The equation is:
[tex]y=-3(x-2)^2+3[/tex]So this is a parabola, so we can graph it with the vertex and the intercections with the x axis
So the vertex is in the coordinat (2,3) becuase of the transformation of -2 in the x axis and +3 in the y axis so the vertex is (2, 3)
now for the interception with the x axis we replace y = 0 and solve for x so
[tex]0=-3(x-2)^2+3[/tex]we open the parenthesis like:
[tex]undefined[/tex]I got this wrong can you tell me what I did wrong and show me?
The value of the car after 10 years at the given rate of depreciation will be approximately $5013.02 .
The current value of the car = $18000
Rate of depreciation = 12%
So using the formula for depreciation we get:
Let the final value be A
∴ A = P ( 1 - R/100 )ⁿ
Substituting the values we get :
A = 18000(1-0.12)¹⁰
Solving we get:
A = $ 5013.01756....
A ≈ $ 5013.02
Due to usage, deterioration, or obsolescence, an asset reduces value over time. The unit of measurement for this drop is depreciation.
A reduction in asset value, or depreciation, can be caused by a number of other factors, such as unfavorable market conditions, etc.
Hence the final value of the car after 10 years is approximately
$ 5013.02 .
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In scientific notation, 0.00000729=?
Answer:
7.29 x 10^-6
Step-by-step explanation:
the number must be between 1 and 9
then the 0 are 6
We put minus because we go to the left
7.29 x 10^ -6
Now, use the angle measurement tool to measure the angles of each polygon. Do the angle measures agree with your results ?
Solution: Answer is correct in three cases.
When we have a triangle, the sum of measures of angles are 180 degrees. In the three pictures of polygons, we have two triangles in each one. So, the sum of angles would be 360 degrees in all cases.
Case A: We have 85+80+100+x = 360. We isolate X,
X=360-85-80-100
X= 95 degrees.
Case B: We have 72+78+60+x = 360. We isolate X,
X=360-72-78-60
X= 150 degrees.
Case C: We have 90+90+30+x = 360. We isolate X,
X=360-90-90-30
X= 150 degrees.
A rectangular park is 60 meters wide and 105 meters long. Give the length and width of another rectangular park that has the same perimeter but a smaller area.
First we find the area of the first park
[tex]\begin{gathered} A=w\times l \\ A=60\times105 \\ A=6300 \end{gathered}[/tex]area is 6300 square meters
now find the perimeter
[tex]\begin{gathered} P=2w+2l \\ P=2(60)+2(105) \\ P=330 \end{gathered}[/tex]perimeter is 330 meters
now we need to write equations to find the measures of the another park and we can write from the statements
has the same perimeter
[tex]2w+2l=330[/tex]but a smaller area
then we choose an area smaller than 6300, for example 6000
[tex]w\times l=6000[/tex]now we have two equations and two unknows
[tex]\begin{gathered} 2w+2l=330 \\ w\times l=6000 \end{gathered}[/tex]then we can solve a unknow from one equation and replace on the other
I will solve w from the first equation and replace on second
[tex]\begin{gathered} 2w=330-2l \\ w=\frac{330-2l}{2} \\ \\ w=165-l \end{gathered}[/tex][tex]\begin{gathered} w\times l=6000 \\ (165-l)\times l=6000 \\ 165l-l^2=6000 \end{gathered}[/tex]rewrite the equation
[tex]l^2-165l+6000=0[/tex]and use quadratic formula to solve L
[tex]\begin{gathered} l=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \\ l=\frac{-(-165)\pm\sqrt[]{(-165)^2-4(1)(6000)}}{2(1)} \\ \\ l=\frac{165\pm\sqrt[]{27225-24000}}{2} \\ \\ l=\frac{165\pm\sqrt[]{3225}}{2} \end{gathered}[/tex]then we have two values for l
[tex]\begin{gathered} l_1=\frac{165+\sqrt[]{3225}}{2}=110.9 \\ \\ l_2=\frac{165-\sqrt[]{3225}}{2}=54.1 \end{gathered}[/tex]we can take any value because both are positive and replace on any equation to find w
I will replace l=110.9 to find w
[tex]\begin{gathered} w\times l=6000 \\ w\times110.9=6000 \\ w=\frac{6000}{110.9} \\ \\ w=54.1 \end{gathered}[/tex]Finally the length and wifth of the other rectangle patks are
[tex]\begin{gathered} l=110.9 \\ w=54.1 \end{gathered}[/tex]meters
72 inches=___ yards please and thank you for your help
We know that:
[tex]1yd=36in\text{.}[/tex]Then:
[tex]1in=\frac{1}{36}yd\text{.}[/tex]Therefore:
[tex]72in=72\cdot(\frac{1}{36}yd)\text{.}[/tex]Simplifying the above result we get:
[tex]72\cdot\frac{1}{36}yd=2yd\text{.}[/tex]Answer:
[tex]72\text{inches}=2\text{yards.}[/tex]given that triangle DEF is a right triangle with acute angles D and F and right angle E, which trigonometric function would be equal to Sin(F).
EXPLANATION
We can represent this situation as shown as follows:
The expression of Sin(F) is equal to Sin F = Opposite/Hypotenuse = DE/DF
[tex]\sin F=\frac{Opposite}{\text{Hypotenuse}}=\frac{DE}{DF}[/tex]The equivalent expression would be:
[tex]Cos\text{ D=}\frac{Adjacent}{\text{Hypotenuse}}=\frac{DE}{DF}[/tex]Point K is the center of the circle. Which segment is a radius?FGGEFHKEGDKHE
SOLUTION
The radius of a circle is a line segment that runs from the center of the circle to any point of the circumference
Hence from the option provided, only the line |KH| runs from the center to a point of the circumference, hence it is a radius
Therefore the right option is the last one
What is the solution to the following equation?
3(x-4)-5 = x - 3A. x = 12B. x=3C. x=8D. x = 7
Given:
3(x-4)-5 = x - 3
Required:
To calculate which option is correct
Explanation:
[tex]\begin{gathered} 3(x-4)-5=x-3 \\ \\ 3x-12-5=x-3 \\ \\ 3x-17=x-3 \\ \\ 3x-x=-3+17 \\ \\ 2x=14 \\ \\ x=\frac{14}{2} \\ \\ x=7 \end{gathered}[/tex]Required answer:
Option D (x=7)
A certain town has two kinds of youth basketball teams. When is a school team (S) and the other is a rec team (R) . On any given Saturday in December the probability that school team will have the game is 0.8, and the probability that a rec team will have a game is 0.7 and probably that both where the game is 0.65.on any given Saturday in December, what is the probability that either a rec team or a school team has a game?Answer Choices:A. 0.65B. 0.7C. 0.8D. 0.85
Answer:
D. 0.85
Explanation:
We were given the following information:
Probability of S = 0.8
Probability of R = 0.7
Probability of S & R = 0.65
The probability that either a rec team or a school team has a game is given by:
[tex]\begin{gathered} P(S)=0.8 \\ P(R)=0.7 \\ P(S\cap R)=0.65 \\ \text{Since the events are overlaaping, the applicable formula is:} \\ P(S\text{ }or\text{ }R)=P(S)+P(R)-P(S\cap R) \\ P(S\text{ }or\text{ }R)=0.8+0.7-0.65 \\ P(S\text{ }or\text{ }R)=1.5-0.65 \\ P(S\text{ }or\text{ }R)=0.85 \\ \\ \therefore P(S\text{o}r\text{R})=0.85 \end{gathered}[/tex]Therefore, the answer is D
Round the value 23.731 g to three significant figures.Express your answer numerically using three significant figures.
23.731 g rounded to three significant figures is 23.7 g.
Rule for significant figures:
All non-zero numbers are significant.
In 23.731, there are 5 non-zero numbers. So, there are 5 significant figures. To get number in 3 significant figures round the number at the first decimal place.
Now, the 23.731 g can be expressed in 3 significant figures as 23.7 g.
I have no idea how to do this please help
Answer:
Initial Value: 19,900
Value after 11 years: 7953
Explanation:
The initial value of the car is its value at t =0. Therefore, to find this initial value, we put in t = 0 to get
[tex]v(0)=19,900(0.92)^0[/tex][tex]\boxed{v\mleft(0\mright)=19,900}[/tex]Hence, the initial value is $19,900.
Now, to find the value after 11 years, we put t = 11 into the equation and get
[tex]v(11)=19,900(0.92)^{11}[/tex]which gives (rounded to the nearest dollar)
[tex]\boxed{v\mleft(11\mright)=7953}[/tex]which is our answer!
Hence, the value after 11 years is $7953.
which graph best repersents tge solution to the system of equations
y=x+4
y=3x-6
The solution to the system of linear equation (x, y) are 5 and 9
Graph of Linear EquationsLinear equations, also known as first-order degree equations, where the highest power of the variable is one. When an equation has one variable, it is known as linear equations in one variable. If the linear equations contain two variables, then it is known as linear equations in two variables, and so on.
The solution of a linear equation in two variables is a pair of numbers, one for x and one for y which satisfies the equation. There are infinitely many solutions for a linear equation in two variables.
Therefore, every linear equation in two variables can be represented geometrically as a straight line in a coordinate plane. Points on the line are the solution of the equation. This why equations with degree one are called as linear equations. This representation of a linear equation is known as graphing of linear equations in two variables.
Using graph to solve this problem, the solution to the equations are (x, y) are 5 and 9 respectively.
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determine wether the point is a solution of the system. (-1,-2) 5x-2y=-1 x-3y=5
Step 1
Given; The system of equation;
[tex]\begin{gathered} 5x-2y=-1--(a) \\ x-3y=5---(b) \\ \text{Required; To know if the point (-1,-2) is a solution to the system} \end{gathered}[/tex]Step 2
Input x=-1 and y=-2 in both equations and find if they will give -1 and 5 respectively.
[tex]\begin{gathered} 5(-1)-2(-2)=-5+4=-1 \\ -1-3(-2)=-1+6=5 \end{gathered}[/tex]Since both equations gave us -1 and 5 respectively when we input x=-1 and y=-2, then we can conclude that the point (-1,-2) is a solution to the system.
I need help with my math
The pythagorean Theorem say:
[tex]h=\sqrt[]{l^2_1+l^2_2}[/tex]In this problem l1 and l2 will be a and b so:
[tex]h=\sqrt[]{14^2+18^2}[/tex]So finally we operate and we get:
[tex]\begin{gathered} h=\sqrt[]{196+324} \\ h=\sqrt[]{520} \\ h=22.8 \end{gathered}[/tex]why does adding and subtracting 2pi or 360 degrees give a coterminal angle?
SOLUTION:
Step 1:
In this question, we are given the following:
Why does adding and subtracting 2pi or 360 degrees give a coterminal angle?
Step 2:
The details of the solution are as follows:
Find the volume of a cylinder whose base has a radius of 3 inches and whose height is 12.5 inches. Use π = 3.14 and round your answer to the nearest tenth37.5 in^3333.8 in^3353.3 in^3421.8 in^3
Answer:
353.3 in^3
Explanation:
Given:
The radius of the base of the cylinder (r) = 3 inches
The height of the cylinder (h) = 12.5 inches
pi = 3.14
To find:
The volume of the cylinder
We'll use the below formula to determine the volume(V) of the cylinder;
[tex]V=\pi r^2h[/tex]Let's go ahead and substitute the given values into the formula and solve for V;
[tex]V=3.14*3^2*12.5=3.14*9*12.5=353.3\text{ in}^3[/tex]So the volume of the cylinder is 353.3 in^3
69). If a restaurant's gross receipts for one day total $39.500, of which $5,600 are expenses that percent of the gross receipts are expenses?
Total receipts = $39,500
Expenses = $5,600
Percentage expenses =
[tex]\frac{5600}{39500}\times100=\frac{5600\times100}{39500}=14.177\approx14.2\text{ \%}[/tex][tex]\text{ \% expenses =}\frac{Actual\text{ expenses}}{\text{Total Receipts}}\times\frac{100}{1}[/tex]Solution: The percentage of expenses is 14.2%
JetLine Airline provides Michael with the following measurements forcarry-on luggage: 14 in x 9 in x 22 in. Convert the dimensions tocentimeters.
Given that:
Dimensons of luggage = 14 in x 9 in x 22 in
Since 1 inch = 2.54 cm,
[tex]\begin{gathered} 14\text{ in = (14}\cdot2.54)cm \\ =35.56cm \end{gathered}[/tex][tex]\begin{gathered} 9\text{ in=(9}\cdot2.54)cm \\ =22.86cm \end{gathered}[/tex][tex]\begin{gathered} 22\text{ in=(22}\cdot2.54)cm \\ =55.88cm \end{gathered}[/tex]The dimension in centimeters is 35.56 cm x 22.86 cm x 55.88 cm.
find the slope (1, 2), (-3, 3)
Given:
The points are (1, 2), (-3, 3).
The slope is calculated as,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)=\mleft(1,2\mright) \\ (x_2,y_2)=(-3,3) \\ m=\frac{3-2}{-3-1} \\ m=\frac{1}{-4} \\ m=-\frac{1}{4} \end{gathered}[/tex]Answer: slope = -1/4
What is the difference between 63,209 and 8,846?
From the question,
We are to find the difference between 63,209 and 8,846
Difference is given as
[tex]63,209-8,846[/tex]Therefore, we have
Therefore the difference between 63,209 and 8,846 is
54,363
Select the correct phrase in the drop-down menu to complete the sentence for the first job down you have G(-1)____the answer can be either greater than h(-1) or equal to h(-1) or less than h(-1) . For the second drop down answer it has G(1)____ the answer can be either greater than h(1) or equal to h(1) or less than h(1)
We are given the graph of a parabola represented by g(x) and the linear function h(x). To determine the value of g(-1) we go to the graph of the function and determine that the value is:
[tex]g(-1)=-2[/tex]To determine the value of h(-1) we replace the value of "x" in h(x) for -1:
[tex]\begin{gathered} h(-1)=-3(-1)+8 \\ h(-1)=3+8 \\ h(-1)=11 \end{gathered}[/tex]Therefore, since:
[tex]11>-2[/tex]we have that g(-1) is less than h(-1).
We do a similar procedure to determine g(1) from the graph:
[tex]g(1)=5[/tex]And we replace x = 1 in h(x) to get h(1):
[tex]\begin{gathered} h(1)=-3(1)+8 \\ h(1)=-3+8 \\ h(1)=5 \end{gathered}[/tex]Since we get the same value this means that g(1) is equal to h(1).
function c is defined by the equation c(n)=50+4n. it gives the monthly cost in dollars of visitiing a gym as a function of the number of visits v. find the value of c (7). show your reasoning and explain what the value means in this situation
The cost function is defined as
[tex]c(n)=50+4n[/tex]The value of c(7) can be determined by substituting 7 for n into the function.
Therefore, c(7) becomes;
[tex]\begin{gathered} c(7)=50+4(7) \\ c(7)=50+28 \\ c(7)=78 \end{gathered}[/tex]This means the cost of 7 visits to the gym is $78.
The cost function shows that there is an amount that doesnt change and that is 50. Then there is one that varies or changes with every visit, or n. That means as the value of n increases or decreases, the total amount also increases or decreases. When n equals zero, then the total cost becomes 50. This means when there is no visit to the gym, the cost still remains $50.
Therefore, n is a variable that can determine changes in the total cost.
Answer: c(7)=78
Step-by-step explanation:
C(n)=50+4n
c(7)=50+4(7)
=50+28
=78
C(7)=78
Find the equation of the line containing the given points. Write the equation in slope-intercept form. (3,8) and (3,-4)
Answer with explanation: We have to find the equation of the line that passes through the given coordinate points, (3,8) (3,-4) the general equation of the line is as follows:
[tex]\begin{gathered} y(x)=mx+b\rightarrow(1) \\ m=\frac{\Delta y}{\Delta x}\rightarrow\text{ Slope of the equation} \end{gathered}[/tex]The slope of the equation is calculated as follows:
[tex]\begin{gathered} P_1(x_1,y_1)=(3,8) \\ P_2(x_2,y_2)=(3,-4) \\ \therefore\rightarrow \\ m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{-4-8}{3-3}=\infty \\ m=\propto \end{gathered}[/tex]This suggests the equation of the line is simply a vertical line at x = 3, the graph of the equation is as follows:
[tex]x=3\text{ Is the equation of the line}[/tex]Which property is shown? 18a X 32b = 325 x 18a a. Associative Property of Multiplication b. Commutative Property of Multiplication c. Distributive Property d. Identity Property
Solution
We have the following equation given:
18a X 32 b = 32 b x 18a
And we can see that the solution is:
b. Commutatitative property of multiplication
since the order of the factors not alter the result
Caculate question a and b
Answer:
a. 9.4cm
b. 12.0cm
Step-by-step explanation:
a. (HYP)² = (ADJ)² + (OPP)²
= 5² + 8²
= 25 + 64
√(HYP)² = √89cm
HYP = 9.4cm
b. (ADJ)² = (HYP)² - (OPP)²
= 17² - 12²
= 289 - 144
√(ADJ)² = √145cm
ADJ = 12.0cm
5.Tyler is solving this system of equations:{4p + 2q = 628p -q=59He can think of two ways to eliminate a variable and solve the system:Multiply 4p + 2q = 62 by 2, then subtract 8p - q = 59 from the result.Multiply 8p - q = 59 by 2, then add the result to 4p + 2q = 62.5. Read the information above about how Tyler is solving the problem. Doboth strategies work for solving the system? Explain or show yourreasoning. *
I) 4p + 2q = 62
II) 8p - q = 59
Both strategies will work for solving the system, since, for the first one, he will eliminate the variable p and get the expression 5q = 65, and, for the second one, he will eliminate the variable q and get the expression 20p = 180
In circle o, a diameter has endpoints (-5,4) and(3, -6). What is the length of the diameter?Answer choices: a.) sqrt 10b.) 2sqrt 41c.) sqrt 2 d.) 2sqrt 2
Diameter has endpoints (-5,4) and (3, -6).
the endpoints of the diameter = (-5,4) and (3,-6)
The length of diameter can be calculated by sqrt 10,11
Distance between two coordinates (-5,4) and (3,-6).
Distance formula is express as
[tex]\begin{gathered} \text{Distance = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^1^{}} \\ \text{Distance}=\sqrt[]{(3-(-5))+(-6+(4))} \\ \text{Diamter = }\sqrt[]{8-(-2)} \\ \text{Diameter = }\sqrt[]{10} \end{gathered}[/tex]Diameter = sqrt 10
Answer: Diameter = sqrt 10
Geometric Vectors in Cartesian Form
Hello there. To talk about geometric vectors in cartesian form, we have to remember some properties about linear algebra.
Given two vectors u and v, we say they are written in cartesian coordinates if they have the following notation:
[tex]\begin{gathered} u=\langle u_1,\,u_2\rangle \\ \\ v=\langle v_1,\,v_2\rangle \end{gathered}[/tex]Of course, this notation is for vectors in two dimensions, so we say that
[tex]u,v\in\mathbb{V}^2[/tex]That is the vector space with two dimensions.
We can extend this to all the plane, considering the coordinates can take all values in the real numbers, hence
[tex]u,v\in\mathbb{R}^2[/tex]And finally extend this to n-dimensions, but in this case we cannot understand it geometrically since we can, at most, geometrically represent a vector up to three dimensions
[tex]u,v\in\mathbb{R}^n[/tex]Some properties about vectors:
They are associative, that means that
[tex](u+v)+w=u+(v+w)[/tex]We have also the distributive property
[tex](u+v)\cdot w=u\cdot w+v\cdot w[/tex]Whereas
[tex]\cdot\text{ is the scalar product operator}[/tex]It also holds for cross products and other kinds of products.
They are commutative
[tex]u+v=v+u[/tex]This holds for the scalar product:
[tex]u\cdot v=v\cdot u[/tex]but it doesn't for the cross product
[tex]u\times v=-v\times u[/tex]Now, we have the geometrical view of vectors.
Say we have a point (x, y) and we want to define a vector from this point.
So we plug the tail of the vector at the origin and its tip in the point, as follows:
We can define a vector from point to point as well, but we say that they are equipollent to a vector with its tail at the origin and has the same magnitude of the vector we found.
In higher dimensions, we have
In cartesian form, we can rewrite the vectors in the following notation:
The scalar product is defined as:
[tex]u\cdot v=\langle u_1,u_2\rangle\cdot\langle v_1,v_2\rangle=u_1v_1+u_2v_2[/tex]For higher dimensions, it holds that
[tex]u\cdot v=\langle u_1,u_2,\cdots,u_n\rangle\cdot\langle v_1,v_2,\cdots,v_n\rangle=\sum_{i=1}^nu_iv_i[/tex]These are the main properties about vectors.
how to compare fractions 15/8 and 12/7
Answer:
To compare fractions 15/8 and 12/7
In order to comapare any two fractions, the denomiator of the two fractions must be same.
For the given fractions denominators are different.
To make the denomiator of the given fractions same, find the LCM of the denominators.
LCM of 8,7: 56
The fractions become,
[tex]\frac{15}{8}=\frac{15\times7}{8\times7}=\frac{105}{56}[/tex][tex]\frac{12}{7}=\frac{12\times8}{7\times8}=\frac{96}{56}[/tex]we get that,
[tex]\frac{105}{56}>\frac{96}{56}[/tex]we get,
[tex]\frac{15}{8}>\frac{12}{7}[/tex]15/8 is greater than 12/7.
Answer is: 15/8 is greater than 12/7
determine the number light . determine the sign of each aggression below
On the number line shown, a is less than 0, which means a is a negative number, while b is greater than 0 which means b is positive. Therefore;
(A) ab (that is a times b) = negative ab
(B) -(ab) = positive ab (observe that ab is already a negative value)
(C) 2a - b = negative (observe that 2a gives a negative result, hence subtracting 3 from a negative number will resut in a negative answer)