The distance between the two points A- (-4,-3) and as B- (0,0) shown in the question is 5 units.
What is Distance ?Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are.
The distance formula in coordinate geometry is used to calculate the distance between two given points. The distance formula to calculate the distance between two points (x1,y1) ( x1 , y1 ) , and (x2,y2) ( x2 , y2 ) is given as, D=√(x2−x1)²+(y2−y1)².
We have given the coordinates which is A- (-4,-3) and B- (0,0).
Now, we will determine the distance between these points,
Distance (d) = √(x2−x1)² + (y2−y1)²
(x1, y1) = Coordinates of the first point
(x2, y2) = Coordinates of the second point
Distance = √{0-(-4)}² + {0-(-3)}²
= √16 + 9 = √25
= 5
Hence the distance between the points AB is 5 units.
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7. Find the value of the following expression when x = 4, y = 8, a=3, b= 5: (4x²-a²¹ (²
a²¹ (x ² + √x + b)) ³
In linear equation, - 23,040 is the value of the expression.
What is linear equation in math?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.x = 4, y = 8, a=3, b= 5
= [tex]4x^{1/2} - ax^{-1} ( yx^{1/3} + \sqrt{x} + b )x^{3}[/tex]
value of x = 4, y = 8, a=3, b= 5
= [tex]4 * 4^{1/2} - 3 * 4x^{-1} ( 8^{1/3} + \sqrt{4} + 5) 4^{3}[/tex]
= 4 * 2 - 3 * 4 * 4 ( 2 + 2 + 5 ) * 64
= 8 - 48 ( 9 ) * 64
= - 40 * 9 * 64
= - 360 * 64
= - 23,040
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a. Tell whether the model represents exponential growth or exponential decay. b. Identify the annual percent increase or decrease in the value of the bike. c. Estimate when the value of the bike will be $50.
we have the function
[tex]y=200(0.75)^t[/tex]In this problem, we have an exponential decay function because the value of the base of the exponential function is less than 1
b=0.75
b< 1 -----> exponential decay function
Part b
Find out the annual percent decrease
b=0.75
b=1-r
0.75=1-r
r=1-0.75
r=0.25
r=25%
therefore
The annual percent decrease is 25%Part c
For y=$50
substitute in the given equation
[tex]50=200(0.75)^t[/tex]Solve for t
[tex]\frac{50}{200}=(0.75)^t[/tex]Apply log on both sides
[tex]\log (\frac{50}{200})=\log (0.75)^t[/tex][tex]\log (\frac{50}{200})=x\cdot\log (0.75)[/tex]x=4.8 yearsWhich would give the coordinates of the center of a circle?aFind the slope of the diameter.Find the midpoint of the diameter.Find the length of the diameter.Find the length of the radius.C Сd
If the endpoint of one diameter of a circle is as follows
[tex](x_1,y_1_{})(x_2_{}_{},y_2)[/tex]Then the centre of the circle can be calculated using the midpoint formula which can be represented below
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Therefore, the answer is b. Find the midp
(x^4 + 3x^3 y^2 + 4x^2y + 8xy + 12x) ( 11x^2y^3)
Given
(x^4 + 3x^3 y^2 + 4x^2y + 8xy + 12x)*( 11x^2y^3)
Procedure
[tex]\mleft(x^4+3x^3y^2+4x^2y+8xy+12x\mright)\cdot\mleft(11x^2y^3\mright)[/tex][tex]\mleft(11x^2y^3\mright)x^4+\mleft(11x^2y^3\mright)\cdot\: 3x^3y^2+\mleft(11x^2y^3\mright)\cdot\: 4x^2y+\mleft(11x^2y^3\mright)\cdot\: 8xy+\mleft(11x^2y^3\mright)\cdot\: 12x[/tex][tex]11x^6y^3+33x^5y^5+44x^4y^4+88x^3y^4+132x^3y^3[/tex]The answer is 11x^6y^3+33x^5y^5+44x^4y^4+132x^3y^3
Please help me with both I’ll mark you brainly
Answer:
See picture below
Step-by-step explanation:
It took a long time for my picture to show up.
Sandra does her grocery shopping for the week. The total is $212.00 including the sales tax. The bill without tax was $200.00. What is the tax on her groceries?Tax is 6%
You know that:
- The total is $212.00 and the sales tax is included.
- The bill without tax was $200.00.
Let be "x" the tax on her groceries (in dollars).
You need to subtract the bill without tax from the total amount of money Sandra paid for the groceries, in order to find the tax in dollars:
[tex]\begin{gathered} x=212-200 \\ x=12 \end{gathered}[/tex]To check it, you can multiply the total by 6%:
[tex]212\cdot\frac{6}{100}=12[/tex]Hence, the answer is: $12.00 (This is 6% of the total bill)
Juanita is tying ribbon on gift bags. She has 24 feet of ribbon and each gift bag uses 0.75 foot of ribbon. The function
r = 24-0.75g represents the amount of
ribbon r Juanita has left after tying ribbon on g gift bags. Find the zero of the function.
Describe
what this value means in the context of this situation
The zero of the function is at
- This
represents that after tying ribbon on bags, Juanita will have
feet of ribbon
left.
gift
This figure indicates that Juanita will run out of ribbon after tying 32 gift bags.
Explain about the zero of a function?A real number that fulfils the equation f(x) = 0 is a real zero of a function f(x). In other words, if f(r) = 0, we can claim that a real number 'r' is a function f(x) zero.Any substitution for the variable in a function that results in a zero answer is known as the zero. The x-intercept(s) of the function's graph, or the actual zero of a function, is the location on a graph where the function's graph crosses the x-axis.The function's zero is 32 gift bags. This indicates that Juanita will run out of ribbon after tying bows on 32 gift bags.Considering the query;
The quantity of ribbon Juanita has left after tying ribbon on gift bags is represented by the function r = 24 -0.75g.
At r = 0, the function's zero is located.
Therefore;
0 = 24 -0.75g
g = 24/0.75
g = 32.
This figure indicates that Juanita will run out of ribbon after tying 32 gift bags.
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hello I'm stuck on this homework problem and need help thank you
Given:
Inner radius circle = 10yd
Outer radius circle = 14 yd
One gallon of coating can cover = 4
Find-: How many gallons of coating do we need?
Sol:
The area of a circle is:
[tex]A=\pi r^2[/tex]The area of the outer circle is:
[tex]\begin{gathered} A=\pi r^2 \\ \\ =\pi(14)^2 \\ \\ =196\pi \end{gathered}[/tex]The area of the inner circle:
[tex]\begin{gathered} A=\pi r^2 \\ \\ A=\pi(10)^2 \\ \\ A=100\pi \end{gathered}[/tex]So the pool area is:
[tex]\begin{gathered} \text{ Area of pool = Area of outer circle - area of inner circle} \\ \\ =196\pi-100\pi \\ \\ =96\pi \end{gathered}[/tex]If one gallon of coating covers 4.
[tex]\begin{gathered} =\frac{96\pi}{4} \\ \\ =24\pi \\ \\ =75.4 \end{gathered}[/tex]So 75 gallons use for coating.
x-3=x^2 determines whether the equation is linear in x.
You have the following equation:
x - 3 = x²
In order to determine if the given equation is linear in x, you consider that a linerar equation is an equation in which the maximum exponet of the variable is 1. In this case you have that the higher exponent of the variable, which is x, is 2. 2 is the higher exponent, Becuase of that, the given equation is not linear, instead of that, the equation is quadratic.
true or false9. 1/i^3=1/i^7
SOLUTION
We are asked true or false if
[tex]\frac{1}{i^3}=\frac{1}{i^7}[/tex]Now
[tex]i=\sqrt[]{-1}[/tex]So,
[tex]\begin{gathered} (\sqrt[]{-1})^3=\sqrt[]{-1} \\ \\ \text{also } \\ \\ \sqrt[]{-1})^7=\sqrt[]{-1} \end{gathered}[/tex]So the statement is true.
Note that since the powers or indices are odd numbers, it would be the same
How are the coordinates of the extreme value and the equation from part B in the form y=(x - h)² - Crelated? extreme value is at (1, -8)
The coordinates of the extreme value or the vertex of the parabola is the (h, -c) of the equation form y = (x - h)² - c.
Solve for x using the "Quadratic Formula". You MUST show every level of work !!!!!!!!!!!!!!!!!
3x^2-5x+1
The solution to the quadratic equation 3x² - 5x + 1 using quadratic formula is; x = (5 + √13)/6 or (5 - √13)/6
How to use the quadratic formula?The general form of any quadratic equation is written as;
ax² + bx + c = 0
The quadratic formula that is used to solve this is given by;
x = [-b ± √(b² - 4ac)]/(2a)
Now, we are given the quadratic equation as;
3x² - 5x + 1
Thus, using quadratic formula we have;
x = [-(-5) ± √((-5)² - (4 * 3 * 1))]/(2 * 3)
x = [5 ± √(25 - 12)]/6
x = (5 ± √13)/6
x = (5 + √13)/6 or (5 - √13)/6
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Admission to a baseball game is $4.00 for general admission and $5.50 for reserved seats. The receipts were $5196.50 for 1181 paid admissions. How many of eachticket were sold?
Given:
Admission to a baseball game is $4.00 for general admission and $5.50 for reserved seats.
Let the number of tickets of general admission = x
Let the number of tickets of reserved seats = y
The receipts were $5196.50 ⇒ 4x + 5.5y = 5196.50
The paid admissions 1181 ⇒ x + y = 1181
So, we have the following system of equations:
[tex]\begin{gathered} 4x+5.5y=5196.50\rightarrow(1) \\ x+y=1181\rightarrow(2) \\ \text{from}(2)\colon x=1181-y\rightarrow(3) \end{gathered}[/tex]Substitute with x from (3) into (1) then solve to find y
[tex]\begin{gathered} 4(1181-y)+5.5y=5196.50 \\ 4\cdot1181-4y+5.5y=5196.5 \\ 4724+1.5y=5196.50 \\ 1.5y=5196.50-4724 \\ 1.5y=472.5 \\ y=\frac{472.5}{1.5}=315 \end{gathered}[/tex]Substitute with y into equation 3 to find x:
[tex]x=1181-315=866[/tex]So, the answer will be:
The number of tickets of general admission = 866
The number of tickets of reserved seats = 315
a line passes through the point (-8, -7) and has a slope of 3/2. write an equation in slope-intercept form for this line.
Answer:
y=(3/2)x+5
Explanation:
Given a line with a slope of 3/2 that passes through the point (-8, -7).
To determine the equation of the line, we first use the point-slope form below.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ m=\frac{3}{2} \\ (x_1,y_1)=(-8,-7) \end{gathered}[/tex]Substituting, we have:
[tex]\begin{gathered} y-(-7)=\frac{3}{2}(x-(-8)) \\ y+7=\frac{3}{2}(x+8) \end{gathered}[/tex]Next, we express the line in the slope-intercept form (y=mx+b).
[tex]\begin{gathered} y+7=\frac{3}{2}x+12 \\ y=\frac{3}{2}x+12-7 \\ y=\frac{3}{2}x+5 \end{gathered}[/tex]The equation of the line in slope-intercept form is:
[tex]y=\frac{3}{2}x+5[/tex]One fifth or r is 15 algebraic expression algebraic expression
The value of the base number, r is 75 and the corresponding algebraic expression is 0.2r = 15.
What is an algebraic expression and how is it formed?
Variables and constants are used to create algebraic expressions using a variety of techniques. It is a mathematical expression made up of terms and includes variables, constants, and algebraic operations like addition, subtraction, etc. When operations like addition, subtraction, multiplication, division, etc. are performed on any variable, the resulting equations are called algebraic expressions. An algebraic expression (or variable expression) is a grouping of terms that have undergone operations like addition, subtraction, multiplication, division, etc.
Given, the base number is = r
One fifth of the base number will be = (1/5)r = 0.2r
Also, one fifth of r is 15, thus 0.2r = 15 ⇒ r = 15/0.2 = 75
Thus, the value of the base number, r is 75 and the corresponding algebraic expression is 0.2r = 15.
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The algebraic expression "One fifth of r is 15" is represented as r/5 = 15. Solving for r, r = 75.
Let's break this down step-by-step:
1. "One fifth of r" means you are dividing r by 5, which in algebraic terms would be represented as r/5.
2. The phrase "is" in algebra typically signifies the equals sign (=).
3. Finally, "15" is just the number 15.
Putting these together, the algebraic expression for "One fifth of r is 15" is r/5 = 15.
To clarify this further, this equation is saying that if you take the value of r, divide it by 5, the result should be 15. This is an equation you can solve to find the value of r.
If you're curious, solving this equation for r would look like this:
Step 1: Start with the equation r/5 = 15.
Step 2: To isolate r, you need to get rid of the division by 5. You can do this by multiplying both sides of the equation by 5.
Step 3: This gives you r = 15 * 5.
Step 4: Calculate 15 * 5 to get 75. So r = 75.
So, if one fifth of r is 15, then r would be 75.
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find the measure of arc GM if KP=PL and GM=36ft.
Given:
KP = PL
GH = 36 ft
Let's find the measure of arc GM.
Apply the angle arc relationship to find the measure of angle KGL:
[tex]KG\text{L}=\frac{HJ}{2}[/tex][tex]KGL=\frac{52}{2}=26\text{ degre}es[/tex]GKP + GLP + KGL + KGP = 360 degrees
90 + 90 + 26 + KPL = 360
206 + KPL = 360
Subtract 206 from both sides:
206 - 206 + KPL = 360 - 206
KPL = 154 degrees
To find the measure of arc GM, we have:
[tex]\begin{gathered} arcGM=\frac{KPL}{2} \\ \\ arcGM=\frac{154}{2} \\ \\ \text{arcGM}=77\text{ degre}es \end{gathered}[/tex]Therefore, the length of arc GM is 77 degrees
ANSWER:
77°
The coaches of a school football team want to know how many families from the school plan to attend this week's game. Each coach takes a different approach to obtain this information. Which sampling method would provide a good representation of the population? F Call all the parents of the football players to ask if their families will attend the game. G Stop every fifth car that enters the school parking lot one morning to ask if their families will attend the game. H Ask all the students in the last period PE class if their families will attend the game. J Choose every fourth student from an alphabetical list of the entire student body and ask if their families will attend the game
The option that takes samples putting the entire families of the students into account is the last option.
Option J is the correct answer
what is the greatest common factor of the numbers 2835 and 8960
35
Step-by-step explanation:
3x3x3x3x5x7
hope it helps have a nice day with apples
I need help with this! I don’t know how to do it!!
Answer:
6c+11≤67
Step-by-step explanation:
To write this as an inequality, since it says 6 times a number, write:
6c
Now, since it is increased by 11, write:
6c+11
Finally, since it says at most 67, write
6c+11≤67.
Hope that helps!
Help 50 points please show your work
DUE TODAY
Answer:
3. 72 questions
4. 180 students
5. 120 students
6. 9 puzzles
Step-by-step explanation:
Question 3[tex]\begin{aligned}\implies \rm 80\% \;of \; 90 \; questions & =80\% \times 90\\&= \dfrac{80}{100} \times 90\\& = \dfrac{7200}{100}\\& = 72\end{aligned}[/tex]
Therefore, a student must answer 72 questions correctly to pass the test.
Question 4[tex]\begin{aligned}\implies \rm 40\%\; of\; 450\; students & = 40\% \times 450\\& = \dfrac{40}{100} \times 450\\& = \dfrac{18000}{100}\\& = 180\end{aligned}[/tex]
Therefore, at least 180 students must plan to attend in order for the school to have the festival.
Question 5[tex]\begin{aligned}\implies \rm 40\% \; of \; 300 \; students & = 40\% \times 300\\& = \dfrac{40}{100} \times 300\\& = \dfrac{12000}{100}\\& = 120\end{aligned}[/tex]
Therefore, 120 students chose recycling.
Question 6If 55% of 20 puzzles are completed, then 45% of 20 puzzles are left to complete, since 100% - 55% = 45%.
[tex]\begin{aligned}\implies \rm 55\% \; of \; 20 \; puzzles & = 45\% \times 20\\& = \dfrac{45}{100} \times 20\\& = \dfrac{900}{100}\\& = 9\end{aligned}[/tex]
Therefore, Magdalena has 9 puzzles left to complete.
please tell me someone knows this
The vertex of the given graph is (0,5).
The axis of symmetry is y = 5x.
The number of zeroes are 3.
The x intercepts are 0 and -5.
the y intercepts are (-3,0) and 0,-3).
What is a parabola?A quadratic function's graph is called a parabola. According to Pascal, a parabola is a circle's projection. Galileo explained that projectiles falling under the influence of homogeneous gravity have a path known as a parabolic path. Many bodily movements have a curvilinear course with the shape of a parabola. In mathematics, a parabola is any mirror-symmetrical plane curve that typically has the shape of a U. Here, our goal is to comprehend the origin of the parabola's standard formula, its several standard forms, and its characteristics. A parabola is an equation of a curve where a point on the curve is equally far from a fixed point.
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help mee pleasee!!
thank you <3
An equation that models the number of people employed in some country as medical assistant in the last year x is y = 359 + 14.35x
In this question, we have been given the number of people employed in some country as medical assistant.
We need to write an equation that models the number of people employed in some country as medical assistant in the last year x.
the number of people employed in some country as medical assistant:
in 2004 = 359 thousand
and by 2014 this number is expected to be 560 thousand.
We find the rate of employment.
Consider (x1, y1) = (0, 359) and (x2, y2) = (14, 560)
m = (560 - 359)/(14 - 0)
m = 201/14
m = 14.35
We have been given the line must pass through points (0, 359) and (14, 560)
And, we get the y-intercept c = 359
with slope m = 14.35 and y-intercept c = 359, the equation of the line would be,
y = 14.35x + 359
Therefore, an equation that models the number of people employed in some country as medical assistant in the last year x is y = 359 + 14.35x
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I need some help please do this
The coefficient of z² is 25 and the constant term is 28. The product of 25 and 28 is 700. The factors of 700 which sum to -55 are -20 and -35, so:
[tex]\begin{gathered} 25z^2-55z+28=(5z-4)(5z-7) \\ so\colon \\ z=\frac{4}{5} \\ and \\ z=\frac{7}{5} \end{gathered}[/tex]The cost C(ar), where a is the number of miles driven, of renting a car for a day is $45 plus $0.25 per mile.
What is the slope of the linear function and its units?
select the correct units
What is the y-intercept and its units?
units
What is the linear function, C(a)? C(x)
C(x) = 0.25x + 45 , Slope is .25 dollars per mile and the y intercept is 45 dollars.
Given,
The cost C(ar), where a is the number of miles driven, of renting a car for a day is $45 + $0.25 per mile.
To find the slope , y - intercept and C(a)
Now, According to the question:
A renting a car for a day is $45 plus $0.25 per mile.
C(x) = 0.25x + 45
This is in the form y = mx + b where m is the slope and b is the y intercept
The slope is .25 dollars per mile and the y intercept is 45 dollars
Hence, C(x) = 0.25x + 45 , Slope is .25 dollars per mile and the y intercept is 45 dollars.
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what is 42,099 rounded to the nearest thousand
We are given 42,099
To round off to the nearest thousand, we need to check the hundredth digit
Ten thousandth digit = 4
Thousandth digit = 2
Hundredth = 0
Tenth = 9
Unit = 9
If the hundredth digit is 0, 1, 2, 3 and 4, then you need to round off to the previous thousand
The answe is 42, 000
7. Use the equation E =2- my for the following questions:2(a) Rearrange the equation so that it's solved for m.Show your work here:Solution:m =
Solution: (a)
Given the equation;
[tex]E=\frac{1}{2}mv^2[/tex]Multiply both sides of the equation by 2;
[tex]\begin{gathered} 2\times E=2(\frac{1}{2})mv^2 \\ 2E=mv^2 \end{gathered}[/tex]Divide both sides by the square of the velocity v;
[tex]\begin{gathered} \frac{2E}{v^2}=\frac{mv^2}{v^2} \\ m=\frac{2E}{v^2} \end{gathered}[/tex]ANSWER:
[tex]m=\frac{2E}{v^2}[/tex](b) Given;
[tex]E=125,000J,v=24ms^{-1}[/tex]We would substitute the value of the energy and the velocity into the formula for mass, we have;
[tex]\begin{gathered} m=\frac{2E}{v^2} \\ m=\frac{2(125000)}{24^2} \\ m=\frac{250000}{576} \\ m=434.03 \end{gathered}[/tex]
you are a freelancer and were offered two gigs. one will pay you $25,000today and the other will pay you $5,000 per year over the next six years. assuming your required return is 8%, which gig should you accept, assuming you are in it just for the money?
The preferred gig is the first one since its today's worth is greater than the today's value of the second gig
What is the today's worth of $5000 each year?
The worth of the second gig, which pays $5000 every year for the next 6 years in today's dollar is the present value of all the six annual cash flows discounted using the present value formula of an ordinary annuity as shown below:
PV=PMT*(1-(1+r)^-N/r
PV=present value of annual payments for 6 years=unknown
PMT=annual payment=$5000
r=required return=discount rate=8%
N=number of annual cash flows=6
PV=$5000*(1-(1+8%)^-6/8%
PV=$5000*(1-(1.08)^-6/0.08
PV=$5000*(1-0.630169626883105)/0.08
PV=$5000*0.369830373116895
/0.08
PV=$23,114.40
The fact that the present value of the second option which pays $5000 annually is lesser than the amount receivable immediately, which is $25,000, hence, the first gig is preferred
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Please I need help please I need help
The number of groups of 1/9 in 2 are 18.
The value of 2 ÷ (4/9) = 9/2.
We can see a number line with equal intervals of 1/9.
We have to find the number of groups of 1/9 in 2 and the value of 2 ÷ (4/9) .
As we can see in the number line,
2 is two intervals after 16/9 , hence,
2 = 16/9 + 1/9 + 1/9 = 16/9 + 2/9 = 18/9
We can write it as,
(1/9)*18
Hence, there are 18 groups of 1/9 in 2.
The value of 2 ÷ (4/9) = 2*(9/4) = 18/4 = 9/2.
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6d. Write an equation to represent the dollar amount in her savingsaccount and the number of weeks of saving. Be sure to specify what eachvariable represents.
Answer:
y = 24x + 80
Where x is the number of weeks of saving and y is the dollar amount in her savings
Explanation:
We need to find the equation of the line. If x is the number of weeks of saving and y is the amount in her savings, the equation has the following form
y = mx + b
Where m is the slope and b is the y-intercept.
The slope can be calculated using two points in the line (x1, y1) and (x2, y2) as follows
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Then, replacing (x1, y1) = (0, 80) and (x2, y2) = (5, 200), we get:
[tex]m=\frac{200-80}{5-0}=\frac{120}{5}=24[/tex]Additionally, the y-intercept is the point where the graph crosses the y-axis. In this case, the point is (0, 80), so the value of b is 80.
Therefore, the equation of the line is
y = 24x + 80
Where x is the number of weeks of saving and y is the dollar amount in her savings
Layla skated x kilometers around the rink. Lamel skated 5/2 less than Layla.
Now write an equivalent equation to show how many kilometers Lamel skated around the rink.
An equivalent equation to show how many kilometers Lamel skated around the rink is x - 5/2.
Linear equations in one variable
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
For example, 2x+3=8 is a linear equation having a single variable in it.
Given that Layla skated x kilometers around the rink, Lamel skated 5/2 less than Layla.
Therefore Lamen skated x - 5/2 kilometers, as Lamen skated 5/2 less than the kilometers skated by Layla
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