The coordinates of P' after the transformation are P'(0, -1)
How to determine the coordinates of P'?From the question, we have the following parameters that can be used in our computation:
M(-1, -1), N(-2, -5), O(1, -4), and P(0, -1)
The transformation is given as
A rotation of 360° clockwise about the origin
The above transformation is represented as
(x, y) = (x, y)
This means that
P'(0, -1) = P(0, -1)
This means that the coordinates of P' are (0, -1)
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Matrix X is a 4 x 3 matrix.
Matrix Y is a 3 x 2 matrix.
What is the order of the product XY?
O a. 4x3
O b.
4x2
O c. 3x3
Od. The matrices cannot be multiplied
Oe. 3 x 2
The order of the product XY would be a 4 x 2 matrix which is the correct answer would be an option (B).
How to determine the order of the product of two matrices?The order of the product of two matrices is determined by the number of rows in the first matrix and the number of columns in the second matrix.
Matrix X is a 4 x 3 matrix.
Matrix Y is a 3 x 2 matrix.
As per the given question, the product XY would have 4 rows (the same as the number of rows in matrix X) and 2 columns (the same as the number of columns in matrix Y).
Size of a matrix = number of rows × number of columns.
Size of a matrix = 4 x 2
Therefore, the order of the product XY would be a 4 x 2 matrix.
Hence, the correct answer would be an option (B).
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Rob and Jeni each recruit three people to be election campaign volunteers. The next week they ask each of those volunteers to recruit three more campaign volunteers. They want all new volunteers each week to recruit three more volunteers.
The number of volunteers recruited for the first 5 weeks is; 486 people
How to calculate the geometric sequence?
A geometric sequence is defined as a sequence in which the result of the division of consecutive terms is always the same, called common ratio r.
The nth term of a geometric sequence is given by:
aₙ = a₁rⁿ⁻¹
where;
a₁ is the first term
r is the common ratio
In this question, on the first week there are 6 people, and since each new people involve three more, the common ratio is 3, hence the parameters for the geometric sequence are:
a₁ = 6
r = 3
Hence the number of people after n weeks is:
aₙ = 6(3)ⁿ⁻¹
Thus, the number of volunteers recruited for the first 5 weeks is;
a₅ = 6(3)⁵⁻¹
a₅ = 6 * 3⁴
a₅ = 486
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Given the explicit formula for an arithmetic sequence find the first five terms and the term named in the problem.
1) a n = -11 +7n Find a 34
2) a n = 65-100n Find a 39
3) a n = -7.1-2.1n Find a 27
4) a n = 118 +1 2 n Find a 23
Answer: 59
Step-by-step explanation:
Question 1
Find the midpoint of the line segment with these
endpoints: (7,-6), (-6, -8)
A) (-18, -10)
B) (6.5, 1)
C) (0,5)
D) (.5, -7)
OB
OC
OA
OD
10 pts
Answer:
D
Step-by-step explanation:
(7+-6)/2
(7-6)/2
1/2
(-6+(-8)/2
(-6-8)/2
-14/2
-7
(.5,-7)
Un article voit son prix augmenter successivement de 10%, de 6 %, puis de 8 %.
Puis en période de solde, son prix baisse de 16 %.
Quel est son taux d'évolution global ?
À quel pourcentage cela correspond-il? (On donnera deux décimales de précision pour le pourcentage.)
a rectangle is 3 feet longer than it is wide. find the dimensions of the rectangle if its area is 208 sq-feet
Dimensions of the Rectangle are : 16 feet by 13 feet .
A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal . A rectangle has two dimensions. we can measure its length and, perpendicular to that, its width.
Rectangle is 3 feet longer than it is wide and its area is 208 sq-feet .
Area of Rectangle = l×b ( Where l = length , b = breadth )
Therefore , Let X be the the width of rectangle . then from given it's length is (X+3).
∴ X × (X+3) = 208
∴ [tex]x^{2}[/tex]+3X-208 = 0
(X+16)(X-13) = 0
X = -16 & X = 13
Distance can't be negative so Width = X = 13 feet.
∴ Length = X+3 = 16 feet.
Thus the Dimensions are 16 feet by 13 feet .
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The real root of the equation x3 10x2 29x 30 = 0 is –6. what are the nonreal solutions? 2 i, 2 – i –2 i, –2 – i –4 2i, –4 – 2i 4 2i, 4 – 2i
The non-real roots of the polynomial x³ - 10x² + 29x - 30 are; x = 2 + i or 2 - i
What is the root of the polynomial?We are given the polynomial as;
x³ - 10x² + 29x - 30
We are told that the real root of the polynomial is -6. Thus, (x + 6) is a factor of the polynomial.
Now, we can use polynomial long division to get;
x³ - 10x² + 29x - 30
- divisor * x² x³ - 6x²
remainder - 4x² + 29x - 30
- divisor * -4x¹ - 4x² + 24x
remainder 5x - 30
- divisor * 5x⁰ 5x - 30
remainder 0
Quotient : x² - 4x + 5 Remainder: 0
x² - 4x + 5_______
(x + 6) | x³ - 10x² + 29x - 30
- x³ - 6x²
-4x² + 29x - 30
- - 4x² + 24x
5x - 30
- 5x - 30
0
Now, using quadratic calculator to find the roots of the quotient, we get;
x = 2 + i or 2 - i
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solve for x.
enter your answer as a mixed number in simplest form in the box.
x =
Answer:
x + x - x = x
explanation:
give us the actual formula lol
NEED HELP ASAP!
Refer to the triangle.
What is the length of side AB?
(Blank) units
After solving the equation the length of AB is [tex]2\sqrt{3}[/tex]
What do you mean by trigonometry?
Trigonometry “triangle” and “measure”) is a branch of mathematics that studies the relationship between the side lengths and angles of triangles.
A trigonometric ratio is the ratio between the edges of a right triangle.
The sine function (sin) defined as the ratio of the opposite side of the angle to the hypotenuse.
In the given triangle ABC , use sin ratio to find AB.
tan θ = P/B
tan 30 = AB/6
[tex]\frac{1}{\sqrt{3} } =AB/6[/tex]
AB = [tex]\frac{6}{\sqrt{3} }[/tex] = [tex]\frac{6}{\sqrt{3} }\times \frac{\sqrt{3}}{\sqrt{3}}= \frac{6\sqrt{3}}{3}=2\sqrt{3}[/tex]
Therefore, length of AB is [tex]2\sqrt{3}[/tex]
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Vashti is designing the cover of the school yearbook. She wants to draw a flower on the cover that looks the same for each rotation of 45 degrees. How many petals should the flower have?
The number of petals that the flower should have is of:
8 petals.
When does a figure has rotational symmetry?A figure has rotational symmetry when it can be rotated by an angle measure which is greater than 0º and less than 360º and the rotated image is equals to the original figure, that is, the image is equals to the pre-image.
In this problem, we want the flower to have a rotation symmetry of 45 degrees.
The total angle measure of the flower is given as follows:
360º.
Then the number of petals needed for the flower to have a rotational symmetry of 45º is calculated as follows:
360/n = 45.
Applying cross multiplication, we have that:
45n = 360
n = 360/45
n = 8 petals.
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Caleb has 5x² yellow pens and 4x green
pens.
He has twice as many pink pens as yellow
pens.
He also has 3 fewer black pens than green
pens.
Write an expression in terms of x for the total
number of yellow, green, pink and black pens
that Caleb has.
Give your answer in its simplest form.
Answer:
10x²+8x-6
Step-by-step explanation:
5x²+4x+5x²×2+4x-3
=10x²×2+8x-3
=10x²+8x-6
Please help! Multiple GEO post
Answer:
[tex]60[/tex]
Step-by-step explanation:
Using the exterior angle theorem, [tex]y=35^{\circ}+25^{\circ}[/tex].
Shaq made 8 out of 15 free throws he attempted in game 6 of the NBA Finals. The Lakers want to know how many consecutive free throws he would have to make to raise the percent of successful free throws to 75% during the game.
write and equation that represents this situation.
The equation that represents the situation in which case the percent of successful free throws is 75% during the game is; ( 8 + x ) = 0.75 ( 15 + x ).
Which equation represents Shaq's situation as described in the task content?It follows from the task content that the equation which represents the situation in which case the percent of successful free throws rises to 75% is to be determined.
As evident in the task content; Initially, Shaq made 8 out of 15 free throws he attempted.
Therefore, let the number of consecutive free throws he has to make to raise the success rate to 75% be; x.
Therefore, it follows from percent proportion that;
( 8 + x ) / ( 15 + x ) = 75 / 100
The simplified equation which represents the required situation is therefore;
( 8 + x ) = 0.75 ( 15 + x ).
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Your are buying a can of tomato soup that weighs 8.5oz. The cost of the can of soup is $0.89. What is the approximate unit price per ounce?
Answer:
$0.10 (nearest cent)
10.5¢
Step-by-step explanation:
Given:
Weight of the can of tomato soup = 8.5 ozCost of the can = $0.89To find the approximate unit price per ounce, divide the cost of the can by the number of ounces in the can:
[tex]\implies \dfrac{0.89}{8.5}=0.104705882...[/tex]
Therefore, the approximate unit price per ounce is $0.10 (nearest cent) or 10.5¢ (nearest half cent).
A student must save at least $675 plus 3% tax to buy a round-trip ticket to London. The student has $98 saved already.
If the student earns $32 per week and plans to save half of the earnings each week toward the ticket cost, how many weeks will it take the student to save enough money for the ticket?
It will take 38 weeks a student to save enough money for the ticket.
What is division?Mathematical operations come in several types, with division being one. The phrases or numbers are divided into the same number of components during this operation.
Given,
a student must save at least $675 plus 3% tax to buy a round-trip ticket to London.
3% of 675
= 3 x 675 / 100
= 20.25
The student has $98 saved already.
Now student needs ($675 - $98) + 20.25 = $577 + 20.25
= $597.25
If the student earns $32 per week and plans to save half of the earnings each week toward the ticket cost.
That means, $32 / 2 = $16 per week.
To find the amount of enough money:
Divide $597.25 by $16.
597.25 /16
= 37.328125
≈ 38 weeks
Therefore, student will save for 38 weeks.
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What should I eat for breakfast?
Answer:
It is a good idea to choose a breakfast that includes a variety of healthy and nutritious foods to fuel your body and mind.
Step-by-step explanation:
It is important to eat a healthy and balanced breakfast to start your day off on the right foot. Some good options for breakfast include whole grain toast with eggs and avocado, oatmeal with fruit and nuts, or a smoothie with yogurt and berries. It is also a good idea to include a source of protein in your breakfast, such as eggs, Greek yogurt, or nuts, to help keep you feeling full and satisfied. Ultimately, the best breakfast for you will depend on your personal preferences and dietary needs. It is a good idea to choose a breakfast that includes a variety of healthy and nutritious foods to fuel your body and mind.
Answer: Eggs
Extra: Bacon
Drink : Milk/OJ
Which formula correctly shows how to find the 21st term in the geometric sequence?
2000, 1000, 500, 250, 125, ...
Answer: Therefore, the correct formula is {a}_{21} = 2000 * 0.5^{20}.
Step-by-step explanation:
A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a constant factor called the common ratio. In this case, the common ratio is 0.5, since each term is found by dividing the previous term by 2.
To find the nth term in a geometric sequence, we can use the formula:
a_n = a_1 * r^(n-1)
where a_1 is the first term in the sequence, a_n is the nth term, and r is the common ratio. In our case, the first term is 2000, the nth term is the 21st term, and the common ratio is 0.5. Therefore, the formula we need to use is:
a_21 = 2000 * 0.5^(21-1)
= 2000 * 0.5^20
Therefore, the correct formula is {a}_{21} = 2000 * 0.5^{20}.
thats all of my points if yo get it right i give u an thanks and i will choose you as the brainlyest answer.
Answer:
3/4
Step-by-step explanation:
B is highlighting 3 for the 4 rows.
Which expression is equivalent to the perimeter of your the rectangle shown below?
The expression that is equivalent to the perimeter of the rectangle in the image shown is, 6x + 8.
How to Find the Perimeter of a Rectangle?To find the perimeter of a rectangle, add all the four sides of the rectangle. The following formula can be used:
Perimeter (P) = 2(length + width).
In the rectangle shown below, the dimensions are:
Length of rectangle = 2x + 3
Width of rectangle = x + 1
Substitute into the perimeter each expression of the dimensions:
Perimeter = 2[(2x + 3) + (x + 1)]
Open the parentheses by applying the distributive property of equality:
Perimeter = 2(2x + 3 + x + 1)
= 2(3x + 4)
= 2(3x) +2(4)
= 6x + 8
Therefore, the expression is, 6x + 8.
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in a symmetric distribution, the first quartile will always equal the third quartile. group of answer choices true false
The statement "In a symmetric distribution, the first quartile will always equal the third quartile" is true
The given statement is "In a symmetric distribution, the first quartile will always equal the third quartile"
The symmetric distribution is defined as the distribution that occurs when the values of variables appear at regular frequencies. Usually the mean, mode and the median all are same point in the symmetric distribution.
In the symmetric distribution the left side of the graph will be the mirror image of the right hand side of the graph. So the first quartile will always equal the third quartile.
Therefore, the given statement is true
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giving barinly to someone who answers in a complete sentence and who is write
Approximate √15 to the nearest integer.
Explain how you got your answer.
The square root of 15 is approximately 4.
To approximate the square root of 15, we can find the perfect squares that are closest to 15. The perfect squares that are closest to 15 are 9 and 16. Since 15 is closer to 16, we can say that the square root of 15 is slightly less than 4.
Another approach could be:
The square root of 15 is approximately 3.87. Rounding to the nearest integer gives us 4. To round a number, we look at the number following the place value we are rounding to. If it is greater than or equal to 5, we round up. If it is less than 5, we round down. In this case, the digit following the ones place is 8, which is greater than 5, so we round up to 4.
The digits in the product of 0.48 and a decimal number between 350 and 400 are 182136. Explain how to correctly place the decimal point without knowing the other factor. Then Place place the decimal point in the product.
The decimal point is to be placed three places to the left.
What are decimal numbers?
When we divide a whole number into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number. After the decimal point, however, when we proceed to the right, we obtain the fractional portion of the decimal number.
Given that, in the question, the product of a decimal number between 350 and 400 and 0.48 results in the numbers 182136. As 0.48 is just 48/100, let's take a decimal number between 350 and 400.
If the number is 370.1, for example, we can write it as 3701/10 because it has one decimal point.
Our denominator will be 1000, because both the denominators are 100 and 10, which is equivalent three decimal places to the left of the result when we multiply 48/100 by 3701/10.
The result provided to us should therefore be written as 182.136, with the decimal point moved three spaces to the left.
The decimal point is to be placed three places to the left.
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If cos2β = 3/4 and ß terminates in quadrant III, find cosβ :
Answer:
cosβ = -1/2
Step-by-step explanation:
Since cos2β = 3/4 and β is in quadrant III, the value of cosβ must be negative. We can find the exact value of cosβ by using the identity cos2β = 2cos^2β - 1. Substituting 3/4 for cos2β and solving for cosβ, we get:
3/4 = 2cos^2β - 1
cos^2β = 1/4
cosβ = 1/2 or -1/2
Since cosβ is negative in quadrant III, the value of cosβ is -1/2. Thus, the answer is cosβ = -1/2.
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Helppppp meeeee guyssss
Four more than the product of a number and 8 is equal to 7.
Answer: x = 0.375
Step-by-step explanation:
Equation: 8x + 4 = 7
Subtract 4 on both sides
8x = 3
Divide by 8 on both sides
x = 3/8 is 0.375 decimal
x = 0.375 (0.38 round-up)
Answer:
x = 3/8
Step-by-step explanation:
Four more than the product of a number and 8 is equal to 7.
4 + 8x = 7
8x = 7 - 4
8x = 3
x = 3/8
---------------------
check
4 + 8 x 3/8 = 7
4 + 3 = 7
7 = 7
the answer is good
Winona goes to the store to buy paper towels for her scout troop party. The paper towels Winona likes are sold in packs of 12 rolls for $9.96 per pack. The scout leader needs to know the cost of each roll of paper towels. What is the unit rate in cost per roll?
Answer:
The unit rate in cost per roll is $0.83 per roll.
what is unit rate? how to calculate unit rate of cost?
Unit rate is a type of ratio that compares the quantity of two different types of units. It is calculated by dividing the cost of a given quantity of an item by the number of units in that quantity. For example, if a bag of apples costs $4 and there are 5 apples in the bag, the unit rate of cost for the apples is $0.80 per apple ($4/5= $0.80). Another example would be if a carton of eggs costs $2.50 and there are 10 eggs in the carton, the unit rate of cost for the eggs would be $0.25 per egg ($2.50/10 = $0.25). Unit rate is a useful tool for understanding the cost of items, especially when comparing items of different sizes or quantities. It can also be used to calculate the cost of a certain number of items, as long as the unit rate is known.
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Type the correct answer in the box. Use numbers instead of words.Isha is a pet sitter.She earns $5 for each cat.She earns $12 for each dog.Last week, Isha pet sat for 11 cats and 7 dogs.How much money did Isha earn pet sitting last week?
By evaluating a revenue equation, we will see that she earned $139 last week.
How much money did Isha earn pet sitting last week?We know that Isha is a pet sitter, and she earns $5 for each cat and $12 for each dog.
So, if she pet sats for x cats and y dogs, the revenue will be:
R(x, y) = $5*x + $12*y
In this case we know that she pet sat for 11 cats and 7 dogs, then we have:
x = 11
y = 7
So we need to evaluate the above revenue function, we will get:
R(11, 7) = $5*11 + $12*7
R(11, 7) = $55 + $84
R(11, 7) = $139
Isha earned $139 last week.
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what is right ?
please help!!!!!
Answer:
[tex]\frac{2w}{5}[/tex]Step-by-step explanation:
[tex]\frac{22w}{55}[/tex]
divide both side by 11
[tex]\frac{2w}{5}[/tex]
Given the functions f(x) = x3 + x2 – 3x + 4 and g(x) = 2x – 4, what type of functions are f(x) and g(x)? Justify your answer. What key feature(s) do f(x) and g(x) have in common? (Consider domain, range, x-intercepts, and y-intercepts.)
1. f(x) - cubic function -- polynomial , g(x) - linear function
similar
domain all real numbers (?)range is all real number, end behavior is the sameThe function f(x) = x³+x²-3x+4 is a polynomial function and g(x) = 2ˣ-4 is an exponential function.
Domain: -∞ < x < ∞
Range: -∞ < y < ∞
y-intercept = 4
x - intercepts = -2.68
Function g(x)
Domain: x > 0
Range: -4 < y < ∞
y - intercept = -4
x - intercepts = none
By comparing the key features above, we can conclude that the common features in both functions are their range
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the distribution of scores on a recent test closely followed a normal distribution with a mean of 22 points and a standard deviation of 2 points. for this question, do not apply the standard deviation rule. (a) what proportion of the students scored at least 27 points on this test, rounded to five decimal places?
Therefore ,0.62097 % proportions of students scored at least 27 points on this test
What do you learn from z-scores?The Z-score provides information on how far a given value deviates from the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations above or below the mean a specific data point falls. The level of variability within a particular data collection is effectively reflected in the standard deviation.
Here,
z = (x - μ)/σ
here ,raw score =x ,standard deviation=σ and mean= μ
μ = 22, σ = 2
For x > 27:
z = (27 - 22)/2 = 1
P(z > 1) = 1 - P(z < 1) = 1 - 0.99379 = 0.0062097
Therefore , 0.62097 % of students scored at least 27 points on this test
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