The smallest angle occurs opposite the shortest side length of the triangle. So by the law of cosines we have
[tex]11^2=13^3+19^2-2\cdot13\cdot19\cos\angle J\implies\cos\angle J=\dfrac{409}{494}\implies\theta\approx\boxed{34^\circ}[/tex]
Answer:
The measure of angle J is 34°
Step-by-step explanation:
Given,
J is the smallest angle in the triangle with sides measuring 11, 13, and 19,
Thus, J must be the opposite angle of the side measuring 11,
Since, the law of cosines,
[tex]a^2 = b^2 + c^2 - 2bc cos A[/tex]
Where, a, b and c are the sides of a triangle ABC,
Such that angle A is opposite to the side measuring a,
By applying the law,
We can write,
[tex]11^2 = 13^2 + 19^2 - 2\times 13\times 19 cos J[/tex]
[tex]121 = 169 + 361 - 494 cos J[/tex]
[tex]\implies cos J = \frac{169+361-121}{494}=\frac{409}{494}[/tex]
[tex]\implies m\angle J=34.1127839945\approx 34^{\circ}[/tex]
Second option is correct.
draw a modelto show that x + 3 is the same as x over 3
Answer:
Step-by-step explanation:
Your equation comes out to x + 3 = x/3. Multiplying all three terms by 3 results in 3x + 9 = x, which simplifies to 2x = -9, so that x = -9/2.
Unsure of what you're asking for by "model."
Given the functions, f(x) = 2x^2 + 2 and g(x) = 3x + 1, perform the indicated operation. When applicable, state the domain restriction.
A)2x2 - 3x + 1
B)2x2 - 3x + 3
C)5x3 + 2x2 + 2
D)6x3 + 6x + 3
Answer:
the one that equals to 7
Step-by-step explanation:
Answer: The answer is B 2x2 - 3x+3
Step-by-step explanation:
Need help with a math question
ACD and ACE are supplementary angles that need to equal 180 degrees
ACE = 180 -100 = 80 degrees.
For this case we have by definition that, a flat angle is the space included in an intersection between two straight lines whose opening measures 180 degrees. So, the angle between A and B is 180 degrees.
If we are told that the ACD angle is 100 degrees, then the DCB angle should be 80 degrees.
The angle ACE is opposite by vertex to the angle DCB, then it is also 80 degrees; since by definition, two angles opposed by the vertex are congruent or equal.
Answer:
80 degrees
Melissa sees a lighthouse from her sailboat. She knows the height of the lighthouse is 154 feet. She uses a measuring device and determines that the angle to the top of the lighthouse from her boat is 35°. How far is the sailboat from the base of the lighthouse?
Answer:
219.9 feet to the nearest tenth.
Step-by-step explanation:
Use trigonometry:
tan 35 = opposite / adjacent side
= 154/x
x = 154 / tan35
= 219.93
Answer:
219.9 ft
Step-by-step explanation:
After looking at pic, cross multiply to get x tan(35)=154
then divide both sides by tan(35) giving x=154/tan(35)
x is approximately 219.9 ft
NEED HELP WITH A MATH QUESTION TO FIND THE VALUE OF X
Answer:
x=6.5 cm
Step-by-step explanation:
The tangent meets the circle at right angles.
Therefore the triangle formed is a right triangle.
From the Pythagorean Theorem;
[tex]x^{2} +20.2^2=(x+14.7)^2[/tex]
We expand to obtain:
[tex]x^{2} +408.4=x^2+29.4x+216.04[/tex]
We group like terms to get:
[tex]x^{2} -x^2+408.4-216.04=29.4x[/tex]
We simplify now to get:
[tex]192.36=29.4x[/tex]
We divide both sides by 29.4 to get:
x=6.5 to the nearest tenth.
A spinner with 6 equally sized slices is shown below. The dial is spun and stop on a slice at random . What is the probability that the dial stop at a grey side . Write your answer as a fraction in simplest form
One grey side or one gray side?
P(one grey side) = 1/6
what is the ratio for the surface areas of rectangle prisims shown below given that they are similar and that the ratio of their edge lengths is 7:3
Answer:
B. 49:9
Step-by-step explanation:
The ratio of surface areas is the square of the ratio of edge lengths:
7² : 3² = 49 : 9
The function f(x) = 7 – 4x + x2 written in vertex form is f(x) = (x – 2)2 + 3. What is the axis of symmetry for the function? X = –3 x = –2 x = 2 x = 3
Answer:
x = 2
Step-by-step explanation:
The vertex form tells you the vertex is (x, y) = (2, 3). The vertical line through the vertex, x=2, is the axis of symmetry.
Answer:
x = 2
Step-by-step explanation:
took the test on edge
Determine whether the relation shown is a function. Explain how you know.
Answer:
It is not a function
Step-by-step explanation:
The plot shows (1, 1) and (1, 3) are both defined by the relation. It does not pass the "vertical line test", which requires the relation be single-valued everywhere.
Answer:
This is not a function
Step-by-step explanation:
To determine whether a relation is a function, we can use the vertical line test. If a vertical line touches the relation in more than one point, it is not a function.
Since a vertical line will touch the relation at two points at x=1
(1,1) and (1,3) this is not a function
In order to unload clay easily, the body of a dump truck must be elevated to at least 50°. The body of a dump truck that is 15 feet long has been raised to 9 feet. Will the clay pour out easily? Show your work and draw a diagram to support your answer.
Please include the following:
• A diagram
• The trig equation you are solving and the steps you take to solve it.
• An answer in the context of the problem.
_________ (Yes or No), The clay ___________ (will or will not) pour out easily when the body of the dump truck is raised to 9 feet. I know this because ______________________________________.
Answer:
No; the angle of elevation of the front bottom of the dump truck body will be only 31°, much smaller an angle than the required 50°
Step-by-step explanation:
Let the body of the truck rest upon the x-axis with the rear body at (0, 0). The front of that body is located at (15, 0). The dump body is elevated to 9 ft.
We thus have a right triangle with base 15 ft and height 9 ft, and want to know what the angle is. The angle is at (0, 0). The front of the body is at (0, 15), and when elevated that point will be located at (15, 9).
The tangent function relates the angle to the opposite side (length 9 ft) and the adjacent side (length 15 ft):
tan Ф = opp / hyp = 9 / 15 = 31 degrees.
NO: the elevation of the front of the dump truck body is only 31° approx. The clay will not easily dump from the body.
This is a rational expression because the denominator contains a variable. This is a polynomial with 3 terms. This is a rational expression because the denominator contains a variable. This is a polynomial with 4 terms. This is a rational expression because the denominator contains a variable. This is a polynomial with 4 terms. This is a rational expression because the denominator contains a variable. This is a polynomial with 3 terms. This is a rational expression because the denominator contains a variable. This is a polynomial with 5 terms.
Answer:
i agree
Step-by-step explanation:
The coins in the stores cash register total $12.50. The cash register contains only nickels, dimes, and quarters. There are twice as many dimes and nickels. There are also twice as many quarters as dimes. How many dimes are in the cash register?
Answer:
20 dimes
Step-by-step explanation:
We can group the coins into groups that are ...
4 quarters + 2 dimes + 1 nickel
Then each group satisfies the ratio requirements, and the total value of a group is $1.25.
Since the total value in the register is $12.50, there must be 10 such groups, hence 20 dimes.
Triangle ABC has coordinates A(1,-1), B(0,2), and C(2,1) and it is reflected over the line y = x to form triangle A'B'C'. What are the coordinates of triangle A'B'C answer the question using complete sentences...please help
Answer:
The coordinates of triangle A'B'C' are A' (-1 , 1) , B' (2 , 0) , C' (1 , 2)
Step-by-step explanation:
* Lets revise some transformation
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
- If point (x , y) reflected across the line y = x
∴ Its image is (y , x)
- If point (x , y) reflected across the line y = -x
∴ Its image is (-y , -x)
* Lets solve the problem
- ABC is a triangle, where A = (1 , -1) , B = (0 , 2) , C = (2 , 1)
- The Δ ABC reflected over the line y = x to form ΔA'B'C'
∵ The image of the point (x , y) after reflected across the line y = x
is (y , x)
∴ We will switch the coordinates of each point in Δ ABC to find the
coordinates of Δ A'B'C'
# Vertex A
∵ A = (1 , -1) ⇒ x = 1 , y = -1
∴ The x-coordinate of the image is -1
∴ The y-coordinate of the image is 1
∴ A' = (-1 , 1)
# Vertex B
∵ B = (0 , 2) ⇒ x = 0 , y = 2
∴ The x-coordinate of the image is 2
∴ The y-coordinate of the image is 0
∴ B' = (2 , 0)
# vertex C
∵ C = (2 , 1) ⇒ x = 2 , y = 1
∴ The x-coordinate of the image is 1
∴ The y-coordinate of the image is 2
∴ C' = (1 , 2)
* The coordinates of triangle A'B'C' are A' (-1 , 1) , B' (2 , 0) , C' (1 , 2)
PLS HELP HOW DO U SLOVE THIS
Explanation:
There is nothing to "solve." This equation is a trig identity.
Often, it works well to express all trig functions in terms of sine and cosine. When you're trying to prove an identity, you usually pick one side to rearrange, and leave the other side alone. Here, we will rearrange the right side.
[tex]\csc\theta=\dfrac{\cot\theta+1}{\cos\theta+\sin\theta}\\\\\csc\theta=\dfrac{\dfrac{\cos\theta}{\sin\theta}+1}{\cos\theta+\sin\theta}=\dfrac{\left(\dfrac{\cos\theta+\sin\theta}{\sin\theta}\right)}{\cos\theta+\sin\theta}=\dfrac{1}{\sin\theta}\\\\\csc\theta=\csc\theta[/tex]
Will give brainliest!
Aubrey was offered a job that paid a salary of $45,000 in its first year. The salary was set to increase by 2% per year every year. If Aubrey worked at the job for 20 years, what was the total amount of money earned over the 20 years, to the nearest whole number?
Aubrey's total earnings over 20 years, given a starting salary of $45,000 and a 2% annual increase, would be approximately $1,157,357, calculated using the formula for an increasing annuity.
Explanation:The subject of this question is compound interest, which is a mathematical concept used to calculate the future value of an investment or loan. In this case, Aubrey's salary is subject to an annual increase of 2%, which is compounded yearly.
To calculate the total amount earned over 20 years, we need to use the formula for the future value of a salary subject to yearly increases: Future Value = Salary * ((1 + Rate)^Years). Substitute the given values into the equation: Future Value = $45,000 * ((1 + 0.02)^20). Calculating this gives a value of approximately $66,207.11, which would be Aubrey's salary in the 20th year.
To find the total earnings over 20 years, you would add each year's salary together. However, it is much more complex due to the increasing salary. In this case, an annuity formula can be used.
The formula is: Total Earnings = Pmt * ((1 - (1 + r) ^ -n) / r). 'Pmt' is the first period payment, 'r' is the interest rate, and 'n' is the number of payments. Here, Pmt = $45,000, r = 2% or 0.02, and n = 20 years. After substituting everything in, the result should be around $1,157,357 rounded to the nearest whole number.
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ONLY PEOPLE WHO ANSWER CORRECTLY AND ANSWER ALL GET BRAINLIEST AND FULL POINTS
Q1: How do you identify the solution to a system of two linear equations in two variables from their graphs?
Q2: What causes a system of two equations in two variables to have no solution? What causes a system of two equations in two variables to have infinitely many solutions?
Q3: How do you determine whether to use substitution or elimination to solve a system of equations?
Q1: The solution of a system of two linear equations in two variables is the point where their graphs intersect. At that point, the (x, y) pair satisfies both equations.
__
Q2: There will be no solution when the lines representing the equations do not intersect. That will only happen when they are parallel. (We say the equations are "inconsistent.")
There will be infinitely many solutions when the lines overlap. That is, the equations for them are essentially the same equation. (We say the equations are "dependent.")
__
Q3: Elimination is easiest when the coefficients of one of the variables are opposites of each other, or if one is a factor of the other. Substitution is easiest if one of the equations is easily put in the form x = ( ) or y = ( ).
If neither or both conditions hold, the choice is by student preference. (In this latter case, solution using Cramer's rule may be simplest.)
greatest common factor.
35+50
Answer:
GCF is 5
Step-by-step explanation:
The factors of 35 are: 1, 5, 7, 35
The factors of 50 are: 1, 2, 5, 10, 25, 50
Please explain how to solve step by step. Thank you.
3x-2 = 5x-14
Subtract 3x from each side:
-2 = 2x -14
Add 14 to each side:
12 = 2x
Divide both sides by 2:
x = 12/2
x = 6
A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through an angle θ. How should θ be chosen so that the gutter will carry the maximum amount of water?
Answer:
θ = 60°
Step-by-step explanation:
The cross sectional area of the trapezoid shape will be that of a trapezoid with bases of 10 cm and (10 cm + 2·(10 cm)·cos(θ)) and height (10 cm)·sin(θ).
That area in cm² is ...
A = (1/2)(b1 +b2)h = (1/2)(10 + (10 +20cos(θ))(10sin(θ)
A = 100sin(θ)(1 +cos(θ))
A graphing calculator shows this area to be maximized when ...
θ = π/3 radians = 60°
_____
A will be maximized when its derivative with respect to θ is zero. That derivative can be found to be 2cos(θ)² +cos(θ) -1, so the solution reduces to ...
cos(θ) = 1/2
θ = arccos(1/2) = π/3
Michael is making a deposit with a check and wants cash back. His deposit slip has his name, his account number, the date, the amount of the check, the amount of cash that he wants, his signature, and what else?
a.his date of birth
b.his social security number
*c.the net deposit amount*
d.the balance of money in the account
(edit) ANSWER: *C*
Answer:
The correct answer option is c. the net deposit amount.
Step-by-step explanation:
We know that Michael is making a deposit with a check and wants some cash back.
According to The Federal Reserve System and The Federal Deposit Insurance Corporation, the deposit slip must have the name his name, his account number, date, amount of the check, amount of cash that he want, his signature and the net deposit amount.
Answer:
C
Step-by-step explanation:
Choose the system of equations which matches the following graph:
a line includes points 0 commas 2 and 5 commas 0
A) 2x − 5y = 10
4x − 10y = 20
B) 2x + 5y = 10
4x + 10y = 20
C) 2x + 5y = 10
4x − 10y = 20
D) 2x − 5y = 10
4x + 10y = 20
Answer:
B
Step-by-step explanation:
If you put (x,y) values in here
(0,2)
2x + 5y = 10
2.0 + 5.2 = 10
0 + 10 = 10
4x + 10y = 20
4.0 + 10.2 = 20
0 + 20 = 20
And the other is
(5,0)
2x + 5y = 10
2.5 + 5.0 = 10
10+0= 10
4x + 10y = 20
4.5 + 10.0 = 20
20 + 0 = 20
All of them is OK.
Answer:
2x + 5y = 10
4x + 10y = 20
Step-by-step explanation:
just took the test
I will give brainliest. please help! <3
Answer:
Given in the problem , as ΔBEC is an equilateral triangle , ∠GCD=90°,m∠ECD=30°
Step-by-step explanation:
Step1:
Statement 2:
as ΔBEC is an equilateral triangle
statement 3:
BG ≅ GC as FG is perpendicular bisector given in the problem.
Statement 4.
∠CFG =60° as as ΔBEC is an equilateral triangle
Staement 5 : Reason : All the angles of an equilateral triangle are 60°
step 2 :-
Statement 1.
as ΔBEC is an equilateral triangle is given in the fourth statement of the problem.
Statement 2.
m∠GCE = 60° as it is contained in ΔBEC which is an equilateral triangle. All the angles of an equilateral triangle are 60°.
Statement 3:
∠GCD =90° as ABCD is a square
Statement 4:
m∠ECD=∠GCD-m∠GCE
=90°-60°
=30°
Hence Proved
Which of the following quadrilaterals have diagonals that are perpendicular to each other? Check all that apply.
Answer: Option B and option D.
Step-by-step explanation:
We know that a quadrilateral is a 2-dimensional closed shape that has four sides.
By definition the diagonals of a quadrilateral are the lines that connect two non-adjacent vertices.
The following quadrilaterals have diagonals that are perpendicular to each other (also known as perpendicular bisector diagonals), which means that they form four angles of 90 degrees (right angles): Rhombus and Square.
Therefore the answers are: the option B and the option D.
The quadrilaterals that have diagonals perpendicular to each other are:
a. Rectangle
b. Rhombus
d. Square
In a rectangle, the diagonals are always perpendicular to each other. The same applies to a rhombus, which is a special case of a parallelogram with all sides equal.
Similarly, a square is a special type of rectangle and rhombus, so its diagonals are also perpendicular. However, in a general parallelogram, the diagonals are not necessarily perpendicular. Therefore, the correct options are a, b, and d.
Therefore, The quadrilaterals that have diagonals perpendicular to each other are:
a. Rectangle
b. Rhombus
d. Square
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AB is tangent to \odot ⊙ O at A (not drawn to scale). Find the length of the radius r, to the nearest tenth.
Answer:
r = 15.2
Step-by-step explanation:
Where AB meets the circle creates a right angle. This is a right triangle problem involving missing sides. This means that we will use Pythagorean's theorem to find the length of the radius. Pythagorean's theorem applies this way:
[tex]10^2+r^2=(r+3)^2[/tex]
Foiling the right side gives us the equation:
[tex]100 + r^2=r^2+6r+9[/tex]
When we combine like terms, we find the squared terms cancel each other out, leaving us with
100 = 6r + 9 and
91 = 6r so
r = 15.2
Please help me find the area of two similar octagons
Answer:
3:5
Step-by-step explanation:
The areas of two similar octagons are 9m² and 25m²
The scale factor of their areas is [tex]\frac{25}{9}[/tex] or 9:25
The scale factor of their side lengths is [tex]\sqrt{25/9}[/tex] or 3:5
ANSWER
3:5
EXPLANATION
The given similar octagons have areas 9 m² and 25m² .
Let the scale factor of their side lengths be in the ratio:
m:n
[tex] {( \frac{m}{n}) }^{2} = \frac{9}{25} [/tex]
We take square root of both sides to get;
[tex] \frac{m}{n} = \sqrt{ \frac{9}{25} } [/tex]
We simplify the square root to get
[tex] \frac{m}{n} = \frac{3}{5} [/tex]
Therefore the scale factor of their side lengths is 3:5
Felicity babysat 2 hours each night for 10 nights.She earned a total of $180 babysitting .Felicity wants to calculate her hourly rate.How much did felicity earn per hour babysitting
Answer:
$9 per hour
Step-by-step explanation:
given that falicity babysat for 2 hours each night for 10 nights
Total hours spent babysitting = 10 nights x 2 hours = 20 hours
hourly rate = total amount earned / total time spent babysitting
= $180 / 20 hrs = $9 per hour
A.
10,000
B.
23,000
C.
55,000
D.
155,000
The best and most correct answer among the choices provided by the question is B.) 23,000
Hope this helps :)
How do you find the length of the legs of an isosceles triangle?
Answer:
Step-by-step explanation:
Geometry PEOPLE HELP
Answer: second option.
Step-by-step explanation:
Given the transformation [tex]T:(x,y)[/tex]→[tex](x-5,y+3)[/tex]
You must substitute the x-coordinate of the point A (which is [tex]x=2[/tex]) and the y-coordinate of the point A (which is [tex]y=-1[/tex]) into [tex](x-5,y+3)[/tex] to find the x-coordinate and the y-coordinate of the image of the point A.
Therefore, you get that the image of A(2,-1) is the following:
[tex](x-5,y+3)=(2-5,-1+3)=(-3,2)[/tex]
You can observe that this matches with the second option.
Find the area of a parallelogram if a base and corresponding altitude have the indicated lengths. Base 3.5 feet, altitude 3/4 feet. 2 1/8 sq. Ft. 2 5/8 sq. Ft. 3 3/8 sq. Ft.
A = bh
A = (3.5)((0.75)
A = 2.625
A = 2_5/8 ft^2