For triangle DEF, angle D = 42 degrees, line e = 30 meters and line d = 25 meters. Determine the number of possible triangles that can be constructed. Show work.
Answers
Answer:
2 triangles
Step-by-step explanation:
The given angle is opposite the shorter of the given sides, so the number of triangles is 2. (30/25·sin(42°) ≈ 0.8 < 1)
_____
Additional comment
For the case where the shorter given side is opposite the given angle, there is the possibility that the triangle could be a right triangle (1 solution) or that there may be no solutions. You can tell the difference by computing ...
(long side)/(short side) × sin(given angle)
If this result is exactly 1, the triangle is a right triangle. If it is greater than 1, the triangle cannot exist (no solutions). Since the sines of most angles are irrational, it is unlikely you will see this result be exactly 1 (except for a 30°-60°-90° right triangle).
These observations are a consequence of the Law of Sines, which tells you ...
sin(A) = (a/b)sin(B)
For real angles, sin(A) ≤ 1.
Related Questions
I would like to have some help please! ❤ thank youu I need help on the 2 question that is "write three expressions containing exponentz so that each expression equals 81."
Answers
Answer:
Below
Step-by-step explanation:
Notice that 81 = 9 * 9
So here is the first expression:
● 9^2
9 is 3^2 so 9^2 is 3^4
That's another expression
● 3^4
81 = 9*9 = 3*3*3*3 = 3^3 *3
That's another expression
● 3*3^3
You can keep manipulating the product and create many expressions like:
● 3^2 * 3^2
● 9 * 3^2
Or 27 times 3 with an exponent of one
Or 5 squared plus 56
calculate the size of angle x. the sides are 8cm, 11cm and 15cm
Answers
Answer:19.93
Step-by-step explanation:
11 x 8 x 15 = 1320
then u would simplify
The value is: angle x is approximately 103.95 degrees.
Here, we have,
To calculate the size of angle x, you can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.
In this case, the sides of the triangle are given as follows:
a = 8 cm (adjacent to angle x)
b = 11 cm (opposite to angle x)
c = 15 cm (hypotenuse)
The Law of Cosines states:
c² = a²+ b² - 2ab*cos(x)
Substituting the given values:
15² = 8² + 11² - 2(8)(11)*cos(x)
225 = 64 + 121 - 176*cos(x)
Simplifying:
225 = 185 - 176*cos(x)
Rearranging the equation:
176cos(x) = 185 - 225
176cos(x) = -40
Now, divide both sides by 176 to isolate the cosine term:
cos(x) = -40/176
cos(x) ≈ -0.2273
To find the value of angle x, take the inverse cosine (cos⁻¹) of -0.2273:
x ≈ cos⁻¹(-0.2273)
x ≈ 103.95 degrees
Therefore, angle x is approximately 103.95 degrees.
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Please answer ASAP
Randomly pick 6 points from a square of side = 1. Show that you can always find 2 points from these 6 that their distance is less or equal to [tex]\frac{\sqrt{2} }{2} }[/tex]
Randomly pick 5 points from a sphere. Show that you can always find a closed semi-sphere ( half a sphere and boundary) that contains 4 points.
Answers
Problem 1.
My thinking is that the furthest you can get is have two points at each opposite corner, so the distance between them is sqrt(2). If we have two other points with this property, then all four corners are filled up. It is possible to pick two points where the distance is 1 unit.
Then a fifth point can be placed at the center such that the distance from it to any of the corners is sqrt(2)/2. We placed the fifth point at the center to try to get as far away as possible from the other four points.
Basically we're trying to find the worst case scenario (leading to the largest distance possible) and seeing how we can fill up the square. This establishes the upper bound. Any other kind of scenario will have a distance less than the upper bound.
===================================================
Problem 2.
For this one, I'm not sure what to make of it. The terminology is a bit strange so I'm not going to be fairly helpful here. Sorry about that.
If I had to guess, I'd assume it has something to do with the fact that a plane is uniquely defined by 3 points. That fourth point is not coplanar with the other three, which helps define the semi-spherical portion. The fifth point is just extra. The points can't be all collinear or else a plane won't form. Though to be honest, I'm still not sure about problem 2. I'd get a second opinion.
URGENT!!! REALLY NEED HELP!!!
FIRST *CORRECT* ANSWER WILL BE BRAINLIST!!!!!
The bar graph shows the percent of students that chose each drink in the school
cafeteria. Which statement about the graph is true?
Answers
Answer:
1st option
Step-by-step explanation:
Because .3*300=90
.3=30%
Answer:
If 300 lunches were served, then 90 chose milk (7).
Step-by-step explanation:
To determine that this is the correct answer, you can just divide 90/300, which is equal to 0.3 or 30%. When you look at the graph, you can see that "milk" is equal to 30%, so this statement is true.
What is the value of y?
Answers
Answer:
63 degrees
Step-by-step explanation:
(180-54)/2=126/2=63
Answer:
The value of y is 63
Step-by-step explanation:
The sum of angles in a triangle is 180°.
The angles in the triangle are 54°, y°, y°
Sum of angles in the triangle = 54° + y° + y° = 54 + 2y°
To find y, equate the sum of the angles in the triangle to 180°
54° + 2y° = 180°
2y° = 180° - 54°
2y° = 126°
y = 126/2 = 63
Find the perimeter of the triangle
Answers
Answer:
26 units
Step-by-step explanation:
Answer:
657.88 i guess becuz by using pythagoras i got 320 for the hypotenous
The tee for the fifth hole on a golf course is 355 yards from the tee. On that hole, Marsha hooked her ball to the left, as sketched below. Find the distance between Marsha’s ball and the hole to the nearest tenth of a yard.
Answers
Answer:
184
Step-by-step explanation:
You buy a new computer for $1,500. The value of the computer decreases by 6%
every year. How much is the computer worth after 4 years?
$999.80
$1,171.05
$1,008.50
$1,225.35
Answers
Answer:
$1171.05
Step-by-step explanation:
1500 × (1-(6 / 100))⁴
Answer:
Hey there!
Each year, the computer is (100-6), or 94% of it's original value.
Thus, we have:
Original: 1500
First year: 1500(0.94)
Second year: 1500(0.94)(0.94)
Third year: 1500(0.94)(0.94)(0.94)
Fourth year: 1500(0.94)(0.94)(0.94)(0.94)
Fourth year: 1171 dollars.
Hope this helps :)
Tyler needs to get the windows in his new home cleaned. The cleaning company needs to know the total number of window panes before it can tell him how much the job will cost. There are 12 windows, each with four window panes across and four window panes down. Tyler can find the total number of window panes by multiplying the number of windows by the number of panes in each window. The total number of window panes is an expression with a whole-number exponent. Write an expression with exponents to find the total number of panes in 12 windows.
Answers
Answer:
I believe it's (4^2)*12
Step-by-step explanation:
To find the correct amount of the window panes there are, we have to find how much window pains are in each of the window's. So we have a 4 by 4 so that's 16. Then we have to do 16*12 to get the total amount of panes since Panes Per Window multiplied by Number Of Windows equals Total Number Of Panes
Hope this helps! ∪ω∪
HELP ME PLEASE !! A duck paddles 4 yards downstream in 24 seconds. It takes the duck 40 seconds to paddle the same distance upstream. How fast can the duck paddle in still water ? What is rate of the current? Duck speed: _____ Current: ________ And if possible you can show me the steps?
Answers
Answer:
1. duck will travel in still water paddles 4 yards = 38,7 sec
up stream speed = 0,63 mph
down stream speed = 0,68 mph
What is 22% of $900?
Answers
Answer:
198
Step-by-step explanation:
Of means multiply and 22% as a decimal is 0.22, so multiply 0.22 by 900.
900*0.22=198
Answer:
198
Step-by-step explanation:
22% of 900
of means multiply
22% * 900
Change to decimal form
.22 * 900
198
Help me throughout this question please!!!!!!
Answers
[tex] \cos(2A)=\cos^2 A-\sin^2A=(\cos A+ \sin A)(\cos A-\sin A)[/tex]
substitute the second term in LHS to get
[tex]{ (\cos A - \sin A)^2 \over \cos(2A))}[/tex]
expand the square, [tex] \frac{1-2\sin A \cos A}{\cos 2A}= \sec2A- \tan 2A[/tex]
([tex] \sin (2\theta)=2 \sin\theta\cos\theta[/tex])
Answer:
Both sides can take the same identity
Step-by-step explanation:
Sec 2A - tan 2A
Express with sin and cos
1/cos (2A) - sin (2A)/cos (2A)
= 1 - sin (2A) / cos (2A)
=
1 - sin (x) = 1-sin (x) = 1 - sin^2 ( x ) / 1 + sin (x)
=
1 - sin ^2 (x) = cos ^2 (x)
=cos ^2 (2A) / 1+sin (2A)/Cos (2A)
simplified
cos (2A) / 1+sin 2A
identity x used = cos 2x = cos ^2 x - sin ^2 x
= 1 + sin (2x) + (cos (x)) + (sin (x))^2
= cos ^2A - sin ^2A / (cos A - sin A) ^2
= cos A - sin A / cos A +sin A
Both sides are true.
Which relationship has a zero slope? A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 3, 1, negative 1, negative 3. A coordinate plane with a straight line starting at (negative 5, negative 5) and passing through the origin, and ending at (5, 5) A coordinate plane with a straight line starting iat (negative 2, 5) and passing the x-axis at (negative 2, 0), and ending at (negative 2, 5).
Answers
Answer:
The answer is B
Step-by-step explanation:
A line has Zero slope is when the line is parallel to the x-axis. The slope of the first pair of coordinates will have no slope or zero slopes.
What is the slope of a line?The slope of a line is given by the formula,
[tex]m = \dfrac{(y_2-y_1)}{(x_2-x_1)}[/tex]
where (x₂,y₂) and (x₁,y₁) are the coordinates of any point on the line of slope.
1. For the first slope, the given coordinates are
(-3,2),(-1,2),(1,2),(3,2)
Now, if we take the first and the last point to calculate the slope of the line, we will get,
[tex]m = \dfrac{(y_2-y_1)}{(x_2-x_1)} = \dfrac{2-2}{-3-3}=\dfrac{0}{-6}=0[/tex]
Thus, the slope of the line is 0. And if we plot the points on the graph we will see that the slope of the line is 0.
2. For the second slope, the given coordinates are
(-3,3),(-1,1),(1,-1),(3,-3)
Now, if we take the first and the last point to calculate the slope of the line, we will get,
[tex]m = \dfrac{(y_2-y_1)}{(x_2-x_1)} = \dfrac{3-(-3)}{-3-3}=\dfrac{6}{-6}=-1[/tex]
Thus, the slope of the line is -1. And if we plot the points on the graph we will see that the slope of the line is -1.
3. For the third slope, the given coordinates are
(-5,-5), (0,0), (5,5)
Now, if we take the first and the last point to calculate the slope of the line, we will get,
[tex]m = \dfrac{(y_2-y_1)}{(x_2-x_1)} = \dfrac{-5-5}{-5-5}=\dfrac{-10}{-10}=1[/tex]
Thus, the slope of the line is 1. And if we plot the points on the graph we will see that the slope of the line is 1.
4. For the fourth slope, the given coordinates are
(-2,5), (-2,0), (-2,5)
Now, if we take the first and the last point to calculate the slope of the line, we will get,
[tex]m = \dfrac{(y_2-y_1)}{(x_2-x_1)} = \dfrac{5-0}{-2-(-2)}=\dfrac{5}{0}[/tex]
Thus, the slope of the line is undefined. And if we plot the points on the graph we will see that the slope of the line is undefined or at 90° from the x-axis.
Hence, the slope of the first pair of coordinates will have no slope or zero slopes.
Learn more about Slope of the line:
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Find the square root of 25 6 4 5 7
Answers
Answer:
5 is the answer
............
Answer:
5
Step-by-step explanation:
What number multiplied by itself gives you 25
5*5 = 25
sqrt(25) = 5
Find the percent of change if the original price is $246.95 and the new price is $199.95. Round to nearest tenth of a percent if necessary. Show your work and state whether this is an increase or decrease.
Answers
Answer:
Percentage change = 19%Step-by-step explanation:
Since the new price is lesser than the original price the percentage change will be a decrease.
To find the percentage change use the formula
[tex]Percentage \: \: change = \frac{change}{original \: \: quantity} \times 100[/tex]
To find the change subtract the new price from the original price
new price = $199.95
original price = $246.95
Change = $246.95 - $ 199.95 = $47
[tex]Percentage \: \: change = \frac{47}{246.95} \times 100[/tex]
Percentage change = 19%Hope this helps you
hope this is right
PLEASE HELP PLEASE WILL MARK BRAINLY
Answers
Answer:
Every 18 miles he uses 3 gallons
divide this:
18 ÷ 3 = 6 miles per gallon
30 miles = 30 ÷ 6 = 5 gallons
7 gallons = 7 x 6 = 42 miles
48 miles = 48 ÷ 6 = 8 gallons
10 gallons = 10 x 6 = 60 miles
Hope this helps :D
PLZZ HELPP!! Water is poured from a 1.5 L water bottle into an empty glass until both the glass and the bottle are 3/4 full. What is the volume of the glass?
Answers
Answer:
0.5 L
Step-by-step explanation:
volume of bottle: 1.5 L
amount of water = 1.5 L
volume of glass: x
3/4 full is the same as 0.75 full
vol of water in bottle + vol of water in glass = total vol of water
0.75(bottle) + 0.75(glass) = 1.5
0.75(1.5) + 0.75x = 1.5
0.75x = 0.375
x = 0.5
In two or more complete sentences, explain the theorem used in solving for the range of possible lengths of the third
side, AB of ^ABC
Answers
Answer:
pythagorean theorem - The length of the hypotenuse squared will always equal the sum of A squared and B sqaured. The equation is A^2 + B^2 = C^2.
Step-by-step explanation:
For Example
A = 4 A^2 = 16
B = 2 B^2 = 4
C = ? C^2 = ?
16 + 4 = 20
[tex]\sqrt{20}[/tex] ≈ 4.5
C/Hypotenuse = 4.5
PLEASE HELP PLEASE WILL MARK BRAINLY
Answers
Step-by-step explanation:
Let's take a look at the dimensions of the cube. Since each cube has a side length of 1, the answer to the question is 1 x the number of cubes. Counting the sides gives 2 x 3 x 4, or 24 yd^3
Part 1: Serena's drawing
Follow these steps to find the angles of the trapezoids in Serena's drawing. If the angles of her
trapezoid match the angles of the trapezoid stone, then her drawing is correct.
Answers
Answer:
BCDE= 100+ 80+100+80 = 360 degree
BAC = 20 degree
DBC = 100 degree
BDE = 80 degree
Shows all is correct
We associate isosceles trapezoid in this question, this helps us prove with angle A in the triangle vertices how we can find one of the adjacent angles from the trapezoid by subtraction when all angles within one single trapezoid = 360 degrees. We can use 20 degree angle A to subtract and find each alternative angle easier.
Step-by-step explanation:
The semi circle shows 9 stones
Where angles are interior to the trapezoid
Where all 4 sided shapes add up to 360 degree
We draw a line of symmetry on BCED angle
To make midway points BC and DE = 90 degree
The two new formed shapes are still 4 sided and add up to 360 degree.
BC + DE = 180 degree
BDE = Triangle 180 -20/2 = 160/2 = 80
BCDE = Trapezoid = 360
Trapezoid angle DBC = 360-80-80/2 = 360-160/2 = 200/2 = 100 degree
Finding interior angle A (BAC)
BAC = 180/9 = 20 degree
BAC * (2) = 360 degree circle
BAC = 360/18 = 20 degree
Proves BAC = 20 degree
20 degree is used in BAC workings above in bold and proves all trapezoid angles are correct. We now know this is an isosceles trapezoid and that is why symmetry and midway points can help us find the angles without any given length.
The box plots display the same data set for the number of touchdowns a quarterback threw in 10 seasons of play. Including outlier: A number line goes from 5 to 30. The whiskers range from 5 to 29, and the box ranges from 18 to 26. A line divides the box at 21.5. Excluding outlier: A number line goes from 5 to 30. The whiskers range from 17 to 29, and the box ranges from 19 to 27. A line divides the box at 21. There is an asterisk at 5. Complete the statements describing the effect of the outlier on the measures of variability. The outlier of the data set is . The range of the data set including the outlier is more than the one excluding the outlier. The interquartile range of the data set including the outlier is more than the one excluding the outlier. The outlier had the most effect on the .
Answers
Answer:
5
12
0
range
Step-by-step explanation:
i just did it, these are the right answers.
Answer:
5,12,0, and the last answer is range
Step-by-step explanation:
Did it on Edge2021. Hope this helps!
The sum of 4 consecutive integers is 130 what is the third number in the sequence
PLZ HELP!!!
Answers
Answer:
33
Step-by-step explanation:
We can write an equation:
x+x+1+x+2+x+3=130
x represents the smallest number of the consecutive integers
By the way, an example of consecutive would be 2, 3, 4, 5 or 10, 11, 12, 13
We can combine like terms from our equation:
4x+6=130
4x=124
x=31
The smallest number is 31. The second number would be 31+1=32, which means the third number is 33!
Hope this helps! :) :)
Answer:
[tex]\huge\boxed{3rd\ number = 33}[/tex]
Step-by-step explanation:
Let the consecutive numbers(Coming one after another) be x, x+1, a+2 and x+3
So,
x+x+1+x+2+x+3 = 130
4x + 6 = 130
Subtracting 6 to both sides
4x = 130-6
4x = 124
Dividing both sides by 4
x = 32
So,
1st number = x = 31
2nd Number = x+1 = 31+1 = 32
3rd number = x+2 = 31+2 = 33
4th number = x+3 = 31+3 = 34
Explain in detail the steps for solving multi-step equations.
i just need the steps no problem is included . Thank you sm !
Answers
Answer:
1) Get rid of grouping symbols like square brackets and parentheses
2) Simplify both sides of the equation. Combine like terms if possible.
3) Choose where you want to keep the variable because that will help you decide where to place the constant.
4) Eliminate numbers or variables by using opposite operations. Remember that addition and subtraction are opposites and so are multiplication and division.
Step-by-step explanation:
Solve for x: 2(10-2x) = 4(3x + 1). Write your answer as a fraction.
Answers
Answer:
[tex]\boxed{x=1}[/tex]
Step-by-step explanation:
[tex]2(10-2x) = 4(3x + 1)[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]20 - 4x = 12x + 4[/tex]
[tex]\sf Subtract \ 12x \ and \ 20 \ from \ both \ sides.[/tex]
[tex]20 - 4x - 12x - 20 = 12x + 4 - 12x - 20[/tex]
[tex]-16x = -16[/tex]
[tex]\sf Divide \ both \ sides \ by \ -16.[/tex]
[tex]\displaystyle \frac{-16x}{-16} =\frac{-16}{-16}[/tex]
[tex]x=1[/tex]
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 1
▹ Step-by-Step Explanation
2(10 - 2x) = 4(3x + 1)
Simple terms are written last:
2(-2x + 10) = 4(3x + 1)
Distributive Property:
-2 * 2x + 2 * 10 = 4 * 3x + 4
x = 1
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
what is the value of a?
a. 55
b. 110
c. 50
d. 100
Answers
Answer:
a i think
Step-by-step explanation:
Jemma has 24 balls. Out of the 24 balls, 12 are yellow, 4 are pink, and the rest are red. What is the ratio of the number of red balls to the number of balls that are either yellow or pink? arrowRight
Answers
Answer:
1 :2
Step-by-step explanation:
12 are yellow, 4 are pink
To find the number of red
24 -12 -4 = 8
There are 8 red balls
We want the ratio of
red: yellow or pink
8 : 12+4
8 :16
Divide each side by 8
8/8 : 16/8
1 :2
Answer:1:2
Step-by-step explanation: 12 yellow + 4 pink= 16
24 balls total minus 16 =8 red balls so 8:16=1:2
Reflections, rotations, and translations are types of transformations. A reflection flips an image, a rotation spins an image, and a translation slides an image. Draw a shape on a piece of paper and cut it out. Then, flip it, spin it, and slide it. Explain how each transformation affects the size and shape of the image you drew. IDK how to answer this PLS HELP
Answers
Answer:
Hey there!
A "flip" can be considered a reflection.
A "spin" is a rotation.
A "slide" is a translation.
None of these transformations change the way a shape looks, or the size of the shape. They only change how the shape is oriented.
Let me know if this helps :)
In this exercise we have to differentiate three geometric terms, in this way we can say that;
Flip is considered a reflection. Spin is a rotation. Slide is a translation.
So in a more in-depth way these geometric terms can be described as:
Flip: the established term, exist a static or exciting concept namely produce by a mirror-reversal of an original across a lying flat point around which something revolves (a fail miserably image happen reflect across the upright point around which something revolves)Spin: When two surfaces bear many point correspondences, they equal. Taken together, the familiarize points and befriend figure create our surface repre-sentation. Because the image era process maybe visualized as a page make go around about the common of a point, the counterpart fashionable our likeness happen named spin-images.Slide: A move smoothly show happen a presentation of a succession of still figure (slides) ahead of a projection screen or photoelectric display symbol, usually fashionable a prearranged series. The changes grant permission exist automatic and repeatedly or they grant permission happen manually controlled by a person who entertains or the witness.See more about geometry at brainly.com/question/7558603
Determine what type of model best fits the given situation: The height of a tree twenty feet tall increases by 2 feet per year.
Answers
Answer:
linear model
Step-by-step explanation:
This is a linear function. The initial value is 20 ft, and the yearly growth is 2ft/yr. Thus, the function is
height(t) = (20 ft) + (2 ft/yr)t, where t is the number of years.
All changes saved
2. The ratio of "D"s to "A"s in the school was 8 to 21. If there were 572 As in the school this term, how many Ds
were there?
Answers
Answer:
218
Step-by-step explanation:
572/21 = 27.23
8 x 27.23 = 217.9
Answer Check:
21/8 = 2.6
572/218 =2.6
8/21 = .38
218/572 = .38
First you divide 572/21
Next you get the quotient of 572/21 and multiple it by 8
Once you do that you should get your answer
3. If a function maps Set A to Set B, do all elements of Set A
have to be used?
Answers
Answer:
So we have a function such that:
Takes elements of Set A, and maps them into Set B.
So Set A is the domain, and Set B is the range.
Where the domain is defined as the set of all the possible inputs of a function, and the range is the set of the possible outputs.
In principle, yes, if f(x) maps Set A into Set B, all the elements of Set A should be used, why?
Because we need to check if there is a problem with Set A, for example the function f(x) = 1/x has a problem when x = 0, so we remove x = 0 from the domain of that function.
So, a function is only a function if it maps ALL the elements of its domain into only one element in the range.
