw a line from point A to B, then point C will be on this line. Furthermore, AC = CB which can be proven using congruent triangles. Reflections preserve distance, meaning the distance from A to the mirror point C, is the same as from B to C as well. In short, we can say C is the midpoint of segment AB.

Answer: B

Step-by-step explanation: You just multiplying 25 with 10 and w which can be simplified as 24(w+10) and adding with the 13.5 x 10 and 13.5 x w, which can be simplified as 13.5(10+w)

Answer:

10x<2x+12

-2x    -2x  

8x<12

--  --

8    8

x<1.5

Step-by-step explanation:

If energy not transformed or changes than nothing will happen light bulb electrical energy will not converted into light energy and heat energy. ... The energy is not transformed into another form, it simply moves. It has a tendency to move, unless it is trapped, until it is released.

Answer:

Perimeter of the triangle = (12x - 9)

Step-by-step explanation:

Property of an equilateral triangle:

- All sides are equal in measure.

- All interior angles are equal.

Since, measure of one side of the triangle = (4x - 3)

And perimeter of a polygon = Sum of all sides of the polygon

Therefore, perimeter of the given triangle = (4x - 3) + (4x - 3) + (4x - 3)

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

                                                                      = (12x - 9)

Perimeter of the triangle = (12x - 9)

Answer:

the answer is 32

Answer:

Wouldn't it be 2?

Step-by-step explanation:

Answer:

(3-21)-(7+6) = -31

Step-by-step explanation:

3-21 = -18 - 13= -31

Answer:

13/30

Step-by-step explanation:

26 / 60 because there's 60 mins in an hour

and you can divide both the numerator and the denominator by 2 to get:

13/30, which is the simplest form.

Answer:

3 apples for 1.29

Step-by-step explanation:

If you divide 1.29 by 3, you will get 0.43 which means each apple then costs 0.43 each. This is less than 0.45 so it is the better value.

Answer:

$1.29 for 3

Step-by-step explanation:

The reason is that $0.45 per apple means for every apple, you have to pay $0.45. That eventually is going to start to add up. $1.29 for 3 means that you are paying $0.43 for 3, which means that you are saving money.

Answer:

Cannot be determined

Step-by-step explanation:

It can't be determined because AB=DE, BC=EF, and <ACB=<DFE not <DEF which makes the rule SSA which doesn't prove congruency.