Answer:
1) [tex]3 a^3 + 8 a^2 b - b^3[/tex]
2) 93 inches
Step-by-step explanation:
1) We know that the lenghts are given by these expressions:
[tex]2ab(a - b)\\\\3a^2(a + 2b)\\\\b^2(2a - b)[/tex]
Then, we need to add them in order to find the expression that represents the total length of the rope:
- Apply Distributive property.
- Add the like terms.
Then:
[tex]=2ba^2-2ab^2+3a^3+6ba^2+2ab^2-b^3\\\\=3 a^3 + 8 a^2 b - b^3[/tex]
2) Knowing that:
[tex]a=2in\\\\b=3in[/tex]
We must substitute these values into [tex]3 a^3 + 8 a^2 b - b^3[/tex] in order to caculate the total lenght of the rope. This is:
[tex]3 (2in)^3 + 8 (2in)^2 (3in) - (3in)^3=93in[/tex]
A secretary works a 35 hour week for which she is paid $262.50. She works 6 hours over- time on Saturday which is paid for at time and a half , and 4 hours overtime on Sunday which is paid for at double time. Calculate her gross wage for the week.
Answer:
$390.
Step-by-step explanation:
first you need to find out hour much the secretary gets paid an hour. So you will divide $262.50 by 35 hours
262.50 / 35 = 7.50
so we know that she worked over time of 6 hours and that will be time and half
to figure out how much for time and a half. We are going to divide her hourly rate by 2.
7.50 / 2 = 3.75
then to find out how much she made for that 6 hours we will add
7.50 + 3.75 = 11.25
to get the amount for over time on Saturday we will multiply
11.25 x 6 = 67.50
Now for the double time we will double her pay so will add
7.50 + 7.50 = 15
so then we are going to multiply to get your pay for the 4 hours overtime
15(4) = $60
Now to find the total amount we are going to add all of our totals together.
262.50 + 67.50 + 60 = 390.
Her total gross wage for the week is $390.
Answer:
$390.
Step-by-step explanation:first you need to find out hour much the secretary gets paid an hour. So you will divide $262.50 by 35 hours
262.50 / 35 = 7.50
so we know that she worked over time of 6 hours and that will be time and half
to figure out how much for time and a half. We are going to divide her hourly rate by 2.
7.50 / 2 = 3.75
then to find out how much she made for that 6 hours we will add
7.50 + 3.75 = 11.25
to get the amount for over time on Saturday we will multiply
11.25 x 6 = 67.50
Now for the double time we will double her pay so will add
7.50 + 7.50 = 15
so then we are going to multiply to get your pay for the 4 hours overtime
15(4) = $60
Now to find the total amount we are going to add all of our totals together.
262.50 + 67.50 + 60 = 390.
Her total gross wage for the week is $390
Diagram shows a framework consisting of 16 wooden rods. The length of each rod is 8 cm.
8
1)All the rods are rearranged to form a square. Calculate the area, in cm, of the square.
Answer:
1024 cm²
Step-by-step explanation:
There are 16 rods. A square has 4 equal sides, so each side must consist of 4 rods. The length of each rod is 8 cm, so the length of each of the square's sides is 32 cm. Therefore, the area of the square is:
A = s²
A = (32 cm)²
A = 1024 cm²
what is the value of the discriminant of the quadratic equation -2x^2 -8x+8 and what does it value mean about the number about the number
Final answer:
The value of the discriminant of the quadratic equation -2x² - 8x + 8 is 128. The positive discriminant suggests that the equation has two distinct real roots.
Explanation:
The discriminant of a quadratic equation can be calculated using the formula D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax² + bx + c = 0.
In the given quadratic equation -2x² - 8x + 8, a = -2, b = -8, and c = 8. Substituting these values into the discriminant formula:
D = (-8)² - 4(-2)(8) = 64 - (-64) = 128.
The value of the discriminant is 128. The discriminant value can provide information about the nature of the roots of the quadratic equation. If the discriminant is positive (greater than 0), then the equation has two distinct real roots. If the discriminant is 0, then the equation has one real root (a repeated root). If the discriminant is negative, then the equation has no real roots.
An initial investment of $3 is worth $108 after 5 years. If the annual growth reflects a geometric sequence, approximately how much will the investment be worth after 11 years?
[tex]\bf \begin{array}{ll} \stackrel{year}{term}&value\\ \cline{1-2} a_1&3\\ a_2&3r\\ a_3&3rr\\ a_4&3rrr\\ a_5&3rrrr\\ &3r^4 \end{array}\qquad \qquad \stackrel{\textit{5th year}}{108}=3r^4\implies \cfrac{108}{3}=r^4\implies 36=r^4 \\\\\\ \sqrt[4]{36}=r\implies \sqrt[4]{6^2}=r\implies 6^{\frac{2}{4}}=r\implies 6^{\frac{1}{2}}=r\implies \sqrt{6}=r[/tex]
[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} r=\sqrt{6}\\ a_1=3\\ n=11 \end{cases}\implies a_{11}=3(\sqrt{6})^{11-1} \\\\\\ a_{11}=3(\sqrt{6})^{10}\implies a_{11}=3\left(6^{\frac{1}{2}} \right)^{10}\implies a_{11}=3\cdot 6^{\frac{10}{2}} \\\\\\ a_{11}=3\cdot 6^5\implies a_{11}=3\cdot 7776\implies a_{11}=23328[/tex]
Answer:
The investment be worth $23328 after 11 years.
Step-by-step explanation:
It is given that the annual growth reflects a geometric sequence.
An initial investment of $3 is worth $108 after 5 years.
It means the initial value of first term of the gp, a₁ = 3
The 5th term of the gp, a₅ = 108
The nth term of a gp is
[tex]a_n=ar^{n-1}[/tex] .... (1)
where, a is first term and r is common ratio.
The 5th term of the gp is
[tex]a_5=ar^{5-1}[/tex]
From the given information it is clear that the 5th term of the gp is 108. Substitute a₅ = 108 and a=3.
[tex]108=(3)r^{4}[/tex]
Divide both sides by 3.
[tex]\frac{108}{3}=r^{4}[/tex]
[tex]36=r^{4}[/tex]
Taking fourth root on both the sides.
[tex]\sqrt{6}=r[/tex]
Substitute r=√6, a=3 and n=11 to find the investment worth after 11 years.
[tex]a_{11}=(3)(\sqrt{6})^{11-1}[/tex]
[tex]a_{11}=3(\sqrt{6})^{10}[/tex]
[tex]a_{11}=23328[/tex]
Therefore the investment worth $23328 after 11 years.
Is the relationship shown by the data linear? If so, model the data with an equation. x y 1 –4 7 –7 13 –10 19 –13
Step-by-step answer:
If x and y both go by equal steps, not necessarily equal steps between x and y, the relation is linear
Here, x goes by steps of 6 (1,7,13,19) and y goes by steps of 3 (4,7,10,13), therefore the relation is linear.
To find the equation passing through all the points, we find first the slope, which is steps in y divided by steps in x, or
slope, m = 3/6 = 1/2
Next, we take any point from the data, say, P0=(x0,y0)=(1,4), and substitute in the point-slope form of the equation
y-y0 = m(x-x0)...........................(1)
since x0=1, y0=4, and m=1/2, we get the equation
y-4 = (1/2)*(x-1) .........................(2)
Simplify (2) to get the slope-intercept form of the linear relation:
y = (1/2)x + 7/2 ........................(3)
Finally, we check the results of the y-values for given values of x, using the relation given in equation (3):
y(1) = 4
y(2)=7
y(3)=10
y(4)=13
all of which correspond exactly to original data, so the equation of the linear relation is correct.
A stunt driver wants to make his car jump over 8 cars parked side by side below a horizontal ramp. The vertical height of the ramp is 1.5m above the cars and the horizontal distance he must clear is 22m. If the ramp is tilted upward so that the takeoff angle is 9 degrees what is the minimum speed? I got 35m but was marked wrong.
Answer:
v=26.41 m/s
Step-by-step explanation:
From the Newtons laws of motions, we sew that x= (2v₁²sin∅os∅)/g where x is the horizontal distance v is the initial speed and ∅ is the launch angle.
From trigonometry we see that 2 sin∅cos∅=sin 2∅
Therefore, x=(v²sin2∅)/g
x=22m
∅=9°
g=9.8m/s²
22m=v²×sin(2×9)/(9.8m/s²)
v²=(22×9.8)/(sin 18)
v²=697.696
v=√697.696
v=26.41 m/s
All of the following are equal except _____. -|5| -|-5| |-5| the opposite of 5
Answer:
|-5| is the answer.
Step-by-step explanation:
The opposite of 5 is -5. The absolute value of a number is always positive (e.g: |-10| = 10 because the negative sign is inside the absolute value bars).
-|5| and -|-5| both equal -5 because there is a negative sign outside of the bars. Since |-5| has a negative sign inside the bars, it equals 5.
I tried hard to explain this, so I hope it makes sense! :)
Hey there Brainly Student! Your answer is I-5I !! I hope this helped! Have a great day!!
Given that B, C, and D are the midpoints of ZYA, find the perimeter of ZYA.
A. 70.6
B. 72.6
C. 76.6
D. 77.6
Answer:
D. 77.6
Step-by-step explanation:
We have been given a triangle ZYA in which B, C, and D are the midpoints. We are asked to find the perimeter of triangle ZYA.
We will triangle mid-segment theorem to solve our given problem.
The triangle mid-segment theorem states that the segment joining midpoints of two sides of a triangle is parallel to 3rd side and half the measure of parallel side.
[tex]\text{Measure of side YA}=2\times BD[/tex]
[tex]\text{Measure of side YA}=2\times 11.1[/tex]
[tex]\text{Measure of side YA}=22.2[/tex]
[tex]\text{Measure of side YZ}=2\times CD[/tex]
[tex]\text{Measure of side YZ}=2\times 13.7[/tex]
[tex]\text{Measure of side YZ}=27.4[/tex]
[tex]\text{Measure of side ZA}=2\times CB[/tex]
[tex]\text{Measure of side ZA}=2\times 14[/tex]
[tex]\text{Measure of side ZA}=28[/tex]
[tex]\text{Perimeter of triangle ZYA}=22.2+27.4+28[/tex]
[tex]\text{Perimeter of triangle ZYA}=77.6[/tex]
Therefore, the perimeter of triangle ZYA is 77.6 units.
HELP PLEASE???!!!!!!!
What is the solution to the system of equations below?
y=3/4x-12 and y=-4x-31
A. (–4, –15)
B. (–4, –12)
C. (4, –9)
D. (4, –47)
Answer:
A. (-4, -15)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=\dfrac{3}{4}x-12&(1)\\y=-4x-31&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\\dfrac{3}{4}x-12=-4x-31\qquad\text{multiply both sides by 4}\\\\3x-48=-16x-124\qquad\text{add 48 to both sides}\\\\3x=-16x-76\qquad\text{add}\ 16x\ \text{to both sides}\\\\19x=-76\qquad\text{divide both sides by 19}\\\\x=-4\\\\\text{Put it to (2):}\\\\y=-4(-4)-31\\y=16-31\\y=-15[/tex]
who can answer this
Answer:
your answer is "18"
Step-by-step explanation:
Formula is:
A= 1/2 (A+B) X H
A = 1/2 (CD + CF) X H
A = 1/2 (5+6) X 3
A = 16.5 CM SQUARED
Hope this is right!
Since ABCF is a rectangle, angle AFC is a right angle. Angle CFE is also a right angle. Since angle DCF is also a right angle, then trapezium CDEF has parallel sides CD and EF.
BC + CD = BD
4 cm + CD = 9 cm
CD = 5 cm
EF = 3 cm
Sides CD and EF are the parallel bases of the trapezium. Side CF is the height of the trapezium.
area of trapezium = (base1 + base2)h/2
area = (5 cm + 3 cm)(6 cm)/2
area = (8 cm)(6 cm)/2
area = 24 cm^2
If x+3/3=y+2/3, then x/3=
A) y/3
B)y-1
C)y/2
D)y+1
Answer:
y/2
Step-by-step explanation:
x+3=y+2
------ --------
3 2
Using cross products
2(x+3) = 3(y+2)
Distribute
2x+6 = 3y+6
Subtract 6 from each side
2x+6-6 = 3y+6-6
2x= 3y
Divide each side by 2
2x/2 = 3y/2
x = 3/2 y
We want to find x/3
Divide each side by 3
x/3 = 3/2 y * 1/3
x/3 = 1/2 y
If the graphs of the linear equations in a system are parallel, what does that mean about the possible solution(s) of the system?
Answer:
No solution.
Step-by-step explanation:
If the linear equations in a system are parallel, that means there is no solution.
I don’t understand this Help please ASAP!!!
Answer:
[tex]4t + 15j > 800[/tex]
Please read explanation below as well.
Step-by-step explanation:
We know the following information:
- The number of T-shirts is represented by the variable [tex]t[/tex]. Each T-shirt costs $4. The total cost depending on the number of T-shirts can be represented by [tex]4t[/tex].
- The number of jeans is represented by the variable [tex]j[/tex]. Each pair of jeans costs $15. The total cost depending on the number of jeans can be represented by [tex]15j[/tex].
- The stores want to sell more than $800. This idea is represented mathematically by writing [tex]>800[/tex].
The total cost of jeans and T-shirts depending on the quantities of each of them is represented as a sum: [tex]4t + 15j[/tex]. This total cost has to be more than $800: [tex]4t + 15j > 800[/tex].
For a standard normal distribution find the approximate value of p(z<0.42)
Answer:
p(z<0.42) = 0.6628
Step-by-step explanation:
A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. That is to say:
μ = 0
σ² = 1
Using a calculator, we find that:
p(z<0.42) = 0.6628 (See picture attached)
Answer:
0.66276.
Step-by-step explanation:
We are asked to find the approximate value of p(z<0.42) for a standard normal distribution.
Our given expression means the probability of getting a z-score less than 0.42.
We need to find the probability of getting the area corresponding to a z-score less than 0.42 under normal distribution curve.
We will normal distribution table to solve our given problem.
[tex]p(z<0.42)=0.66276[/tex]
Therefore, the approximate value of our given expression would be 0.66276.
The coordinates A(2, 1), B(7, 1), C(2, 4) form what type of polygon?
Think for a minute.
Three points are given.
What geometric shape has three points?
Answer: Triangle
Solve the system of equations given by 5x - 2y = -6 and 15x - 6y = 6
A. Infinitely many solutions
B. (1, 1)
C. No solution
D. ( -2, -2)
To solve the system of equations, we can use the method of substitution. However, when we substitute the expression for x in the second equation, we get an equation that is not true, indicating that the system has no solution.
Explanation:To solve the system of equations given by 5x - 2y = -6 and 15x - 6y = 6, we can use the method of substitution. First, we can solve one of the equations for either variable, then substitute that expression into the other equation to solve for the other variable. Let's solve the first equation for x:
5x - 2y = -6
5x = 2y - 6
x = (2y - 6)/5
Now, substitute this expression for x in the second equation:
15((2y - 6)/5) - 6y = 6
6y - 18 - 6y = 6
-18 = 6
This leads to the equation -18 = 6, which is not true. Therefore, the system of equations has no solution. So, the correct answer is C. No solution.
Aimee noticed her plant grew 2/3 of an inch every week since it sprouted. She created this graph to show its growth.Which statement about Aimee’s graph is true?
Answer:
The correct answer is A. Aimee's graph is correct because the ratio [tex]\frac{2}{3} :1[/tex] is equal to 2:3, which her graph shows in each point.
Step-by-step explanation:
We are given that Aimee noticed her plant grew 2/3 of an inch every week since it sprouted and a graph is drawn to show the plant growth.
We are to determine whether which of the given statements is correct.
The ratio [tex]\frac{2}{3} :1[/tex] is basically equal to 2:3. Therefore, the graph is correct as it shows the same ratio at each point.
For the points (6, 4) and (3, 2) = [tex]\frac{4-2}{6-3} =\frac{2}{3}[/tex]
Answer:it’s A great got it right on edge
Step-by-step explanation:
There are 5 persons and at a time only 3 can be arranged. What is the total number of arrangements?
a. 80
b. 240
c. 60
d. 120
Answer:
If there are 5 persons and at a time only 3 can be arranged, the total number of arrangements is 60
Option C is correct
Step-by-step explanation:
There are 5 persons and at a time only 3 can be arranged.
The total number of arrangements = nPr = n!/(n-r)!
Here n = 5 and r = 3
nPr = n!/(n-r)!
nPr = 5!(5-3)!
nPr = 5!/2!
nPr = 5*4*3*2!/2!
nPr = 5*4*3
nPr = 60
So, if there are 5 persons and at a time only 3 can be arranged, the total number of arrangements is 60
Option C is correct.
help me to do this question friends
Answer:
10 square unitsStep-by-step explanation:
It's a right triangle.
The formula of an area of a right triangle:
[tex]A=\dfrac{ab}{2}[/tex]
a, b - legs
Find x-intercept and y-intercept of a line 4x + 5y = 20.
x-intercept (y = 0):
4x + 5(0) = 20
4x + 0 = 20
4x = 20 divide both sides by 4
x = 5
y-intercept (x = 0):
4(0) + 5y = 20
0 + 5y = 20
5y = 20 divide both sides by 5
y = 4
Therefore the legs are a = 5, b = 4.
Substitute:
[tex]A=\dfrac{(5)(4)}{2}=\dfrac{20}{2}=10[/tex]
Look at the picture.
Which translation maps the graph of the function fx=x2 onto the function gx= x2+(-8x)+7
Answer:
Shift the graph of f(x) 4 units to the rightand 7 units upStep-by-step explanation:
f(x) + n - shift a graph of f(x) n units up
f(x) - n - shift a graph of f(x) n units down
f(x + n) - shift a graph of f(x) n units to the left
f(x - n) - shift a graph of f(x) n units to the right
=============================================
We have
[tex]f(x)=x^2,\ g(x)=x^2+(-8x)+7[/tex]
Convert the equation of g(x) to the vertex formula:
[tex]y=a(x-h)^2+k[/tex]
[tex]g(x)=x^2+(-8x)+7\\\\g(x0=x^2-2(x)(4)+7\\\\g(x)=\underbrace{x^2-2(x)(4)+4^2}-4^2+7\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\g(x)=(x-4)^2+7=f(x-4)+7\\\\\text{shift the graph of f(x) 4 units to the right and 7 units up}[/tex]
I Need Help Answer Plz!!!
Answer:
The SAS PostulateStep-by-step explanation:
SAS - Side Angle Side
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.
the opposite sides have the same lengths.
the angles formed by these sides are right angles
f(x) = 8x^2 - 2x + 3
g(x) = 12x^2 + 4x-3
What is h(x) = f(x) – g(x)?
h(x) = 20x^2 + 2x
h(x) = -4x^2 - 6x
h(x) = -4x^2 - 6x + 6
h(x) = -4x^2 + 2x
Answer:
-4x^2-6x+6
(third choice)
Step-by-step explanation:
To do f(x)-g(x) we must insert the expression for f(x) and g(x) into this:
This will give us:
(8x^2-2x+3)
-(12x^2+4x-3)
--------------------
-4x^2-6x+6
Horizontally if you prefer:
(8x^2-2x+3)-(12x^2+4x-3)
Distribute and get rid of paranthesis:
8x^2-2x+3-12x^2-4x+3
Pair up like terms:
8x^2-12x^2-2x-4x+3+3
Combine the like terms:
-4x^2-6x+6
Answer:
h(x) = -4x^2 - 6x + 6
Step-by-step explanation:
f(x) - g(x)
= 8x^2 - 2x + 3 - (12x^2 + 4x - 3) (Note the parentheses around g(x))
Distributing the negative over the parentheses:
= 8x^2 - 2x + 3 - 12x^2 - 4x + 3
= -4x^2 - 6x + 6 = h(x).
the Town Theater received $22,540.75 by selling 435 tickets to the opening night of the play. if the full price of a ticket is $6.25 and discount tickets for students and seniors are $5.25 each how many full-price tickets were sold
I tried solving the problem and it didn't make sense until assuming that 22540.75 was a typo for 2540.75.
Answer:
2540.75 = 6.25x + 5.25y
435 = x + y
x = number of adult tickets
y = number of student and senior tickets
Question is asking to find x
- - - - - - - - - - - - - - - - - -
435 = x + y
2283.75 = 5.25x + 5.25y
Elimination method:
2540.75 = 6.25x + 5.25y
-(2283.75 = 5.25x + 5.25y)
257 = x
257 full priced tickets were sold.
Please mark for Brainliest!! :D Thank you!!
For any questions, please comment!!
Answer:
Full tickets sold were 257 in count and discounted tickets were 178.
Step-by-step explanation:
Let the full tickets be = f
Let the discounted tickets be = d
Total tickets sold = 435
This can be written as :
[tex]f+d=435[/tex] or[tex]f=435-d[/tex] .....(1)
The full price of a ticket is $6.25 and discount price is $5.25 and total earning is $2540.75.
In equation form, it can be written as :
[tex]6.25f+5.25d=2540.75[/tex] ....(2)
Substituting the value of f in (2)
[tex]6.25(435-d)+5.25d=2540.75[/tex]
[tex]2718.75-6.25d+5.25d=2540.75[/tex]
[tex]-1d=-178[/tex]
so , d = 178
And[tex]f+d=435[/tex]
So,[tex]f=435-178=257[/tex]
Hence, full tickets sold were 257 in count and discounted tickets were 178.
If the equation of a circle is (x + 5)2 + (y - 7)2 = 36, its center point is (5, 7) (-5, 7) (5, -7)
Answer:
center ( -5 , 7).
Step-by-step explanation:
Given : If the equation of a circle is (x + 5)² + (y - 7)² = 36.
To find : Find its center .
Solution : We have given (x + 5)² + (y - 7)² = 36.
Standard equation of circle : (x – h)² + (y – k)² = r².
Where, (h ,k) = center , r = radius .
On comparing (x + 5)² + (y - 7)² = 36.
h = -5 , k = 7
So, the center ( -5 , 7).
Therefore, center ( -5 , 7).
Hey, guys how to convert dates?
Ex: 96 hours ≈ 4 days
This is one way to convert dates.
I am joyous to assist you anytime.
Converting dates involves understanding time zones and the International Date Line. When crossing the date line from west to east, the date decreases by one day, and when crossing from east to west, the date increases by one day.
Explanation:Converting dates can be done by understanding the concept of time zones and the International Date Line. Time zones are regions that have the same standard time, while the International Date Line is an imaginary line that marks where the date changes by one day. When crossing the date line from west to east, the date is decreased by one day, and when crossing from east to west, the date is increased by one day.
Learn more about Converting dates here:https://brainly.com/question/33936831
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what is the equation for the line of reflection?
x=6
y=6
y=x
y=2
Answer:
Hi there!
The answer to this question is: x=6
Step-by-step explanation:
All the points are being mirrored across the line x=6.
Answer:
The answer is x=6
Step-by-step explanation:
The two shapes are mirror images of each other around x=6
A group of students is collecting books to add to their library. The table shows the number of books in the library after 1, 3, and 5 days. If the relationship between days and books continues to be linear, which ordered pairs could appear in the table? Check all that apply.
(0, 8)
(2, 23)
(4, 32)
(6, 48)
(7, 48)
Answer:
B and E are the correct answer
Step-by-step explanation:
Because (2,23) and (7,48) are linear
Your question is incomplete and lacks the table. Please check below for the full content.
A group of students is collecting books to add to their library. The table shows the number of books in the library after 1, 3, and 5 days. If the relationship between days and books continues to be linear, which ordered pairs could appear in the table? Check all that apply.
(0, 8)
(2, 23)
(4, 32)
(6, 48)
(7, 48)
The missing table is given below.
The correct options are option 2:(2,23) and 5:(7,48) The ordered pair (2,23),(7,48) will appear in the table.
What is linear equation?The equation where highest degree of the variable used in the equation is 1 is called linear equation. Foe example ax+by+c=0
Here given the relationship between days and books is linear.
From the table, it clear that In day 1 the book collected is 18.
in day 3 book collected is 28.
x₁=1,y₁=18
x₂=3,y₂=28
The linear equation will be
(y-y₁)/(x-x₁)=(y₂-y₁)/(x₂-x₁)
⇒(y-18)/(x-1)=(28-18)/(3-1)
⇒(y-18)/(x-1)=10/2
⇒(y-18)/(x-1)=5
⇒y-18=5(x-1)
⇒y-18=5x-5
⇒y=5x-5+18
⇒y=5x+13
So the linear equation will be y=5x+13
By ckecking every option,
1. (0, 8)- y=5*0+13=13≠8 Option 1 is incorrect.
2. (2,23)- y=5*2+13=23 Option 2 is correct.
3. (4,32)- y=5*4+13=33≠32 Option 3 is incorrect.
4.(6,48)- y=5*6+13=43≠48 Option 4 is incorrect.
5. (7,48) y=5*7+13=48 Option 5 is correct.
Therefore the correct options are option 2 and 5 i.e. The ordered pair (2,23) , (7,48) will appear in the table.
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What is the most precise name for quadrilateral ABCD with vertices A(−5,7), B(6,−3), C(10,2), and D(−1,12)?
Answer:Answer:
the figure is parallelogram
Explanation:
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As The mutually edges are parallel each other and equal,
the name of figure is parallelogram .
Step-by-step explanation:
Answer with explanation:
The vertices of Quadrilateral ABCD are ,A(−5,7), B(6,−3), C(10,2), and D(−1,12).
Distance formula between two points (a,b) and (c,d), is given by
[tex]=\sqrt{(a-c)^2+(b-d)^2[/tex]
[tex]AB=\sqrt{[-5-6]^2+[7-(-3)]^2}\\\\AB=\sqrt{121+100}\\\\AB=\sqrt{221}\\\\BC=\sqrt{[10-6]^2+(2+3)^2}\\\\BC=\sqrt{16+25}\\\\BC=\sqrt{41}\\\\CD=\sqrt{[10+1]^2+[2-12]^2}\\\\CD=\sqrt{121+100}\\\\CD=\sqrt{221}\\\\DA=\sqrt{[-1+5]^2+[12-7]^2}\\\\DA=\sqrt{16+25}\\\\DA=\sqrt{41}\\\\AC=\sqrt{[10+5]^2+[2-7]^2}\\\\AC=\sqrt{225+25}\\\\AC=\sqrt{250}\\\\BD=\sqrt{[6+1]^2+[-3-12]^2]}\\\\BD=\sqrt{49+225}\\\\BD=\sqrt{274}[/tex]
Opposite side of Quadrilateral[AB=CD, AD=BC] is equal, but Diagonals are not equal.
So, it is a Parallelogram.
Simplify (9.5)(-2)(-5)
Answer:
95
Step-by-step explanation:
(9.5)(-2)(-5)
First multiply the first two terms:
9.5* -2(-5)
9.5* -2 = -19
= -19(-5)
now multiply the product of solved terms by -5
-19(-5)
Negative signs will change into positive because - * - = +
95....
Thus the answer is 95....
Answer:
your answer is 95
Step-by-step explanation:
you multiply (9.5) (-2)(5) and you get 95
How do I find the answer?
Step-by-step explanation:
Hi there!
The best way to approach this problem is Soh Cah Toa.
In this case you can use sine. sine is opposite over hypotenuse.
so sin(17)= b/15
then to solve for b you multiply 15 on both sides to get 4.4
Answer:
Step-by-step explanation:
This question is an application of the sine law
Equation
b/sin(B) = c / Sin(C)
Givens
b = ????
B = 17
c = 15
C = 140
Solution
Keep in mind that this may not work.
b/sin(17) = 15 / sin(140) Multiply both sides by sin(17)
b = 15*sin(17)/sin(140)
sin(17) = 0.2924Sin(140) = 0.6428b = 15*0.2924/0.6428
b = 6.8233