Step 1:
In order to determine the number of cubbies high, we just need to divide the total height x² - 2x - 3 by the height of one cubby x + 3:
x² divided by x: x
x multiplied by (x + 3): x² + 3x
x² - 2x - 3 minus x² + 3x: -5x - 3
-5x divided by x: -5
-5 multiplied by (x + 3): -5x - 15
-5x - 3 minus -5x - 15: 12
The division doesn't have remainder 0, so let's write the division as a fraction:
[tex]\text{number of cubbies}=\frac{x^2-2x-3}{x+3}[/tex]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
fing the length of the missing side
The area is given as
[tex]x^2-6x+9[/tex]We can either divide the area by the side given and get the other side
OR
We can simply factorize the area and hence determine the two factors that were multiplied together. Note that one factor has already been given (that is x-3).
To factorize the polynomial;
[tex]\begin{gathered} x^2-6x+9 \\ =(x-3)(x-3) \end{gathered}[/tex]This means the other side is also (x - 3)
Length of carrier A is about how many football fields ?
Given:
The total length of carriers A and B, T=4198 feet.
The difference in lengths of the carriers is, D=10 feet.
The length of football field, L=100 yards.
Let a be the length of carrier A and b be the length of carrier B. It is given that carrier A is longer than carrier B.
Hence, the expression for the difference in lengths of the carriers can be written as,
[tex]\begin{gathered} D=a-b \\ 10\text{ =a-b ----(1)} \end{gathered}[/tex]The total length of carriers A and B can be written as,
[tex]\begin{gathered} T=a+b \\ 4198=a+b\text{ ----(2)} \end{gathered}[/tex]Add equations (1) and (2) to find the value of a.
[tex]\begin{gathered} 2a=10+4198 \\ 2a=4208 \\ a=\frac{4208}{2} \\ a=2104\text{ f}eet \end{gathered}[/tex]We know, 1 yard=3 feet.
So, 1 feet=(1/3) yard
The length of carrier A in yards is,
[tex]a=2104\text{ f}eet\times\frac{\frac{1}{3}\text{yard}}{\text{ 1 fe}et}=\frac{2104}{3}\text{yards}[/tex]We know, the length of a football field is l=100 yards
Now, the ratio between a and l can be found as
[tex]\frac{a}{l}=\frac{\frac{2104}{3}\text{ yards}}{100\text{ yards}}\cong7.0[/tex]Hence, we can write
[tex]a=7.0\times l[/tex]Since l is the length of a football field, the length of carrier A is about 7.0 football fields.
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:
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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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
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.
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]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
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.
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]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]How can you represent Pattered from every day life by using tables,expressions and graphs
For example, we can look at the variations of temperature by the time of the day.
We can write it in a two column table, where we can write the hour in one column and the temperature in the other column.
This will show us a relationship between them that is oscillating.
We can graph this and have something like:
Then, we can adjust a function to that, like a trigonometrical function that can model this relation between temperature and hour of the day. There you wil have an expression for this pattern.
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.
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
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)
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
108010 -8 -62IC-Find the slope of the line.Slope = m =Enter your answer as an integer or as a reduced fraction in the form A/B.Question Help: Video Message
The slope formula is givenb by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]To get the slope from the graph, we will pick out two points lying on the line:
Point 1: (x, y) = (-6, 10)
Point 2: (x, y) = (0, -8)
We will then proceed to use these points to calculate the slope, we have:
[tex]\begin{gathered} m=\frac{-8-10}{0--6}=-\frac{18}{6} \\ m=-3 \end{gathered}[/tex]The slope (m) = -3
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
please help me with this pleasethe direction is write the equations in slope interception form
In this case, we'll have to carry out several steps to find the solution.
Step 01:
7.
Data
point 1 ( -4 , -2) x1 = -4 y1 = -2
point 2 ( 3 , 3 ) x2 = 3 y2 = 3
Step 02:
Slope formula
m = (y2 - y1) / (x2 - x1)
[tex]m\text{ = }\frac{(3-(-2))}{(3-(-4))}=\text{ }\frac{3+2}{3+4}=\frac{5}{7}[/tex]Slope-intercept form of the line
y = mx + b
intercept (0 , 1 )
b = 1
m = 5 / 7
y = 5/7 x + 1
The answer is:
y = 5/7 x + 1
How much interest in dollars is earned in 5 years on $8,200 deposited in an account paying 6% interest compounded semiannually round to the nearest cent
Using compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
A = Amount
P = Principal = 8200
r = Interest rate = 6% = 0.06
n = Number of times interest is compounded per year = 2
t = time = 5
so:
[tex]\begin{gathered} A=8200(1+\frac{0.06}{2})^{2\cdot5} \\ A=11020.11 \end{gathered}[/tex]Therefore, the interest is the amount minus the amount invested:
[tex]\begin{gathered} I=A-P \\ I=11020.11-8200 \\ I=2820.11 \end{gathered}[/tex]Answer:
$2820.11
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]The function f(x)=2,500(1.012)^x represents the amount, in dollars, in a savings account after x years. Which statement is true? A. The account earns 0.12% interest per year. B. The account earns 0.012% interest per year. C. The initial amount in the account was $2.500. D. The amount in the account increases by $2,500 each year,
Answer:
C. The initial amount in the account was $2,500.
Explanation:
The function that represents the amount, in dollars, in a savings account after x years is given as:
[tex]f\mleft(x\mright)=2,500\mleft(1.012\mright)^x[/tex]When x=0 (Initially)
[tex]\begin{gathered} f\mleft(0\mright)=2,500\mleft(1.012\mright)^0 \\ =2,500\times1 \\ =\$2,500 \end{gathered}[/tex]Therefore, the initial amount in the account was $2,500.
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.
392196 divided by 87(using king division)
Answer: The result of 392,196 divided by 87 is 4,508
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
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
Which of the following is irrational?A.24.3B./2D. /25C.7
a) 24.3 is a rational number
[tex]\frac{243}{10}[/tex]b)
[tex]\begin{gathered} \sqrt{2}=1.41421 \\ \sqrt{2}\text{ is irrational} \end{gathered}[/tex]c) 7 is a rational number
d)
[tex]\begin{gathered} \sqrt{25}=5 \\ \sqrt[]{25}\text{ is rational} \end{gathered}[/tex]Answer: Letter B
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
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