State the various transformations applied to the base function ƒ(x) = x^2 to obtain a graph of the function g(x) = −2[(x − 1)^2 + 3].

(A) A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 2 units to the right, and a vertical shift downward of 6 units.

(B) A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift downward of 6 units.

(C) A reflection about the y-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift downward of 6 units.

(D) A reflection about the y-axis, a vertical stretch by a factor of 2, a horizontal shift of 2 units to the right, and a vertical shift downward of 6 units.

Recall that

[tex]\cos2\theta=2\cos^2\theta-1[/tex]

and

[tex]\tan^2\theta+1=\sec^2\theta=\dfrac1{\cos^2\theta}[/tex]

Then

[tex]\cos2\theta=\dfrac2{\tan^2\theta+1}-1\implies\cos2\theta=\boxed{\dfrac7{25}}[/tex]

Answer:

[tex]cos2\theta=\frac{7}{25}[/tex]

Step-by-step explanation:

This is a question of Trigonometric Identities. In addition to this, In quadrant IV the cosine of the angle is naturally negative. This explains the negative value for [tex]tan\theta=-3/4[/tex]

The double angle formula

Let's choose a convenient identity, for the double angle [tex]cos2\theta[/tex]

[tex]\\tan \theta=-3/4 \\ cos2\theta =cos^{2}\theta -sen^{2}\theta\\cos2\theta =2cos^{2}\theta-1\\\\1+tan\theta^{2} =sec^{2}\theta\\\\ 1+(\frac{-3}{4})^{2} =\frac{1}{cos^2 \theta} \\\\\frac{25}{16}=\frac{1}{cos^{2}\theta}\\ cos^{2}\theta=\frac{16}{25}[/tex]

Finally, we can plug it in:

[tex]cos2\theta =2cos^{2}\theta -1\\cos2\theta =2\left ( \frac{16}{25} \right )-1 \Rightarrow cos2\theta=\frac{7}{25}[/tex]

Answer:

5 meters

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z -----> the scale factor

P1 -----> the perimeter of the reduced rectangle on the right

P2 ----> the perimeter of the original rectangle on the left

[tex]z=\frac{P1}{P2}[/tex]

substitute

[tex]z=\frac{24}{30}=0.8[/tex]

step 2

Find the width of the reduced rectangle on the right

[tex]P1=2(L+W)[/tex]

substitute the given values

we have

[tex]L=8\ m[/tex] ---> see the attached figure to better understand the problem

[tex]24=2(8+W)[/tex]

[tex]12=8+W[/tex]

[tex]W=4\ m[/tex]

step 3

Find the width of the original rectangle on the left

To find the width of the original rectangle on the left, divide the width of the reduced rectangle on the right by the scale factor

so

[tex]W=4/0.8=5\ m[/tex]

Answer:

A. 5 meters

Step-by-step explanation:

Answer:

Part 1) The x-component of the vertex is 2 and the y-component of the vertex is -18

Part 2) The discriminant is 144

Step-by-step explanation:

we have

[tex]f(x)=2x^{2}-8x-10[/tex]

step 1

Find the discriminant

The discriminant of a quadratic equation is equal to

[tex]D=b^{2}-4ac[/tex]

in this problem we have

[tex]f(x)=2x^{2}-8x-10[/tex]

so

[tex]a=2\\b=-8\\c=-10[/tex]

substitute

[tex]D=(-8)^{2}-4(2)(-10)[/tex]

[tex]D=64+80=144[/tex]

The discriminant is greater than zero, therefore the quadratic equation has two real solutions

step 2

Find the vertex

Convert the quadratic equation into vertex form

[tex]f(x)+10=2x^{2}-8x[/tex]

[tex]f(x)+10=2(x^{2}-4x)[/tex]

[tex]f(x)+10+8=2(x^{2}-4x+4)[/tex]

[tex]f(x)+18=2(x-2)^{2}[/tex]

[tex]f(x)=2(x-2)^{2}-18[/tex] -----> equation in vertex form

The vertex is the point (2,-18)

therefore

The x-component of the vertex is 2

The y-component of the vertex is -18

Answer:

Consider the quadratic function f(x) = 2x2 – 8x – 10.

The x-component of the vertex is

✔ 2

The y-component of the vertex is

✔ –18

The discriminant is b2 – 4ac = (–8)2 – (4)(2)(–10) =

✔ 144

Answer:

85

Step-by-step explanation:

I assume by 2x3 you mean 2x^3 and 3y2 means 3y^2. If so then just plug in the values:

2x^3 + 3y^2 - 17 = ?

2(3)^3 + 3(4)^2 - 17 = ?

2(27) + 3(16) - 7 = ?

54 + 48 - 17

102 - 17 = ?

85 = ?

Final answer:

Lynda Davis' total expenses for the month are $425. Her expenses for the year are $5100. Her rental income for the year is $14400. Her rate of income is approximately 282.35%.

Explanation:

To calculate Lynda Davis' total expenses for the month, we need to add up all of her monthly expenses. These include $70 for depreciation, $50 for property tax, $25 for insurance, $80 for repairs, and $200 for interest. So her total monthly expenses would be $70 + $50 + $25 + $80 + $200 = $425.

To calculate her expenses for the year, we can multiply her total monthly expenses by 12 since there are 12 months in a year. So her annual expenses would be $425 * 12 = $5100.

Her rental income for the year would be the monthly rental income of $1200 multiplied by 12. So her rental income for the year would be $1200 * 12 = $14400.

To calculate her rate of income, we need to find the percentage of her rental income compared to her total expenses. We can use the formula: (rental income / total expenses) * 100. So her rate of income would be ($14400 / $5100) * 100 ≈ 282.35%.

Answer:

A,D,E

Step-by-step explanation:

If it just lists out the numbers then it is discrete.  So the following are not discrete since it isn't just a list:  B and C.

The following are lists:  A,D,E

Answer:

I have put my answer in the form (x,y,z)

One solution (3,2,4)

Another solution (-5,-4,-6)

Step-by-step explanation:

I'm going to try to do this by a bunch of substitution.

I'm going to solve first equation for x, second for y, and third for z.

Commutative property x+xy+y=11

Distributive property x(1+y)+y=11

Subtraction property  x(1+y)=11-y

Division property x=(11-y)/(1+y)

I'm going to do the other 2 equations in a similar way:

So the second equation solving for y:    y=(14-z)/(1+z)

The third equation solving for z:  z=(19-x)/(1+x)

I'm going to plug my new first equation into my third equation giving me:

z=(19-[(11-y)/(1+y)])/(1+[(11-y)/(1+y)]

Now I'm going to clean this up by multiplying by compound fraction by (1+y)/(1+y).

z=(19(1+y)-(11-y)]/[1(1+y)+(11-y)]

z=[19+19y-11+y]/[1+y+11-y]

z=[8+20y]/[12]

Simplify

z=(2+5y)/3

Now I'm going to sub this into my non-rewrite of equation 2:

y+(2+5y)/3+y(2+5y)/3=14

Multiply both sides by 3 to clear fractions

3y+(2+5y)+y(2+5y)=42

3y+2+5y+2y+5y^2=42

5y^2+10y+2=42

Subtract 42 on both sides

5y^2+10y-40=0

Divide both sides by 5

y^2+2y-8=0

Factor

(y+4)(y-2)=0

So y=-4 or y=2

If y=-4  then x=(11-(-4))/(1+(-4))=15/-3=-5 and z=(2+5*-4)/3=-18/3=-6

So one solution is (-5,-4,-6)

If y=2 then x=(11-2)/(1+2)=9/3=3 and z=(2+5*2)/3=12/3=4

So another solution is (3,2,4)

Answer:

3/4x + (7 × Q)

∆

|

That's an x not multiplication

Answer:

[tex]7q + \frac{3}{4}x[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcl}\text{Product of 7 and q} & = & 7q\\\\\text{Three-fourths of x} & = & \frac{3}{4}x \\\\\text{Three fourths of x added to product of 7 and q} & = & 7q + \frac{3}{4}x \\\\\end{array}[/tex]

Answer:7/20 = 0.35 = 35%=500x.35 =175 men

40%=.40x500 =200 women

200+170=370

500-370

125 children

Step-by-step explanation:

Answer:

There are 175 men, 200 women, and 125 children.

Step-by-step explanation:

7/20 = M/500; M = 175

0.4 x 500 = W; W = 200

175 + 200 + C = 500; C = 125

[tex]\boxed{x \approx 3.064}[/tex]

There is no general property  that we can use to rewrite:

[tex]log_{a}(u\pm v)[/tex]

Then, we'll solve this problem graphically. Let's say that we have two functions:

[tex]f(x)=log(x+1) \\ \\ g(x)=-x^2 +10[/tex]

[tex]f(x)[/tex] is a logarithmic function translated one unit to the left of the pattern logarithmic function [tex]log(x)[/tex]. On the other hand, [tex]g(x)[/tex] is a parabola that opens downward and whose vertex is [tex](0,10)[/tex]. So:

[tex]f(x)=g(x)[/tex]

implies that we'll find the value (or values) where these two functions intersect. When graphing them, we get that this x-value is:

[tex]\boxed{x=3.064}[/tex]

Then, for [tex]x=3.064[/tex]:

[tex]f(x)=log(x+1) \\ \\ f(3.064)=log(3.064+1) \\ \\ f(3.064)=log(4.064) \\ \\ Using \ calculator: \\ \\ f(3.064) \approx 0.6 \\ \\ \\ g(x)= -x^2 +10 \\ \\ g(3.064)= -(3.064)^2 +10 \\ \\ g(3.064)=-9.388+10 \\ \\ g(3.064) \approx -0.6[/tex]

Answer:

[tex]x(x+2)(x-1)(x-3)^2[/tex]

Please let me know the choices to better help you.

Step-by-step explanation:

I see zeros at x=-2 , x=0 , x=1 , x=3.

Any time it makes like a little U or upside down U at a zero you are going to have a even power on your factor (for which the zero occurs).  If it goes through the zero increasing or decreasing (not making a kind of U shaped upside down or upside right), it is an odd power.

So at x=-2, (x+2) is going to have an odd power

So at x=0,  (x-0) or (x+0) or even just x is going to have a odd power

So at x=1,  (x-1) is going to have an odd power

So at x=3, (x-3) is going to have an even power

So the polynomial could be represented by

[tex]x(x+2)(x-1)(x-3)^2[/tex]

distance = √(x1 - x2)^2 + (y1 - y2)^2

distance = √(-6 + 1)^2 + (7 - 1)^2

              = √25 + 36

              = √61

To the nearest whole unit:

√61 = 8

So your answer is:

about 8 units

Answer:

About 8 units

Step-by-step explanation:

I got it right :)

[tex]\bf -2(bx-5)=16\implies bx-5=\cfrac{16}{-2}\implies bx-5=-8\implies bx=-8+5 \\\\\\ bx=-3\implies \boxed{x=\cfrac{-3}{b}} \\\\[-0.35em] ~\dotfill\\\\ b=3\qquad \qquad x=\cfrac{-3}{\underset{b}{3}}\implies \boxed{b=-1}[/tex]

Answer:

[tex]V=312\pi\ mm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the composite figure is equal to the volume of a semi-sphere plus the volume of the cone

so

[tex]V=\frac{4}{6}\pi r^{3} +\frac{1}{3} \pi r^{2} h[/tex]

we have

[tex]r=6\ mm[/tex]

[tex]h=14\ mm[/tex]

substitute

[tex]V=\frac{4}{6}\pi (6)^{3} +\frac{1}{3} \pi (6)^{2} (14)[/tex]

[tex]V=144\pi +168\pi[/tex]

[tex]V=312\pi\ mm^{3}[/tex]

Answer:

312 πmm^2

Step-by-step explanation:

On edg

Answer:

opposite angles in parralelograms are congruent

Step-by-step explanation:

Answer:

equal

Step-by-step explanation:

Opposite angles in parallelograms are equal.

Answer:

So, Allison averages 1/6 of the route every hour, right?

1/6 + 1/a = 1/4

Once we apply the common denominator, 12a, we only wirk with the numerators.

2a + 12 = 3a

a = 12

Her associate can finish the route in 12 hours by herself.

Step-by-step explanation:

it would take 12 hours for her associate to complete the route by herself

This problem is related to the speed of completing the route.

To solve this problem, we must state the formula for the speed.

[tex]\large {\boxed {v = \frac{x}{t}} }[/tex]

where:

v = speed of completing the route ( m³ / s )

x = route distance ( m³ )

t = time taken ( s )

Let's tackle the problem!

Allison can complete a sales route by herself in 6 hours.

[tex]\text{Allison Speed} = v_a = x \div t_a[/tex]

[tex]v_a = x \div 6[/tex]

Her associate can complete the route by herself in t_s

[tex]\text{Associate Speed} = v_s = x \div t_s[/tex]

[tex]v_s = x \div t_s[/tex]

Working with an associate, she completes the route in 4 hours

[tex]\text{Total Speed} = v = v_a + v_s[/tex]

[tex]\frac{x}{t} = \frac{x}{t_a} + \frac{x}{t_s}[/tex]

[tex]\frac{1}{t} = \frac{1}{t_a} + \frac{1}{t_s}[/tex]

[tex]\frac{1}{4} = \frac{1}{6} + \frac{1}{t_s}[/tex]

[tex]t_s = \frac{ 6 \times 4 }{6 - 4}[/tex]

[tex]t_s = \frac{ 24 }{2}[/tex]

[tex]t_s = 12 ~ \text{hours}[/tex]

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point

Answer:

Week: $173.25

Month: $693

Year: $8,316

Step-by-step explanation:

Answer:

=√18

Step-by-step explanation:

The absolute value of a complex number is its distance from zero on graph. The formula for absolute value of a complex number is:

|a+bi|= √(a^2+b^2 )

where a is the real part of the complex number and b is the imaginary part of the complex number.

So for the given number,

a= -4

b=-√2

Putting in the formula:

|-4-√2 i|= √((-4)^2+(-√2)^2 )

= √(16+2)

=√18  ..

ANSWER

[tex]3 \sqrt{2} \: units[/tex]

EXPLANATION

The absolute value of the complex number

[tex] |a +b i| = \sqrt{ {a}^{2} + {b}^{2} } [/tex]

This is also known as the modulus of the complex number.

This implies that:

[tex]| - 4 - \sqrt{2} i| = \sqrt{ {( - 4)}^{2} + {( - \sqrt{2} )}^{2} } [/tex]

[tex]| - 4 - \sqrt{2} i| = \sqrt{ 16 +2 } [/tex]

We simplify further to get;

[tex]| - 4 - \sqrt{2} i| = \sqrt{ 18 } = 3 \sqrt{2} \: units[/tex]

Answer:

The domain is all real numbers. The range is {y|y ≤ 16}

Step-by-step explanation:

we have

[tex]f(x)=-x^{2}-2x+15[/tex]

This is the equation of a vertical parabola open downward

The vertex is a maximum

Find the vertex of the quadratic equation

[tex]f(x)-15=-x^{2}-2x[/tex]

[tex]f(x)-15=-(x^{2}+2x)[/tex]

[tex]f(x)-15-1=-(x^{2}+2x+1)[/tex]  

[tex]f(x)-15-1=-(x^{2}+2x+1)[/tex]

[tex]f(x)-16=-(x^{2}+2x+1)[/tex]

[tex]f(x)-16=-(x+1)^{2}[/tex]

[tex]f(x)=-(x+1)^{2}+16[/tex] -----> equation in vertex form

The vertex is the point (-1,16)

therefore

The domain is the interval ----> (-∞,∞)  All real numbers

The range is the interval ----> (-∞,16]  All real numbers less than or equal to 16

Answer:

The Answer Is B

Step-by-step explanation:

domain is all real numbers. The range is {y|y ≤ 16}.

Answer:

The figures are not similar

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

so

Verify

BC/JI=AB/FJ=ED/GH

substitute the given values

5.1/3.6=2.8/2.1=3.7/2.7

1.417=1.333=1.370 ------> is not true

therefore

The figures are not similar

Answer:

96

Step-by-step explanation:

Answer:

e^x = -3 = -1*3  

x = ln(-3) = ln(-1) + ln(3)  

= (2n+1)iπ + ln(3)  

where n is any integer. For the principal value, choose n=0:  

= iπ + ln(3)

Step-by-step explanation:

Answer:

3.

Step-by-step explanation:

Calculate the median, which is the middle number of an ordered range with an odd number. 3.

Calculate the medians of the bottom and top halves, omitting the middle number. Since these are now even-numbered sets, we'll take the average of the middle two numbers of each. Lower is 1.5, upper is 4.5.

Calculate the difference of the upper median and lower median, so 4.5 - 1.5 = 3.

A lock with 60 digits and a combination involving turning right to the first number, left to the second number, and right to the third number can have 212,400 possible combinations.

A lock with 60 digits and a combination involving turning right to the first number, left to the second number, and right to the third number can have 60 x 59 x 60 possible combinations.

Here's the explanation:

By multiplying these options together, you get the total number of possible combinations: 60 x 59 x 60 = 212,400.

Final answer:

The total number of possible combinations for a lock with a 60-digit combination, turning right, left, and right is 60 × 60 × 60, leading to 216,000 unique combinations.

Explanation:

To calculate the number of possible combinations for a lock with a 60-digit sequence where you turn right to the first number, left to the second number, and right to the third number, you need to apply the basic principle of counting. Each of the three steps in the combination can be any of the 60 digits, with the choice of one step not affecting the choices for the other steps. Therefore, each step has 60 options, and the total number of possible combinations is the product of these options.

The calculation for the total number of combinations is: 60 × 60 × 60, which simplifies to 60^3. When you calculate that, you get 216,000 possible combinations for the lock.

The figure that is shaded 6/8 is the square.

If you split the square on more time along like a box pizza, you will get 8 slices and 6 of them shaded.

Answer:

option B. the square of the sum of 2 times x and 5

Step-by-step explanation:

we have

[tex](2x+5)^{2}[/tex]

we know that

The algebraic expression [tex](2x)[/tex] is equal to the phrase " Two times x" (the number two multiplied by x)

The algebraic expression [tex](2x+5)[/tex] is equal to the phrase " The sum of two times x and 5" (the number two multiplied by x plus the number 5)

The algebraic expression [tex](2x+5)^{2}[/tex] is equal to the phrase " The square of the sum of two times x and 5"

Answer:

B: 5^4

Step-by-step explanation:

however many of the same numbers is the little exponent

Exponent means exactly repeated multiplications of the same number: [tex]a^b[/tex] means that you have to multiply [tex]a[/tex] by itself [tex]b[/tex] times.

So, [tex]5\times5\times5\times5[/tex] means to multiply 5 by itself 4 times, which is written as [tex]5^4[/tex].

Answer:

I and III only

Step-by-step explanation:

step 1

we know that

In this problem

A, B and C are collinear

so

A', B' and C' are collinear too

because the transformation is a translation

The translation does not modify the shape or length of the figure

AB=A'B'

AC=A'C'

BC=B'C'

step 2

The distance

AA'=BB'=CC'

because AB and A'B' are parallel

Answer:

x = 9.6

Step-by-step explanation:

The figure is a similar figure and the quadrilaterals (4 sides) created are related to each other by the same ratio.

So we can say:

8 goes with x as (8+12) goes with 24

We can setup a ratio and solve for x:

[tex]\frac{8}{x}=\frac{8+12}{24}\\\frac{8}{x}=\frac{20}{24}\\20x=8*24\\20x=192\\x=\frac{192}{20}\\x=9.6[/tex]

So x = 9.6

The value of x in the figure drawn is 9.6

we can create a proportional expression thus :

8 = x

(8 + 12) = 24

This means

8 = x

20 = 24

cross multiply

20x = 24 × 8

20x = 192

divide both sides by 20 to isolate x

x = 192/20

x = 9.6

Learn more on similar shapes :https://brainly.com/question/32325828

#SPJ3

Answer:

a) 4/11

b) 2/11

c) 1/11

d) 7/11