Which function results after applying the sequence of transformations to
f(x) = x^5?
• stretch vertically by 3
• translate up 1 unit
• translate left 2 units
​

Answer:

Part 1) The scale factor is [tex]1.5[/tex]

Part 2) The altitude QS is [tex]4\ units[/tex]

Part 3) The scale factor is [tex]\frac{2}{3}[/tex]

Part 4) The value of x is [tex]12\ units[/tex]

Part 5) The perimeter of ABCDE is [tex]46\ units[/tex]

Step-by-step explanation:

Part 1) Find the scale factor of triangle TQR to triangle NQP

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

Let

z-----> the scale factor

[tex]z=\frac{NP}{RT}[/tex]

substitute the values

[tex]z=\frac{24}{16}=1.5[/tex]

Part 2) Find the length of the altitude QS

we know that

To find the altitude QS, divide the altitude of triangle NQP by the scale factor

so

[tex]QS=\frac{6}{1.5}=4\ units[/tex]

Part 3) Find the scale factor of FGHJK to ABCDE

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

Let

z-----> the scale factor

[tex]z=\frac{AB}{FG}[/tex]

substitute the values

[tex]z=\frac{10}{15}=\frac{2}{3}[/tex]

Part 4) Find the value of x

we know that

The value of x is equal to multiply the length side FK by the scale factor

so

[tex]AE=FK(z)[/tex]

substitute the values

[tex]AE=18(2/3)=12\ units[/tex]

Part 5) Find the perimeter of ABCDE

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

x-----> the perimeter of ABCDE

y-----> the perimeter of FGHJK

[tex]z=\frac{x}{y}[/tex]

we have

[tex]z=\frac{2}{3}[/tex]

[tex]y=15+9+12+15+18=69\ units[/tex]

substitute the values

[tex]z=\frac{x}{y}[/tex]

[tex]x=(z)(y)=\frac{2}{3}(69)=46\ units[/tex]

For this case we must solve the following equation for x:

[tex]\frac {1} {3} (6x-15) = \frac {1} {2} (10x-4)[/tex]

We apply distributive property to the terms of parentheses:

[tex]2x-5 = 5x-2[/tex]

We subtract 5x on both sides of the equation:

[tex]2x-5x-5 = -2\\-3x-5 = -2[/tex]

Suamos 5 on both sides of the equation:

[tex]-3x = -2 + 5\\-3x = 3\\x = - \frac {3} {3}\\x = -1[/tex]

Answer:

[tex]x = -1[/tex]

Answer:

The father is 40 and the son is 4.

Step-by-step explanation:

40 + 5 = 45.

4 +5=9.

45 divided by 5 = 9

Answer:

The father is 40 and the son is 4.

Step-by-step explanation:

Answer:

[tex]y-12=13(x-15)[/tex]

Step-by-step explanation:

we know that

The equation of the line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=13[/tex]

[tex](x1,y1)=(15,12)[/tex]

substitute

[tex]y-12=13(x-15)[/tex] -----> equation of the line into point slope form

Answer:

Y-12=13(x-15)

Step-by-step explanation:

Answer:

P = 73%

Step-by-step explanation:

We look for the percentage of employees who are not more than 40 years old.

This is:

[tex]P = \frac{x}{n} *100\%[/tex]

Where x is the number of new employees who are not over 40 years old and n is the total number of new employees.

We do not know the value of x or n. However, the probability of randomly selecting an employee that is not more than 40 years old is equal to [tex]P = \frac{x}{n}[/tex]

Then we can solve this problem by looking for the probability that a new employee selected at random is not more than 40 years old.

This is:

[tex]P(X< 40)[/tex]

Then we find the z-score

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

We know that:

μ = 34 years

[tex]\sigma = 10[/tex] years

So

[tex]Z = 0.6[/tex]

Then

[tex]P (X<40) = P (\frac{X- \mu}{\sigma} < \frac{40-34}{10})\\\\P(X<40) = P(Z<0.6)[/tex]

So we have

[tex]P(Z<0.6)[/tex]

Looking in the normal standard tables:

[tex]P(Z<0.6)=0.726[/tex]

Finally P = 73%

Answer:

Translation

Step-by-step explanation:

You just move the shape down

Answer:

Step-by-step explanation: translation.

Translation is a term used in geometry to describe a function that moves an object a certain distance. The object is not altered in any other way. It is not rotated, reflected or re-sized. In a translation, every point of the object must be moved in the same direction and for the same distance.

Answer:

$100 + $66.67 + $55 = $221.67/month, which is the amount that must be deposited into Pam's escrow account each month....

Step-by-step explanation:

Pam's annual taxes are $1200 per year. It means her escrow each month needs to have 1/12 of that amount. 1200/12 = $100 per month

Her homeowner's insurance is $800 per year, that's 1/12 of that needs to be in her escrow account each month:

$800 / 12, or $66.67/month.

And PMI is $55/month

Add these three together:

$100 + $66.67 + $55 = $221.67/month, which is the amount that must be deposited into Pam's escrow account each month....

Answer: (3, 10)

Step-by-step explanation:

X=3 y=10

Answer:

x = 3

y = 10

Step-by-step explanation:

Equation (1) : -2x + y = 4

Equation (2) : y = 3x + 1​

Substitute (2) into (1):

-2x + (3x + 1) = 4

-2x + 3x + 1 = 4

x + 1 = 4

x = 3

Sub x = 3 into (2):

y = 3(3) + 1

y = 10

Answer:

Step-by-step explanation:

This question is too general.  We can take a look at the behaviors of the two different graphs:

f(x)=3^x-3 is an exponential function whose y-intercept is (0, -2).  Note that 3^0 = 1.  To draw this function, we'd drawn f(x)=3^x first and then translate the whole graph down by 3 units.  The graph appears in Quadrants III, IV and I, in that order.

g(x)=7x^2-3 is not an exponential function, but rather a quadratic whose graph is a parabola.  Here the parabolic graph opens up.  Its y-intercept is (0, -3).  This graph will intersect that of f(x)=3^x-3 in two places.

A:  False.  It is g that has minimum y value of -3.  The minimum y value of f is -2.

B:  The smallest y value f can have is just above y = -2.  y = -2 is the horizontal asymptote for this function.  The smallest y value g can have is -3.  So B is False.

C:  True.  g has the smallest possible y-value; it is -3.

D:  True.  The min. y-value of g is -3.

Answer: C and D are true

Step-by-step explanation:

A P E X

Answer:

D. Robin, Sparrow, Pelican

Step-by-step explanation:

They are the only animals that can do both

d, they are the only animals that can do both

Answer:

[tex]\large\boxed{-1<x<4}[/tex]

Step-by-step explanation:

[tex]-6<2x-4<4\qquad\text{add 4 to all sides}\\\\-6+4<2x-4+4<4+4\\\\-2<2x<8\qquad\text{divide all sides by 2}\\\\\dfrac{-2}{2}<\dfrac{2x}{2}<\dfrac{8}{2}\\\\-1<x<4[/tex]

Answer:

radius = 4

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x - 2)² + (y - 8)² = 16 ← is in standard form

with r = [tex]\sqrt{16}[/tex] = 4

Answer:

4i - 10

Step-by-step explanation:

9x - 7 - 5x - 3 = 4i -10

Answer:

(6, -11)

Step-by-step explanation:

The translation (x-2,y+3) means "subtract 2 from x coordinate" and "add 3 to the y coordinate".

After the transformation, we have the point B'(4,-8). Which point, let it be (x,y), after being transformed is B'(4,-8)??

According to the transformation rule, we have to "subtract 2 from x coordinate" and "add 3 to the y coordinate", thus

x-2=4

x=4+2

x=6

and

y+3=-8

y=-8-3

y=-11

THe coordinate of B are (6,-11)

The answer is A.) ( 4, -3 )

Answer:

x = 16

Step-by-step explanation:

Note that vertical angles are congruent, hence

4x + 20 = 84 ( subtract 20 from both sides )

4x = 64 ( divide both sides by 4 )

x = 16

Answer:

YOur answer would be -1/5.

Step-by-step explanation

rise/run

-4--5/-2-3

=-1/5

For this case we have by definition, that the slope of a line is given by:

 the following formula:

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

Having two points through which the line passes:

[tex](x_ {1}, y_ {1}): (- 2, -4)\\(x_ {2}, y_ {2}) :( 3, -5)[/tex]

Substituting:

[tex]m = \frac {-5 - (- 4)} {3 - (- 2)}\\m = \frac {-5 4} {3 2}\\m = \frac {-1} {5}[/tex]

Finally, the slope of the line is:

[tex]m = - \frac {1} {5}[/tex]

Answer:

[tex]m = - \frac {1} {5}[/tex]

Answer:

[tex]a_n=a_{n-1}+16[/tex]

Step-by-step explanation:

The given arithmetic sequence is

14,30,46,62

The first term of this sequence is

[tex]a_1=14[/tex]

The common distance is obtained by subtracting a subsequent term from a previous term;

d=30-14

The common difference is

d=16

The recursive formula is given by:

[tex]a_n=a_{n-1}+d[/tex]

We now plug in the known value for the common difference to get;

[tex]a_n=a_{n-1}+16[/tex]

The recursive formula for the arithmetic sequence 14, 30, 46, 62 is an = aₙ₋₁ + 16 with the initial term a₁ = 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. In this case, we have the sequence: 14, 30, 46, 62.

Step-by-Step Process

1. Determine the common difference (d) by subtracting the first term from the second term:

2. Using the first term (a1) and the common difference (d), we can now write the recursive formula.

Therefore, each subsequent term is obtained by adding 16 to the previous term.

Answer:

Step-by-step explanation:

3 - 2 = 1 apple

Sally has 1 apple.

Hope this helps.

Please mark as brainliest.

Answer:

P = 76%

Step-by-step explanation:

We look for the percentage of employees who are at least 25 years old.

We know that:

μ = 32 years

[tex]\sigma = 10[/tex] years

And we want to find

[tex]P(X\geq25) [/tex]

Then we find the z-score

[tex]Z =\frac{X - \mu}{\sigma}[/tex]

So

[tex]Z = -0.7[/tex]

Then

[tex]P (X\geq25) = P(\frac{X- \mu}{\sigma}\geq\frac{25-32}{10})\\\\\P (X\geq25) = P (Z\geq -0.7)[/tex]

By symmetry of the distribution

[tex]P(Z\geq -0.7)= 1-P(Z<-0.7)[/tex]

[tex]P(Z\geq -0.7)= 1-0.242[/tex]

Looking in the normal standard tables

[tex]P(Z\geq -0.7)= 0.758[/tex]

Finally P = 76%

Answer: three type of life cycles are Haploid life cycle,Diploid life cycle, and alternation of generations.

The three main life cycles in multicellular organisms are the haploid life cycle, found in some fungi and algae, the diploid life cycle, common in animals like humans, and the alternation of generations, seen in plants and some algae. Insects may undergo complete metamorphosis, with distinct life stages.

Types of Life Cycles in Multicellular Organisms

There are three main types of life cycles in multicellular organisms, which are characterized by the prominence of either the haploid or diploid stages and the process of alternation between these stages. In the haploid life cycle, organisms spend most of their life in the haploid state, such as many single-celled eukaryotes. Fertilization briefly produces a diploid zygote, which immediately undergoes meiosis to form new haploid gametes. An example of this life cycle can be found in certain fungi and algae.

The diploid life cycle is where organisms spend the majority of their lives as diploid individuals. Here, only the gametes are haploid. Most animals, including humans, follow this type of life cycle.

The alternation of generations life cycle is characterized by alternating haploid and diploid stages. This is common in plants and some types of algae. The diploid stage, called the sporophyte, produces haploid spores by meiosis that develop into the haploid stage, known as the gametophyte, which in turn creates haploid gametes. Fertilization of these gametes will result in a new sporophyte, continuing the cycle.

In summary, sexual reproduction leads to varying life cycle types based on the dominancy and alternation of haploid and diploid stages, each vital for the propagation and genetic diversity of species.

Additionally, in the context of insects, which undergo distinct transformations, there are three types of metamorphosis: no metamorphosis, gradual metamorphosis (or incomplete), and complete metamorphosis. Most insects, such as butterflies, undergo complete metamorphosis, exhibiting different forms at each stage of their life cycle: egg, larva, pupa, and adult.

Answer:

d=[0,12]

Step-by-step explanation:

Answer:

The function is f(4)=32, so the domain is (-infinity,infinty)

The domain is infinty :)

Answer: 5

Step-by-step explanation:

= P(roll 4) = 1/6

= Expected # of 4 in 30 rolls = (1/6)*30 = 5

Therefor, the answer is 5

~ Hopefully this helps:) Mark me the  brainliest:)!!

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Answer:

x=15/8

Step-by-step explanation:

Inverse variation is given by

xy = k

Substituting x=5 and y=12

5*12 = k

60 =k

Our original equation is xy = 60

Now let y=32

x*32 = 60

Divide each side by 32

32x/32 = 60/32

Divide top and bottom by 4

x = 15/8

Hi, it's me again!

Your answer would be B.

3x + 6 = 21

3(5) + 6

15 + 6

21 = 21

Answer:b is your best bet

Step-by-step explanation:

first simplify the numerator (x+3)(x-2)=x^2-2x+3x-6=x^2+x-6

now factor the numerator (x+3)(x-2)

now find the restriction 3x-6=0  3x=6  x=2

now factor the denominator 3(x-2)

((x+3)(x-2))/3(x-2)

now cross off the (x-2)

and you are left with (x+3)/3

ANSWERS:

The restriction is X=2

The simplified fraction is (x+3)/3

Answer:

First simplify the numerator (x+3) (x-2) = x^2 -2x + 3x - 6 = x^2 + x-6

now factor the numerator (x+3) (x-2)

now find the restriction 3x-6=0  3x=6  x=2

now factor the denominator 3(x-2)

(x+3)(x-2)/3(x-2)

now cross off the (x-2)

and you are left with (x+3)/3

The restriction is X=2

The simplified fraction is (x+3)/3

Answer:

the answer is A.  10/8 cubic in.

Step-by-step explanation:

V = LWH

length is 2 (1/3 in)

width is 3 (1/3 in)

height is 5 (1/3 in)

V = 2/3 in * 3/3 in * 5/3 in.

V = 10/9 cubic in.

The volume of the prism is 10 cubic inches, making the correct answer option b.

To find the volume of the prism made up of cubes each measuring 1/3 of an inch on one side, we first need to understand the volume of one cube.

The volume of a cube is calculated using the formula:

Given that each side of the small cube is 1/3 inch, we calculate:

Next, we need to determine the total number of these small cubes that make up the prism. Let's assume the prism consists of 270 of these small cubes.

The total volume of the prism is calculated by multiplying the volume of one small cube by the total number of cubes:

Thus, the correct answer is:

Answer:

The answer is C! I just took the quiz and got 100% shout out to all the cheaters out there, let's get this E2020 bread!

The percentage profit on a wheelbarrow is 512%

The percentage profit of an item is the amount of profit when the item is sold, expressed in terms of percentage

The selling price is given as:

SP = $42.50

The cost price is given as:

CP = $6.94

The percentage profit is then calculated as:

[tex]Profit = \frac{SP - CP}{CP} * 100\%[/tex]

This gives

P = (42.50 - 6.94)/6.94 * 100%

Evaluate the difference

P = 35.56/6.94 * 100%

Evaluate the quotient

P = 5.12 * 100%

Evaluate the product

P = 512%

Hence, the percentage profit on a wheelbarrow is 512%

Read more about percentage profit at:

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62 plus 48 is 110

Then add everyone together to find the total 62+48+36 which is 152

110 over 152 is the probability that a person selected at random will be a doctor or woman

Hope this helps;)

The probability that a person at random from the conference is either a doctor or a woman (or both) is 74%, computed from the principle of inclusion and exclusion.

The probability of a person at the conference being a Doctor or a Woman (or both) can be found by adding the individual probabilities - that of being a woman and that of being a doctor - and subtracting the probability of being both a doctor and a woman because this is counted twice in the addition. This is called the principle of inclusion and exclusion in probability theory. So by substituting the given percentages, P(Doctor or Woman) = P(Doctor) + P(Woman) - P(Doctor and Woman) = 62% + 48% - 36% = 74%. So, the probability that a person chosen at random from the conference is either a doctor or a woman (or both) is 74%.

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Answer:

440 ft

Step-by-step explanation:

Perimeter(p) of a rectangle is 2l + 2w

Where 'l' is the length and 'w' is the width.

p = 2(96ft) + 2(124ft) = 192 ft + 248 ft = 440 ft