When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative
What is the explanation?
U(2, 7) → U'(-7, 2)
V(10, 7) → V'(-7, 10)
W(2, 3) → W'(-3, 2)
Step-by-step explanation:
From the picture attached,
Coordinates of the vertices of the given triangle,
U → (2, 7)
V → (10. 7)
W → (2, 3)
Since rule for the coordinates of a point P(x, y) after a rotation of 90° counterclockwise about the origin is,
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Evaluate the quantity of x cubed minus 2x squared plus 3x minus 7 end quantity divided by the quantity of x minus 1 end quantity period. x squared minus x plus 2 minus 5 divided by the quantity x minus 1 end quantity x squared minus 2x plus 2 minus 9 divided by the quantity x minus 1 end quantity x squared minus x plus 4 minus 9 divided by the quantity x minus 1 end quantity x cubed minus 2x plus 2 minus 5 divided by the quantity x minus 1 end quantity
Answer:
(x^3 + 3x^2 - 2x + 7)/x- 2
Expand the numerator in the above expression
(x^3 + 5x^2 - 2x^2 + 8x - 10x - 16 + 23)/(x - 2)
Rearrange the terms of the numerator in the above expression
(x^3 + 5x^2 + 8x - 2x^2 - 10x - 16 + 23)/(x- 2)
Factorize the numerator in the above expression
[x(x^2 + 5x + 8) - 2(x^2 + 5x + 8) + 23]/(x - 2)
Factor out x^2 + 5x + 8
[(x -2)(x^2 + 5x + 8) + 23]/(x - 2)
Split the fractions
(x -2)(x^2 + 5x + 8)/(x - 2) + 23/(x - 2)
Divide the common factors
(x^2 + 5x + 8) + 23/(x - 2) hope this help btw your welcome
Answer:
The answer is really option A. x^2 - x +2-5/x-1
Step-by-step explanation:
I just took the test and got it right :)
Help please i forgot about this
Whats the product of 3 plus 4
whats 5 times 8
F(x)=3x^2-4x+8G(x)=2x-5 use the functions above to find the value of g(f(-2)) I don’t understand how to do this
Given,
[tex]f(x)=3x^2-4x+8,\text{g(x)=2x-5}[/tex]To find g(f(-2)). we first find the value of f(-2).
The value of f(-2) is,
[tex]\begin{gathered} f(-2)=3(-2)^2-4(-2)+8 \\ \text{ =3(4)+8+8} \\ \text{ =12+8+8} \\ \text{ =28} \end{gathered}[/tex]So now to find the value of g(f(-2)),
[tex]g(f(-2))=g(28)[/tex]So the value of g(28) is,
[tex]\begin{gathered} g(28)=2(28)-5 \\ \text{ =56-5} \\ \text{ =51} \end{gathered}[/tex]So the value of g(f(-2)) is 51.
PLEASE HURRYYYY
The segment contains points S(a, b) and T(c, d). Which formula should be used to find the midpoint of the segment?
is 12x17=6x34 true or is it flase i cant do it
how do i multiply these ? (5x-6.9)(2x+12.2)
Answer:
10x^2 + 47.2x - 84.18
Step-by-step explanation:
You distribute both terms in the first set of parentheses (5x-6.9) to the terms in the second set (2x+12.2) So when you're doing it 5x gets multiplied by 2x and 12.2 and -6.9 gets multiplied by 2x and 12.2. Then you simplify as much as possible
John's commute to work is 20kmhr while Sheri's commute is 500mmin.
Who has the fastest commute to work in mihrif 1.61km=1mi?
By 6.2 miles per hour, Sheri commutes more quickly.
We are given that,
John travels to work = 20km/hr
Sheri travels to work = 500m/min converting this into km/hr we get ,
1.61km/hr or 1 mile
John travels to work at the following rate:
[tex]\frac{20 km}{1 hr} * \frac{1 mile}{1.61km} = 12.42 miles/hr[/tex]
Sheri travels work at the following rate:
[tex]\frac{500m}{1min} *\frac{1km}{1000 m}*\frac{1mile}{1.61km}*\frac{60min}{1hr}=18.63 miles/hr[/tex]
Computing the difference between the two,
18.63 miles/hr - 12.42 miles/hr = 6.21 miles/ hr ≈ 6.2 miles/ hr
thus, by 6.2 miles per hour, Sheri commutes more quickly.
What are conversions in maths?
An amount that is multiplied or divided between one set of units and another is known as a conversion factor. In the event that a conversion is necessary, it must be carried out with the proper conversion factor to produce an equivalent value. For instance, when translating between inches and feet, 12 inches equals one foot.
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Consider the matrices.
What matrix results from B + A?
Enter your answer by filling in the boxes.
Answer:
Step-by-step explanation:
[tex]\displaystyle\\A=\left[\begin{array}{ccc}-1&6\\-2&2\\4&9\\-5&-11\end{array}\right] \ \ \ \ \ \ \ \ \ B=\left[\begin{array}{ccc}-4&-1\\-8&8\\2&-7\\-6&5\end{array}\right] \\\\A+B=B+A\ (commutativity)\\\\\Rightarrow B+A=\left[\begin{array}{ccc}-4+(-1)&-1+6\\-8+(-2)&8+2\\2+4&-7+9\\-6+(-5)&5+(-11)\end{array}\right] \\\\\\ \Rightarrow B+A=\left[\begin{array}{ccc}-5&5\\-10&10\\6&2\\-11&-6\end{array}\right][/tex]
What number does
2(x+3)²
3(x-1)²
represent WHEN x = 3?
Answer:
72 and 12
Step-by-step explanation:
substitute x = 3 into the expressions
2(x + 3)²
= 2(3 + 3)²
= 2(6)²
= 2 × 36
= 72
--------------------
3(x - 1)²
= 3(3 - 1)²
= 3(2)²
= 3 × 4
= 12
(X) 1.10.PS-7
Simplify the expression. Write the answer in scientific notation.
(7×10¯²) (9×10¯²)
(7×10¯²) (9×10¯²) = ¯
(Simplify your answer. Use scientific notation. Use the multiplication symbol in the r
Enter you
The scientific notation is 6.3 × [tex]10^{-3}[/tex]
The expression is ( 7 ×[tex]10^{-2}[/tex] )( 9 × [tex]10^{-2}[/tex])
Calculate the product or quotient
=63 × ([tex]10^{-2}[/tex] ×[tex]10^{-2}[/tex])
Simplify using the exponent rule with the same base [tex]a^{n} . a^{m}[/tex] = [tex]a^{n + m}[/tex]
=63 × [tex]10^{-2-2}[/tex]
=63 ×[tex]10^{-4}[/tex]
= 6.3 × [tex]10^{-3}[/tex]
Therefore the scientific notation is 6.3 ×[tex]10^{-3}[/tex].
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Would the image be categorized as a function or as a relation? Use at least one sentence to explain your answer.
Answer:
This is a relation, not function.Step-by-step explanation:
The attached graph is NOT a function, since it doesn't pass the vertical line test.
If a vertical line cuts the graph more than once, then this relation is not a function.
The table shows the percent of each type of movie in Brayden's collection. What is the ratio of Action movies to all of the movies in Brayden's collection?
Movie Type Percent of Collection
Comedy 20%
Action 40%
Drama 15%
Science Fiction 25%
Select all that apply.
A.
2 : 5
B.
3
20
C.
2
3
D.
2
5
E.
3 : 20
the ratio of action movies to all movies is 2: 5 .
In mathematics, a ratio illustrates how frequently one number appears in another. On a fruit tray, the ratio would be eight to six if there were eight oranges and six lemons.
Ratios can be lowered by dividing each quantity by the sum of all the common factors between the numbers (much like fractions are).When the ratio's numbers are the smallest practical integers, the fraction is said to be in its simplest form.The ratio's antecedent and consequent are frequently referred to as A and B, respectively.Let Brayden has x number of movies in total.
Total number of action movies in his collection = 40% of x = 0.4 x
Other movies = 1 - 0.4x = 0.6 x
Ratio of action movies to all movies = 0.4x : x = 2: 5
Therefore the ratio of action movies to all movies is 2: 5 .
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35 = u/5 + 12 solve for u and simplify the answer as much as possible
Answer:
u = 115
Step-by-step explanation:
35 = u/5 + 12
35 - 12 = u/5
(35 - 12) * 5 = u
u = (35 - 12) * 5
u = 115
The dash triangle is a dilation image of the solar triangle with a center at the origin. Is a dilation and enlargement or a reduction find the scale factor of the dilation.
Because the scaling factor is a whole number, which is 3, the enlargement of the dashed triangle is a dilatation.
Recall:
Dilation enlarges or shrinks a figure or shape.The original image prior to any reduction or expansion is the image of a dilatation.The new image created following any necessary reduction or enlargement is the scale copy.Any side length of the new image divided by the corresponding side length of the old image gives the scale factor.The dilation is a reduction if the scale factor is a fraction.The dilatation is an enlargement if the scale factor is a whole number.Thus:
For the dashed triangle, measure the separation between the points (2, -2) and (0, -2).
(2, -2) to (0, -2) is separated by 2 units.Using the coordinates (6, -6) and (0, -6) for the solid triangle, calculate the equivalent distance:
(6, -6) and (0, -6) are separated by 6 units.Scale factor = 6/2 = 3
The dilation is an enlargement because the scale factor is a whole number.
In conclusion, the enlarged dashed triangle indicates a dilatation because the scale factor, which is 3, is a whole number.
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Question 12
REASONING Given: 2a²
a
= 72. Conjecture: a = 6. Write a counterexample.
A counterexample to show that 2a^2 = 72 where a = 6 is that a = -6 will still arrive at 72
What is counterexample?This is a term that counters a statement. we can therefore say that counterexample is one that proves a statement to be false.
How to write the counterexamplegiven data
2a² = 72
Conjecture: a = 6
The counterexample is a = -6
substituting a = -6 into the given equation
= 2a²
= 2 * ( -6 )^2
= 2 * ( 36 )
= 72
Since a = -6 gave same answer of 72 as a = 6 then a = -6 is the counterexample
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Given mn, find the value of x.
Answer:
(2x+5)° (8x+5)°
Submit Answer
m
00
Step-by-step explanation:
2x+(-8x) +5-5
-5=0. u Wii collect like terms and if u do that that's the answer if am wrong let me know
If g(x) = -x, for what value of x does
g(x) = -9?
Answer:
x = 9
Step-by-step explanation:
given g(x) = - x and g(x) = - 9 , the equate right sides
- x = - 9 ( multiply both sides by - 1 )
x = 9
In a Sports league each team has 36 players and 3 coaches. There are also a number of team assistants. The ratio of team assistants to players is 1/6. What is the ratio of coaches to assistants?
Answer:
1/2
Step-by-step explanation:
We know that each team has the following:
36Players + 3Coaches + ?Assistants = Sports League
We know that the ratio of assistants to players is 1/6, rewrite the equation accordingly:
36Players + 3Coaches + 6Assitants = Sports League
Now find the ratio of coaches to assistants:
3Coaches / 6Assistants = 1/2
What is the
Range??
Help me out plsss
Answer:
1≤x≤|R+
Step-by-step explanation:
since range is from the y axis
the starting point is 1 UpTo positive real numbers and it doesn't include 0
3.if the m∠1 is 57° , find the measure of ∠6.
Show your work
123°
180°-57°=<6=123°
A straight road makes an angle of 15 degrees with the horizontal. When the angle of elevation of the sun is 57 degrees, a vertical pole at the side of the road casts a shadow 75 feet long directly down the road, as shown in the figure. Approximate the length of the pole. Round to the nearest hundredth.
The length of the pole is 19.15 feet.
What is the angle of elevation?The angle of elevation is the angle created when an observer looks at an object placed above its height in relation to the eye level or the horizontal line. An angle of elevation is, for example, the angle created between the line of sight and the horizontal line when a man on Earth observes the Sun.
Given:
Angle made by straight road = 15°
Angle of elevation of the sun = 57°
Length of the shadow = 75 feet
∠ACB = 90° - 57° = 33°
∠CAB = 57° - 15° = 42°
Using Sine Law to find BC i.e.length of the pole.
[tex]\frac{BC}{sin A} = \frac{AB}{sin C}[/tex]
[tex]\frac{BC}{sin 42} = \frac{75}{sin 33}[/tex]
[tex]BC= \frac{75sin 42}{sin 33}[/tex]
BC ≅ 19.15 feet (to the nearest hundredth.)
Hence, the approximate length of the pole is 19.15 feet.
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A car journey is m
miles long.
One kilometre is equivalent to x
miles.
The car uses one litre of fuel to travel a distance of f
kilometres.
Fuel for the car costs p
pence per litre.
Which of the following expressions gives the cost of fuel for this journey, in pounds?
The expression gives the cost of fuel for this journey is option H mp / 100 fx
Given,
The total distance of a car journey = m miles
One kilometer = x miles
The amount of petrol needed to travel a distance of f kilometers = 1 liter
Cost of the fuel = p pence/ liter
Now we have to find the expression which gives the cost of fuel for this journey in pounds.
1 pound = 100 pence
So,
The distance in miles we can travel with 1 liter of petrol = fx
Total liter of petrol needed for the journey = m/fx
Total cost of petrol for the journey = mp / fx100
That is,
The expression gives the cost of fuel for this journey is option H mp / 100 fx
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The question is incomplete. Completed question is given below:
A car journey is m miles long.
One kilometre is equivalent to x miles.
The car uses one litre of fuel to travel a distance of f kilometres.
Fuel for the car costs p pence per litre.
Which of the following expressions gives the cost of fuel for this journey, in pounds?
(There are 100 pence in one pound.)
A. 100fmpx
B. 100fmp/x
C. 100mpx/f
D. 100mp/fx
E. fmpx/100
F. fmp/100x
G. mpx/100f
H. mp/100fx
Determine which answer in the solution set will make the equation true.
2p + 9 = 4p − 13
S: {−11, 0, 11, 22}
Answer:
11
Step-by-step explanation:
If you input the number and then solve, you should get that #=#
2(11)+9=4(11)-13
22+9=44-13
31=31
Answer: 11
Step-by-step explanation: 2(11)+9=4(11)-13, 22+9=44-13, 31=31
On your own sheet of paper, use long division to find the quotient of 5,550 ÷ 39. What is the remainder?
Answer: Quotient 142
Remainder 12
Step-by-step explanation:
The quotient is 142 and the remainder is 12.
The long division method is as follows :
[tex]142[/tex]
[tex]39\sqrt{5550}[/tex]
-39
165 (3rd 5 taken down )
-156
90 ( 0 taken down )
-78
12
step 1 : take the first two digits (55) of the divident , now multiply 39 with such a number that the product of those two must not go above 55 but should be closest to it.
step 2 : write the number on top and subtract the answer from 55.
step 3 : Now bring down the third 5 and write it after the answer of the subtraction. So the number becomes 165.
step 4 : Again multiply 39 with such a number that the product of those two must not go above 165 but should be closest to it.
step 5 : write that number on top after the previous number and subtract the answer from 165.
step 6 : Now bring down the 0 and write it after the answer of the subtraction. So the number becomes 90.
step 7 : Again multiply 39 with such a number that the product of those two must not go above 90 but should be closest to it.
step 8 : write that number on top after the previous number and subtract the answer from 90.
We have to repeat these steps until all the digits from the divident are used and the remainder comes out to less than the divisor.
Here all the digits of divident are used and the remainder (12) is also less than the divisor (39), so we stopped.
Hence the quotient is 142 and the remainder is 12.
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If the height of a cone is three
times of the radius of the base and its volume is
343 cm³, then find the radius of the base of the cone
As a result, the cone's volume is equal to three times its radius √343/π .
How to understand the concept of mensuration?The word "mensuration" literally means "to measure." It is typically employed when dealing with geometric shapes when it is necessary to calculate different physical values like perimeter, area, volume, or length. Mensuration is the term for measuring these amounts.
According to the given data:So with respect to the information provided to us :
Height of a cone =3* radius of the base
let height be h and radius be r
h=3r
The Formula for volume of cone is:
V=1/3hπr²
Putting the value we get:
343=1/3*π*r²*3r:
r= √343/π
Therefore ,
the volume of the cone whose height is three times its radius is:
√343/π
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i give brainlest can somebdy pls help me
After evaluating the given fraction, the resultant answer is (C) 1¼.
What are fractions?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions.So, 8 ÷ 6⅖:
Now, evaluate as follows
8 ÷ 6⅖8 ÷ 30+2/58 ÷ 32/58/1 × 5/325/4Which can also be written as 1¼.
Therefore, after evaluating the given fraction, the resultant answer is (C) 1¼.
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The population of a city increases by 3.1% per year. If this year's population is
290,000, what will next year's population be, to the nearest individual?
Answer:
the next year population is 122,689
Step-by-step explanation:
The computation of the next year population is as follows:
= This year population × increase percentage
= 119,000 × (1 + 0.031)
= 119,000 × 1.031
= 122,689
Hence, the next year population is 122,689
The above formula is applied so that the correct value of the population could come
and the same is relevant
The Smith twins, Joe and John, have a car collection.
The number of cars is represented by x.
The number of cars in Joe's collection is 2 times the number in John's collection.
The total number in both is 78. What is x, the number in John's collection?
A. 26 Cars
B. 54 Cars
C. 39 Cars
D. 78 Cars
Answer:
Step-by-step explanation:
x = 39
C. 39 Cars
A robot can complete 5 tasks in 3/4 hour. each task is the same. how long does it take the robot to complete one task
The robot will take 0.15 hours to complete one task.
What is the unitary method of problem solving?
A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. In the unitary method, the value of a unit quantity is determined before the values of other units are determined. Direct variation and inverse variation are its two different forms of variations. When there is a direct variation, an increase or decrease in one quantity will result in an equivalent rise or fall in the other. If we increase one quantity in inverse variation, the value of another quantity will drop.
Given, time taken by robot to complete five tasks = 0.75 hours
Thus, time taken by robot to complete one task = (0.75/5) = 0.15 hours
Therefore, the robot will take 0.15 hours to complete one task.
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[3^2 x (189 divided by 9] -30
Step-by-step explanation:
[tex]3 {}^{2} (189 \div 9) - 30 \\ 9 \times 189 \div 9 - 30 \\ 189 \div 1 - 30 \div 1 \\ 189 - 30 \div 1 \\ = 159[/tex]
according to bodmas
Answer:
159
Step-by-step explanation:
Using BODMAS - Bracket Of Division Multiplication Addition Subtraction
Step 1: Bracket
189/9=21
Hence [3^2 x (21)]-30
Step 2:
3^2= 9
Step 3: Calculate within parentheses [9* 21] : 189
9*21=189
Step 4: Open bracket
[189]-30=159