The fourth vertex of the parallelogram is (3,-5) .
What is a vertex?A vertex is a point on a polygon where the sides or edges of an object meet, or where two rays or line segments meet. The plural form of vertex is vertex.
vertex - side or edge
For example, in the figure above, points A, B, C, D, and E are vertices.
Let A(-1, 0), B(1, 3), C(5,-2) and D(x, y) be the vertices of a parallelogram ABCD taken in order. Since, the diagonals of a parallelogram bisect each other.
∴ Coordinates of the mid-point of AC=Coordinates of the mid-point of BD(
([tex]\frac{-1+5}{2}[/tex],[tex]\frac{0-2}{2}[/tex])=([tex]\frac{1+x}{2}[/tex],[tex]\frac{3+y}{2}[/tex])
([tex]\frac{4}{2}[/tex],[tex]\frac{-2}{2}[/tex])=([tex]\frac{1+x}{2}[/tex],[tex]\frac{3+y}{2}[/tex])
Equating both side coordinate respectively
[tex]\frac{1+x}{2}[/tex]=2
1+x=4
x=3
[tex]\frac{3+y}{2}[/tex]=-1
3+y=-2
y=-5
⇒x=3andy=-5
Hence, the fourth vertex of the parallelogram is (3,-5)
To know more about parallelogram visit:
https://brainly.com/question/970600
#SPJ1
Simplify each expression.
(a^2b^-3/a^-2b^2), a and b don’t equal 0
Answer:
[tex]a^4b^{-5}\text{ or }\frac{a^4}{b^5}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{a^2b^{-3}}{a^{-2}b^2}=a^{2-(-2)}b^{-3-2}=a^4b^{-5}=\frac{a^4}{b^5}[/tex]
Area of Trapezoids and Other Figures quick check
The area of the triangle is 11.55 square meters.
The correct option is B.
What is a Triangle?The polygon which has three sides and three vertices is called as triangle.
The sum of all the angles of the triangle is 180°.
A triangle is given.
The height of the triangle = 5.5 meters.
The base of the triangle = 4.2 meters.
The area of the triangle = 1/2 x base x height
The area of the triangle = 1/2 x 4.2 x 5.5
The area of the triangle = 11.55 square meters.
Therefore, area is 11.55 square meters.
To learn more about the triangle;
https://brainly.com/question/2773823
#SPJ1
need help pls ty
Vincent and Joaquin are eating a snack. They spent a total of 24 dollars buying juice and tornados. Each juice cost 5 dollars and each tornado cost 3 dollars. They spent 4 minutes drinking each juice and spent 2 minutes per tornado. It took them 30 minutes to finish their snacks. Define your variables and write your equations.
Write your variables.
Write down your equations.
Solve and check.
The juice is 27 and the tornadoes are 21.
What is the equation?An equation is a mathematical statement that shows that two expressions are equal by using an equal sign (=). Equations are used to find the value of an unknown variable or to show the relationship between variables.
We know that the number of the juice and the tornadoes can be x and y
We then have that;
5x + 3y = 24 ----- (1)
4x + 2y = 30 ----- (2)
Multiply equation 1 by 4 and equation 2 by 5 we have that;
20x + 12y = 96 ---- (3)
20x + 10y = 150 ----- (4)
Subtract (3) from (4)
-2y =54
y = -27
Then;
5x + 3(-27) = 24
x = 21
Learn more about equation:https://brainly.com/question/29657983
#SPJ1
Astronomers often measure large distances using astronomical units (AU) where 1 AU is the average distance from Earth to the Sun. In the image, d represents the distance from a star to the Sun. Using a technique called "stellar parallax," astronomers determined 0 is 2°.
How far away is the star from the Sun in astronomical units? Show your reasoning.
The distance between the star from the Sun in astronomical units
is 28.6 AU.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecent/hypotenuse and
tan = opposite/adjacent.
From the reference angle of 2 degrees, d can be thought of as the adjacent side and the distance from the Sun and the Earth can be thought of as the opposite side.
Now, We know tan = opposite/adjacent.
tan2° = 1/d.
d = 1/0.035.
d = 28.6 AU.
learn more about trig ratios here :
https://brainly.com/question/14977354
#SPJ1
solution to 4d+9=21?
Answer:
d = 3
Step-by-step explanation:
4d+9=21
4d = 12
d = 3
Let's check
4(3) + 9 = 21
12 + 9 = 21
21 = 21
So, d = 3 is the correct answer.
Answer: 3 = d
Step-by-step explanation:
4d + 9 = 21
- 9 - 9
4d = 12
— —
4 4
d = 3
Please help. I’m having some problems with this
The equation of the horizontal asymptote will be y = -2.
What is asymptote?An asymptote is a line that constantly reaches a given curve but does not touch at any infinite distance.
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
From the graph, the horizontal asymptote is parallel to the x-axis and the equation of the horizontal asymptote is given as,
y = - 2
The equation of the horizontal asymptote will be y = -2.
More about the asymptote link is given below.
https://brainly.com/question/17767511
#SPJ1
Please help me!!!!! Pic provided! (A lot points)
Find the corresponding range viewing the window [-5,5]
From the graph, the range in the viewing window is [-3,3]
What are domain and range of a function ?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
f(x)= -100|x| + 75
Take few values for x and find corresponding f(x) values
The graph will be symmetrical in nature
It is absolute value function
Example:
when x=0.75
f(x) = -100(0.75)+75
= -75+75
= 0
Range is the y values
From the graph, the range in the viewing window is [-3,3]
To learn more about the domain and range from the given link
https://brainly.com/question/28801359
#SPJ1
Kweku drives about 18,000 miles a year. How much would he save in a year buying electricity for the Desla electric compared to buying gas for the deswagon? and about how long would it take to makeup for the higher sale price of the desla electric?
Kweku would save $180 in a year buying electricity for the Desla electric compared to buying gas for the Deswagon.
To make up for the higher sale price,
it will take him more than 66 years.
What is subtraction?Subtraction is a mathematical operation. Which is used to remove terms or objects in the expression.
Given:
Deselectric costs $11900 more than the Deswagon.
Unit cost:
Deselectric: $0.11 per mile.
Deswagon: $0.12 per mile.
Kweku drives about 18,000 miles a year.
That means
the cost for each car;
Deselectric: 18000 x 0.11 = $1980
Deswagon: 18000 x 0.12 = $2160
The more cost is,
= $2160 - $1980
= $180 of savings in a year.
Now, the make-up for the higher sale price,
= 11900/180
= 66.11 in years.
Therefore, it will take him more than 66 years.
To learn more about subtraction;
https://brainly.com/question/2346316
#SPJ1
Differentiate the function
y=(5x² +7√x)/(4x)
y’=
Refer to the attached image.
Which system(s) of linear equations has (have) (2,−1) as its (their) unique solution? Select the THREE (3) systems that apply. Responses
The system of linear equations that has an unique solution has this feature:
Different slopes.
Then we must replace into the equations the variables x = 2 and y = -1, and verify if the equations are satisfied.
How to obtain the number of solutions of a system of equations?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the linear function.The intercept b represents the initial amount.The number of solutions for a system of two linear functions is defined as follows:
Zero solutions: same slope and different intercept.One solution: different slopes.Infinite solutions: same slope and same intercept.More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
A rectangle is 8 cm longer than it is wide the perimeter of the rectangle is 72 cm how wide is the rectangle
Answer:
32cm
Step-by-step explanation:
Let x represent the width
if the width = x
therefore the length = x+8
The perimeter = 72cm
Now write it as an equation[tex]x + x + 8 = 72[/tex]
[tex]x + x + 8 - 8 = 72 - 8[/tex]
[tex]x + x = 64[/tex]
[tex]x + x = 2x[/tex]
[tex]2x = 64[/tex]
[tex] \frac{2x}{2} = \frac{64}{2} [/tex]
[tex]x = 32[/tex]
Answer:
18cm
Step-by-step explanation:
wide = 8cm + length
perimeter = 2(L + B)
. if all 256 students from both the online and the in person sta 381 classes decide to play the game, how many total extra credit points would you expect to be rewarded (rounded to the nearest integer)?
You would expect a total of 2560 extra credit points to be rewarded (rounded to the nearest integer).
You must multiply the total number of extra credit points awarded by the number of pupils in order to find the answer to this question.
The equation would be as follows, assuming that each student receives the same number of extra credit points:
Total Extra Credit Points = Amount of Extra Credit Points per Student * Total Amount of Students
Therefore, in this case, the total amount of extra credit points to be rewarded would be:
Total Extra Credit Points = 10 * 256 = 2560
Therefore, If all 256 students from the in-person and online STA 381 classrooms choose to participate in the game, you can anticipate receiving a total of 2560 extra credit points (rounded to the nearest integer).
To learn more about extra credit, visit the link below:
https://brainly.com/question/17864794
#SPJ4
In the years from 2010 to 2015, the population of the District of Columbia is expected to decrease about 0.9% annually. In 2010, the population was about 530,000. What is the population of the District of Columbia expected to be in 2015?
Answer: 506,150
First we must divided 0.9 into 530,000 to find out how much of the population will decrease each year.
0.9% of 530,000 is 4770. Which means that each year, 4,770 people will move the District of Columbia. From 2010 to 2015, that is 5 years, which means that we have to multiply 4,770 by 5.
4770 x 5 is 23850.
Next we have to subtract the amount of people who moved.
530,000- 23,850 is 506,150
This means by 2015, the expected population will be 506,150 in the District of Columbia.
I hope this helped & Good Luck <3 !!!
An earthquake near New Zealand measured 4.2 on the Richter scale. Use the formula R = log(4) to determine approximately
how many times stronger the wave amplitude of the earthquake was than Ao.
The wave amplitude was A = 15849 Ao times stronger the wave amplitude of the earthquake was than Ao.
How to solve for the waveThe formula to solve this is given as
K = log (A / Ao)
Where we have k to be the constant that is measured on the richter scale as 4.2
Then when we put this in the formula, we would have:
4.2 = log (A / Ao)
take the log of both sides of the equation
[tex]10^4^.^2 = \frac{A}{Ao}[/tex]
15848.9 approximately 15849
15849 = A / Ao
cross multiply to get the value of A
A = 15849 Ao
Read more on Richter scale here:https://brainly.com/question/17791739
#SPJ1
A 95% confidence interval is found to be (28, 32). The sample standard deviation is 7 and the sample size is 49. If you wanted a smaller interval, what could you do?
C. Increase sample size to 64
Answer:
See below
Step-by-step explanation:
If we increase the sample size, we will decrease the margin of error, creating a smaller interval. This is why option C is the most appropriate answer!
A remote camera at ground level is filming the lift-off
of an Atlas rocket at a point 800 meters from the launch
pad. Let 0 be the angle of elevation to the rocket and let
s be the height of the rocket. Find 0 when s = 1500 meters.
Answer:
Step-by-step explanation:
Use SOH CAH TOA.
Using TOA or tangent = tan0 = opp/adj.
tan0 = 1500m/800m -> tan0 = 1.875
Use inverse tan or tan^-1.
0 = tan^-1(1.875)
0 = 61.93 degrees.
A boat is heading towards a lighthouse, whose beacon-light is 150 feet above the water. From point A, the boat’s crew measures the angle of elevation to the beacon, 12∘, before they draw closer. They measure the angle of elevation a second time from point B at some later time to be 21∘. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
The distance from point A to point B is 313.6 feet.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
From the given information AB = AC - BC.
We know, tan = opposite/adjacent.
tan12° = 150/AC.
AC = 150/0.213.
AC = 704.23.
Again,
tan21° = 150/BC.
BC = 150/0.384.
BC = 390.63.
Therefore, AB = 704.23 - 390.63 = 313.6 feet.
learn more about trig ratios here :
https://brainly.com/question/14977354
#SPJ1
A wheel chair ramp is to built 5 feet off the ground. The ramp will create an angle of elevation of 5. 22 degrees. How long should the ramp be
The Length of wheel chair ramp should be 54.94 feet. as we calculated this by given height of ramp is 5 feet and angle of elevation is 5.22 degree.
Here it is given that the height of ramp from ground is 5 feet and angle of elevation is 5.22 degree .Now we can see that this is a height and distance question. For that we have to use trigonometric ratio. And all trigonometric ratio are the angle of right angle triangle so here we have to find tangent of angle
so tanФ = perpendicular /base
and in this question the perpendicular is 5 feet and and the base we have to find and angle 5.22 degree.
let the length of ramp is = y and then put the value on formula we have
tan 5.22 = 5/y
y = 5/(tan5.22) = 5/0.091 =54.94
The length of wheel chair ramp is 54.94 feet .
Learn more on height and distance here;
https://brainly.com/question/28920316
#SPJ4
a regular hexagon is a six-sided figure with all sides equal and all six angles equal. find the length of the sides if the perimeter of the regular hexagon is 372in.how do you find the mean height
The mean height of the hexagon is 21.33 in.
The Mean of HexagonTo find the length of the sides of a regular hexagon with a perimeter of 372 inches, you must divide the perimeter by 6. This gives you a result of 62 inches for the length of each side. The other steps are:
To find the mean height of the hexagon, you must first calculate the area. To do this, you can use the formula for the area of a regular hexagon, which is A = (3√3)/2 × a², where a is the length of one side. Substituting the side length of 62 inches, the area of the hexagon is A = (3√3)/2 × 62² = 7943.3 sq. in. From this, the mean height of the hexagon can be calculated by dividing the area by the perimeter, which gives a mean height of h = 7943.3/372 = 21.33 in.Learn more about The Hexagon here:
https://brainly.com/question/29762907
#SPJ4
A bag contains red and blue counters in the ratio 3:5. There are 90 red counters in the bag. What is the total number of counters in the bag?
Answer:
The total number of counters in the bag is 150.
Step-by-step explanation:
There are 90 red counters and the ratio of red to blue is 3:5, which means that for every 3 red counters there are 5 blue counters. Thus, 90 red counters would mean that there are 5/3 times as many blue counters, or 150/3 = 50 blue counters. Therefore, 90 red counters + 50 blue counters = 150 counters in total.
The price for calculating the price to deliver a parcel of mass m kg is price ($) = 7 + 3.5m
What is the mass, in kg, of a parcel with a delivery price of $70?
Answer:
18 Kg
Step-by-step explanation:
We can use algebra to solve for the mass, m, given the delivery price, $70.
Starting with the formula:
price ($) = 7 + 3.5m
We can substitute $70 for price ($) and solve for m:
$70 = 7 + 3.5m
Subtracting 7 from both sides:
$63 = 3.5m
Dividing both sides by 3.5:
m = 18
Therefore, the mass of the parcel is 18 kg.
What is (f+g)(x)?
f(x)=4x+6
g(x)= -5x
Write your answer as a polynomial or a rational function in simplest form.
Answer:
(f + g)(x)= -x + 6.
Step-by-step explanation:
The sum of two functions, f(x) and g(x), is given by (f + g)(x) = f(x) + g(x).
So, for f(x) = 4x + 6 and g(x) = -5x,
(f + g)(x) = f(x) + g(x) = (4x + 6) + (-5x) = -x + 6.
The result is a linear function and is already in the simplest form, so it cannot be further simplified.
Find CD.
4.5
5.3
5.5
6.3
Answer:
(d) 6.3
Step-by-step explanation:
You want the measure of side CD in ∆CDE ~ ∆CFG with CG=6, GE=2.4, and FD=1.8.
ProportionThe corresponding sides of the two triangles are proportional:
CD/CE = FD/GE
CD = CE×FD/GE = (6+2.4)×1.8/2.4
CD = 6.3
__
Additional comment
Lengths on segment CD are 3/4 of those on segment CE, so CF = 4.5. CD is the sum of CF and FD: 4.5 +1.8 = 6.3.
Find the value of x that makes triangle ABC congruent to triangle DEF
Answer:
4
Step-by-step explanation:
3*9=9(x-1)
x-1=3
x=4
a²-(b+c)²/
c²-(a-b)²
The expanded form of the expression [tex]\frac{a^2 - (b + c)^2}{c^2 - (a - b)^2}[/tex] is [tex]\frac{a^2 - b^2 - 2bc - c^2}{c^2 - a^2 + 2ab - b^2}[/tex].
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, An expression [tex]\frac{a^2 - (b + c)^2}{c^2 - (a - b)^2}[/tex].
We know, (a ± b)² = a² ± 2ab + b².
Therefore, [tex]\frac{a^2 - (b + c)^2}{c^2 - (a - b)^2}[/tex]
[tex]= \frac {a^2 - (b^2 + 2bc + c^2)}{c^2 - (a^2 - 2ab + b^2)}[/tex]
[tex]= \frac{a^2 - b^2 - 2bc - c^2}{c^2 - a^2 + 2ab - b^2}[/tex]
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ1
K
A formula is given, along with the values of all but one of the variables in the formula. Fi
not given.
4
P =
RT
T=8, 1=$7140, R = 0.17
P= $ (Simplify your answer.)
Using the formula of Interest I = PRT and given values the value of P is $5250.
What is Interest?Interest is the sum over and above the original amount (the amount borrowed) that is paid to a lender or depositor by a borrower or deposit-taking financial institution at a set rate. Interest differs from profit, in that interest is received by a lender, whereas profit is received by the owner of an asset, investment or enterprise.
Given that, the formula is I = PRT
I = $7140, R = 0.17, T = 8
To find the value of P, from the formula
7140 = P * 0.17 * 8
⇒ 7140 = P * 1.36
divide both sides with 1.36 we get
⇒ 7140/1.36 = P
⇒ P = $5,250
To learn more about interest rate visit:
brainly.com/question/12246997
#SPJ1
Sami invests £400 for 2 years at 5% per year simple interest. Work out the total interest Sami gets.
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \pounds 400\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &2 \end{cases} \\\\\\ I = (400)(0.05)(2) \implies I = 40[/tex]
Using appropriate properties, find: 7/5 * 1/3 + 3/5 * (- 2/9) + 7/5 * (- 5/6)
The value of the expression is -5/6.
What is PEMDAS?The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.
Given:
An expression,
7/5 × 1/3 + 3/5 × (- 2/9) + 7/5 × (- 5/6).
Solving further with the help of PEMDAS,
7/5 × 1/3 + 3/5 × (- 2/9) + 7/5 × (- 5/6)
= 7/15 - 6/45 - 35/30
= (42- 12 - 105)/90
= -75/90
= -5/6
Therefore, the value is -5/6.
To learn more about the PEMDAS;
https://brainly.com/question/36185
#SPJ1
What do I put in the boxes? Please help this is due today
What is the quotient?
49 ÷ 3
This model describes the division calculation.
Answer:
See attached
Step-by-step explanation:
You want the numbers for quotient, dividend, and remainder in the area model of 49÷3.
Area modelThe number in each rectangle is its area, which is the product of the divisor on the left and the quotient at the top. These can be considered the length and width of the rectangle. The rectangle area is their product.
The remainder is put in the box at upper right. It is a value that is smaller than the divisor on the left.
The line at the bottom summarizes the division. The quotient is the sum of the quotient values at the top of the model, and the remainder is what's left over: the number that is too small to divide further.