How much did she spend?
She had 80 dollars, and after buying them she had 16 dollars. Then she spent
80 - 16 = 64
she spent $64 on 8 books.
How much did each book cost?
Since 8 books cost $64, each one should cost:
64 ÷ 8 = 8
each one cost $8.
Answer: $8Write 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 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]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]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
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
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).
Express 4√90 in simplest radical form.
ANSWER
[tex]\text{12}\sqrt[]{10}[/tex]EXPLANATION
We want to find the simplest radical form of 4√90.
To do this, we have to reduce the number in the square root in factor form and then reduce it with the square root.
We have:
[tex]\begin{gathered} 4\sqrt[]{90} \\ \Rightarrow\text{ 4 }\cdot\text{ }\sqrt[]{\text{9 }\cdot\text{ 10}}\text{ = 4 }\cdot\text{ }\sqrt[]{3\cdot\text{ 3 }\cdot\text{ 10}} \\ \Rightarrow\text{ 4 }\cdot\text{ 3 }\cdot\text{ }\sqrt[]{10} \\ \Rightarrow\text{ 12}\sqrt[]{10} \end{gathered}[/tex]That is the simplest radical form.
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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*Will mark brainiest* Rectangle ABCD is rotated 90° clockwise about the origin to produce Rectangle A'B'CD' What is the length, in units of line segment CD'?
When the given rectangle is rotated 90° around origin point, you obtain the same rectangle, but instead of a horizonatl rectangle as before, you get a vertical rectangle with height CD' and width A'D'.
The length of the segment CD' is 6 units
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
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
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]
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.
what are the coordinates of the vertex for x^2+ 5x - 24 = 0
Solution:
We are required to find the coordinates of the vertex for x^2+ 5x - 24 = 0
[tex]The\text{ x-coordinate of the vertex is x=}\frac{-b}{2a}[/tex][tex]\begin{gathered} For\text{ x}^2+5x-24=0 \\ a=1 \\ b=5 \\ x=-\frac{5}{2(1)} \\ x=-\frac{5}{2} \\ x=-2.5 \end{gathered}[/tex]To get the y coordinate, substitute x = -5/2 into the equation
[tex]\begin{gathered} \begin{equation*} \text{x}^2+5x-24=0 \end{equation*} \\ =(\frac{-5}{2})^2+5(\frac{-5}{2})-24 \\ \\ =\frac{25}{4}-\frac{25}{2}-\frac{24}{1} \\ =\frac{25-50-96}{4} \\ \\ =\frac{-121}{4} \\ \\ =-30.25 \end{gathered}[/tex]Hence, the coordinate of the vertex is (-2.5, -30.25)
Calculate the product between 897 and 645
We need to calculate the product:
[tex]undefined[/tex]Answer:
578565
Step-by-step explanation:
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
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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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).
A physical education teacher divides the class into teams of 5 to play floor hockey. There are atotal of 4 teams. How many students, s, are in the class? Solve the equation 8 + 5 = 4 to find thenumber of students.
we know that
the number of students (s) is equal to the number of teams, multiplied by the number of students in each team
so
s=4*5
s=20
answer is 20 students
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
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 -
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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estimate the product by rounding to the nearest 10: 28×56×76
EXPLANATION
Given the operation:
28------> rounded to 30
56-------> rounded to 50
76 ------> rounded to 80
Now, we can mentally calculate that:
3x5= 15 so 30x50 = 1500 (two zeros)
15x8 = 120 so,
1500x80 = 120,000
The answer is 144,000.
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)
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
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]
Priya rewrites the expression 8 − 24 as 8( − 3). Han rewrites 8 − 24 as2(4 − 12). Are Priya's and Han's expressions each equivalent to 8 − 24? Explain your reasoning.
The given expression is
[tex]8y-24[/tex]Priya rewrite the expression as
[tex]8(y-3)[/tex]Expanding priya's expression gives
[tex]\begin{gathered} 8(y-3)=8\times y-8\times3 \\ 8(y-3)=8y-24 \end{gathered}[/tex]Hence Priya's expression is equivalent to 8y - 24
Han's rewrite the expression as
[tex]2(4y-12)[/tex]Expanding Han's expression gives
[tex]\begin{gathered} 2(4y-12)=2\times4y-2\times12 \\ 2(4y-12)=8y-24 \end{gathered}[/tex]Hence, Han's expression is equivalent to 8y - 24
You went to the mall to buy a sweater that was 30% off and you had an additional 20% off coupon. The cashier took the 20% off first and then the 30% off of the reduced amount second. The manager said "No, you are supposed to take the 30% off first and then the 20% off the reduced amount second. Would it matter which way this was done? Why or why not?
Explanation
let's check every case,
Step 1
A)The cashier took the 20% off first and then the 30% off of the reduced amount second.
let x represents the original price
to find the 20% we can use
[tex]\begin{gathered} new\text{ price = original price *\lparen}\frac{100-discount}{100}) \\ so \\ new\text{ price= x*\lparen}\frac{100-20}{100}=x*(\frac{80}{100})=0.8x \\ new\text{ price =}0.8c \end{gathered}[/tex]then,the 30 % of the reduced amount, so
[tex]\begin{gathered} final\text{ price = original price *\lparen}\frac{100-discount}{100}) \\ so \\ final\text{ price= \lparen0.8x\rparen *\lparen}\frac{100-30}{100}=(0.8x)*(\frac{70}{100})=(0.8x)(0.7)=0.56x \\ final\text{ price =0.56x} \end{gathered}[/tex]Step 2
B)The manager said "No, you are supposed to take the 30% off first and then the 20% off the reduced amount second
so
i) 30 of the first
[tex]\begin{gathered} new\text{ price = original price *\lparen}\frac{100-discount}{100}) \\ so \\ new\text{ price= x*\lparen}\frac{100-30}{100})=x*(\frac{70}{100})=0.7x \\ new\text{ price =}0.7c \end{gathered}[/tex]then, 20 % off the reduced amount
[tex]\begin{gathered} final\text{ price = original price *\lparen}\frac{100-discount}{100}) \\ so \\ final\text{ price= \lparen0.7x\rparen *\lparen}\frac{100-20}{100}=(0.7x)*(\frac{80}{100})=(0.7x)(0.8)=0.56x \\ final\text{ price =0.56x} \end{gathered}[/tex]Step 3
so, we can conclude in both cases the final price will be the same, becuase we have a triple product
[tex]\begin{gathered} x*0.8*0.7=x*0.7*0.8 \\ 0.56x=0.56x \end{gathered}[/tex]so, the answer is
it does not matter which way the calculation is done, because the order does not affect the product
I hope this helps you
Consider this prism. Enter the volume of the rectangular prism, in cubic centimeters. 3 3/4, 3 1/3, 2 1/2.
Solution
For this case we have the following dimensions:
x = 3 3/4 = 15/4
y= 3 1/3 = 10/3
z= 2 1/2 = 5/2
Then we can find the volume with the following formula:
[tex]V=x\cdot y\cdot z=\frac{15}{4}\cdot\frac{10}{3}\cdot\frac{5}{2}=\frac{125}{4}ft^3[/tex]Then we can convert to cm^3 like this:
[tex]\frac{125}{4}ft^3\cdot\frac{(30.48\operatorname{cm})^3}{1ft^3}=884901.46\operatorname{cm}^3[/tex]16 ft.8 ftSurface Area =