Question 4
Simplify

Answer:

The translation vector can be drawn on the coordinate grid or written as

\vec{v}=\langle a,b\rangle

v

=⟨a,b⟩

. For example, a translation vector that moves a figure

3

3

units right and

2

2

units down can be represented mathematically as

\vec{v}=\langle3,-2\rangle

v

=⟨3,−2⟩

, or graphically as

It doesn’t matter where the vector is positioned in the plane. In this figure, the vector starts at

(1,1)

(1,1)

and ends at

(4,-1)

(4,−1)

. But the initial point and terminal point of the vector are irrelevant. What matters is the length of the vector and the direction in which it points, so all you have to look at is how many units the vector moves in the

y

y

-direction and how many units the vector moves in the

x

x

-direction.

Answer:

U are doing right but don't move ur compass when u are doing the line (i mean opposite line)otherwise ur line at not bisect

Answer:

Step-by-step explanation:

(1,8) (-1,-2)

Slope: (-2-8)/(-1-1) = -10/-2 = 5

y -8 = 5 (x - 1)

y - 8 = 5x - 5

y = 5x +3

Step-by-step explanation:

The area of any 2-d quadrilateral is equal to the base of the shape times the height, though we can just sub in length and width here. The key bits of information here is the aspect ratio (4:3) and the given area (300 in^2).

So far this gives us L∗W=300in2

Now, the aspect ratio given implies for every 4 inches in length, there will be 3 inches in width. This allows us to factor out a 4 and a 3 from the Length and Width respectively and give them the same constant variable, like so:

4x∗3x=300in2

Now, some might be tempted to go ahead with 12x here, but let’s expand the left side out to see what’s really going on:

4∗x∗3∗x=300in2

From here, let’s resolve like terms Our constants will multiply together and give us 12, and x * x of course gives us x^2 to give us the following:

12x2=300in2

From here, simply divide through by 12 to isolate x on one side,x2=25

And finally take the square root of both sides to work out what your common factor is,

x=5

Now that we have out common factor, let’s plug it back into our original formula to find our Length and Width, like so.

(4∗5)in∗(3∗5)in=300in2

20in∗15in=300in2

Therefore, the Length of our rectangle is 20in, and the Width of our rectangle is 15in

Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

41)

[tex]1+2+3+4+...+n=\dfrac{(n+1)*n}{2} \\\\2+4+6+...+2n=2*(1+2+3+4+...+n)=2*\dfrac{(n+1)*n}{2} =(n+1)*n\\\\[/tex]

42)

the square of the sum of the first n natural integers equals the sum of the cubes of these

Answer:

-$79

Step-by-step explanation:

If i read that correctly, Rylee had -$23 in her account.

Then, she was charged $56, meaning we have to subtract $56 from -$23. When we do -23 - 56, we get -79. Meaning, Rylee now has a balance of -$79.

Answer:

Step-by-step explanation:

The original price of Rylee’s groceries was $23.50. This money is leaving her bank account, so represent the amount with a negative sign:

-$23.50.

Rylee got a 20% discount on her purchase. In other words, she got 20% of her money back. The expression that represents the net change in her bank account is

-$23.50 – (-$23.50 × 0.2).

Further simplify the expression by factoring -$23.50 from both terms:

-$23.50 – (-$23.50 × 0.2)

=

-$23.50(1 – 0.2)

=

-$23.50(0.8).

Answer:

Each bag costs 0.35 cents

Step-by-step explanation:

divide 9.88 by 28 and that gives you the total for each bag of chips

Answer:

locks that raise or lower the boat. Traveling East a boat would have to be lowered 12' at Amsterdam, 11' at Trives Hill, and 8' at Randall. By how much does the elevation of the boat change between Amsterdam and Randall

Q) 5 × (2/6) = ?

→ 5 × (2/6)

→ 10/6

→ 5/3 {final answer}

Answer:

y = 2x - 8    OR     4 - 2x = -4 - y

Step-by-step explanation:

Use the point-slope form m(x₁-x₂) = (y₁-y₂); m means slope

plug in your numbers:

2(2-x₂) = (-4-y₂)

4 - 2x = -4 - y

or to put it into Y=mx + b:

y = 2x + 8

Answer:

37

Step-by-step explanation:

LMN is one big line

LM=22

LM=15

LN=22+15=37

Answer:

LN = LM + MN = 37

Step-by-step explanation:

L————————-M———————-N

22. 15

L————————-37———————-N

Answer:

true

Step-by-step explanation:

5(1+2x)= 5 +10x =10x + 5

Answer:

Yes, they are eqivelant.

Step-by-step explanation:

5(1+2x) and 10x+5

The first step is to set them equal to each other, to see if they are equivelent.

5(1+2x) = 10x+5

Distribute the 5 to both terms in the parentheses by multiplying.

5(1) + 5(2x) = 10x +5

5 + 10x = 10x +5

The communative property of addition proves that these are equal.

Answer:

Step-by-step explanation:

Answer:

32.5cm

Step-by-step explanation:

Using the formula A=h_b*b/2

We get 5*13/2=32.5

Answer:

18

Step-by-step explanation:

Answer:

7(10−[tex]2^{3}[/tex])+ [tex]\frac{8}{2}[/tex]

=18

Step-by-step explanation:

7(10−[tex]2^{3}[/tex])+[tex]\frac{8}{2}[/tex]

=7(10−8)+ [tex]\frac{8}{2}[/tex]  

=(7)(2)+[tex]\frac{8}{2}[/tex]  

=14+[tex]\frac{8}{2}[/tex]  

=14+4

=18

Answer:

No solution

Step-by-step explanation:

To solve first you need to isolate the absolute value sign. Do this by subtracting 7 from each side.

Now an expression inside absolute value bars is set to a negative. Since absolute value makes terms and expressions positive, there is no x-value that could make this true. Therefore, there are no solutions.

[tex]\\ \tt\Rrightarrow |3x-8|+7=2[/tex]

[tex]\\ \tt\Rrightarrow |3x-8|=2-7[/tex]

[tex]\\ \tt\Rrightarrow |3x-8|=-5[/tex]

Because of absolute vale there is no solution

Answer:

x=0 , x = 1/2

Step-by-step explanation:

(4x-1)=1 —> 4x-1=1—> 4x=1+1—> 4x=2 —> x=2/4 —> x= 1/2

-(4x-1)=1—>-4x+1=1—> 4x= 1-1 —> x=0

Hello there!

We are given the equation:

[tex] \displaystyle \large{ |4x - 1| = 1}[/tex]

Definition/Property

[tex] \displaystyle \large{ |a| = \sqrt{ {a}^{2} } } \\ \displaystyle \large{ |a| = b \longrightarrow a = \pm b} \\ \displaystyle \large{ |a| = \begin{cases} a \: \: (x \geqslant 0) \\ - a \: \: (a < 0) \end{cases}}[/tex]

First, cancel the absolute value sign and write plus-minus beside 1.

[tex] \displaystyle \large{ |4x - 1| = 1} \\ \displaystyle \large{ 4x - 1 = \pm 1} \\ [/tex]

Break in two cases.

[tex] \displaystyle \large{ 4x - 1 = \begin{cases} 1 \\ - 1 \end{cases}} \\ \displaystyle \large{ 4x = \begin{cases} 1 + 1 \\ - 1 + 1 \end{cases}} \\ \displaystyle \large{ 4x = \begin{cases} 2 \\ 0 \end{cases}} \\ \displaystyle \large{ x = \begin{cases} \frac{2}{4} \\ \frac{0}{4} \end{cases}}[/tex]

Therefore, x = 0 or 1/2

Let me know if you have any questions!

Topic: Absolute Value Function - Equations

Answer:

-4.75

Step-by-step explanation:

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

So applying the formula

(-29-9)/(15-7)

= -38/8 = -4.75

Answer: -4

Step-by-step explanation:

Start with -6, since there is nothing to solve in the parenthesis.

Subtract -2 from -6, which will get you -4.

[tex]\small\tt\red{Question : 2x + 3(5x - 7) = 47 } \\ \\ \small\tt\orange{solution : - } \\ \\ \small\tt\blue{2x + 3(15x - 7) = 47} \\ \\ \small\tt\blue{2x + 15 - 21 = 47} \\ \\ \small\tt\blue{17 = 47 + 21} \\ \\ \small\tt\blue{17x = 68} \\ \\\small\tt\blue{x = \cancel \frac{68}{17} } \\ \\\\\small\tt\green{\boxed{x = 4 \: \: is \: your \: answer}} \\ \\ \\\small\tt\pink{\boxed{\boxed{hope \: it \: help \: you \: dear}}}[/tex]

1 inch= 10 miles

1 inch * 1 inch = 1 in^2 = 10 miles * 10 miles = 100 miles^2

so

1 in^2 is 100 mi^

You're letting x = 0.325325325…, which means

1000x = 325.325325325…   (or 325.325, but pretend the underline is actually an overline)

Then the next box you'd fill in with 0.325325325… (or 0.325).

Subtracting these, you have

1000x - x = 325.325325325… - 0.325325325…

999x = 325

Finally, solving for x gives

x = 325/999

Answer:

-7 × (-6)

Step-by-step explanation:

7 × (-6) = -42

-6 × 7 = -42

-7 × (-6) = 42

-7 × 6 = -42

Answer:

[tex] - 7 + ( - 6) = 42[/tex]

I hope I helped you^_^