The given table is
x 2 4 6 8
y 5 1 -3 -7
The formula for determining the slope of a line is expressed as
slope = (y2 - y1)/(x2 - x1)
From the table,
x1 = 2, x2 = 4
y1 = 5, y2 = 1
Slope = (1 - 5)/(4 - 2)
Slope = - 4/2
Slope = - 2
I definitely absolutely recommend this needed a tutor for it can one help me out if your available
The given coordinates : ( 5, 5 ) & ( 11, 3 )
The expression for the mid point is :
[tex]x=\frac{x_1+x_2}{2},\text{ y=}\frac{y_1+y_2}{2}[/tex]Substitute the value of coordinates as :
[tex]\begin{gathered} x_1=5,y_1=5,x_2=11,y_2=3 \\ x=\frac{5+11}{2} \\ x=\frac{16}{2} \\ x=8 \\ y=\frac{5+3}{2} \\ y=\frac{8}{2} \\ y=4 \end{gathered}[/tex]So, the mid point between (5, 5) & (11, 3) is ( 8, 4)
At time the position of a body moving along the s- axis is s = t ^ 3 - 6t ^ 2 + 9t m Find the body's acceleration each time the velocity is zero . Find the body's speed each time the acceleration is zero .
The body's acceleration each time the velocity is zero is 6 [tex]m/s^{2}[/tex] or -6 [tex]m/s^{2}[/tex] and the body's speed each time the acceleration is zero is -3m/s.
According to the question,
We have the following information:
s = [tex]t^{3} -6t^{2} +9t[/tex]
Velocity = ds/dt
Velocity = [tex]3t^{2} -12t+9[/tex]
Acceleration = dv/dt
Acceleration = 6t-12
When velocity is zero:
[tex]3t^{2} -12t+9= 0[/tex]
Taking 3 as a common factor:
[tex]t^{2} -4t+3=0\\t^{2} -3t-t+3=0[/tex] (Factorizing by splitting the middle term)
t(t-3)-1(t-3) = 0
(t-3)(t-1) = 0
t = 3 or t = 1
Now, putting these values of t in acceleration's equation:
When t =3:
A = 6*3-12
A = 18-12
A = 6 [tex]m/s^{2}[/tex]
When t = 1:
A = 6*1-12
A = 6-12
A = -6 [tex]m/s^{2}[/tex]
Now, when acceleration is zero:
6t-12 = 0
6t = 12
t = 2 s
Now, putting this value in velocity's equation:
[tex]3*2^{2} -12*2+9[/tex]
3*4-24+9
12-24+9
21-24
-3 m/s
Hence, the body's acceleration each time the velocity is zero is 6 [tex]m/s^{2}[/tex] or -6 [tex]m/s^{2}[/tex] and the body's speed each time the acceleration is zero is -3m/s.
To know more about acceleration here
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let f(x)= - |x-3|+4 what interval describes when f is decreasing
Answer:
(3, ∞)
Explanation:
Given the function:
[tex]f\mleft(x\mright)=-|x-3|+4[/tex]The graph of the function is attached below:
The interval when f(x) is decreasing is therefore:
[tex](3,\infty)[/tex]39An amusement park issued a coupon to increase the number of visitors to the park each week. The function below representsthe number of visitors at the amusement park x weeks after the issuance of the couponVx) = 500(1.5)What is the approximate average rate of change over the interval [2,6]?OA 949 visitors per weekB 281 visitors per weekC1,143 visitors per weekD. 762 visitors per weekResetSubmitCrved12-39
The Solution.
Given the exponential function below:
[tex]V(x)=500(1.5)^x[/tex]The average rate of change over the interval [2,6] is given as below:
[tex]\text{Average rate of change =}\frac{V(6)-V(2)}{6-2}[/tex]To find V(6):
[tex]V(6)=500(1.5)^6=500\times11.3906=5695.313[/tex]To find V(2):
[tex]V(2)=500(1.5)^2=500\times2.25=1125[/tex]So, substituting for the values of V(6) and V(2) in the above formula, we get
[tex]\begin{gathered} \text{Average rate of change over \lbrack{}2,6\rbrack =}\frac{5695.313-1125}{6-2} \\ \\ \text{ = }\frac{4570313}{4}=1142.578\approx1143\text{ visitors per week} \end{gathered}[/tex]Thus, the correct answer is 1143 visitors p
392196 divided by 87(using king division)
Answer: The result of 392,196 divided by 87 is 4,508
Use the linear regression model ^ Y=-13.5x+857.78 to predict the y-value for x=31
We will predict the value for x = 31 as follows:
[tex]y=-13.5(31)+857.78\Rightarrow y=439.28[/tex]So, the predicted y-value for x = 31 is y = 439.28.
I need to know the steps to solve this equation using the quadratic formula.
Given a quadratic equation with the following form
[tex]ax^2+bx+c=0[/tex]By the quadratic formula, the solutions are given by the following expression
[tex]x_{\pm}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]In our problem we have the following equation
[tex]4x^2-7x+3=0[/tex]Therefore, our coefficients are
[tex]\begin{gathered} a=4 \\ b=-7 \\ c=3 \end{gathered}[/tex]Plugging those values into the quadratic formula, we have
[tex]x_{\pm}=\frac{-(-7)\pm\sqrt{(-7)^2-4(4)(3)}}{2(4)}[/tex]Solving this equation, we have
[tex]\begin{gathered} x_{\operatorname{\pm}}=\frac{-(-7)\pm\sqrt{(-7)^2-4(4)(3)}}{2(4)} \\ =\frac{7\pm\sqrt{49-48}}{8} \\ =\frac{7\pm1}{8} \\ \implies\begin{cases}x_+={1} \\ x_-={\frac{3}{4}}=0.75\end{cases} \end{gathered}[/tex]Jerry's Paint Service use 3 gallons ofpaint in 2 hours. At this rate howmany hours will it take them to use 14 gallons of paint?
Jerry's Paint Service uses 3 gallons of
paint in 2 hours. At this rate how
many hours will it take them to use 14 gallons of paint?
Apply proportion
2/3=x/14
solve for x
x=14*2/3
x=9.33 hours or 9 1/3 hours
How to make the proportion
2 ways
First
2 hours/3 gallons=x hours/14 gallons
solve for x
multiply in cross
14*2=3x
x=28/3
second way
3 gallons/2 hours=14 gallons/x hours
solve for x
multiply in cross
3x=14*2
x=28/3
the result is the same both ways
Part CCreate two tables that represent proportional relationships betweentwo quantities. Explain or show proof that the table representsproportional relationships.
Given:
It is required to create a table that represents a proportional relationship between two quantities.
Let the first table: represents the relation between the money saved every month and the number of months
Let the number of months = x, And the total saving = y
Assume we save $2 per month
so, we will have the following table:
April 25 ft long has got into three pieces. it's a first rope is 2x feet long, the second piece is 5X feet long, and the third piece is 4 ft long. A) Write an equation to find X.B) Find the length of the first and second pieces.
Given:
The length of the total rope = 25 ft
It is divided into three pieces
it's the first rope is 2x feet long, the second piece is 5X feet long, and the third piece is 4 ft long.
A) Write an equation for x.
The equation will be:
[tex]2x+5x+4=25[/tex]Which can be simplified to :
[tex]7x+4=25[/tex]so, the equation is 7x + 4 = 25
B) Find the length of the first and the second pieces
First, we will solve the equation to find x
[tex]\begin{gathered} 7x=25-4 \\ 7x=21 \\ \\ x=\frac{21}{7}=3 \end{gathered}[/tex]So, the length of the first piece = 2x = 6 ft
The length of the second piece = 5x = 15 ft
what is the explicit rule of 4, -16, 64, -256
Given sequence is
4, -16, 64, -256
If we have a look closely, we can see a common ratio between the consecutive terms. For example
-16/4 = -4
64/-16 = -4
-256/64 = -4
If there is a common ratio (r) between the consecutive terms of a sequence, it is called a geometric sequence. The explicit rule for such a sequence is:
[tex]a_n=a_1\cdot r^{n-1}[/tex]
Here, r is the common ratio, that is -4 in this case.
a1 is the first term, that is 4.
Now, put the values of a and r in the equation to get the explicit formula
[tex]a_n=4_{}\cdot(-4)^{n-1}[/tex]You can verify the sequence by placing different values of n.
The minimum of a parabola is located at (–1, –3). The point (0, 1) is also on the graph. Which equation can be solved to determine the a value in the function representing the parabola?1 = a(0 + 1)^2 – 31 = a(0 – 1)^2 + 30 = a(1 + 1)^2 – 30 = a(1 – 1)^2 + 3
Given:
The minimum of a parabola is located at (–1, –3).
The general equation of the parabola will be as follows:
[tex]y=a(x-h)^2+k[/tex]Where (h,k) is the vertex of the parabola
given the vertex is the minimum point (-1, -3)
So, h = -1, k = -3
substitute into the general form, so, the equation of the parabola will be:
[tex]y=a(x+1)^2-3[/tex]The point (0, 1) is also on the graph.
So, when x = 0, y = 1
substitute with the given point to determine the value of (a)
So, the equation will be:
[tex]1=a(0+1)^2-3[/tex]So, the answer will be the first option:
1 = a(0 + 1)^2 – 3
A man wishes to invest $3500. He can buy savings bond which pay Simple Interest at the rate of 12% per annum or he can start a savings account which pays Compound Interest at the same rate.
Calculate the difference in the amount of the two investments at the end of 3 years.
F(x) = log10 X
The question is which answer represents the domain of the logarithmic function below?
Answer:hi
Step-by-step explanation:1+1
Find the volume of this cylinder. Use 3 for A.5 ftV = 7r2h=12 ftV V [?]ft
We're going to find the volume of the cylinder using the following equation:
[tex]V=\pi\cdot r^2\cdot h[/tex]Since the radius measures 5 ft, the height measures 12 ft and the problem tells us that we should take pi as 3, we could replace:
[tex]\begin{gathered} V\approx3\cdot(5ft)^2\cdot12ft \\ V\approx3\cdot25ft^2\cdot12ft \\ V\approx900ft^3 \end{gathered}[/tex]Therefore, the volume is approximately 900ft3.
A.) 0, 1, 2, 3, 4B.) 0, 2, 4, 7, 8C.) 1, 2, 3, 4, 5D.) 1, 3, 5, 7, 9
Answer
1, 2, 3, 4, 5
Explanation
Given the following data
a(0) = 0
a(i + 1) = a(i) + 1
Find a(0) to a(5)
Step 1: find a(i) when i = 0
a(0 + 1) = a(0) + 1
Where a(0) = 0
a(1) = 0 + 1
a(1) = 1
Find a(2) when i = 1
a(i + 1) = a(1) + 1
a(1) = 1
a(1 + 1) = 1 + 1
a(2) = 2
find a(3) when i = 2
a(2 + 1) = a(2) + 1
a(3) = 2 + 1
a(3) = 3
Find a(4) when i = 3
a(3 + 1) = a(3) + 1
a(4) = 3 + 1
a(4) = 4
Find a(5) when i= 4
a(4+1) = a(4) + 1
a(5) = 4 + 1
a(5) = 5
Therefore,
a(1) = 1
a(2) = 2
a(3) = 4
a(4) = 4
a(5) = 5
The answer is 1, 2, 3, 4, 5
a1 = -20 ; an = 0.5a n - 1? what are the first five terms
The first five terms are:
-20, -10, -5, -2.5, and -1.25
Explanation:Given that:
[tex]\begin{gathered} a_1=-20 \\ a_n=0.5a_{n-1} \end{gathered}[/tex]For n = 2
[tex]\begin{gathered} a_2=0.5a_1 \\ =0.5\times20 \\ =-10 \end{gathered}[/tex]For n = 3
[tex]\begin{gathered} a_3=0.5a_2 \\ =0.5\times10 \\ =-5 \end{gathered}[/tex]For n = 4
[tex]\begin{gathered} a_4=0.5a_3 \\ =0.5\times5 \\ =-2.5 \end{gathered}[/tex]For n = 5
[tex]\begin{gathered} a_5=0.5a_4 \\ =0.5\times2.5 \\ =-1.25 \end{gathered}[/tex]Therefore, the first five terms are:
-20, -10, -5, -2.5, and -1.25
Solve each system by graphing. Check your solution. (I'll send the photo)
The equations in the system are equal and therefore the graph results in one over the other.
Pablo deposited $600 in an account earning 2% interest compounded annually.To the nearest cent, how much interest will he earn in 3 years?Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
The given information is:
- The initial amount is $600
- The interest rate is 2% (compounded annually)
The given formula is:
[tex]B=p(1+r)^t[/tex]Where B is the balance (final amount), p is the principal (starting amount), r is the interest rate as a decimal, and t is the time in years.
By replacing the known values we obtain the balance after 3 years:
[tex]\begin{gathered} B=600*(1+0.02)^3 \\ B=600(1.02)^3 \\ B=600*1.06 \\ B=636.72 \end{gathered}[/tex]The answer is $636.72
What is the perimeter and the area of the following trapezoid. Round to the nearest whole number if needed
First, we need to find the length of the bottom base.
The next right triangle is formed inside the trapezoid:
From definition:
[tex]\cos (angle)=\frac{\text{adjacent side}}{hypotenuse}[/tex]Substituting with data from the picture:
[tex]\begin{gathered} \cos (60)=\frac{x}{22} \\ \frac{1}{2}\cdot22=x \\ 11=x \end{gathered}[/tex]Since there are two congruent angles, then the opposite sides are also congruent, that is, there are two sides with lengths equal to 22.
Then, the length of the bottom base is 11 + 25 + 11 = 47.
The perimeter of the figure is obtained by adding the length of all its sides. In this case, the perimeter is 47 + 22 + 25 + 22 = 116
The area of a trapezoid is computed as follows:
[tex]A=\frac{a+b}{2}\cdot h[/tex]Where a and b are the bases and h is the height
The height of the shape can be calculated with the help of the previous right triangle, as follows:
[tex]\begin{gathered} \sin (angle)=\frac{\text{opposite side}}{hypotenuse} \\ \sin (60)=\frac{h}{22} \\ \frac{\sqrt[]{3}}{2}\cdot22=h \\ 11\cdot\sqrt[]{3}=h \end{gathered}[/tex]Substituting into area's formula:
[tex]\begin{gathered} A=\frac{25+47}{2}\cdot11\cdot\sqrt[]{3} \\ A=36\cdot11\cdot\sqrt[]{3} \\ A=396\cdot\sqrt[]{3}\approx686 \end{gathered}[/tex]a carpet measures 7 feet long and has a diagonal measurement of (74) square root feet. find the width of the carpet
Let's use Pythagorean Theorem to solve this problem:
[tex]\sqrt[]{74}^2=w^2+7^2[/tex][tex]74=w^2\text{ + 49}[/tex]Solving for w:
[tex]\begin{gathered} w\text{ = }\sqrt[]{74\text{ - 49}} \\ w\text{ = 5} \end{gathered}[/tex]w = 5ft
Find g(1) and find one value of x for which g(x)=-1.
To solve g(1) = ? we must do a vertical line at x = 1, it goes DOWN! because the graph is below the x-axis, if we do the line we will see that it will stop at y = -4, therefore, g(1) = -4
[tex]g(1)=-4[/tex]To find out the value of x for which g(x) = -1 we will start the process by doing a horizontal line at y = -1, if we do it we will see two possible values: -2 and 2, they're both correct! So you can choose which one you will put as your answer.
just need help understanding how to do these step by step explanation please
Solution:
Given the simultaneous equations:
[tex]\begin{gathered} 4x+3y=15\text{ --- equation 1} \\ 5x-2y=13\text{ ---- equation 2} \end{gathered}[/tex]To solve for x and y, using the elimination method, we have
[tex]\begin{gathered} 2\times(4x+3y=15)\Rightarrow8x+6y=30\text{ --- equation 3} \\ 3\times(5x-2y=13)\Rightarrow15x-6y=39\text{ --- equation 4} \end{gathered}[/tex]Add up equations 1 and 2.
thus, this gives
[tex]\begin{gathered} 8x+15x+6y-6y=30+39 \\ \Rightarrow23x=69 \\ divide\text{ both sides by the coefficient of x, which is 23} \\ \frac{23x}{23}=\frac{69}{23} \\ \Rightarrow x=3 \end{gathered}[/tex]To solve for y, substitute the value of 3 for x into equation 1.
thus, from equation 1
[tex]\begin{gathered} 4x+3y=15 \\ when\text{ x = 3,} \\ 4(3)+3y=15 \\ \Rightarrow12+3y=15 \\ add\text{ -12 to both sides,} \\ -12+12+3y=-12+15 \\ 3y=3 \\ divide\text{ both sides by the coefficient of y, which is 3} \\ \frac{3y}{3}=\frac{3}{3} \\ \Rightarrow y=1 \end{gathered}[/tex]Hence, the solution to the equation is
[tex]\begin{gathered} x=3 \\ y=1 \end{gathered}[/tex]In the coordinate plane, three vertices of rectangle PQRS are P(0,0), Q(0,b), S(c,0). What are the coordinates of point R?Answers:A.(c,b)B.(b,c)C.(2b,2c)D.(2c,2b)
B.(b,c)
Explanation
Step 1
let's graph the rectangle
we know that in a rectangle the angles are rigth, so, we have vertical and horizontal lines
the missing point is the intersection of the lines
y=c
and
x=b
so
the answer is
B.(b,c)
I hope this helps you
Solving equations using quadratic formula m² -5m - 14 = 0
Given:
an equation is given as m² -5m - 14 = 0
Find:
we have to solve the given quadratic equation.
Explanation:
Compare the given equation with am² + bm + c = 0, we get
a = 1, b = -5, c = -14
we will solve the given equation as following
[tex]\begin{gathered} ()=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-(-5)\pm\sqrt{(-5)^2-4(1)(-14)}}{2(1)} \\ ()=\frac{5\pm\sqrt{25+56}}{2}=\frac{5\pm\sqrt{81}}{2} \\ ()=\frac{5\pm9}{2} \\ ()=\frac{5+9}{2},\frac{5-9}{2} \\ ()=\frac{14}{2},-\frac{4}{2} \\ ()=7,-2 \end{gathered}[/tex]Therefore, the solution of given equation is m = 7, -2
Answer:
x = 7 ; -2
Step-by-step explanation:
Solving equations using quadratic formula:[tex]\sf \boxed{\bf x = \dfrac{-b \± \sqrt{b^2 - 4ac}}{2a}}[/tex]
m² - 5m - 14 = 0
a = 1 ; b = -5 ; c = -14
b² - 4ac = (-5)² - 4 *(1)*(-14)
= 25 + 56
= 81
[tex]\sf x = \dfrac{-(-5) \± \sqrt{81}}{2*1}\\\\x = \dfrac{5 \± 9}{2}\\\\\\x = \dfrac{5+9}{2} \ ; x =\dfrac{5-9}{2}\\\\\\x = \dfrac{14}{2} \ ; x =\dfrac{-4}{2}\\\\[/tex]
x = 7 or -2
The area of a soccer field is ( 24x^2 + 100x + 100) m^2. The width of the field is (4x + 10)m. What is the length?Please help, need right away.Be sure to show work. NEED HELP BEEN ON THIS PROBLEM FOR 2 DAYS
hello
to solve this question, we have to understand that a soccer field is rectangular in shape and we can find this length from factoring the area
formula of area of a rectangle
[tex]\begin{gathered} A=L\times W \\ A=\text{area} \\ L=\text{length} \\ W=\text{width} \end{gathered}[/tex][tex]\begin{gathered} A=24x^2+100x+100 \\ W=4x+10 \\ L=\text{ ?} \end{gathered}[/tex]we can proceed to solve this by dividing the polynomial or simply checking it from the options
from the options given,
we have option A
3x + 10
let's multiply both the L and W to see if it gives us the answer
[tex](4x+10)\times(3x+10)=12x^2+70x+100_{}[/tex]option A is incorrect
let's test for option B
L= 6x + 10
[tex]\begin{gathered} A=L\times W \\ (6x+10)\times(4x+10)=24x^2+100x+100_{} \end{gathered}[/tex]option B is correct
let's test for option C
L= 6x + 1
[tex]\begin{gathered} A=L\times W \\ (6x+1)\times(4x+10)=24x^2+70x+10 \end{gathered}[/tex]option C is also incorrect and so it'll be for option D
from the calculations above, only option B corresponds with the value of length for the soccer field
Explain how you know that the function represented by the data in the given table is quadratic.XV0-17123-13-313
Given:
Here a table of equation is given
Required:
How to know that the function represented by the data in the given table is quadratic.
Explanation:
here the first differences of y values are as below
[tex]\begin{gathered} -13-(-17)=-13+17=4 \\ -3-(-13)=-3+13=10 \\ 13-(-3)=13+3=16 \\ 35-13=22 \\ 63-35=28 \end{gathered}[/tex]now again take difference of the first difference which is called as second difference.
[tex]\begin{gathered} 10-4=6 \\ 16-10=6 \\ 22-16=6 \\ 28-22=6 \end{gathered}[/tex]so here we can see that the second difference is same which is 6
now if second difference of any table is equal we can say that the given table is the table of quadratic equation.
Final answer:
The second differences are all 6
help me please I want to learn how to solve this
SOLUTION
In this question, we are meant to find the slope of the line represented
by 5x - 12 y = 24.
Re-arranging the equation, we have: 12 y = 5x - 24
Dividing both sides by 12,
[tex]\begin{gathered} y\text{ = }\frac{1}{12}(\text{ 5x -24 )} \\ y\text{ = }\frac{5}{12}x\text{ - 2} \\ \text{CONCUSION: The slope of the line is }\frac{5}{12}\text{ ------OPTION J} \end{gathered}[/tex]Please help me find the equation for the problem and the total amount :(
To find the equation for S to W, we have
[tex]S=350+60W[/tex]Then, for the second question, we need to replace W = 18 in the equation that was found
[tex]\begin{gathered} S=350+60(18) \\ S=1430 \end{gathered}[/tex]Pamela is 15 years younger than Jiri. The sum of their ages is 29 . What is Jiri's age?
To determine the age of jiri:
Let P represent Pamela age
Let J represent Jiri age
p + j = 29 (their ages added together is 29)
p = j - 15 (Pam is 15 years younger (less) than Jiri)
We have a value for Pam, so plug it in:
j -15 + j = 29
2j - 15 = 29
Add 15 to both sides:
2j = 44
Divide by 2:
j = 22
Now find Pamela's age:
p = 22 - 15
p = 7
check:
7 + 22 = 29
29 = 29
Therefore the age of Jiri is 22 years