The new coordinates after the dilation with scale factor 1/4 is
a' = (5/2 , 3/2)
To get the new coordinates when the point is dilated is to multiply the scale factor with the coordinates of the point.
According to the question we have been given that
center of dilation = (0,0)
Scale factor = 1/4
coordinate of the point, a = (10,6)
To get the new coordinates we will multiply the given coordinates by the scale factor that is ,
a' = 1/4*(10,6)
= (10*1/4 , 6*1/4)
a' = (5/2 , 3/2)
Hence the new coordinates after the dilation is a' = (5/2 , 3/2)
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A civil engineer counted the cars that passed through an intersection.If 2457 cars passed through the intersection in one hour how many cars would pass through 8 hours
Also need you to send the working out please you would help the best
The number of cars that would pass through the intersection in 8 hours is 19,656.
How many cars would pass through in 8 hours?In order to determine the number of cars that would pass through the intersection in 8 hours, the cars that passed through in one hour would be multiplied by the number of hours.
Multiplication is the mathematical operation that is used to determine the product of two or more numbers. Multiplication is the process of adding one number to another over a number of times. The sign used to represent multiplication is x.
Total number of cars that passed through in 8 hours = cars that passed through in one hour x number of hours
2457 X 8
2457
x 8
19,656
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he cost in dollars of making x items is given by the function C(x) = 10x + 500.
a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item.
b. What is the cost of making 25 items?
c. Suppose the maximum cost allowed is $1500. What are the domain and range of the cost function, C(x)?
We get the fixed cost as $ 150, cost of 25 items as $ 750, range as [0, 1500] and the domain as [0,150].
We are given the cost function:
C(x) = 10x + 500.
Fixed cost is when x = 0
C(0) = Fixed cost = 10 ( 0 ) + 500
Fixed cost = $ 500
Cost of making 25 products is x = 25
C(25) = 10 (25) + 500
C(25) = 250 + 500 = $ 750
Maximum cost allowed = $ 1500
Function becomes:
10x + 500 ≤ 1500
x + 50 ≤ 150
x ≤ 150 - 50
x ≤ 100
Range = [0, 1500]
Domain = [0, 150]
Therefore, we get the fixed cost as $ 150, cost of 25 items as $ 750, range as [0, 1500] and the domain as [0,150].
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Use the triangle below to find the measure of angle G.
Answer:
59.3° (nearest tenth)
Step-by-step explanation:
Cosine Rule (for finding angles)
[tex]\boxed{\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}}[/tex]
where:
C = anglea and b = sides adjacent the anglec = side opposite the angleFrom inspection of the given triangle:
C = angle Ga = side GI = 6b = side GH = 15c = side HI = 13Substitute the values into the formula and solve for G:
[tex]\implies \sf \cos(G)=\dfrac{6^2+15^2-13^2}{2(6)(15)}[/tex]
[tex]\implies \sf \cos(G)=\dfrac{36+225-169}{180}[/tex]
[tex]\implies \sf \cos(G)=\dfrac{92}{180}[/tex]
[tex]\implies \sf G=\cos^{-1} \left(\dfrac{92}{180}\right)[/tex]
[tex]\implies \sf G=59.26213133...^{\circ}[/tex]
Therefore, the measure of angle G is 59.3° (nearest tenth).
Boris has a deck of 10 cards numbered 1 through 10. He is playing a game of chance.
This game is this: Boris chooses one card from the deck at random. He wins an amount of money equal to the value of the card if an odd numbered card is drawn. He loses $4.50 an even numbered card is drawn.
a) find the expected value of playing the game.
___ dollars
b) what can Boris expect in the long run, after playing the game many times? (He replaces the card in the deck each time)
a) Boris can expect to gain money. He can expect to win ___ dollars per draw
b) Boris can except to lose money. He can except to lose ___ dollars per draw.
c) Boris can except to break even( neither gain or lose money)
Boris can expect to break even ( neither gain or lose money) is the answer.
The probability of a number is calculated by dividing Favorable outcome by Total outcome.
The probability of a number between 1 to 10 = Favorable outcome/Total outcome
Favorable outcome =1 (any one number )
Total outcome = 10
Here p(x) is equal to 1 divided by 10
P(X)= 1/10= 0.1
The table gives us the Amount when we multiple X to P(X),
Expected value = (XiP(Xi))
When we substitute the value we get,
=(10.1)+(-50.1)+(30.1)+(-50.1)+(50.1)+(-50.1)+(70.1)+(-50.1)+(90.1)+(-50.1)
=0
So we will get zero after substituting the value.
Hence, option C Bories can Expect to break even (Neither gain or lose money) is the correct answer.
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K
For each of the functions y = f(x) described below, find f(0).
(a) x
-1
1 2
f(x)
1
2
(b) y = 12 - 2x2
(c)
-10 -
0
7
조
8
10
IN 2 1
-
3
3
-6
6 8 10
(a) f(0) = ㅁ
The values of f(0) that can be read from (a similar question in part (a) and (c)) the table, functions, and graph in the question are;
(a) f(0) = 1
(b) f(0) = 12
(c) f(0) = -2
How can the table, function, and graph be evaluated to find f(0)?Part of the question appears missing. From a similar question online, we have;
(a) A table of values;
x: -1, 0, 1, 2, 3
y: 7, 1, 6, -3, -4
Taking the function, f(x) = y, we have;
From the above values in the table, when x = 0, y = f(0) = 1
Therefore;
f(0) = 1(b) y = 12 - 2•x²
Taking the function, f(x) = y, we have;
At x = 0, y = f(0) = 12 - 2 × 0² = 12
Therefore;
f(0) = 12(c) A graph of a parabola passing through the points (-1, 3), (2, -6), (5, 3)
Let f(x) = a•x² + b•x + c, represent the function, we have;
f(-1) = 3 = a•(-1)² + b•(-1) + c = a - b + c
3 = a - b + c...(1)f(2) = -6 = a•(2)² + b•(2) + c = 4•a + 2•b + c
-6 = 4•a + 2•b + c...(2)f(5) = 3 = a•(5)² + b•(5) + c = 25•a + 5•b + c
3 = 25•a + 5•b + c...(3)Solving the system of linear equations, (1), (2), (3) using a graphing calculator gives;
a = 1, b = -4, c = -2
Which gives;
f(x) = x² - 4•x - 2
Therefore;
f(0) = 0² + 4×0 - 2 = -2
Which gives;
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A figure is fully contained in Quadrant Il.
Looking at the coordinate plane below, which letter represents this quadrant?
From the division of quadrants in the xy-plane, it is found that letter K represents the second quadrant.
What are the signals of the coordinates in each quadrant?There are four quadrants of points (x,y), and their signals are given as follows:
Quadrant 1: x is positive(left of y-axis) and y is positive(above the x-axis).Quadrant 2: x is negative(right of y-axis) and y is positive(above the x-axis).Quadrant 3: x is negative(right of y-axis) and y is negative(below the x-axis).Quadrant 4: x is positive(left of y-axis) and y is negative(below the x-axis).In this problem, we want Quadrant 2, in which:
x is negative, that is, to the left of the y-axis.y is positive, that is, above the x-axis.Hence:
Letter K represents the second quadrant.
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HELP ME PLEASE THS IS ABOUT GEOMETRY THNKS
Using proportions, the coordinates of point C are given as follows:
C(0, -0.67).
What is a proportion?A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.
Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.
For this problem, the points are given as follows:
A(-4,-6), B(5,6), C(x,y).
The ratio of AC to CB is of 4:5, hence the following equation is constructed:
C - A = 4/9(B - A).
As the ratio of 4:5 means that the distance is 4/(4 + 5) = 4/9.
The x-coordinate of C is found applying the above equation as follows:
x + 4 = 4/9(5 + 4)
x + 4 = 4
x = 0.
The y-coordinate of C is also found applying the equation, as follows:
y + 6 = 4/9(6 + 6)
y + 6 = 5.33.
y = -0.67.
Hence the coordinates of point C are given as follows:
C(0, -0.67).
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Two angles are supplementary is the measure of one angle is 65.3 degrees what is the measure of the
other angle? Answer to the first decimal place, ie 79.5
The measure of the other angle is 114.7.
Given that the angles are supplementary,
Let the other angle be 'x'.
x + 65.3 = 180 degree
x = 114.7
hence, The other angle is 114.7 degrees.
The term "supplementary angles" refers to a pair of angles that always add up to 180°. These two perspectives are known as supplements. The term "supplementary" is derived from the Latin words "supply" and "plere," where "supply" means "supply" and "plere" means "fill." As a result, "supplementary" means "something that is supplied to complete a thing."
If two angles add up to 180 degrees, they are said to be supplementary angles. When supplementary angles are combined, they form a straight angle (180 degrees). In other words, if Angle 1 + Angle 2 = 180°, angles 1 and 2 are supplementary. Angles 1 and 2 are referred to as "supplements" in this case.
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i really do need help with this geometry questions please hlep
the coordinate of X is at 8 units of P and at 4 units to the left of Q
So the coordinate of X is: -5 + 8 = 3
How to find the coordinates of point x?
We know that point X is between points P and Q, in such a way that the ratio between the lengths of the segments PX and XQ is 2:1
First, we can length of the segment PQ is equal to the difference between their coordinates, so we get:
L = 7 - (-5) = 12
Then the length of segment PQ is 12 units, if we divide that in 3 we will get:
12/3 = 4 units.
So the segment PQ can be divided into 3 segments of 4 units each.
If the ratio PX to XQ is 2:1
Then the segment PQ must be divided into 3 parts, such that PX takes two of these parts and XQ is the remaining one.
Then the coordinate of X is at 8 units of P and at 4 units to the left of Q
So the coordinate of X is: -5 + 8 = 3
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Beinggreat78 and subtomex0 are amazing
ignore that I selected A it was an accident-
Answer:
B
Step-by-step explanation:
Because 3/20 is 15%, 20%, 25%, 33%
All my work and answer is provided in the attached screenshot!
Have a great day!
5.
Solve the equation 18 = (36.4-n) using your preferred method.
After solving the Linear equation, the value of the n becomes 18.4.
According to the statement
We have to find that the value of the n.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
The equation is 18 = (36.4-n)
Then we have to solve it
(36.4-n) = 18
36.4 -18 = n
After rearrange it then
n = 36.4 -18
Now subtract the equation, then
n = 18.4.
So, After solving the Linear equation, the value of the n becomes 18.4.
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find the quotiont: 2,009 ÷ 87=
please help
find the area of the circle 8
Answer:
50.24 in²
Step-by-step explanation:
[tex]A = \frac{1}{4} \times (22/7) \times 8^2 = 0.25 \times 3.14 \times 64\\= 50.24[/tex]
➲ Hope this helps.
➲ Wish you the best of luck. :)
diameter of circle= 8 inch.
so, radius of circle= d/2 = 4 inch
now
area of circle=πr²
22/7 × (4)²
50.24 inc.
find the value of x -7 when x=20.
Answer:
13
Step-by-step explanation:
When x=20
=x-7
=20-7
=13
A local pizza shop has a membership program for frequent buyers. The membership costs $20 per month and members get a discounted price of $1.25 per slice of pizza. Chee purchased a membership to this pizza shop. How much would Chee have to pay the pizza shop if she bought 12 slices of pizza this month? What would be the monthly cost for x slices of pizza?
Answer:
$35 for 12 slices
Monthly cost for x slices of pizza = 20 + 1.25x
Step-by-step explanation:
Monthly Membership cost = $20
Discounted cost per slice of pizza = $1.25
Discounted total cost for 12 slices = $1.25 x 12 = $15
Total cost = 20 + 15 = $35 this momth
For x slices of pizza, monthly cost = 20 + 1.25x
Order the numbers from greatest to least 44.912 , 44.102 , 44.120
Answer:
44.912, 44.120, 44.102,
Step-by-step explanation:
Is -22 a rational number?
Yes, it is a rational number
What is -y+9z-16y-25z+4 written in simplest form
graph each equation by using a table -3=5x-y
The graph of the equation is shown below
Graph of linear equations
From the question, we are to graph the given equation
The given equation is
-3 = 5x - y
To graph the equation,
First we will determine the x-intercept and y-intercept
x-intercept
Put y = 0 in the equation
-3 = 5x - 0
-3 = 5x
x = -3/5
y-intercept
Put x = 0 in the equation
-3 = 5(0) - y
-3 = 0 - y
-3 = -y
y = 3
Using the x-intercepts and y-intercepts, we can plot the graph of the equation.
The graph of the equation is shown below
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What is the answer to 534÷112?
Answer: it is 4.76785714286
Step-by-step explanation:
Can someone help me please? Giving lots of points!
Answer:
14 units,
Step-by-step explanation:
Just count down the graph
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
Answer:
the answer would be 14 units
Step-by-step explanation:
you can count down between the distance with the first point and the second point
Find the slope of the line if it exists.
Answer: 5/4
Step-by-step explanation: You go up five from point (-6,0) and across for to point (-2,4)
FIND VALUE
A) tan 30° + cot 30° + sin 60°
Answer: [tex]\frac{4\sqrt{3} }{3} +\frac{1}{2}[/tex]
Step-by-step explanation:
You can either do this manually or use your calculator. Using your calculator, make sure that your calculator is in degree mode, then enter tan(30) + (1/tan(30)) + sin(60). [1/tan(30) is equal to cot(30) because tangent and cotangent are inverse functions].
Manually, use the unit circle. Tangent is sine over cosine. Sine of 30 degrees is 1/2. Cosine of 30 degrees is [tex]\sqrt{3} /2[/tex]. 1/2 divided by [tex]\sqrt{3}/2[/tex] is [tex]\sqrt{3}/3[/tex]. Cotangent is 1/tangent so take 1/[tex]\sqrt{3}/3[/tex] which is [tex]\sqrt{3}[/tex]. Then we already said that sine of 30 degrees is 1/2, so add them all together.
[tex]\sqrt{3}/3+\sqrt{3}+\frac{1}{2}[/tex] which is equal to [tex]\frac{4\sqrt{3} }{3} +\frac{1}{2}[/tex] or approximately 2.8094.
There are about 7,000,000,000 people in the world. In Australia, there is a population of about
2.306 x 107 people. What is the difference between the world's and Australia's populations?
If there are about 7,000,000,000 people in the world and In Australia, there is a population of about 2.306 x [tex]10x^{7}[/tex] people, then the difference between the world's and Australia's populations is 697.694×[tex]10^{7}[/tex]
Given,
The total population of world = 7,000,000,000 peoples
Convert to suitable standard form
7,000,000,000 peoples = 700× [tex]10^{7}[/tex] peoples
The population of Australia = 2.306×[tex]10^{7}[/tex]
The difference = The population of world - The population of Australia
=700× [tex]10^{7}[/tex]-2.306×[tex]10^{7}[/tex]
=(700-2.306)×[tex]10^{7}[/tex]
=697.694×[tex]10^{7}[/tex]
Hence, If there are about 7,000,000,000 people in the world and In Australia, there is a population of about 2.306 x [tex]10x^{7}[/tex] people, then the difference between the world's and Australia's populations is 697.694×[tex]10^{7}[/tex]
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Multiplication equation-
X
Groups
10. Write a multiplication equation for each one.
a) 2+2+
2+2 + 2 =
b.) 5+5+5+5+5=
c.) 4 groups of 3 =
Draw a picture of 4 groups of 3
------->
--->
->
X
X
X
=
we get the the multiplication equations are 2 + 2 + 2 + 2 + 2 = 2 × 5, 5 + 5 + 5 + 5 + 5 = 5 × 5 and 4 groups of 3 = 3 × 4.
We are given some expressions and we need to find the multiplication equation for each one.
a) 2 + 2 + 2 + 2 + 2 will be
Since, 2 is repeating 5 times, we get that:
multiplication equation will be:
2 + 2 + 2 + 2 + 2 = 2 × 5
b) 5 + 5 + 5 + 5 + 5 will be
Since, 5 is repeating 5 times, we get that:
multiplication equation will be:
5 + 5 + 5 + 5 + 5 = 5 × 5
c ) 4 groups of 3 will be
Since, 3 is repeating 4 times, we get that:
multiplication equation will be:
4 groups of 3 = 3 × 4
Therefore, we get the the multiplication equations are 2 + 2 + 2 + 2 + 2 = 2 × 5, 5 + 5 + 5 + 5 + 5 = 5 × 5 and 4 groups of 3 = 3 × 4.
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What is the answer to this?
$8.72 - $4.90
$8.72 - ___________ = $3.72
____________ + $0.10= _______
71500 divided by 8 long division
Answer:
The answer is 8,937.5
Step-by-step explanation:
71500÷8
8×8=64
71-64=7
7500÷8
8×9=72
75-72=3
300÷8
8×3=24
30-24=6
60÷8
8×7=56
60-56=4
4.0÷8
8×5=40
40-40=0
Please show work, and brainliest will be yours.
Now, because the conditional and converse are true, then we have a biconditional relation between P and Q.
From that, we conclude that the truth values for the two above statements is true for both
What are the truth values of the contrapositive and inverse statements?
A conditional statement is of the form:
If P, then Q.
The inverse statement is:
if Q, then P.
We assume that these two are true.
An example of this is:
P = a number is even.
Q = a number is a multiple of 2.
Then the two above statements are:
conditional: If a number is even, then the number is a multiple of 2.converse: if a number is a multiple of 2, then it is even.Now the inverse statement is:
if not P, then not Q.
The contrapositive is:
If not Q, then not P.
Now, because the conditional and converse are true, then we have a byconditional relation between P and Q.
From that, we conclude that the truth values for the two above statements is true for both, but let's check with our propositions:
Inverse: If a number is not even, then it is not a multiple of 2. (this is true)
Contrapositive: If a number is not multiple of 2, then it is not even (also true).
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A cone-shaped pile of sawdust has a base diameter of 40feet, and is 17feet tall. Find the volume of the pile.
Answer:
7120.94 cubic feet
Step-by-step explanation:
volume of a cone =
pi times radius squared times (height ÷ 3)
pi times 20 squared times (17 ÷ 3)
Solve this solution. WILL GIVE BRAINLIEST
Answer:
impossible
Step-by-step explanation:
what is in the absolute value have to be positive so it's impossible that |2x+5| is < or = at -7