Answers
Answer:
[tex]x=32[/tex]°
Step-by-step explanation:
The law of sines is a property of all triangles that relates the sides and angles of a triangle. This property states the following:
[tex]\frac{sin(a)}{A}=\frac{sin(b)}{B}=\frac{sin(c)}{C}[/tex]
Where side (A) is the side opposite angle (<a), side (B) is the side opposite angle (<b), and side (C) is the property opposite angle (<c).
Substitute each of the sides and respective angles into the formula, and solve for the unknown angle (<x). Please note that a triangle with two congruent sides (referred to as an isosceles triangle) has a property called the base angles theorem. This states that the angles opposite the congruent sides in an isosceles triangle are congruent. Therefore, there can be two (<x)'s in this triangle.
[tex]\frac{sin(a)}{A}=\frac{sin(b)}{B}=\frac{sin(c)}{C}[/tex]
[tex]\frac{sin(x)}{10}=\frac{sin(116)}{17}=\frac{sin(x)}{10}[/tex]
One can shorten the equation so it only holds the parts that will play a role in solving this equation,
[tex]\frac{sin(x)}{10}=\frac{sin(116)}{17}[/tex]
Now take the cross product in this equation to simplify it further,
[tex]\frac{sin(x)}{10}=\frac{sin(116)}{17}[/tex]
[tex]17(sin(x))=10(sin(116))[/tex]
Inverse operations, solve this equation for (x),
[tex]17(sin(x))=10(sin(116))[/tex]
[tex]sin(x)=\frac{10(sin(116))}{17}[/tex]
[tex]x=sin^-^1(\frac{10(sin(116))}{17})[/tex]
[tex]x=31.91782...[/tex]
[tex]x\approx32[/tex]
Answer:
hello,
Step-by-step explanation:
the triangle is isocele,
x+x+116=180
x=(180-116)/2
x= 32° (thirty-two , trente-deux in french)
Related Questions
Can you answer this math homework? Please!
Answers
Answer: (3.5,-2)
Step-by-step explanation:
To solve this problem, all we have to do is plug in y=-2 into either equations from step one to find the coordinate. To make sure we have the right x-coordinate, let's plug in y for both equations.
4x-7y=28 [plug in y=-2]
4x-7(-2)=28 [multiply]
4x+14=28 [subtract both sides by 14]
4x=14 [divide both sides by 4]
x=3.5
------------------------------------------------------------------------------------------------------------
6x-5y=31 [plug in y=-2]
6x-5(-2)=31 [multiply]
6x+10=31 [subtract both sides by 10]
6x=21 [divide both sides by 6]
x=3.5
Now, we know the solution to the system is (3.5,-2).
Answer:
(3.5, -2)
Step-by-step explanation:
Hi there!
We are given a system of equations, and the value for y is already solved (y=-2)
We want to find the value of x
To do that, substitute -2 as y into either one of the equations in the system (the system has the equations 4x-7y=28 and 6x-5y=31) and solve for x
Let's use 4x-7y=28, although picking 6x-5y=31 is completely fine
Substitute -2 as y into the equation
4x-7(-2)=28
Multiply
4x+14=28
Subtract 14 from both sides
4x=14
Divide both sides by 4 and simplify
x=7/2, or 3.5
We found the value of x in the system
Substitute the values of x and y into a point form (x, y)
The solution is (3.5, -2)
Hope this helps!
A ball is thrown into the air. The path it takes is modeled by the equation: -3t+24t = h, where t is the time in seconds and h is the height of the ball above the ground, measured in feet. Write an inequality to model when the height of the ball is at least 36 feet above the ground. For how long is the ball at or above 36 feet?
Answers
Given:
The given equation is:
[tex]-3t^2+24t=h[/tex]
Where, t is the time in seconds and h is the height of the ball above the ground, measured in feet.
To find:
The inequality to model when the height of the ball is at least 36 feet above the ground. Then find time taken by ball to reach at or above 36 feet.
Solution:
We have,
[tex]-3t^2+24t=h[/tex]
The height of the ball is at least 36 feet above the ground. It means [tex]h\geq 36[/tex].
[tex]-3t^2+24t\geq 36[/tex]
[tex]-3t^2+24t-36\geq 0[/tex]
[tex]-3(t^2-8t+12)\geq 0[/tex]
Splitting the middle term, we get
[tex]-3(t^2-6t-2t+12)\geq 0[/tex]
[tex]-3(t(t-6)-2(t-6))\geq 0[/tex]
[tex]-3(t-2)(t-6)\geq 0[/tex]
The critical points are:
[tex]-3(t-2)(t-6)=0[/tex]
[tex]t=2,6[/tex]
These two points divide the number line in 3 intervals [tex](-\infty,2),(2,6),(6,\infty)[/tex].
Intervals Check point [tex]-3(t-2)(t-6)\geq 0[/tex] Result
[tex](-\infty,2)[/tex] 0 [tex](-)(-)(-)=(-)<0[/tex] False
[tex](2,6)[/tex] 4 [tex](-)(+)(-)=+>0[/tex] True
[tex](6,\infty)[/tex] 8 [tex](-)(+)(+)=(-)<0[/tex] False
The inequality is true for (2,6) and the sign of inequality is [tex]\geq[/tex]. So, the ball is above 36 feet between 2 to 6 seconds.
[tex]6-2=4[/tex]
Therefore, the required inequality is [tex]-3t^2+24t\geq 36[/tex] and the ball is 36 feet above for 4 seconds.
The function f(x) is shown on the graph.
What is f(0)?
0 only
-6 only
-2,-1,1, and 3 only
-6,-2,-1,1,and 3 only
Answers
Answer: -6 only (choice B)
This is because the point (0,-6) is on the blue line. This is the y intercept.
Choice C would be true if you wanted to solve f(x) = 0, instead of f(0) itself.
Answer:
-6
Step-by-step explanation:
f(0) means what is the output when the input is 0
x=0 y= -6
Which statements are true about finding the difference of the expressions? Select three options
[tex]\frac{3p+1}{6p}[/tex] and [tex]\frac{2p-3}{2px^{2} }[/tex]
A. The common denominator is 6p.
B. The first fraction rewritten with the LCD is [tex]\frac{3px^{2} +p}{6px^{2} }[/tex]
C. The second fraction rewritten with the LCD is [tex]\frac{6p-9}{6p}[/tex]
D. The diffrence is [tex]\frac{3px^{2} -5p+9}{6px^{2} }[/tex]
E. The difference is a rational expression.
Answers
Answer:
CAUTION HERE !!!!!
if you suggested edits are accurate the solution would be...
[tex]\frac{3p^2 - 5p+9}{6p^2}[/tex]
that is not one of your choices, but is is almost identical to choice "D"
which is different by [tex]6px^2[/tex] vs [tex]6p^2[/tex]
which i think is your comment ????
Step-by-step explanation:
Sipho buys a bread on Monday and eats a third of it. On Tuesday he eats half of what is left over. If the bread is cut in 21 slice how many slice are left for Wednesday?
Answers
Answer:
7 slices
Step-by-step explanation:
1/3 of the bread would be seven slices (21/3), and he would be left with 2/3, half of which is 1/3; another seven slices were eaten. On Wednesday, he will have 7 slices left over.
A boy borrowed his boat 531 feet out into the ocean. When he looked back he saw the house on a cliff above the beach where he set out. He estimated the angle of elevation was 26 degrees. Estimate to the nearest foot. the height of the house above the water
Answers
Answer:
259 ft.
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. Types of triangles are isosceles. scalene, equilateral, acute, obtuse and right angled triangle.
A right angled triangle is a triangle in which one of the angles is 90 degrees. Trigonometric ratios show the relationship between the angles of a right angle triangle and its sides.
Let h represent the height of the house above water, hence using trigonometric ratios:
tan(26) = h / 531
h = 531 * tan(26)
h = 259 ft.
Use the coordinates of the labeled point to find the point-slope equation of the line.
(12, -1)
Answers
Answer:
Choice C.
[tex]y + 1 = - 2(x - 2)[/tex]
Step-by-step explanation:
When converting to
[tex]y = mx + b[/tex]
We are left with:
[tex]y = - 2x + 3[/tex]
Which fits both the x-intercept and y-intercept.
Bagels cost 35p each how much is 6?
Answers
Answer:
1 = 35p
6 = 35p×6
= 240p
Therefore, 6 bagels cost 240 p
6 = 35 x 6 = 210
210p = £2.10
please evaluate P(7,1)
Answers
Answer:
7
Step-by-step explanation:
Using the definition
n[tex]P_{r}[/tex] = [tex]\frac{n!}{(n-r)!}[/tex]
where n! = n(n - 1)(n - 2)..... 3 × 2 × 1
Then
7[tex]P_{1}[/tex] = [tex]\frac{7!}{(7-1)!}[/tex] = [tex]\frac{7!}{6!}[/tex] ← cancel out the multiples 6 ×5 × 4 × 3 × 2 × 1 , then
7[tex]P_{1}[/tex] = 7
The digits 1, 7, and 8 and 2 copies of the digit 5 are all arranged to form a 5-digit integer. How many different integers can be formed?
Answers
Step-by-step explanation:
You have 5 digits.Youdonot say if duplication is allowed. I will assume not
For the first digit you have 5 choices. One of the 5 digits is gone.
You now have 4 digits to choose from. You pick one. Now you have but 3 left.
The total answer if 5*4*3*2*1 = 120
if x=2+√5 find the value of x²-1/x²
Answers
Answer:
[tex]{ \tt{ {x}^{2} - \frac{1}{ {x}^{2} } }} \\ = { \tt{ {(2 + \sqrt{5} )}^{2} - \frac{1}{ {(2 + \sqrt{5}) }^{2} } }} \\ = { \tt{ \frac{(2 + \sqrt{5} ) {}^{4} - 1}{ {(2 + \sqrt{5} )}^{2} } }} \\ = { \tt{ \frac{(9 + 4 \sqrt{5}) {}^{2} }{ {(9 + 4\sqrt{5}) }}}} \\ = { \tt{9 + 4 \sqrt{5} }}[/tex]
Answer:
[tex]8\sqrt{5}[/tex]
Step-by-step explanation:
[tex]x = 2 + \sqrt{5}\\\\ x^{2} = (2+ \sqrt{5})^{2} \\\\ \ \ \ \ = 2^{2}+2* \sqrt{5}*2+( \sqrt{5})^{2}\\\\[/tex]
[tex]= 4 + 4 \sqrt{5}+5\\\\= 9+4 \sqrt{5}[/tex]
[tex]\frac{1}{x^{2}}=\frac{1}{9+4\sqrt{5}}\\\\=\frac{1*(9-4\sqrt{5}}{(9+4\sqrt{5})(9-4\sqrt{5})}\\\\=\frac{9-4\sqrt{5}}{9^{2}-(4\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-4^{2}(\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-16*5}\\\\=\frac{9-4\sqrt{5}}{81-80}\\\\=\frac{9-4\sqrt{5}}{1}\\\\=9-4\sqrt{5}[/tex]
[tex]x^{2}-\frac{1}{x^{2}}= 9 + 4\sqrt{5} -(9 - 4\sqrt{5})\\\\[/tex]
[tex]= 9 + 4\sqrt{5} - 9 + 4\sqrt{5}\\\\= 9 - 9 + 4\sqrt{5} + 4\sqrt{5}\\\\= 8\sqrt{5}[/tex]
There are 5 pears, 10 grapes, and 4 strawberries in a bag. What is the ratio of all pieces of fruits to pears?
Answers
Answer:
19: 5
Step-by-step explanation:
Total fruit is 5+10+4 = 19
fruit: pears
19: 5
Answer:
19:5
Step-by-step explanation:
5+10+4= 19
Pears= 5
FIND THE EQUATION OF THE LINE SHOWN: QUICK I NEED TO SUMBIT MY HW
Answers
Answer:
y = -1/4x +2
Step-by-step explanation:
First find the slope using two point
(0,2) and (4,1)
m = (y2-y1)/(x2-x1)
= (1-2)/(4-0)
= -1/4
The y intercept is 2
The slope intercept form of a line is
y= mx+b where m is the slope and b is the y intercept
y = -1/4x +2
Answer:
the equation of the line is y = -1/4x +2
Step-by-step explanation:
The first step is to see where the line intercepts on the y-axis, which is 2. The next step is to see what the slope is so because it goes down 1 right 4, you find out that the slope of the line is -1/4.
Hope this helps!
classify the following as a chemical or physical: hydrogen gas is very explosive
Answers
Answer:
chemical
Step-by-step explanation:
What is the range of the function f(x) = -2(6^x) + 3?
o (-inf,-2]
0 (-inf,3)
O [-2,inf)
O [3,inf)
Answers
Answer:
write question in short form
Step-by-step explanation:
4.
a. The total area of the model is 130 m2. Write an equation to find x. b. Solve the equation by completing the square.
A. (x + 2)(2x + 2) = 130; x = 5.12 m
B. (x + 2)(2x + 2) = 130; x = 6.70 m
C. (x + 2)(x + 2) = 130; x = 9.40 m
D. (x + 2)(2x + 2) = 130; x = 6.58 m
Answers
Answer:
(x+2)(2x+2) = 130
x=6.58m
Step-by-step explanation:
The shape of the whole figure is a triangle. Hence the area of the whole figure is expressed as:
Area = Length * Width
Given
Length = 2 + x + x = 2+2x
Width = 2 + x
Area = 130m²
Substitute the resultng values into the formula;
(2+2x)(2+x)= 130
(x+2)(2x+2) = 130
Expand the bracket:
[tex]2x^2+2x+4x+4=130\\2x^2+6x+4=130\\[/tex]
Divide through by 2
[tex]x^2+3x+2=65\\x^2+3x=65-2\\x^2+3x = 63[/tex]
Complete the square by adding the square of the half of the coefficient of x to both sides:
[tex](x^2+3x+(\frac{3}{2} )^2)=63+(\frac{3}{2} )^2[/tex]
[tex](x+\frac{3}{2} )^2=63 + \frac{9}{4} \\(x+\frac{3}{2} )^2=\frac{252+9}{4} \\(x+\frac{3}{2} )^2=\frac{261}{4}\\(x+\frac{3}{2} )^2=65.25[/tex]
Take the square root of both sides
[tex]\sqrt{(x+(\frac{3}{2} ))^2} = \sqrt{65.25}\\x+\frac{3}{2}= 8.078\\x=8.078-1.5\\x=6.58m[/tex]
Hence the value of x is 6.58m
The sum of three consecutive numbers is 117.what is the largest of the three numbers?write an equation to represent this scenario and solve for the variable
Answers
Answer:rrrrrrrr
rrrrrrrrrr
Step-by-step explanation:
rrrrrrrrrrrrrrr
The equation for the scenario is x + x+1 + x+2 = 117 and largest number is 40.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let x be the first number:
The other numbers are:
x+1, x+2
The sum of three consecutive numbers is 117:
x + x+1 + x+2 = 117
3x + 3 = 117
3x = 114
x = 38
x+ 1 = 38+1 = 39
x+2 = 38+2 = 40
Thus, the equation for the scenario is x + x+1 + x+2 = 117 and largest number is 40.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ2
Ella has two 8-ft. long boards. She
needs to cut pieces that are 15 inches
long. How many 15-inch pieces can
she cut from the two boards?
My sister needs help?
Answers
Answer:
Step-by-step explanation:
DB is a diagonal of parallelogram ABCD
What is the measurement of
Please help ASAP
Answers
Answer:
m∠DAB+m∠ADC=180
115+ 29 + m∠ADB=180
m∠ADB=180 - 115 -29
= 36°
A line plot with the lengths of meteors is shown. Two more identical meteor measurements were added so that the total length of all meteors measured is 16 inches. What is the length of each new meteor?
A line plot with the title, length of meteors. The data is measurement in inches. The line plot goes from two eighths to one and seven eighths, with fourteen tick marks in all. The first tick mark is two eighths and has one data point. The second tick mark is three eighths and has three data points. The third tick mark is four eighths and has two data points. The fourth tick mark is five eighths and has no data points. The fifth tick mark is six eighths and has two data points. The sixth tick mark is seven eighths and has no data points. The seventh tick mark is one and has no data points. The eighth tick mark is one and one eighth and has no data points. The ninth tick mark is one and two eighths and has one data point. The tenth tick mark is one and three eighths and has two data points. The eleventh tick mark is one and four eighths and has no data points. The twelfth tick mark is one and five eighths and has no data points. The thirteenth tick mark is one and six eighths and has two data points. The fourteenth tick mark is one and seven eighths and has one data point.
1 inch
one and one eighth inches
one and two eighths inches
one and three eighths inches
Answers
Answer:The answer is 1 3/8 (D)
Step-by-step explanation:
If you added the amounts of each tick mark (which would be 13 2/8), and then subtracted it by 16, it would be 2 6/8. 2 6/8 divided by two (because we need to find the length of both of the indentical meteors) would be 1 3/8.
Now, to make sure it is 1 3/8: 13 2/8 + 1 3/8 + 1 3/8 = 16.
It is confirmed, 1 3/8 (Answer D) is the correct answer.
(Also, I took this test and got it correct :D)
Step-by-step explanation:
How do I solve this math equation: 7=8-p
Answers
Answer:
p = 1
Step-by-step explanation:
7 = 8 - p
7 + p = 8
p = 8-7
p = 1
Answered by Gauthmath
Solve the equation sine Ф=0.6792 for 0°≤Ф≤360
Answers
Answer:
42.78⁹, 137.22⁹.
Step-by-step explanation:
sine Ф=0.6792
Angle Ф in the first quadrant = 42.78 degrees.
The sine is also positive in the second quadrant so the second solutio is
180 - 42.78
= 137.33 degres.
help asap! what does sinø=
Answers
Answer:
-3/5
Step-by-step explanation:
Pythagorean formula :
x^2 + y^2 = r^2
(-8)^2 + (-6)^2 = r^2
64 + 36 = 100
r^2 = 100
r= 10
sin is the y coordinate over the radius :
-6/10
-3/5
HEELLLPPPPPP what’s the answer????????????????????????? HEELLLLLLLPPPPPPPPPPPPPP
Answers
Answer:
(-2,-2)
Step-by-step explanation:
x^2 + y^2 = 9
A circle has an equation of the form
(x-h)^2 + (y-k)^2 = r^2
where the center is at ( h,k) and the radius is r
The circle is centered at (0,0) and has a radius 3
The only point entirely within the circle must have points less than 3
(-2,-2)
Help with question 24 the answer is (y-2)(a-b) but I need explain I don’t understand
Answers
Answer:
a(y_2)_b(y_2) =a_b)(y_2(
4.Find the first five terms of the recursive sequence
Answers
Answer:
5, 12, 19, 26, 33
Step-by-step explanation:
Using the recursive rule and a₁ = 5 , then
a₂ = a₁ + 7 = 5 + 7 = 12
a₃ = a₂ + 7 = 12 + 7 = 19
a₄ = a₃ + 7 = 19 + 7 = 26
a₅ = a₄ + 7 = 26 + 7 = 33
The first 5 terms are 5, 12, 19, 26, 33
What is the range of g ( x ) = 3x − 2, if the domain is { − 1, 0, 1, 2 }?
Answers
Answer:
range{-5,4)
Step-by-step explanation:
3(-1)-2= -5
3(2)-2=4
write equation!!
twice the difference of a number and seven equals five 
Answers
Answer:
Its either 2(A+7=5) or 2(A+7) =5
I will mark you the brainiest for the correct answer, please be correct, Have a good day and take care, thanks. ( VIEW THE IMAGE TO ANSWER).
Answers
Mistake in Line 2 : Was in the determining the values for a ,b,c
Mistake in Line 4 : Not taking the square roots of both sides.
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
First Mistake : Line 2
[tex]a = x \\ b = 6 \\ c = 10[/tex]
Second Mistake : Line 4
[tex]136 = {x}^{2} \\ not \\ 136 = x[/tex]
Correct Solution :
[tex] {x}^{2} + {6}^{2} = {10}^{2} \\ {x}^{2} = {10}^{2} - {6}^{2} \\ {x}^{2} = 100 - 36 \\ [/tex]
[tex] {x}^{2} = 64 \\ \sqrt{ {x}^{2} } = \sqrt{64} \\ x = 6[/tex]
Lines AB and CD (if present in the picture) are straight lines. Find x. Give reasons to justify your solutions.
Answers
Answer:
180- 110= 70
70+x+90=180
160+x=180
180-160=x
20=x
