HELPP!!!!
Solving for the Missing Variable
Ex. 1 Determine the range of possible values of x,
Answers
9514 1404 393
Answer:
21 ≤ x < 48.3343
19.4030 < t ≤ 62 1/3
Step-by-step explanation:
This sort of geometry has shown up in a number of different problems. Perhaps the most difficult was one in which the angles were given a specific linear relationship. Here, one of the angles is fixed, making the problem somewhat simpler.
The most straightforward approach is to simply say the unknown angle must lie between 0° and 180°. It turns out that is not the possible range of values. Rather there is a limit on the unknown angle. It will have an extreme value when both triangles are isosceles. The lengths of the equal sides in that case can be determined using the triangle with both angle and base length specified.
__
a) For the triangle to be isosceles (MA = MH = MY), the side lengths must satisfy ...
AM·sin(62°/2) = 7.1/2
AM = 3.55/sin(31°) ≈ 6.89269
At that point, angle HMY will satisfy ...
AM = (6.33/2)/sin((2x -42)°/2)
3.55/sin(31°) = 3.165/sin(x-21°)
(x -21)° = arcsin(3.165/3.55·sin(31°)) ≈ 27.3343°
x = 48.3343
Because angle HMY can be smaller than this value, its minimum is 0:
2x -42 = 0
x -21 = 0
x = 21
That is, x can range between 21 and 48.3343.
__
b) Using similar logic on the other triangles, we find the unknown angle has an extreme value when the triangles are isosceles: CA = CB = CD = CD. As above, this will occur when ...
(3t -7)° = 2·arcsin(17/16·sin(24°)) ≈ 51.2091°
t = 19.4030
In this geometry, because AB > DE, the angle can only get larger than 51.2091°. Its upper limit is 180°, meaning that ...
3t -7 ≤ 180
3t ≤ 187
t ≤ 62 1/3
In this geometry, the value of t can range between 19.4030 and 62 1/3.
_____
Additional comment
As we said at the beginning, your computer may be expecting you to come up with an answer that makes the unknown angle lie between 0 and 180°. For that range of angles, you have ...
0 ≤ 2x-42 ≤ 180 ⇒ 0 ≤ x -21 ≤ 90 ⇒ 21 ≤ x ≤ 111
0 ≤ 3t -7 ≤ 180 ⇒ 0 ≤ t -7/3 ≤ 60 ⇒ 7/3 ≤ t ≤ 187/3
Related Questions
Suppose y varies directly with x. Write an equation if y = 4 when x = 0.4.
Answers
0.04
step by step explanation:
i’m here for the points sorry
Find the highest common factor of 55 and 605
Answers
Answer:
55
Step-by-step explanation:
Factors for 605: 1, 5, 11, 55, 121, and 605
Factors for 55: 1, 5, 11, and 55
So the highest common factor they have is 55.
HCF = 55
While on a business trip to Brookfield, Haley treated her co-workers to a meal that cost $50. Haley knew that when the bill came, she would need to pay Brookfield sales tax of 14% and would want to leave an 18% tip on the original $50. Including tax and tip, how much did Haley's meal cost?
Answers
Answer:
$66
Step-by-step explanation:
The meal cost $50 without taxes.
The cost of tax:
$50*%14= $7
so she will pay a $7 tax
Also, she wants to tip %18 of the original $50 so:
$50*%18= $9
so she will tip $9
$50 + $7 + $9 = $66
solve inequality for v
Answers
Answer:
[tex]\displaystyle v > \frac{-28}{5}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of EqualityStep-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{-10}{7}v > 8[/tex]
Step 2: Solve for v
Divide both sides by [tex]\displaystyle \frac{-10}{7}[/tex]: [tex]\displaystyle v > \frac{-28}{5}[/tex]Here we see that any value v greater than [tex]\displaystyle \frac{-28}{5}[/tex] would work as a solution to the inequality.
-7/10 and simplify.
Inequality Form:
v< −28/5
Interval Notation:
(∞, −28/5)
A circle has an arc whose measure is 80° and whose length is 88. What is the diameter of the circle?
Answers
Answer:
length of arc=80/360×2πr
88×360=80×2×22/7×r
31680×7/(80×2×22)=r
r=221760/3520=63
diameter=2r=2×63=126
$1400 is divided between two accounts. One account pays $3%$ interest, while the other pays $4%$. At the end of the interest period, the interest earned was $50. How much was invested in each account?
Answers
Answer:
$60
Step-by-step explanation:
one of them got $40 and the other one $20
please find the x for these
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Answer:
x=b-8a/8
x=b+8a/a
x=2-2c/c
What is the answer? Please
Answers
Answer:
i would say the 3rd one
Step-by-step explanation:
Given three points, it is possible to draw a circle that passes through all three. The perpendicular bisectors of a chords always passes through the center of the circle. By this method we find the center and can then draw the circle. This is virtually the same as constructing the circumcircle a triangle.
Calculate the total cost of a meal that cost $45.12 if the sales tax is 5.2% and yo want to leave a
17% tip.
Answers
Answer:
55.53
Step-by-step explanation:
45.12
5.2%= 1.052
new price= original(1+5.2%)
x=45.12(1.052)
×=47.46624+17%
=55.53
Solve the following multi-step equation: 4(2 - 4x) - 3x = 65
Answers
Answer:
x = -3
Step-by-step explanation:
4(2 - 4x) - 3x = 65
Distribute the 4.
8 - 16x - 3x = 65
Combine like terms.
8 - 19x = 65
-19x = 57
Divide by -19 to isolate x.
x = 57/-19
x = -3
Check.
4(2 - 4(-3)) - 3(-3) = 65
4(2 - (-12) + 9 = 65
4(14) + 9 = 65
56 + 9 = 65
65 = 65
The solution of the given linear equation 4(2 - 4x) - 3x = 65 is -3.
Two algebraic expressions separated by an equal symbol in between them and with the same value of the expression are called equations.
Example = 2x +4 = 12
here, 4 and 12 are constants and x is variable.
The solution of the equation 4(2 - 4x) - 3x = 65 is calculated as:
4(2 - 4x) - 3x = 65
Multiply the expressions inside the brackets,
8 - 16x -3x = 65
8 - 19x = 65
Subtract 8 from both the sides,
-19x = 65- 8
-19x = 53
Divide both side by -19
[tex]x = \dfrac{-53}{19}[/tex]
Thus, the value of x is -3.
Learn more about equations here:
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A video game is now being sold at 22% off for a price of $31.20. What was the original price of the video game?
Answers
$38.06
Explanation:
Multiply $31.20 by 0.22 (22%)
Which equals 6.864
Add that to $31.20 and you get 38.064
Then you round it and get $38.06
Please help fast!!
composition of functions
g(x)=2x-5 h(x)=x^2-2
find g(h(-8))
Answers
Answer:
g(h(- 8)) = 119
Step-by-step explanation:
Evaluate h(- 8), then substitute the result obtained into g(x), that is
h(- 8) = (- 8)² - 2 = 64 - 2 = 62, then
g(62) = 2(62) - 5 = 124 - 5 = 119
Hope this helps
Find the slope on the graph
Answers
Answer:
im pretty sure it would be 5/3
Step-by-step explanation:
u go up 5 squares and then over 3
Answer:
[tex]\frac53[/tex]
Step-by-step explanation:
Hello!
Slope is calculated by the formula [tex]\frac{Rise}{Run}[/tex].
Rise is the change in y between two pointsRun is the change in x between two pointsThe two points I'm going to pick are (0,-1) and (3,4).
Now let's find the changes in x and y.
Change in y (-1 and 4) is 5Change in x (0 and 3) is 3Plugging it into the formula, you get a slope of [tex]\frac53[/tex].
Determine the value of x.
Answers
Answer:
The value of x is 14.75 ⇒ (2)
Step-by-step explanation:
If the vertices of a quadrilateral lie on the circumference of a circle, then this quadrilateral is a cyclic quadrilateralIn the cyclic quadrilateral, every two opposite angles are supplementary (the sum of their measures is 180°)In the given figure
∵ The vertices of the quadrilateral BCED lie on the circumference of circle A
→ By using the 1st rule above
∴ BCED is a cyclic quadrilateral
∵ ∠B and ∠E are opposite angles in the cyclic quadrilateral BCED
→ By using the 2nd rule above
∴ m∠B + m ∠E = 180°
∵ m∠B = 6x + 10
∵ m∠E = 81.5°
∴ 6x + 10 + 81.5° = 180°
→ Add the like terms on the left side
∴ 6x + 91.5 = 180
→ Subtract 91.5 from both sides
∵ 6x + 91.5 - 91.5 = 180 - 91.5
∴ 6x = 88.5
→ Divide both sides by 6 to find x
∴ x = 14.75
are the following terms like terms 3m+4n yes or no
Answers
If C is the midpoint of AB, find the value of x.
Answers
Answer:
5x+6= 10x-8
14= 5x
x= 2.8
Step-by-step explanation:
Rewrite 5 X 2/3 using a whole number and a unit fraction
Answers
Answer: 3 1/3
Step-by-step explanation:
Im assuming the big ol "X" is a multiply sign.
The answer is three and one third.
Mario's plumbing service
Charges $40 to make a house
Call plus $25 an hour.
y=40+25h
Fill in the chart
Answers
Answer:
So, hour 0 and charge is 0. hour 1 is 25, hour 2 is 50, hour 3 is 75, hour 4 is 100 and hour 5 is 125
Step-by-step explanation:
For every hour, add 25 in each box.
Can anyone help with these maths questions about transformations please?
Answers
B. Reflection over y axis, reflection over y = 1
C. I'm guessing you just have to draw this one, just put the center on (2,0) and enlarge it by the scale factor
Please Help! I will give brainliest
Answers
Answer:
-6.3n + 8.6
Step-by-step explanation:
you add the terms together
Answer: -6.3n + 8.6
Step-by-step explanation:
If you spin the spinner, what is the probability of the pointer landing in the y section
Answers
Answer:
1/8
Step-by-step explanation:
What's the answers to theseeeee help need it bye 12:00
Answers
what are the next 2 terms in the sequence
Answers
Answer:
4 1/4 and 4 3/4
Step-by-step explanation:
its adding 2/4 each time
Answer:
4.25 and 4.75
Step-by-step explanation:
just add 0.50
The graph 4x^2-4x-1 is shown. Use the grpah to find the estimates for the solutions of 4x^2-4x-1=0 and 4x^2 - 4x-1=2
Answers
Answer:
a) The estimates for the solutions of [tex]4\cdot x^{2}-4\cdot x -1 = 0[/tex] are [tex]x_{1}\approx -0.25[/tex] and [tex]x_{2} \approx 1.25[/tex].
b) The estimates for the solutions of [tex]4\cdot x^{2}-4\cdot x -1 = 2[/tex] are [tex]x_{1}\approx -0.5[/tex] and [tex]x_{2} \approx 1.5[/tex]
Step-by-step explanation:
From image we get a graphical representation of the second-order polynomial [tex]y = 4\cdot x^{2}-4\cdot x -1[/tex], where [tex]x[/tex] is related to the horizontal axis of the Cartesian plane, whereas [tex]y[/tex] is related to the vertical axis of this plane. Now we proceed to estimate the solutions for each case:
a) [tex]4\cdot x^{2}-4\cdot x -1 = 0[/tex]
There are two approximate solutions according to the graph, which are marked by red circles in the image attached below:
[tex]x_{1}\approx -0.25[/tex], [tex]x_{2} \approx 1.25[/tex]
b) [tex]4\cdot x^{2}-4\cdot x -1 = 2[/tex]
There are two approximate solutions according to the graph, which are marked by red circles in the image attached below:
[tex]x_{1}\approx -0.5[/tex], [tex]x_{2} \approx 1.5[/tex]
HELP ME PLEASE I NEED HELP
Answers
try the other answer.
Answer:
a. x=2
b. y=5
Step-by-step explanation:
a. 2(11x+7)=58
22x+14=58
x=2
b. 16y+10=90
16y=80
y=5
If angle A =90 degree , b=1 cm and a =2 cm then solve the following right angled triangle ABC
Answers
Answer:
Angle A = 90 degrees, side a = 2.Angle B = 30 degrees, side b = 1.Angle C = 60 degrees, side c = [tex]\sqrt{3}[/tex].Side c:
If angle A is 90 degrees, side a is the hypotenuse.[tex]c^{2} + b^{2} = a^{2}[/tex] <--- this is NOT the correct way to write the Pythagorean theorem. I changed it to fit the side lengths. Normally, it is [tex]a^{2} + b^{2} = c^{2}[/tex], where c is the hypotenuse. Since a is the hypotenuse, I switched the variables.[tex]c^{2} + (1)^{2} = (2)^{2}[/tex] [tex]c^{2} + 1 = 4[/tex] [tex]c^{2} = 3[/tex][tex]c = \sqrt{3}[/tex]Finding the angles:
In a 30-60-90 right triangle, the...Shortest leg = xLongest leg = [tex]x\sqrt{3}[/tex] Hypotenuse = 2x In this case, the shortest leg is 1, the longer leg is [tex]\sqrt{3}[/tex] (or [tex]1*\sqrt{3}[/tex]), and the hypotenuse is 2 (or [tex]2*1[/tex]).As a result, this is a 30-60-90 triangle -- angle B is 30 degrees while angle C is 60 degrees.Find the probability of this event. Enter each answer as a fraction in simplest form, as a decimal, and as a percent.
You draw one card at random from a shuffled deck of 52 playing cards. The deck has four 13−card suits (diamonds, hearts, clubs, spades).
The card is a diamond or a heart.
The probability expressed as a fraction is:
The probability expressed as a decimal is:
.
The probability expressed as a percent is:
Find the probability of this event. Enter each answer as a fraction in simplest form, as a decimal, and as a percent.
2. You draw one card at random from a shuffled deck of 52 playing cards. The deck has four 13−card suits (diamonds, hearts, clubs, spades).
The card is a diamond or a heart.
The probability expressed as a fraction is:
The probability expressed as a decimal is:
.
The probability expressed as a percent is:
Answers
Answer:
There we go!!!
Cos(A) = ?
13/5
12/5
12/13
5/13
Answers
Answer:
cosA = [tex]\frac{5}{13}[/tex]
Step-by-step explanation:
cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{5}{13}[/tex]
Only answer the part where it says her bonus will be______
Answers
Answer:
her bonus will be a big paycheck of 99999
These dot plots show lengths (in feet) from a sample of crocodiles and alligators.
Compare the outliers and interquartile ranges (IQRs) for the data sets. Which
statement is true?
A. Alligators have a smaller IQR because there were some very long
alligators (high outliers).
B. Crocodiles have a greater IQR because most of the crocodiles
were about the same length.
C. Alligators have a smaller IQR because there were some very short
alligators (low outliers).
D. Alligators have a greater IQR because there were some very long
alligators (high outliers).
Answers
Alligators have a greater IQR because there were some very long alligators (high outliers)
D: Alligators have a greater IQR because there were some very long alligators (high outliers)
How to find outliers and the interquartile range?Use the interquartile rule to find outliers and calculate the interquartile range of data.
Multiply the interquartile range (IQR) by 1.5 (a constant used to identify outliers). 44 Adds 1.5x (IQR) to the 4th interquartile range. Numbers larger than this are suspected of being outliers.
Subtract 1.5x (IQR) from the first interquartile range.
If you subtract 1.5xIQR from the first quartile, data values smaller than this number are considered outliers. If you add 1.5 x IQR to the third interquartile, data values larger than this number are considered outliers.
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