Answer:
a
Step-by-step explanation:
The pentagon is dilated 3 units to the left and 3 units vertically down and the rule is ( x , y ) → ( x + 3 , y - 3 )
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the pentagon be represented as A
Now , the dilated pentagon is represented as A'
Now , the center of dilation is the origin O ( 0 , 0 )
where it is dilated 3 units to the left
So , the x coordinate is changed to x + 3
And , dilated vertically downward by 3 units
So , the y coordinate is changed to y - 3
Hence , the dilated pentagon is ( x , y ) → ( x + 3 , y - 3 )
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Escribe dos numeros cuyo maximo comun divisor sea 210 y que esten entre 10000 y 11000
Let [tex]p[/tex] and [tex]q[/tex] be two numbers, such that
[tex]10000 < 210p < 11000, \quad 10000 < 210q < 11000[/tex]
If [tex]p[/tex] and [tex]q[/tex] have no common factors, the greatest common factor between [tex]210p[/tex] and [tex]210 q[/tex] is obviously 210.
If we divide the inequalities above by 210, we see that
[tex]\dfrac{10000}{210} < p < \dfrac{11000}{210}, \quad \dfrac{10000}{210}< q< \dfrac{11000}{210}[/tex]
And rounding to the nearest integer, we deduce that [tex]p[/tex] and [tex]q[/tex] must be between 48 and 52.
We may pick [tex]p=49[/tex] and [tex]q=50[/tex], because they have no common factors. So, our numbers would be
[tex]210\cdot 49=10290,\quad 210\cdot 50=10500[/tex]
Please help. Solve 9= -3(x + 6)
Answer:
x=-9
Step-by-step explanation:
9=-3(x+6)
9=-3x-18
27=-3x
-9=x
Name the property that the statement illustrates.
Answer:
Transitive property of segment congruence
Step-by-step explanation:
The reflexive, symmetric, and transitive properties are the criterion for an equivalence relation. In terms of congruence,
The reflexive property states that [tex]\overline{XY} \cong \overline{XY}[/tex] (a segment is congruent to itself)The symmetric property states that if [tex]\overline{AB} \cong \overline{CD}[/tex], then [tex]\overline{CD} \cong \overline{AB}[/tex] (this is essentially commutativity)The transitive property states that if [tex]\overline{AB} \cong \overline{CD}[/tex] and [tex]\ovelrine{CD} \cong \overline{EF}[/tex], then [tex]\overline{AB} \cong \overline{EF}[/tex].In terms of general equivalence relations,
The reflective property states that [tex]a = a[/tex].The symmetric property states that if [tex]a=b[/tex], then [tex]b=a[/tex].The transitive property states that if [tex]a=b[/tex] and [tex]b=c[/tex], then [tex]a=c[/tex].That's the transitive property.
The fact that congruence is transitive means exactly what you have written: if A is congruent to B and B is congruent to C, then you can "bridge" from A to C.
A fraction is which type of number?
Rational or Irrational
Answer:
Rational
Step-by-step explanation:
All rational numbers can be written as fractions.
One hundred people are recruited for an experimental study to determine whether
exercising 30 minutes before lunch or 30 minutes after lunch will help improve heart health more. They will be split into two groups that do not necessarily need to be the same size. One group will exercise and then eat, and the other group will do the same exercises after eating instead. After a month, each person's heart health improvement will be assessed by the same doctor, and the groups will be compared. The participants' names will be on a numbered list based on the order in which they agreed to join the experiment.
Select all the methods that can be used to randomly assign people in the experimental study into two groups. (select multiple answers)
Flip a coin for each person on the list. If the coin comes up heads, they will be put in the group that exercises before lunch. If the coin comes up tails, they will be put in the group that exercises after
lunch
Participants are divided based on their birth month. Those born in January through June will exercise before lunch, and those born in July through December will exercise after lunch.
Participants choose which group to join based on convenience for their work or school schedule.
The names are put into a bowl and mixed around. The first 50 names drawn will be put in the group that exercises before lunch, and the others will exercise after lunch.
The odd-numbered people will be in the group that exercises before lunch, and the even-numbered
people will be in the group that exercises after lunch.
Answer:
B.) Flip a coin for each person on the list. If the coin comes up heads, they will be put in the group that exercises before lunch. If the coin comes up tails, they will be put in the group that exercises after lunch.
D.) The names are put into a bowl and mixed around. The first 50 names drawn will be put in the group that exercises before lunch, and the others will exercise after lunch.
Step-by-step explanation:
These are all the random ones I picked.
The two methods that can be adopted are Option 1 and 3
What do you understand by Random sampling ?Random Sampling is the sampling method where samples are chosen randomly.
each unit has an equal chance of being selected in a sample.
It is given that
One hundred people are recruited for an experimental study to determine whether
exercising 30 minutes before lunch or 30 minutes after lunch will help improve heart health more.
They will be split into two groups that do not necessarily need to be the same size
the methods that can be used to randomly assign people in the experimental study into two groups.
1. Flip a coin for each person on the list. If the coin comes up heads, they will be put in the group that exercises before lunch. If the coin comes up tails, they will be put in the group that exercises after lunch
2.The names are put into a bowl and mixed around. The first 50 names drawn will be put in the group that exercises before lunch, and the others will exercise after lunch.
Therefore Option 1 and 3 are the two methods that can be adopted.
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Please Help !!!! I need ASAP
The area of rectangular kitchen tile is 6x^2-8x-30. The width is 2x-6.
A) what is the length of the kitchen tile?
B) Find the perimeter
Answer:
L=6x^2-4x+5
P=12x^2-4x-2
Step-by-step explanation:
A=WL
So, we know the area is 6x^2-8x-30 and the width is 2x-6
Substitute
(6x^2-8x-30)=(2x-6)(L)
L=(6x^2-8x-30)/(2x-6
Divide
L=6x^2-4x+5
P=2L+2W
Substitute
P=2(6x^2-4x+5)+2(2x-6)
P=12×^2-8x+10+4x-12
Simplify
P=12x^2-4x-2
which system of inequalities is shown in the graph?
A)
[tex]y \leqslant 5 \: \: and \: \: y \geqslant 3x - 2[/tex]
B)
[tex]y > 5 \: \: and \: \: y < 2x - 3[/tex]
C)
[tex]y > 5 \: \: and \: \: y \geqslant 2x - 3[/tex]
D)
[tex]y \leqslant 5 \: \: and \: \: y > 3x - 2[/tex]
Answer:
sry I can't understand how to do this question
What is the inverse of the function f(x) = 1/4x - 12?
Oh(x) = 48x - 4
Oh(x) = 48x + 4
O h(x) = 4x - 48
O h(x) = 4x + 48
Happy Holidays! :)
[tex]\large\boxed{h(x) = 4x + 48}[/tex]
[tex]f(x) = \frac{1}{4}x - 12[/tex]
Find the inverse. Begin by swapping the x and y (f(x)) variables:
[tex]x= \frac{1}{4}y - 12[/tex]
Begin isolating for y. Add 12 to both sides:
[tex]x + 12 = \frac{1}{4}y[/tex]
Multiply both sides by 4:
[tex]4(x + 12) = \frac{1}{4}y * 4[/tex]
[tex]4x + 48 = y[/tex]
Therefore:
[tex]h(x) = 4x + 48[/tex]
The net of a triangular prism and its dimensions are shown in the diagram. what is the lateral surface area of the triangular prism in square centimeters
A-264 cm
B-240cm
C-225cm
D “Not here”
Answer: 120 sq in.
Step-by-step explanation:
At the end of 2006, the population of Riverside was 400 people. The population for this small town can be modeled by the equation below, where t represents the number of years since the end of 2006 and P represents the number of people. Based on this model, approximately what was the increase in the population of Riverside at the end of 2009 compared to the end of 2006?
The correct format of the question is
At the end of 2006, the population of Riverside was 400 people. The population for this small town can be modeled by the equation below, where t represents the number of years since the end of 2006 and P represents the number of people. [tex]P = 400 ( 1.2 )^ t[/tex] Based on this model, approximately what was the increase in the population of Riverside at the end of 2009 compared to the end of 2006?
(A) 291
(B) 691
(C) 1040
(D) 1440
Answer:
The increase in the population at the end of 2009 is 291 people
Step-by-step explanation:
We are given the equation as [tex]P = 400 ( 1.2 )^ t[/tex]
where
P = No of People
t= No of Years
it is given that in the year 2006 the population is 400
this will only happen when we take t= 0
so for
Year value of t
2006- t = 0
2007- t = 1
2008- t = 2
2009 t = 3
No of people in 2009 will be
[tex]P = 400(1.2)^3[/tex]
= 400*1.728
P = 691.2
Since the equation represents no of people so it can't be in decimals, Therefore the population will be 691
Increase = P(2009) - P(2006)
= 691 - 400
= 291
The increase in the population at the end of 2009 is 291 people.
Peyton has p pennies and n nickels. She has at most 18 coins altogether. Write this situation as an inequality.
Answer:
p + n ≠ 18
Step-by-step explanation:
Nancy had eighty - two dollars to spend on six books. After
buying them she had sixteen dollars. How much did each book cost?
Answer:
11 dollars
Step-by-step explanation:
82-16=66
You subtract the money she has left over and then divide that number by the amount of books that were bought
66 Divided by 6 = 11
Mia discovered that if she takes half her age and adds 3, it produces the same result as taking one-fourth of her age and adding 7. How old is Mia?
Answer:
she would be 16 years old
Step-by-step explanation:
hope this helps!! :D
From the given information we found out that age of Mia is 16 years.
What is a linear equation?A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.
Given, Mia discovered that if she takes half her age and adds 3,
Assuming Mia's age to be x years.
∴ (1/2)x + 3...(i)
It produces the same result as taking one-fourth of her age and adding 7,
∴ (1/4)x + 7...(ii)
So, (1/2)x + 3 = (1/4)x + 7.
(1/2)x - (1/4)x = 7 - 3.
(1/4)x = 4.
x = 4×4/1.
x = 16.
So, Age of Mia is 16 years.
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HMMMMMMMMMMMMMMMMMMM
Do you know??
2)
An Airplane is ascending at a speed of 400 km/hr along a line making an angle of 60' with the
ground. How fast is the altitude of the plane changing?
Answer:
The altitude is changing at a speed of 200 √3 km/hr
Step-by-step explanation:
Here, we want to know how far the altitude of the plane is changing
we are told that the airplane makes an angle of 60 degrees with the ground
So therefore , the rate of change of its altitude will be ;
sin 60 = x/ 400
x = 400 sin 60
x = 400 * √3/2
x = 200 √3 km/hr
The altitude is increasing at a rate of 346.61 km/hr.
The diagram below denotes the given scenario.
Then from the diagram we have,
[tex]sin60^{\circ}=\frac{y}{z}\\\frac{\sqrt{3}}{2} =\frac{y}{z}\\ y=\sqrt{3}\\z=2[/tex]
Then,
[tex]sin\theta =\frac{y}{z}\\cos\theta \frac{d\theta}{dt}\\=\frac{z\frac{dy}{dt}-y\frac{dz}{dt}}{z^2} \\\frac{dy}{dt}=\frac{z^2cos\theta\frac{d\theta}{dt+y\frac{dz}{dt}}}{z}\\\frac{dy}{dt} =\frac{2^2(cos60^{\circ})+\sqrt{3}(400)}{2}\\ \frac{dy}{dt}=346.41 km/hr[/tex]
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find all numbers that satisfy the following statement: the square of the number is 5 more then twice the number.
Answer:
I think it is 5 + 2x
Step-by-step explanation:
Jenn made 18 correct and 12 incorrect decisions for a total of 30 points. Mara made 16 correct and 8 incorrect decisions for a total of 32 points
Answer:
Jenn: 12/30 incorrect 18/30 correct
Mara. 8/24 incorrect 16/24 correct
Step-by-step explanation:
Could you ask the question???? This isn’t a questions it more like a statement so I tried to do my best and I just made them into fractions
anybody solve this i made it its easy
3(55x2) + 9 + 44 +88 x 9 = your number + 163593
Answer:
165*6+53+792= 990+845 = 1,835
Step-by-step explanation:
Please help me out!!!!!
Answer:
Start by identifying which solutions have a degree of 2 Degree of two is the sum of all the exponential powers.You have a coefficient leading of 1 so x^2 would be the correct first term.Hope this helps.A meat packer has 180 kilograms of ground meat. He will divide it equally into 50 packages. How much will each package weigh?
Answer:
3.6 kg
Step-by-step explanation:
A meat packer has 180 kilograms of ground meat. He will divide it equally into 50 packages. How much will each package weigh??
Since he is dividing equally, we have:
50 packages = 180 kg
1 package = x kg
Cross Multiply
x kg × 50 packages= 180kg × 1 packages
x kg = 180 kg × 1/50 packages
x kg = 3.6 kg
Hence, 1 package would weigh 3.6 kg(kilograms)
what points do i have to put ? please help
All you have to do is reflect the triangle over the line x = -1.
The answer is in the graph below.
How far can a car travel on 1 gallon of gasoline?
Answer:
25 miles
Step-by-step explanation:
50/2=25
Answer:
25 miles
Step-by-step explanation:
it would be half of 50 so it would be 25 because it goes up by 25 each time
7 Alan is self-employed. He earned $22,500 one year and was taxed at
the FICA rate of 15.02%. What was the total amount he had to pay in
FICA taxes?
a. $3,379.50
b. $1,689.75
c. $1,652.20
d. $3,304.40
8 Art is self-employed. He earned $28,500 one year and was taxed at
the FICA rate of 15.02%. What was the total amount he had to pay in
FICA taxes?
a. $2,140.35
b. $4,205.60
c. $2,102.80
d. $4,280.70
9 Edith earns an annual gross salary of $17,500. She has 28% of her
gross salary withheld for taxes and other deductions. What is the net
pay of each paycheck if she is paid weekly?
a. $274.04
b. $43.87
c. $242.31
d. $438.76
10 Nancy earns an annual gross salary of $16,250. She has 26% of her
gross salary withheld for taxes and other deductions. What is the net
pay of each paycheck if she is paid semimonthly?
a. $62.50
b. $541
c. $462.50
d. $501.04
13 Olga deposited $1,500 in a savings account that pays 7.5% interest,
compounded quarterly. What is the balance in her account at the
beginning of the fourth quarter?
a. $1,590
b. $1,560
c. $1,585.97
d. $1,591.81
Answer:
7. A
8. D
9. C
10. D
13. D
Step-by-step explanation:
Hope that helps :)
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Answer:
Ummmmm ehhhhhh
I need points for a hw
A group of students collect a number of shells on the beach. They sort the shells into three piles based on the size of each shell. Pile 1 has half as many shells as the total amount they collected. Pile 2 has 10 fewer shells than the first pile. Pile 3 has the remaining shells. Write an expression that represents the number of shells in Pile 2.
Answer:
Three piles
Let No. of shells =S
pile1=0.5 S
pile2=0.5S-10
pile 3=10
The required expression is [tex]y=x-10[/tex]
Computation:
Let us that,
The number of shells in pile 1 be[tex]'x'[/tex]
The number of shells in pile 2 be [tex]'y'[/tex]
The number of shells in pile 3 be [tex]'z'[/tex]
Now,
The number of shells in pile 2 is 10 fewer than the number of shells in pile 1.
So, the expression is, [tex]y = x - 10[/tex]
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Can anyone help me with this?
[tex]the \: surface \: area \: of \: both \: cone = 2(\pi{rl} + \pi{ {r}^{2} } ) \\ total \: surface \: area \: of \: both \: cone = 2(\pi{( \frac{1.4}{2} )(2.7)} + \pi{ {( \frac{1.4}{2} )}^{2} } ) \\ total \: surface \: area \: of \: both \: cone = \boxed{4.76\pi} \\ \\ the \: surface \: area \: of \: the \: cylinder = 2\pi{rl} +2 \pi{ {r}^{2} } \\ the \: surface \: area \: of \: the \: cylinder = 2\pi{( \frac{1.4}{2} )(7.5)} +2 \pi{ {( \frac{1.4}{2} )}^{2} } \\ the \: surface \: area \: of \: the \: cylinder = \boxed{11.48\pi} \\ \\ therefore \: the \: surface \: area \: of \: the \: composite \: object \: = \boxed{4.76\pi + 11.48\pi} \\ the \: surface \: area \: of \: the \: composite \: object \: = \boxed{16.24\pi}[/tex]
Solve for x
If you don’t know how to do it don’t answer
PLS HELP ME ANSWER THISSSS
Answer:
WAIT WHERE IS THE QUESTION
Step-by-step explanation:
Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 3 at x = −3 and a local minimum value of 0 at x = 1.
Answer:
The cubic function is f(x) = (27/32)·x - 3/32·x³ - -9/32·x² - 9/32
Step-by-step explanation:
The given function is f(x) = a·x³ + b·x² + c·x + d
By differentiation, we have;
3·a·x² + 2·b·x + c = 0
3·a·(-3)² + 2·b·(-3) + c = 0
3·a·9 - 6·b + c = 0
27·a - 6·b + c = 0
3·a·(1)² + 2·b·(1) + c = 0
3·a + 2·b + c = 0
a·(-3)³ + b·(-3)² + c·(-3) + d = -3
-27·a + 9·b - 3·c + d = -3...(1)
a + b + c + d = 0...(2)
Subtracting equation (1) from equation (2) gives;
28·a - 8·b + 4·c = 3
Therefore, we have;
27·a - 6·b + c = 0
3·a + 2·b + c = 0
28·a - 8·b + 4·c = 0
Solving the system of equations using an Wolfram Alpha gives;
a = -3/32, b = -9/32, c = 27/32 from which we have;
a + b + c + d = 0 3 × (-3/32) + 2 × (-9/32) + (27/32) + d = 0
d = 0 - (0 3 × (-3/32) + 2 × (-9/32) + (27/32)) = -9/32
The cubic function is therefore f(x) = (-3/32)·x³ + (-9/32)·x² + (27/32)·x + (-9/32).