3) How many plates of vehicles consisting of 4 different digits can be made out of the integer 4,5,6,7,8,9? How many of these number are divisible by 2.
Answers
Answer:
A)360
B)180
Step-by-step explanation:
Part-A:
For this question, we don't have to care about what integer they are, we just need to care about the number of integers we are given. considering the question, we understand that we are dealing with permutation .we're given 6 numbers so we want to figure out the permutation of 4 out of 6. the formula which is used for permutation is given by,
\( \displaystyle P(n,r) = \frac{n!}{(n - r)!} \)
where:
n refers to total number of objectsr means the number of objects selectedwe've already sorted out that
\(n = 6\)\(r = 4\)substitute:
\( \displaystyle P(6,4) = \frac{6!}{(6 - 4)!} \)
simplify parentheses:
\(\displaystyle P(6,4) = \frac{6!}{2!} \)
simplify division:
\( \rm\displaystyle P(6,4) = \frac{6!}{2!} = \frac{6 \times 5\times 4 \times 3 \times2! }{2!} = \boxed{360}\)
hence,
360 plates of vehicles consisting of 4 different digits can be made out of the integer 4,5,6,7,8,9
Part-B:
to solve this question, we need to know about the divisibility rule of 2 which is A number is divisible by 2 if the last digit is an even number
notice that half the values of the set are even, thus half of our total permutations will be even and thus divisible by 2, since we have already figured out the permutations of 4 digits plate out of 6 i.e 360 therefore 180 of these number will be divisible by 2
Alternate:
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so it is a four digit plate. After we choose the last digit, we only need 3 digits, choosing from 5 values left. The answer can be therefore be found by multiplying of possible values for the last digit (3) by the number of ways re-arrange 3 distinct values (3!) by the number of ways to choose 3 values from 5, giving the same answer of 3 x 3! x C(5,3) = 180.
Answer:
Step-by-step explanation:
A)Since all the numbers are different, we will have the placement\(\large \boldsymbol { \displaystyle A_n^k=\frac{n!}{(n-k)!} }\)Where n is the number of numbers ; k is the digit of the number \(\large \boldsymbol {} \displaystyle A_{6}^4=\frac{6!}{(6-4)!} = \frac{720}{2!} =\boxed{360}\) B) In this case, the last digit must necessarily be divisible by 2; since the resulting 4 digit number must be divisible by 2 Let's write out the numbers that are multiples of two that can be part of this number :4 ; 6 ; 8 These numbers must necessarily be in the category of units and correspondingly occupy one digit out of 4_ _ _ 4 => 5*4*3=60
_ _ _ 8 => 5*4*3=60
_ _ _ 6 => 5*4*3=60
Total number of methods\(\large \boldsymbol {} 60+60+60=\boxed{180}\)Related Questions
Why are there so many songs about rainbows
And what's on the other side?
Rainbows are visions, but only illusions
And rainbows have nothing to hide
So we've been told, and some choose to believe it
I know they're wrong, wait and see
Someday we'll find it, the rainbow connection
The lovers, the dreamers, and me
Who said that every wish would be heard and answered
When wished on the morning star?
Somebody thought of that, and someone believed it
Look what it's done so far
What's so amazing that keeps us stargazing
And what do we think we might see?
Someday we'll find it, the rainbow connection
The lovers, the dreamers, and me
All of us under its spell
We know that it's probably magic
Have you been half asleep, and have you heard voices?
I've heard them calling my name
Is this the sweet sound that calls the young sailors?
The voice might be one and the same
I've heard it too many times to ignore it
It's something that I'm supposed to be
Someday we'll find it, the rainbow connection
The lovers, the dreamers, and me
rainbow connection- the muppets have a good day everyone
Answers
Answer:
That is a very Nice poem!
A dilation is a transformation in which the _____, but not the shape, of a geometric figure is changed.
Answers
no explanation really
like dilation 2x, 2y makes the size bigger but the shapes rhe same
Amya is making a swayed flower bed with a circular fountain in the middle she wants to figure out mthe area if the part where she will plant flowers
Answers
Answer:
A
Step-by-step explanation: if u read closely and think about it hard enough youll see
Convert 51.7% to a fraction in simplest form and a decimal.
Answers
Make a matrix A whose action is described as follows: The hit by A rotates everything Pi/4 counterclockwise radians, then stretches by a factor of 1.8 along the x-axis and a factor of 0.7 along the y-axis and then rotates the result by Pi/3 clockwise radians.
Answers
Answer:
The required matrix is\(A = \left[\begin{array}{ccc}1.07&-0.21\\-0.86&1.35\end{array}\right]\)
Step-by-step explanation:
Matrix of rotation:
\(P = \left[\begin{array}{ccc}cos\pi/4&-sin\pi/4\\sin\pi/4&cos\pi/4\end{array}\right]\)
\(P = \left[\begin{array}{ccc}1/\sqrt{2} &-1/\sqrt{2} \\1/\sqrt{2} &1/\sqrt{2}\end{array}\right]\)
x' + iy' = (x + iy)(cosθ + isinθ)
x' = x cosθ - ysinθ
y' = x sinθ + ycosθ
In matrix form:
\(\left[\begin{array}{ccc}x'\\y'\end{array}\right] = \left[\begin{array}{ccc}cos\theta&-sin\theta\\sin \theta&cos\theta\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right]\)
The matrix stretches by 1.8 on the x axis and 0.7 on the y axis
i.e. x' = 1.8x
y' = 0.7y
\(\left[\begin{array}{ccc}x'\\y'\end{array}\right] = \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right]\)
\(Q = \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right]\)
According to the question, the result is rotated by pi/3 clockwise radians
\(R = \left[\begin{array}{ccc}cos(-\pi/3)& -sin(-\pi/3)\\-sin(\pi/3)&cos(\pi/3)\end{array}\right]\)
\(R = \left[\begin{array}{ccc}1/2&\sqrt{3}/2 \\-\sqrt{3}/2 &1/2\end{array}\right]\)
To get the matrix A, we would multiply matrices R, Q and P together.
\(A = RQP = \left[\begin{array}{ccc}1/2&\sqrt{3}/2 \\-\sqrt{3}/2 &1/2\end{array}\right] \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right] \left[\begin{array}{ccc}1/\sqrt{2} &-1/\sqrt{2} \\1/\sqrt{2} &1/\sqrt{2}\end{array}\right]\)
\(A = \left[\begin{array}{ccc}1.07&-0.21\\-0.86&1.35\end{array}\right]\)
what is the volume of the rectangular prism ?
Answers
Answer:
180 \(cm^2\)
Step-by-step explanation:
L x W x H
6 x 5 x 6
180
Answer: 180 cubic centimeters
Step-by-step explanation:
Each little blue cube measures 1 cm in each direction - width, height, and depth.
The volume of the whole figure is just the volume of all the little cubes, added up.
The block of cubes is 5 cubes wide and has a depth of 6 cubes. So each horizontal layer is 5 * 6 = 30 cubes, total.
The block of cubes is 6 layers deep, so we have 6 layers of 30 cubes each = 6 * (30 cubes) = 180 cubes in all.
Each cube is 1 cubic centimeter (abbreviated 1 cc), so 180 of them have a combined volume of 180 cc.
A shorter way to say all this is to say that V = width * depth * height =
= 5 cm * 6 cm * 6 cm = (5)(6)(6) cm³ = 180 cubic centimeters
Order cube root of eighty-eight, twenty-eight ninths, square root of nineteen from greatest to least.
cube root of eighty-eight, twenty-eight ninths, square root of nineteen
twenty-eight ninths, square root of nineteen, cube root of eighty-eight
twenty-eight ninths, cube root of eighty-eight, square root of nineteen
cube root of eighty-eight, square root of nineteen, twenty-eight ninths
Answers
Answer:
(a) twenty-eight ninths, square root of nineteen, cube root of eighty-eight
Step-by-step explanation:
When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.
OrderThe attachment shows the ordering, least to greatest, to be ...
\(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)
__
Additional comment
We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.
One way to do the comparison is to convert these to values that need to have the same root:
√19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)
∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)
The roots will have the same ordering as 19³ and 88².
Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...
19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859
88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744
Then the ordering is ...
28/9 < 19³ < 88² ⇒ 28/9 < √19 < ∛88
Answer:
the ordering is
28/9 < 19³ < 88² ⇒ 28/9 < √19 < ∛88
Step-by-step explanation:
please help me as soon as you see this 10 points or five points going out for you
3×1+ 2×(1/10) + 6x (1/100) +5×(1/1000)?
Answers
Answer:
653/200 or 3 53/200
Step-by-step explanation:
3×1+2×1/10 +6× 1/100+ 5×1/1000
3+1/5+3× 1/50+1/200
3+1/5+3/50+1/200
= 653/200
20 POINTS
look at the rectangle below. the sum of the measures of the 3 interior angles of any triangle is always 180° . What is the measure of
A- 30°
B- 45°
C- 60°
D- 120°
Answers
Please guys help me please with this question please please please please
Answers
Answer:
x = 18
Step-by-step explanation:
Given:
160 total learners34 play soccer and rugby40 play soccer and hockey42 play hockey and rugby36 play soccer only72 play hockey8 play rugby only28 play none of these sportsx play all three sportsAs "x" learners play all three sports, the Venn diagram should have three overlapping circles labelled soccer (S), rugby (R) and hockey (H).
x play all three sports: Label the area that's in S, R and H with x.
8 play rugby only: Label the area that is R only with 8.
36 play soccer only: Label the area that is S only with 36.
28 play none of these sports: Place 28 outside the three circles.
34 play soccer and rugby: Place "34 - x" in the area that's in S and R.
40 play soccer and hockey: Place "40 - x" in the area that's in S and H.
42 play hockey and rugby: Place "42 - x" in the area that's in H and R.
72 play hockey
72 is the total for all the sections of H.
⇒ H = 72 - x - (40 - x) - (42 - x)
⇒ H = 72 - x - 40 + x - 42 + x
⇒ H = x - 10
Place "x - 10" in the area that is H only.
The total number of learners is 160.
Therefore, to find x, sum the areas of the Venn diagram and equal to 160:
⇒ 36 + 8 + 28 + 34 - x + x + 40 - x + 42 - x + x - 10 = 160
⇒ 36 + 8 + 28 + 34 + 40 + 42 - 10 - x + x - x - x + x = 160
⇒ 178 - x = 160
⇒ x = 178 - 160
⇒ x = 18
Finally, substitute x = 18 into the Venn diagram.
Pleaseee help I need a visual to do this. I'll really appreciate it
Answers
The visual that can help you in creating a 3D structure using rectangular prism and others is given in the image attached.
What is the 3D structure creation?3D structure creation is the method of planning and building three-dimensional structures or objects utilizing various materials and methods. This may make use of physical development with the use of materials such as wood, metal, and plastic, as well as virtual development utilizing computer program programs.
In virtual 3D structure creation, creators make use of program to make 3D models of structures or objects. These models can be seen and controlled in virtual space, and can be utilized to reenact how the structure will see and work within the real world.
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See text below
1. Start by creating a rectangular prism
as the base of your structure. This will
be the main structure that includes
the walls and interior rooms.
2. Add a cylindrical tower to one corner of the rectangular prism. Adjust the size and height to your liking.
3. Add another cylindrical tower to the opposite corner of the rectangular
prism. Again, adjust the size and
height to your liking.
4. Add a pyramid-shaped roof to one of the cylindrical towers, and a cone-
shaped roof to the other cylindrical tower.
5. Add a second rectangular prism on top of the first one, with a different orientation or size. This can serve as an additional room or tower.
6. Add a pyramid-shaped roof to the second rectangular prism, and a cone-shaped roof to the cylindrical tower that does not have one yet.
7. Add a rectangular prism
perpendicular to the main structure,
creating an L-shape. This can be a
separate building or an extension of
the main structure.
8. Add a pyramid-shaped roof to the new
rectangular prism, and a cone-shaped roof to the cylindrical tower on the
opposite side of the main structure. 9. Finally, add spheres as decorative
elements to the walls and towers. You can also add other shapes, such as additional rectangular prisms,
pyramids, or cones, as long as you have at least 2 of each of the 5
required shapes.
A fence with 2 gates in it surrounds a lion enclosure.
Each gate is 4 m wide.
an image
What is the length of the fence around the enclosure not including the gates?
Answers
The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m
To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.
Let's assume the length of the rectangle is 'l' and the width is 'w'.
From the given data, we know that each gate is 4 m wide.
Therefore, the width of the rectangle is:
Width = w + (4 m + 4 m) = w + 8 m
The perimeter of the rectangle is:
P = 2l + 2(w + 8 m) = 2l + 2w + 16 m
Now, we need to subtract the combined length of the two gates from the perimeter:
P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m
So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m
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You roll a die and pick a card. How many outcomes are possible?
567
8
Answers
The number of possible outcomes when you roll the die would be 6
How to solve for the possible outcome in a dieA die is known to have only 6 faces. The 6 faces are numbered from number 1 to number 6
Such that the sample space that we would have would be given as
SS = {1, 2, 3, 4, 5, 6}
Hence the number of outcomes that we would be able to have from one die would be given as 6
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The boat is traveling at a rate of 1 meter per second. How long does it take the barnacle to get back to its starting point?
Answers
Answer:
D
Step-by-step explanation:
Edge 2020
The time taken by the barnacle to get back to its starting point is A = 2π seconds
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the radius of the circle be represented as r
Now , the value of r = 1 m
And , the boat is traveling at a rate of 1 m/s
where the total path of the barnacle = circumference of the circle
So , the time taken by the barnacle to get back to its starting point A = circumference of the circle / speed of the boat
On simplifying , we get
The circumference of the circle = 2πr = 2π meters
The time taken by the barnacle to get back to its starting point A = ( 2π / 1 )
The time taken by the barnacle to get back to its starting point A = 2π seconds
Therefore , the value of A is 2π seconds
Hence , the time taken for the circular path is 2π seconds
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The complete question is attached below :
The boat is traveling at a rate of 1 meter per second. How long does it take the barnacle to get back to its starting point?
Evaluate.
38−(7+2×4)+182
Enter your answer in the box.
the answer is 32
Answers
\(205\)
hope it helps
Bookwork code: N84
Look at the poster below showing the price of pencils in a stationery shop.
Annabel wants to buy exactly 76 pencils. What is the lowest amount she can
pay?
Give your answer in pounds (£).
spar
..
Pencils for sale!
30p each
Pack of 10
pencils for £2
Answers
Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20
How is the lowest amount determined?The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.
Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.
If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).
If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].
Pencils for sale
30p each
Pack of 10 pencils for £2
Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.
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If log 5 = p and log 2=q then log 200 can be written in terms of p and q as?
Answers
Work Shown:
log(200) = log(2^3*5^2)
log(200) = log(2^3) + log(5^2)
log(200) = 3*log(2) + 2*log(5)
log(200) = 3*q + 2*p
log(200) = 2p + 3q
The log rules I used were
log(A*B) = log(A)+log(B)
log(A^B) = B*log(A)
The equivalent expression of log(200) is 2p + 3q
The logarithmic expression is given as:
\(\mathbf{log 200}\)
Rewrite as:
\(\mathbf{log(200) = log (25 \times 8)}\)
Express as exponents
\(\mathbf{log(200) = log (5^2 \times 2^3)}\)
Split
\(\mathbf{log(200) = log (5^2) +log(2^3)}\)
Apply law of logarithms
\(\mathbf{log(200) = 2log (5) +3log(2)}\)
From the question;
log(5) = p and log(2) = q
So, we have:
\(\mathbf{log(200) = 2p +3q}\)
Hence, the equivalent expression of log(200) is 2p + 3q
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You have recently been hired to survey water park! The park attractions can be found at the locations shown in the table on your grid map. Use this data to answer the questions to follow. Location Ordered Pairs Help Center (2, 3) Large Whirlpool (3, 14) Water Slide #1 (-6, 3) Water Slide #2 (16, 4) Water Slide #3 (-7, 6) Toddler Area (-3, -9) Lazy River (-7, 10) Concessions (6, -6) Gift Shop (8, -9) Restrooms (2, -9) Security Desk (5, 4) After identifying each attraction’s location with ordered pairs, you are now ready to calculate the slope between attractions using the slope formula. Help Center to Water Slide #1 Toddler Area to Concessions Gift Shop to Restrooms Security Desk to Water Slide #2 Lazy River to Large Whirlpool Now calculate the point between these attractions by applying the midpoint formula. Help Center to Water Slide #1 Toddler Area to Concessions Gift Shop to Restrooms Security Desk to Water Slide #2 Lazy River to Large Whirlpool Using your slope and end points calculate a linear equation, y = mx + b. and solve for b. Help Center to Water Slide #1 Toddler Area to Concessions Gift Shop to Restrooms Security Desk to Water Slide #2 Lazy River to Large Whirlpool
Answers
Help Center to Water Slide #1: Level line, y = 3. Toddler area to Concessions: Negative incline, y = (-1/3)x - 7. Gift Shop to Restrooms: Level line, y = -9. Security desk to Water Slide #2: Even line, y = 4. Lazy river to large Whirlpool: Positive incline, y = (2/5)x + 61/5.
How to calculate the slope between attractions using the slope formula.To calculate the slope between attractions and discover the midpoints, we'll utilize the given requested sets for each fascination. Here are the calculations:
Help Center to Water Slide #1:
Slope = ((y2 - y1) / (x2 - x1)) = ((3 - 3) / (-6 - 2)) = / -8 =
Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((2 + (-6)) / 2), ((3 + 3) / 2)) = (-2, 3)
Toddler area to Concessions:
Slope = ((y2 - y1) / (x2 - x1)) = ((-6 - (-3)) / (6 - (-3)) = (-3 / 9) = -1/3
Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((-3 + 6) / 2), ((-9 + (-6)) / 2)) = (1.5, -7.5)
Gift Shop to Restrooms:
Slope = ((y2 - y1) / (x2 - x1)) = ((-9 - (-9)) / (8 - 2)) = / 6 =
Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((8 + 2) / 2), ((-9 + (-9)) / 2) = (5, -9)
Security desk to Water Slide #2:
Slope = ((y2 - y1) / (x2 - x1)) = ((4 - 4) / (16 - 5)) = / 11 =
Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((5 + 16) / 2), ((4 + 4) / 2) = (10.5, 4)
Lazy River to Large Whirlpool:
Slope = ((y2 - y1) / (x2 - x1)) = ((10 - 14) / (-7 - 3)) = (-4 / -10) = 2/5
Midpoint = ((x1 + x2) / 2)), ((y1 + y2) / 2)) = ((-7 + 3) / 2), ((10 + 14) / 2)) = (-2, 12)
Presently, let's calculate the linear equations for each case:
Help Center to Water Slide #1:
The Slope is 0, and the y-coordinate is consistent, so the equation is y = 3.
Toddler area to Concessions:
The Slope is -1/3, and the y-intercept can be calculated utilizing the midpoint facilitates:
-7.5 = (-1/3)(1.5) + b
-7.5 = -0.5 + b
b = -7
Gift Shop to Restrooms:
The Slope is 0, and the y-coordinate is steady, so the equation is y = -9.
Security desk to Water Slide #2:
The Slope is 0, and the y-coordinate is steady, so the equation is y = 4.
Lazy River to Large Whirlpool:
The Slope is 2/5, and the y-intercept can be calculated utilizing the midpoint arranges:
12 = (2/5)(-2) + b
12 = -4/5 + b
b = 61/5
The Linear equations for each case are as follows:
Help Center to Water Slide #1: y = 3
Toddler area to Concessions: y = (-1/3)x - 7
Gift Shop to Restrooms: y = -9
Security desk to Water Slide #2: y = 4
Lazy River to Large Whirlpool: y = (2/5)x + 61/5
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Chocolate bar is 53% cocoa. Weight
Answers
The number of grams of cocoa is 50.9 grams
What is weight?This is the mass of an object
How to find the number of grams of cocoa contained in the chocolate bar?Since we have that a chocolate bar contains 53% cocoa and the weight of the chocolate bar is 96 grams.
Let
x = number of grams of cocoa, W = weight of chocolate bar and p = percentage of cocoa in chocolate barSo, we have that
x = pW
Given that
p = 53 % = 0.53 and w = 96 gramsSubstituting the values of the variables into the equation, we have that
x = pW
x = 0.53 × 96 grams
x = 50.88
x ≅ 50.9 grams
So, the number of grams of cocoa is 50.9 grams
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Translate the following figure 2 units left and 7 units up: T: (-3,-3), J: (-1, -2), K:(-1,-5)
Answers
The figure must be translated using this translation:
(x, y) ---> (x-2, y+7)
\(\begin{gathered} (-3,-3)\rightarrow(-3-2,-3+7)=(-5,4) \\ (-1,-2)\rightarrow(-1-2,-2+7)=(-3,5) \\ (-1,-5)\rightarrow(-1-2,-5+7)=(-3,2) \end{gathered}\)The image of the figure is:
I'=(-5,4)
J'=(-3,5)
K'=(-3,2)
If the probability that a vaccine you took will protect you from getting the flu is 0.977, what is the probability that you will get the flu?
Probability that you will get the flu =
Answers
Answer:
Step-by-step explanation:
0.033
Antoinette needs to solve this system of equations by graphing. Which statements explain how she should graph the equations? Check all that apply. 2 x minus 7 y = 56. y = negative 2.5 x + 4. She should rewrite both equations in slope-intercept form. She should rewrite the first equation in slope-intercept form. She should find that the second equation has a slope of 4. When rewriting the first equation, she should subtract 2x from each side of the equation to get –7y by itself. After rewriting the first equation in slope-intercept form, she should find that both lines have negative slopes.
Answers
Answer:
A. She should rewrite both equations in slope-intercept form.
(this step is true in general, but only the first requires the rewriting for this particular example, so become ambiguous).
B. She should rewrite the first equation in slope-intercept form.
D. When rewriting the first equation, she should subtract 2x from each side of the equation to get –7y by itself.
(this is just the first part of the step of the rewriting)
Step-by-step explanation:
Antoinette needs to solve this system of equations by graphing. Which statements explain how she should graph the equations? Check all that apply.
2 x minus 7 y = 56.
y = negative 2.5 x + 4.
A. She should rewrite both equations in slope-intercept form.
B. She should rewrite the first equation in slope-intercept form.
C. She should find that the second equation has a slope of 4.
D. When rewriting the first equation, she should subtract 2x from each side of the equation to get –7y by itself.
E. After rewriting the first equation in slope-intercept form, she should find that both lines have negative slopes.
Answer:
The answer is b and d
Step-by-step explanation:
I took the test on edge and got it wrong because of the other person
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If the terms of a polynomial do not have a GCF, does that mean it is not factorable?
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Convert 2.8 radians to degree measure. Round your answer to the nearest hundredth.
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Answer:
16.04°
Step-by-step explanation:
\(2.8 \: rad = x \: degrees \\ \)
1rad × 180/π = 57.296°
\(x = 2.8 \times \frac{180}{\pi} = 16.0428 \\ x = 16.04\)
Perform the indicated operation. 22 6/11 x 1 1/2
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Answer:
\(1\frac{1}{2}\) <2<2 \(\frac{6}{11}\)
Step-by-step explanation:
\(1\frac{1}{2}\) is less than 2 is less than 2 \(\frac{6}{11}\)
\(\frac{33}{22} < \frac{44}{22} < \frac{56}{22}\)
Qué número tiene el valor que 14 decenas
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Answer:
140
Step-by-step explanation:
14 x 10 = 140
On the past two quizzes, a student scored a 75 and 83. Write and solve a compound inequality to find the possible values for the 3rd quiz score that would give her an average between 85 and 90, inclusive.
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The possible values for a third quiz score that would give her an average between 85 and 90, inclusive is: 97 ≤ x ≤ 112.
How to determine the average?In Mathematics, the average of these quiz scores can be calculated by using the following formula:
Average = Sum of quiz score/Number of quiz scores
Note: Let the variable q represent the student's score on the third (3rd) quiz.
Substituting the given parameters into the formula, we have the following;
Average = (75 + 83 + q)/3
Average = (158 + q)/3
This ultimately implies that, an average between 85 and 90, inclusive is given by this compound inequality:
85 ≤ (158 + q)/3 ≤ 90
Multiplying all through by 3, we have the following:
255 ≤ (158 + q) ≤ 270
Subtracting 158 from both sides of the inequality, we have the following:
97 ≤ x ≤ 112
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For positive integer n, the factorial notation n! represents the product of the integers from n to 1. (For example, 6!= 6.5.4.3. 2. 1.) What value of N satisfies the following equation? 5!.9!= 12. N! (A)10 (B)11 (C)12 (D)13 (E)14
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The value of N that satisfies the following equation, 5!9!= 12N!, is 10.
Factorial notation (n!) means to multiply a series of descending natural numbers. Also stated in the problem that for positive integer n, the factorial notation n! represents the product of the integers from n to 1.
Take for example 6! which can be written as 6 x 5 x 4 x 3 x 2 x 1 = 720.
Given the equation 5!9!= 12N!, expand the factorial notation.
(5 x 4 x 3 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = (4 x 3) N!
N! = (5 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
N! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
N = 10
Therefore, the value of N that satisfies the following equation, 5!9!= 12N!, is 10.
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I will give 20 points for this question please help because this is hard
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Area of triangle A = 7.5 square units.
Area of triangle B = 15 square units.
Area of the whole figure = 22.5 square units.
How to Find the Area of a Triangle?To find the area of a triangle, the formula used is expressed as: A = 1/2 × length of the base of the triangle × height of the triangle.
Calculate the area of triangle A:
Height of triangle A = 3 units
Length of the base of triangle A = 5 units
Area of triangle A = 1/2 × 5 × 3
Area of triangle A = 7.5 square units.
Calculate the area of triangle B:
Height of triangle B = 3 units
Length of the base of triangle B = 10 units
Area of triangle B = 1/2 × 10 × 3
Area of triangle B = 15 square units.
Calculate the area of the whole figure:
Area of the whole figure = area of A + area of B
Area of the whole figure = 7.5 + 15
Area of the whole figure = 22.5 square units.
In summary, we have:
Area of triangle A = 7.5 square units.
Area of triangle B = 15 square units.
Area of the whole figure = 22.5 square units.
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For the function ƒ(x) = 2 (x − 10)² + 6, find ƒ−¹(x).
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For the function ƒ(x) = 2 (x − 10)² + 6 then F⁻¹ = \(\frac{x- 6}{2}\) + 10 is the inverse of the given functions.
Calculating the problem:y = \(\frac{x - 6}{2}\) + 10
F⁻¹ = \(\frac{x -6 }{2}\) + 10
Inverse functions:A function that is capable of reversing into another function is referred to as an inverse function or anti function. Simply put, if a function is denoted by "f" or "F," then the inverse function is denoted by "f-1" or "F-1." The inverse function returns the original value for which a function provided the output.
If any function "f" takes x to y, then the inverse of "f" will take y to x. A function that consists of its inverse retrieves the original value when considering functions, where f and g are inverses, and f(g(x)) = g(f(x)) = x. Then, the opposite of f(x) is g(y) = (y-5)/2 = x.
How is the inverse of a function or relationship determined?The equation of the inverse relation can be obtained by substituting every y in the equation for every x in the equation that describes the relation between the variables x and y.
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