Answer:
[tex]b\approx 21.435332[/tex]
Step-by-step explanation:
The Law of Sines is a property that relates the sides and angles of any triangle. This property states the following:
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]
Where (A), (B), and (C) are the angles of the triangles. The sides (a), (b), and (c) are the sides opposite their respective angles, (side (a) is the opposite angle (<A); side (b) is the opposite angle (<B); and side (c) is the opposite angle (<C)). Substitute the given information into the formula and solve for the unknown:
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]
[tex]\frac{sin(A)}{a}=\frac{sin(72)}{b}=\frac{sin(53)}{18}[/tex]
Remove the parts of the equation that are not relevant to the problem,
[tex]\frac{sin(A)}{a}=\frac{sin(72)}{b}=\frac{sin(53)}{18}[/tex]
[tex]\frac{sin(72)}{b}=\frac{sin(53)}{18}[/tex]
Take the cross product of the proportion,
[tex]\frac{sin(72)}{b}=\frac{sin(53)}{18}[/tex]
[tex]18(sin(72))=b(sin(53))[/tex]
Inverse operations,
[tex]18(sin(72))=b(sin(53))[/tex]
[tex]b=\frac{18(sin(72)}{sin(53)}[/tex]
[tex]b\approx 21.435332[/tex]
Calculate the surface area of a solid box in the shape of a cube with side length 7cm.
Step-by-step explanation:
a=7
=6a^2
=6×(7)^2
=6×49
=294
Answer:
Surface area of the cube = 294cm^2
Step-by-step explanation:
A cube has the same side lengths for every side
Surface area of one face is length * length
7 * 7 = 49cm^2
A cube has 6 faces
49 * 6 = 294cm^2
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
If x+2 is a factor of x^3-6x^2-11x+k then k=
Step-by-step explanation:
From the question given above, the following data were obtained:
f(x) = x³ – 6x² – 11x + k
Factor => x + 2
Value of k =?Next, we shall obtained the value of x from x + 2. This can be obtained as follow:
x + 2 = 0
Collect like terms
x = 0 – 2
x = –2Finally, we shall determine the the value of k. This can be obtained as illustrated below:
f(x) = x³ – 6x² – 11x + k
x = –2
Value of k =?f(–2) = 0 since x + 2 is a factor
x³ – 6x² – 11x + k = 0
(–2)³ – (–2)² – 11(–2) + k = 0
–8 – (4) + 22 + K = 0
–8 – 4 + 22 + K = 0
10 + k = 0
Collect like terms
k = 0 – 10
k = –10Therefore, the value of k is –10
Learn more: https://brainly.com/question/13587979
Consider the scenario and use complete sentences to answer the question.
Two players each roll an ordinary number cube. The sum is found of the two numbers showing. If the sum is an even number, player A gets 1 point. If the sum is an odd number, player B gets 1 point. The game ends after 6 rounds.
Is this a fair game? Use the possible results of the game to support your answer.
Answer:
yes both chances are 1/2 = equal
Step-by-step explanation:
Factorize the following by splitting the middle term:-
(a) 3x^2 +11x+30
Answer:
See explanation
Question has been corrected
Step-by-step explanation:
Given:
3x² + 11x + 30
To factorise, multiply the coefficient of x² by 30
= 3 * 30
= 90
Find two numbers that have a product of 90 and a sum of 11
** There are no such two numbers, therefore the question can't be solved using factorization
Correcting the error in the question:
x² + 11x + 30
To factorise, multiply the coefficient of x² by 30
= 1 * 30
= 30
Find two numbers that have a product of 30 and a sum of 11
6 and 5
6 + 5 = 11
6 * 5 = 30
x² + 11x + 30
= x² + 6x + 5x + 30
= x(x + 6) + 5(x + 6)
= (x + 6) (x + 5)
need help with this question plz picture of question added
Answer:
The domain of the function is (-2,&)
Can you answer this math homework? Please!
Evaluate the function.
f(x) = 4x² + 73 – 18
Find f(-9)
Answer:
379
Step-by-step explanation:
4(-9)²+73-18
4(81)+55
324+55
379
simplify (4^3)^5 someone help
Answer:
Exact Form:
235235
Decimal Form:
4.64.6
Mixed Number Form:
4 3/5
Answer:
5649
Step-by-step explanation:
4^3=64
64^5=5649
A 2-column table with 5 rows. Column 1 is labeled Number of chores, x with entries 2, 4, 6, 8, 10. Column 2 is labeled Days, y with entries 1, 2, 3, 4, 5.
The table shows the number of days required to perform a given number of chores. The number of days varies directly with the number of chores. What is the constant of variation?
2
3
One-half
One-third
Answer:
C: 1/2
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
Bc i passed it
Find the 20th term of the following sequence.
-6, -4,-2, O,...
Step-by-step explanation:
An=-6+(20-1)×2
=-6+19(2)
=-6+38
=32
Give an example of a monomial and a binomial having degrees as 82 and 99, respectively.
Answer:
An example of monomial having a degree of 82 = x⁸²
An example of a binomial having a degree of 99 = x⁹⁹ + x
Answered by GAUTHMATH
Passing through point (4, 9) and perpendicular to the line y= -1/5x -3
Answer:
y = 5x-11
Step-by-step explanation:
The slope intercept form of a line is y =mx+b where m is the slope
y = -1/5 x-3
The slope is -1/5
Lines that are perpendicular have negative reciprocal slopes
-1 /(-1/5)
-1 * -5/1
5
The slope of the line that is perpendicular is 5
y=5x+b
Using the point (4,9)
9 = 5(4)+b
9 = 20+b
9-20 =b
-11
y = 5x-11
what is the length of ad A. 1 unit B. 2 units C. 3 units D. 4 units
Answer:
3
Step-by-step explanation:
Answer:
Step-by-step explanation:
please help with this too
Answer:
The area of the sector in circle G formed by segments [tex]\overline{AG}[/tex], and [tex]\overline {GB}[/tex] is approximately 125.66 square units
Step-by-step explanation:
The given parameters are;
The radius of the circle with center G, r = 15
The measure of the given angle, m∠AGB = 64°
The area of a sector is given as follows;
Area of a sector of a circle = (θ/360°) × π × r²
Therefore;
The area of the sector in circle G formed by segments [tex]\overline{AG}[/tex], and [tex]\overline {GB}[/tex] is given as follows;
The area of the sector in circle G = (64°/360°) × π × 15² ≈ 125.66 square units
Write the words that represent s + 21.
Answer:
A number s plus 21
Step-by-step explanation:
s+21
A number s plus 21
25 x square - 4y Square = 36 equation 1
5 x - 2 y=2equation 2
It is hard to find out question cn u pls take a pic and upload so it will more easier to find out the question
Anyone knows the answer?
Answer:
a) yes
b) y = -x
c) yes it goes thru the origin (0,0)
Step-by-step explanation:
a) x**2 + y**2 = 17
(-4)**2 + (-1)**2 = 17
16 + 1 = 17 YES
b) the slope of DE is
(y1 - y2)/(x1 - x2)
(-1 -4)/(-4 -1) = -5/-5 = 1, so a perpendicular segment will have a
slope of - 1/current slope or -1.
The midpoint of DE is
x = (x1 + x2)/2 = (-4 +1)/2 = -3/2
y = (y1 + y2)/2 = (-1 +4)/2 = 3/2 so
y = mx + b
y = -x + b plug in the point (-3/2,3/2)
3/2 = -(-3/2) + b
b = 0 SO y = -x
c) The circle equation dictates that it has no offset so centers around the origin (0,0) and the equation of the bisector y = -x indeed fits (0,0).
Which equation can be used to find the number of students needed to make 1,500 in profit ?
Answer:
we can use simple equation
simplify
(−5abc − 6ac + 7cb) − (10abc + 6ac − 8bc)
Answer:
-15abc - 12ac + 15bc
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
(-5abc - 6ac + 7cb) - (10abc + 6ac - 8bc)
Step 2: Simplify
[Distributive Property] Distribute negative: -5abc - 6ac + 7cb - 10abc - 6ac + 8bcCombine like terms: -15abc - 12ac + 15bcPoint A is located at (2, 6), and point M is located at (−1, 8). If point M is the midpoint of segment AB, find the location of point B.
(5, 4)
(0.5, 7)
(0, 6)
(−4, 10)
Answer:
(−4, 10)
Step-by-step explanation:
B = (x, y)
(2 + x) ÷ 2 = -1
therefore x is -4
(6 + y) ÷ 2 = 8
therefore y is 10
Feel free to message me if you still have questions :)
The coordinate point of point B (x₁, y₁) will be (−4, 10). Then the correct option is D.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
Point A is located at (2, 6), and point M is located at (−1, 8). If point M is the midpoint of segment AB.
Then the coordinate of the point B(x₁, y₁) will be
We know that the mid-point formula
[tex]\rm (x,y) \ \ = \left ( \dfrac{x_2+x_1}{2}, \dfrac{y_2+y_1}{2} \right )\\\\(-1, 8) = \left ( \dfrac{2+x_1}{2}, \dfrac{6+y_1}{2} \right )[/tex]
Then the value of x₁ and y₁ will be
[tex]\rm x_1 = -4\\\\y_1 = 10[/tex]
Then the coordinate point of B (x₁, y₁) is (−4, 10).
More about the coordinate geometry link is given below.
https://brainly.com/question/1601567
A square pyramid has a base with an area of 20 square meters, and its lateral faces have a slant height of x meters. Sydney is constructing a second square pyramid with the same size base, but the lateral faces of her pyramid have a slant height twice as long, 2x. Which statement best describes how the surface area of Sydney’s pyramid compares to the surface area of the original pyramid?
Sydney’s pyramid will have the same surface area because the One-half in the expression for the area of the triangular faces will make up for the slant height being doubled.
Sydney’s pyramid will have the same surface area because the slant height is not used when finding surface area.
Sydney’s pyramid will have a surface area that is exactly double the original pyramid’s because the slant height is used when finding the area of every lateral face.
Sydney’s pyramid will have a surface area that is greater than the original pyramid’s but not double the area because the slant height is not used when finding the area of the base.
1. Consider the pyramid ABCDE in the figure 1 attached:
Each side of the square base equals (units)
Area of 1 lateral side of pyramid ABCDE is
so the total lateral area is (units squared)
and the total surface area is (units squared)
2. Now consider the second figure KLMNP, Sydney's pyramid:
The lateral area is
so the total area of the second pyramid is
So 2 things can be said about the areas:
i) the lateral area of Sydney's pyramid is times larger than the lateral area of the original pyramid.
ii) The total area of Sydney's pyramid is units squared larger than the total area of the original pyramid.
Hastings Diner reported losses of $475 each day for three days. What wa the loss for the three days?
Answer:
-1425
Step-by-step explanation:
Day 1 - 475
Day 2 -475
Day 3 - 475
-475+ -475 + -475 = -1425
Write the equivalent fraction, the reduced fraction, and the decimal equivalent for 45%. Jenny solved this problem and her work is shown below. What mistake did she make? 45% = StartFraction 45 Over 100 EndFraction = StartFraction 9 Over 20 EndFraction = 4.5
Answer: See explanation
Step-by-step explanation:
The equivalent fraction of 45% is solved as follows:
First, we'll change the percentage to fraction which will be:
45% = 45/100
Then, we'll reduce to lowest term which will be:
45/100 = 9/20
Now, we'll convert the fraction to decimal which will be:
9/20 = 0.45
The mistake that Jenny made was that she divided 90 by 20. This will give 4.5.
Answer: The decimal equivalent is not correct. The decimal point is in the wrong position. The decimal point should be to the left of the 4, so the correct answer is 0.45.y-step explanation:
Do someone mind helping me pls :)
=========================================================
Explanation:
The uppercase E represents "ten to the"
So saying E8 means "ten to the 8th power"
In other words, 9.837 E 8 = 9.837 * 10^8
The exponent positive 8 tells us to move the decimal point over to the right 8 spots.
So that's how we go from 9.837 * 10^8 to 983,700,000
There are 5 zeros in that value after the "9837" portion.
When we move from 9.837 to 9837.0, that's exactly 3 spots so far. Then the decimal point has to move another 5 spots to go from 9837.0 to 983,700,000 which is therefore 3+5 = 8 total shifts to the right.
The number 983,700,000 is slightly over 983 million. If anything, it's more closer to 984 million.
Answer: Standard Form = 983, 700, 000
Step-by-step explanation:
Concept:
The term "E" is usually used in calculators or on-screen which stands for exponents. It has been used to display numbers in scientific notations.
Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form. Usually in the form of [ a × 10ᵇ ] where a is a number 0<a<10 and b are integer exponents.
"E" in simpler words is basically the base "10" in scientific notation, while the number after "E" would be the exponents on "10"
Solve:
Given = 9.837 E 8
"E" = 10
"8" = ⁸
E 8 = 10⁸
10⁸ basically means that there are 8 zeros after 1.
Therefore, to find the standard form of 9.837E8, we have 3 zeros to get 9.837 to become an integer, then add the remaining 5 zeros at the end to get the final answer.
9.837 × 10⁸ = 983,700,000Hope this helps!! :)
Please let me know if you have any question
A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?
Answer:
120 kg in morning and 240 kg in afternoon
Step-by-step explanation:
x+2x=360 kg
Work:
x + 2x = 360 kg
3x = 360 kg
3x/3 = 360 kg/3
x = 120
2x=2(120 kg) =240 kg
Final Answer:
So, 120 kg in morning and 240 kg in the afternoon.
Hope this helps!
congruent figure help please :)
Answer:
x = 29
Step-by-step explanation:
ΔABC ≅ ΔDEC,
So, ∠BAC ≅∠CDE {Corresponding parts of congruent triangles}
∠BAC = 74°
InΔABC,
∠ABC + ∠BAC + ∠BCA = 180
2x + 74 + 48 = 180
2x + 122 = 180
Subtract 122 from both sides
2x = 180 - 122
2x = 58
Divide both sides by 2
x = 58/2
x = 29
Marcel invests $2500 for 3 years at a rate of 1.6% per year simple interest. Jacques invests
$2000 for 3 years at a rate of x% per year compound interest.
At the end of the 3 years Marcel and Jacques receive the same amount of interest.
Calculate the value of x correct to 3 significant figures.
Answer:
x= 1.961
Step-by-step explanation:
Marcel's ,P = 2500 , T = 3, R = 1.6%
SI = PRT/100
=(2500×1.6×3)÷100
Jacques's , P = 2000 , T = 3, R = x%
CI = P( 1 + R/100)^T -P
2000(1 + x/100)^3 -2000
But this is equal to 120
(1 + x/100)^3 = 2120/2000
x= 1.961
I hope this helps !!!!!!!!!!!
I need help and fast I was supposed to turn this in last week
Answer:
The answer is below
Step-by-step explanation:
If two lines intersected by a transversal form congruent corresponding angles, then the lines are parallel.
If two angles are supplementary to the same angle, then the two angles are congruent.
Statement Reason
1) line p is parallel to line q Given
2) angle 1 and angle 4 are Given
supplementary i.e. ∠1 + ∠4
= 180° (definition of supplementary)
3) angle 3 and angle 4 are consecutive interior angles
supplementary
4) angle 1 congruent to angle 3 congruent supplements theorem
supplementary
5) line r parallel to line s corresponding angle converse
Solve for the product (6x−−√)(15x3−−−−√)without a perfect square factor in the radicand. Group of answer choices 90x4−−−−√ 3x210−−√ 310x4−−−−√ 3x410−−√
Answer:
[tex]3x^{2} \sqrt10[/tex]
Step-by-step explanation:
find the inverse of the following function
f-¹(x)=[tex]\frac{2-7x}{x+2}[/tex]
Answer:
Solution given:
f(x)=[tex]\frac{-2x+2}{x+7}[/tex]
Let f(x)=y
y=[tex]\frac{-2x+2}{x+7}[/tex]
Interchanging role of x and y
x=[tex]\frac{-2y+2}{y+7}[/tex]
doing crisscrossed multiplication
x(y+7)=-2y+2
now solve it:
xy+7x=-2y+2
keep like terms in one side
xy+2y=2-7x
take common
y(x+2)=2-7x
make a value of y
y=[tex]\frac{2-7x}{x+2}[/tex]
So,
f-¹(x)=[tex]\frac{2-7x}{x+2}[/tex]
Answer:
ƒ^-1 (x) = [tex]\frac{2-7x}{2+x}[/tex]
Step-by-step explanation:
Substitute y for f (x)
[tex]y = \frac{-2x+2}{x+7}[/tex]
Interchange x and y
[tex]x=\frac{-2y+2}{y+7}[/tex]
Swap the sides of the equation
[tex]\frac{-2y+2}{y+7} = x[/tex]
Multiply both sides of the equation by y + 7
-2y + 2 = (y + 7)x
Distribute x through the parentheses
-2y + 2 = xy + 7x
Move the expression/constant to the left-hand side and change its sign
-2y - xy + 7x - 2
Factor out from the expression
(-2 - x)y = 7x - 2
Divide both sides of the equation by -2 - x
[tex]y = \frac{7x-2}{-2-x}[/tex]
Simplify the expression
[tex]y = \frac{2-7x}{2+x}[/tex]
Substitute ƒ ^-1 (x) for y
[tex]f^{-1} (x) = \frac{2-7x}{2+x}[/tex]
