16, 4, 1....
2^4, 2^2, 2^0
[tex]2^4,2^2,2^0,2^{-2},2^{-4},2^{-6},2^{-8}\ldots[/tex]6th term would be 2^-6:
[tex]2^{-6}[/tex]Series
Explicit rule that describes the rent in ‘n’ years. (Question 5)
Answer::
[tex]f(n)=62000(1.03)^n[/tex]Explanation:
• The first year rent = $62,000
,• The rate of increase, r = 3% = 0.03
Since the rent increases by a common factor each year, we can find the explicit rule by using the formula for the nth term of a geometric sequence.
The nth term of a geometric sequence is calculated using the formula:
[tex]T_n=a_1(r)^{n-1}[/tex]In this case:
• a1 = 62,000
,• r=1+0.03=1.03
Thus, an explicit rule that describes the rent after n years is:
[tex]f(n)=62000(1.03)^n[/tex]
A triangle has sides 25 centimeters, 26 centimeters, and 32 centimeters. What is the perimeter (distance10around the edges) of the triangle in centimeters? Express your answer in mixed number form, and reduce if possible.2355
Given that a triangle has sides of the following dimensions
[tex]25\frac{2}{5}cm,26\frac{9}{10}cm\text{ and 32}\frac{5}{8}cm[/tex]The diagram of the triangle can be seen below
To find the perimeter, P, of a triangle, the formula is
[tex]P=a+b+c_{}[/tex]Where
[tex]\begin{gathered} a=32\frac{5}{8}=\frac{261}{8}cm \\ b=26\frac{9}{10}=\frac{269}{10}cm\text{ and } \\ c=25\frac{2}{5}=\frac{127}{5}cm \end{gathered}[/tex]Substitute the values to find the perimeter, P, of the triangle
[tex]\begin{gathered} P=a+b+c_{} \\ P=\frac{261}{8}+\frac{269}{10}+\frac{127}{5}=\frac{1305+1076+1016}{40}=\frac{3397}{40}=84\frac{37}{40}cm \\ P=84\frac{37}{40}cm \end{gathered}[/tex]Hence, the perimeter, P, of the triangle is
[tex]84\frac{37}{40}cm[/tex]ur4) Find the missing sides of the triangle. Leave your answersas simplified radicals. (2 points)452√645MALOrc
SOLUTION:
Case: Triangles
Method:
First, It is an Isosceles triangle
When the base angles are equal, the opposite sides are equal too
[tex]x=2\sqrt{6}[/tex]Next, find y using Pythgoras theorem
[tex]\begin{gathered} y^2=(2\sqrt{6})^2+(2\sqrt{6})^2 \\ y^2=4\times6+4\times6 \\ y^2=24+24 \\ y^2=48 \\ y=\sqrt{48} \\ y=\sqrt{16\times3} \\ y=4\sqrt{3} \end{gathered}[/tex]Final answer:
[tex]\begin{gathered} x=2\sqrt{6} \\ y=4\sqrt{3} \end{gathered}[/tex]If a line passes through (-4,3) and (6,2) what's the equation if an equation isn't possible say no
First, let's find the slope of the line that passes through the points (-4,3) and (6,2):
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{2-3}{6-(-4)}=\frac{-1}{6+4}=-\frac{1}{10} \end{gathered}[/tex]Now we can use the first point to get the equation of the line:
[tex]\begin{gathered} (x_1,y_1)=(-4,3) \\ y-y_1=m(x-x_1) \\ \Rightarrow y-3=-\frac{1}{10}(x-(-4))=-\frac{1}{10}(x+4)=-\frac{1}{10}x-\frac{4}{10}=-\frac{1}{10}x-\frac{2}{5} \\ \Rightarrow y=-\frac{1}{10}x-\frac{2}{5}+3=-\frac{1}{10}x-\frac{2}{5}+\frac{15}{5}=-\frac{1}{10}x+\frac{13}{5} \\ y=-\frac{1}{10}x+\frac{13}{5} \end{gathered}[/tex]therefore, the equation of the line is y=-1/10x+13/5
In a recent survey of 1,050 people, 42 said that their favorite color of car was red. What percent of the people surveyed liked red cars?
In order to calculate the percentage of surveyed people that liked red cars, we need to divide this amount of people by the total amount of people surveyed.
So we have:
[tex]p=\frac{42}{1050}=0.04=4\text{\%}[/tex]Therefore the percent of the people surveyed that liked red cars is 4%.
Find an equation that fits the graph below; choose one of the following forms
Step 1:
Write the two equations
[tex]y\text{ = }A\sin \lbrack B(x\text{ - C)\rbrack + D and y = Asin\lbrack{}B(x-C)\rbrack + D}[/tex]Step 2:
The amplitude of graph A = 2
The midline of the graph is D = 0
The graph is a sin graph.
y = 2sin[B(x - C)] + 0
y = 2sin[B(x - C)]
Final answer
y = 2sin[B(x - C)] + D
What answer shows two pairs of adjacent angles in the figure?angles 2 and 5; angles 2 and 4angles 1 and 4; angles 2 and 5angles 4 and 5; angles 2 and 4angles 1 and 4; angles 1 and 2
Step 1
Given;
[tex]A\text{ pair of angles in a figure}[/tex]Required; To find which answer shows two pairs of adjacent angles in the figure.
Step 2
Adjacent angles are two angles that have a common side and a common vertex (corner point) but do not overlap in any way.
Therefore, the pair of adjacent angles is;
[tex]\text{Angles 4 and 5; Angles 2 and 4}[/tex]Hence, the answer is: angles 4 and 5; angles 2 and 4
NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 10z
Answer:
(-2, 13)(1, 10)=====================
Given systemy = x² + 9 x + y = 11Substitute the value of y into second equationx + x² + 9 = 11x² + x - 2 = 0x² +2x - x - 2 = 0x(x + 2) - (x + 2) = 0(x + 2)(x - 1) = 0x + 2 = 0 and x - 1 = 0x = - 2 and x = 1 Find the value of yx = -2 ⇒ y = 11 - (-2) = 13x = 1 ⇒ y = 11 - 1 = 10Answer:
[tex](x,y)=\left(\; \boxed{-2,13} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{1,10} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}\phantom{bbbb}y=x^2+9\\x+y=11\end{cases}[/tex]
To solve by the method of substitution, rearrange the second equation to make y the subject:
[tex]\implies y=11-x[/tex]
Substitute the found expression for y into the first equation and rearrange so that the equation equals zero:
[tex]\begin{aligned}y=11-x \implies 11-x&=x^2+9\\x^2+9&=11-x\\x^2+9+x&=11\\x^2+x-2&=0\end{aligned}[/tex]
Factor the quadratic:
[tex]\begin{aligned}x^2+x-2&=0\\x^2+2x-x-2&=0\\x(x+2)-1(x+2)&=0\\(x-1)(x+2)&=0\end{aligned}[/tex]
Apply the zero-product property and solve for x:
[tex]\implies x-1=0 \implies x=1[/tex]
[tex]\implies x+2=0 \implies x=-2[/tex]
Substitute the found values of x into the second equation and solve for y:
[tex]\begin{aligned}x=1 \implies 1+y&=11\\y&=11-1\\y&=10\end{aligned}[/tex]
[tex]\begin{aligned}x=-2 \implies -2+y&=11\\y&=11+2\\y&=13\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y)=\left(\; \boxed{-2,13} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{1,10} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Calculate the tangential speed of a disk with a radius of 15 meters, which completes one revolution every 7 seconds.
The tangential speed of a disk is 94.23.
Given:
radius (r) = 15meters
time t = 7 sec
tangential speed = 2[tex]\pi[/tex]r/t
= 2x 3.141x 15/7
= 94.23
What is tangential speed?Tangential speed is the linear component of its velocity as it moves in a circle. If an object moves along a circular path at a distance r from the centre of the circle, the velocity of the object is tangent to the circle at some point.
In mathematics, a tangent is a line that touches a curve at one point. A quantity is tangent to another if it touches the other quantity once and then moves in the other direction.
Therefore, the tangential speed is a measure of the speed at any point where the tangent curves in this circular motion. Tangential velocity is useful for circular motion because it allows angular motion to be transformed into linear motion.
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So the box in the photo is an 8th graders girls locker and the question says to find the surface area of the locker.
Solution
We are given that
Length (l) = 4ft
Width (w) = 2ft
Height (h) = 3ft
Note: Formula for Surface Area of the Locker
[tex]Surface\text{ }Area=2(lw+lh+wh)[/tex]Substituting the parameters
[tex]\begin{gathered} Surface\text{ A}rea=2(lw+lh+wh) \\ Surface\text{ A}rea=2((4\times2)+(4\times3)+(2\times3)) \\ Surface\text{ A}rea=2(8+12+6) \\ Surface\text{ A}rea=2(26) \\ Surface\text{ }Area=2\times26 \\ Surface\text{ A}rea=52ft^2 \end{gathered}[/tex]Therefore, the surface area is
[tex]52ft^2[/tex]Plot -5½ and 8½ on the number line below.
1) Let's plot those values on a number line. Since -5 1/2 and 8 1/2 can be written as -5.5 and 8.5
2) There we have:
Simplify the absolute value -17
Answer
The answer is 17.
Explanation
The absolute value of any number is taking the positive part of any number. For example, the absolute value of -2 = | -2 | = 2, the absolute value of -99 = | -99 | = 99.
So, the absolute value of -17 = | -17 | = 17.
Hope this Helps!!!
If a rotation angle is 540 degrees how is it possible that the location is Quadrant 1 with a reference angle of 0?
Since a whole revolution has 360º, when we have an angle bigger than 360º the angles start to repeat.
We can subtract 360º to the given angle to find the coterminal angle. In this case:
[tex]540º-360º=180º[/tex]And from an reference angle of 0º, this is exactly a half revolution. Thus, the angle is in the x axis, and it's coterminal angle is 180º
Solve: 5(x + 3) = 2x -3
we need to isolate x
first solve the parenthesis
[tex]5x+15=2x-3[/tex]now solve x
[tex]\begin{gathered} 5x-2x=-3-15 \\ 3x=-18 \\ x=-\frac{18}{3} \\ x=-6 \end{gathered}[/tex]the value of x is -6
Look at the system of equations below y = -3x + 2 y = 2x - 3 Which of the graphs above represents this system of equations?
We have the following:
We must calculate the solution since that is the point of intersection.
[tex]\begin{gathered} y=-3x+2 \\ y=2x-3 \end{gathered}[/tex]we equalize the equations and we have:
[tex]\begin{gathered} -3x+2=2x-3 \\ 3x+2x=3+2 \\ 5x=5 \\ x=\frac{5}{5} \\ x=1 \end{gathered}[/tex]for y:
[tex]y=2\cdot1-3=-1[/tex]The point is (1, -1)
Therefore, the answer is the graph A.
Which choice shows the correct solution to 2247 - 7? 35 R2 OA : 21 -35 B. اب اسے SUS
the given expression is,
[tex]\frac{2247}{7}=321[/tex]so the correct answer is option B
the quotient is 321
How to convert 9.4 degrees into feet and inches
The value of 9.4 degrees in feet is 0.1884 feet and in inches is 2.26 inches.
To calculate feet from degrees, divide the angle by 360, multiply by 2 times pi, then finally, multiply by the radius.
And feet to inches we know 1 foot equals 12 inches.
Converting degrees to feet is commonly discussed while looking at a circle and converting an angle to the length of the arc of that angle. When discussing latitude and longitude, that circle is frequently the earth.
The following formula is used to convert an angle in degrees to length in feet.
L = (a/360) * 2 * pi * r
Where,
L is the length in the feet.
a is the angle in degrees.
r is the radius of the circle in feet.
We are given 9.4 degrees.
Let r = 1 feet
Put the given values in the above formula, we will get;
L = (9.4/360) * 2 * pi * 1
L = 0.03 * 2 * 3.14 * 1
L = 0.1884 feet
L = 0.1884 * 12 = 2.26 inches.
Thus, the value of 9.4 degrees in feet is 0.1884 feet and in inches is 2.26 inches.
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Danielle plans to open a savings account with $2000. The bank offers 8% interest,compounded yearly. Which of the following functions can be used to find the projectedvalue of the account after t years?A.V (t) = 2,000 (1.08t)B. V (t) = 2,000 (1.8)^tC.V (t) = 2,000 (1.08)^tD. V (t) = 2,000 (1.008)^t
the formula for the compound interest is given as follows,
[tex]A=P(1+\frac{R}{100})^t[/tex]here P = 2000 , R = 8 % , t = t.
so the value(V) is
[tex]\begin{gathered} V=2000(1+\frac{8}{100})^t \\ V=2000(1+0.08)^t \end{gathered}[/tex][tex]V=2000(1.08)^t[/tex]so the answer is option C
what are the following transformations: f(-x)-4a. reflection over the y-axis and 4 units down b. reflection over the x axis and 4 units down c. reflection over the x axis and 4 units right d. reflection over the y-axis and 4 units right
a. reflection over the y-axis and 4 units down
Explanations:Note:
If f(x) is reflected over the x-axis, it becomes -f(x) because the y coordinate is negated.
If f(x) is reflected over the y-axis, it becomes f(-x) because the x coordinate is negated.
Therefore, for f(-x)-4, f(x) is reflected over the y-axis, and then translated 4 units down
If f(x) = 3tan2x, find f'(pi/2)
Given the function f(x) defined as:
[tex]f(x)=3\tan(2x)[/tex]We need to find the derivative first. Using the chain rule, we know that:
[tex](\tan u)^{\prime}=u^{\prime}\cdot\sec²u[/tex]Then, taking the derivative if u = 2x:
[tex]\begin{gathered} f^{\prime}(x)=3(2)\sec²(2x) \\ \\ \Rightarrow f^{\prime}(x)=6\sec²(2x) \end{gathered}[/tex]Using this result, we can evaluate the derivative at x = π/2:
[tex]\begin{gathered} f^{\prime}(\frac{\pi}{2})=6\sec²(2\cdot\frac{\pi}{2})=6\sec²(\pi)=6\cdot(-1)² \\ \\ \therefore f^{\prime}(\frac{\pi}{2})=6 \end{gathered}[/tex]I do not understand how to tell which one should be for which multiplicity
Given
[tex]f(x)=8x^2(x-9)(x+5)^2[/tex]To find the zeros of multiplicity one, multiplicity 2, multiplicity 3.
Now,
The zeros of multiplicity 1 are,
[tex]\begin{gathered} x-9=0 \\ x=9 \end{gathered}[/tex]The zeros of multiplicity 2 are,
[tex]\begin{gathered} x=0 \\ x+5=0 \\ x=-5 \end{gathered}[/tex]There are no zeros of multiplicity three since the polynomial has no factor to the power 3.
Which equation represents a line which is parallel to the line 3y - 2x = -24?Submit AnswerOy= -x - 7Oy= - žx – 2Oy= {x +3Oy= x +4
ANSWER
[tex]y=\frac{2}{3}x+3[/tex]EXPLANATION
Parallel lines have the same slope. First we should rewrite the given line in the slope-intercept form by clearing y, so that we can see what is the slope:
[tex]\begin{gathered} 3y-2x=-24 \\ 3y=2x-24 \\ y=\frac{2}{3}x-8 \end{gathered}[/tex]The slope of the line is 2/3, so the slope of the parallel line must be 2/3 too. From this options, the equation with a slope of 2/3 is:
[tex]y=\frac{2}{3}x+3[/tex]Point Yof AwXY is (7.-8). What is the image of Vafler AWXY using the transformation (x+3y - 4)? A (21.-24) B (21,32) c (10.-12) D (10,-4)
The vertex Y is triangle WXY is (7, -8)
The triangle will translate by the rule (x + 3, y - 4)
That means it will be moved right 3 units and down 4 units
So we will add the x-coordinate of point Y by 3 and subtract its y-coordinate by 4 to get its image Y'
The image of point Y is
Y' = (7 + 3, -8 - 4)
Y' = (10, -12)
The correct answer is C
The graph of the absolute value parent function, (x) = 1X1, is stretchedhorizontally by a factor of 5 to create the graph of g(x). What function is g(x)?A. g(x) = 1514B. g(x) = 51Mc. 9(20) = 13aD. 9(x) = 12 + 51SUBMIT
we get that the answer is
[tex]g(x)=|\frac{x}{5}|=|\frac{1}{5}x|[/tex]A scientist was in a submarine below sea level, studying ocean life. Over the next ten minutes, she descended 21.4 feet. How many feet had she been below sea level, if she was 90.6 feet below sea level after she descended?
Step 1:
Let the height below sea level before she descends = h feet
The length she descended after 10 minutes = 21.4 feet
The height of the submarine after descended below the sea level = 90.6 feet
Step 2:
Height of the submarine before descended below the sea level
x = 90.6 - 21.4
x = 69.2 feet
Final answer
69.2 feet
use the numbers shown to complete the table for each value of m. Numbers may be used once, more than once, or not at all. will send image
Part 1
we have
2(3m+7)
For m=1 ------> 2(3(1)+7)=2(10)=20
For m=2-----> 2(3(2)+7)=2(13)=26
we have
6m+14
For m=1 -----> 6(1)+14=20
For m=2----> 6(2)+14=26
Remember that
2(3m+7) is the same that 6m+14
what is the value of u for the equation -4+2u=6
We are given the following equation:
[tex]-4+2u=6[/tex]Where are asked to find the value of "u". To do that we need first to solve for "u", first by adding 4 on both sides:
[tex]\begin{gathered} -4+4+2u=6+4 \\ 2u=10 \end{gathered}[/tex]Now, we will divide by 2 on both sides:
[tex]\begin{gathered} \frac{2u}{2}=\frac{10}{2} \\ u=5 \end{gathered}[/tex]Therefore, the value of "u" is 5
Jessica had eighty dollars to spend on eight books. After buying them she had sixteen dollars. How much did each book cost? Please show work
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: $81. Which of the following is not a radical expression that is equivalent to √1087A.B.C.D.√2-√54√3-√36√5-√21√6-√18
The radical expression √108 is not equivalent to the expression √5√21 .
Given the radical expression as √108 .
Now the number 108 can be broken down into factors as
108 = 54 × 2 , 36 × 3 , 18×6
therefore we can see that the radical expression is equivalent to
√108 = √54 × √2
√108 = √36 × √3
√108 = √18 × √6
But 21 × 5 = 105 ≠ 108.
Therefore the radical expression √108 is not equivalent to √5√21 .
Expressions in mathematics are statements with variables, numbers, or both, and at least two terms joined by an operator. Mathematical operations include addition, subtraction, multiplication, and division.
In mathematics, there are two types of expressions: numerical expressions, which only contain numbers, and algebraic expressions, which also contain variables.
A symbol with an unknown value is called a variable. A term can be made up of a single constant, a single variable, or a group of variables and constants multiplied or divided. A number that has been further multiplied by a variable serves as the coefficient in an equation.
Disclaimer: The complete question is :
Which of the following is not a radical expression that is equivalent to √108?
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A garden has 9 rows of tomato plants each row had 8 each row. How many tomato plants are there ?
Answer:
Nine rows X 8 in the row= 72
Step-by-step explanation:
Answer: For this question you would just multiply 8 and 9 and get 72.
Step-by-step explanation:
Because there are 9 rows of tomato plants and each row has 8 tomatos, you would be doing 9x8 and get your answer of 72. Hope this makes sense!