Answer: [tex]\frac{1}{8}[/tex] or [tex]1:8[/tex]
Step-by-step explanation:
First, you can convert the mixed number [tex]1\ \frac{1}{2}[/tex] into a decimal number. To do this, you need to divide the numerator (which is 1) by the denominator (which is 2) of the fraction:
[tex]\frac{1}{2}=0.5[/tex]
Now you must add 0.5 to the whole number part. Then:
[tex]1+0.5=1.5[/tex]
In order to find the ratio of cleaner to water, you must divide 1.5 cups of cleaner by 12 cups of water.
Therefore, the ratio is:
[tex]ratio=\frac{1.5}{12}=\frac{1}{8}[/tex] or [tex]1:8[/tex]
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
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
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.
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
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]
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]
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
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
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!!
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
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 Big Burger recipe calls for 3 meat patties, 2 slices of cheese, and four pickles. How many meat patties are needed if 52 pickles are used?
39
52 divided by 4 is 13. 52 pickles divided into 4 pickles for each meal is 13. 39 patties divided by 3 patties is 13 aswell so. the answer: 39
The number of meat patties that are needed if 52 pickles are used is:
39 meat patties.
Step-by-step explanation:It is given that:
The Big Burger recipe calls for 3 meat patties, 2 slices of cheese, and four pickles.
This means that for every 4 pickles there are 3 meat patties.
This means that for every 1 pickles there are: 3/4 meat patties.
Hence, for every 52 pickles there are: 3/4×52 meat patties
= 39 meat patties.
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.
A model of a rectangular patio at a landscaping business will be enlarged by a scale factor of 2 when it is installed in a customer’s back yard. The area of the new enlarged patio will be 160 square feet. Which is the area of the landscaper’s model?
Answer: [tex]80\ ft^2[/tex]
Step-by-step explanation:
You know that the model of a rectangular patio at a landscaping business will be enlarged by a scale factor of 2 and the new area will be 160 square feet.
Since you know that the area of the new enlarged patio will be 160 square feet, you need to divide the area of the new enlarged patio in order to find the area of the landscaper’s model.
This is:
[tex]Area_(model)=\frac{160\ ft^2}{2}\\\\Area_(model)=80\ ft^2[/tex]
Answer:
I think its 40
Step-by-step explanation:
i come back and see:)
I got it right. good luck
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
Is x^2 = 144 rational or irrational
Answer:
The roots are rational
Step-by-step explanation:
Given
x² = 144 ( take the square root of both sides )
x = ± [tex]\sqrt{144}[/tex] = ± 12 ← both rational
A rational number can be expressed in the form
[tex]\frac{a}{b}[/tex] where a and b are integers.
12 = [tex]\frac{12}{1}[/tex] ← thus rational
- 12 = [tex]\frac{-12}{1}[/tex] ← thus rational
Answer:
The answer is that x^2=144 is rational
A music Web site announced that over
4 X 10^9 songs were downloaded by 5 X 10^7
registered users. What is the average number
of downloads per user?
Step-by-step explanation:
Average=total numbers of songs /registered users
Average= 4*10^9/5*10^7
Average=40*10^8/5*10^7
Average=8*10^(8-7)
Average=8*10^(1)
Average=80 songs downloaded per user
The Average number is 80 songs downloads per user.
What is Average?The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average.
The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers.
Given:
Total Registered user = 5 x [tex]10^7[/tex]
Downloaded songs = 4 x [tex]10^9[/tex]
So, Average=total numbers of songs /registered users
Average = 4 x [tex]10^9[/tex]/ 5 x [tex]10^7[/tex]
Average= 40 x [tex]10^8[/tex]/ 5 x [tex]10^7[/tex]
Average = 8 x [tex]10^{(8-7)[/tex]
Average= 8 x 10
Average= 80 songs.
Hence, 80 songs downloaded per user.
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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
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.
Learn more about linear equation
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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.
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).
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.
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
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:
enter image source here
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.
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:
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).
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.
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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.
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.