The length of segment AB is 13 units.
What is the distance formula?The distance between the two points (a,b) and (c,d) is given by:
[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex].
The given coordinates of A and B are A(0,12) and B(5,0).
The length of segment AB is given by:
[tex]AB = \sqrt{(5-0)^2 + (0 - 12)^2}\\\\AB=\sqrt{25 + 144}\\\\AB = \sqrt{169}\\\\AB = 13[/tex]
Hence, the length of segment AB is 13 units.
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The function g is defined by g(x) = ( 2x – 3 )( x + k )
Given that g(0) = – 15 find (i) k (ii) x such that g(x) = 0
Answer:
Step-by-step explanation:
(-3)(k) = -15
-3k = -15
k = -15/-3
k = 5
(2x+3)(x+5) = 0
2x + 3 = 0
2x = -3
x = -3/2
x+ 5 = 0
x = -5
What is the equation of the blue line
Answer:
[tex]y=\frac{1}{2}x+2[/tex]
Step-by-step explanation:
Using the points [tex](0,2)[/tex] and [tex](2,3)[/tex], the gradient is [tex]\frac{3-2}{2-0}=\frac{1}{2}[/tex].
The [tex]y[/tex]-intercept is [tex](0,2)[/tex], so the equation is [tex]y=\frac{1}{2}x+2[/tex].
Aaliyah is going to invest in an account paying an interest rate of 5% compounded continuously. How much would Aaliyah need to invest, to the nearest hundred dollars, for the value of the account to reach $181,000 in 19 years?
Based on the given parameters, the value of the money to invest initially is $99341.383
How to determine the amount of investment?The given parameters about the compound interest are
Amount, A = $181000
Interest Rate, R = 5%
Time, t = 19 years
Number of times, n = 365 i.e. continuously
To calculate the amount, we have:
A = P + CI
Where
C = P(1 + R)^t
So, we have
A = P(1 + R)^t
This can be rewritten as
A = P(1 + R/n)^nt
Substitute the known values in the above equation
181000 = A * (1 + 5%/365)^(12*365)
So, we have
A = 181000 /[(1 + 5%/365)^(12*365)]
Evaluate the expression
A = 99341.383
Hence, the amount of the investment is $99341.383
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The points L(5,0) , M(-4,0) and N(5,-4) form a triangle find the perimeter of the triangle . Round your answer to the nearest tenth if necessary .
Answer:
9.1 units
Step-by-step explanation:
See diagram below ....using pythagorean theorem
Find the indicated real nth root(s) of a. n = 4, a = 625
Answer:
5
Step-by-step explanation:
Sam tries to draw lines of reflection through a rectangle so that the rectangle can be reflected onto itself. How many lines of reflection can sam draw? enter the answer in the box.
Therefore the solution of this question is Sam can draw 2 lines of reflection.
What is line of reflection?If a figure is reflected in a line or a point, the image and preimage are consistent. A reflection converts each point in a figure into an image along a predetermined line. Line of Reflection refers to the fixed line.
To determine the quantity of lines that will reflect a rectangle back onto itself.
Due to the fact that the line of reflection is the perpendicular bisector of the segment connecting a point with its image. The perpendicular bisector of a side must be the line of reflection if one side of the rectangle is to map to itself.
A rectangle has two distinct perpendicular bisectors of its sides, leading to two lines of reflection that map a rectangle to itself.
Therefore Sam can draw 2 lines of reflection.
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pls help due tomorrow !!!
The required quadratic equation is x² - 12x + 36 Or (x - 6)².
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
We know (a - b) = a² - 2ab + b².
Given, An expression 36 - 12x + __
now, here b² = 36 ⇒ b = 6,
∴ - 2ab = - 2(a)(6).
So, a = 1.
∴ The required quadratic equation is x² - 12x + 36 Or (x - 6)².
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is 0.04x=y proportional
in 2016, a 1952 Willie Mays rookie card from Topps sold for $478,000! Currently, a toaster may cost $25. How many toasters could you buy with the money spent on the willie Mays rookie card?
Answer: 19120 Toaster
Step-by-step explanation: We just need to take $478000 divided by 25, equal to 19120 Toaster!
A roller-coaster goes over a 12 m tall hill then approaches a 30 m hill. What is the minimum velocity the roller-coaster would need when going over the 12 m hill to make it to the top of the 30 m hill?
254.8 m/s
15.96 m/s
Not enough information to answer
18.78 m/s
Not enough information to answer
Option C is the correct answer.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
A roller-coaster goes over a 12 m tall hill and then approaches a 30 m hill.
The minimum velocity the roller-coaster would need when going over the 12 m hill to make it to the top of the 30 m hill.
To find the minimum velocity we need to know the acceleration of the roller coaster that comes down the 12 m tall hill.
The value of the acceleration is not given.
So,
We can not find the minimum velocity.
Thus,
Not enough information to answer
Option C is the correct answer.
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please help me i’ve got midterms and i’ve been stuck on this for like 45 minutes Dx
Answer:
f(x) = ³√(x–1) + 4
f-¹(x) = (x + 1)³ + 4
Step-by-step explanation:
i hope this helped
A store is instructed by corporate headquarters to put a markup of 11% on all items. An item costing $18 is displayed by the store manager at a selling price of $2. As an employee, you notice that this selling price is incorrect. Find the correct selling price. What was the manager's likely error?
The manager's likely error is $20 if a store is instructed by corporate headquarters to put a markup of 11% on all items. An item costing $18 is displayed by the store.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
A markup of 11% on all items. An item costing $18 is displayed by the store manager at a selling price of $2.
The manager’s likely error was forgetting to add the $2 back to the $18.
$2= 11% of $18 = 1.98(=2)
For a markup,
= $2 + $18
= $20
Thus, the manager's likely error is $20 if a store is instructed by corporate headquarters to put a markup of 11% on all items. An item costing $18 is displayed by the store.
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Rotate triangle P 90° clockwise about the point (2, -1).
54
3
2
1
-5 -4 -3 -2 -1 0
-1
2345
-4
1 2 3 4 5
P
Answer:
p=12345
Step-by-step explanation:
Answer:
see attached
Step-by-step explanation:
You want the graphed triangle rotated 90° CW about the point (2, -1).
RotationAfter rotation 90° CW, points will be as far to the south and west of the center of rotation as they are east and south in the original image. This is shown by the blue triangle in the attachment.
Arrange the steps in the correct order to solve the equation,
3(22-5) - 4 = 10
Add 4 to each side of the
equation:
3/22 - 5) = 14
Use the Exponential Property and
write in decimal form:
(2 - 5)log2 = log4. 67
log4. 67
Find the value of Toga
and substitute
2-5 = 2. 23
Simplify
23. 625
Take the log of each side:
log(22+ - 5) = log('9).
2 - 5 - 1034. 87
Divide each side by log 2
Tog?
Add 5 to each side of the
equation
2+ = 2. 23 +5
Divide both sides of the equation
The correct order to solve the equation is given below .
In the question ,
it is given that ,
the equation is 3*([tex]2^{2 t - 5}[/tex]) - 4 = 10 ,
Step(1) , adding 4 to each side of the equation ,
3*([tex]2^{2 t - 5}[/tex]) = 14
Step(2) , dividing both sides of the equation by 3 ,
we get , ([tex]2^{2 t - 5}[/tex]) = 14/3 .
Step(3) , taking log on each side ,
log([tex]2^{2 t - 5}[/tex]) = log(14/3)
Step(4) , Using the Exponential Property and writing 14/3 in decimal form ,
we get ,
(2t - 5)*log(2) = log(4.67)
Step(5) , Dividing each side by log(2) ,
we get , 2t-5 = log(4.67)/log(2) .
Step(6) , Add 5 to each side of equation
we get , 2t = 2.23 + 5 ;
Step(7) , Simplifying we get ,
we get , t = 3.625 .
Therefore , the the solution of the given equation is t = 3.625 .
The given question is incomplete , the complete question is
Arrange the steps in the correct order to solve the equation,
3*([tex]2^{2 t - 5}[/tex]) - 4 = 10 .
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(
Write the equation
of the line in
Slope-Intercept
Form.
Answer: y= -2/3x + 0
Step-by-step explanation: y=mx+b
The Y-intercept is at (0,0), so b is 0
Slope is -2/3
So the equation is y=-2/3x + 0
What is the radius of 6 inches
Answer:
28.27 sq. units or 9π sq.
Step-by-step explanation:
Vincent is completing his math homework about the process of Completing the Square to solve quadratic equations. His work is shown below.
solve: x²-3x+7=0
step 1: x²-3x = -7
step 2: x²-3x+9=-7 +9
step 3: (x-3)² = 2
step 4: X-3= = √2
x=3 = √2
Did Vincent make a mistake as he solved the quadratic using Completing the Square? If so, in what
step did he first make a mistake? (Step numbers are labeled in blue on the left)
Answer:
Step-by-step explanation:
He made a mistake in step one turning the 7 into a -7
[tex]x^{2}[/tex] - 3x + 7 = 0
Solving:
[tex]1x^{2}[/tex] - 3x + 7 = 0 ← If the term doesn't have a coefficient, it is considered that the coefficient is 1.
[tex]1x^{2}[/tex] + (-3x) + 7 = 0 ← Identify the coefficients a, b, and c of the quadratic equation.
a = 1, b = -3, c = 7
x = - (-3) ±√[tex](-3)^{2}[/tex] - 4 x 1 x 7
2 x 1
x = 3 ± √[tex](3)^{2}[/tex] - 4 x 7
2
x = 3 ± √9 - 4 x 7
2
x = 3 ±√9 - 28
2
x = 3 ± √-19
2
The square root of a negative number does not exist in the set of real numbers.
x = ∉ R
Answer the question and help a brother out
Answer:
25
Step-by-step explanation:
first add the degrees: 50+30+25=105, then 180-105 is 75, 75=3s, s is 25
(im not sure completely im only in 7th grade)
Write an equation in slope-intercept form of the line that is parallel to the one given and passes through the given point
(1,3); y=7x+5
a paper company needs to ship paper to a large printing business. the paper will be shipped in small boxes and large boxes. the volume of each small box is 7 cubic feet and the volume of each large box is 14 cubic feet. a total of 21 boxes of paper were shipped with a combined volume of 252 cubic feet. write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. define the variables that you use to write the system.
The required system of equations is x+y = 21 and 7x +14y = 252.
Systems of equations are sets of equations where the solution is the intersecting point(s) between the equations.There are three methods typically used to solve systems of linear equations: graphing, the substitution method, and the elimination method. These methods can be applied to more complex systems of nonlinear equations as well.
Let the number of small boxes be x.
Let the number of large boxes be y.
The volume of each small box is 7 cubic feet.
The volume of each large box is 14 cubic feet.
The total number of boxes is 21.
Total volume of all boxes is 252 cubic feet.
So, x+y = 21.
This is the first equation.
Also, the total volume is equal to the sum of the volumes of all individual boxes.
So, 7x + 14y = 252
Thus, the required system of equations is x+y = 21 and 7x +14y = 252.
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The required system of equations is x + y = 21 and 7x + 14y = 252 using the concept of equations.
What are system of equations?A system of equations in algebra is made up of two or more equations that are solved together to obtain the solution for a two or more variable problem.
Volume of each small box is 7 cubic feet and volume of each large box is 14 cubic feet. Take the number of small boxes to be x and number of large boxes to be y.
Given total number of boxes shipped is 21. Therefore using the concept of equation,
x + y = 21 --- (1)
Total volume of small box is given by:
Total volume of small box = (Volume of a small box) * (Number of small box)
Total volume of small box = 7x
Similarly the total volume of large box is,
Total volume of small box = 14y
Given the total volume of carried box is 252 cubic feet. Using the concept of equations,
7x + 14y = 252 ---(2)
The equations (1) and (2) gives the required system of equations.
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a. Prove ABD is congruent to CBD.
b. Determine whether all four triangles in the diagram are congruent.
c. Explain your reasoning.
Answer:
a. The proof is in your picture
b. Yes
c. All four triangles are congruent by the HL theorem
Step-by-step explanation:
Given AB≅CB in ∆ABC with BD⊥AC, you want to show ∆ABD≅∆CBD, and you want to know if these are congruent to ∆CEG and ∆FEG.
a. Left trianglesYour picture correctly shows a proof that ∆ABD≅∆CBD by the HL postulate.
b. Right trianglesSides CE and FE are marked congruent to each other and sides AB and CB. The altitudes BD and EG of these isosceles triangles are marked as congruent. Hence all four triangles, ∆ABD, ∆CBD, ∆CEG, and ∆FEG are congruent by the HL theorem.
c. All trianglesThe same HL theorem reasoning applies to all of the triangles.
__
Additional comment
The distance from the light to the stage is said to be the same for both lights. That would be measured perpendicular to the stage, and is the shortest such distance. We are assuming that BD and EG are those perpendicular distances, as we see no markings on the diagram indicating right angles.
A polygon has vertices at (-5, 3), (-1, 3), (1, 0), and (-3, 0). Which represents a geometric translation of the give
polygon 4 units to the right and 5 units down?
Answer:
(-1, 3), (3, 3), (5, 3), (1, 0)
Step-by-step explanation:
A translation of 4 units to the right means adding 4 to every x-coordinate.
The new coordinates are:
(-1, 3), (3, 3), (5, 3), (1, 0)
a rumor spreads among a group of 400 people. the number of people who have heard the rumor after t hours is given by:
Time required to spread the rumor so that half of the given heard the rumor is equal to 15 hours (approximately).
As given in the question,
Number of people among whom rumor is spread = 400
Number of people is represented by N(t)
Time is represented by 't' hours
Function representing relation between number of people who heard about the rumor and time
N(t) = 400/ ( 1+ 399 × e^(-0.4t) )
Condition : Half of the given number of people heard the rumor
N(t) = 400/2
= 200
Substitute the value in the function we get,
200 = 400/ ( 1+ 399 × e^(-0.4t) )
⇒ ( 1+ 399 × e^(-0.4t) ) = 400 ÷ 200
⇒ 1 + 399 × e^(-0.4t) = 2
⇒ 399 × e^(-0.4t) = 2 - 1
⇒ e^(-0.4t) = 1 ÷ 399
⇒ e^(-0.4t) = 0.002506
⇒ -0.4t = [tex]log _{e}[/tex] (0.002506)
⇒ t= 14.97 hours
⇒ t= 15 hours (round off)
Therefore, time required to spread the rumor among half of the given number of people is equal to 15hours(approximately).
The complete question is:
A rumor spreads among a group of 400 people. The number of people, N(t), who have heard the rumor by the time t in hours since the rumor started to spread can be approximated by a function of the form
N(t) = 400 / (1+399e^(-0.4t))
Approximately how long will it take until half the people have heard the rumor?
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If a boy grow 5 inche, he will be one half a tall a hi iter , hi iter i 68 inche tall. How tall i the boy?
If a boy grows 5 inches, he will be one half a tall as his sister , his sister is 68 inches tall. So the height of the boy is 29 inches
What is division?In mathematics, the opposite of multiplication is the process called division. Finding the number of times one quantity is included within another is the procedure. The letters "/" or "" are typically used to denote this. For instance, 8 boys divided by 2 may be expressed as 8/2 or 82. The outcome in this situation would be 4, which is the quantity that 2 may be found in 8 times. The quotient, or outcome of the division, and the remainder, or quantity remaining after dividing, may both be found using division. Calculus, algebra, geometry, and other branches of mathematics all make use of the crucial mathematical notion of division.
How to solve?
If the boy grows 5 inches, he will be 68/2 =34 inches tall
The boy's current height is 34 - 5 = 29 inches
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i’m so lost and i really need help :’). this is 9th grade algebra
Answer:
1 and 2 are functions, 3 is not a function.
Step-by-step explanation:
One x-value can lead to one y-value. If the x-value leads to more than one y-value like #3, then the relation is not a function.
If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.
I need help with this geometry please i don’t understand. Just #1 please
Answer:
a) CE=PR
b) TR=FE
c) <F=<T
d) <P=<C
e) RPT=ECF
Step-by-step explanation:
Two fair number cubes have faces labeled with the numbers 1 through 6. The two cubes will be rolled simultaneously. What is the probability that at least one of the cubes will have the face labeled 5 showing and that the sum of the showing faces will be greater than 8 ?.
The probability that at least one of the cubes will have the face labeled 5 showing and that the sum of the showing faces will be greater than 8 is 5/36.
What is the probability?A probability is a numerical representation of the possibility or chance that a specific event will take place. Probabilities can be written as percentage between 0 and 1.
Number of sample spaces that are labeled 5 and display a sum more than 8 / total sample space gives the likelihood that at least one of the cubes will have the face labeled 5 showing and that the sum of the faces showing will be greater than 8.
When two cubes are rolled, the total sample space is 36.
The sample space that is labelled 5 and has a sum greater than 5 are: (4,5) , (5, 4) , (5, 5), (5, 6) , (6,5) = 5
The probability = 5/36
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Mr. Reynolds, the gym teacher, divided a class of 16 students into 2 equal teams. How many students were on the team?
Answer:
8
Step-by-step explanation:
16 divided by 2 is 8.
Answer: 8 students
Step-by-step explanation: 16/2=8
James earned a total of $68 last week. He earned $48 washing cars and won x dollars in an art contest. Which equation can be used to find the number of dollars James won in the art contest?
Answer:
Step-by-step explanation:
since $68 is your total, let's use the example z=y+x
z is our total, and we know that he made a total of $68, therefore z is the number 68.
We also know that James made a total of $48 washing cars, which gives us the answer 48 as y. So in order to find x, we would need to subtract 68 and 48, which is called using the communtative property. Thsi answer would give us the remaining amount of money we do not yet know.
So 68-48= 20. therefore James made $20 at the art contest.
suppose the continuous random variable, x, is uniformly distributed between 2 and 10. what is the probability that x is either less than 3 or greater than 8?
The probability that x is either less than 3 or greater than 8 is 0.375 .
In the question ,
it is given that ,
a continuous random variable X , is uniformly distributed between 2 and 10 ,
So , alpha(α) = 2 and beta(β) = 10 .
the probability that x is either less than 3 or greater than 8 can be calculated by :
P(X < 3 or X > 8) = 1 - (8 - 3)/(β - α)
= 1 - (8 - 3)/(10 - 2)
= 1 - 5/8
On simplifying further ,
we get ,
= 0.375
Therefore , the probability P(X < 3 or X > 8) is = 0.375 .
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