Show how you would simplify the following expressions. Show your work.

Answer:

Fourth option is correct. The length of B'C' is 1 unit.

Step-by-step explanation:

The vertices of triangle ABC are A = (2, 2), B = (4, 3), and C = (6, 3).

Distance formula:

The length of BC is 2 units.

It is given that ΔABC is dilated by a scale factor of 0.5 with the origin as the center of dilation, resulting in the image ΔA′B′C′.

It means the ΔABC and ΔA′B′C′ are similar and corresponding sides of ΔA′B′C′ and ΔABC are proportional.

The scale factor is 0.5.

Therefore the length of B'C' is 1 unit and fourth option is correct

Answer:

D= 1 unit

Step-by-step explanation:

Answer:

what does lmno means

Step-by-step explanation:

Answer:

Axis is a vertical line at x = 2

Vertex is (2, -1)

y-intercept is (0, 3)

Solutions are x = 1 and x = 3

Step-by-step explanation:

To draw the graph of the quadratic equation you must find at least 5 points lie on the graph by choose values of x and find their values of y

Let us do that

Use x = -1, 0, 1, 2, 3, 4, 5

∵ y = x² - 4x + 3

∵ x = -1

∴ y = (-1)² - 4(-1) + 3 = 1 + 4 + 3 = 8

→ Plot point (-1, 8)

∵ x = 0

∴ y = (0)² - 4(0) + 3 = 0 + 0 + 3 = 3

→ Plot point (0, 3)

∵ x = 1

∴ y = (1)² - 4(1) + 3 = 1 - 4 + 3 = 0

→ Plot point (1, 0)

∵ x = 2

∴ y = (2)² - 4(2) + 3 = 4 - 8 + 3 = -1

→ Plot point (2, -1)

∵ x = 3

∴ y = (3)² - 4(3) + 3 = 9 - 12 + 3 = 0

→ Plot point (3, 0)

∵ x = 4

∴ y = (4)² - 4(4) + 3 = 16 - 16 + 3 = 3

→ Plot point (4, 3)

∵ x = 5

∴ y = (5)² - 4(5) + 3 = 25 - 20 + 3 = 8

→ Plot point (5, 8)

→ Join all the points to form the parabola

From the graph

∵ The axis of symmetry is the vertical line passes through the vertex point

∵ x-coordinate of the vertex point is 2

∴ Axis is a vertical line at x = 2

∵ The coordinates of the vertex point of the parabola are (2, -1)

∴ Vertex is (2, -1)

∵ The parabola intersects the y-axis at point (0, 3)

∴ y-intercept is (0, 3)

∵ x² - 4x + 3 = 0

∵ The solutions of the equation are the values of x at y = 0

→ That means the intersection points of the parabola and the x-axis

∵ The parabola intersects the x-axis at points (1, 0) and (3, 0)

∴ Solutions are x = 1 and x = 3

Step-by-step explanation:

2/3 x 2/2 = 4/6

2/3 x 3/3 = 6/9

2/3 x 4/4 = 8/12

Answer:

235

Step-by-step explanation:

Answer:

235

20 percent (calculated percentage %) of what number equals 47? Answer: 235.

Step-by-step explanation:

I hope this Helps c:

Answer:

Company B is offering the lowest price/lb at $12.72/lb.

Step-by-step explanation:

Answer: 35

Step-by-step explanation: 85% of 40 basically you multiply 0.85 by 40 :)

Answer:

Yes

Step-by-step explanation:

-2(9)+4= -14  and -14 is equal to -14.

Answer:

f(x)=20+4x = -5

Step-by-step ;

answer is -5 .

Answer:

-30x3 because you are subtracting 30 3 times

Step-by-step explanation:

Answer:

13/16 is the answer. Bad handwriting but try to understand .

Answer:

After 10 months, both salespersons will sell 160 cars.

Step-by-step explanation:

We are given two different salesperson's statistics of sales. We can use this information to set up a system of equations and solve for our variable.

Let us name the first salesperson Person 1 and the other salesperson Person 2.

Now, for Person 2:

Now, because we have these equations, we can set up a table that will determine the number of months that will elapse before the salespersons will sell the same amount of cars.

For Person 1, the equation will be the increase of the y-value by 13 cars after an initial sale of 30 vehicles. Therefore, we can create a table of values.

[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 30 \\ \cline{1-2} 1 & 43 \\ \cline{1-2} 2 & 56 \\ \cline{1-2} 3 & 69 \\ \cline{1-2} 4 & 82 \\ \cline{1-2} 5 & 95 \\ \cline{1-2} 6 & 108 \\ \cline{1-2} 7 & 121 \\ \cline{1-2} 8 & 134 \\ \cline{1-2} 9 & 147 \\ \cline{1-2} 10 & 160 \\ \cline{1-2} \end{array}[/tex]

For Person 2, we can use the same formatting to create a table. However, the rule changes - we must start at 50 cars being sold and increase it by only 11 cars a month.

[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 50 \\ \cline{1-2} 1 & 61 \\ \cline{1-2} 2 & 72 \\ \cline{1-2} 3 & 83 \\ \cline{1-2} 4 & 94 \\ \cline{1-2} 5 & 105 \\ \cline{1-2} 6 & 116 \\ \cline{1-2} 7 & 127 \\ \cline{1-2} 8 & 138 \\ \cline{1-2} 9 & 149 \\ \cline{1-2} 10 & 160 \\ \cline{1-2} \end{array}[/tex]

Now, we need to see where the y-values are the same in both tables. We can see that we have a value of (10, 160) in both tables, so after 10 months, the salespersons will sell the same amount of cars.

There is an alternative method of solving the problem that is much quicker and will require much less work.

We are given two equations that are both equal to y. Therefore, we can set them equal to each other (dropping the y) and solving for x.

Our value of x will be the amount of months in which the sales are equal.

[tex]\displaystyle{13x+30=11x+50}\\\\2x + 30 = 50\\\\2x = 20\\\\\boxed{x = 10}[/tex]

Therefore, after 10 months of sales, the salespersons will have sold the same amount of cars. We can plug this information into one of the equations to see how many cars will be sold at that point.

[tex]y = 13(10) + 30\\\\y = 130 + 30 \\\\y = 160[/tex]

In 10 months, 160 cars will be sold. If we set the equations equal to each other and substitute x, we should get a true statement.

[tex]13(10)+30=11(10)+50\\\\130 + 30 = 110 + 50\\\\160 = 160[/tex]

Because we get a true statement, each salesperson will sell 160 cars after 10 months of initial sales.

Answer:

The value of n is -6

Step-by-step explanation:

∵ k(x) = x²

→ Its graph is a parabola with vertex (0, 0)

∴ The vertex of the prabola which represents it is (0, 0)

∵ The given graph is the graph of p(x)

∵ Its vertex is (0, -6)

∴ h = 0 and k = -6

∵ a = 1

→ Substitute them in the form above

∴ p(x) = 1(x - 0)² + -6

∴ p(x) = x² - 6

→ Substitute x² by k(x)

∴ p(x) = k(x) - 6

∵ p(x) = k(x) + n

→ By comparing the two right sides

∴ n = -6

∴ The value of n is -6

Look at the attached figure for more understanding

The red parabola represents k(x)

The blue parabola represents p(x)

The value of the n is -6.

y = a(x-h)2 + k

where,

(h, k) are the coordinates of the vertex of the parabola in form (x, y);

a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.

k(x) = x^2

p(x) = k(x) + n

p(x) = k(x)+n

p(x) = x² + n

Comparing with the Equation of a parabola,

y = a(x-h)2 + k

p(x) = x² + n

Therefore, the value of n is k which is the y coordinate of the vertex of the parabola.

Looking at the coordinates of the vertex of the parabola,

(h, n) = (0, -6)

Hence, the value of the n is -6.

Learn more about Parabola:

https://brainly.com/question/4443998

Answer:

use desmos.

Step-by-step explanation:

demos. All you have to do is out the equation into Desmos and it will graph it for you. You can look and learn.

Answer:

let the number be x

thrice of the number=3x

one-half of the number=(1/2)x

so from the expression we:

3x-x/2=2500

(6x-x)/2=2500

6x-x=2*2500

5x=5000

x=5000/5

x=1000

Answer:12

Step-by-step explanation:

it’s 12 because 4 x 3 = 12

Answer:

48π units³

Step-by-step explanation:

The volume (V) of a cylinder is calculated as

V = πr²h ( r is the radius of the base and h the height )

Here r = 4 and h = 3 , thus

V = π × 4² × 3

   = π × 16 × 3

    = 48π units³ ← exact answer

Answer:

sin^2α

Step-by-step explanation:

I will just  pose  x instead  of alpha  here to make things simpler

[tex]\tan ^2\left(x\right)\left(2\cos ^2\left(x\right)+\sin ^2\left(x\right)-1\right)\\\\[/tex]

we know that sin^2x = 1 -  cos^2x so...

[tex]=\left(-1+1-\cos ^2\left(x\right)+2\cos ^2\left(x\right)\right)\tan ^2\left(x\right)[/tex]

[tex]=\cos ^2\left(x\right)\tan ^2\left(x\right)[/tex]

we can rewrite using trigonometric identities (tan = sin/cos)...

[tex]=\left(\frac{\sin \left(x\right)}{\cos \left(x\right)}\right)^2\cos ^2\left(x\right)\\= \sin ^2\left(x\right)[/tex]

Answer:

b = 8.5

Step-by-step explanation:

hope this halps ya!

Answer:

B

Step-by-step explanation:

I am sorry if this is wrong

Answer: 24

Step-by-step explanation:

i did the problem and got it right

Answer:

absolute value of 8.7 is 8.7

Answer:

1) The mean = 41

The standard deviation = 13.379

2) The mean = 40.67

The standard deviation = 12.365

3) The mean and standard deviation will remain the same

4) The new mean = 44.5  

The new standard deviation = 13.58

5) The mean = 42.25

The standard deviation = 13.83

Step-by-step explanation:

The combines mean is given by the formula;

[tex]\overline {x_{12}} = \dfrac{n_1 \bar x + n_2 \bar x}{n_1 + n_2}[/tex]

The combined standard deviation is given as follows;

[tex]\sigma_{12} = \sqrt{\dfrac{n_1 \times \left (\sigma^2_{1} + d^2_1 \right) + n_2 \times \left (\sigma^2_{2} + d^2_2 \right)}{n_1 + n_2} }[/tex]

d₁ = [tex]\overline{x_{12}}[/tex] - [tex]\overline {x_1}[/tex]

d₂ = [tex]\overline{x_{12}}[/tex] - [tex]\overline {x_2}[/tex]

Substituting the known values, we have;

[tex]\overline {x_{12}} = \dfrac{ 42 + 40}{2}=41[/tex]

d₁ = 41 - 42 = -1

d₂ = 41 - 40 = 1

[tex]\sigma_{12} = \sqrt{\dfrac{ \left (16^2 + 1 \right) + \left (10^2 +1 \right)}{2} } = 13.379[/tex]

2) When n₁ = 1, n₂ = 2, we have;

[tex]\overline {x_{12}} = \dfrac{ 2 \times 42 + 4 \times 40}{6} \approx 40.67[/tex]

d₁ = 40.67 - 42 = -1.33

d₂ = 40.67 - 40 = 0.67

[tex]\sigma_{12} = \sqrt{\dfrac{ 2 \times \left (16^2 + 1.33^2 \right) + 4 \times \left (10^2 +0.67^2 \right)}{6} } \approx 12.365[/tex]

3) The mean and standard deviation will remain the same

4) The new mean = (42 + 47)/2 = 44.5  

The new standard deviation [tex]\sigma_{12} = \sqrt{\dfrac{ \left (16^2 + 2.5^2\right) + \left (10^2 +2.5^2\right)}{2} } \approx 13.58[/tex]

5) [tex]\overline {x_{12}} = \dfrac{ 44.5 + 40}{2}=42.25[/tex]

[tex]\sigma_{12} = \sqrt{\dfrac{ \left (16^2 + 2.5^2\right) + \left (10^2 +4.5^2\right)}{2} } \approx 13.83[/tex]

Step-by-step explanation:

2 /4

3. 5

doing reciprocal

2× 5

3. 4

= 8×15

12

= 120

12

=10 ans

hope it help u..