The B points are ( 8, -2 ) of Endpoint B when M is the midpoint of line AB.
What is midpoint of a segment?
The midway of a line segment in geometry is where it meets the other end. The centroid of the segment and the endpoints, it is equally spaced from both endpoints. It cuts the section in half.M is the midpoint of line AB.
Endpoint A is (4, 2).
Midpoint M is (6, 0)
Let mid points are ( x,y) and A points are ( x₂ , y₂ ) and B points are ( x₁ , y₁)
x = x₁ + x₂/2 , y = y₁ + y₂/2
6 = x₁ + 4/2 , 0 = y₁ + 2/2
12 = x₁ + 4 , 0 = y₁ + 2
x₁ = 12 - 4 , y₁ = -2
x₁ = 8 , y₁ = -2
So, the B points are ( 8, -2 )
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The right arrow symbol used to show the transition from a point to its image after a transformation is not contained within the Equation Editor. If such a symbol is needed, type "RightArrow." For example: P(0, 0) RightArrow P′(1, 2).
Triangle ABC has coordinates
A
(
1
,
4
)
;
B
(
3
,
−
2
)
;
and
C
(
4
,
2
)
.
Find the coordinates of the image
A
'
B
'
C
'
after a reflection over the x-axis.
Answer:
Step-by-step explanation:
Given:
Vertices of triangle ABC are A (1,4), B(3,−2) and C(4,2).
Triangle ABC reflected over the x-axis to get the triangle A'B'C'.
To find:
The coordinates of the image A'B'C'.
Solution:
If a figure reflected over the x-axis, then rule of transformation is
Now, using this rule, we get
Therefore, the coordinates of the image A'B'C' after a reflection over the x-axis are A'(1,-4), B'(3,2) and C'(4,-2).
A water tank initially contained 56 liters of water. It is being drained at a constant rate of 2.5 liters per minute. How many liters of water are in the tank after 9 minutes?
Harry HAS 1 1/2 KG whole-wheat flour. He uses 3/4 of the flour to bake bread. How much flour did he use?
Given the following parameter
Mass of flour wheat flour = 1 1/2 kg
If Harry used 3/4 of these flour to bake bread, the amount of flour used is expressed as:
[tex]A=\frac{3}{4}\text{ of 1}\frac{1}{2}[/tex]Convert the mixed fraction into an improper fraction to have:
[tex]\begin{gathered} A=\frac{3}{4}\times\frac{3}{2}kg \\ A=\frac{9}{8}kg \\ A=1\frac{1}{8}kg \end{gathered}[/tex]This shows that Harry used 1 1/8kg of the wheat flour to bake the bread
i want to ask a question
We got to use the Secant-Tangent Theorem, here. It says that AC² is equal to the distance BC times the distance from C to the circumference. Let's denote the point in OC where it intercepts the circumference by D, so:
[tex]\begin{gathered} AC^2=CD\cdot BC \\ 20^2=CD\cdot BC \end{gathered}[/tex]Beucase the radius is equal in all points of the circumference, OA=OB=OD, so BC = OA + OC, and CD = OC - OA. So,
[tex]\begin{gathered} 20^2=CD\cdot BC=(OC-OA)\cdot(OA+OC)=OC^2-OA^2=OC^2-8^2 \\ 20^2=OC^2-8^2 \\ OC^2=20^2+8^2=464 \\ OC=\sqrt[]{464}=21.54\approx22\operatorname{cm} \end{gathered}[/tex](a) Write the number 302.658 correct to 2 decimal places, (b) Write the number 302.658 correct to 2 significant figures.
The given number is,
302.658
to corrct to 2 decimal places,
302.66.
im having a little trouble understanding the commutative property and closure property, not a specific problem just would like a small explanation thanks!
Commutative property:
For addition and multiplication if you change the order of the addernds or factor is doesn't change the sum or multiplication.
Example:
Addition
[tex]\begin{gathered} a\pm b=b\pm a \\ \\ 5+3=3+5 \\ 8=8 \end{gathered}[/tex]Multiplication:
[tex]\begin{gathered} a\times b=b\times a \\ \\ 5\times3=3\times5 \\ 15=15 \end{gathered}[/tex]Closure property:
When you add or subtract any two intergers, the result will always be an interger.
Example:
[tex]\begin{gathered} a+b=c \\ \\ a,b,c\text{ are intergers} \\ \\ 8+13=21 \\ \end{gathered}[/tex]8, 13 and 21 are intergers
Domain and range of the quadratic function F(x)=-4(x+6)^2-9
Answer:
Domain: (-∞, ∞)
Range: (-∞, -9]
Step-by-step explanation:
Aldo will take the 11:49 train to San Diego. The train is estimated to arrive in 4 hours and 32 minutes. What is the estimated arrival time?
Kevonta, this is the solution:
Time of departure : 11:49
Time of travel : 4:32
In consequence, the estimated arrival time if the train departs in the morning is:
11 + 4 = 15 hours
49 + 32 = 81 minutes
81 minutes = 1 hour + 21 minutes
4:21 pm
If the train departs at night, the estimated time of arrival is:
4:21 am
Given g(x) = -2√x², find g(8 + x).
Answer:
g(8 + x) = - 2(8 + x)
Step-by-step explanation:
substitute x = 8 + x into g(x)
g(8 + x) = - 2[tex]\sqrt{(8+x)^2}[/tex] = - 2(8 + x)
A visitor in a Las Vegas casino lost $200, won $100, and then lost $50. What was the change in the gambler's net worth (how much did the gambler win or lose overall)?
The gambler in a Las Vegas casino lost $150.
According to the question,
We have the following details:
The visitor lost $200 and $50 in a Las Vegas casino.
The visitor won $100.
So, in total, the visitor lost $250 overall.
Now, compare the amount the gambler lost and the gambler won in the casino. So, we notice that the gambler lost more amount.
Now, we will find the total amount lost:
Gambler's net worth = The amount lost - the amount won
Gambler's net worth = $(250-100)
Gambler's net worth = $150
Hence, the gambler lost $150 overall in the casino.
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how do I find the first five terms of the geometric sequence?
To find the next term of a geometric sequence, the previous term is multiplied by the common ratio r.
[tex]\begin{gathered} r=\frac{1}{2} \\ a_{1=}20 \\ a_2=20\times\frac{1}{2}=10 \\ a_3=10\times\frac{1}{2}=5 \\ a_4=5\times\frac{1}{2}=\frac{5}{2} \\ a_5=\frac{5}{2}\times\frac{1}{2}=\frac{5}{4} \end{gathered}[/tex]At a sale a sofa is being sold for 67% of the regular price. The sale price is $469. What is the regular price?
We have the following information:
• At a sale, a sofa is being sold for ,67% of the regular price
,• The sale price is $469
And we need to determine the regular price.
To find it, we can proceed as follows:
1. Let x be the regular price. Then we have:
[tex]\begin{gathered} 67\%=\frac{67}{100} \\ \\ 67\%(x)=\frac{67}{100}x \\ \\ \text{ Then we know:} \\ \\ \frac{67}{100}x=\$469 \end{gathered}[/tex]2. Now, we have to solve for x as follows:
[tex]\begin{gathered} \text{ Multiply both sides by }\frac{100}{67}: \\ \\ \frac{67}{100}*\frac{100}{67}x=\frac{100}{67}*\$469 \\ \\ x=\frac{100*\$469}{67}=\$700 \\ \\ x=\$700 \end{gathered}[/tex]Therefore, in summary, the regular price is $700.
Abigail and her friend Jaya are going to a carnival that has games and rides. Abigail played 7 games and went on 2 rides and spent a total of $24.75. Jaya played 3 games and went on 6 rides and spent a total of $33.75. Determine the cost of each game and the cost of each ride.
The cost of each game is $2.25.
The cost of each ride is $4.50.
What is the cost of each game and each ride?Here are the system of linear equations that can be derived from the question:
7g + 2r = 24.75 equation 1
3g + 6r = 33.75 equation 2
Where:
g = price of each game r = price of each rideIn order to determine the value of g, multiply equation 1 by 3:
21g + 6r = 74.25 equation 3
Subtract equation 2 from equation 3:
40.50 = 18g
g = 40.50 / 18
g = 2.25
In order to determine the value of r, substitute for g in equation 1 :
7(2.25) + 2r = 24.75
15.75 + 2r = 24.75
2r = 24.75 - 15.75
2r = 9
r = 9 /2
r = 4.50
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help me with my work please
In the first one, the word increase means you will be add something
+42000
In the second one, the word withdrew means you will subtract something
-40
Which of the following identities is used to expand the polynomial (3x - 4y)2?
Recall that to expand a binomial we can use the following formula:
[tex](a+b)^2=a^2+2ab+b^2.[/tex]The above is known as the square of the binomial.
Answer:
Square of binomial.
Trisha is using the recipe show to make a fruit salad. She wants to use 20 diced strawberries in her fruit salad. How many bananas, apples, and pears show Trisha use in her fruit salad? Fruit Salad Recipe 4 bananas 3 apples 6 pears 10 strawberries bananas apples pears
The original recipe has half of the number of strawberries She wants to use in her salad in this case we will need double the fruits of the recipe given
Bananas
4x2=8 bananas
Apples
3x2=6 apples
Pears
6x2=12 pears
9. Rosie's Bakery just purchased an oven for $1,970. The owner expects the oven to last for 10years with a constant depreciation each year. It can then be sold as scrap for an estimatedsalvage value of $270 after 10 years. (20 points)a) Find a linear equation modeling the value of the oven, y, after x years of use.b) Find the value of the oven after 2.5 years.c) Find the y-intercept. Explain the meaning of the y-intercept in the context of this problem.d) Graph the equation of the line. Be sure to label the axes.
a)
The oven devaluated from $1970 to $270 in 10 years.
Since each year it looses the same value, divide the change in the price over the time interval to find the rate of change of the value with respect to time.
To find the change in price, substract the initial price from the final price:
[tex]270-1970=-1700[/tex]The change in price was -$1700.
Divide -1700 over 10 to find the change in the price per year:
[tex]-\frac{1700}{10}=-170[/tex]The initial value of the oven was $1970, and each year it looses a value of $170.
Then, after x years, the value will be equal to 1970-170x.
Then, the linear equation that models the value of the oven, y, after x years of use, is:
[tex]y=-170x+1970[/tex]b)
To find the value of the oven after 2.5 years, substitute x=2.5:
[tex]\begin{gathered} y_{2.5}=-170(2.5)+1970 \\ =-425+1970 \\ =1545 \end{gathered}[/tex]Then, the value of the oven after 2.5 years is $1545.
c)
To find the y-intercept, substitute x=0:
[tex]\begin{gathered} y_0=-170(0)+1970 \\ =1970 \end{gathered}[/tex]The y-intercept is the initial value of the oven when 0 years have passed.
d)
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3≤x≤6
STEP - BY - STEP EXPLANATION
What to find?
Rate of change of the given function.
Given:
Step 1
State the formula for rate of change.
[tex]Rate\text{ of change=}\frac{f(b)-f(a)}{b-a}[/tex]Step 2
Choose any two point within the given interval.
(3, 59) and (6, 44)
⇒a=3 f(a) =59
b= 6 f(b)=44
Step 3
Substitute the values into the formula and simplify.
[tex]Rate\text{ of change=}\frac{44-59}{6-3}[/tex][tex]=\frac{-15}{3}[/tex][tex]=-5[/tex]ANSWER
Rate of change = -5
Eva counts up. by 3s, while Jin counts up by 5s. What is the least
number that they both say?
Explanation:
This is the LCM (lowest common multiple) of 3 and 5
3*5 = 15
Eva: 3, 6, 9, 12, 15, 18, 21, ...
Jin: 5, 10, 15, 20, 25, ...
Is-7+9 = -9 + 7 true, false, or open?
A word problem made out of the equation 1/4+3-7/8x<-2
The word problem of the expression is "Seven eighths of a number less three and a quarter is less than 2"
How to determine the word problem?The inequality expression is given as
1/4 + 3 - 7/8x < 2
From the above expression, we can see that:
The right-hand side of the inequality is 2 and the inequality symbol is less than
This means that the word problem must end in "less than 2"
Next, we analyse the left-hand side
1/4 + 3 - 7/8x
A statement that represents the above is
Seven eighths of a number less three and a quarter is less than 2
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how many irrational numbers are there between 1 and 6? is it infinite?
infinite numbers
Explanation
An Irrational Number is a real number that cannot be written as a simple fraction,for example Pi()
[tex]\pi=3.141592654[/tex]Step 1
between 0 an 6 we have 6 integers numbers :(1,2,3,4,5,6)
Step 2
Now check this
a number for example
[tex]\begin{gathered} 3.14 \\ is\text{ different to } \\ 3.145 \\ and\text{ it is diferrent to} \\ 3.1458 \end{gathered}[/tex]so, the answer is infinite numbers
Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis,each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a/maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 persale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weeklysalary is $900.This task build on important concepts you've learned in this unit and allows you to apply those concepts to a variety ofsituations. Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis,each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with amaximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 persale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weeklysalary is $900. Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis,each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with amaximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 persale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weeklysalary is $900.
Given:
Salesman A earn = 65 per sale.
Salesman B earn = 40 per sales and 300weekly salary.
Salesman C earn = 900 weekly salary
Let "x" represent the number of sales each man
Salesman A earn is:
[tex]y=65x[/tex]Salesman B earn is:
[tex]y=40x+300[/tex][tex]\begin{gathered} 65x=40x+300 \\ 65x-40x=300 \\ 25x=300 \\ x=\frac{300}{25} \\ x=12 \end{gathered}[/tex]So total sales is 12 then.
S=0 For Zero week
[tex]\begin{gathered} \text{Salesman A} \\ y=65x \\ y=0 \end{gathered}[/tex][tex]\begin{gathered} \text{Salesman B} \\ y=40x+300 \\ y=40(0)+300 \\ y=300 \end{gathered}[/tex][tex]\begin{gathered} \text{ Salesman C} \\ y=900 \end{gathered}[/tex]For S=1
[tex]\begin{gathered} \text{Salesman A:} \\ y=65x \\ y=65(1) \\ y=65 \\ \text{Salesman B}\colon \\ y=40x+300 \\ y=40(1)+300 \\ y=340 \\ \text{Salesman C:} \\ y=900 \end{gathered}[/tex]For s=10
[tex]\begin{gathered} \text{Salesman A:} \\ y=65x \\ y=65(10) \\ y=650 \\ \text{Salesman B:} \\ y=40x+300 \\ y=40(10)+300 \\ y=700 \\ \text{Salesman c:} \\ y=900 \end{gathered}[/tex]−|a+b|/2−c when a=1 2/3 , b=−1 , and c=−3
ENTER YOUR ANSWER AS A SIMPLIFIED FRACTION IN THE BOX.
The value of the expression −|a + b|/2 − c when a =1 2/3 , b=−1 , and c=−3 is 8/3
How to evaluate the expression?From the question, the expression is given as
−|a + b|/2 − c
Also, we have the values of the variables to be
a =1 2/3 , b=−1 , and c=−3
Rewrite a as
a = 5/3
So, we substitute a = 5/3 b=−1 , and c=−3 in −|a + b|/2 − c
This gives
−|a + b|/2 − c = −|5/3 - 1|/2 + 3
Evaluate the difference in the expression
−|a + b|/2 − c = −|2/3|/2 + 3
Divide
−|a + b|/2 − c = −|1/3| + 3
Remove the absolute bracket and solve
−|a + b|/2 − c = 8/3
Hence, the solution is −|a + b|/2 − c = 8/3
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The required simplified value of the given expression is 8/3.
As per the given data, an expression −|a+b|/2−c is given when a=1 2/3, b=−1, and c=−3 the value of the expression is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the solution be x,
x = −|a+b|/2−c
Substitute value in the above equation,
x = - |1 + 2 / 3 - 1|/2 - (-3)
x = -1/3 + 3
x = -1+9 / 3
x = 8/3
Thus, the required simplified value of the given expression is 8/3.
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A police car traveling south toward Sioux Falls, Iowa, at 160km/h pursues a truck east away from Sioux Falls at 140 km/h. At time t=0, the police car is 60km north and the truck is 50km east of Sioux Falls. Calculate the rate at which the distance between the vehicles is changing at t=10 minutes, (Use decimal notation. Give your answer to three decimal places)
The rate of change of the distance between the police car and the truck after 10 minutes is approximately 193.66 m/s
What is a rate of change of a function?The rate of change of a function is the rate at which the output of the function is changing with regards to the input.
The velocity of the police car = 160 km/h south
The velocity of the truck = 140 km/h east
Distance of the police car from Sioux Falls = 60 km north
Distance of the truck from Sioux Falls = 50 km east
Required;
The rate at which the distance between the vehicles is changing at t = 10 minutes
Solution;
Let d represent the distance between the vehicles, we have;
d² = x² + y²
Where;
x = The distance of the truck from Sioux falls
y = The distance of the police car from Sioux Falls
Which gives;
[tex] \displaystyle{ \frac{d}{dt} d^2= \frac{d}{dt}(x^{2}) +\frac{d}{dt} (y^{2}) }[/tex]
Which gives;
[tex] \displaystyle{ 2 \cdot d \cdot \frac{d}{dt} d=2 \cdot x \cdot \frac{dx}{dt} + 2 \cdot y \cdot\frac{dy}{dt} }[/tex]
After 10 minutes, we have;
y = 60 - (10/60)×160 = 100/3
x = 50 + (10/60)×140 = 220/3
d = √((100/3)² + (220/3)²) = 20•(√146)/3
[tex] \displaystyle{ \frac{d}{dt} d=\frac{2 \cdot x \cdot \frac{dx}{dt} + 2 \cdot y \cdot\frac{dy}{dt} }{2 \cdot d }}[/tex]
Which gives;
[tex] \displaystyle{ \frac{d}{dt} d= \frac{2 \times \frac{220}{3} \times 140 + 2 \times \frac{100}{3} \times 160}{2 \times \frac{20 \times \sqrt{146}}{3}}}[/tex]
[tex] \displaystyle{ \frac{2 \times \frac{220}{3} \times 140 + 2 \times \frac{100}{3} \times 160}{2 \times \frac{20 \times \sqrt{146}}{3}}\approx 193.66}[/tex]
Therefore;
[tex] \displaystyle{ \frac{d}{dt} d \approx 193.66}[/tex]
The rate of change of the distance between the vehicles with time, [tex] \displaystyle{ \frac{d}{dt} d}[/tex] after 10 minutes is approximately 193.660 m/sLearn more about rate of change of a function here:
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An initial investment of $200 is appreciated for 20 years in an account that earns 6% interest, compounded continuously. Find the amount of money in the account at the end of the period.
To calculate the final amount of money at the end of the period, considering that the interest is compounded continuously you have to use the following formula:
[tex]A=P\cdot e^{rt}[/tex]Where
A is the accrued amount at the end of the given time
P is the principal amount
r is the annual nomial interes expressed as a decimal value
t is the time period in years
For this investment, the initial value is P= $200
The interest rate is 6%, divide it by 6 to express it as a decimal value
[tex]\begin{gathered} r=\frac{6}{100} \\ r=0.06 \end{gathered}[/tex]The time is t= 20 years
[tex]\begin{gathered} A=200\cdot e^{0.06\cdot20} \\ A=200\cdot e^{\frac{6}{5}} \\ A=664.02 \end{gathered}[/tex]After 20 years, the amount of money in the account will be $664.02
Find the equation for the line that passes through the point (−2,5), and that is perpendicular to the line with the equation x=−4.
The equation of the line perpendicular to x = -4 that passes through the point (-2,5) is y = 5 .
In the question ,
it is given that
the required line is perpendicular to x = -4
the slope of x = -4
x + 4 = 0
0.y = x + 4
slope = 1/0
so the slope of the perpendicular line [tex]=[/tex] 0 .
the equation of the perpendicular line passing through (-2,5) and slope as 0 is
(y - 5) [tex]=[/tex] 0*(x + 2)
y -5 = 0
y = 5
Therefore , The equation of the line perpendicular to x = -4 that passes through the point (-2,5) is y =5 .
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A gardener makes a new circular flower bed. The bed is ten feet in diameter. Calculate the circumference and the area of the circular flower bed.
Answer:
C = 31.4159
A = 78.5398
Step-by-step explanation:
diameter = 10
radius = 5
plug into formula: C = 2π5
A = π * 5²
The graph of F(x), shown below, has the same shape as the graph ofG(x) = x - x? Which of the following is the equation of F(x)?F(x) = ?
The graph of G(x) is symmetric with respect to the y-axis. It also passes through the origin.
Since the graph of F(x) moved 4 units upward, we must add 4 to the right of the equation. Thus, the equation of F(x) is as follows.
[tex]F(x)=x^4-x^2+4[/tex]A scale drawing for an apartment is shown below. In the drawing, 3cm represents 5m.
7,7,3,6
Actual area of the real back yard is 96 [tex]m^{2}[/tex]
[scale]=[drawing]/[real] —-> [real]=[drawing]/[scale]
scale=4 m/3 cm —> 0.75 cm/m
The backyard's measurements in the drawing are 9 x 6 cm.
Determine the backyard's actual dimensions
[Real]=[Drawing]/[Scale] for 9 cm
[real]=[9]/[0.75]——> 12 m
[Real]=[Drawing]/[Scale] for 6 cm
[real]=[6]/[0.75]——> 8 m
The backyard's actual measurements are 8 m × 12 m, and its actual size is 8 * 12 = 96 [tex]m^{2}[/tex].
Therefore the original area of the rectangle is 96 [tex]m^{2}[/tex].
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The complete question is as follows:
Below is a scale representation of a piece of land. In the illustration, 3 cm stands in for 4 m. Find the actual backyard space assuming the back is rectangular?