answer all of the questions please

Given:

x, y and z are integers.

To prove:

If [tex]3x-y+5z[/tex] is even, then at least one of x, y or z is even.

Solution:

We know that,

Product of two odd integers is always odd.          ...(i)

Difference of two odd integers is always even.          ...(ii)

Sum of an even integer and an odd integer is odd.      ...(iii)

Let as assume x, y and z all are odd, then [tex]3x-y+5z[/tex] is even.

[tex]3x[/tex] is always odd.          [Using (i)]

[tex]5z[/tex] is always odd.          [Using (i)]

[tex]3x-y[/tex] is always even.       [Using (ii)]

[tex](3x-y)+5z[/tex] is always odd.       [Using (iii)]

[tex]3x-y+5z[/tex] is always odd.

So, out assumption is incorrect.

Thus, at least one of x, y or z is even.

Hence proved.

Answer:

The rule of dilation is [tex]P'(x,y) = 3\cdot P(x,y)[/tex].

The vertices of the dilated triangle are [tex]A'(x,y) = (-21, -18)[/tex], [tex]B'(x,y) = (-15,-10)[/tex] and [tex]C'(x,y) = (-3,-15)[/tex], respectively.

Step-by-step explanation:

From Linear Algebra, we define the dilation by the following definition:

[tex]P'(x,y) = O(x,y) + k\cdot[P(x,y)-O(x,y)][/tex] (1)

Where:

[tex]O(x,y)[/tex] - Center of dilation, dimensionless.

[tex]k[/tex] - Scale factor, dimensionless.

[tex]P(x,y)[/tex] - Original point, dimensionless.

[tex]P'(x,y)[/tex] - Dilated point, dimensionless.

If we know that [tex]O(x,y) = (0,0)[/tex], [tex]k = 3[/tex], [tex]A(x,y) = (-7,-6)[/tex], [tex]B(x,y) = (-5,-2)[/tex] and [tex]C(x,y) =(-1,-5)[/tex], then dilated points of triangle ABC are, respectively:

[tex]A'(x,y) = O(x,y) + k\cdot [A(x,y)-O(x,y)][/tex] (2)

[tex]A'(x,y) = (0,0) + 3\cdot [(-7,-6)-(0,0)][/tex]

[tex]A'(x,y) = (-21, -18)[/tex]

[tex]B'(x,y) = O(x,y) + k\cdot [B(x,y)-O(x,y)][/tex] (3)

[tex]B'(x,y) = (0,0) + 3\cdot [(-5,-2)-(0,0)][/tex]

[tex]B'(x,y) = (-15,-10)[/tex]

[tex]C'(x,y) = O(x,y) + k\cdot [C(x,y)-O(x,y)][/tex] (4)

[tex]C'(x,y) = (0,0) +3\cdot [(-1,-5)-(0,0)][/tex]

[tex]C'(x,y) = (-3,-15)[/tex]

The rule of dilation is:

[tex]P'(x,y) = 3\cdot P(x,y)[/tex] (5)

The vertices of the dilated triangle are [tex]A'(x,y) = (-21, -18)[/tex], [tex]B'(x,y) = (-15,-10)[/tex] and [tex]C'(x,y) = (-3,-15)[/tex], respectively.

Answer:

x = 40 y = 140

Step-by-step explanation:

The angles on the same side of the isoceles trapezoid are equal and the opposite sides are supplementary to the other angles.

Answer: 3 and 3/8 or 27/8

Step-by-step explanation:

First step, you will need to move the decimal to the side by 1 place value.

0.8 --> 8. and 2.7--> 27.

Then just do your normal dividing.

27/8 = 3 and 3/8

The answer to 2.7÷0.8 can be either a mixed number or an improper fraction.

You have to move the decimal places to the right as many times as you need in order to make the number a while number you move the decimal place the same times as you did to the number outside the box which makes is 8 divided by 27 8 can’t go into 2 so u add a 0 and 8 can go into 27 3 times. You add a decimal point and subtract 24 from 27 u get 3 then you add a decimal point with a 0 8 can go into 30 3 times so it’s 6 add a decimal point to make it 60. Then 8 can go into 60 7 times subtract 56 from 60 and you get 4 add a decimal point and you get 40 8 can go into 40 5 times and your answer is 3.375

I added picture so u can see how it looks when you do it.

Answer: For #6, domain is {-3≤x<4}, range is {-3<y≤-1}

Step-by-step explanation: For #6 domain, the leftmost point on the graph is -3, with a closed circle. This means that x is greater than or equal to -3 (-3≤x). The rightmost point is 4, with an open circle, meaning that x is less than 4 (x<4). Put them together in the standard format, and you get {-3≤x<4}. Same principle for range; lowest point is -3, with an open circle (-3<y), and highest point is -1, with a closed circle (x≤-1). Result is {-3<y≤-1}.

I'm not sure whether you are a beginner at this or if it's just this one that you're stuck on, I hope my answer was sufficient.

9514 1404 393

Answer:

Step-by-step explanation:

For dilations about the origin, such as these, the scale factor is always the ratio of any image point coordinate* to the corresponding preimage point coordinate. If the scale factor is k, the transformation can be written as ...

  (x, y) ⇒ (kx, ky)

__

  S(9,12) ⇒ S'(6, 8) . . . . scale factor is 6/9 = 2/3; relation is (x, y) ⇒ (2/3x, 2/3y)

  U(8, 18) ⇒ U'(4, 9) . . . scale factor is 4/8 = 1/2; relation is (x, y) ⇒ (1/2x, 1/2y)

  I(0,8) ⇒ I'(0, 7) . . . scale factor is 7/8; relation is (x, y) ⇒ (7/8x, 7/8y)

  X(16, 8) ⇒ X'(4, 2) . . . scale factor is 2/8 = 1/4; relation is (x, y) ⇒ (1/4x, 1/4y)

_____

* The origin is the one invariant point in a dilation, so the chosen coordinate cannot be zero.

Every line from the tangent to the centre is 90°. This is said in the circle theorems.

So angle OBC and ODC are 90°.

angle O is twice the size of angle F. This is another circle theorem.

Therefore angle O is 152°.

The quadrilateral of ODBC would equal to 360°. Which means 90° + 90° + 152° = 332°

360° - 332° = 28°.

The answer is 28°

Answer:

∠BCD = 28°

Step-by-step explanation:

arc BD = 2 x inscribed angle ∠BFD = 2 x 76 = 152

arc BFE = 360 - arc BD = 360 - 152 = 208

tangent-tangent angle ∠BCD = (arc BFE - arc BD)/2 = (208 - 152)/2 = 28

Divide by 2

Y = 2x - 2.5

x intercept: when y = 0

0 = 2x - 2.5

2.5 = 2x, x = 1.25

y intercept: when x = 0

Y = 2(0) - 2.5, y = -2.5

Solution: (1.25, 0) and (0, -2.5)

Step-by-step explanation:

y = x - 4 and y = 4x + 2

=> x - 4 = 4x + 2

=> 3x = -6

=> x = -2

y = x - 4 = (-2) - 4 = -6

The solutions are x = -2 and y = -6.

Answer:

x = -2

y = -6

Step-by-step explanation:

y = x - 4

y = 4x + 2

y = y

then:

x-4 = 4x+2

x - 4x = 4 + 2

-3x = 6

x = 6/-3

x = -2

y = x - 4

y = -2 - 4

y = -6

Complete Question

Mr. Nguyen bought a package of 3 chicken legs and a package of 7 chicken wings. Ms. Dawes bought a package of 3 chicken legs and a package of 6 chicken wings. Mr. Nguyen bought 45 ounces of chicken. Ms. Dawes bought 42 ounces of chicken. How much did each chicken leg and each chicken wing weigh?​

Answer:

Weight of Chicken leg = x = 8 ounces

Weight of Chicken wing = y = 3 ounces

Step-by-step explanation:

Let us represent

Weight of Chicken leg = x

Weight of Chicken wing = y

Mr. Nguyen bought a package of 3 chicken legs and a package of 7 chicken wings.Mr. Nguyen bought 45 ounces of chicken.

3x + 7y = 45 ounces.... Equation 1

Ms. Dawes bought a package of 3 chicken legs and a package of 6 chicken wings. Ms. Dawes bought 42 ounces of chicken.

3x + 6y = 42 ounces... Equation 2

Combining both Equations together we solve by Elimination method

3x + 7y = 45.... Equation 1

3x + 6y = 42... Equation 2

We eliminate x by subtracting Equation 2 from Equation 1

Hence:

y = 3 ounces

Solving for x

3x + 6y = 42 ounces... Equation 2

3x +6(3) = 42 ounces

3x + 18 = 42 ounces

3x =( 42 - 18) ounces

3x = 24 ounces

x = 24 ounces/3

x = 8 ounces

Hence:

Weight of Chicken leg = x = 8 ounces

Weight of Chicken wing = y = 3 ounces

Answer:

chicken leg- 8 oz

chicken wing- 3 oz

Step-by-step explanation:

Answer:

98,635

Step-by-step explanation:

Answer:

c

Step-by-stepexplanation:

Answer:

i believe the answer is a

i'm not sure...........

hope its right

:)

Answer:

x = 8

y = -11

Step-by-step explanation:

In this question, we have to find out the value of "x" and "y".

Solve:

Lets solve for y first.

-2(3x + 4y = -20)

6x + 5y = -7

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

-6x - 8y = 40

6x + 5y = -7

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

-3y = 33

Divide both sides by -3

y = -11

We now know what the value of "y" is, now we must find the value of x. To do this, we would plug -11 to "y" in one of our equations.

Solve for x:

3x + 4y = -20

3x + 4(-11) = -20

3x - 44 = -20

Add 44 to both sides.

3x = 24

Divide both sides by 3

x = 8

Now we know that our answer are:

x = 8

y = -11

Answer:

x=54

Step-by-step explanation:

1/3 x 54 = 18, 18 - 2 = 16

:)

Answer:

x=3.6

Step-by-step explanation:

multiply 4 by 9 and then divide by 10

Answer:

x/4=9/10

x*10=9*4

x=(9*4)/10

X=3.6

Answer:

m%(n)

Step-by-step explanation:

whenever the word "of" comes up in a math problem, it's going to mean to multiply.  This case is no exception.

m% of n = m%(n)

n=number

m=the percent number

Ex: m=25

n=315

plug the values into m%(n)

25%(315)

There are two different forms you can do to solve this expression.

fraction: 25/100(315)=7875/100=78.75

the reason why it would be 25/100 hundred is because, %=per cent.  Cent=100 and per would mean you would have to divide.

decimal: 0.25(315)=78.75

if 25% is 25/100 that means that 25 would be in the hundreths place in a decimal(0.ab)

Answer:

tell me the choices so i can help you............

Answer:

dude what type of question is this

Answer:

how many times did you post this?

Step-by-step explanation:

Answer:

A does

Step-by-step explanation:

5+3+10+6=24x56310B=A+B=A

Answer:

(f - g)(x) = x² - 3x - 70

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = x² - 2x - 63

g(x) = x + 7

(f - g)(x) is f(x) - g(x)

Step 2: Find (f - g)(x)

Given:

The graph of a function.

To find:

The zeros of this function on the graph.

Solution:

We know that, zeros are the values at which the values of the function is 0. It means, the points where the graph of function intersect the x-axis are know as zeros of the function.

From the given graph it is clear that, the graph intersect the x-axis at two points.

Therefore, the marked points on the below graph are the zeros of the function.

9514 1404 393

Answer:

  see below

Step-by-step explanation:

I like a spreadsheet for doing repetitive calculations. The matchup is shown in the attachment.

The sale price is 100% - 35% = 65% = 0.65 times the regular price.

__

Here, you can also identify the matches by putting the prices in numerical order. The lowest regular price will correspond to the lowest sale price.

  regular, sale

  3.09, 2.01

  3.29, 2.14

  3.77, 2.45

  4.19, 2.72

Answer: 11

Step-by-step explanation: SAS Postulate states that any two triangles that share the same Side, Angle, Side, are congruent. Since those two triangles share the side length of 5, and then a 90 degree right angle, and the side PM every corresponding side and angle with equal each other. Such as side MN and ML.

Answer:

x = 7/a

Step-by-step explanation:

2ax + 9 = 23

Inverse operations

2ax + 9 = 23

       -9     -9

2ax = 14

/2        /2

ax = 7

/a    /a

x = 7/a

Answer:

(-5/2,5)

I hope it will be useful.

The coordinates of the point on the directed line segment that partitions the segment into a ratio of 1 to 3 is (1/2, -5).

In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line that is between end points.

Now the given coordinates are,

(-4,10) and (2,-10)

Thus, we have,

x₁  = -4

y₁ = 10

x₂ = 2

y₂ = -10

Given ratio, m₁ : m₂ = 1 : 3

⇒ m₁ =  1; m₂ =  3

Let (x,y) be the coordinates of the point on the directed line segment from (-4,10) to (2,-10) that partitions the segment into a ratio of 1 to 3.

Since the section formula is given as,

So, x = (m₁x₁ + m₂x₂) / (m₁ + m₂)  

y =  (m₁y₁ + m₂y₂) / (m₁ + m₂)  

Put the values,

x = [1(-4) + 3*2)] / (1 + 3) = (-4+6) / 4 = 2/4

⇒ x = 1/2

Similarly y = [1(10) + 3*(-10)] / (1 + 3) = (10-30) / 4 = -20/4

⇒ y = -5

So, the required coordinates are (1/2, -5)

Thus, the coordinates of the point on the directed line segment that partitions the segment into a ratio of 1 to 3 is (1/2, -5).

To learn more about line segment :

brainly.com/question/12774890

#SPJ2

Answer:

the quotient of -30/6 and 30/ -6 are same ie. -5, because if the numerator or denominator is negative the quotient will be negative.

hope it helps!

Answer:

35%

Step-by-step explanation:

40%+25%=65%

100%-65%=35%

Answer:

$9.60

Step-by-step explanation:

The question above is a simple interest question.

The formula for the amount of money after a given period of time using simple interest is given as:

A = P(1 + rt)

Where

P = Initial Amount saved or invested = $8

R = Interest rate = 5%

t = Time in years = 4

Calculation:

First, converting R percent to r a decimal

r = R/100 = 5%/100 = 0.05 per year.

Solving our equation:

A = 8(1 + (0.05 × 4)) = 9.6

A = $9.60

The amount of money that will be in a bank account after 4 years is $9.60