Evaluating the given algebra fraction (x - 1)²/(1 - x)² at x = 0 gives; 1
How to Evaluate Algebra Fractions?
We want to evaluate the algebra fraction;
(x - 1)²/(1 - x)² at x = 0.
Now, let us first break down the expression to get;
[(x - 1) * (x - 1)]/[(1 - x) * (1 - x)]
At x = 0, we have;
[(0 - 1) * (0 - 1)]/[(1 - 0) * (1 - 0)]
⇒ (-1 * -1)/(1 * 1)
⇒ 1
Read more about Algebra Fractions at; https://brainly.com/question/24705296
#SPJ1
Question 16 (5 points) What's the volume of a cube with a side length of 3 inches? O27 cubic inches O 12 square inches O 12 cubic inches O27 square inches
Answer:
27 cubic inches
Step-by-step explanation:
A cube by definition has all the side lengths equal to each other. Kind of like how a square has all equal sides, except with a cube, there's depth. So the volume of the cube would be the width*length*depth, but since the width=length=depth, you only need one side, and you just cube it, or raise it to the third power. So you have the equation: [tex]A=(3\text{ inches})^3=27\text{ inches}^3[/tex] which is read as 27 cubic inches
Find the next term in the following number pattern: 1, 16, 81, 256, 625, ____
The amount of syrup that people put on their pancakes is normally distributed with mean 60 mL and standard deviation 11 mL. Suppose that 12 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.
What is the distribution of
X
?
X
~ N(
,
)
What is the distribution of
¯
x
?
¯
x
~ N(
,
)
If a single randomly selected individual is observed, find the probability that this person consumes is between 59.3 mL and 61.2 mL.
For the group of 12 pancake eaters, find the probability that the average amount of syrup is between 59.3 mL and 61.2 mL.
For part d), is the assumption that the distribution is normal necessary? YesNo
Using the normal distribution and the central limit theorem, we have that:
The distribution of X is [tex]X \approx N(60,11)[/tex].The distribution of [tex]\bar{X}[/tex] is [tex]\bar{X} \approx (60,3.1754)[/tex].0.0637 = 6.37% probability that a single person consumes between 59.3 mL and 61.2 mL.0.2351 = 23.51% probability that the sample mean of the consumption of 12 people is between 59.3 mL and 61.2 mL. Since the sample size is less than 30, a normal distribution has to be assumed.Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, the parameters are given as follows:
[tex]\mu = 60, \sigma = 11, n = 12, s = \frac{11}{\sqrt{12}} = 3.1754[/tex].
Hence:
The distribution of X is [tex]X \approx N(60,11)[/tex].The distribution of [tex]\bar{X}[/tex] is [tex]\bar{X} \approx (60,3.1754)[/tex].The probabilities are given by the p-value of Z when X = 61.2 subtracted by the p-value of Z when X = 59.3, hence, for a single individual:
X = 61.2:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{61.2 - 60}{11}[/tex]
Z = 0.11
Z = 0.11 has a p-value of 0.5398.
X = 59.3:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{59.3 - 60}{11}[/tex]
Z = -0.06
Z = -0.06 has a p-value of 0.4761.
0.5398 - 0.4761 = 0.0637.
0.0637 = 6.37% probability that a single person consumes between 59.3 mL and 61.2 mL.
For the sample of 12, we have that:
X = 61.2:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{61.2 - 60}{3.1754}[/tex]
Z = 0.38
Z = 0.38 has a p-value of 0.6480.
X = 59.3:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{59.3 - 60}{3.1754}[/tex]
Z = -0.22
Z = -0.22 has a p-value of 0.4129.
0.6480 - 0.4129 = 0.2351 = 23.51% probability that the sample mean of the consumption of 12 people is between 59.3 mL and 61.2 mL. Since the sample size is less than 30, a normal distribution has to be assumed.
More can be learned about the normal distribution and the central limit theorem at https://brainly.com/question/24188986
#SPJ1
{f(x)=2x+1 g(x)=x2+2x−8
The value of g(x) = 2[f(x)]² - 1 is g(x) = 8x² + 8x + 1
How to find a function?f(x) = 2x+1
Find
g(x) = 2[f(x)]² - 1
Hence,
g(x) = 2[2x + 1]² - 1
g(x) = 2[4x² + 4x + 1] - 1
g(x) = 8x² + 8x + 2 - 1
g(x) = 8x² + 8x + 1
learn more on function here: https://brainly.com/question/1442153
#SPJ1
Johnny earns $2334.50 from his job each month. he pays $1437 for monthly expenses Johnny is planning a vacation in 3-month times that he estimates will cost $1750 total. how much will Johnny have leftovers from 3 months of saving once he pays for his vacation?
1) $948.50
2) $584.50
3) $852.50
4) $942.50
The amount of money left from 3 months of saving once he pays for his vacation is $942.50
SavingsNumber of months = 3Amount earned per month = $2334.50Total earned = 3 × $2334.50= $7,003.50
Monthly expenses = $1437
Total expenses = 3 × $1437
= $4,311
Cost of vacation = $1750
Total balance = $7,003.50 - ($4,311 + $1750)
= 7,003.50 - 6061
= $942.50
Learn more about savings:
https://brainly.com/question/25787382
#SPJ1
Juanita has 60 horses on her ranch. If 60% of the horses are thoroughbreds, how many are not thoroughbreds?
A.) 45
B.) 22
C.) 21
D.) 24
Answer: d
Step-by-step explanation:
60*0.6=36
60-36=24
24 are not thoroughbreds
I need help with this please
There are 36 possible combinations that can occur when 2 dice are rolled. For the sake of this question, we'll count instances where dice 1 = 3/dice 2 = 2 and dice 1 = 2/dice 2 = 3.
Now, let's think about all of the possible ways a total of 5 could be rolled.
1 + 4
2 + 3
3 + 2
4 + 1
That's 4 possibilities to roll a total of 5 out of 36 possible outcomes.
4 / 36 = ? / 180
---Now, we need to use a proportion in order to figure out the possibilities out of 180.
36x = 720
x = 20
If you rolled a pair of fair dice 180 times, you would expect to roll a total of 5, 20 times.
Hope this helps!
I need Help with calculus please, thank you! 10points
3) We have
[tex]f(x) = \sec\left(\dfrac{\pi x}2\right) = \dfrac1{\cos\left(\frac{\pi x}2\right)}[/tex]
which has vertical asymptotes (i.e. infinite discontinuities) whenever the denominator is zero. This happens for
[tex]\cos\left(\dfrac{\pi x}2\right) = 0[/tex]
[tex]\implies \dfrac{\pi x}2 = \cos^{-1}(0) + 2n\pi \text{ or } \dfrac{\pi x}2 = -\cos^{-1}(0) + 2n\pi[/tex]
(where [tex]n[/tex] is any integer)
[tex]\implies \dfrac{\pi x}2 = \dfrac\pi2 + 2n\pi \text{ or } \dfrac{\pi x}2 = -\dfrac\pi2 + 2n\pi[/tex]
[tex]\implies x = 1 + 4n \text{ or } x = -1 + 4n[/tex]
So the graph of [tex]f(x)[/tex] has vertical asymptotes whenever [tex]x=4n\pm1[/tex] and [tex]n\in\Bbb Z[/tex].
4) Given
[tex]h(t) = \begin{cases} t^3+1 & \text{if } t<1 \\ \frac12 (t+1) & \text{if } t\ge1 \end{cases}[/tex]
we have the one-sided limits
[tex]\displaystyle \lim_{t\to1^-} h(t) = \lim_{t\to1} (t^3+1) = 1^3+1 = 2[/tex]
and
[tex]\displaystyle \lim_{t\to1^+} h(t) = \lim_{h\to1} \frac{t+1}2 = \frac{1+1}2 = 1[/tex]
The one-sided limits don't match, so the two-sided limit [tex]L[/tex] does not exist. In other words, the limit does not exist at [tex]x=1[/tex] because the function approaches different values from the left and right side of [tex]x=1[/tex].
The numbers 1 through 15 are written on cards. One card is chosen at random. Event A is choosing a
multiple of 5. Event B is choose an even number. What is the probability of choosing a number that
is not a multiple of 5?
Step-by-step explanation:
the probability is always the number of desired cases over the number of all possible cases.
in our situation we have 15 cards.
that is the total possible cases when a random card is chosen.
how many desired cases do we have ?
a number NOT a multiple of 5.
how many are there ?
it is easier to say how many numbers there are being a multiple of 5 : 5, 10, 15
so, 3 numbers out of the 15 are multiple of 5.
that means
15 - 3 = 12 numbers of the 15 are NOT multiples of 5.
so, the probability to draw a card that is not a multiple of 5 is
12/15 = 4/5 = 0.8
the information about event B and even numbers is irrelevant for the question.
Which of the following are solutions to the equation below?
Check all that apply.
x²-2x-24 = 0
Answer:
[tex]x=6, x=-4[/tex]
Step-by-step explanation:
1) Let's solve this quadratic equation by factorizing. We need to find two numbers that multiply to -24 and add up to -2 simultaneously. If we pull out the factors of -24, two of them will be -6 and 4, which multiply to -24 as well as add up to -2.
3) Write [tex]-2x[/tex] as a sum.
[tex]x^2-6x+4x-24=0[/tex]
Now, we can factor them out by grouping.
[tex]x^2-6x+4x-24=0\\x(x-6) + 4(x-6)=0[/tex]
Since, [tex]x -6[/tex] is common in both of the factors, we only take one of the [tex]x -6[/tex] along with [tex]x[/tex] and [tex]4[/tex] and all equated to 0.
[tex](x-6)(x+4) = 0[/tex]
Solve for x: [tex]x-6=0[/tex]
[tex]x=0+6\\x=6[/tex]
Solve for x: [tex]x+4=0[/tex]
[tex]x=0-4\\x=-4[/tex]
Therefore, our solutions to this quadratic equation are [tex]x=6, x=-4[/tex].
tommy starts walking from school to home at the same time that his dad starts walking home to school the both depart at 300pm tommy is walking at a speed of 1.35meters pr second and his dad is walking at a speed of 1.65 meters per second. the distance between home and school is 720 meters at what time wil they meet
Tommy and his father will meet after 2400 seconds or 40 minutes. So they will meet at 3:40 pm.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.
Given that:-
Tommy starts walking from school to home at the same time that his dad starts walking home to school they both depart at 300pm Tommy is walking at a speed of 1.35meters per second and his dad is walking at a speed of 1.65 meters per second. the distance between home and school is 720 meters at what time will they meetThe time will be calculated by using the relative speed concept.
Relative speed = Speed of father - Speed of Tommy
Relative speed = 1.65 - 1.35
Relative speed = 0.3 meter per second
Relative speed = Distance / Time
0.3 = 720 / Time
Time = 720 / 0.3
Time = 2400 seconds = 2400/ 60 = 40 minutes
We know that both departed at 3 pm they will meet at 3:40 pm.
Therefore Tommy and his father will meet after 2400 seconds or 40 minutes. So they will meet at 3:40 pm.
To know more about Speed follow
https://brainly.com/question/6504879
#SPJ1
6. The length of the minor arc AB of a circle, centre O, is 2π cm and the length of the major arc is 22π cm. Find:
a) the radius of the circle
b) the acute angle AOB.
Answer:
a) 24 [cm]; b) 30°.
Step-by-step explanation:
a) the length of full the circle is: min_arc(AB)+maj_arc(AB)=π(22+2)=24π [cm]. Then the radius is: r=L/π; ⇒ r=24π/π=24 [cm];
b) if the full circle is 360° (L=24π), then m(∠AOB):2=360°:24 and the required measure of the acute angle AOB is:
m(∠AOB)=360*(1/12)=30°.
find the area of a triangle whose sides are 5 m, 6 m and 9m,( use root 2 =-1.41 m)
The area of the triangle is 14.1 square meters
How to determine the triangle area?The side lengths are given as:
5m, 6m and 9m
Calculate the semi-perimeter (s) using
s = (5 + 6 + 9)/2
Evaluate
s = 10
The area is then calculated as:
[tex]Area = \sqrt{s(s -a)(s-b)(s-c)[/tex]
This gives
[tex]Area = \sqrt{10 * (10 -5)(10-6)(10-9)[/tex]
Evaluate the products
[tex]Area = \sqrt{200[/tex]
Evaluate the exponent
Area = 14.1
Hence, the area of the triangle is 14.1 square meters
Read more about areas at:
https://brainly.com/question/27683633
#SPJ1
What is another name for Angle 2? Lines E H and D F intersect at point G. Angle 2 is formed by line segments D G and G E and angle 1 is formed by line segments E G and G F. Angle D G E Angle G E D Angle E G F Angle G E F
When two straight lines or rays intersect at a shared endpoint, an angle is generated. The correct option is A.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
The diagram for the given problem can be made as shown below. Therefore, the other name for angle 2 will be ∠DGE.
Hence, the correct option is A.
Learn more about Angle:
https://brainly.com/question/7116550
#SPJ1
Answer:
a
Step-by-step explanation:
got it right
Need help please with number 2!!!
Answer:
Step-by-step explanation:
Use the Divergence Theorem to evaluate
Integral of (9x + 2y + z2) dS
where S is the sphere
x2 + y2 + z2 = 1.
The value of the integral is [tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]
How to evaluate the integral?The expression is given as:
[tex]\int\limits^{}_s {9x + 2y + z^2} \, dS[/tex]
[tex]x^2 + y^2 + z^2 = 1[/tex]
Rewrite the integral as:
[tex]\int\limits^{}_s {9x + 2y + z*z} \, dS[/tex]
As a general rule, we have:
[tex]\int\limits^{}_s {Px + Qy + R*z} \, dS[/tex]
By comparison, we have:
P = 9
Q = 2
R = z
By the divergence theorem, we have:
F = Pi + Qj + Rk
So, we have:
F = 9i + 2j + zk
Differentiate
F' = 0 + 0 + 1
F' = 1
The volume of a sphere is:
[tex]V = \frac{4}{3}\pi r^3[/tex]
Where:
r = F' = 1
So, we have:
[tex]V = \frac{4}{3}\pi (1)^3[/tex]
Evaluate
[tex]V = \frac{4}{3}\pi[/tex]
This means that:
[tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]
Hence, the value of the integral is [tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]
Read more about divergence theorem at:
https://brainly.com/question/17177764
#SPJ1
f(x)=(2x−1)(3x+5)(x+1) has zeros at x= -5/3, x= -1 and x= 1/2 What is the sign of f on the interval -5/3
The sign of f on the interval -5/3 is negative
How to determine the sign?The function is given as:
f(x)=(2x−1)(3x+5)(x+1)
The zeros of the function are
x= -5/3, x= -1 and x= 1/2
Next, we plot the graph of the function
At x = -5/3, the function approaches negative infinity
This means that the sign of f on the interval -5/3 is negative
Read more about function intervals at:
https://brainly.com/question/27831985
#SPJ1
Which inequalities would have a closed circle when graphed? check all that apply. x > 2.3 5.7 less-than-or-equal-to p one-half greater-than y m greater-than-or-equal-to 10 s < –7.6
Option B and D would have closed circles when graphed
The domain and range of a function are the components of a function. The domain is the set of all the input values of a function and range is the possible output given by the function.
At the endpoints of the domain, we draw open circles to indicate where the endpoint is not included because of a less-than or greater-than inequality; we draw a closed circle where the endpoint is included because of a less-than-or-equal-to or greater-than-or-equal-to inequality.
∴ Option B and D that are 5.7 ≤ p and [tex]\frac{1}{2}[/tex] ≥ y respectively would have closed circles
Learn more about domain and range here :
https://brainly.com/question/13856645
#SPJ4
Select the correct answer from each drop-down menu.
Consider these account options. Then complete the statement.
• Account 1 compounds annually at a rate of 3.00%.
• Account 2 compounds monthly at a rate of 3.25%.
• Account 3 compounds weekly at a rate of 3.10%.
• Account 4 compounds daily at a rate of 3.15%.
Account
yields the highest annual interest rate at
The account that yields the highest annual interest rate is account 2.
Which account yields the highest annual interest rate?
In order to determine the account that yields the highest interest, the effective annual interest has to be calculated. The effective annual interest is the interest rate that an account actually earns when compounding is accounted for.
Effective annual rate = (1 + APR / m ) ^m - 1
M = number of compounding
Account 2: (1 + 0.0325/12)^12 - 1 = 3.3%
Account 3 : (1 + 0.0310 / 52)^52 - 1 = 3.15%
Account 4: (1 + 0.0315 /365)^365 - 1 = 3.2%
To learn more about the effective annual rate, please check: https://brainly.com/question/4064975
#SPJ1
What set of transformations could be applied to rectangle ABCD to create A″B″C″D″? 'Rectangle formed by ordered pairs A at negative 4, 2, B at negative 4, 1, C at negative 1, 1, D at negative 1, 2. Second rectangle formed by ordered pairs A double prime at 2, negative 4, B double prime 1, negative 4, C double prime at 1, negative 1, D double prime at 2, negative 1. Reflected over the x‒axis and rotated 180° Reflected over the y-axis and rotated 180° Reflected over the x‒axis and rotated 90° counterclockwise Reflected over the y-axis and rotated 90° counterclockwise
The set of transformations that could be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°
What is reflection?"It is a geometric transformation where all the points of an object are reflected on the line of reflection."
For the given question,
The Rectangle ABCD is formed by ordered pairs A at (-4, 2), B at (-4, 1), C at (-1, 1), D at (-1, 2)
The Rectangle A″B″C″D″ is formed by ordered pairs A" at (-4, -2), B" at (-4, -1), C" at (-1, -1) and D" at (-1, -2)
We can observe that the coordinates of ABCD are of the form (-x, y) where x, and y, are positive numbers
The form of the ordered pair of the vertices of the A″B″C″D″ will be (-x, -y)
The coordinates of the point (-x, y) after a reflection over the y-axis would be of the form (x, y)
And after rotation of 180°, the coordinates would be (-x -y).
Hence, the set of transformations that could be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°.
Learn more about geometric transformations here:
brainly.com/question/15577335
#SPJ1
The length of a rectangle is four times its width. The perimeter is 100 cm. What is the number of square centimeters in the area of the rectangle?
let width be 'x'
according to the question,
length = 4x
perimeter = 100 cm
we know ,
perimeter of rectangle = 2(l+b)
100= 2(4x+x)
100= 10x
x= 10
then length = 4x = 4×10= 40
and , area of rectangle = l×b
= 40 × 10 = 400
area of rectangle is 400cm
Answer:
Step-by-step explanation:
let width=x
length=4x
2(x+4x)=100
2×5x=100
x=100/10=10
width=10 cm
length=4×10=40 cm
area=l×b=40×10=400 cm²
Help!
The parallel circuit works if one connector works or both work.
Suppose that connectors work independently of each other and, further,
the probability of each component working is 0.84 and 0.72 respectively. What is the probability the parallel circuit works?
Now A and B are independent
Both connectors must work together to make the parallel circuit work
P(A and B)
P(A)*P(B)(0.84)(0.72)0.6048Connectors be C1 and C2
P(C1)=0.84P(C2)=0.72We need P(C1.C2)
Note the formula
For independent events
[tex]\boxed{\sf P(AB)=P(A)P(B)}[/tex]
[tex]\\ \tt{:}\dashrightarrow P(C1C2)=P(C1)P(C2)[/tex]
[tex]\\ \tt{:}\dashrightarrow 0.84(0.72)[/tex]
[tex]\\ \tt{:}\dashrightarrow 0.6[/tex]
Help with exercise
The number of calories in a 1.5-ounce chocolate bar is 225. Suppose that the distribution of calories is normally distributed with the standard deviation o = 10. a) What is the probability that a randomly selected chocolate bar will have between 200 and 220 calories? Show all your steps.
Hint use the z table and z score and formula Also use less than and grater sign correctly
b) What is the probability that a randomly selected chocolate bar will have less than 190 calories? Show all your steps.
The probability that a randomly selected chocolate bar will have between 200 and 220 calories is 3.97%
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The zscore is given a:
z = (raw score - mean) / standard deviation
mean = 225, standard deviation o = 10.
a) For x = 200:
z = (200 - 225) / 200 = -0.125
For x = 220:
z = (220 - 225) / 200 = -0.025
P(-0.125 < z < -0.025) = P(z < -0.025) - P(z < -0.125) = 0.4880 - 0.4483 = 3.97%
b) For x = 190:
z = (190 - 225) / 200 = -0.175
P(z < -0.025) = P(z < -0.175) = 0.4286
The probability that a randomly selected chocolate bar will have between 200 and 220 calories is 3.97%
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Determine if the following relations are functions. If not, explain.
Answer:
Graph 3 represents a function
Graph 4 is not a function
Step-by-step explanation:
By definition :
A function is a rule or law which relates all the elements of one set with some UNIQUE element of another set.
Which means that from a given value of the input x, there will be only one value of y in a function f(x) = y
Graphically it would represent that for a given point x , there would only be one value of y corresponding to that x.
In graph 4, we can see that for one x, there exists two values of y.
Example : at x = 5, we have y=5 AND y= -5; which is not possible in case of a function.
Consider the equation y = 12 – 3x.
Which of the following is a graph of this equation?
Answer:
second graph
Step-by-step explanation:
looking at the y intercept. 12 is y int
Answer:
Second line
Step-by-step explanation:
our equation rearranged is y=-3x+12
meaning that y-intercept is 12, that is where the line cuts the y axis
we find that the second line cuts the y axis around that 12 therefore it is the most relevant line here
solve for x
A:10 B:14.5 C:20 D:6÷3
By applying Cathetus theorem, the value of x is equal to 10 units.
How to determine the value of x?In order to determine the value of x, we would apply Cathetus theorem (leg rule), which states that each leg of a right-angled triangle is the geometric mean that's directly proportional between the hypotenuse and the part of the hypotenuse that's directly below the leg.
In this context, we have:
x² = m × a
x² = (21 + 4) × 4
x² = 25 × 4
x² = 100
x = √100
x = 10 units.
Read more on Cathetus theorem here: https://brainly.com/question/11357448
#SPJ1
URGENT! PLS ANSWER QUICK!!!!!!!!
Which best describes the relationship between the line that passes through the points (9, –5) and (5, –2) and the line that passes through the points (–4, –2) and (–8, 1)?
Since the lines have the same slopes, hence they are parallel lines
How to determine the relationship between linesWe can determine the relations by knowing the slopes of the line
For the line with coordinates (9, –5) and (5, –2)
Slope = -2+5/5-9
Slope = -3/4
For the line with coordinates (–4, –2) and (–8, 1)
Slope = 1+2/-8+4
Slope = -3/4
Since the lines have the same slopes, hence they are parallel lines
Learn more on parallel lines here: https://brainly.com/question/16742265
#SPJ1
You are flying a kite and have let out 30 feet of string but it got caught in an 8ft tree. What is the angle of elevation to the location of the kite? Show your work finding the angle of elevation and state the measure of the angle. You are flying a kite and have let out 30 feet of string but it got caught in an 8ft tree . What is the angle of elevation to the location of the kite ? Show your work finding the angle of elevation and state the measure of the angle . PLEASE SHOW ALL WORK !!!
Answer:
use a sin cos tan calculator.
Step-by-step explanation
on calculator
2nd tan
tan x = 30/8
there's ur answer
Need help with number 9 and number 10
Answer:
9. 3 acute angles
10: a) Acute Isosceles
b) Acute Scalene
Step-by-step explanation:
9: Sum of Interior angle theorem: Sum of the interior angles of a Triangle = 180°
An Acute angle is a angle that is less than 90°
the sum of the two acute angles must be less than 180°
The base angles of an isosceles triangle are congruent.
So For example,
the base angles of the isosceles are ∠1 and ∠2
Lets make the three angle measure closer:
if ∠1 = 46° then ∠2 also have to be 46° and ∠3 = 88°
all three angle are less than 90° and two angles are congruent.
What is the approximate area of a circle with a radius of 10 in?
[tex]\huge\boxed{\textsf{A.}\ 78.5\ \text{in}^2}[/tex]
Correction to your question text: diameter, not radius.
The area of a circle is given by:
[tex]A=\pi r^2[/tex]
The radius is half of the diameter.
[tex]A=\pi\cdot\left(\dfrac{10}{2}\right)^2[/tex]
Substitute and solve.
[tex]\begin{aligned}A&=\pi\cdot\left(\frac{10}{2}\right)^2\\&=\pi\cdot5^2\\&=\pi\cdot25\\&\approx\boxed{78.5}\end{aligned}[/tex]