Answer:
Step-by-step explanation:
Tough question.
Spiritual.
Love (if ever there was a misused word, it is love). I used to ask my classes what this sentence means "I love hunting." Try that one on. I don't know if you are dating someone, but how can you say "I love you." and "I love hunting." and not have something terribly wrong with the definition of the verb. One implies treasuring someone. The other means outfoxing a fox and murder.
Religion. Why are there so many different ones? The claim that there is only one true one makes the definition elusive to say the least. And it has caused a great deal of trouble.
==============================
Geometry: You have to know what a line segment is before you can say that one segment bears a relationship to another one.
You have to be able to define a point before you can calculate an intersection point of 2 lines or 2 curves or more.
You have to be able to define almost any term in geometry so that you can restrict enough to make it useful.
The ages of students in a school are normally distributed with a mean of 16 years and a standard deviation of 1 year. Using the empirical rule, approximately what percent of the students are between 14 and 18 years old?
Answer:
95% of students are between 14 and 18 years old
Step-by-step explanation:
First we calculate the Z-scores
We know the mean and the standard deviation.
The mean is:
[tex]\mu=16[/tex]
The standard deviation is:
[tex]\sigma=1[/tex]
The z-score formula is:
[tex]Z = \frac{x-\mu}{\sigma}[/tex]
For x=14 the Z-score is:
[tex]Z_{14}=\frac{14-16}{1}=-2[/tex]
For x=18 the Z-score is:
[tex]Z_{18}=\frac{18-16}{1}=2[/tex]
Then we look for the percentage of the data that is between [tex]-2 <Z <2[/tex] deviations from the mean.
According to the empirical rule 95% of the data is less than 2 standard deviations of the mean. This means that 95% of students are between 14 and 18 years old
A sequence of numbers a1, a2, a3, . . . is defined as follows: a1 = 3, a2 = 5, and every term in the sequence after a2 is the product of all terms in the sequence preceding it, e.g., a3 = (a1)(a2) and a4 = (a1)(a2)(a3). If an = t and n > 2, what is the value of an+2 in terms of t ?
(A) 4t (B) t^2 (C) t^3 (D) t^4 (E) t^8
Answer:
(D) t^4
Step-by-step explanation:
You have defined ...
a3 = a2·a1
a4 = a3·(a2·a1) = a3²
a5 = a4·(a3·a2·a1) = a4² = (a3²)² = a3⁴
Then if a3 = t, a5 = t⁴
Let's begin by understanding the given sequence and the pattern it follows.
We are given the initial terms:
a1 = 3
a2 = 5
For n > 2, the next term is defined as the product of all preceding terms. Therefore,
a3 = a1 * a2
a4 = a1 * a2 * a3
and so on.
Now, let's generalize this for any term an where n > 2. According to the problem, an = t.
The term immediately after an would be an+1, which equals the product of all preceding terms:
an+1 = a1 * a2 * a3 * ... * an-1 * an
Since an = t, and every term before it has been multiplied to give t (by definition of the sequence), we have:
an+1 = t * t
an+1 = t^2
Now, let's find an+2. This term is the product of all preceding terms, which now includes an+1:
an+2 = a1 * a2 * a3 * ... * an-1 * an * an+1
From above, we know an = t and an+1 = t^2. Hence:
an+2 = t * t^2
an+2 = t^3
Therefore, the value of an+2 in terms of t is t^3. The correct answer is (C) t^3.
WANT FREE 20 POINTS + BRAINLIEST? answer this geometry question correct and i got you
Which statements are true based on the diagram? Select three options.
A. Points N and K are on plane A and plane S.
B. Points P and M are on plane B and plane S.
C. Point P is the intersection of line n and line g.
D. Points M, P, and Q are noncollinear.
E. Line d intersects plane A at point N.
Answer:
the three options i chose:
A. n and k are on plane A and s
C. p is the inteersection of n and g
D. those 3 lines are noncollinear
Answer:
The correct options are A, C and D.
Step-by-step explanation:
From the given figure it is clear that points N and K lie on the line f, and line f is the intersection line of plane A and S.
So, points N and K are on plane A and S. Option A is correct.
Points P and M lie on the line n, and line n is not the intersection line of plane B and S.
We clearly see that point M is not on the plane S.
So, option B is incorrect.
Point P is the intersection of line n and line g.
So, option C is correct.
Point M and P lie on line n and point P and Q lie on line g.
Three points are collinear if they are lie on a straight line.
Since points M, P and Q are not collinear, therefore they are noncollinear.
So, option D is correct.
Line d intersects plane A at point L.
So, option E is incorrect.
A box at a miniature golf course contains contains 4 red golf balls, 8 green golf balls, and 7 yellow golf balls. What is the probability of taking out a golf ball and having it be a red or a yellow golf ball? Express your answer as a percentage and round it to two decimal places.
Answer:
=57.89%
Step-by-step explanation:
The total number of golf ball is 4+8+7 = 19
P (red or yellow) = number of red or yellow
------------------------------------
total number of golf balls
= 4+7
-----
19
=11/19
Changing this to a percent means changing it to a decimal and multiplying by 100%
= .578947368 * 100%
=57.8947368%
Rounding to two decimal places
=57.89%
The probability of drawing a red or yellow golf ball from the box can be calculated by dividing the total number of red and yellow balls (11) by the total number of balls in the box (19), resulting in a probability of 11/19 or approximately 57.89%.
Explanation:To calculate the probability of drawing a red or yellow golf ball from the box, we first need to figure out the total number of balls in the box. This is found by adding up the number of each color of balls: 4 red balls + 8 green balls + 7 yellow balls = 19 total balls.
Next, we consider the total number of red and yellow balls, which is 4 red + 7 yellow = 11.
To find the probability, we divide the number of desired outcomes (red or yellow balls) by the total number of outcomes (total balls). So, the probability is 11/19.
To express this as a percentage rounded to two decimal places, we can multiply the result by 100, which gives us approximately 57.89%. So, there is a 57.89% chance of drawing a red or yellow ball from the box.
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A rancher has 800 feet of fencing to put around a rectangular field and then subdivide the field into 2 identical smaller rectangular plots by placing a fence parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms.
Answer:
The dimensions of enclosed area are 200 and 400/3 feet
Step-by-step explanation:
* Lets explain how to solve the problem
- There are 800 feet of fencing
- We will but it around a rectangular field
- We will divided the field into 2 identical smaller rectangular plots
by placing a fence parallel to one of the field's shorter sides
- Assume that the long side of the rectangular field is a and the
shorter side is b
∵ The length of the fence is the perimeter of the field
∵ We will fence 2 longer sides and 3 shorter sides
∴ 2a + 3b = 800
- Lets find b in terms of a
∵ 2a + 3b = 800 ⇒ subtract 2a from both sides
∴ 3b = 800 - 2a ⇒ divide both sides by 3
∴ [tex]b=\frac{800}{3}-\frac{2a}{3}[/tex] ⇒ (1)
- Lets find the area of the field
∵ The area of the rectangle = length × width
∴ A = a × b
∴ [tex]A=(a).(\frac{800}{3}-\frac{2a}{3})=\frac{800a}{3}-\frac{2a^{2}}{3}[/tex]
- To find the dimensions of maximum area differentiate the area with
respect to a and equate it by 0
∴ [tex]\frac{dA}{da}=\frac{800}{3}-\frac{4a}{3}[/tex]
∵ [tex]\frac{dA}{da}=0[/tex]
∴ [tex]\frac{800}{3}-\frac{4}{3}a=0[/tex] ⇒ Add 4/3 a to both sides
∴ [tex]\frac{800}{3}=\frac{4}{3}a[/tex] ⇒ multiply both sides by 3
∴ 800 = 4a ⇒ divide both sides by 4
∴ 200 = a
- Substitute the value of a in equation (1)
∴ [tex]b=\frac{800}{3}-\frac{2}{3}(200)=\frac{800}{3}-\frac{400}{3}=\frac{400}{3}[/tex]
* The dimensions of enclosed area are 200 and 400/3 feet
Jemmma has 24 balls. Out of the 24 balls, 12 are yellow, 4 are pink, and the rest are red. What ratio of the number of red balls to the number of balls that are either yellow or pink?
ΔABC is a right triangle in which ∠B is a right angle, AB = 1, AC = 2, and BC = sqrt(3).
cos C × sin A =
I think the answer is 3/4, because cos(c) = adj / hypot and sin(a) = opposite / hypot
cos(c) = sqrt(3) / 2
sin(a) = sqrt(3) / 2
which is 3/4 when multiplied.
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
cosC = cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex]
sinA = sin60° = cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]
Hence
cosC × sinA = [tex]\frac{\sqrt{3} }{2}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] = [tex]\frac{3}{4}[/tex]
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Since,
[tex]\sin \theta=\frac{Opposite leg of }\theta}{\text{Hypotenuse}}[/tex]
[tex]\cos \theta=\frac{Adjacent leg of }\theta}{\text{Hypotenuse}}[/tex]
Given,
In triangle ABC,
AB = 1 unit, AC = 2 unit, and BC = √3 unit
Thus, by the above formule,
[tex]\cos C = \frac{\sqrt{3}}{2}[/tex]
[tex]\sin A=\frac{\sqrt{3}}{2}[/tex]
[tex]\implies \cos C\times \sin A = \frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}= \frac{3}{4}[/tex]
Find the equation of the line that passes through ( 4 , 1 ) and is parallel to the line passing through ( 7 , 11 ) and ( 10 , 20 ) .
Answer:
[tex]y-1=3(x-4)[/tex] -----> equation into point slope form
[tex]y=3x-11[/tex] -----> equation into slope intercept form
[tex]3x-y=11[/tex] -----> equation in standard form
Step-by-step explanation:
we know that
If two lines are parallel, then their slopes are the same
step 1
Find the slope of the line passing through ( 7 , 11 ) and ( 10 , 20 )
The slope m is equal to
[tex]m=(20-11)/(10-7)=3[/tex]
step 2
Find the equation of the line with m=3 that passes through (4,1)
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
substitute
[tex]y-1=3(x-4)[/tex] -----> equation into point slope form
Convert to slope intercept form
[tex]y=mx+b[/tex]
isolate the variable y
[tex]y=3x-12+1[/tex]
[tex]y=3x-11[/tex] -----> equation into slope intercept form
Convert to standard form
[tex]Ax+By=C[/tex]
[tex]3x-y=11[/tex] -----> equation in standard form
The slope of the given line passing through (7, 11) and (10, 20) is 3. Since parallel lines have equal slopes, the line passing through (4, 1) will also have a slope of 3. Plugging in the slope and point into the slope-intercept form, we find the equation of the line to be y = 3x - 11.
To find the equation of the line that passes through the point (4, 1) and is parallel to another line, we first need to determine the slope of the given line that passes through (7, 11) and (10, 20).
The slope of a line is found by taking the difference in the y-coordinates divided by the difference in the x-coordinates between two points on the line, which is often expressed as Δy/Δx or (y2-y1)/(x2-x1).
The slope of the line passing through (7, 11) and (10, 20) is calculated as follows:
Δy = 20 - 11 = 9
Δx = 10 - 7 = 3
Slope (m) = Δy/Δx = 9/3 = 3
Since parallel lines have the same slope, the line passing through (4, 1) will also have a slope of 3.
The equation of a line in slope-intercept form (y = mx + b) can then be used, where 'm' is the slope and 'b' is the y-intercept.
As we have the slope and a point on the line, we can substitute them into the equation to solve for 'b'.
The equation will look like this:
y = mx + b
1 = 3(4) + b
1 = 12 + b
b = 1 - 12
b = -11
The equation of the line that goes through (4, 1) and is parallel to the line through (7, 11) and (10, 20) is therefore y = 3x - 11.
Compare the functions below: Which function has the smallest minimum?
A. F(x)
B. G(x)
C. H(x)
D. All three functions have the same minimum value
Answer:
D. All three functions have the same minimum value
Step-by-step explanation:
f(x) = -3 sin (x-pi) +2
Sin has a minimum value of -1, but since it is multiplied by a negative, we want its maximum value
sin has a maximum of 1
f (min) = -3(1) +2 = -1
g(x) has a minimum at x =3
g(minimum) = -1
h(x) = (x+7)^2 -1
The smallest a squared value can be is zero
= 0 -1
h(min) =-1
Answer:
D. All three functions have the same minimum value
Step-by-step explanation:
Just did this :)
The length of each side of a square increases by 2.5 inches to form a new square with a perimeter of 70 inches. The length of each side of the original square was inches.
Check the picture below.
Answer:
15
Step-by-step explanation:
70 = 4 x (a + 2.5)
70 = 4a + 10
70-10 = 4a
60 ÷ 4 = a
15= a
f(x)=8−4x−x^3
g(x)=x^2+7x−9
Find f(x)+g(x).
Select one:
a. x^3+x^2+3x−1
b. −x^3+x+3x−1
c. −x^3+x^2+11x−9
d. 8x^2+3x−9x^3
Answer:
its answer is -x^3+x^2+3x-1
Step-by-step explanation:
f(x) +g(x)
= 8-4x-x^3+x^2+7x-9
= -x^3+x^2+3x-1
Answer:
The value of f(x)+g(x) is [tex]-x^3+x^2+3x-1[/tex].
Step-by-step explanation:
The given functions are
[tex]f(x)=8-4x-x^3[/tex]
[tex]g(x)=x^2+7x-9[/tex]
We have to find the value of f(x)+g(x).
[tex]f(x)+g(x)=(8-4x-x^3)+(x^2+7x-9)[/tex]
[tex]f(x)+g(x)=8-4x-x^3+x^2+7x-9[/tex]
On combining like terms we get
[tex]f(x)+g(x)=-x^3+x^2+(-4x+7x)+(8-9)[/tex]
On simplification we get
[tex]f(x)+g(x)=-x^3+x^2+3x-1[/tex]
Therefore the value of f(x)+g(x) is [tex]-x^3+x^2+3x-1[/tex].
In a survey, adults and children were asked whether they prefer hamburgers or pizza. The survey data are shown in the relative frequency table.
About 60% of adults prefer pizza.
Compare this with the percentage of children who prefer pizza.
Hamburgers Pizza Total
Adults 0.24 0.36 0.60
Children 0.11 0.29 0.40
Total 0.35 0.65 1.00
Select the true statement.
A. A smaller percentage of children (43%) prefer pizza.
B. A smaller percentage of children (30%) prefer pizza.
C. A greater percentage of children (about 70%) prefer pizza.
D. A greater percentage of children (64%) prefer pizza.
The 60% of adults who like pizza was found by dividing the adults who like pizza ( 0.36) by the total adults ( 0.60): 0.36 / 0.6 = 0.6 = 60%
To find the percent of children that like pizza divide 0.29 by 0.40:
0.29 / 0.40 = 0.725 = 72.5%, which is about 70%
The answer would be C. A greater percentage of children (about 70%) prefer pizza.
The percentage of children that prefer pizza are about 70%, which is Option(c) .
What is percentage?A relative figure reflecting hundredth parts of any quantity is called a percentage.
How to calculate percentage?Determine the total amount of quantity.Find the amount of which you want to find percentage.Divide them both and multiply by 100Children who like pizza = 0.29
Total No. of children = 0.40
Percentage of children who like pizza = (0.29 / 0.40) * 100
Percentage = 72.5% (about 70%)
The percentage of children who like pizza are about 70%(Option - c)
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Huixian needs to pack 171 pens, 63 pencil, and 27 erasers into identical bags so that each item is equally distributed among the gift bags. Find the largest number of gift bags that can be packed, and the number of each item in a gift bag
Answer:
87 gift bags
Step-by-step explanation:
Answer:
6 pens
2 pencils
1 eraser in each gift bag
Most number of Gift Bags = 27.
Step-by-step explanation:
There will be some bags left over. The limiting factor is the erasers. At most, you can have 27 erasers and therefore 27 gift bags.
171 pens: 171/27 = 6 (you have to round down). The number of pens left over is 9.
(27*6 = 162)
171 - 162 = 9
63 Pencils: 63/27 = 2 pencils per gift bag. There will be
63 - 2*27
63 - 54
9 pencils will be left over.
What is the difference between the GCF and LCM?
Answer:
GCF -The greatest real number shared between two integers. On the other hand, the Lowest Common Multiple (or LCM) is the integer shared by two numbers that can be divided by both number.
Step-by-step explanation:
Jake wanted to measure the height of the Great Sphinx of Giza. He placed a mirror on the ground and then walked backwards until he was able to see the top of the statue in the mirror. If his eyes were 5.5 feet above the ground, how tall is the statue, to the nearest foot?
Answer:
65
Step-by-step explanation:
Jake measured the height of the Great Sphinx of Giza by using a mirror and the Law of Reflection. Doubling the height of the mirror gives us an approximation of the statue's height.
Explanation:In order to measure the height of the Great Sphinx of Giza, Jake used the concept of the Law of Reflection.
He placed a mirror on the ground and walked backwards until he could see the top of the statue in the mirror.
If his eyes were 5.5 feet above the ground, the mirror's height would be equal to half the height of the statue.
Since Jake's eyes are at a height of 5.5 feet, the distance from the ground to the top of the mirror should also be 5.5 feet.
Therefore, the height of the Great Sphinx of Giza can be calculated by doubling the height of the mirror, which gives us 11 feet.
So, the approximate height of the statue is 11 feet.
Bina kept a list of her expenses and income for one month. If she started the month with no money, how much money did she have left at the end of the month?
Answer:
Step-by-step explanation:
Income less expenses
Answer:
15
Step-by-step explanation:
i got it right pls mark brainliest
Find the value for tan θ given the point (-3, 4) on the terminal side. Leave your answer in fraction form
Find the value for sec θ given the point (-3, 4) on the terminal side. Leave your answer in fraction form.
Answer:
Step-by-step explanation:
The point (-3, 4) is in QII. If we plot this point and drop an altitude then connect the point to the origin, we have a right triangle with side opposite measuring 4 units and side adjacent measuring |-3|. The tangent of the reference angle is the ratio side opposite/side adjacent, so
[tex]tan\theta=-\frac{4}{3}[/tex]
Since secant is the reciprocal of cosine, let's find the cosine of the reference angle and then flip it upside down. The cosine of the angle is the side adjacent (got it) over the hypotenuse (don't have it). We can find the hypotenuse using Pythagorean's Theorem:
[tex]c^2=-3^2+4^2[/tex] s0
[tex]c^2=25[/tex] and
c = 5
The cosine of the angle theta is
[tex]cos\theta=-\frac{3}{5}[/tex]; therefore,
[tex]sec\theta=-\frac{5}{3}[/tex]
The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the population mean. He selects and weighs a random sample of 49 trucks and finds the mean weight is 15.8 tons. The population standard deviation is 3.8 tons. What is the 95% confidence interval for the population mean?
Answer:
(14.7 , 16.9)
Step-by-step explanation:
it is given that [tex]\bar{x}=15.8[/tex] tons
σ=3.8 tons
n=49
at 95% confidence level α=1-.95=0.05
[tex]z_\frac{\alpha }{2}=z_\frac{0.05}{2}=z_{0.025}\\[/tex]
=1.96 ( from the standard table)
at 95% confidence level the coefficient interval for μ is
[tex]\bar{x}\pm z_\frac{\alpha }{2}\times \frac{\sigma }{\sqrt{n}}[/tex]
[tex]15.8\pm 1.96\times \frac{3.8}{ \sqrt{49}}[/tex]
[tex]15.8\pm 1.1[/tex]
(14.7, 16.9)
Please help!! If you really love math!! 50 POINTS!!!!!!
Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are added together, the x term is eliminated?
1/5x + 3/4y = 9
2/3x - 5/6y = 8
A: –10 times the first equation and 3 times the second equation
B: 10 times the first equation and 3 times the second equation
C: –3 times the first equation and 5 times the second equation
D: 3 times the first equation and 5 times the second equation
The multipliers of this system of equations have been determined to create opposite terms of the x-variable.
12(-1/6x - 2/3y = -5 )--------> -2x-8y=-60
5(2/5x + 1/5y = -9)----------> 2x+y=-45
What is the value of y?
A: –30
B:–15
C: 15
D: 30
Examine the system of equations. Which is an equivalent form of the first equation that when added to the second equation eliminates the y terms?
-5x + 3/4y = 12
8x + 12y = 11
A: 10x – 12y = –192
B:–10x + 12y = 192
C: 5x – 12y = 96
D: –5x + 12y = 96
Answer:
A: –10 times the first equation and 3 times the second equationC: 15none of the choices shown. Should be 80x -12y = -192Step-by-step explanation:
1. The multiplier for the first equation can be found by the ratio ...
-(second equation x-coefficient)/(first equation x-coefficient)
= (-2/3)/(1/5) = -10/3
This tells you that multiplying the first equation by -10 and the second equation by 3 will make the x-terms cancel. Matches selection A.
__
2. Adding the two equations shown gives ...
(-2x -8y) +(2x +y) = (-60) +(-45)
-7y = -105
y = -105/-7 = 15 . . . . matches selection C.
__
3. Using the rule shown in question 1, the multiplier for the first equation will be ...
-(second equation y-coefficient)/(first equation y-coefficient)
-12/(3/4) = -16
Multiplying the first equation by -16 gives ...
-16(-5x +3/4y) = -16(12)
80x -12y = -192 . . . . no matching answer choice
(Sometimes, the problems have errors in their answers. This is one of those times. Choice A will probably be graded as correct, even though it is not.)
What is the discontinuity of the function f(x) = the quantity of x squared minus 4 x minus 12, all over x plus 2?
A. (−6, 0)
B. (6, 0)
C. (−2, −8)
D. (2, −4)
Answer:
C. (-2, -8)
Step-by-step explanation:
The function reduces to ...
f(x) = (x^2 -4x -12)/(x +2) = (x -6)(x +2)/(x +2) = x -6 . . . . x ≠ -2
At x=-2, the function would evaluate to ...
f(-2) = -2 -6 = -8
but cannot, because there is a hole in the function definition at that point.
There is a hole at (-2, -8).
Identify the area of the figure rounded to the nearest tenth. HELP PLEASE!!
This is equivalent to an 11x15 rectangle with 2 circles each of radius 2cm cut out of it (4 semi-circles = 2 circles in area).
11x11 rectangle = 165cm^2 area.
2 circles of 2cm radius = 2*4pi = 8pi = 25.13
165 - 25.13 = 139.87 [tex]\approx[/tex] 139.9 [tex]cm^2[/tex] (A)
Answer:
139.9
Step-by-step explanation:
First find the area of the circles.
A = pi*r^2
So pi*2^2
2^2 = 4
4*pi = 12.57
Then divide 12.57 by 2 because its only half a circle.
12.57/2 = 6.285
Then multiply 6.285 by 4 since there are 4 half circles.
6.285*4 = 25.14
Now find the area of the square.
A = lw
A= 15*11
A = 165
Now subtract 165 and 25.14.
165 - 25.14 = 139.86
Now round 139.86 to the nearest tenth
So 139.9
Drag each label to the correct location on the chart.
Classify the expressions based on whether they represent real numbers or complex numbers.
The numbers are √(-5)^2, 400, -9+10i^2, 0+5i, i^8, √-16, -2+6i, and √10
Thank you!
Answer:
Step-by-step explanation:
Can someone help me with this math question WILL GIVE 20 POINTS. By the way it’s not 51.496
Below is the formula for the circumference of a circle
C = 2πr
This question gives us the diameter. To find the radius (r) you would divide the diameter by two like so...
16.4/ 2 = 8.2
Plug what you know into the formula and solve...
π = 3.14
r = 8.2
C = 2(3.14)(8.2)
C = 6.28(8.2)
C = 51.496
In the question it asks to round to the nearest tenth like so...
51.5
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
Step-by-step explanation:
51.496 rounded to the nearest tenth is 51.5
VWX and NOP are similar. If mV = 44° and mP = 66°, what is
mW?
A.
22°
B.
33°
C.
35°
D.
70°
Answer:
D. 70 degrees.
Step-by-step explanation:
Because the 2 triangles are similar corresponding angles are congruent.
So m < P = m< X = 66 degrees.
And since there are 180 degrees in a triangle:
m < W = 180 - (m < V + m < X)
= 180 - (44 + 66)
= 70 degrees.
The measure of the angle ∠W is 70°.
What is triangle?A triangle is a two - dimensional figure with three sides and three angles.
The sum of the angles of the triangle is equal to 180 degrees.
∠A + ∠B + ∠C = 180°
Given is that two sides of a triangle measure 7 feet and 19 feet.
Since the triangles VWX and triangle NOP are similar, we can say that the corresponding angles of both triangles is same.
∠W = ∠O
Also -
∠O + ∠N + ∠P = 180
∠O = 180 - 110
∠O = 70°
∠W = ∠O = 70°
Therefore, the measure of the angle ∠W is 70°.
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Given: ∠LKM ≅ ∠JKM
∠LMK ≅ ∠JMK
Prove: ∆LKM ≅ ∆JKM
Which method can you use to prove these triangles congruent?
the ASA Postulate
the SAS Postulate
the HL Theorem
the AAS Theorem
Answer:
ASA
Step-by-step explanation:
Answer: the ASA Postulate
Step-by-step explanation:
In the given picture , we have two triangles ∆LKM and ∆JKM , in which we have
[tex]\angle{LKM}\cong\angle{JKM}\\\\\angle{LMK}\cong\angle{JMK}[/tex]
[tex]\overline{KM}\cong\overline{KM}[/tex] [common]
By using ASA congruence postulate , we have
∆LKM and ∆JKM
ASA congruence postulate tells that if two angles and the included side of a triangle are congruent to two angles and the included side of other triangle then the triangles are congruent.
Graph the parametric equation x = 2t y = t + 5, -2 ≤ t ≤ 3
Just fun I'm going to add something above the below.
You can write an equation for this without the parameter.
You have y=t+5 and x=2t. If you multiply both sides of y=t+5 by 2 you should get 2y=2t+10 and guess what you can replace 2t with x since you have x=2t. So you can write 2y=x+10 as your equation to represent the parametric version they have here.
This is a linear equation as our graph appears to be below. Solve for y by dividing both sides by 2 gives you y=x/2 +5. The slope is 1/2 and the y-intercept is 5. If t is between -2 and 3 then x is between -4 and 6 since x is doubled t (inclusive here since we have those equal signs along with those inequalities).
So you could have just graph the line y=x/2+5 on the interval [tex]-4 \le x \le 6 [/tex]/
Anyways, I'm also going to look at this without the rewrite:
I'm going to make a table with 4 columns. The first column is t. The second is x(t), the third is y(t), and the fourth will be a list of points (x,y) our relation will go through).
t | x(t) | y(t) | (x,y)
------------------------------------------------------
-2 2(-2)=-4 -2+5=3 (-4,3)
-1 2(-1)=-2 -1+5=4 (-2,4)
0 2(0)=0 0+5=5 (0,5)
1 2(1)=2 1+5=6 (2,6)
2 2(2)=4 2+5=7 (4,7)
3 2(3)=6 3+5=8 (6,8)
Now I'm going to graph the points in the last column on a coordinate-plane.
The horizontal axis is your x-axis and the vertical axis is your y-axis. I did the x-axis going up or down by two's while the y-axis is going up and down only by one's.
Solve sin θ+1= cos2θ on the interval 0≤ θ<2 pi.
Show work
Answer:
[tex]\theta \in \{0,\pi,\frac{7\pi}{6},\frac{11\pi}{6}\}[/tex]
Step-by-step explanation:
[tex]\sin(\theta)+1=\cos(2\theta)[/tex]
Applying double angle identity:
[tex]\cos(2\theta)=1-2\sin^2(\theta)[/tex]
Doing so would give:
[tex]\sin(\theta)+1=1-2\sin^2(\theta)[/tex]
We need to get everything to one side so we have 0 on one side.
Subtract 1 on both sides:
[tex]\sin(\theta)=-2\sin^2(\theta)[/tex]
Add [tex]2\sin^2(theta)[/tex] on both sides:
[tex]\sin(\theta)+2\sin^2(\theta)=0[/tex]
Let's factor the left-hand side.
The two terms on the left-hand side have a common factor of [tex]\sin(\theta)[/tex].
[tex]\sin(\theta)[1+2\sin(\theta)]=0[/tex].
This implies we have:
[tex]\sin(\theta)=0 \text{ or } 1+2\sin(\theta)=0[/tex].
We need to solve both equations.
You are asking they be solved in the interval [tex][0,2\pi)[/tex].
[tex]\sin(\theta)=0[/tex]
This means look at your unit circle and find when you have your y-coordinates is 0.
You this at 0 and [tex]\pi[/tex]. (I didn't include [tex]2\pi[/tex] because you don't have a equal sign at the endpoint of [tex]2\pi[/tex].
Now let's solve [tex]1+2\sin(\theta)=0[/tex]
Subtract 1 on both sides:
[tex]2\sin(\theta)=-1[/tex]
Divide both sides by 2:
[tex]\sin(\theta)=\frac{-1}{2}[/tex]
Now we are going to go and look for when the y-coordinates are -1/2.
This happens at [tex]\frac{7\pi}{6}[/tex] and [tex]\frac{11\pi}{6}[/tex].
The solution set given the restrictions is
[tex]\theta \in \{0,\pi,\frac{7\pi}{6},\frac{11\pi}{6}\}[/tex]
Which is the correct awnser ?
Answer:
△ABC ~ △DEF
Step-by-step explanation:
the AA (angle angle) postulate is a postulate that says two triangles can be similar if they have two congruent angles. using this postulate with how each triangle has a 90° angle and ∠F is congruent to ∠C, we can determine that △ABC ~ △DEF.
The correct answer is C. OBC DE because of the definition of similarity in terms of similarity transformations.
A similarity transformation is a transformation that maps a figure onto a similar figure. A similar figure is a figure that has the same shape as the original figure, but may be a different size and orientation.
A rigid transformation is a transformation that maps a figure onto a congruent figure. A congruent figure is a figure that has the same size and shape as the original figure.
Since a series of rigid transformations maps F onto C where F is congruent to C, then the rigid transformations must have preserved the shape and size of F. This means that the rigid transformations must have been similarity transformations.
Therefore, the statement "OBC DE because of the definition of similarity in terms of similarity transformations" is true.
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HELPPPP!!!!
Which model does the graph represent?
Answer:
C. y = Ae^(-(x-b)²/c)
Step-by-step explanation:
A is a model of exponential growth.
B is a model of exponential decay.
D is a "logistic function" model of growth in an environment of limited resources. It produces an "S" shaped curve.
The given bell-shaped curve can be described by the function of C, which decays either side of an axis of symmetry.
The model that the graph represent is C that is y = Ae^(-(x-b)²/c).
A is an exponential growth model.
B is an exponential decay model.
D is a "logistic function" model of growth in a resource-constrained setting. It results in a "S" shaped curve.
The function of C, which decays either side of an axis of symmetry, can be used to describe the provided bell-shaped curve.
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What is the end behavior of the graph of the polynomial function f(x)=-x^5+9x-4
Answer:
Because it's an odd function, the "tails" go off in different directions. Also, because it's a negative function, the left starts from the upper left and the right goes down into negative infinity. If it was a positive, the tails would be going in the other directions, meaning that the left would come up from negative infinity and the right would go up into positive infinity.
Step-by-step explanation:
Answer:
C on Edge: As x--> -∞, y-->+∞ and as x-->+∞, y-->-∞
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