Answer: We have to find the next solution step for the following equation:
[tex]6x=84[/tex]The solution steps are:
[tex]\begin{gathered} 6x=84 \\ \\ \text{ Divide both sides by 6} \\ \\ \frac{6x}{6}=\frac{84}{6}\Rightarrow x=\frac{84}{6}=14 \\ \\ x=14 \end{gathered}[/tex]A town has a population of 10000 and grows at 2% every year. To the nearest year, how long will it be until the population will reach 12700?
A town has a population of 10000 and grows at 2% every year. To the nearest year, how long will it be until the population will reach 12700
Given the data as
Population = P_0 = 10,000
Growth rate = r = 2%
Let us assume the time would be 12 years, so
Time = t = 12
The formula for calculating the population after given time at given rate is:
[tex]P = P_{0}(1+r)^{t}[/tex]
Inserting the given values in the above formula:
[tex]P = (10,000)(1+0.02)^{12}[/tex]
[tex]= (10,000)(1.02)^{12}[/tex]
[tex]= 10,000+1.268\\\\= 12682[/tex]
Hence the answer is 12 years to be until the population to reach 12700
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Solve algebraicallyX+4=-2
SOLUTION:
Step 1:
In this question, we are given the following:
Solve algebraically
[tex]x\text{ + 4 = -2}[/tex]Step 2:
The details of the solutio are as follows:
[tex]\begin{gathered} x\text{ + 4 = -2} \\ collecting\text{ like terms, we have that:} \\ x\text{ = - 2 - 4} \\ x\text{ = - 6} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]x\text{ = - 6}[/tex]what is the only value of x not in the domain ?
The Solution:
Given:
Required:
Find the domain of the function. What is the value of x that is not in the domain of f(x).
Graphing the function, f(x), we get:
So, the domain of the function is:
[tex](-\infty,-1)\cup(-1,\infty)[/tex]To find the value of x that is not in the domain, we need to find the value of x for which the function is undefined. That is,
[tex]\begin{gathered} 6x+6=0 \\ 6x=-6 \\ \\ x=\frac{-6}{6}=-1 \end{gathered}[/tex]Thus, the value of x not in the domain is:
[tex]x=-1[/tex]
Please see picture. I am looking for help on part b of #5
5.a).
GIven:
Principal P= $ 5000.
Interest rate R = 7 % =0.07.
The number of years T=x.
Consider the following formula to find the amount.
[tex]A=P(1+r)^t[/tex]Substitute A=y P=5000, R=0.07, and T=x in the equation, we get
[tex]y=5000(1+0.07)^x[/tex][tex]y=5000(1.07)^x[/tex]Which is of the form
[tex]y=a(b)^x[/tex]We know that this is the exponential growth function.
Hence the exponential function is
[tex]y=5000(1.07)^x[/tex]b)
Consider the y values from the table.
5,10,15,20,25,30,...
The difference between 5 and 10 = 10-5 =5.
The difference between 10 and 15 = 15-10 =5.
Proceed this way to find the common difference.
The common difference is 5.
The y value is increasing by the common value of 5.
The slope =5 and the y-intercept is 5 from point (0,5).
The equation is
[tex]y=5+5x[/tex]This is a linear equation.
Ms. Tui is having new floors installed in her house. Floor Company A charges $90for installation and $9 per square yard of flooring. Floor Company B charges $50for installation and $13 for each square yard.
We have two cost functions.
Company A charges a fixed value of $90 and a variable cost of $9 per sq yd.
[tex]C_A=90+9x[/tex]Company B chargesa fixed value of $50 and a variable cost of $13 per sq yd.
[tex]C_B=50+13x[/tex]The breakeven point for the square yard of the floor, when both cost are the same, can be calculated as:
[tex]\begin{gathered} C_A=C_B \\ 90+9x=50+13x \\ 90-50=13x-9x \\ 40=4x \\ x=\frac{40}{4} \\ x=10 \end{gathered}[/tex]The breakeven point is x=10 sq yd.
If x>10, company B is more expensive that company A.
What is the 13th term of the geometric sequence with this explicit formula?an-3-(-2)(n-1)
Answer:
C. 12,288
Explanation:
Given the explicit formula of a given geometric sequence:
[tex]a_n=3(-2)^{n-1}[/tex]To find the 13th term, substitute n for 13:
[tex]\begin{gathered} a_{13}=3\times(-2)^{13-1} \\ =3\times(-2)^{12} \\ =3\times4096 \\ =12,288 \end{gathered}[/tex]The 13th term of the geometric sequence is 12,288.
Option C is correct.
Find the semiperimeter of the following triangle: a = 12 ft, b = 16 ft, c = 24 ft
The semi-perimeter of the triangle is 26 feet.
We are given a triangle. The sides of the triangle are represented by the letters a, b, and c. The lengths of the sides a, b, and c are 12 feet, 16 feet, and 24 feet, respectively. We need to find the semi-perimeter of the triangle. We will first find the perimeter of the triangle. The perimeter is the sum of the lengths of all the sides of the triangle. The perimeter is P = a + b + c = 12 + 16 + 24 = 52 feet. The semi-perimeter is half the perimeter of the triangle. The semi-perimeter is S = 52/2 = 26 feet.
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Solve the following system using the elimination method. Enter your answer as an ordered pair in the form (x,y) If there is one unique solution. Enter all if there are infinitely many solutions and enter none if there are no solutions 6x - 5y = 41 2x + 6y = 6
Okay, here we have this:
Considering the provided system, we are going to solve it using the elimination method, so we obtain the following:
[tex]\begin{gathered} \begin{bmatrix}6x-5y=41 \\ 2x+6y=6\end{bmatrix} \\ \begin{bmatrix}6x-5y=41 \\ (-3)2x+6y=6(-3)\end{bmatrix} \\ \begin{bmatrix}6x-5y=41 \\ -6x-18y=-18\end{bmatrix} \end{gathered}[/tex]Now we will add the equations to eliminate the y term:
[tex]\begin{gathered} \begin{bmatrix}-23y=23\end{bmatrix} \\ \begin{bmatrix}y=\frac{23}{-23}\end{bmatrix} \\ \begin{bmatrix}y=-1\end{bmatrix} \end{gathered}[/tex]Finally, let's replace in the first equation to find the value of x:
[tex]\begin{gathered} \begin{bmatrix}6x-5(-1)=41\end{bmatrix} \\ \begin{bmatrix}6x+5=41\end{bmatrix} \\ \begin{bmatrix}6x=36\end{bmatrix} \\ \begin{bmatrix}x=\frac{36}{6}\end{bmatrix} \\ \begin{bmatrix}x=6\end{bmatrix} \end{gathered}[/tex]Finally we obtain that the unique solution for the system is the ordered pair: (6, -1).
Find the length of the Latus Rectum with the following equation: y= x^2 +6
We have the next equation
[tex]y=x^2+6[/tex]First, we need to find the focus of this parabola the vertice is in (0,6)
[tex]4p\mleft(y-k\mright)=\mleft(x-h\mright)^2[/tex]where in our case h =0, k=6
[tex]4\cdot\frac{1}{4}(y-6)=x^2[/tex]Therefore the focus will be
[tex](0,6+\frac{1}{4})=(0,\frac{25}{4})[/tex]Then for Latus Rectum is located between the next points
[tex](-0.5,\frac{25}{4})\text{ and (}0.5,\frac{24}{5}\text{)}[/tex]the latus Rectum
[tex]4p=4(\frac{1}{4})=1[/tex]the length of the latus rectum is 1
Use the given row transformation to transform the following matrix.
The 2 x 2 matrix is given
[tex]\begin{bmatrix}{2} & {8} \\ {10} & {7} \\ {} & {}\end{bmatrix}[/tex]The row transformation given is:
[tex]\frac{1}{2}R_1[/tex]this means we take half of all the elements of Row 1
The process is shown below:
[tex]\begin{gathered} \begin{bmatrix}{\frac{1}{2}\times2} & {\frac{1}{2}\times8} & \\ {10} & {7} & {} \\ {} & {} & {}\end{bmatrix} \\ =\begin{bmatrix}{1} & {4} & \\ {10} & {7} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex]Hence, the final matrix Row 2 is same as previous matrix, but Row 1 is half of the elements of previous matrix.
Answer:
[tex]\begin{bmatrix}{1} & {4} & \\ {10} & {7} & {} \\ {} & {} & {}\end{bmatrix}[/tex]16 ft.8 ftSurface Area =
Lucy's mom started a 529 college fund for her when she was 4 years old inorder to save money for college. She put $9,000 into an account that earnsa 5% compounded annually. Lucy wants to know how much money she willhave when she is 18. Look at her work below.Is her solution correct? If not, describe the mistake(s) in her work.y = 900011+ 9(e)y = 9000 (1.5) 18y = 8133010 26.92
Explanation:
P = $9000
i = 5% 0.05
We nee to apply the formula:
[tex]\begin{gathered} \frac{FV}{(i+i)^n}=\text{ PV} \\ FV\text{ = }PV\text{ }(1+i)^n \\ FV=9000(1+0.05)^{18}\text{ } \end{gathered}[/tex][tex]undefined[/tex]Using f(x) = 3x - 3 and g(x) = -x, find g(f(x)).3x+33-3x-3-3x2x-3I am not sure if my answer is right please help me
Given
[tex]\begin{gathered} f(x)=3x-3 \\ g(x)=-x \end{gathered}[/tex]Then,
[tex]\begin{gathered} g(f(x))=g(3x-3) \\ =-(3x-3) \\ =3-3x \end{gathered}[/tex]Hence, the correct option is (B)
Tickets for the school football game cost $10 for students and $12 for non-students. A total of 150 ticketswere sold and $1440 was collected.Let x = the # of student tickets soldLet y = the # of non-student tickets sold
x = students = $10
y = non students = $12
total tickets = 150
Equations
x + y = 150
10x + 12y = 1440
x = 150 - y
10(150 - y) + 12y = 1440
1500 - 10y + 12y = 1440
2y = 1440 - 1500
2y = -60
y = -60/2
y = 30
x = 150 -
Subtract this question
[tex]{ \frac{5}{3}} [/tex]
Step-by-step explanation:
[tex]{ \purple{ \sf{3 \frac{2}{6} - 1 \frac{2}{3}}}} [/tex]
[tex]{ = \purple{ \sf{ \frac{18 + 2}{6} - \frac{3 + 2}{3}}}} [/tex]
[tex]{ = \purple{ \sf{ \frac{20}{6} - \frac{5}{3}}}} [/tex]
[tex]{ = \purple{ \sf{ \frac{20}{6} \times \frac{1}{1} - \frac{5}{3} \times \frac{2}{2}}}} [/tex]
[tex]{ = \purple{ \sf{ \frac{20}{6} - \frac{10}{6}}}} [/tex]
[tex]{ = \purple{ \sf{ \frac{20 - 10}{6}}}} [/tex]
[tex]{ = \purple{ \sf{ { \frac{ \cancel{10}^{ \green{ \sf{5}}} }{ \cancel{ 6_{ \green{ \sf{3}}} }}}}}}[/tex]
[tex]{ = \purple{ \boxed{ \red{ \sf{ \frac{5}{3}}}}}} [/tex]
The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object and the center of the Earth. If anastronaut weighs 215 pounds on the surface of the Earth, what will this astronaut weigh 2650 miles above the Earth? Assume that the radius of the Earth is 4000miles. Round your answer to one decimal place if necessary
Given:
F is inversely proportional to the square of the distance means that
[tex]F=\frac{k}{d^2}[/tex]So the value of "k" is:
[tex]\begin{gathered} 215=\frac{k}{4000^2} \\ k=215\times(4000)^2 \\ k=3440000000 \end{gathered}[/tex]Weigh in 2650 mile above
[tex]\begin{gathered} F=\frac{k}{d^2} \\ F=\frac{3440000000}{(2650)^2} \\ F=\frac{3440000000}{7022500} \\ F=489.85\text{ pound} \end{gathered}[/tex]5) 5x + 7y + 3 is an example of a O monomial O binomial O trinomial O polynomial
Problem Statement
The question asks us for what the following expression is an example of
[tex]5x+7y+3[/tex]Solution
Monomial:
A monomial is an expression with only one term. For example:
[tex]x^2[/tex]Binomial:
A binomial is an expression with only two terms. For example:
[tex]2+3x[/tex]Trinomial:
A trinomial is an expression with 3 terms. For example:
[tex]5x+7y+3[/tex]Final Answer
Therefore, the answer is Trinomial
If D and R denote the degree and radian measure of an angle, then prove that D/180=R/pie
Given: D and R denote the degree and radian measure of an angle
To Determine: The prove that D/180=R/pie
Solution
Please note that
[tex]180^0=\pi radians[/tex]So
[tex]1^0=\frac{\pi}{180^}radian[/tex]Then
[tex]\begin{gathered} D^0=D\times\frac{\pi}{180}radian \\ D^0=\frac{D\pi}{180}radians \end{gathered}[/tex]Therefore
[tex]\frac{D\pi}{180}=R[/tex]Let us divide both sides by pie
[tex]\frac{D\pi}{180}\div\pi=R\div\pi[/tex][tex]\begin{gathered} \frac{D\pi}{180}\times\frac{1}{\pi}=R\times\frac{1}{\pi} \\ \frac{D}{180}=\frac{R}{\pi} \end{gathered}[/tex]Hence, the above help to prove that D/180 = R/pie
the value of x in the equation below represents the number of siblings i have, solve the equation and tell me how many siblings do i have?3(×+4)=3×+10-2×+23-×
to solve for x, we'll first of all open the bracket and the collect like terms
[tex]3(x\text{ + 4) = 3x + 10 - 2x + 23 - x}[/tex][tex]\begin{gathered} 3x\text{ + 12 = 3x + 10 - 2x + 23 - x} \\ 3x\text{ - 3x + 2x + x = 10 - 12 + 23} \\ 3x\text{ = 21} \\ \end{gathered}[/tex]divide both sides by 3
[tex]\begin{gathered} 3x\text{ = 21} \\ \frac{3x}{3}\text{ = }\frac{21}{3} \\ x\text{ = 7} \end{gathered}[/tex]x = 7
your gonna need a calculator for this I don't have one help please
The correct answer is the option a) because in the table we can note that the values of the weight are strictly increasing, and the only option that meets this condition is the option a).
Calculate the product between 897 and 645
We need to calculate the product:
[tex]undefined[/tex]Answer:
578565
Step-by-step explanation:
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on yourUse the number line to determine which statement is true.RSQP+ +24++61618202214128100The value at point P is greater than the value at point S.The value at point S is less than the value at point Q.The value at point S is greater than the value at point R.The value at point Q is less than the value at point P.
The values on the number line increases as we move towards the right. Looking at the number line,
Point P comes before point S. This means that the value of point P is lesser than that of point S. The first statement is wrong
Point S comes after point Q. This means that the value of point S is greater than that of point Q. The first statement is wrong
Point S comes after point R. This means that the value of point S is greater than that of point R. The first statement is true
Point Q comes after point P. This means that the value of point Q is greater than that of point P. The first statement is false
The perimeter of the rectangle below is units. Find the length of side .Write your answer without variables.
SOLUTION
From the question, the perimeter of the rectangle is 102 units, we want to find XY. Note that side XY = side WV, so XY = 4z.
But we need to find z. To do this we add all the sides and equate it to 102, we have
[tex]\begin{gathered} 2(3z+2)+2(4z)=102 \\ 6z+4+8z=102 \\ 6z+8z+4=102 \\ 14z=102-4 \\ 14z=98 \\ z=\frac{98}{14} \\ z=7 \end{gathered}[/tex]So z is 7, and XY becomes
[tex]\begin{gathered} XY=4z \\ XY=4\times7 \\ =28 \end{gathered}[/tex]Hence the answer is 28
How many ways can 6 different students be arranged in a line?
It is required to find the number of ways 6 different students can be arranged.
Since the students are different and they are required to be arranged in a line, the number of ways is:
[tex]n![/tex]Where n is the number of items.
Hence, for 6 students the number of ways of arranging them on a line is:
[tex]6!=6\cdot5\operatorname{\cdot}4\operatorname{\cdot}3\operatorname{\cdot}2\operatorname{\cdot}1=720\text{ ways}[/tex]The answer is 720 ways.
Answer:720 ways
Step-by-step explanation:
The total number of ways 6 students can be arranged in a line is = n!
= 6!
=720 ways
Write the following parametric equations as a polar equation.x = 2ty=t²
ANSWER:
2nd option: r = 4 tan θ sec θ
STEP-BY-STEP EXPLANATION:
We have the following:
[tex]\begin{gathered} x=2t\rightarrow t=\frac{x}{2} \\ \\ y=t^2 \end{gathered}[/tex]We substitute the first equation in the second and we are left with the following:
[tex]\begin{gathered} y=\left(\frac{x}{2}\right)^2 \\ \\ y=\frac{x^2}{2^2}=\frac{x^2}{4} \end{gathered}[/tex]Now, we convert this to polar coordinates, just like this:
[tex]\begin{gathered} x=r\cos\theta,y=r\sin\theta \\ \\ \text{ We replacing:} \\ \\ r\sin\theta=\frac{(r\cos\theta)^2}{4} \\ \\ r\sin\theta=\frac{r^2\cos^2\theta^{}}{4} \\ \\ r\sin\theta=\frac{r^2\cos\theta\cdot\cos\theta{}}{4} \\ \\ \frac{r^2\cos\theta\cdot\cos\theta}{4}=r\sin\theta \\ \\ r=4\frac{\sin\theta}{\cos\theta}\cdot\frac{1}{\cos\theta} \\ \\ r=4\tan\theta\cdot\sec\theta \end{gathered}[/tex]So the correct answer is the 2nd option: r = 4 tan θ sec θ
The graph of y = x 2 has been translated 7 units to the left. The equation of the resulting parabola is _____.y = (x - 7) 2y = (x + 7) 2y = x 2 - 7y = x 2 + 7
The translation of a function to the left or to the right is a horizontal translation. Horizontal translation can be defined as the movement toward the left or right of the graph of a function by the given units. It should be noted that the shape of the function remains the same. The horizontal translation is also known as the movement/shifting of the graph along the x-axis. For any base function f(x), the horizontal translation by a value k can be given as
[tex]f(x)=f(x\pm k)[/tex]If the function is shifted to the right, the translation function would be
[tex]f(x)=f(x-k)[/tex]If the function is shifted to the left, the translation would be
[tex]f(x)=f(x+k)[/tex]If the graph of y = x² has been translated 7 units to the left. The equation of the resulting parabola would be
[tex]y=(x+7)^2[/tex]Hence the equation of the resulting parabola is (x+7)²
what us the alpha and betta of 3X square - 4x minutes and kisses ever
[tex] \frac{4x}{ {3 \times }^{2}} [/tex]
The values of α and β = 4/〖3x〗^2
A quadratic equation is a second-order polynomial equation in a single variable x
ax2+bx+c=0. with a ≠ 0
Given quadratic equation is 3x2 – 4x = 0
We have to alpha and beta from the given equation
We know that in the quadratic expression
α + β = -b/a. αβ = c/a.
from the equation expression
α + β = 4/〖3x〗^2
αβ = 0/3 ---- (1)
αβ = 0 ----- (2)
If we consider α = 0 from equation (2) then
α + β = 4/〖3x〗^2
β = 4/〖3x〗^2
If we consider β = 0 from equation (2) then
α + β = 4/〖3x〗^2
α = 4/〖3x〗^2
Therefore the values of α = β = 4/〖3x〗^2
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Part A: Colby's experiment follows the model:Part B: Jaquan's experiment follows the model:
Answer:
C
D
The population of bacteria after x days that are growing with a constant factor goes by:
[tex]P(x)=ab^{nx}[/tex]Where:
a = initial population
b = growth factor
n = number of periods in a day
a.) Colby's experiment:
a = 50
b = 2
Since they are doubling every 2 hours:
n = 24/2 = 12
Therefore, Colby's experiment follows:
[tex]y=50\cdot2^{12x}[/tex]b.) Jaquan's experinment:
a = 80
b = 2
Since they double every 3 hours:
n = 24/3 = 8
Therefore, Jaquan's experiment follows the model:
[tex]y=80\cdot2^{8x}[/tex]6. Write the equation of the line below. 1-10 7 6 5 3 2 का 2 3 4 5 6 7 8 9 10
Let the two points in the graph are (0,7) and (1,3).
Then, the slope of the line is,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{3-7}{1-0} \\ m=-4 \end{gathered}[/tex]Use the equation y=y1=m(x-x1) to find the equation of the line.
[tex]\begin{gathered} y-7=-4(x-0)\text{.} \\ y-7=-4x \\ y=-4x+7 \end{gathered}[/tex]Therefore, the equation of the line is y=-4x+7.
Game System C Last month, you sold 21 systems. The total for the last two months is 37. Write and solve an equation to find how many systems you sold this month. Let c = number of systems sold this month Equation: Systems Sold:
You sold 21 systems last month.
The total systems sold in the last two months is 37 (that means this month and last month)
How many systems have you sold this month?
Let c = number of systems sold this month
Then we may write the following equation
[tex]c+21=37[/tex]Where c represents the number of systems sold this month
21 represents the number of systems sold last month
Then the sum of these two months must be equal to 37 (total systems sold in two months)
Now let us solve the equation for c
[tex]\begin{gathered} c+21=37 \\ c=37-21 \\ c=16 \end{gathered}[/tex]Therefore, you have sold 16 systems this month