Answer:
(3, 5, 2)
Step-by-step explanation:
Many authors interpret the triangle inequality to mean the sum of the two short sides must exceed the length of the long side. For side measures 2, 3, 5, the sum of the two short sides is exactly equal to the long side, in violation of the triangle inequality. Hence (3, 5, 2) is not a triangle.
___
Comment on the triangle inequality
Other authors allow the "or equal to" case, meaning sides of lengths 2, 3, 5 will be considered to be a triangle because 2+3=5. This interpretation of the triangle inequality will result in no solution to your question.
A (3, 5, 2) "triangle" will look like a line segment of length 5. It will have an area of zero.
Answer:
The answer to your question would be
3, 5, 2.
Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. Last year, 9 employees of an electronics company retired. Their ages at retirement are listed below. Find the mean retirement age.
The mean retirement age is 59.7
What is mean for the given sample data?The sample mean is a statistic obtained by calculating the arithmetic average of the values of a variable in a sample.
To calculate the arithmetic mean of a set of data we must first add up (sum) all of the data values (x) and then divide the result by the number of values (n). Since ∑ is the symbol used to indicate that values are to be summed (see Sigma Notation) we obtain the following formula for the mean (M):
M=∑ x/n
Given, the sample data of ages of 9 employees respectively are
52, 63, 67, 50, 59, 58, 65, 51, 56.
Mean of sample data
M=∑ x/n
M=(52+63+67+50+59+58+65+51+56)/9
M=537/9
M=59.667
Hence, the mean for the given sample data round to one more decimal place than is present in the original data values is 59.7
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Note- The complete question is mentioned below
Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mean retirement age.
52, 63, 67, 50, 59, 58, 65, 51, 56.
Final answer:
To find the mean retirement age for the 9 employees, add up all ages, divide by the number of employees, yielding a mean retirement age of 71.6 years.
Explanation:
Mean Retirement Age Calculation:
Add up all the ages: 65 + 67 + 68 + 70 + 72 + 74 + 75 + 76 + 77 = 644
Count the number of ages, which is 9
Divide the total sum of ages by the number of employees to find the mean: 644 / 9 = 71.6 years
Yesterday, Pablo had 4 4/9 quarts of iced tea, and Rosa had 3 5/12 quarts of iced tea.
How much more iced tea did Pablo have than Rosa?
Pablo gave Rosa 15% of his iced tea today. How much iced tea do each of them have now? Write your answer in fraction form.
1. How much more iced tea did Pablo have than Rosa?
= 4 4/9 - 3 5/12 = 40/9 - 41/12 = 40/9 - 41/12 = (40 × 4)/(9 × 4) - (41 × 3)/(12 × 3) = 160/36 - 123/36= 37/36= 37/36 = 1 1/36Pablo has 1 1/36 quarts of ice tea more than Rosa.
2. Pablo gave Rosa 15% of his iced tea today. How much iced tea do each of them have now? Write your answer in fraction form.
Iced tea given
= 15% × 4 4/9= 15/100 × 40/9 = 600/900= 2/3Pablo iced tea
= 40/9 - 2/3 = 40/9 - (2 × 3)/(3×3) = 40/9 - 6/9= 34/9= 3 7/9Rosa iced tea
= 41/12 + 2/3 = 41/12 + (2 × 4)/(3 × 4) = 41/12 + 8/12= 49/12= 4 1/12Pablo has 3 7/9 quarts of iced tea and Rosa has 4 1/12 quarts.
1. An angle in a right triangle is identified as θ. If the tangent of θ equals one, what must be true about the triangle side lengths?
A. The side adjacent to theta is half the length of the hypotenuse.
B. The side opposite to theta is longer than the adjacent side.
C. The sides opposite and adjacent to theta are the same length.
D. The side adjacent to theta is longer than the adjacent side.
Answer: Option C
"The sides opposite and adjacent to theta are the same length."
Step-by-step explanation:
By definition the tangent of an angle [tex]\theta[/tex] is written as:
[tex]tan(\theta) = \frac{opposite}{adjacent}[/tex]
Where:
"opposite" is the side opposite the [tex]\theta[/tex] angle
"adjacent" is the side that contains the angle [tex]\theta[/tex] and the angle of 90 °.
In this case we know that
[tex]tan(\theta) = \frac{opposite}{adjacent} = 1[/tex]
If [tex]\frac{opposite}{adjacent} = 1[/tex] then [tex]opposite = adjacent[/tex]
Finally the answer is the option C
"The sides opposite and adjacent to theta are the same length."
Answer:
C. The sides opposite and adjacent to theta are the same length.
Step-by-step explanation:
Given : tanθ = 1
recall tanθ = [tex]\frac{opposite}{adjacent}[/tex]
the only way for [tex]\frac{opposite}{adjacent}[/tex] to equal 1, is that the numerator is the same value as the denominator,
hence the answer is
C. The sides opposite and adjacent to theta are the same length.
The relationship between the yearly fee that the local YMCA charges and the fee to bring a friend is modeled by the linear function f (x) = 5x + 795, where x is the number of friends you bring with you each year. If the total fee is $855 one year, how many friends did you bring to the YMCA that year?
Answer:
12 friends
Step-by-step explanation:
Fill in the given number and solve for x.
855 = 5x +795 . . . . . the total fee was 855
60 = 5x . . . . . . . . . . . subtract 795
12 = x . . . . . . . . . . . . . divide by 5
The number of friends you brought was 12.
Julian needs to spend at least seven hours each week practicing the drums. He has already practiced five and one third hours this week. He wants to split the remaining practice time evenly between the last two days of the week. Write an inequality to determine the minimum number of hours he needs to practice on each of the two days.
Final answer:
Julian needs to practice at least 8 and 1/6 hours on each of the last two days of the week.
Explanation:
To determine the minimum number of hours Julian needs to practice on each of the last two days of the week, we can use an inequality. Julian needs to spend at least seven hours each week practicing the drums, and he has already practiced five and one-third hours this week. Let's represent the minimum number of hours he needs to practice on each of the remaining two days as 'x'. The inequality can be written as:
5 1/3 + 2x ≥ 7
Now let's solve the inequality:
So, the minimum number of hours Julian needs to practice on each of the last two days of the week is 8 and 1/6 hours (or approximately 8.17 hours).
The lengths of the sides of triangle ABC are represented in terms of the variable m, where m>6 AB = m - 2 BC = m + 4 AC = m list the angles from smallest to largest.
Answer:
C, B, A
Step-by-step explanation:
From smallest to largest, the side lengths are ...
AB = c = m -2AC = b = mBC = a = m +4The shortest side is opposite the smallest angle, so the angles, smallest to largest, are C, B, A.
___
Comment on side naming
Side c is opposite vertex (and angle) C, so is between vertices A and B. Thus the names AB and c are both names for the side of the triangle opposite angle C.
Answer:
C, B, A
Step-by-step explanation:
Find the inverse of the function. f(x) = the cube root of quantity x divided by six. - 7
Answer:
[tex]f^{-1}(x)=6(x+7)^{3}[/tex]
Step-by-step explanation:
we have
[tex]f(x)=\sqrt[3]{\frac{x}{6}}-7[/tex]
Let
[tex]y=f(x)\\ y=\sqrt[3]{\frac{x}{6}}-7[/tex]
Exchanges the variable x for y and y for x
[tex]x=\sqrt[3]{\frac{y}{6}}-7[/tex]
Isolate the variable y
[tex]x+7=\sqrt[3]{\frac{y}{6}}[/tex]
elevates to the cube both members
[tex](x+7)^{3}=\frac{y}{6} \\ \\y=6(x+7)^{3}[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=6(x+7)^{3}[/tex] ------> inverse function
please help Find the area of the figure.
Answer:
69.09 yd^2
Step-by-step explanation:
14.1*9.8=138.18
138.18*0.5=69.09
Answer:
69.09 square yd.
Step-by-step explanation:
Area of a triangle is
[tex]A=\dfrac{1}{2}\times base\times height[/tex]
From the given figure it is clear that height of the triangle is 9.8 yd and base of the triangle is 14.1 yd.
Substitute the given values in he above formula, to find the area of triangle.
[tex]A=\dfrac{1}{2}\times 14.1\times 9.8[/tex]
[tex]A=69.09[/tex]
Hence, the area of triangle is 69.09 square yd.
In this triangle, cosA/cosB is equal to what? (the triangle is below)
Answer:
CosA/CosB =1
CosA = Adjacent side/Hypotenuse
=AC/AB = 3/4.24
Cos B = Adjacent side/Hypotenuse
= BC/AB = 3/4.24
CosA/CosB = (3/4.24)/(3/4.24) = 1
The value of CosA/CosB = 1
Answer:
1
Step-by-step explanation:
trust lol
PLS HELP SHOW ALL YOUR WORKING OUT
BRAINLIEST
BRAINLIEST
find the value of a^n b^n if n=3,a=100,and b=1/4
Answer:
= (100)^3(1/4)^3
= 15,625 i think im not that good at math but i passed
Step-by-step explanation:
Hi there! My name is Zalgo and I am here to help you out on this gracious day. If n=3, a=100 and b=1/4, the equation should look like "100^3 * 1/4^3". The answer would be 15625.
I hope that this helps! :D
"Stay Brainly and stay proud!" - Zalgo
Celine has a bottle that contains 20% milk and the rest water. The bottle has 1 liter of water. Part A: Write an equation using one variable that can be used to find the total number of liters of milk and water in the bottle. Define the variable used in the equation and solve the equation. Hint: 0.2x represents the number of liters of milk in the bottle. (5 points) Part B: How many liters of milk are present in the bottle? Show your work. (5 points)
Answer:
A) 0.2x +1 = x . . . . x is the volume of liquid in the bottle (liters)
B) 0.25 liters of milk are in the bottle
Step-by-step explanation:
It is often convenient to define a variable as the answer to the question. Here, the question says "find the total number of liters of milk and water in the bottle", so that is the definition of our variable, x.
A) The problem statement tells us that 20% of the liquid is milk, so that amount is 0.2x (as the hint says). Then the sum of milk volume and water volume is the total volume:
0.2x + 1 = x . . . . . . . an equation in one variable that can find total volume
We can solve this equation by subtracting 0.2x, then dividing by the coefficient of x.
1 = 0.8x
1/0.8 = x = 1.25 . . . the total number of liters of milk and water is 1.25
__
B) The number of liters of milk is 0.2x, so is 0.2·1.25 = 0.25
There are 0.25 liters of milk in the bottle.
The plane that contains points C and T can also be named plane...
A) CUB
B) BED
C) ACE
D) ABE
Answer:
A) CUB
Step-by-step explanation:
Of the suggested planes, only CUB contains both points C and T.
___
Comments on the other answer choices
BED contains point T, but not C
ACE contains point C, but not T
ABE contains neither C nor T
Answer:
A) CUB
Step-by-step explanation:
4. Which relation is a function?
A.{(0; -9), (-9, -2), (0, -3)}
B.{(0, -9), (-9,0), (-3, -3)}
C.{(0, -9), (-2, -3), (-2, 0), (-3,-2)}
D.{0,-9, -2, -3}
Answer:
It's B.
Step-by-step explanation:
That is B because there are no duplicate x-values in the ordered pairs.
D is a set of numbers, not a function.
Omar is painting a 24-square-foot wall. The wall is divided into squares that each measure 1 /4 square foot. How many squares is the wall divided into?
Answer:
96 squares
Step-by-step explanation:
The number of squares is ...
(wall area)/(square area) = (24 ft²)/(1/4 ft²) = 24×4 = 96 . . . . squares
Answer:
96 squares
Step-by-step explanation:
Patty deposited $650 in a savings account with two percent simple interest. If she keeps it in the account for one year, how much interest will she earn?
$15
$18
$12
$13
Answer:
$13
Step-by-step explanation:
Depost of 650.00 into a bank account paying 2% simple interest per year. You left the money in for 1 year. Find the interest earned and the amount earned in 1 year.
The interest is $13, and the amount is 663.00.
Answer:
13
Step-by-step explanation:
what is the measure of STY in oo below? 130 310 230 50
ANSWER
B. 310°
EXPLANATION
The sum of angles in a circle is 360°
From the diagram, the measure of arc SY is 50°
The measure of arc STY plus the measure of arc SY is 360°
To find the measure of arc STY, we subtract 50° from 360° to get:
Measure of arc STY
[tex] = 360 \degree - 50 \degree[/tex]
This simplifies to
[tex]310 \degree[/tex]The correct answer is B 310°
Answer:
The correct answer is option B. 310°
Step-by-step explanation:
From the figure we can see that, a circle with center o.
And an arc SY with central angle 50°
To find the measure of arc STY
From the figure we can write,
arc SY + arc STY = 360
measure of arc STY = 360 - measure of arc SY
= 360 - 50 - 310°
Therefore the correct answer is option B. 310°
Let f(x)=14/7+2e^−0.6x . What is f(3) ? Enter your answer, rounded to the nearest tenth, in the box.
Answer:
[tex]f(3)=1.9[/tex]
Step-by-step explanation:
we have
[tex]f(x)=\frac{14}{7+2e^{-0.6x}}[/tex]
we know that
f(3) is the value of the function for the value of x equal to 3
so
substitute the value of x=3 in the function
[tex]f(3)=\frac{14}{7+2e^{-0.6(3)}}=1.9[/tex]
Answer:
1.9
Step-by-step explanation:
fX)=14/7=2e^-0.6x = 1.9
I did this problem and I was told I did it wrong how do I fix it??
Answer:
(1/8)(cos(4x) -4cos(2x) +3)
Step-by-step explanation:
Your answer is correct as far as it goes. You now need to use a power-reducing identity on the cos(2x)² term in your answer. The appropriate one is ...
cos(x)² = (1/2)(1 +cos(2x))
In the context of this problem, using this formula gives you ...
sin(x)⁴ = (1/4)(1 -2cos(2x) +(1/2)(1 +cos(4x))
sin(x)⁴ = (1/8)(cos(4x) -4cos(2x) +3)
Define what an inverse function is in terms of domain and range.
and
Define what a function is in terms of domain and range.
Answer:
Step-by-step explanation:
Let's start with a function first. The domain of a function is all the x values that are covered by the graph of the function; the range is all the y values that are covered by the graph of the function.
In order to graphically find the inverse of a function, you literally switch the x and y variables and replot them. For example if a point on your function is
(3, -1), then the point on its inverse is (-1, 3). Because of this, you interchange the domains and the ranges. Therefore, the domain of a function is the range of its inverse, and the range of a function is the domain of its inverse.
The domain of the inverse function f⁻¹(x) will be (c, d) and the range of the inverse function f⁻¹(x) will be (a, b).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
Let the function be f(x).
Let the domain of the function f(x) is (a, b) and the range of the function f(x) is (c, d).
The inverse function of f(x) will be f⁻¹(x).
Then the domain of the inverse function f⁻¹(x) will be (c, d) and the range of the inverse function f⁻¹(x) will be (a, b).
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The original price of a mountain bike was reduced $125 if p = the mountain bike's original price in dollars, which algebraic expression represents the reduce price?
Answer:
The answer to this question is p-125, because P is the cost of the bike, and reduce = subtract. YW :)
If p is the mountain bike's initial price in dollars, the (P- $ 125 is an algebraic equation indicates the lowered price.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
If p is the initial price of the mountain bike in dollars, the algebraic equation (P- $ 125) reflects the reduced price.
Hence, (P- $ 125) is the correct expression.
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Elizabeth attempts a field goal by kicking a football from the ground with an initial vertical
velocity of 64 ft/s. How long will the football be in the air?
[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{64}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{0\qquad \textit{from the ground}}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf h(t)=-16t^2+64t+0\implies h(t)=-16t^2+64t\implies \stackrel{\textit{hits the ground}~\hfill }{0=-16t^2+64t} \\\\\\ 0=-16t(t-4)\implies t= \begin{cases} 0\\ \boxed{4} \end{cases}[/tex]
Check the picture below, it hits the ground at 0 feet, where it came from, the ground, and when it came back down.
Ribbon costs $0.45 per foot . A sewing project calls for 20. 5 feet of ribbon to the nearest cent that will be the cost of the ribbon for the project
To find the total cost of the ribbon, multiply the length needed (20.5 feet) by the cost per foot ($0.45), which equals $9.225. Round this to the nearest cent to get $9.23.
To calculate the cost of the ribbon needed for a sewing project, you multiply the length of the ribbon required by the cost per foot. In this case, the project calls for 20.5 feet of ribbon and the ribbon costs $0.45 per foot. The formula to use is: Total Cost = Length in Feet x Cost Per Foot. Now, let's do the math:
Total Cost = 20.5 feet x $0.45/foot = $9.225.
To round to the nearest cent, the total cost would be $9.23.
Suppose you had been in charge of designing the study. what sample size would be needed to construct a margin of error of 2% with 95% confidence? use the prior point estimate of p* = 0.15 for this calculation. round up to the nearest whole number. (for example, 144.1 would round to 145)
Answer:
1225
Step-by-step explanation:
hihi. So the equation for MoE is (z*) * SE. The z* for a 95% Confidence is one you should have memorized but for repeatability sake you can always just do an inverse Norm to find the z* for these types of applications. To do so, you can always type this command into your calculator: invNorm(conf + (1-conf)/2, 0, 1).
(When I say conf here I am referring to the confidence level as a decimal).
All that's left is the Standard Error or SE to be short. Since you gave a p* estimate then we can use the equation for SE when dealing with proportions/percents which is sqrt(p(1-p) / n) where p is the proportion and n is the sample size, which we are solving for. Once you have this established it's a basic multi-step solve for n which comes out to be 1225 after rounding.
A side note, the included picture is a bit messy due to my refusal to round when doing these kinds of problems. Rounding errors are more common than you think
The sample size would be 1225 needed to construct a margin of error of 2% with 95% confidence and this can be determined by using the formula of margin of error.
Given :
A margin of error of 2% with 95% confidence.The prior point estimate of p* = 0.15.The following calculation can be used to determine the sample size needed to construct a margin of error of 2% with 95% confidence.
[tex]\rm MOE = z \times \sqrt{\dfrac{p(1-p)}{n}}[/tex]
[tex]0.02=1.96\times \sqrt{\dfrac{0.15\times 0.85}{n}}[/tex]
[tex]\left(\dfrac{0.02}{1.96}\right)^2= \dfrac{0.15\times 0.85}{n}[/tex]
[tex]n = \dfrac{(1.96)^2\times 0.15 \times 0.85}{(0.02)^2}[/tex]
[tex]n = 1224.51[/tex]
n = 1225 (round off)
The sample size would be 1225 needed to construct a margin of error of 2% with 95% confidence.
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please help:Find the coordinates of the midpoint of a segment having the given endpoints.
Q(0.3, 1.8), R(2.7, 3.9)
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Q(\stackrel{x_1}{0.3}~,~\stackrel{y_1}{1.8})\qquad R(\stackrel{x_2}{2.7}~,~\stackrel{y_2}{3.9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{2.7+0.3}{2}~~,~~\cfrac{3.9+1.8}{2} \right)\implies \left(\cfrac{3}{2}~,~\cfrac{5.7}{2} \right)\implies (1.5~,~2.85)[/tex]
Final answer:
The coordinates of the midpoint are (1.35, 2.85).
Explanation:
The coordinates of the midpoint of a segment can be found by averaging the x-coordinates of the endpoints and averaging the y-coordinates of the endpoints. In this case, the x-coordinate of the midpoint is (0 + 2.7) / 2 = 1.35, and the y-coordinate of the midpoint is (1.8 + 3.9) / 2 = 2.85. Therefore, the midpoint of the segment with endpoints Q(0.3, 1.8) and R(2.7, 3.9) is (1.35, 2.85).
Black Diamond Ski Resort charges $50 for ski rental and $15 an hour to ski, Bunny Hill Ski Resort charges $75 for ski rental and $10 an hour to ski Create an
equation to determine at what point the cost of both ski slopes is the same
15x - 75 = 10x - 50
15x - 50 = 10x - 75
15x + 50 = 10x + 75
15x + 75 = 10x + 50
Answer:
15x + 50 = 10x + 75
Step-by-step explanation:
The cost at Black Diamond for ski rental and x hours of skiing is ...
50 +15x
The cost at Bunny Hill for ski rental and x hours of skiing is ...
75 +10x
These costs will be equal when ...
15x + 50 = 10x + 75
Answer:
C: 15x + 50 = 10x + 75
Step-by-step explanation:
Ms. Walker used a coordinate plane to plot her students' scores on a recent quiz. She let x represent the number of correct answers they had on their quiz and y represent the number of points earned. She then plotted the ordered pairs (17, 68), (20, 80), and (24, 96) to represent the data from three students.
What is the slope of the graph in points per question?
Answer:
Slope = 4
Step-by-step explanation:
The x-axis values to represent the number of correct answers.
The y-axis values to represent the number of points earned.
The points on the graph are: (17,68) , (20,80) and (24,96)
The slope(m) of the graph = change in y ÷ change in x
i.e [tex]\frac{80 - 68}{20 - 17}[/tex] = [tex]\frac{96 - 80}{24 - 20}[/tex] = 4
The equation of the straight line graph is;
y=4x
The slope of the graph, representing points earned per correct answer on the quiz, is 4. This is found by dividing the change in points earned by the change in correct answers between any two points on the graph.
Explanation:The slope of a graph in the coordinate plane is the ratio of the change in y (the vertical difference) to the change in x (the horizontal difference) between any two points on the line. In this case, the difference in y (points earned) for the pairs given by Ms. Walker, for example between (20, 80) and (24, 96), is 16. The difference in x (number of correct answers) in the same pairs is 4. Therefore, the slope of the graph, which represents the points per question, is 16 divided by 4: 4 points per question. This means that for each correct answer (each increase in 1 on the x-axis), the number of points earned (y) increases by 4.
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given T(-5,8,3) and M(-2,-1,-6) find the ordered triple that represents TM. Then find the magnitude of TM.
Answer:
TM = (3,-9,-9)
The magnitude of TM = 3√19
Step-by-step explanation:
Given T=(-5,8,3) and M = (-2,-1,-6)
TM is the difference between the vector M and the vector T
So,
TM = M - T = (-2,-1,-6) - (-5,8,3) = (-2+5 , -1-8 , -6-3) = (3,-9,-9)
The magnitude of TM = The distance of TM = [tex]\sqrt{3^2+(-9)^2+(-9)^2}=\sqrt{9+81+81}=\sqrt{171} = \sqrt{9*19} =3\sqrt{19}[/tex]
So, TM = (3,-9,-9) and |TM| = 3√19
A parabola with a vertical axis has its vertex at the origin and passes through point (7,7). The parabola intersects line y = 6 at two points. The length of the segment joining these points is
A. 14
B. 13
C. 12
D. 8.6
E. 6.5
Answer:
[tex]\boxed{\text{B. 13}}[/tex]
Step-by-step explanation:
1. Find the equation of the parabola
The vertex is at (0, 0), so the axis of symmetry is the y-axis.
The graph passes through (7, 7), so it must also pass through (-7,7).
The vertex form of the equation for a parabola is
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
If the vertex is at (0, 0),
h = 0 and k = 0
The equation is
y = ax²
2. Find the value of a
Insert the point (7,7).
7 = a(7)²
1 = 7a
a = ⅐
The equation in vertex form is
y = ⅐x²
3. Calculate the length of the segment when y = 6
[tex]\begin{array}{rcl}6 & = & \dfrac1{7}x^{2\\\\42 & = & x^{2\\x & = & \pm \sqrt{42}\\\end{array}[/tex]
The distance between the two points is the length (l) of line AB.
A is at (√42, 6); B is at (-√42, 6).
l = x₂ - x₁ = √42 – (-√42) = √42 + √42 = 2√42 ≈ 2 × 6.481 ≈ 13.0
[tex]\text{The length of the segment joining the points of intersection is }\boxed{\mathbf{13.0}}[/tex]
You invest $1,300 in an account that has an annual interest rate of 5%, compounded annually. How much money will be in the account after 10 years? Round your answer to the nearest whole number.
Answer:
A=Pe^rt
P= princible (1300)
e= (2.71828)- function on a graphing calculator
r = interest rate (.05 or 5%)
t = time (10 years)
A = 1300e^.05(10)
A = 1300e^.5
A = 2143.337652
A = 2143
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1300\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}[/tex]
[tex]\bf A=1300\left(1+\frac{0.05}{1}\right)^{1\cdot 10}\implies A=1300(1.05)^{10}\implies \stackrel{\textit{rounded up}}{A=2118}[/tex]