If $4,500 is invested at an interest rate of 5.25% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)
(a) 4 years
(b) 8 years
(c) 12 years
a) The value of the investment after 4 years is $5,544.90.
b) The value of the investment after 8 years is $6,849.42.
c) The value of the investment after 12 years is $8,453.35.
The formula for calculating the value of an investment that is compounded continuously is given by:
A = [tex]Pe^{(rt)[/tex]
where A is the final value of the investment, P is the initial investment amount, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate expressed as a decimal, and t is the time period in years.
(a) To find the value of the investment after 4 years, we can substitute the given values in the formula as follows:
A = 4500[tex]e^{(0.05254)[/tex]
A = 4500[tex]e^{0.21[/tex]
A = 45001.2322
A = $5,544.90
(b) To find the value of the investment after 8 years, we can substitute the given values in the formula as follows:
A = 4500[tex]e^{(0.05258)[/tex]
A = 4500[tex]e^{0.42[/tex]
A = 45001.5221
A = $6,849.42
(c) To find the value of the investment after 12 years, we can substitute the given values in the formula as follows:
A = 4500[tex]e^{(0.052512)[/tex]
A = 4500[tex]e^{0.63[/tex]
A = 45001.8785
A = $8,453.35
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9. Economists in the country of Flatland, a closed economy, have collected the following information about their economy for a particular year: Y=15,000; C=9,000; T=3,000; G=3,600. The economists also estimate that the investment function is I=3,900-100r, where r is the country’s real interest rate, expressed as a percentage.
Calculate private saving, public saving, national saving, investment, and the equilibrium real interest rate. Does the government of Flatland have a budget surplus or budget deficit?
Answer:
Private saving (Sprivate) is equal to disposable income minus consumption:
Sprivate = Y - T - C = 15,000 - 3,000 - 9,000 = 3,000
Public saving (Spublic) is equal to government revenue minus government spending:
Spublic = T - G = 3,000 - 3,600 = -600
National saving (S) is equal to the sum of private and public saving:
S = Sprivate + Spublic = 3,000 - 600 = 2,400
Investment (I) is given by the investment function:
I = 3,900 - 100r
Equating investment to national saving gives:
I = S
3,900 - 100r = 2,400
Solving for r:
r = 15%
Therefore, the equilibrium real interest rate is 15%.
Substituting r = 15% into the investment function gives:
I = 2,400
Therefore, investment is 2,400.
Finally, to determine if the government has a budget surplus or deficit, we need to calculate the government's budget balance, which is equal to government revenue minus government spending:
Budget balance = T - G = 3,000 - 3,600 = -600
Since the budget balance is negative, the government of Flatland has a budget deficit.
50 Points! Multiple choice Algebra question. State the number of real zeros for the function whose graph is shown. Photo attached. Thank you!
The number of real zeros for the function whose graph is shown include the following: D. 0.
What is a polynomial function?In Mathematics and Geometry, a polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.
This ultimately implies that, a polynomial graph touches the x-axis at real zeros, roots, solutions, x-intercepts, and factors with even multiplicities.
In this context, we can reasonably and logically deduce that the real zeros of a polynomial function are all of the values (x-intercepts) on the x-coordinate that makes this polynomial function equal to zero and it is non-existent on the graph above.
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Assistance needed pls and thanks
By using the parallelogram method, the addition of the vectors [tex]\vec a + \vec b[/tex] is (3, 1).
How to add vectors by using the head to tail method or parallelogram method?In Mathematics, a vector typically comprises two (2) points. First, is the starting point which is commonly referred to as the "tail" and the second (ending) point that is commonly referred to the "head."
Furthermore, the head to tail method of adding two (2) vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).
By adding the given vectors algebraically, we have the following:
[tex]\vec a + \vec b[/tex] = (2, -3) + (1, 4)
[tex]\vec a + \vec b[/tex] = [(2 + 1), (-3 + 4)
[tex]\vec a + \vec b[/tex] = (3, 1).
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A projectile is fired upward from a height of 160 feet above the ground, with an initial velocity of 600ft/sec. Recall that projectiles are modeled by the function h(t)=−16t2+v0t+y0. How long will the projectile be in flight? Round your answer to the nearest hundredth.
Answer:
t ≈ 37.76 seconds (rounded to the nearest hundredth)
Step-by-step explanation:
To solve the problem, we can use the equation for the height of a projectile at time t: h(t) = - 16 * t^2 + v0 * t + y0
where v0 is the initial velocity and y0 is the initial height.
In this case, we have: v0 = 600 ft/sec (upward)
y0 = 160 ft (above the ground)
We want to find the time at which the projectile hits the ground, which is when h(t) = 0.
So we can set up the equation: 0 = -16 * t^2 + 600 * t + 160
We can solve for t using the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -16, b = 600, and c = 160.
Plugging in the values, we get:
t = (-600 ± sqrt(600^2 - 4(-16)(160))) / 2(-16)
t = (-600 ± sqrt(360000 + 10240)) / (-32)
t = (-600 ± sqrt(370240)) / (-32)
We can simplify this expression by taking the negative root since the positive root would give a negative time, which is not physically meaningful in this context: t = (-600 - 608.47) / (-32)
t ≈ 37.76 seconds (rounded to the nearest hundredth)
Therefore, the projectile will be in flight for about 37.76 seconds before hitting the ground.
Find each angle measure.
Answer:
The answer for <M is 28°
Step-by-step Explanation:
<P=180-48
<P=132°
base angles in an isosceles are equal
<M+<N+<P=180
3y+1+2y+2+132=180
3y+2y+3+132=180
5y+135=180
5y=180-135
5y=45
divide both sides by 5
5y/5=45/5
y=9
<M=3(9)+1=27+1=28°
Write a slope-intercept equation for a line passing(3,-2) through the point that is parallel to the line 3X+4Y= 9. Then write a second equation for a line passing through the point (3,-2) that is perpendicular to the line 3X+4Y= 9.
Put the expressions in order from the least to greatest
Step-by-step explanation:
[tex] { ({4}^{ - 4} )}^{3} \\ = {4}^{ - 12} [/tex]
[tex] \frac{ {4}^{15} }{ {4}^{5} } \\ = {4}^{10} [/tex]
[tex] {4}^{ - 5} \times {4}^{ - 4} \\ = {4}^{ - 9} [/tex]
[tex] \frac{1}{ {4}^{ - 12} } \\ = {4}^{12} [/tex]
least to greatest
[tex]1)\: {4}^{ - 12} \\ 2) \: {4}^{ - 9} \\ 3) \: {4}^{10 } \\ 4) \: {4}^{12} [/tex]
#CMIIWA research study indicated a negative linear relationship between two variables: the number of hours per week spent exercising (exercise time) and the number of seconds it takes to run one lap around a track (running time). Computer output from the study is shown below.
Assuming that all conditions for inference are met, which of the following is an appropriate test statistic for testing the null hypothesis that the slope of the population regression line equals 0 ?
The appropriate statistic for testing the null hypothesis is given as D (-2.20/0.07)
How tp get the statisticCoefficient for slope variable (Exercise time) = -2.20
Standard error of coefficient = 0.07
Therefore, the test statistic value to verify whether or not there is an apparent slope on a population regression line can be estimated as follows.
Test statistic = Coefficient for slope variable/Standard error of coefficient = -2.20/0.07
Therefore its correct answer is D (-2.20/0.07)
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Create a matrix for this linear system: 3x+2y+z = 26 X-4y = -11 2x+z = 13 The determinant of the coefficient matrix is _______. x = y = z =
Answer:
[tex]\mathrm{Matrix \: Form:}[/tex]
[tex]\begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}\begin{pmatrix}x\\ y\\ z\end{pmatrix} = \begin{pmatrix}26\\ -11\\ 13\end{pmatrix}[/tex]
[tex]\mathrm{Determinant\; of \;coefficient \;matrix = - 6}[/tex]
Step-by-step explanation:
The system of linear equations provided in the question:
[tex]\begin{aligned}3x+2y+z &= 26\\ x-4y&=-11\\ 2x+z&=13\\\\\end{aligned}[/tex]
can be represented in matrix form as
[tex]\begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}\begin{pmatrix}x\\ y\\ z\end{pmatrix} = \begin{pmatrix}26\\ -11\\ 13\end{pmatrix}[/tex]
The coefficient matrix is
[tex]\begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}[/tex]
The determinant of this matrix can be obtained by the expansion formula:
[tex]\det \begin{pmatrix}a&b&c\\ \:d&e&f\\ \:g&h&i\end{pmatrix}=a\cdot \det \begin{pmatrix}e&f\\ \:h&i\end{pmatrix}-b\cdot \det \begin{pmatrix}d&f\\ \:g&i\end{pmatrix}+c\cdot \det \begin{pmatrix}d&e\\ \:g&h\end{pmatrix}[/tex]
Therefore
[tex]det \begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}[/tex]
[tex]= 3\cdot \det \begin{pmatrix}-4&0\\ 0&1\end{pmatrix}-2\cdot \det \begin{pmatrix}1&0\\ 2&1\end{pmatrix}+1\cdot \det \begin{pmatrix}1&-4\\ 2&0\end{pmatrix}[/tex]
[tex]\mathrm{Find\:the\:matrix\:determinant\:according\:to\:formula}:\quad \det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}\:=\:ad-bc[/tex]
[tex]\det \begin{pmatrix}-4&0\\ 0&1\end{pmatrix} = \left(-4\right)\cdot \:1-0\cdot \:0 = -4[/tex]
[tex]\det \begin{pmatrix}1&0\\ 2&1\end{pmatrix} = 1\cdot \:1-0\cdot \:2 = 1[/tex]
[tex]\det \begin{pmatrix}1&-4\\ 2&0\end{pmatrix} = 1\cdot \:0-\left(-4\right)\cdot \:2 =8[/tex]
Finally,
[tex]det \begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}\\\\\\ = 3\cdot \det \begin{pmatrix}-4&0\\ 0&1\end{pmatrix}-2\cdot \det \begin{pmatrix}1&0\\ 2&1\end{pmatrix}+1\cdot \det \begin{pmatrix}1&-4\\ 2&0\end{pmatrix}\\\\\\= 3\left(-4\right)-2\cdot \:1+1\cdot \:8\\\\= -12 - 2 + 8\\\\= -6[/tex]
what is the measure of an angle if it is 590 less than six times its own supplement
This is a word problem involving supplementary angles. To solve it, we need to follow these steps:
Identify the given information and the unknown quantity. In this problem, we are given that an angle is 590 less than six times its own supplement. The unknown quantity is the measure of the angle.
Write an equation that relates the given information and the unknown quantity. We can use the fact that supplementary angles are two angles with a sum of 180°1. Let x be the measure of the angle. Then its supplement is 180 - x. The equation is:
x=6(180−x)−590
Solve the equation for the unknown quantity. We can simplify and rearrange the equation to get:
xx7xxx=6(180−x)−590=1080−6x−590=490=7490=70
Therefore, the measure of the angle is 70°.
Find the next three numbers in the pattern: 2,0,6,−4,10,−8,
The next "three-umbers" in the pattern "2,0,6,-4,10,-8,..." are 14, -12, and 18.
To find the next three numbers in the pattern 2, 0, 6, -4, 10, -8, we need to analyze the pattern and identify the rule for it.
The pattern seems to be alternating between adding and subtracting the "odd-multiples" of 2.
The pattern is as follows : 2 - (2×1) = 0,
0 + (2×3) = 6,
6 - (2×5) = -4,
-4 + (2×7) = 10,
10 - (2×9) = -8,
Using this rule, we can find the next three numbers in the pattern as follows:
Add 22 because : -8 + (2×11) = 14,
Subtract 26 because : 14 - (2×13) = -12,
Add 30 , because : -12 + (2×15) = 18,
Therefore, the next three numbers in the pattern are 14, -12, and 18.
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What is the measure (in radians) of central angle θ in the circle below?
Enter an exact expression. (in radians)
HELP NEEDED ASAP
The measure (in radians) of central angle θ in the circle below is π/3.
We have,
radius = 3 cm
Arc length = π
We can use the formula relating the arc length (s) to the central angle (θ) and radius (r) of a circle:
s = r Ф
Now,
π = 3 x Ф
Ф = π/3
Thus,
The measure (in radians) of central angle θ in the circle below is π/3.
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Select the correct answer. A parabola declines through (negative 2, 4), (negative 1 point 5, 2), (negative 1, 1), (0, 0) and rises through (1, 1), (1 point 5, 2) and (2, 4) on the x y coordinate plane. The function f(x) = x2 is graphed above. Which of the graphs below represents the function g(x) = (x + 1)2? A parabola declines through (negative 2, 5), (negative 1 point 5, 3), (negative 1, 2), (0, 1) and rises through (1, 2), (1 point 5, 3) and (2, 5) on the x y coordinate plane. W. A parabola declines through (negative 2, 3), (negative 1 point 5, 1), (1, 0), (0, negative 1) and rises through (1, 1), (1 point 5, 1) and (2, 2) on the x y coordinate plane. X. A parabola declines through (negative 3, 4), (negative 2 point 5, 2), (negative 2, 1), (negative 1, 0), (0, 1), (0 point 5, 2) and (1, 4) on the x y coordinate plane. Y. A parabola declines through (negative 1, 4), (negative 0 point 5, 2), (0, 1) and (1, 0) and rises through (2, 1), (2 point 5, 2) and (3, 4) on the x y coordinate plane. Z. A. W B. X C. Y D. Z Res
Thw correct option based on the information given about the parabola will be B. X.
How to explain the parabolaThe observed parabola has its vertex situated at (0, 0), declining until (0, 0) then again rising. Its equation falls in the form of f(x) = a(x - 0)² + 0, which simplifies to ax².
In order to detect the value of 'a' we can utilize any point on the parabola itself. Let's take (1, 1):
1 = a(1)²
1 = a
Therefore, the formula for the presented parabola is exsiting in the form of f(x) = x².
Now consider g(x) = (x + 1)² such that it's merely a horizontal movement of function f(x) = x². The vertex of g(x) stands at (-1, 0) and linearly declines until (-1, 1) prior to onching higher again. All this leaves us with option X as the only conceivable graph for g(x).
Therefore, the answer is B) X.
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Jennifer deposits money into a bank account. The amount of money in her account is measured in dollars, and can be modelled by the function A(m)= 1750(1.025)^m, where m is the number of months since the initial deposit.
What is the percent change in Jennifer's account balance each month? Is it increasing or decreasing? Justify answer.
a) The percent change in Jennifer's account balance each month is 2.5%.
b) Based on the future value function, A(m)= 1750(1.025)^m, the account balance is increasing because the growth factor is 1.025 and not less than 1.
What is a growth function?A growth function is a mathematical equation that shows a constant rate in increase or growth in value of the dependent variable.
A growth function is modeled by a growth factor greater than 1 while a decay function shows a decay.
Percentage change = 2.5% (1.025 - 1)
2.5% = 2.5 ÷ 100 = 0.025
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The whole page Tysm plsssssss step by step btw
The sum of all the pets in the list is 11.
The average number of pets that the students own is 1.375.
How to calculate the sumIt should be noted that to find the sum of all the pets in the list, we simply add up all the values:
0 + 1 + 2 + 3 + 1 + 2 + 0 + 2 = 11
Therefore, the sum of all the pets in the list is 11.
Since Cameron asked eight of his classmates, we divide the sum of pets by 8 to find the mean:
11 ÷ 8 = 1.375
Therefore, the average number of pets that the students own is 1.375.
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The measures of center can be used to summarize the number of pets that students own. Cueton asked eight of his classmates how many pets they own. The results are listed below.
0 1 2 3 1 2 0 2
What is The sum of all the pets in the list
What is the average number of pets that the students own
Suppose the function f(t) = e^t describes the growth of a colony of bacteria, where t is hours. find the number of bacteria present at 5 hours
a) 59.598
b) 148.413
c) 8.155
d) 79. 432
The number of bacteria present at 5 hours is (b) 148.413
How can the number of bacteria present be described?From the question, we were given,
f(t) = eᵗ
Then f(t) = number of bacterials present at a particular time t.
f(5) = number of bacterial present at 5 hours
So, we have
f(5) = e⁵
f(5) = 148.413
Then this can be written in the whole number as 148 which implies that the second option is correct because using f(t) = eᵗ to describes the growth of a colony of bacteria will provide us with the answer
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Which of the following statements about the number line
is true?
A. Number lines can't help you compare numerals.
B. Numbers get larger as you move to the left on the
number line.
C. Numbers get smaller as you move to the left on the
number line.
D. Number lines end with the number 10.
Evaluate.
(49)−2⋅(34)−2
Answer: To evaluate this expression, we need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) and work from left to right:
(49)^(-2) * (34)^(-2)
First, we can simplify the exponents:
1/(49^2) * 1/(34^2)
Next, we can calculate the values of 49^2 and 34^2:
1/2401 * 1/1156
Then, we can multiply the fractions:
1/2785456
Therefore, the value of the expression (49)^(-2) * (34)^(-2) is approximately 0.000000359.
Step-by-step explanation:
Graph the function f(x) = 14(0.87)x. Does this function show growth or decay? What is the equation of the asymptote? Growth; y = 0 Growth; y = 14 Decay; y = 0 Decay; y = 14
The truth statements about the function f(x) = 14(0.87)^x is Growth; y = 0
Does the function show growth or decay?From the question, we have the following parameters that can be used in our computation:
f(x) = 14(0.87)^x
An exponential function is represented as
y = ab^x
Where
a = initial value
b = growth/decay factor
In this case, the exponential function is a decay function
This means that
The value of b is less than 1 i.e.
b = 0.87 and 0.87 < 1
Hence, the function is a decay function
What is the equation of the asymptote?Recall that
f(x) = 14(0.87)^x
So, we have
y = 0 as the the equation of the asymptote
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if the volume of a rectangular prism is 26,214 m3 and it has a height of 17 m what is the value of b , the area of the base ? A. 13,062 m2 B. 13,062 m3 C.1,542 m2 D. 1,542 m3
Answer:
C
Step-by-step explanation:
The area of a rectangle is 2 dimensions so it would be measured in square meters.
a = lwh
26241 = lw(17) Divide both sides by 17
1542 = lw
The lw is he area of the base.
Helping in the name of Jesus.
the set of five number each of which is divisble by 3
Answer:
Here's a set of five numbers, each of which is divisible by 3:
{ 3, 6, 9, 12, 15 }
All the numbers in this set are multiples of 3, so they are all divisible by 3.
find the standard equation of a circle with the points (-18;-5), (-7;-16) and (4;-5)
Answer:
Step-by-step explanation:
To find the equation of a circle given three non-collinear points, we can use the following steps:
Find the equations of the perpendicular bisectors of the line segments connecting the pairs of points.
Find the intersection point of the two perpendicular bisectors. This point is the center of the circle.
Find the distance between the center and any one of the three points. This distance is the radius of the circle.
Let's apply these steps to the given points:
Find the midpoint and slope of the line segments connecting the pairs of points:
Midpoint of (-18, -5) and (-7, -16): ((-18+(-7))/2, (-5+(-16))/2) = (-12.5, -10.5)
Slope of (-18, -5) and (-7, -16): (-16 - (-5))/(-7 - (-18)) = -11/11 = -1
Midpoint of (-18, -5) and (4, -5): ((-18+4)/2, (-5+(-5))/2) = (-7, -5)
Slope of (-18, -5) and (4, -5): (-5 - (-5))/(4 - (-18)) = 0
Midpoint of (-7, -16) and (4, -5): ((-7+4)/2, (-16+(-5))/2) = (-1.5, -10.5)
Slope of (-7, -16) and (4, -5): (-5 - (-16))/(4 - (-7)) = 11/11 = 1
The equations of the perpendicular bisectors passing through the midpoints are:
x + 12.5 = -1(y + 10.5) or x + y + 23 = 0
y + 5 = 0
Find the intersection point of the two perpendicular bisectors:
Solving the system of equations:
x + y + 23 = 0
y + 5 = 0
yields: x = -18, y = -5
So, the center of the circle is (-18, -5).
Find the distance between the center and any one of the three points:
Using the distance formula:
Distance between (-18, -5) and (-18, -5): sqrt(((-18)-(-18))^2 + ((-5)-(-5))^2) = 0
Distance between (-18, -5) and (-7, -16): sqrt(((-18)-(-7))^2 + ((-5)-(-16))^2) = sqrt(221)
Distance between (-18, -5) and (4, -5): sqrt(((-18)-4)^2 + ((-5)-(-5))^2) = 22
The radius of the circle is sqrt(221).
Therefore, the equation of the circle in standard form is:
(x + 18)^2 + (y + 5)^2 = 221
The standard equation of a circle with the points (-18;-5), (-7;-16) and (4;-5) is:
(x + 13)² + (y + 1)² = 41
Standard equation of a circleFrom the question, we are to determine the standard equation of a circle with the given points
The given points are:
(-18;-5), (-7;-16) and (4;-5)
The standard equation of a circle is given by:
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle
and r is the radius.
Using the given points (-18, -5), (-7, -16), and (4, -5), we can find the equation of the circle as follows:
Find the midpoint of the line segments connecting the pairs of points:
Midpoint of (-18, -5) and (-7, -16): ((-18 + -7)/2, (-5 + -16)/2) = (-12.5, -10.5)
Midpoint of (-7, -16) and (4, -5): ((-7 + 4)/2, (-16 + -5)/2) = (-1.5, -10.5)
Midpoint of (-18, -5) and (4, -5): ((-18 + 4)/2, (-5 + -5)/2) = (-7, -5)
Find the equations of the perpendicular bisectors of the line segments:
Perpendicular bisector of the line connecting (-18, -5) and (-7, -16):
Slope of the line: (−16 + 5)/(-7 + 18) = -11/5
Slope of the perpendicular bisector: 5/11
Midpoint: (-12.5, -10.5)
Equation: y + 10.5 = (5/11)(x + 12.5)
Perpendicular bisector of the line connecting (-7, -16) and (4, -5):
Slope of the line: (-5 + 16)/(4 + 7) = 11/7
Slope of the perpendicular bisector: -7/11
Midpoint: (-1.5, -10.5)
Equation: y + 10.5 = (-7/11)(x + 1.5)
Perpendicular bisector of the line connecting (-18, -5) and (4, -5):
Slope of the line: 0
Slope of the perpendicular bisector: undefined (perpendicular bisector is a vertical line)
Midpoint: (-7, -5)
Equation: x + 7 = 0
Find the point of intersection of any two perpendicular bisectors:
Intersection of perpendicular bisectors 1 and 2:
y + 10.5 = (5/11)(x + 12.5)
y + 10.5 = (-7/11)(x + 1.5)
Solving for x and y, we get:
x = -13
y = -1
Thus,
The center of the circle is (-13, -1).
Find the radius of the circle:
Using the center (-13, -1) and one of the given points, say (-18, -5):
r² = (-18 - (-13))² + (-5 - (-1))²
r² = 25 + 16
r² = 41
Hence, the equation of the circle is:
(x + 13)² + (y + 1)² = 41.
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14. Peter makes $15 per hour as a gardener. He gets a 10% raise. Which of the following
statements are true about Peter's new rate of pay? Select the three correct answers,
A Peter will make an additional 1/100 of his salary per hour.
(B) Peter will make an additional $1.50
per hour.
C Peter's new hourly rate is $16 per hour.
D After working 5 hours at the new rate, Peter will make $82.50.
E If Peter gets an additional 10% raise, his new pay rate will be $18.15.
Find the slope of the line that passes through the given points.
(−1,−1) and (3,−4)
Answer: [tex]\frac{-3}{4}[/tex]
Step-by-step explanation:
To find the slope of the line, we will use change in y over change in x.
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} } =\frac{-4--1}{3--1} =\frac{-4+1}{3+1} =\frac{-3}{4}[/tex]
Which choice is the correct graph of |x|< 3
The graph that shows the solution set for the given inequality is the one in option B.
Which one is the graph of the given inequality?Here we want to identify the graph of the inequality:
|x| ≤ 3
So, the absolute value of x is smaller or equal to 3, that means that the graph of the solution set is a segment whose endpoints are closed circles at x = -3 and x = 3.
(We use closed circles because these values are also solutions for the inequality).
With that in mind, we can see that the correct option in this case will be graph B.
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Can Anyone HELP?
The length of the base of an isosceles triangle is 4 inches less than the length of one of the two equal sides of the triangles. If the perimeter is 32, find the three sides of the triangle. If x represents one of the equal sides of the triangle, then which equation can be used to solve the problem?
A. 2x - 4 = 32
B. 3x + 4 = 32
C. 3x - 4 = 32
Let x be the length of each of the equal sides of the isosceles triangle. Then the length of the base is x - 4. The perimeter of the triangle is the sum of the lengths of the three sides, which is:
x + x + (x - 4) = 3x - 4
We know that the perimeter is 32, so we can set 3x - 4 equal to 32 and solve for x:
3x - 4 = 32
Adding 4 to both sides gives:
3x = 36
Dividing by 3 gives:
x = 12
Therefore, one of the equal sides of the triangle is 12 inches long, and the length of the base is 12 - 4 = 8 inches.
So the three sides of the triangle are 12 inches, 12 inches, and 8 inches.
The correct equation to solve the problem is (C) 3x - 4 = 32.
Solve for x. Round to the nearest tenth, if necessary.
The value of x in the triangle to the nearest tenth is 2.6.
What is the value of x?The figure in the image is a right triangle.
angle H = 43 degreeAdjacent to angle H = 2.8Opposite to angle H = xTo solve for the missing side length x, we use the trigonometric ratio.
Note that: tangent = opposite / adjacent
Hence:
tan( H ) = opposite / adjacent
Plug in the given values and solve for x.
tan( 43° ) = x / 2.8
Cross multiply
x = tan( 43° ) × 2.8
x = 2.6 units
Therefore, the value of x is 2.6.
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8
Jonah is decorating a cake. He uses vanilla frosting on 1/5of the cake, lemon
frosting on 2/5 of the cake, and chocolate frosting on the rest of the cake.
Write and solve an equation to show the part of the cake with vanilla or
lemon frosting.
Show your work.
Answer
The part of the cake with vanilla or lemon frosting is 1/5 by using arithmetic and algebraic expression.
Let's start by defining the variable "x" as the part of the cake with vanilla or lemon frosting.
According to the problem, Jonah uses vanilla frosting on 1/5 of the cake, which can also be written as x = 1/5.
Similarly, he uses lemon frosting on 2/5 of the cake, which can be written as x = 2/5.
We know that the sum of the parts of the cake with vanilla, lemon, and chocolate frosting should equal the whole cake. Since there are only three types of frosting, we can write:
x + x + chocolate frosting = 1
2x + chocolate frosting = 1
We also know that chocolate frosting covers the remaining part of the cake, which is 3/5. Therefore, we can write:
chocolate frosting = 3/5
Substituting this value into the previous algebraic expression, we get:
2x + 3/5 = 1
Subtracting 3/5 from both sides of the equation, we get:
2x = 2/5
x = 1/5
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A farmer separated 7 hens from a group of chickens and placed them in a new coop If these 7 hens represent 20% of the total number of chickens the farmer owns, how many chickens does the farmer own?
The total number of chickens the farmer owns is 35.
What is percentage?A quantity or proportion can be expressed as a percentage of 100 by using the word "percentage." It is represented by the sign %.
For instance, when we state that 50 percent of a group of people are women, we mean that 50 out of every 100 people in the group are women.
We can deduce here the total chickens the farmer owns in % = 100%
Hens placed in a new coop = 20% = 7
Let the total number of chickens = x
Thus,
7 / x = 20 / 100
To solve for x, we can cross-multiply and simplify:
7 × 100 = 20 × x
700 = 20x
x = 35
Thus, the total number of chickens = 35.
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