The triangles shown are similar. Which side of triangle PQR corresponds to side LN in triangle MNL?

a. RQ
b. PQ
c. PR
d. LM

The domain of g(x)= 3x^2 is Real number and it's range is {y∈R / y≥0}

The domain of h(x)= -3x^2 is Real number and it's range is {y∈R / y ≤0}

The domain of a function f(x) is the set of all values for which the function is defined, and the domain of a function is the set of all values that f takes on. The domain and range are defined for a relation and are the sets of all x-coordinates and all y-coordinates of ordered pairs.

The graph of f(x)= x^2 is given

We need to find the domain and range of g(x)=3x^2 and h(x)= -3x^2

The Graph of 3x^2 is different from x^2 in terms of plotting

When ,

x= -2 g(x)=12

x=-1 g(x)=3

x=0 g(x)=0

x=1 g(x)=3

x=2 g(x)=12

The Graph of -3x^2 is different from x^2 in terms of plotting

When ,

x= -2 g(x)=-12

x=-1 g(x)= -3

x=0 g(x)=0

x=1 g(x)= -3

x=2 g(x)=-12

Domain of g(x) is R and it's range is {y∈R / y≥0}

Domain of h(x) is R and it's range is {y∈R / y ≤0}

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The factorized expression using difference of squares is as follows,

9a²b⁵ (2+3a⁶b⁵)(2-3a⁶b⁵)

Difference of Squares

Difference of squares is a factorization method where an expression can be factored as (a + b) (a - b) when considered as the difference of two perfect squares,  a²-b². For instance, factoring x²-25 results in (x+5) (x-5). By enlarging the parentheses in (a + b) (a - b), the pattern (a + b) (a - b)=a²-b² is used as the foundation for this technique.

Factorization Using Difference of Squares

Given expression is,

36a⁴b¹⁰ - 81a¹⁶b²⁰

= (6a²b⁵)² - (9a⁸b¹⁰)²

Using square of differences, we have

a² - b² = (a + b) (a - b)

Here, a = 6a²b⁵ and b = 9a⁸b¹⁰

Thus, we get,

(6a²b⁵ + 9a⁸b¹⁰)(6a²b⁵ - 9a⁸b¹⁰)

Further Factorization

We can take out 3 common from both the bracket terms after applying difference of squares

3×3(2a²b⁵ + 3a⁸b¹⁰)(2a²b⁵ - 3a⁸b¹⁰)

= 9(2a²b⁵ + 3a⁸b¹⁰)(2a²b⁵ - 3a⁸b¹⁰)

Further, we can take out a²b⁵ as common from both the bracket terms

= 9a²b⁵ (2+3a⁶b⁵)(2-3a⁶b⁵)

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Answer:

See my picture below for the answer.

Step-by-step explanation:

If you look at the unit circle and locate 240 degrees.  You will see an ordered pair.  The first number -1/2 is the cos of 240 and the second number is the sin.

Answer:

it’s the square root of 3, divided by 2 (sorry, can’t type any special characters at the moment)

Step-by-step explanation:

-240 = 120 because you measure negative angles clockwise starting at 0.

Using unit circle, value of sin for an angle is the 2nd number

Answer:

B

Step-by-step explanation:

when a square pyramid is cross sectioned the shape that will appear is the same as that of the base

Here is the completed table:

                                                           Plays a sport      Doesn't play a sport

Plays a musical instrument                  0.46                         0.54

Doesn't play a musical instrument       0.73                          0.27

Relative frequency measures how often a value appears relative to the sum of the total values.

                                                    Plays a sport              Doesn't play a sport

Plays a musical instrument              (6/13)  = 0.46                   (7/13)  = 0.54

Doesn't play a musical instrument       (8/11) 0.73                       (3/11) =0.27

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Answer:

x = -0.01685

(Is the equation written correctly?  This feels like a very unfortunate number)

Step-by-step explanation:

(2x+5/60-95x-3/30=3/2

2x+(5/60)-95x-(3/30)=3/2

2*(2x+(5/60)-95x-(3/30))=3     [Multiply both sides by 2]

4x+(10/60)-190x-(6/30))=3      

(2/30)-186x-(6/30))=3              [Simplify]

-186x-(4/30)=3

-186x=3+(4/30)

-186x=(90/30)+(4/30)

x = (94/30)/(-186)

x = -0.01685

The correct answer is

2 loaves of pumpkin bread and 6 loaves of banana bread. Option C.

For the solution for the Pumpkin bread:

4 eggs

3 1/2 cups of flour

Banana bread:

1 egg

1 (0.5) cups of flour

Available ingredients:

14 eggs

16 cups of flour

Assume 2 loaves of pumpkin bread and 6 loaves of banana bread

For the solution for the Pumpkin bread:

PB=4 eggs* 2

PB= 8 eggs

PB=3 *0.5 * 2

PB = 7 cups of flour

For the solution of the Banana bread:

BB =1 *6

BB= 6 eggs

For cups

BB= 1 (0.5) * 6

BB= 9 cups of flour

In conclusion, The solution of the Total used ingredients

I=8 + 6

I= 14 eggs

For cups

IC=7 + 9

IC= 16 cups of flour

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Answer:

C 2 loaves of Pb and 6 loaves of BB

Step-by-step explanation:

Answer:

  8.  yes; 18

  9.  no

  10.  no

  11.  yes; -9

Step-by-step explanation:

The equation for inverse variation is y = k/x. The constant k will be the product of x and y: k = xy.

Products are (-3)(-6) = (2)(9) = (4.5)(4) = 18.

Inverse variation with k = 18.

Products are ...

  (5)(4) ≠ (10)(8).

Not inverse variation.

Products are ...

  (2)(25) ≠ (2.5)(16).

Not inverse variation.

Products are (3)(-3) = (9)(-1) = (12)(-.75) = -9.

Inverse variation with k = -9.

21 % is the answer.

Problem is that the height of this plant 6.3 and 7.8 cm

P (6.3 <x< 7.8)

12 -5 = 7cm

7.8 - 6.3 = 1.5cm

1.5 / 7 = 0.21

=21%

Probability is a field of mathematics that deals with the numerical description of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the impossibility of the event and 1 indicating certainty.

Probability is a measure of the likelihood that an event will occur. Many events cannot be predicted with absolute certainty. You can only predict the probability that an event will occur.

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The tabular values can be used to derive the formula relationship between x and P which gives the percentage commission of Zachary as 1%

From the above table, we have;

Where;

y = The fixed percentage commission Zachary makes

b = Zachary's base pay

Therefore;

Subtracting equation (1) from (2), gives;

110 - 105 = (3500 - 3000) × y + b - b = 0

5 = 500•y

y = 5/500 = 0.01 = 1%

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The approximate wage of someone with 0 years of experience is -4.64

The dataset of wages is

Wages = 8, 20, 10, 12, 16, 14

The mean is calculated as:

Mean = Sum/Count

This gives

Mean = (8+ 20+ 10+ 12+ 16+ 14)/6

Mean = 13.33

The variance is

Variance = ∑(x- mean)²/n-1

This gives

Variance = [(8 - 13.33)^2 + (20 - 13.33)^2 + (10 - 13.33)^2 + (12 - 13.33)^2 + (16 - 13.33)^2 + (14 - 13.33)^2]/5

Evaluate

Variance = 18.67

The standard deviation is

Standard deviation = √Variance

This gives

Standard deviation = √18.67

Evaluate

Standard deviation = 4.32

The dataset of experience is

Wages = 1, 10, 2, 4, 4, 6

The mean is calculated as:

Mean = Sum/Count

This gives

Mean = (1+ 10+ 2+ 4+ 4+ 6)/6

Mean = 4.5

The variance is

Variance = ∑(x- mean)²/n-1

This gives

Variance = [(1 - 4.5)^2 + (10 - 4.5)^2 + (2 - 4.5)^2 + (4 - 4.5)^2 + (4 - 4.5)^2 + (6 - 4.5)^2]/5

Evaluate

Variance = 10.3

The standard deviation is

Standard deviation = √Variance

This gives

Standard deviation = √10.3

Evaluate

Standard deviation = 3.21

See attachment for the scatter plot and the straight line that best fits the data points.

The equation of the straight line is

y = 0.69x - 4.64

The approximate wage of someone with 0 years of experience is

y = 0.69 * 0 - 4.64

Evaluate

y = -4.64

Hence, the approximate wage of someone with 0 years of experience is -4.64

This is calculated as:

Cov(x,y) = ∑(x - x mean)(y - y mean)/N - 1

So, we have:

Cov(x,y) = [(8 - 13.33) * (1 - 4.5) + (20 - 13.33)*(10 - 4.5) + (10 - 13.33)*(2 - 4.5) + (12 - 13.33)*(4 - 4.5) + (16 - 13.33)*(4 - 4.5) + (14 - 13.33)*(6 - 4.5)]/5

Evaluate

Cov(x,y) = 12.80

Hence, the covariance of wages and experience is 12.80

Is this consistent with the line you drew in part c?

Yes it is

Here, we use a graphing calculator.

From the graphing calculator, we have:

r = 0.9231

Hence, the correlation of wages and experience is 0.9231

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For the given data,

Mean = 2.12

Median = 2

Mode = 2

Range = 3

From the question we are to determine the mean

From the given table

Scoops of Ice cream     Male      Female     Other         Total frequencies

1                                        7              3               3                       13

2                                       8              11              2                        21

3                                       10             1               0                        11

4                                        2              1              1                          4

∴ [tex]Mean = \frac{(1 \times 13) + (2 \times 21) +(3 \times 11) + (4 \times 4)}{13 +21+11+4}[/tex]

[tex]Mean = \frac{(13) + (42) +(33) + (16)}{49}[/tex]

[tex]Mean = \frac{104}{49}[/tex]

Mean = 2.12

Median = 2

Mode = 2

Range = 4 - 1 = 3

Hence, for the given data

Mean = 2.12

Median = 2

Mode = 2

Range = 3

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The variation equation is p = kr^2

The variables are give as:

Pressure = P

Radius= r

The direct variation from p to the square of r is represented as:

[tex]p\ \alpha\ r^2[/tex]

Express as an equation

p = kr^2

Where k represents the constant of variation

Hence, the variation equation is p = kr^2

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Answer:

The correct answer is the 3rd option

Answer: 7(8x + 6) = -1: Exact form: x = -43/56, decimal form: x = -0.76785714

Thats all i have because you can't solve for x for the second one!

Answer:

y<7

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer: y < 7

Step-by-step explanation:

We can assume that the less than sign is an equals sign and use algebra to isolate y.

[tex]5y+1-1 < 36-1\\ 5y < 35\\\frac{5y}{5} < \frac{35}{5}\\ y < 7[/tex]

We first subtracted 1 from both sides to get rid of the +1.

Then we divided both sides by 5 to isolate y.

Answer:

-16/9

Step-by-step explanation:

( [tex]\frac{2}{5}[/tex] ÷ [tex]\frac{3}{8}[/tex] ) ÷ [tex]-\frac{3}{5}[/tex]

= ( [tex]\frac{2}{5} * \frac{8}{3}[/tex] ) ÷ [tex]-\frac{3}{5}[/tex]

= [tex]\frac{16}{15}[/tex] ÷ [tex]-\frac{3}{5}[/tex]

= [tex]\frac{16}{15} * -\frac{5}{3}[/tex]

= -16/9

Using translation concepts, the change of f(x) = x to g(x) = x - 90 can be described as follows:

The base graph has been shifted down 90 units.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, we have that g(x) = f(x) - 90, that is, the base graph was shifted down 90 units.

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The terms that are possible on the domain of a sequence are given as follows:

13, 25, 60.

A sequence is a list containing numbers, that may be related or not. It has a 1st term, 2nd term, and so on until the nth term.

The domain is the indexes of the terms, which starts at one and goes until n, hence the possible numbers are:

13, 25, 60.

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Answer:

a. 50 students are randomly selected from the school; 11 drive to school

b. 407

Step-by-step explanation:

a. to get an accurate viewing, use random people that share 1 large common denominator (from the same school) that also has to do with the question

b. 11/50 is only between 50 students. make the denominator the same (1850) and multiply the same to the numerator

1850/50 = 37

11/50 x 37 = 407/1850

Answer:

w= 9

Step-by-step explanation:

[tex] \sqrt{ - 4w + 61} = w - 4[/tex]

Square both sides:

-4w +61= (w -4)²

[tex]\boxed{(a - b)^{2} = a^2 -2ab + b^2 }[/tex]

Expand:

-4w +61= w² -2(w)(4) +4²

-4w +61= w² -8w +16

Simplify:

w² -8w +16 +4w -61= 0

w² -4w -45= 0

Factorize:

(w -9)(w +5)= 0

w -9= 0 or w +5= 0

w= 9 or w= -5 (reject)

Note:

-5 is rejected since we are only taking the positive value of the square root here. If the negative square root is taken into consideration, then w= -5 would give us -9 on both sides of the equation.

Why do we use negative square root?

When solving an equation such as x²= 4,

we have to consider than squaring any number removes the negative sign i.e., the result of a squared number is always positive.

In the case of x²= 4, x can be 2 or -2. Thus, whenever we introduce a square root, a '±' must be used.

However, back to our question, we did not introduce the square root so we should not consider the negative square root value.

Answer: w=9.

Step-by-step explanation:

[tex]\sqrt{-4w+61}=w-4[/tex]

Tolerance range:

[tex]\left \{ {{-4w+61\geq 0} \atop {w-4\geq 0}} \right. \ \ \ \ \left \{ {{4w\leq 61\ |:4} \atop {w\geq 4}} \right. \ \ \ \ \left \{ {{w\leq 15,25} \atop {w\geq 4}} \right. \ \ \ \ \Rightarrow\ \ \ \ \\w\in[4;15,25].[/tex]

Solution:

[tex](\sqrt{-4w+61})^2=(w-4)^2\\-4w+61=w^2-2*w*4+4^2\\-4w+61=w^2-8w+16\\w^2-4w-45=0\\D=(-4)^2-4*1*(-45)\\D=16+4*45\\D=16+180\\D=196.\\\sqrt{D}=\sqrt{196}\\\sqrt{D}=14 \\w_{1,2}=\frac{-(-4)б14}{2} \\w_1=\frac{4-14}{2} \\w_1=\frac{-10}{2} \\w_1=-5\ \notin tolerance\ range.\\w_2=\frac{4+14}{2}\\ w_2=\frac{18}{2} \\w_2=9\ \in tolerance \ range.[/tex]

Using division of fractions, the equivalent expression is:

B. [tex]\frac{4}{d - 6}[/tex].

To divide two fractions, we multiply the first by the inverse of the second.

In this problem, we have that:

Applying the multiplication, we have that:

[tex]\frac{2(d - 3)}{(d + 8)(d - 6)} \times \frac{2(d + 8)}{d - 3} = \frac{4}{d - 6}[/tex].

Hence option B is correct.

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Answer:

Step-by-step explanation:

Givens

line: 5y + 2x =  10

point (-2 , 5)

Discussion and Solution

You have to rearrange the given line to get the slope. It isn't nice, but it's not impossible.

5y + 2x = 10                            Subtract 2x from both sides

5y + 2x - 2x = -2x + 10           Simplify

5y = - 2x + 10                          Divide by 5

5y/5 = -2x/5 + 10/5                 Simplify

y = -0.4x + 2            

So the new equation is going to have a slope of - 0.4

So far what you have is

y =  - 0.4x + b

Now use the point to find the y intercept. What you should be thinking about the point is that when x = -2 then y = 5. Substitute that into the new equation.

5 = -0.4*-2 + b

5 = 0.8 + b                                Subtract 0.8 from both sides

5 - 0.8 = 0.8 - 0.8 + b               Simplify

4.2 = b

Answer

y = -0.4x + 4.2

The ordered pairs from the options given that is from the table is: D. (6,5).

An ordered pair is written in the form, (x, y). The first number in the bracket is the x-value on the table, and the second number is its corresponding y-value form the table.

From the table given, the ordered pairs are: (3, 4), (4, 4), (5, 2), and (6, 5).

The number pair from the table from the given options is: D. (6,5).

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Answer:  [tex]f^{-1}(\text{x}) = (\text{x}-9)^2+4[/tex] when [tex]\text{x} \ge 9[/tex]

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

Work Shown:

[tex]f(\text{x}) = 9 + \sqrt{\text{x} - 4}\\\\\text{y} = 9 + \sqrt{\text{x} - 4}\\\\\text{x} = 9 + \sqrt{\text{y} - 4}\\\\\text{x}-9 = \sqrt{\text{y} - 4}\\\\(\text{x}-9)^2 = (\sqrt{\text{y} - 4})^2\\\\(\text{x}-9)^2 = \text{y}-4\\\\(\text{x}-9)^2+4 = \text{y}\\\\f^{-1}(x) = (\text{x} - 9)^2+4[/tex]

Explanation:

I replaced f(x) with y. After that I swapped x and y, then solved for y to get the inverse.

The smallest that [tex]\sqrt{\text{x}-4}[/tex] can get is 0, which means the smallest f(x) can get is 9+0 = 9. The range for f(x) is [tex]\text{y} \ge 9[/tex]

Since x and y swap to determine the inverse, the domain and range swap roles. Therefore, the domain of the inverse [tex]f^{-1}(\text{x})[/tex] is [tex]\text{x} \ge 9[/tex]

So we will only consider the right half portion of the parabola.

The graph is below. The red curve mirrors over the black dashed line to get the blue curve, and vice versa.

Answer:

[tex]f^-^1(x)=(x-9)^2+4[/tex]   OR [tex]x^2-18x+85[/tex] if you simplify it

Step-by-step explanation:

to find the inverse function you have to switch x and y with each other and solve for y.

[tex]y=9+\sqrt{x-4}\\x=9+\sqrt{y-4}[/tex]           step 1: switch x and y with each other

[tex]x-9=\sqrt{y-4}[/tex]           step 2: subtract 9 from both sides

[tex](x-9)^2=\sqrt{y-4}^2[/tex]     step 3: square both sides to get rid of the square root

[tex](x-9)^2=y-4\\(x-9)^2+4=y\\[/tex]         step 4: add 4 to both sides

you could leave the answer like this or you can simplify to get [tex]x^2-18x+85[/tex]

Answer:

Hey there :) The answer is 0.25 minutes.

Step-by-step explanation:

1 minute = 60 seconds

So, 15 ÷ 60 = 0.25 minutes

Answer:

3. Completing the Square

4. 0, 1, or 2

Step-by-step explanation:

Hello!

a) Graphing

Graphing is a useful method as it lays the answer out in front of you. Once you graph the parabola, you simply take the intersections of the graph and x-axis as your x-intercepts. Therefore, it is a method.

b) Factoring

Factoring can be used to find x-intercepts, and after factoring, you can set each factor to 0 and solve for x, which are the x-intercepts. This method is also called the Zero Product Property.

c) Quadratic Formula

The quadratic formula is meant to solve for the x-intercepts, as the formula uses values of the coefficients to isolate x and solve for it.

Standard form of a Quadratic: [tex]ax^2 + bx + c = 0[/tex]

Quadratic Formula: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]

Plugging in the values of a, b, and c give you the solutions for x.

d) Completing the Square

Completing the square CAN be used to find the x-intercepts, but not directly so. It is used to convert standard form into a different form, known as the vertex form. It is meant so find the vertex, not the x-intercepts.

Therefore, Completing the Square is NOT a method to find the x-intercepts.

The number and types of solutions depend on the discriminant of the quadratic (the part under the square root in the QF).

Types of roots:

That means that a quadratic equation can have 0, 1, or 2 roots.

Answer:

Completing the square and 2, 1, and 0.

Step-by-step explanation:

Person above is correct!!

The answer choice which represents the quotient of the expression given is; 1/(t+4)².

It follows from the task content that the quotient which is to be evaluated is;

(t+3)/t+4) ÷ (t²+7t +12)

The quotient can therefore be evaluated as follows;

= (t+3)/t+4) ÷ (t+3)(t+4)

= (t+3)/t+4) × 1/(t+3)(t+4)

= 1/(t+4) × 1/(t+4)

= 1/(t+4)².

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Answer:

c

Step-by-step explanation:

c

Answer:

y = 5x + 2

Step-by-step explanation:

Standard form of Equation of line: y = mx + c

where m = slope or gradient,

c = y-intercept

From the question we know that:

x = - 1

y = - 3

m = 5

We will substitute these values into the equation to find c.

- 3 = (5)(- 1) + c

- 3 = - 5 + c

c = - 3 + 5 = 2

Therefore the equation of this line is: y = 5x + 2

Answer:

  (c)  y = -3x +6

Step-by-step explanation:

The equation can be written in slope-intercept form when we know the slope and the y-intercept.

The slope-intercept form of the equation of a line is ...

  y = mx +b . . . . . . where m is the slope and b is the y-intercept

The y-intercept is the y-value where the line crosses the y-axis. It is 6. This eliminates choices A and D, leaving choices ...

The line goes down to the right. This is a negative slope, eliminating choice B.

The equation of the line is y = -3x +6.

__

Additional comment

The line intersects the x-axis at x=2. This means the "rise" of the line is -6 units for a "run" of 2 units. The numerical value of the slope is ...

  m = rise/run = -6/2 = -3

Now, we know the parameters of the equation are m=-3, b=6, and the equation of the line is

  y =-3x +6

Answer:

B

Step-by-step explanation:

area = 10x^2 + 20x

base = 20x

10x^2 + 20x = 0.5(20x)(height)

10x^2 + 20x = 10x(height)

(10x^2 + 20x) / 10x = height

[tex]\frac{10x^2 + 20x}{10x} = \frac{10x + 20}{10} = \frac{x + 2}{1} = x + 2[/tex]

The answer is B