The left-hand side of the equation becomes (x - 4)² while the right side of the equation is 25
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The standard form of a quadratic equation is given by:
0 = Ax² + Bx + C
Where A, B and C are constants.
Given the quadratic equation:
x² - 8x = 9
To solve the quadratic equation using the completing square method, add to both sides the square of half the coefficient of x, hence:
x² - 8x + (-4)² = 9 + (-4)²
(x - 4)² = 9 + 16
(x - 4)² = 25
The solution to the equation is (x - 4)² = 25
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Leaves and acorns are falling from the trees, but to work out the exact number of each you need to solve the following equation.
If l number of leaves = 46, what does a (acorns) equal?
l + 3a = 145
Using the equation, the number of acorns that fell if 46 leaves fell is 33.
How to find the number of acorns?Leaves and acorns are falling from the trees. To work out the exact number of each you need to solve the following equation.
l + 3a = 145
where
l = number of leavesa = number of acornsLet's find the number of acorns that fell if 46 leaves fell off from th tree.
Therefore,
l + 3a = 145
46 + 3a = 145
3a = 145 - 46
3a = 99
divide both sides by 3
a = 99 / 3
a = 33
Therefore,
number of acorns = 33
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Two sides of a triangle have the following measures. Find the range for the measure of the third side.
7,10
A.3 < x < 14
B.4
C.5 < x < 10
D.3 < x < 17
Help please
I really need help
The range for the third side will be around 5<x<10
What is Pythagoras theorem?
Pythagoras theorem is a theorem applied to right angled triangle. It states that sum of squares of sides of a right triangle is equal to the square of the hypotenuse.
Let use consider that the given triangle is right triangle
We know the length of the hypotenuse is 10
And one of the side is of length 7
Let the side of the triangle be 'x'
Hence by Pythagoras theorem
We have
7^2+x^2=10^2
49+x^2=100
x^2= 51
x= 7.2
Hence this range is in between 5<x<10
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Please helpppp it’s due today!!!
There are two pairs of triangles given. Using transformation of triangles we can say that ΔABC and ΔEFG are congruent. ΔDEF and ΔJKL are non-congruent to each other.
There are three types of transformations in triangles. They are translations, rotations and reflections.
Translation is nothing but changing the position of the figure without disturbing its shape and size. Two triangles are said to be congruent if their corresponding sides and angles are proportional.
In triangles ΔABC and ΔEFG, the sides AB and EF are proportional to each other, AC and EG are proportional to each other and BC and FG are proportional to each other. Translation is seen in ΔABC and ΔEFG.
In triangles ΔDEF and ΔJKL, neither the sides nor the angles are proportional to each other. Hence, ΔDEF and ΔJKL are not congruent to each other.
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A researcher estimates that the average height of the buildings of 30 or more stories in a large city is at least 700 feet. A random sample of 10 buildings is selected, and the heights in feet are shown. At = 0.025, is there enough evidence to reject the claim? 485 511 841 725 615 520 535 635 616 582
Yes At = 0.025 is there enough evidence to reject the claim.
Given:
A random sample of 10 buildings is selected, and the heights in feet are shown.
485 511 841 725 615 520 535 635 616 582
Mean x = 6065/10
= 606.5
H : μ ≤ 700
n = 10
s = 109.08
α = 0.25
Test stat t = x - μ / s/[tex]\sqrt{n}[/tex]
on submitting the above values
t = -2.71.
so reject h.
Therefore Yes At = 0.025 is there enough evidence to reject the claim.
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Urgent!! Need some help please!
Four adults took their five children to a movie. The price for 9 people was $160. The 5 children received a 20% discount on their tickets. The cost for a child ticket was $___ less than the cost of an adult ticket.
The cost for a child ticket was $4 less than the cost of an adult ticket.
Given that, 4 adults took their 5 children to a movie. The price for 9 people was $160.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the cost of adult tickets be x.
The 5 children received a 20% discount on their tickets.
Now, x-20% of x
= x-20/100 × x
= x-0.2x
= 0.8x
Here, 4x+5×0.8x=160
⇒ 4x+4x=160
⇒ 8x=160
⇒ x=20
So, the cost of children is 20-20% of 20
= 20-0.2×20
= 20-4
= 16
Therefore, the cost for a child ticket was $4 less than the cost of an adult ticket.
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please help me it's due now, please
Which image shows a rotation? A, B, or C
Answer: B
Step-by-step explanation: A is a translation, C is reflection and B is the reflection.
Hoped This Helped!
identify the transformations used to graph g(x)=-1/2(x-3)^3 from its parent function f(x)=x^3
Answer:
The transformations that have been done are reflected vertically -1/2 and moved to the right by 3 units.
Step-by-step explanation:
To find out what transformations differ from your parent graph, look at the a,h, and k values.
A value means if it is being vertically stretched or reflected
In this case, -1/2 is a vertically reflection(upside down).
We also have -3 as our h value. This tells us how many units right or left our graph moves. If the value is negative, it moves to the right. If the value is positive, it moves to the left.
Now you know how to find transformations that differ from the parent graph
Which of the following statements is best supported by this lesson? (1 point)
If you want to save money, you should stop talking to people altogether.
Rewarding yourself with a small treat every now and then is probably okay.
Cell phones are always cheaper than land-line phones.
You only really need to limit your big-ticket purchases.
Answer:
B. Rewarding yourself with a small treat every now and then is probably okay
Step-by-step explanation:
The lesson talks about shopping and how it’s not bad to go shopping.
What is the answer to the expression "the difference of 9 and 2"?
the difference between 9 and 2 is 7
Answer:
7?
Step-by-step explanation:
Uhhhh
You subtract 9 and 2
7
That's crazy now
what’s equivalent to 2 to the power of 6
[tex]\fbox{64 or 8*8}[/tex]
[tex]2^6=64[/tex]
[tex]8\times8=64[/tex]
Need Asap(i will give 10 points)
Answer:
The answer is C
Step-by-step explanation:
-3/9 is bigger than -1 and -9/3 is smaller than -1
Kyle had 17 cookies and then he bought 25,more cookies. He wants to
share them between himself and 6 friends. How many cookies will each
friend get?
Answer:
6 cookies
Step-by-step explanation:
himself + 6 friend = 7
(17+25)/7
= 42/7
= 6
Each friende get:
6 cookies
Answer:
6 cookies each person
Step-by-step explanation:
kyle had 17 cookieshe then bought 25 more meaning he had now 42 cookies(17+25=42)
he wanted to share them equally between himself and his 6 friends meaning they were 7 people in total thus 42÷7=6The diameter of a spherical is 3/2 inches. What is the exact volume of the ball bearing? Enter your answer in the box as a simplified fraction.
The Volume of the Ball Bearings is 1.76 cubic. inches
Given :
The diameter of the ball bearings = 3/2 inches
The radius of the ball bearings = 3/4 inches
Now, The Volume of the Sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]
Putting the value of radius = 3/4 in the formula of the Volume,
We have :
The volume of the ball bearings =
[tex]V =\frac{4}{3} \pi (\frac{3}{4} )^{3} = \frac{4}{3} *\frac{22}{7}*\frac{3}{4} *\frac{3}{4} *\frac{3}{4}\\ \\V = 1.76[/tex]
Hence, The Volume of the Ball Bearings = 1.76 cubic. inches
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Find the transformation of the point A (3,-5) please help 0-0
The image of the rotation in the transformation is (-1, 4)
How to determine the image of the transformation?The coordinates of the point are given as
Point = (3, -5)
The transformations are given as
T₁, ₄ rₓ-axis R₉₀°
Mathematically, this is represented as
(x, y) = (x + 1, y + 4) = (x + 1, -y - 4) = (y + 4, x + 1)
So, we have
(x, y) ⇒ (y + 4, x + 1)
Recall that
Point = (3, -5)
This gives
Image = (-5 + 4, 3 + 1)
Evaluate
Image = (-1, 4)
Hence, the coordinates of the image are (-1, 4)
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the average remaining lifetimes for women of various ages in a certain country are given in the following table
i wish you good luck
solve the question please
Answer:
the answer is A
Step-by-step explanation:
you are dividing with a - so the signs will switch
Principal is
•
A. The original amount invested
•
B. The total amount earned
•
C. Interest plus original amount invested
•
D. Interest on a loan
As per the concept of simple interest the term principal refers the original amount invested.
Simple interest:
Basically, the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
Given,
Here we need to find the correct definition of the term principal.
As per the definition of the concept simple interest, then term principal refers the amount to be invested on the particular assets.
And at the nd of the particular, period the principal amount is either increase or decrease based on the interest applied on it.
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TB MC Qu. 07-135 (Algo) On July 9, Mifflin Company receives...
On July 9, Mifflin Company receives an $8,200, 120-day, 6% note from customer Payton Summers to replace an account receivable. What entry should be made by
Mifflin on the maturity date assuming the maker pays in full, and no adjusting entries have been made related to the note? (Use 360 days a year.)
Multiple Choice
Debit Cash $8,364, credit Interest Revenue $164; credit Notes Receivable $8,200
Debit Cash $8,282; credit Interest Revenue $82, credit Notes Receivable $8,200.
Debit Notes Receivable $8,200, debit Interest Receivable $164; credit Sales $8,364.
Debit Cash $8,200, credit Notes Receivable $8,200.
Answer:
a
Step-by-step explanation:
cause
Can you kindly help with this please good people.
Answer:
A. Yes
Step-by-step explanation:
Each input corresponds to only one output, which satisfies the definition of a function.
51. Minimizing Average Cost Suppose the total cost
function for manufacturing a certain product is
C1x 2 5 0.210.01x 2 1 1202 dollars, where x represents
the number of units produced. Find the level of production that will minimize the average cost.
The level of production that minimizes the average cost is the quantity of units produced when the value of the average cost function has a minimum value, which is 110 units of production
What is the minimum value of a function?The minimum value of a function is given by the point of the graph of the function where the value is minimum.
The total cost function is C(x) = 0.2·(0.01·x² + 120)
x = The number of units produced (manufactured)
The average cost is the cost to produce one unit
Therefore;
[tex]Average\, cost, \, AC = \dfrac{Total \, cost }{Quantity \, produced}[/tex]
Therefore;
[tex]Average\, cost \, function,\, f(x) = \dfrac{0.2\cdot (0.01\cdot x^2 + 120)}{x}[/tex]
The quantity that minimizes the average cost is given by the minimum value of the average cost function, which is the point at which the slope of the function, f'(x) is zero as follows;
[tex]f'(x) =\dfrac{d}{dx} \left( \dfrac{0.2\cdot (0.01\cdot x^2 + 120)}{x}\right) = 0[/tex]
[tex]\dfrac{d}{dx} \left( \dfrac{0.2\cdot (0.01\cdot x^2 + 120)}{x}\right) =\dfrac{x^2-12000}{500\cdot x^2} = 0[/tex]
x² - 12000 = 0
x² = 12000
x = √(12000) = 20·√(30) ≈ 110
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Lee Anne and Mary got their allowance and went to their favorite store.
A. Lee Anne has $ 30 to spend and wants to buy 3 pairs of sunglasses. She estimates by rounding $ 14.72 to the nearest ten, which is $ 10 and then multiplying $10x3=$ 30. Is Lee Anne's estimate reasonable? Explain how you know.
B. Mary buys a pair of earrings and two bookmarks. She pays with a twenty-dollar bill. How much change will she receive?
C. The store is running a special deal- Buy 3 pairs of earring, Get one pair free! Lee Anne decides doesn't want sunglasses anymore. Will her 30 be enough to take advantage of this deal? Exp how you know.
A. Her estimate is not reasonable, as she does not have enough money to buy the 3 sunglasses.
B. The change that she will receive is of $4.67.
C. Her $30 will be enough to take advantage of the deal.
How to obtain the values?The values are obtained applying the proportions, which are the prices of each product in this problem.
For item a, the cost of three sunglasses should be of:
3 x 14.72 = $44.16.
The estimate to the nearest tenth is not reasonable, as she does not have enough money to buy the sunglasses.
The cost in item b is given as follows:
9.83 + 2 x 2.75 = $15.33.
The change is given by the amount paid subtracted by the total cost, hence:
Change = 20 - 15.33 = $4.67.
The amount paid in item c is of:
3 x 9.83 = $29.49.
Which is less than $30, hence her $30 will be enough to take advantage of the deal.
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a. Using variables, write out the formula for the point-slope form of the equation.
b. Determine the slope of the line that passes through the points (-2, 1) and (0, 1).
c. Identify the point (-2, 1) as (x1, y1).
d. Write the equation of the line in point-slope form.
Show all work on how you found the slope or determined the slope from the graph. Use the box provided to submit all of your calculations and final answers. Simplify the answer as needed.
The point-slope form of the equation is y - 1 = 0
The formula for the point-slope form of the equationFrom the graph, we have the following points
(-2, 1) and (0, 1)
Start by calculating the slope of the points
This is calculated as
slope = (y₂ - y₁)/(x₂ - x₁)
This can be rewritten as
m = (y₂ - y₁)/(x₂ - x₁)
Where
slope = m
(x, y) = (-2, 1) and (0, 1)
So, we have
m = (1 - 1)/(0 + 2)
Evaluate the expression
m = 0
From the question, we understand that:
(x₁, y₁) = (-2, 1)
The equation of the line is then calculated as
y - y₁ = m(x - x₁)
Substitute the known values in the above equation, so, we have the following representation
y - 1 = 0(x + 2)
Evaluate
y - 1 = 0
Hence, the equation of the line is y - 1 = 0
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A cable is 8.9 m long. 10 decimeters =1 meter; therefore, how long this is in decimeters?
Answer:
89 decimeters I THINK...
Step-by-step explanation:
1 m → 10 dm
8.9 m → L(dm)
Solve the above proportion to obtain the length L in decimeters:
L(dm) = 8.9 m × 10 dm
L(dm) = 89 dm
The final result is:
8.9 m → 89 dm
Answer:
89 decimeters
Step-by-step explanation:
8.9 m × 10 = 89 dm
IXL Help Fast Please ! Almost finished with this one!
Answer:
x=8
Step-by-step explanation:
2x+122=154-2x
4x+122=154
4x=32
X=8
hopes this helps
UGENT!
UGENT!
UGENT!
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UGENT!
what is 1+1!!
Answer:
2
Step-by-step explanation so, you got the question 1+1? let me help. So the first 1 in the question right? You add another 1 that equals 2 hope this helps.
Answer:
24
Step-by-step explanation:
well u see 1+1 would usually = 2 but because i dont like the number 2 by its self i add another 2 therefore its 22 and then i like to spice it up with adding another 2 to the last 2 then u have 24.
HOPED THIS HELPED!!!!! :b
AP Statistics (Multiple Choice)
(Image above) PLEASE HELP ME ILL GIVE YOU BRAINLIST ANSWER!!!
Answer:
A
Step-by-step explanation:
Answer:
A)
Step-by-step explanation:
To find the percentage of the Pie-Chart , Divide each corresponding Number by the Total Frequency
Total Frequency = 9 + 20 + 25 + 39 = 93
% of Motorcycle = [tex]\frac{9}{93}* 100=9.7 %[/tex] %
% of Sedan = [tex]\frac{20}{93}* 100=21.5 %[/tex] %
% of SUV = [tex]\frac{25}{93}* 100=26.9 %[/tex] %
% of Truck = [tex]\frac{39}{93}* 100=41.9 %[/tex] %
This is represented by Choice A)
During a recent year, the temperatures in Chicago ranged from -19 degrees Celcius to 33 degrees Celsius. Choose the compound inequality that represents this range.
The compound inequality that represents this range is D) -19≤temp≤33.
What is inequality?
A mathematical statement known as an inequality in algebra uses the inequality symbol to show the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols. When the symbols ">," <" are used to connect two real numbers or algebraic expressions, the relationship is referred to as an inequality.
Here during the recent year the temperature in Chicago ranged from -19 degree celsius to 33 degree celsius.
Here from -19 degree increased to 33 degree. then the inequality is ,
=> -19 [tex]\leq temp\leq 33[/tex]
Hence the correct option is D) -19 [tex]\leq temp\leq 33[/tex] .
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Please help me understand this.
Answer:
Hopefully this image helps, I am pretty sure you just have to rotate the shape by 270 degrees on the graph.
A kangaroo hops 2 km in 5 minutes at this rate how far does the kangaroo travel in 3 minutes?
The kangaroo traveled 1.2 km in 3 minutes.
What is distance?
The distance between two points is the length of a straight line segment that links them. The distance of a point from a line is the length of the shortest line segment from the point to the line. This will also be perpendicular to the line.
Given,
kangaroo travel the distance in 5 min = 2
in 1 min, the distance covered by kangaroo = 2/5
and in 3 minutes, kangaroo will traveled = 2/5(3) = 1.2 km.
Hence, the distance covered by the Kangaroo in 3 minutes is 1.2 km.
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One sample has n = 18 with SS = 102 and M = 12. A second sample has n =
5 with SS = 171 and M = 8. Which of the following is the 95% confidence
interval for the mean difference in confidence between the two samples?
05±6.0956
O 5±3.7856
O4 ±3.7856
O4±6.0956
Option-3 is correct. The mean difference in confidence between the two samples' 95% confidence interval falls between 4±3.7856.
Given that,
A sample has n = 18, SS = 102, and M = 12 for one sample. In a second sample, the n is 5, the SS is 171, and the M is 8.
We have to find The mean difference in confidence between the two samples' 95% confidence interval falls between which of the following ranges.
n₁=18 and SS=102
We get,
S₁=[tex]\sqrt{SS/n_{1}-1 }[/tex]=[tex]\sqrt{102/18-1}[/tex]=2.45
n₂=5 and SS=8
We get,
S₂=[tex]\sqrt{SS/n_{2}-1 }[/tex]=[tex]\sqrt{8/5-1}[/tex]=6.54
C is 95%=0.95
d=0.05
Pooled variance is
S²p=273.13/21=13.01
Standard error= S₁-S₂= 1.82
Confidence interval is
μ₁-μ₂
4±3.7856
Therefore, Option-3 is correct. The mean difference in confidence between the two samples' 95% confidence interval falls between 4±3.7856.
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