If , choose the line of reflection between the two congruent triangles.
Answers
The line of reflection of the given congruent angles is the y-axis.
What is the line of reflection?
A line of reflection is defined as a line that lies in a position between two identical mirror images so that any point on one image is the same distance from the line as the same point on the other flipped image
Now, from the attached image, we see that the two given congruent triangles are; ΔAHJ and ΔADB
Now, we see that the coordinates are transformed as folllows;
D(5, 2) → H(-5, 2)
B(3, 0) → J(-3, 0)
Now, this type of transformation follows the transformation rule; (x, y) → (−x, y). This means it was reflected over the y-axis.
This the line of reflection of the given congruent angles is the y-axis.
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Related Questions
What is the turning point of the graph of ƒ(x) = |x| +4 ? (0,4) (0, – 4) (4,0) (-4, 0)
Answers
The turning point of the function f(x) = |x| + 4 lie on the y - axis and has coordinates (0, 4).
What is Turning point of a graph?A stationary point is called a turning point if the derivative changes sign (from positive to negative, or negative to positive ) at that point. There are two types of turning points - local maxima and local minima.
Given in the question is a modulus function -
f(x) = |x| + 4
In order to determine the turning point, we will first have to plot the graph of this function -
f(x) = |x| + 4
Now, we can write f(x) as -
f(x) = { (x + 4) for x ≥ 0 and (- x + 4) for x < 0} }
Alternatively, you can plot the graph of |x| and positive shift it by 4 units. Refer to the graph attached with the answer. From the graph you can see that after the coordinate (0, 4) the slope becomes positive. Slope of a line gives the rate of change of y with respect to x. So (0, 4) represents the turning point.
Therefore, the turning point of the function f(x) = |x| + 4 lie on the y - axis and has coordinates (0, 4).
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2. 7th-grade easy math PLEASE Answer this is for a grade
SHOW YOUR WORK AND TAKE A PICTURE
PLS
PLEASE Answer correctly this is for a grade
SHOW YOUR WORK AND TAKE A PICTURE
Answers
The expression on the table shows that the shelf pace that the books take is 1 inch per book.
How to calculate the value?Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
It should be noted that from the table, the relationship between the books and the inches is illustrated on the table.
Relationships between two variables that are proportional occur when their ratios are equal. Therefore, this is a proportional relationship and is illustrated as:
= 2/2
= 1
Therefore, there's 1 inch per book.
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How do I solve this problem?
Answers
Answer:
y = 16(x +2)
Step-by-step explanation:
The equation of the tangent to a curve at a point can be written using the point-slope form of the equation for a line. The point is (x, f(x)), and the slope is the derivative, f'(x).
Point and slopeThe point where you want the tangent line has y-value ...
y = 2(-2)³ -8(-2) = 2(-8)+2(8) = 0 . . . . . point (x, y) = (-2, 0)
The slope at the point where you want the tangent is ...
y' = 2·3x² -8 = 6(-2)² -8 = 24 -8 = 16 . . . . . slope m = 16
Equation of the tangent lineThe point-slope equation of a line is ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
y -0 = 16(x -(-2)) . . . . . line with slope 16 through (-2, 0)
y = 16(x +2) . . . . . simplified
An equation of the tangent line is ...
y = 16(x +2)
Adventure Travel has an Adjusted Trial Balance for Year Ended December 31, 20XX with the following account balances:
DEBITS: Cash: 25,000; Accounts Receivable: 15,000; Office Supplies: 4,300; Office Equipment: 29,600
CREDITS: Accumulated depreciation - office equipment: 5,000; Salaries Payable: 2,800; Long-term notes payable: 22,200; Common Stock: 20,000; Retained Earnings: 10,260
DEBIT: Cash Dividends: 1,000
CREDITS: Fees Earned: 75,000
DEBITS: Salaries Expense: 32,800; Rent Expense: 16,800; Depreciation expense - office equipment: 3,960; Advertising expense: 4,000; Office supplies expense: 2,800.
Total Debits = 135,260; Total Credits = 135,260
You have prepared the financial statements for December 20XX. Now, it is time to make the closing entries.
We will close the revenue accounts first: what dollar amount will I record for the debit and credit accounts? Specify as a whole number.
Answers
The closing entries to record the given transaction is: Debit Fees earned $75,000, Credit Income summary $75,000.
Closing journal entriesAdventure Travel journal entries
1. Debit Fees earned $75,000
Credit Income summary $75,000
2. Debit Income summary $60,360
Credit Salaries expense $32,800
Credit Rent expense $16,800
Credit Depreciation expense-Office equipment $3,960
Credit Advertising expense $4,000
Credit Office supplies expense $2,800
3. Debit Income summary $14,640
($75,000 - $60,360)
Credit A. Garcia, Capital $14,640
4. Debit A. Garcia, Capital $1,000
Credit A. Garcia, Withdrawals $1,000
Therefore the closing entries to record the given transaction is: Debit Fees earned $75,000, Credit Income summary $75,000.
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Consider two markets: the market for cat food and the market for dog food. The initial equilibrium for both markets is the same, the equilibrium price is $6.50, and the equilibrium quantity is 35.0. When the price is $6.75, the quantity supplied of cat food is 59.0 and the quantity supplied of dog food is 101.0
Using the midpoint formula, calculate the elasticity of supply for dog food. Please round to two decimal places.
Answers
The elasticity of supply for dog food is 25.71
What is the elasticity of supply?Price elasticity of supply measures the responsiveness of quantity supplied to changes in price of the good.
Price elasticity of supply = midpoint change in quantity supplied / midpoint change in price
Midpoint change in quantity supplied = change in quantity supplied / average of both supply
change in quantity supplied= 101 - 35 = 66
average of both supply = (101 + 35 ) / 2 = 68
Midpoint change in quantity supplied = 66 / 68 = 0.97
Midpoint change in price = change in price / average of both price
Change in price = 6.75 - 6.50 = $0.25
Average of both price = (6.75 + 6.50) / 2 = $6.625
Midpoint change in price = 0.25 / 6.625 = 0.03774
Price elasticity of supply = 0.97 / 0.03774 = 25.71
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How to make 10 + 4 x 12 -6 34
Answers
Answer:
(10 + 4) * (12 - 6) = 84Step-by-step explanation:
(10 + 4) * (12 - 6) = 34= 14 * 6 = 34= 84 ≠ 34The original one is false, with the answer being 84.
If there is 6 A of current through the filament of a lamp, how many coulombs of charge move through the filament in 1.75 s?
Answers
In 6A, 10.5 coulomb of charge is moved through the filament in 1.75 seconds.
What is charge?The electrical current that flows across conducting wires is carried by electrons, which are tiny particles. Negatively charged particles are electrons.
Charge is expressed in coulombs, or C.
The charge of an electron is 1.6 x[tex]10^{-19}[/tex]C.
The connection between current I and charge amount Q
Charged particle flow is what makes up an electric current.
One ampere of current flows when one coulomb of charge passes through a certain place in a circuit once every second.
The magnitude of an electric current affects how quickly charges flow.
I =[tex]\frac{quantity of charge(Q)}{Time taken (t)}[/tex]
Given: current I= 6A at time t=1.75s,
I = Q / t
Q = I x t
Q = 6 x 1.75
Q = 10.5 coulomb
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Consider the equation 2y-5x = 30. Determine the x-intercept.
Enter your response in the boxes.
2.
-5r = 30
_52 = 30
- 30
x =
Answers
The value of the x-intercept is -6
According to the question we have been the equation which is :
2y - 5x = 30 (1)
The general expression of slope intercept form is given as :
y = mx + c
where, m = slope
c = y-intercept
To find the value of x-intercept we will write equation (1) as an equation for x that is
-5x =-2y + 30
Dividing both the sides by -5 we get
x = 2/5y + (-6)
Which is in the form of slope intercept form which is
x = my + c and the x- intercept will be c = -6
Hence the x-intercept is -6
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Help please with this question
Answers
Answer:
perimeter: 26 unitsarea: 22 square unitsStep-by-step explanation:
You want the perimeter and area of the given composite figure.
PerimeterYou will notice that the sum of vertical lengths on the right side of the figure has the same total as the vertical length on the left side:
2 + 1 + 1 = 4 . . . . units high
Likewise, the horizontal lengths at the top of the figure have the same total as the horizontal length at the bottom:
4 + 1 + 4 = 9 . . . . units wide
The perimeter is the sum of all side lengths, so is ...
P = 2(L+W) = 2(9 +4) = 26
The perimeter of the polygon is 26 units.
CompositionThe blue lines in the attachment show the area can be divided into rectangles whose area is easily computed. The top rectangle has a width of 4 units and a height of 2 units, so its area is ...
A = WH = (4)(2) = 8 . . . . square units
The middle rectangle has a width of 5 units and a height of 1 unit, so its area is ...
A = WH = (5)(1) = 5 . . . . square units
The bottom rectangle has a width of 9 units and a height of 1 unit, so its area is ...
A = WH = (9)(1) = 9 . . . . square units
AreaThe total area of the polygon is the sum of the areas of its parts:
area = top rectangle + middle rectangle + bottom rectangle
= (8 + 5 + 9) square units = 22 square units
The area of the polygon is 22 square units.
perimeter = 26 units
Area = 22 square units
Step by step
The perimeter is found by adding up all the sides. This polygon has many sides. See the attachment for help how to add the sides and find the unknown side lengths.
If you add the horizontal lengths of 4 + 1 + 4 = 9, the base will equal 9 also.
If you add the vertical lengths of 1 + 1 + 2 = 4, the unknown vertical side will also equal 4.
9 + 9 + 4 + 4 = 26 units perimeter
Area is found by multiplying length x width. For area, I broke the figure into three rectangular shapes to find equal sides for multiplying.
The three shapes are
4x4 = 16
2 x 1 = 2
4 x 1 = 4
________
Total area is 22 square units
Problem solved!
LESSON 8.2
Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.
Answers
Based on the central angle theorem:
1. m<RQS = 100°
2. m<IJH = 70°
3. m<TQR = 100°
What is the Central Angle Theorem?The measure of the central angle of a circle is the same as the measure of the intercepted arc, according to the central angle theorem.
1. m<RQS = measure of arc RS [central angle theorem]
Measure of arc RS = 180 - 80
Measure of arc RS = 100°
m<RQS = 100°
2. m<IJH = measure of arc HI [central angle theorem]
Measure of arc HI = 360 - 140 - 150
Measure of arc HI = 70°
m<IJH = 70°
3. m<TQR = measure of arc TR [central angle theorem]
Measure of arc TR = 360 - 120 - 140
Measure of arc TR = 100°
m<TQR = 100°
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Help, please! I can't figure out how to solve this problem for my geometry class. Please give me a clear, step-by-step answer to receive 20 points for your brainly score. Thanks!
Answers
The equation is 2x - 8 + 11 = x + 10
The value of x is 7
The value of RS is 6
The value of RT is 17
Solving linear equationsFrom the question, we are to write and solve an equation for x
From the given information,
RS = 2x - 8
ST = 11
RT = x + 10
From above, we can write that
RS + ST = RT
Thus,
2x - 8 + 11 = x + 10
Solve the equation for x
2x - 8 + 11 = x + 10
2x - x = 10 - 11 + 8
x = 7
∴ The value of x is 7
Now,
For the values of RS and RT
RS = 2x - 8
∴ RS = 2(7) - 8
RS = 14 - 8
RS = 6
and
RT = x + 10
RT = 7 + 10
RT = 17
Hence,
The equation is 2x - 8 + 11 = x + 10
The value of x is 7
The value of RS is 6
The value of RT is 17
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-Solve the equation. Write a reason for each step. 12x = 28 - 16x
Answers
1. Add 16x to both sides
We do this step because we need to eliminate the variable from the right side of the equation. There is a -16 on the right side, and in proper form, x would have to be isolated on the left side. This would look like:
12x + 16x = 28 - 16x + 16x
2. Simplify
We do this step because it makes the equation easier to solve. This would look like:
28x = 28
3. Divide both sides by 28
We do this step because we need to get x by itself on both sides. To do that, we divide by whatever number is the coefficient. This would look like:
28x / 28 = x
28 / 28 = 1
x = 1
This isn’t a required step, but we can plug 1 in for x to make sure our answer is correct:
12(1) = 28 - 16(1)
12 = 28 - 16
12 = 12
Our answer is correct.
Answer Recap: x = 1
Ex.1. Nine counters numbered 1, 2, 3, 4, 5, 6, 7, 8, 9 are placed in a bag One is taken out at random. What is the probability that it is: (a) a 5 (c) less than 5 (b) divisible by 3 (d) divisible by 4.
Answers
The probabilities for the given situations are:-
a) 1/10
b) 2/5
c) 3/10
d) 1/5
Probability = Number of Favorable Outcomes/Number of outcomes
For a) P( getting 5) = 1/10
b) P( getting less than 5) = 4/10 , (Favorable outcomes = 1,2,3,4)
= 2/5
c) P (divisible by 3 ) = 3/10 , (Favorable outcomes = 3,6,9)
d) P( divisible by 4) = 2/10 , (Favorable outcomes = 4, 8)
= 1/5
So, the probabilities for the given situations are:-
a) 1/10
b) 2/5
c) 3/10
d) 1/5
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Type an equation for the following pattern.
Answers
Answer:
Slope(green box) = -3
Intercept(grey box) = 8
Step-by-step explanation:
To determine the best equation to represent the given pattern, we need to find two things.
First: we need to figure out the slope of the function, or in other words, how much the y value changes by each time the x value changes.
Second: we need to find the y-intercept, which is the value of y when x = 0. This value will be the constant of the function which is added to the equation each time.
To start, let's analyze the pattern to find the slope of the function...
As the x -values go up by 1 each time, the y-values are as follows:
5 --> 2 --> -1 --> -4 --> -7
It looks like the numbers decrease by 3 each time, so we can safely assume our slope is -3.
Now, let's find our intercept. We can do this by going to our lowest x value, and adding 3 (opposite direction of our slope) from its y-value to find the y-value of x = 0.
So...
When x = 1, y = 5
5 + 3 = 8
So when x = 0, y = 8, our intercept!
If two triangle angles are 37 and 69 what is the third angle?
Answers
Answer:
37+69=106
180/106= 74
Step-by-step explanation:
its 74
Answer: 74°
Step-by-step explanation:
the two angles are first added
the sum of a triangle is 180° so the third angle equal 180- sum of angles.
37+69=106
180-106= 74°
An architect has designed two tunnels. Tunnel A is modeled by x2 + y2 + 28x + 52 = 0, and tunnel B is modeled by x2 – 36x + 16y + 68 = 0, where all measurements are in feet. The architect wants to verify whether a truck that is 8 feet wide and 13.5 feet high can pass through the tunnels.
Part A: Write the equation for Tunnel A in standard form and determine the conic section. Show your work. (4 points)
Part B: Write the equation for Tunnel B in standard form and determine the conic section. Show your work. (4 points)
Part C: Determine the maximum height of each tunnel. Is the truck able to pass through either tunnel without damage? If so, which tunnel(s) and why? Show your work. (7 points)
Answers
Considering the equations of a circle and of a parabola, we have that:
a) Tunnel A is a circle, with it's radius meaning that both the width and the height are of 12.
b) Tunnel B is a parabola, with it's vertex and it's roots meaning that it has a width of 32 feet and a height of 16 feet.
c) The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
For Tunnel A, the equation is given by:
x² + y² + 28x + 52 = 0
Completing the squares:
(x + 14)² + y² = -52 + 14²
(x + 14)² + y² = 144.
Hence:
Tunnel A is a circle, with it's radius meaning that both the width and the height are of 12.
What is the vertex of a quadratic equation?A parabolic(quadratic) equation is modeled by:
y = ax^2 + bx + c
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]For Tunnel B, the equation is given as follows:
x² - 36x + 16y + 68 = 0.
16y = -x² + 36x - 68.
Simplifying by 16:
y = -0.0625x² + 2.25x - 4.25.
Hence the coefficients are a = -0.0625, b = 2.25, c = -4.25, and the maximum height is:
[tex]y_v = -\frac{(2.25)^2 - 4(-0.0625)(-4.25)}{(-0.0625)} = 16[/tex]
The width is the difference between the roots, which, using a calculator, are:
2 and 34, hence the width is of 32 feet, as 34 - 2 = 32.
Hence:
Tunnel B is a parabola, with it's vertex and it's roots meaning that it has a width of 32 feet and a height of 16 feet.
For item c, considering the previous items, we have that:
The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.
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Tamika has 48 pencils and 80 pens that she is dividing up evenly in teacher supply boxes that
will contain both pencils and pens.
(a) What is the greatest number of boxes she can use so that each box contains the same
number of pencils and each box contains the same number of pens? Justify.
Hint: Look at the bold underlined word, that should be a good clue as to what strateg
to use.
(b) Based on your answer to (a), how many pencils and how many pens will be in each b
The Upside Down Birthday Cake/Ladder Method works great here.
Answers
(a) The greatest number of boxes she can use so that each box contains the same number of pencils and pens is 48.
(b) There will be 48 pencils and pens in each box.
We have given that Tamika has 48 pencils and 80 pens.
So, the greatest number of boxes is 48, because the total number of pencils is 48, in order to share the same number of pencils and pens, the greatest number of boxes would be 48.
And,
Based on above answer and according to question's statement (each box contains the same number of pencils and each box contains the same number of pens), so, there will be one pencil and one pen in each box.
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i know how to do a and b, but how do i do c and d? thanks
Answers
Answer:
1c 12
1d 4x - 3
2c 10x + 20
2d 60x² + 160x + 100
3c
Domain is -3 ≤ x ≤ 3
Range is -2 ≤ g(x) ≤ 2
Step-by-step explanation:
Question 1 : f(x) = 2x - 3
1c. 3 - f(-3)f(-3) = 2(-3) - 3 = -6 - 3 = -9
3 - f(-3) = 3 - (-9) = 12
1d. f(2x)
f(2x) = 2(2x) - 3 = 4x - 3
Question 2: f(x) = 8x + 10, g(x) = 2x
2c: 2f(x) - 3g(x)2f(x) - 3g(x) = 2(8x + 10) - 3(2x) = 16x + 20 - 6x = 10x + 20
2d : (f(x))² - (g(x))²
f(x)² - g(x)² = ( f(x) + g(x) ) . (f(x) - g(x)).
This uses the fact that a² - b² = (a+b)(a-b)
f(x) + g(x) = 8x + 10 + 2x = 10x + 10
f(x) - g(x) = 8x + 10 - 2x = 6x + 10
f(x)² - g(x)² = (10x + 10) . (6x + 10)
Apply FOIL method: (a + b)(c + d) = ab + bc +cd + bd
(10x + 10) x (6x + 10) = (10x)(6x) + (10x)(10) + (10)(6x) + (10)(10)
= 60x² + 100x + 60x + 100
= 60x² + 160x + 100
100 POINTS NEED HELP ASAP
A line passes through point (2,3) and has a slope of -4.
Write an equation in Ax + By = C form for this line.
Use integers for A, B, and C.
Answers
Answer:
Step-by-step explanation:
Point slope formula y - y1 = m( x - x1)
y - 3 = -4(x - 2)
y - 3 = -4x + 8
y = -4x + 11
check
(2,3)
Y = -4x + 11
3 = -4(2) + 11
3 = -8 + 11
3 = 3
Standard form 4x + y = 11
what is the answer to
-33/11?
Answers
Answer: -3
Step-by-step explanation: -33 ➗11= -3
amplitude and period of y = 1 + cos 0
Answers
Amplitude and period of y = 1 + cos 0 are amplitude: = 1 and period: 2π respectively.
The cosine function cosx is one of the basic functions encountered in trigonometry
y = 1 + cos 0
Rewrite the expression as
−cos(x)+1.
Use the form
acos(bx−c)+d
To find the variables used to find the amplitude, period, phase shift, and vertical shift.
a =-1
b =1 = d
c=0
Find the amplitude
Let
Amplitude: = 1
Phase Shift: = 0
List the properties of the trigonometric function.
Amplitude: 1
Period: 2π
Phase Shift: None
Vertical Shift: 1
So the amplitude and period of the equation y = 1 + cos 0 are 1 and 2 correspondingly.
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The amplitude and period of the equation y = 1 + cos 0 are 1 and 2 correspondingly.
The cosine formula One of the fundamental trigonometry functions is cosx.
y = 1 + cos 0
Change the wording to
−cos(x)+1.
Apply the form
acos(bx−c)+d
to identify the parameters used to calculate the vertical shift, phase shift, amplitude, and period.
a =-1
b =1 = d
c=0
Measure the amplitude.
Let
Amplification: 1
0 for phase shift
Describe the trigonometric function's characteristics.
1 amplitude
Duration: 2
No phase shift
Shift Vertically: 1
As a result, y = 1 + cos 0 has an amplitude and period of 1 and 2, respectively.
What is the value of x?
Answers
Answer:
x=2
Step-by-step explanation:
All of the dimensions on the Left (hex) = all of the dimensions summed on the Right (tri)
6 (5x) = x+14 + x+17 + 8x+9
30x = 10x + 40
20x=40
x = 2
Answer:
x = 2
Step-by-step explanation:
6(5x) = x + 14+ x +17 + 8x +9
30x = (10x + 40)
Substrate 10x from both sides.
30x-10x = 30x-10x+40
20x = 40
Divide both sides by 20
x = 2
Therefore x = 2
To check out your work
the both sides are equal.
Substitute x for 2.
6(5x) = x + 14+ x +17 + 8x +9
60 = 60
find the smallest number which when doubled will be exactly divisible by 4, 10, 15
Answers
60:4=15
60:10= 6
60:15= 4
Let the number be x
So 2x is divisible by 4,10,15
Divisible means find the LCM of those three numbers which is 60
2x=60
Divide both sides by 2
x=30
An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in. tall, and the initial velocity of the ball is 40 ft per sec. The height s of the ball in feet is given by the equation s equals negative 2.7 t squared plus 40 t plus 6.5s=−2.7t2+40t+6.5, where t is the number of seconds after the ball was thrown. Complete parts a and b. a. After how many seconds is the ball 10 ft above the moon's surface?
Answers
The ball when thrown at initial velocity of 40ft/sec is 10 ft above the moon's surface after approximately 0.09 seconds and 14.73 seconds .
When an item is moving, its velocity is the rate at which its direction is changing as seen from a certain point of view and as measured by a specific unit of time.
The given equation for the height of the ball from the surface after t seconds is given by :
s=-2.7t²+40t+6.5
The initial velocity is 40ft/second.
the height of the ball is 10 ft from the surface.
therefore: s=10
Substituting the value in the equation we get:
10=-2.7t²+40t+6.5
or, -2.7t²+40t-3.5=0
This is a quadratic equation in t . Solving by the quadratic formula we get:
We know that for a equation: ax²+bx+c=0
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}[/tex]
So using the above equation we get:
[tex]{\displaystyle x={\frac {-40\pm {\sqrt {40^{2}-4(-2.7)(-3.5)}}}{2(-2.7)}}}[/tex]
either x=14.726... or x= 0.088...
Therefore x≈14.73 and x≈ 0.09
So the ball will be 10 ft above the moon's surface after approximately 0.09 seconds or 14.73 seconds .
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The area of the garden is 289 square feet, how many feet of fencing needs to be brought? If fencing costs $9, how much will it cost?
Answers
The cost of fencing the garden is 2601 dollars.
How to find the cost of fencing the garden?The area of the garden is 289 square feet.
The fencing cost 9 dollars per square feet's.
Therefore, the cost to fence a garden with area of 289 square feet can be calculated as follows:
Hence,
1 square feet's = 9 dollars
289 square feet = ?
cross multiply
Hence,
cost of fencing the garden = 9 × 289
cost of fencing the garden = 2601
cost of fencing the garden = 2601 dollars
Therefore, the cost of fencing the garden is 2601 dollars.
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The length of a Fruity Chew is a normally distributed random variable X with an average width of
1.2 cm and a standard deviation of 0.12 cm (Ms Pitt did a lot of "research").
a.
Find the probability, correct to four decimal places, that the length of a selected Fruity
Chew is
i.
between 0.8 and 1.5 centimetres
Answers
The probability that a selected fruity chew length is between 0.8 and 1.5 cm is 0.00578.
A fruity chew's length is normally distributed with random variable X with an average width of 1.2 cm.
The standard deviation is 0.12 cm.
Therefore, mean μ = 1.2 cm and;
Standard deviation, σ = 0.12 cm
Now, the probability is given as:
z = ( x - μ ) / σ
The probability that the length of a selected fruity chew is between 0.8 and 1.5 cm.
P( 0.8 < x < 1.5 )
For, P( X > 0.8)
z = ( x - μ ) / σ
z = ( 0.8 - 1.2 ) / 0.12
z = - 0.4 / 0.12
z = - 3.33
Using the z score table,
P( X > 0.8 ) = 0.99957
For P( x < 1.5),
z = ( x - μ ) / σ
z = ( 1.5 - 1.2 ) / 0.12
z = 2.5
Using the z score table,
P( X < 1.5) = 0.99379
Therefore, the probability is between 0.8 and 1.5 cm will be:
= 0.99379 - 0.99957 = 0.00578
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HELP ASAP PLEASE AND THANK YOUUU i will mark you brainliest!!!!!!!
Answers
Answer:
(2,0)
Step-by-step explanation:
Answer:
2,0
Step-by-step explanation:
brainliest please, also have a nice day ^^
Please help me with this question asap. it’s due tonight
Answers
The horizontal line passing through the point (2/3, 1/2) is represented by the equation y = 1/2.
What is slope intercept form?y=mx+c
where m is the slope.
As stated in the problem the line is horizontal. This means that its slope is zero.
y-y1=m(x-x1)
y-1/2=0(x-2/3)
y-1/2=0
y=1/2.
Mathematically it means that it is a line parallel to the x-axis and passing through y = 1/2.
The horizontal line passing through the point (2/3, 1/2) is represented by the equation y = 1/2.
Therefore horizontal line passing through the point (2/3, 1/2) is represented by the equation y = 1/2.
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For someone to solve this question for me
Answers
1.) Read through the questions and interpret what it means. Ask yourself, what is the slope and y-intercept and how do I find them? What is slope-intercept form and how do I input this information into it?
2.) First, recall slope-intercept form, slope, and y-interception. The name “slope-intercept” means the equation form with the slope and y-intercept, hence, “slope-intercept.” Remember, anytime you hear this, decode it to slope and y-intercept. So, you know that slope-intercept is in the form: y=mx+b. With this, m=slope, and b=y-intercept. More specifically, the slope (m) is ratio of rise over run of the graph, so m=rise/run. The y-intercept is the starting point and where the graph intercepts the y-axis.
3.) So, we need to find the slope and y-intercept to use y=mx+b, since this is the required information in this form to graph the equation.
• m(slope) formula = y2-y1/x2-x1
- This formula is the difference of y-values over the difference of x-values, which simplifies to vertical change/lateral change or rise/run.
4.) Pick two coordinate pairs, so we can use the slope formula. Remember, two coordinate pairs looks like: (x1, y1) and (x2, y2).
The points (0,4) and (6, 2) are exact intercepts, meaning they intercept the coordinates exactly, so they don’t contain decimals or fractions.
5.) Input these points into the slope formula:
• m=(2)-(4)/(6)-(0)
- note that parenthesis are used when substituting in for a variable.
• m=-2/6
- remember to simplify the slope to a unit rate.
• m=-1/3
So, the graph goes down 1 unit and over 3 units.
6.) To find the y-intercept, we can look at the graph and see where it intercepts the y-axis, or substitute in x=0. Both methods will tell us that b=4.
7.) Input m and b into y=mx+b:
y=(-1/3)x+(4); m=-1/3 and b=4
Use the diagrams. Name a pair of nonadjacent supplementary angles.
1. KJL
2. KJM
3. MJN
4. MJP
5. FGH
6. LJM
7. FGE
8. NJP
9. LJN
Answers
From the given diagram, the pair of angles that are non-adjacent and supplementary are given as follows:
5. FGH
6. LJM
What are non-adjacent and supplementary angles?Supplementary angles are angles whose measures add to 180º.Non-adjacent angles do not have a common arm neither a common vertex.Hence, we need one angle among vertices E, F, G and H, and other with vertices K, J, L, M, N, P, to guarantee the non-adjacency. The angles are:
5. FGH
6. LJM
As:
FGH = 124º.LJM = 56º.124 + 56 = 180º, meaning that they are supplementary.
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