Answer:
Following system of equations have exactly one solution:
[tex]2 x + 4 y = 6\\ 3 x - 4 y = 9[/tex]
Step-by-step explanation:
Given 4 system of equations:
1st
[tex]4 x + 2 y = 8\\ -4 x -2 y = 3[/tex]
2nd
[tex]-5 x + y = 6\\ 5 x - y = - 6[/tex]
3rd
[tex]- 3 x + 4 y = 2\\ 3 x - 4 y = 0[/tex]
4th
[tex]2 x + 4 y = 6\\ 3 x - 4 y = 9[/tex]
To find: Which system of equations has only one solution?
Solution:
First of all, let us learn the concept.
Let the equation of lines be:
[tex]a_1x+b_1y+ c_1=0[/tex] and [tex]a_2x+b_2y+ c_2=0[/tex]
1. No solution:
There exists no solution if:
[tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]
2. Infinite solutions:
There exist infinitely many solutions if:
[tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}[/tex]
3. One solution:
There exists one solution if:
[tex]\dfrac{a_1}{a_2}\neq\dfrac{b_1}{b_2}[/tex]
Now, let us consider the given equations one by one.
1st system of equations:
The ratio is:
[tex]\dfrac{4}{-4} , \dfrac{2}{-2} , \dfrac{8}{3}\\-1 =-1\neq \dfrac{8}{3}[/tex]
So, no solution.
2nd system of equations:
The ratio:
[tex]\dfrac{-5}{5} , \dfrac{-1}{1} , \dfrac{6}{-6}\\-1 =-1=-1[/tex]
So, infinitely many solutions.
3rd system of equations:
[tex]\dfrac{3}{-3} , \dfrac{-4}{4} , \dfrac{0}{2}\\-1 =-1\ne0[/tex]
So, no solution.
4th system of equations:
[tex]\dfrac{2}{3} , \dfrac{4}{-4} , \dfrac{6}{9}\\\dfrac{2}{3} \ne-1[/tex]
Hence, only one solution.
So, the answer is:
Following system of equations have only one solution:
[tex]2 x + 4 y = 6\\ 3 x - 4 y = 9[/tex]
Answer:
4
Step-by-step explanation:
Micah is handing out miniature chocolate bars and butterscotch hard candies for Halloween. He wants tohave a total of 7 pounds of candy, but he doesn't want to spend more than $11.00 total on the candy. If miniature chocolate bars costs $1.80 per pound, and butterscotch hard candies costs $1.00 per pound, how many pounds of each type of candy should he buy?
Answer:
5 pounds of miniature chocolate and 2 butterscotch hard candies
Step-by-step explanation:
5 x $1.80 =$9 for 5 pounds of candy
2 x $1.00 =$2 for 2 pounds of candy
2 + 5 =7 pounds
7 pounds of candy using $11.00
is the square root of 34 rational or irrational
Answer:
irrational
Step-by-step explanation:
If a square root is not a perfect square, then it is considered an irrational number.
The square root of the number 34 is not a rational number
How to determine the type of the numberFrom the question, we have the following parameters that can be used in our computation:
The square root of the number 34
When evaluated, we have
The square root of the number 34 = √34
So, we have
The square root of the number 34 = 5.83.....
The above number cannot be represented by the quotient of 2 integers
Using the above as a guide, we have the following:
We can conclude that the number is an irrational number
Read more about rational number at
brainly.com/question/22221295
#SPJ6
Jackson is attending a lacrosse game that is halfway through the first quarter.
4) What fractional part of the game is leh?
3) If 74 minutes of playing time have past, how many total minutes of playing
time are there in the game?
6) How many minutes of playing time are left in the game?
(okay so I have to draw the picture so someone please help meh :p)
Answer:
7/8 of the game is left. The game lasts for 592 minutes.
Step-by-step explanation:
It is halfway through the first quarter so it is 1/8. So that's 7/8 part of the game left. if 74 minutes of playing time has past, then you do 74*8 so that's 592 minutes.
Answer:
4) 1/8
3)74x8=592
6)592-74= 518
Step-by-step explanation:
HElp Find the line of symmetry for the parabola whose equation is y = 2x∧2 - 4x + 1.
x = 2
x = -1
x = 1
Answer:
x = ---------- = 1
Step-by-step explanation:
The formula for the axis of symmetry is x = -b/(2a). In this case b = -4 and a = 2, and so the axis of symmetry is
-(-4)
x = ---------- = 1
2(2)
Answer:
x=1
Step-by-step explanation:
because I said so
Help ASAP!! This one's is difficult for me to understand!! Help me please!
Answer:
Ok so im in 7thgrade so ima try to help answer is x= 8x9
this squared based pyramid is cut horizontally at a height of 15cm to leave this frustum base area=10cm
Answer:
583.33 cm³
Step-by-step explanation:
From the image attached, the total height (H) of the pyramid is 30 cm, the height of the frustrum (h) = 15 cm, the Frustrum base = lower base = B = 10 cm . To find the length of the upper base (b), we use:
[tex]\frac{b}{H-h}=\frac{B}{H}\\ b=(H-h)\frac{B}{H}\\b=(30-15)\frac{10}{30}=5\\b=5\ cm[/tex]
The volume of the frustrum is given by:
[tex]V=\frac{1}{3}h(B_1+B_2+\sqrt{B_1B_2} )\\ Where\ B_1\ is \ the\ area \ of\ the\ upper\ base= 5cm*5cm=25cm^2\\B_1\ is \ the\ area \ of\ the\ lower\ base= 10cm*10cm=100cm^2\\V=\frac{1}{3}(10)(25+100+\sqrt{25*100} )=583.33\\V=583.33\ cm^3[/tex]
Martin uses 8 5/8 of a gallon of paint to cover 4/5 of a wall. What is the unit rate at which Martin paints in walls per gallon?
Answer: 32/345 wall per gallon
Step-by-step explanation:
Rate is defined as ratio between two quantities with different units.
Gallons of paint used by Martin = 8 5/8 gallons = 69/8 gallons
Portion of wall Martin wishes to pint = 4/5 wall
Rate at which Martin paints the wall:
= Portion of wall covered / paint used
=
4/5 / 69/8 = 32/345 wall per gallon
Answer:
Martin paints 0.093 walls per gallon of paint
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Amount of paint used by Martin = 8 5/8 of a gallon
Ratio of wall painted by Martin with 8 5/8 of a gallon = 4/5
2. What is the unit rate at which Martin paints in walls per gallon?
Let's convert the mixed fractions to decimals this way:
8 5/8 = 8 + 0.625 = 8.625
4/5 = 0.8
Now, let's use the Direct Rule of Three, this way:
Gallons Walls
8.625 0.8
x 1
Solving for x :
0.8x = 8.625 * 1
x = 8.625/0.8
x = 10.78125
x = 10.8 (rounding to next tenth) gallons
For painting a wall, we will use 10.8 gallons of paint. Now, we can calculate the unit rate at which Martin paints in walls per gallon, this way:
Gallons Walls
10.8 1
1 x
Solving for x :
10.8x = 1
x = 1/10.8
x = 0.09259
x = 0.093 (rounding to the next hundredth) walls per gallon of paint
Find the length of x.
If the quadratic formula is used to solve 2x2-3x - 1 = 0, what are the solutions?
1-3 + fin 3 - i7)
4.
4.
0 -3-17 3 - 171
4
4
이
13 +17 3 - (1)
4
4
Answer:
x = (3 +/- sqrt(17) / 4.
Step-by-step explanation:
x = [-(-3) +/- sqrt((-3)^2 - 4*2*-1)] / 4
x = (3 +/- sqrt(17) / 4.
How many houses are on Prince Street?
Answer:
25 houses on prince street
Step-by-step explanation:
add them up and bam
Answer:
25 houses
Step-by-step explanation:
You need to add up all the houses and u will get the ans..
Have a good day !!
Hope this helps..
Pls mark my ans as branliest :)If u mark my ans as brainliest then u are the "bestestest " person in the world :)Please help me answer my questions...
Answer:
80$
Step-by-step explanation:
total amount of needed=200
Total =Tef +Angelina+Jason
200=90+30+Angelina
Angelina=200-120
Angelina=80$
five sixths of a number equals 200. What is the number?
Answer: 240
Step-by-step explanation:
5/6x=200
(6/5)5/6x=200(6/5)
1x=40(6/1)
x=40(6)
x=240
The lengths of the sides of a triangle are in the ratio of 6:6:5. The perimeter of the triangle
is 34 centimeters. Find the length of each side of the triangle.
Hello!
Answer:
12 cm, 12 cm, 10 cm.
Step-by-step explanation:
Given:
Perimeter, or P = 34 cm
Ratio of sides = 6 : 6 : 5
To find the length of each side, we can use a variable in the ratio to find the perimeter:
34 = 6x + 6x + 5x
Combine like terms:
34 = 17x
Solve for x:
34/17 = 17x/17; x = 2
Plug in this value of "x" into each expression for the side-lengths:
6(2) = 12 cm
6(2) = 12 cm
5(2) = 10 cm
Therefore, the lengths of each side of the triangle are 12 cm, 12 cm, 10 cm.
Hope this helped you! :)
Answer:
12, 12 and 10 cm.
Step-by-step explanation:
6 + 6 + 5 = 17
So one side = 6/17 * 34 = 12 cm
One other side is also 12 cm
The third side = 5/17 * 34 = 10 cm.
Please help ASAP!
Rearrange the equation so x is the independent variable. -5x - 4y = -8
Answer:
Hey there!
Original Equation
-5x-4y=-8
Multiply by -1
5x+4y=8
Subtract 4y
5x=8-4y
Divide by 5
x=(8-4y)/5
Let me know if this helps :)
Answer:
x = -4/5y + 8/5
Step-by-step explanation:
So to single out x we use the communicative property,
its the moving of numbers and variables to each side of the equation.
So we have,
-5x - 4y = -8
+4y
-5x = 4y - 8
Divide -5 by both sides,
x = -4/5y + 8/5
Thus,
the equation rearanged is x = -4/5y + 8/5.
Hope this helps :)
Please I need help!
Write the equation of the line that passes through the points (7, -4) and ( 1, 3), first in point-slope form, and then in
slope intercept form
The slope of the line is
When the point (7, -4) is used, the point-stope form of the line is
The slope intercept form of the line is
Answer:
1)
[tex]\text{ Slope = -3}[/tex]
2)
[tex]y+4=-\frac{7}{8}(x-7)[/tex]
3)
[tex]y=-\frac{7}{8}x+\frac{17}{8}[/tex]
Step-by-step explanation:
We want to write the equation of the line that passes through the points (7, -4) and (-1, 3) first in point-slope form and then in slope-intercept form.
1)
First and foremost, we will need to find the slope of the line. So, we can use the slope-formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let (7, -4) be (x₁, y₁) and let (-1, 3) be (x₂, y₂). Substitute them into our slope formula. This yields:
[tex]m=\frac{3-(-4)}{-1-7}[/tex]
Subtract. So, our slope is:
[tex]m=\frac{7}{-8}=-7/8[/tex]
2)
Now, let's use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
We will substitute -7/8 for our slope m. We will also use the point (7, -4) and this will be our (x₁, y₁). So, substituting these values yield:
[tex]y-(-4)=-\frac{7}{8}(x-7)[/tex]
Simplify. So, our point-slope equation is:
[tex]y+4=-\frac{7}{8}(x-7)[/tex]
3)
Finally, we want to convert this into slope-intercept form. So, let's solve for our y.
On the right, distribute:
[tex]y+4=-\frac{7}{8}x+\frac{49}{8}[/tex]
Subtract 4 from both sides. Note that we can write 4 using a common denominator of 8, so 4 is 32/8. This yields:
[tex]y=-\frac{7}{8}x+\frac{49}{8}-\frac{32}{8}[/tex]
Subtract. So, our slope-intercept equation is:
[tex]y=-\frac{7}{8}x+\frac{17}{8}[/tex]
And we're done!
Answer: Shown Below
Step-by-step explanation:
1. -7/8
2. y+4= (-7/8)(x-7)
3. y=(-7/8)x+ (17/8)
Just did it
Please answer quickly.
Answer:
Option 4
Step-by-step explanation:
=> [tex]\frac{4}{5} x^{-9}y^6z^8[/tex]
If there is any variable having a negative exponent, we should move it to its opposite side (Denominator to numerator and vice versa) So that it's exponent become positive.
=> [tex]\frac{4y^6z^8}{5x^9}[/tex]
Answer: D) [tex]\frac{4y^6z^8}{5x^9}[/tex]
Step-by-step explanation:
(4/5)x^-9y^6z^8 = [tex]\frac{4x^{-9}y^6z^8}{5}[/tex]
Any negative exponent can be taken to the other side of the fraction to be positive. Thus,
[tex]\frac{4x^{-9}y^6z^8}{5}[/tex] = [tex]\frac{4y^6z^8}{5x^9}[/tex]
Hope it helps <3
Which of the following geometric series converges?
All three series converge, so the answer is D.
The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.
Consider a geometric sequence with the first term a and common ratio |r| < 1. Then the n-th partial sum (the sum of the first n terms) of the sequence is
[tex]S_n=a+ar+ar^2+\cdots+ar^{n-2}+ar^{n-1}[/tex]
Multiply both sides by r :
[tex]rS_n=ar+ar^2+ar^3+\cdots+ar^{n-1}+ar^n[/tex]
Subtract the latter sum from the first, which eliminates all but the first and last terms:
[tex]S_n-rS_n=a-ar^n[/tex]
Solve for [tex]S_n[/tex]:
[tex](1-r)S_n=a(1-r^n)\implies S_n=\dfrac a{1-r}-\dfrac{ar^n}{1-r}[/tex]
Then as gets arbitrarily large, the term [tex]r^n[/tex] will converge to 0, leaving us with
[tex]S=\displaystyle\lim_{n\to\infty}S_n=\frac a{1-r}[/tex]
So the given series converge to
(I) -243/(1 + 1/9) = -2187/10
(II) -1.1/(1 + 1/10) = -1
(III) 27/(1 + 1/3) = 18
Jamila wrote the numbers 1-100 and placed them in a bag. If she selects a number without looking, what is the probability that the number is divisible by 5? Input your answer as a decimal or fraction.
100 total numbers.
20 Numbers divisiblae by 5: 5, 10, 15, 20, 25, 30, 35,40,45,50,55,60,65,70,75,80,85,90,95,100
Probability = 20/100 = 2/10
Answer:
1/5
Step-by-step explanation:
There are total 100 numbers.
Numbers divisible by 5 through 1-100 are:
5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100
There are 20 numbers that are divisible by 5.
20/100 = 1/5
A painter leans a 25-foot ladder against the wall. The bottom of the ladder is 20 feet from the base of the wall. The painter then moves the bottom of the ladder 13 feet closer to the wall. How much higher is the top of the ladder on the wall?
Answer:
9 ft
Step-by-step explanation:
a²+b²=c²
20²+b²=25²
400=b²=625
b²=625-400
b²=225
b=15 (the distance up the wall the ladder is to begin with)
20-13=7
7²+b²=25²
49+b²=625
b²=625-49
b²=576
b=24 (The distance up the wall the ladder is after moving it)
24-15=9
How can you decompose the composite figure to determine its area?
Answer:Área y perímetro de figuras compuestas
por Luz | Dic 5, 2014 | Geometría, Matematicas | 39 Comentarios
Obtener el área o perímetro es de las habilidades más fáciles y básicas en geometría. Sin embargo, al momento de combinar varias figuras planas se forma figuras compuestas, que pueden incluir: cuadrados, círculos, triángulos, rectángulos, trapecio, etc.
Answer: D
Step-by-step explanation:
There’s a trapezoid a rectangle and two squares at the bottom
1. What is the value of x? Show all of your work.
Answer:
9 cm
Step-by-step explanation:
Pythagorean's Theorem: a^2+b^2=c^2
x^2+6^2=117 (the square root of 117, squared)
X^2+36=117
x^2=117-36
x^2=81
x=9
Answer:
x = 9 cm
Step-by-step explanation:
Use the Pythagorean Theorem to find the length of the missing side.
a² + b² = c²
a² + (6)² = (√117)²
a² + 36 = 117
a² = 81
a = √81
a = 9
X is equal to 9 cm.
Hope this helps.
please help with this
Answer:
158m^3
Step-by-step explanation:
First, let's figure out the total amount of water in the tank.
It measures 4.5m by 6m by 8m. The volume of a rectangular prism is V=lwh.
Therefore, the volume is:
[tex]V=(4.5)(6)(8)=216 m^3[/tex]
We are told is it filled to the brim, so we can conclude that there are 216 cubic meters of water in the tank.
We used 58 cubic meters of water, so we simply need to subtract that from 216:
[tex]216m^3-58m^3=158m^3[/tex]
There is still 158 cubic meters of water left in the tank.
Answer:
158 m^3
Step-by-step explanation:
Volume of the tank
= 4.5 * 6 * 8
= 216 m^3.
So amount left in the tank
= 216 - 58
= 158 m^3.
Plz Help me solve this
Answer:
Step-by-step explanation:I think the answer is 12?
For the following right triangle, find the side length x, Round your answer to the nearest hundredth.
Answer:
x ≈ 15.59
Step-by-step explanation:
We need to use the Pythagorean Theorem to solve for x. The equation for that is a^2 + b^2 = c^2. Side a is 9. Side b is x. Side c is 18 and 18 is also the hypotenuse. Let's solve for x(side b):
a^2 + b^2 = c^2
9^2 + x^2 = 18^2
81 + x^2 = 324
Subtract 81 from both sides to get x^2 alone on one side.
x^2 = 243
Square root both sides to isolate x.
x = 9sqrt3)
x ≈ 15.59
What is the Domain and Range *DON'T FORGET PARENTHESES AND BRACKETS*
Answer:
Domain: (-5,-4,-3,-2,-1,0,1,2,3,4,5)
Range: (0,1,2,3,4, -1, -2)
Step-by-step explanation:
Domain means all of the x-axis values on the graph, so for example in (-2,0), -2 would be part of the domain and 0 part of the range. Therefor, what you would do would be take all of the plots and put all x values as the domain and all y values as the range. Hope this helped!
write a system of equations for the problem, and then solve the system. if a plane can travel 340 miles per hour with the wind only 260 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air. please show step by step
Answer:
The speed of plane = 40 m/s
The speed of the wind = 300 m/s
Step-by-step explanation:
Let the speed of the plane = Y
And the speed of the wind = X
If the plane then travel 340 miles per hour with the wind, that means the plane and the wind are moving in the same direction. Therefore,
X + Y = 340 ..... ( 1 )
Also, 260 miles per hour against the wind. That is, the plane is moving opposite to the direction of the wind. Therefore,
X - Y = 260 ..... ( 2 )
Solve the two equations simultaneously by addition. That will eliminate Y
X + Y = 340
X - Y = 260
2X = 600
X = 600/2
X = 300 m/s
Substitutes X in equation (1)
300 + Y = 340
Make Y the subject of formula by collecting the like terms
Y = 340 - 300
Y = 40 m/s
Therefore, the speed of the plane is 40 m/s. While the speed of the wind is 300 m/s.
plz help me plz if u get it correct i will mark brainlist if i can
The function ƒ(x) = 6x is vertically shrunk by a factor of ½ and translated 9 units in the negative y- direction. Select the correct graph of the resulting function. Question 9 options: A) image B) image C) image D) image
Answer:
A
Step-by-step explanation:
help please. Find the length of x.
Answer:
x=10
Step-by-step explanation:
The triangles are similar so we can use ratios to solve
6.5 (6.5+6.5)
------ = -----------------------
5 x
6.5 (13)
------ = -----------------------
5 x
Using cross products
6.5x = 65
Divide by 6.5
6.5x/6.5 = 65/6.5
x = 10
is 3 over the square root of 27 rational or irrational
Answer:
rational (I think
Step-by-step explanation: