System 2x2
Find slopes of k1 and k2
k1 slope = (10--2)/(4-0) = 12/4 = 3
k2 slope= (-9 -9)/ (8-0) = 8/-18 = -4/9
Now find k1, and k2 interceptions with y
k1 , interception= -2
k2 ,interception = 4
Then now, form the 2 equations
y = 3x - 2
and
y = (-4/9)x + 4
Now rewrite equations
3x - y = 2
and
9y + 4x = 36
Then now looking at options ,we find that
ANSWER IS
OPTION A)
3x - y = 2
Use the diagram to calculate the measure of angle 5
Answer:
m∠5=22 °
Explanation:
In the diagram:
• Angles 4 and 90 degrees, are ,vertical angles,.
,• Angles 2 and 68 degrees, are ,vertical angles,.
Since the measure of vertical angles is equal:
[tex]\begin{gathered} m\angle4=90\degree \\ m\angle2=68\degree \end{gathered}[/tex]In the triangle:
[tex]m\angle2+m\angle4+m\angle5=180\degree\text{ (sum of angles }in\text{ a triangle)}[/tex]Substitute the measures of angle 2 and 4 obtained earlier:
[tex]\begin{gathered} 90\degree+68\degree+m\angle5=180\degree \\ 158\degree+m\angle5=180\degree \\ Subtract\text{ }158\degree\text{ from both sides of the equation.} \\ m\angle5=180\degree-158\degree \\ m\angle5=22\degree \end{gathered}[/tex]The measure of angle 5 is 22 degrees.
18. The weights of four puppies are shown in pounds. 9.5 9 9.125 9 Which list shows these weights in order from greatest to least F. 99.5 9 9.125 w 9.5 9 9.125 9.125 9 9.5 9 + J. 9 9 9.5 9.125
The correct list is
[tex]9\frac{3}{4},\text{ 9.5, 9}\frac{3}{8},9.125[/tex]This is option F
Jenny originally bought her car for $42,000. Four years later, she sold it to a used car salesman for $14,000. What is the ratio for the amount she sold it for to the amount that it depreciated?
SOLUTION
The amout that Jenny sold the car for is $14,000
The amout that the car depriciated will be
$42,000 - $14,000 = $28,000
The ratio for the amount she sold it for to the amount that it depreciated becomes
[tex]\begin{gathered} \frac{14,000}{28,000} \\ \\ =\text{ }\frac{1}{2} \\ \\ =\text{ 1 : 2} \end{gathered}[/tex]Hi dear how do I get to know you and
Given the picture, we have:
Enclosed area: A = x*y
Fence Length: F= 2x+y
The length of a new rectangular playing field is 7 yards longer than quadruple the width. If the perimeter of the rectangular playing field is 454 yards, what are its dimensions?
The dimensions of new rectangular playing field are 183 yards and 44 yards, by the concept of perimeter of rectangle.
What is perimeter of rectangle?The whole distance that the sides or limits of a rectangle cover is known as its perimeter. Since a rectangle has four sides, its perimeter will be equal to the sum of those four sides. Given that the perimeter is a linear measurement, the rectangle's perimeter will be expressed in meters, centimeters, inches, feet, etc.
Formula, perimeter of rectangle =2× (length +width)
Given, perimeter of rectangular playing field = 454 yards (equation 1)
Let us assume, width =x
According to question length = 4x+7 (quadruple=4times)
By the above equations,
Perimeter=2×(4x+7+x)
2×(5x+7) =454 (by equation 1)
Dividing the above equation by 2 both the sides
(5x+7) =227
Subtracting the above equation by 7 both the sides
5x=220
Dividing the above equation by 5 both the sides
x=44
Therefore, the required width of new rectangular playing field is 44 yards and length of new rectangular playing field is 183 yards
To know more about perimeter of rectangle, visit:
https://brainly.com/question/15287805
#SPJ13
Find the missing side of the right triangle. Leave your answer in simplest radical form. show work
Applying the Pithagorean Theorem
we have
[tex]12^2=x^2+(8\sqrt[]{2})^2[/tex]solve for x
[tex]\begin{gathered} 144=x^2+128 \\ x^2=144-128 \\ x^2=16 \\ x=\sqrt[]{16} \end{gathered}[/tex]x=4 mi64 is 2/3percent of what number
We have to find the number x for which 64 is the 2/3.
Solve the inequality: 3x + 4 ≤ 5
Answer in interval notation.
Answer: [tex]x\leq 1/3\\[/tex]
Step-by-step explanation:
Ms wash investdd $22000 in two accounts, one yielding 8% interest and the other yielding 11%. if she recieved a total of $1910 in interest at the end of the year, how much did she invest in each accouny
Take into account the following formula for the simple interest:
[tex]I=P\cdot r\cdot t[/tex]where:
P: principal investment
r: interest rate
t: time
In order to determine the investments for both accounts, proceed as follow:
-Consider that both investments are represented by P1 and P2 respectively, then, you have:
[tex]\begin{gathered} P_1+P_2=22000 \\ P_2=22000-P_1 \end{gathered}[/tex]- Next, use the given values for parameters r and t for each investment:
8% = 0.08
11% = 0.11
t = 1 year
[tex]\begin{gathered} I_1=P_1\cdot0.08\cdot1=0.08P_1 \\ I_2=P_2\cdot0.11\cdot1=0.11P_2 \end{gathered}[/tex]- Next, consider that the sum of the total earnings is $1910, then:
[tex]I_1+I_2=1910[/tex]- Replace I1 and I2 by the expressions in terms of P1 and P2 and write down the resultant expression in terms of P1, as follow:
[tex]\begin{gathered} 0.08P_1+0.11P_2=1910 \\ 0.08P_1+0.11(22000-P_1)=1910 \\ 0.08P_1+2420-0.11P_1=1910 \\ -0.03P_1=-510 \\ P_1=\frac{510}{0.03}=17000 \end{gathered}[/tex]And for P2:
[tex]\begin{gathered} P_2=22000-P_1 \\ P_2=22000-17000=5000 \end{gathered}[/tex]Hence, the amount of money invested in each account was $5000 and $17000
I really need help make sure that your answer is 7th grade appropriate
Examples:
1. Five increased by four times a number
[tex]5+4n[/tex]where n is the number
2.The product of 4, and a number decreased by 7
[tex]4(n-7)[/tex]Question 19 of 25Which of the following equations is an example of inverse variation betweenthe variables x and y?O A. y -O B. y = 8xO C. y -OD. y=x+8SUBMIT
Where 8 is the constant
The Final answerOption CThis table shows the top athletes that play both basketball and track. What is the intersection between the set of basketball players and the set of track athletes? Basketball Track Arnold Berenson Nickerson Eaton Yun Tadesse McDonald Jones Tadesse Nickerson Yang Martin
The intersection between the set of basketball players and the set of track athletes is given by:
{Tadesse, Nickerson}
What is the intersection between two sets?The intersection between two sets is the set containing the elements that belong to both sets which we are calculating the intersection.
In the context of this problem, the sets are given as follows:
List of basketball players: {Arnold, Nickerson, Yun, McDonald, Jones, Tadesse}List of track athletes: {Berenson, Eaton, Tadesse, Nickerson, Yang, Martin}.The intersection is composed by athletes that are both basketball players and track athletes, hence it is given as follows:
{Tadesse, Nickerson}
More can be learned about the intersection between two sets at https://brainly.com/question/4699996
#SPJ1
the Missing Angles (plus angle review)<8 of 16Whats the measure of each of the angle in degrees? Label the angles, then answer,Subm104056°
A is angle opposite by the vertex with the angle of 104 degrees, that is why it also measure 104 degrees
The three inner angles of any triangle add 180 degrees, then 56 + A + B = 180
Solving for B: B = 180 - 56 - A = 180 - 56 - 104 = 20
A train leaves a station and travels north at a speed of 175 km/h. Two hours later, a second train leaves on a parallel track and travels north at 225 km/h. How far from the station will theymeet?The trains will meet (?) away from the station(Type an integer or a decimal.)
Given,
The speed of first train is 175km/h.
The speed of second train is 225 km/h.
Consider, the time taken by first train to meet is x h.
The time taken by the second train to meet is (x-2) h.
The distance is calculated as,
[tex]\text{Distance}=\text{speed}\times time[/tex]At the meeting point the distance covered by both train is same,
So, taking the distance equation of both trains in equal,
[tex]\begin{gathered} 175\times x=225\times(x-2) \\ 175x=225x-450 \\ -50x=-450 \\ x=9 \end{gathered}[/tex]The first train meet to second train after distance,
[tex]d=175\times9=1575\text{km}[/tex]The second train meet to first train after distance,
[tex]d=225\times(9-2)=1575\text{ km}[/tex]Hence, both train meet after 1575 km from the station.
Find the measures of the numbered angles in rhombus DEFG. I just need someone to shown me how to find each of the numbered angles
Step 1
Properties of a Rhombus
Below are some important facts about the rhombus angles:
Rhombus has four interior angles.
The sum of interior angles of a rhombus add up to 360 degrees.
The opposite angles of a rhombus are equal to each other.
The adjacent angles are supplementary.
In a rhombus, diagonals bisect each other at right angles.
The diagonals of a rhombus bisect these angles.
Step 2
From the figure
Angle DGF = Angle DEF = 118
Step 3
Since adjacent angles are supplementary, that is add to 180 degrees
[tex]\begin{gathered} \angle\text{DGF + }\angle GFE\text{ = 180} \\ 118\text{ + }\angle GFE\text{ = 180} \\ \angle GFE\text{ = 180 - 118} \\ \angle GFE\text{ = 62} \end{gathered}[/tex]Step 4
The diagonals of a rhombus bisect these angles
[tex]\begin{gathered} \angle3\text{ = }\angle4\text{ = }\frac{62}{2}\text{ = 31} \\ \angle3\text{ = }\angle4\text{ = 31} \end{gathered}[/tex]Step 5
The opposite angles of a rhombus are equal to each other.
[tex]\angle1\text{ = }\angle\text{ 2 = 31}[/tex]Final answer
[tex]\angle\text{1 = }\angle\text{ 2 = }\angle\text{ 3 = }\angle4\text{ = 31}[/tex]What is the quotient of 2.592 x 10^7 and 7.2 x 10^4 expressed in scientific notation?
Answer:
Explanation:
Given the expression:
[tex]\frac{2.592\times10^7}{7.2\times10^4}[/tex]We can rewrite it as:
[tex]\frac{2592\times10^{-3}\times10^7}{72\times10^{-1}\times10^4}[/tex]Combine all powers of 10:
[tex]\begin{gathered} =\frac{2592\times10^{-3+7}}{72\times10^{-1+4}^{}} \\ =\frac{2592\times10^4}{72\times10^3} \\ =\frac{2592}{72^{}}\times\frac{10^4}{10^3} \\ =36\times10 \\ =3.6\times10^1\times10^1 \\ =3.6\times10^{1+1} \\ =3.6\times10^2 \end{gathered}[/tex]The quotient expressed in scientific notation is 3.6 x 10².
HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
The rational number between -1/3 and 1/-2 could be; -6 / 18, -6/12.
What are natural numbers, rational numbers, and irrational numbers?Natural numbers are: 1, 2, 3, ..Rational numbers are numbers which can be written in the form of a/b where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5). Irrational numbers are those real numbers which are not rational numbers.
We are asked to find that rational number between -1/3 and 1/-2.
LCM of 3 and 2
3 x 2 = 6
Then we get;
-1/3 x 6/6 = -6 / 18
1/-2 x 6/6 = -6/12
Hence, the rational number between -1/3 and 1/-2 could be; -6 / 18, -6/12.
Learn more about numbers here;
https://brainly.com/question/3151755
#SPJ1
I don’t understand how to explain this question
The segments cannot be set equal since the constant terms 15 is greater than two. The variable x remains like a constant term in both sides of the point B. we say that 15x > 2x
What is inequality?In mathematics, the signs used inequality calculations are
greater thanless thangreater than or equal toless than or equal toUsing the picture as evidence the mark represented by B is not the midpoint hence the equality sign will not be used here. The sign to be used is the inequality sign.
In addition, the constants 15 and 2 shows that 15 is greater than 2. and there is no other addition to the variable x to help check the effect of the greatness of 15
Read more on inequality here: https://brainly.com/question/25275758
#SPJ1
Please help with this
Answer:
228
Step-by-step explanation:
Top 6x 6 = 36
4 sides 4(6x8)
4(48)
192
192 + 36 = 228
Answer:264
Step-by-step explanation: the surface area is every side added together and you calculate each side by multiplying the width height and length
Antonio has a balance of $4273.56 on a credit card with an annual percentage rate of 21.1%. He decides to not make any additional purchases with his card until he has paid off the balance. a) Many credit cards require a minimum monthly payment of 2% of the balance. What is Antonio's minimum payment on the balance of $4273.56? b) Find the amount of interest charged this month
a) To calculate the minimum payment of the balance, you calculate the 2% of $4273.56. You proceed as follow:
(2/100)(4273.56) = 85.47
Hence, the mimum payment of the balance is $85.47
b) You calculate the amount of interest charged this month as follow:
convert the annual percentage rate to decimal form:
21.1/100 = 0.211
divide the previous result by 12 to get the monthly interest rate:
0.2111/12 = 0.0175
multiply the previoues result by the balance:
0.0175 x 4273.56 = 75.143 ≈ 75.14
convert the monthly rate to a percentage:
0.0175 x 100 = 1.75%
Hence, the amount of interest was $75.14, which corresponds to a 1.75%
3 /17% of a quantity is equal to what fraction of the quantity
Given:
The objective is to find the fraction of 3/17% of the quantity.
Consider the quantity as x. The fraction of 3/17% of the quantity can be calculated as,
[tex]\begin{gathered} =\frac{3}{17}\frac{1}{100}x \\ =\frac{3}{1700}x \end{gathered}[/tex]Hence, the required fraction of quantity is 3/1700 of x.
57. do not use the answer under the line in the explanation itself, only refer to it to make sure of your work. USE DERIVITIVES NOT GRAPHING
Explanation
Question 57
[tex]\:f\left(x\right)=2x^3-15x^2+24x[/tex]To find the extreme values
[tex]\begin{gathered} \mathrm{Suppose\:that\:}x=c\mathrm{\:is\:a\:critical\:point\:of\:}f\left(x\right)\mathrm{\:then,\:} \\ \mathrm{If\:}f\:'\left(x\right)>0\mathrm{\:to\:the\:left\:of\:}x=c\mathrm{\:and\:}f\:'\left(x\right)<0\mathrm{\:to\:the\:right\:of\:}x=c\mathrm{\:then\:}x=c\mathrm{\:is\:a\:local\:maximum.} \\ \mathrm{If\:}f\:'\left(x\right)<0\mathrm{\:to\:the\:left\:of\:}x=c\mathrm{\:and\:}f\:'\left(x\right)>\:0\mathrm{\:to\:the\:right\:of\:}x=c\mathrm{\:then\:}x=c\mathrm{\:is\:a\:local\:minimum.} \\ \mathrm{If\:}f\:'\left(x\right)\mathrm{\:is\:the\:same\:sign\:on\:both\:sides\:of\:}x=c\mathrm{\:then\:}x=c\mathrm{\:is\:neither\:a\:local\:maximum\:nor\:a\:local\:minimum.} \end{gathered}[/tex]So, we will have the steps below
Step 1:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=0\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=0 \\ \mathrm{Minimum}\left(0,\:0\right) \end{gathered}[/tex]Step2:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=1\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=11 \\ \mathrm{Maximum}\left(1,\:11\right) \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=4\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=-16 \\ \mathrm{Minimum}\left(4,\:-16\right) \end{gathered}[/tex]Step 4:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=5\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=-5 \\ \mathrm{Maximum}\left(5,\:-5\right) \\ \end{gathered}[/tex]Thus, we will have
[tex]\mathrm{Minimum}\left(0,\:0\right),\:\mathrm{Maximum}\left(1,\:11\right),\:\mathrm{Minimum}\left(4,\:-16\right),\:\mathrm{Maximum}\left(5,\:-5\right)[/tex]Hence, our answer is
[tex]\begin{gathered} \begin{equation*} \mathrm{Minimum}\left(4,\:-16\right) \end{equation*} \\ \begin{equation*} \mathrm{Maximum}\left(1,\:11\right) \end{equation*} \end{gathered}[/tex]A family eats at a restaurant. The bill is $42. The family leaves a tip and spends $49.77. How much was the tip as a percentage of the bill?
Percentage of the bill = 0.185*100=18.5%
Select the correct answer.Using long division, what is the quotient of 3r4 + 2023 + 1422 + 17= + 30 and I + 67
EXPLANATION
we are asked to use the long division method to solve the division
[tex]\frac{3x^4+20x^3+14x^2+17x+30}{x+6}[/tex]We will have
Question 12 pls help
The equation of the line is found as y + 2 = (-2/3)(x - 5).
What is termed as the equation of a line?The equation of line is just an algebraic representation of a set of points in a coordinate system that form a line. The numerous points in the coordinate axis that form a line are depicted as a set of factors x, y to form an algebraic expression known as an equation of a line.For the given question.
The passing coordinates of the line is given as;
(x1, y1) = (-1, 7)
(x2, y2) = (5, -2)
Find the slope using the equation.
slope = m = (y2 - y1)/(x2 - x1)
Put the values.
m = (-2 - 7)/(5 + 1)
m = -9/6
m = -3/2
Use the point slope formula to find the equation of line in slope intercept form.
y - y1 = m(x - x1)
y + 2 = (-2/3)(x - 5)
Thus, the equation of the line is found as y + 2 = (-2/3)(x - 5).
To know more about the equation of a line, here
https://brainly.com/question/25969846
#SPJ13
Type your response in the box.Use the information in the table to determine some similarities and differences between linear and exponentialequations. Include observations about the forms of both equations and the placement of the independent variablein the equations.f(3) = 5(3)s() = 2x+55057121192
Ok let's talk about some similarities and differences between linear and exponential equations.
In the linear functions the rate of change is constant. While in the exponential fuctions the rate of change is not constant.
In linear function the graph is a straight line. in the exponential fuctions graph is an exponential curve.
In linear functions the placement of the independent variable is is multiplying a coefficient. In the exponential fuctions the placement of the independent variable is as the power of a coefficient.
Can you guys help me simplify this?
-2x^5y^3/6x^7y^2
what is the curved surface area of a cone on top of a half circle if the cone has a volume and the circle has a 10 area?
Given a cone with base radius, r, and perpendicular height, h,
the volume, V, is given by
[tex]V=\frac{1}{3}\times\pi\times r^2\times h[/tex]In this case,
r = 10ft,
h = 17ft,
Therefore,
[tex]V=\frac{1}{3}\times\pi\times10^2\times17=\frac{1700}{3}\pi[/tex]Hence, V = 1780.24 cubic feet
The volume of the cone is 1780.24 cubic feet
what is the rate change of the equation?Y=8x+20Remember Y=MX+B
The general equation of the line : y = m * x + b
where m is the slope , b is y -intercept
Given the function :
[tex]y=8x+20[/tex]The rate of change of the equation = the slope of the function
So, by comparing the given equation to the general from
The slope = m = 8
So, the rate of change = 8
find the measure of each segment
The value of each line segment is found as 26 units.
What is defined as the mid point?A midpoint is a point in the center of a line connecting two points. The two points of reference are the line's endpoints, and the midpoint is located between the two. The midpoint splits the line connecting such two points in half. Furthermore, a line drawn to bisect the line connecting these two points passes through midpoint.For the given question.
The line is given as DE and the mid point of line is D.
Thus,
CD = DE .....eq 1
The value of each term are given as;
CD = 2x + 7
DE = 4(x - 3)
Put the value in equation 1.
2x + 7 = 4(x - 3)
2x + 7 = 4x - 12
Bring variables and constants on the different sides.
4x - 2x = 7 + 12
2x = 19
x = 9.5
Put the value in each side;
CD = 2×9.5 + 7 = 26 unitsDE = 4(9.5 - 3) = 26 unitsThus, the value of each line segment is found as 26 units.
To know more about the mid point, here
https://brainly.com/question/12223533
#SPJ13
