For the following exercises, graph the given functions by hand.
48. f(x) = | 2x − 4 | − 3

Answer:

Step-by-step explanation:

Both triangles are similar by SAS property,

that means corresponding sides are proportional,so,

5/6 = 15/N

= 6/5 = N/15

N = (6×15)/5

N = 6×3

N = 18

The approximate solution of the above equation is: 55/15 (Option A). This is solved using the quartic formula, not quadratic equation.

The quartic formula has up to four various solutions including real and imaginary numbers. Read on for more explanation.

First we restate the above equation:

x²-3x+2= √(x-2) + 2

Next we remove square roots

[tex]x^{4}[/tex] - 6x³ + 9x² = x - 2

Add two to both sides

→ [tex]x^{4}[/tex] - 6x³ + 9x²+2 = x - 2 +2

→  [tex]x^{4}[/tex] - 6x³ + 9x²+2 = x

Subtract X from both sides

→  [tex]x^{4}[/tex] - 6x³ + 9x²+2 -x = x -x

→  [tex]x^{4}[/tex] - 6x³ + 9x²+2 - x= 0

Using the Quartic formula to solve the fourth order equation:
a[tex]x^{4}[/tex] + bx³ + cx² + dx + e

The resolution of x is given as:

x = 2.691085, 3.346753

Because the fraction nearest to 3.4 is 55/16

hence, the correct answer is Option A.

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The distance travelled by the train with constant speed of r miles will be 3r.

We know the formula of distance linking the speed and the time.

Distance = speed × time

Substituting the given values to get:

Distance = r × 3

Distance = 3r

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Answer: [tex]5(3)^{n-1}[/tex]

Step-by-step explanation:

The common ratio is 15/3 = 5.

The first term is 3.

So, the explicit rule is [tex]5(3)^{n-1}[/tex]

Find length CD first, which is the hypotenuse of the triangle.

PD = opposite

Opposite & hypotenuse = SOH or sin

Sin(27) = 15/H

x h, then ÷ sin(27)

H = 15/sin(27)

H = 33.04....

Move to triangle CDR:

15 is length opposite the angle we're after.

So far, we've got the hypotenuse (which we just found to be 33.04....) & the opposite of our triangle

Hypotenuse & opposite = SOH

Sin(x) = 15/33.04... but, to find the angle we do inverse of sin

sin-1(15/33.04...) = x

x = 27

(33.04... means I used the full numbers displayed on my calculator)

Thus, RCD is 27 degrees

Hope this helps!

The reason that this represent in Mikal’s proof regarding the triangle is SAS.

It should be noted that a triangle is a shape that has three sides and angles.

The SAS implies the side angle side. It shows that any two sides and angles that are included between the sides of an angle are equal to the other two sides.

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Answer:

AAS

Step-by-step explanation:

2022 edge

The longest possible integer length of the third side of the triangle is 6 < x < 28

The sum of any two sides must be greater than the third side for a triangle to exist

let the third side be x

x + 11 > 17 and x + 17 > 11 and 11 + 17 > x

x > 6 and x > - 6 and x < 28

The longest possible integer length of the third side of the triangle is 6 < x < 28

The length of the 3 sides of a triangle needs to always be among (however no longer the same) the sum and the difference of the opposite two sides. As an example, take the instance of two, 6, and seven. and. consequently, the third side period should be extra than 4 and less than 8.

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Answer:

27

Step-by-step explanation:

Let the third side length be s. Then, by the Triangle Inequality, we know that s satisfies the inequalities

[tex]s + 11 & > 17, \\ s + 17 & > 11, \\ 11 + 17 & > s.[/tex]

[tex]\begin{align*} s + 11 & > 17, \\ s + 17 & > 11, \\ 11 + 17 & > s.\end{align*}[/tex]

The first two inequalities hold as long as s > 6 and the third holds if s < 28. The largest possible integer s that satisfies all of these is 27.

Answer:

[tex]y = \frac{17}{15}x + \frac{16}{15}[/tex]

Step-by-step explanation:

So the slope-intercept form is given as: y=mx+b where m is the slope and b is the y-intercept (since if you plug in 0 as x, mx will be 0 leaving only b). You can calculate the slope with the slope formula: [tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex] which is essentially [tex]\frac{rise}{run}[/tex]. So for this example (-8, -8) will be ([tex]x_1, y_1[/tex]) and (7, 9) will be ([tex]x_2, y_2[/tex]).

Plug values into equation:

[tex]\frac{9 - (-8)}{7 - (-8)}[/tex]

cancel out negatives

[tex]\frac{9+8}{7+8}\\[/tex]

Simplify

[tex]\frac{17}{15}[/tex]

The fraction is in the most simplified form unless you want to have a mixed fraction, otherwise you can't do anything else to the fraction.

so now we have the slope we have one part of the equation: [tex]y=\frac{17}{15}x + b[/tex], but now we need to solve for b. This can be done by using either of the points and plugging in x and y, but for this example I'll use (7, 9).

Plug in (7, 9) as (x, y)

[tex]9 = \frac{17}{15}(7) + b[/tex]

Multiply

[tex]9 = \frac{119}{15}+b[/tex]

Subtract

[tex]9-\frac{119}{15}=b[/tex]

Rewrite 9 as a fraction

[tex]\frac{135}{15} - \frac{119}{15} = b[/tex]

Subtract numerators

[tex]\frac{16}{15} = b[/tex]

now we have both pieces of information

[tex]y = \frac{17}{15}x + \frac{16}{15}[/tex]

The additive inverse of the polynomial is 6x³-4x²+4x.

Given The polynomial is -6x³+4x²-4x.

A polynomial is an expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. It consists of indeterminates and coefficients.

The number that results in zero when a number is added to it is said to be a number's additive inverse. The opposite, a shift in the sign, and negation are other names for this number.

The given polynomial is -6x³+4x²-4x.

To find the additive inverse of the polynomial, multiply the polynomial with minus sign, we get

-(-6x³+4x²-4x)=6x³-4x²+4x.

Hence, the additive inverse of the polynomial -6x³+4x²-4x is 6x³-4x²+4x.

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Answer:

c.) 6 1/2

Step-by-step explanation:

Volume = length × width × height

2 1/6 × 1 1/5 × 2 1/2

13/6 × 6/5 × 5/2

13/5 × 5/2

13/2 = 6 1/2

Answer:

1.  A(-8,3) B(-8,-2) C(-4,-2)

2. A'(8,3) B'(8,-2) C'(4,-2)

3. A"(-12,1.5) B"(-12,-3) C"(-6,-3)

4. they give you the coordinates, haha. Just graph and connect the dots.

5. Coordinates of ABC: A(-8,3) B(-8,-2) C(-4,-2)

   Coordinates of A'''B'''C''': A'''(-3,10) B'''(-3,5) C'''(1,5)

The correct coordinates for a 90 degree rotation is: A''''(3,8) B''''(-2,8) C''''(-2,4)

Most of these are formulas so I hope you have this memorized in preparation for tests! Good luck!

The dimensions i.e. length and width of the deck in the drawing is 8 and 6.4 inches respectively.

Given that the length of the previous deck = 15 feet

The width of the previous deck = 12 feet

Since the new deck will add 5 feet to the length and 4 feet to the width,

The length of the new deck = 15 + 5 = 20 feet

The width of the new deck = 12 + 4 = 16 feet

Also given that a drawing of the new deck uses a scale of 1 inch = 2.5 feet.

So, The length of the deck in the drawing = 20/2.5 inches = 8 inches

The width of the deck in the drawing = 16/2.5 inches = 6.4 inches

Therefore, the dimensions i.e. length and width of the deck in the drawing is 8 and 6.4 inches respectively.

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Answer:

The answer is a since non of the other answer would go throught that point

Hope This Helps!!!

The system of linear inequalities which satisfy the region R are:

Mathematically, the standard equation of a straight line is given by y = mx + b.

In order to determine the system of linear inequalities that satisfy the region R, we would identify the points through which the lines passes through.

For the broken line, we have:

y-intercept = 3.

x-intercept = -3.

Points (x, y) = (0, 3) and (-3, 0).

Since the line is broken (not equal to), the inequality is given by:

y < x - 3.

For the other line, we have:

y-intercept = 5.

x-intercept = -5/2.

Points (x, y) = (0, 5) and (-5/2, 0).

(x/-5/2) + y/5 ≤ 1

-2x + y ≤ 5

y ≤ -2x + 5

For the line passing through the origin, we have:

y - x ≥ 0

y ≥ x.

In conclusion, the system of linear inequalities which satisfy the region R are:

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Answer:

6 StartRoot 3 EndRoot units

Step-by-step explanation:

Okay, first you need to understand that function of x, (or f(x)) is y.

We now plug in x.

f(-2) or y=-2(3)+(2•2)+4(-2)+8
f(-2)=-6+4+-8+8

f(-2)=-2

When x=-2, y=-2. Lets plug it back in to see if its true.

-2=-2(3) + (2x2) + (4(-2)) + 8

-2 = -6 + 4 + -8 + 8

-2 = -2.

Heart if it helps, comment if you need help.

Answer:

14641

Step-by-step explanation:

[tex]formular \: for \: the \: digits \: in \: each \\ row \: of \: a \: pascal \: triangle \: is \: = 11 {}^{n} \\ row \: 0 = \: 11 {}^{0} = 1 \: \\ row \: 1 \: = 11 {}^{1} = 11 \\ row \: \: 2 \: = 11 {}^{2} = 121 \\ row \: 3 = \: 11 {}^{3} = 1331 \\ row \: 4 = 11 {}^{4} = 14641 \\ therefore \: the \: fourth \: row \: is \: 14641[/tex]

Based on the given texts in the table about the graph of the function, the true statements are:

The function, 4x - 15 shows that 15 is the y-intercept which means that the graph will cross the y-axis at (0,15).

The point of discontinuity is x = - 2 and we see this with the gap created at x < -2 and -2 ≤ x ≤ 4.

The graph is indeed increasing over the interval (4, ∞o) because any value of x that is greater than 4 will increase f(x) = [tex]3^x^-^4[/tex].

The domain of the function is also all real numbers as it begins at negative infinity and ends at infinity, (-∞, ∞).

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The two triangles are similar by SSA similarity. Option B is correct.

A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.

If the ratio of the sides are same as well as the one angle is common between the two triangles then in that condition there will be SSA similarity.

From the triangle ABC and DEC

The ratio of the sides is;

[tex]\rm \frac{10}{12}= \frac{8}{9.6} \\\\ \frac{5}{6}= \frac{5}{6}[/tex]

One angle c is common in the two triangles.

The two triangles are similar by SSA similarity.

Hence, option B is correct.

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Answer: [tex]|f(x)-8| < 0.03[/tex]

Using the given linear function of best-fit, the most likely approximate height of the plant after 8 weeks would be of 7.4 centimeters.

A linear function is modeled by:

y = mx + b

In which:

The line of best-fit goes through points (0,1) and (5,5). Point (0,1) means that the y-intercept is of b = 1. The slope is given as follows:

m = (5 - 1)/(5 - 0) = 4/5 = 0.8.

Hence the equation that gives the approximate height after x weeks is:

y = 0.8x + 1.

After 8 weeks, the expected height is:

y = 0.8 x 8 + 1 = 6.4 + 1 = 7.4 centimeters.

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Answer:

The equation for the line which passes through the points given as (a, b) and (a, b+1), is x=a, which represents a vertical line.

Step-by-step explanation:

It is given that a line passes through the points whose coordinates are (a, b) and (a, b+1).

It is asked to find the linear equation which passes through the given points.

To do so, first determine the slope of the given line using the coordinates and the formula for the slope. Accordingly, proceed to find the equation of the given line.

Step 1 of 2

Determine the slope of the line.

The points through which the line passes are given as (a, b) and (a, b+1). Next, the formula for the slope is given as,

[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

Substitute b+1&b for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and a&a for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,

[tex]m=\frac{b+1-b}{a-a}$\\ $m=\frac{1}{0}$[/tex]

b+1. So the equation of the line cannot be found using the general point-slope form equation.

Step 2 of 2

Write the equation of the line.

So, by definition, the line that passes through the given points is a vertical line. Now, as its x- coordinate is a, so the equation of the line is given as x=a.

Answer:

Check the first box, third box and fifth box

Explanation:

1st box:

Rewrite the fraction: 48

- ----

17

Check equivalency: True

Answer: True

2nd box:

Check equivalency: False

Answer: False

3rd box:

Convert the improper fraction into a mixed number:

2 × 17 + 14

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

17

Calculate the product or quotient: 34 + 14

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

17

Calculate the sum or difference: 48

- ----

17

Check equivalency: True

Answer: True

4th box:

Rewrite the fraction: 17

----

48

Check equivalency: False

Answer: False

5th box:

Rewrite the fraction: 48

- ----

17

Check equivalency: True

Answer: True

I hope this helps!

The number of teams that can be made is 10.

In order to determine the number of teams he can make, divide the number of friends by the total number of people that must be in the team. Division is the process of grouping a number into equal parts using another number.

31 / 3 = 10 remainder 1

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The figure ABCD reflected over the y-axis followed by a translation to the left by 2 unit to form figure A'B'C'D'

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.

Dilation is the increase or decrease in the size of a figure.

The figure ABCD reflected over the y-axis followed by a translation to the left by 2 unit to form figure A'B'C'D'

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- Please see the attached picture for full solution!:)

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Answer:

D. 2730

Step-by-step explanation:

I just had this question on FLVS yesterday.
you use factorials for this:

15!/12!

15*14*13*12!/12!

15*14*13

2730

Number of ways in which 3 positions can be filled are 2730.

The number of ways in which objects from a set may be selected, generally without replacements, to form subsets. This selection of subset is called permutation when order of selection is a factor.

If n things taken r at a time and n!  = n × (n-1) × (n-2) × (n-3)..........3 × 2 × 1

⇒Permutation,

                              [tex]P(n,r) =\frac{n!}{(n-r)!}[/tex]

Now it is given that number of candidates, n = 15

and number of position, r = 3

Hence number of ways positions can be filled-

                           [tex]P(n,r) =\frac{15!}{(15-3)!}[/tex]

⇒                         [tex]P(15,3) =\frac{15!}{12!}[/tex]

⇒                         P(15,3) =  (15 × 14 × 13)12!/12!

⇒                         P(15,3) =  (15 × 14 × 13)

⇒                         P(15,3) =  2730

∴ Number of ways in which 3 positions can be filled are 2730.

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