We can use sine ratio in given right angled triangle.
The sine of ∠Q is represented by ratio 48/73.
Given data:
∠R=90°,
QP = 73,
PR = 48,
RQ = 55
We know that;
The sine of a given angle in a right angle triangle is the ratio of perpendicular and hypotenuse seen from the viewpoint of that angle.
Since, against ∠Q lies the side PR, thus, PR is perpendicular. The side PQ is hypotenuse.
Thus, we have:
sin Q = PR/PQ
= 48/73
Thus, the sine of ∠Q is represented by ratio,
48/73.
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What is the slope intercept of the line below
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option D, y = 2x - 3}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{The graph}[/tex]
Find: [tex]\textsf{The equation in slope intercept form}[/tex]
Solution: Looking at the graph, we can see that the line intersects the y-axis at -3 therefore that is the y-intercept. All we need to do now is find a second point so we can determine the slope. The line crosses at (1, -1) so we will use that as the second point. Then we just plug all of the values into the slope intercept form.
Determine the slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex][tex]m = \frac{-1 - (-3)}{1 - 0}[/tex][tex]m = \frac{-1 + 3}{1}[/tex][tex]m = \frac{2}{1}[/tex][tex]m = 2[/tex]Plug in the values
[tex]y = mx + b[/tex][tex]y = 2x - 3[/tex]Therefore, the option that would best fit the graph that was provided would be option D, y = 2x - 3.
indicate whether the statement is true of false.
please provide a explanation
A linear system with three variables and three equations has a unique solution.
The statement is false, as the system can have no solutions or infinite solutions.
Is the statement true or false?
The statement says that a system of linear equations with 3 variables and 3 equations has one solution.
If the variables are x, y, and z, then the system can be written as:
[tex]a_1*x + b_1*y + c_1*z = d_1\\\\a_2*x + b_2*y + c_2*z = d_2\\\\a_3*x + b_3*y + c_3*z = d_3[/tex]
Now, the statement is clearly false. Suppose that we have:
[tex]a_1 = a_2 = a_3\\b_1 = b_2 = b_3\\c_1 = c_2 = c_3\\\\d_1 \neq d_2 \neq d_3[/tex]
Then we have 3 parallel equations. Parallel equations never do intercept, then this system has no solutions.
Then there are systems of 3 variables with 3 equations where there are no solutions, so the statement is false.
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Which equation is equivalent to log3(x+5) = 2
Answer:
[tex]3^2=x+5[/tex]
Step-by-step explanation:
Given equation:
[tex]\log_3(x+5)=2[/tex]
Method 1
[tex]\textsf{Using the Log law:} \quad \log_ab=c \:\: \Longleftrightarrow \:\: a^c=b[/tex]
[tex]\implies \log_3(x+5)=2[/tex]
[tex]\implies 3^2=x+5[/tex]
Method 2
Make both sides of the equation the index to base 3:
[tex]\implies \log_3(x+5)=2[/tex]
[tex]\implies 3^{\log_3(x+5)}=3^2[/tex]
Apply the log law [tex]a^{\log_ax}=x[/tex] :
[tex]\implies x+5=3^2[/tex]
Swap sides:
[tex]\implies 3^2=x+5[/tex]
Solve for x
Although the question hasn't asked to solve for x, here is the solution:
[tex]\implies 3^2=x+5[/tex]
[tex]\implies 9=x+5[/tex]
[tex]\implies x=9-5[/tex]
[tex]\implies x=4[/tex]
Check
Substitute the found value of x into the original equation:
[tex]x=4 \implies \log_3(4+5)=\log_39=2 \quad \leftarrow\textsf{correct}[/tex]
[tex]\\ \rm\Rrightarrow log_3(x+5)=2[/tex]
log_a^b=c then b=a^c[tex]\\ \rm\Rrightarrow x+5=3^2[/tex]
[tex]\\ \rm\Rrightarrow x+5=9[/tex]
[tex]\\ \rm\Rrightarrow x=9-5[/tex]
[tex]\\ \rm\Rrightarrow x=4[/tex]
A linear function contains the following points. What are the slope and y-intercept of this function?
Answer:
slope: -1
y-intercept: 6
Step-by-step explanation:
y-intercept is when x is 0 so it's 8 and the slope can be found using the slope formula (y2-y1)/(x2-x1)
(6-8)/(0 - (-2)) = -2/2 = -1
ratio of pi?
3. whats an estimation that's fraction form?
Answer:
22/7
Step-by-step explanation:
22/7 is not very close to pi, but it is sometimes used as an estimation for pi
Answer:
22/7 is estimation
A hole the size of a photograph is cut from a red piece
of paper to use in a picture frame.
3
What is the area of the piece of red paper after the hole
for the photograph has been cut?
O 17 square units
O 25 square units
O 39 square units
O 47 square units
Answer:
D)
Step-by-step explanation:
47 is the right answer! Have an cool day!
The area of the piece of red paper after the hole for the photograph has been cut is,
⇒ 47 square units.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Now, First, find the area of the two squares:
The photograph have vertices:
(-3, -2), (-2, 2), (2, 1), and (1, -3).
Since, The square is diagonally aligned, so we need to find the length between two points in order to find the area.
For (1, -3) and (2, 1).
There is a 1 unit length and a 4 unit height.
We can use the Pythagorean theorem to find the hypotenuse of the triangle, which is the length of the square's side:
1² + 4² = x²
1 + 16 = x²
x = √17
The side length for the square of the photograph is the square root of 17,
so the area of the photograph is 17 units²
Now, The red paper has side lengths of 8. The distance between (-4, 4) and (4, 4) is 8 units wide, so we do not need to use the Pythagorean theorem.
Now , we know the area of the red paper and photograph, you can subtract the area to find the red paper with the hole:
64 - 17 = 47 square units.
Thus, The area of the piece of red paper after the hole for the photograph has been cut is,
⇒ 47 square units.
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Simplify (3^1\2x2^1\3)^1\2
Answer:
1.37
Step-by-step explanation:
3^1=3/2=1.5
2^(1/3)=1.26
1.5×1.26=1.89
1.89^(1/2)=1.37
A movie theater offers three types of tickets: child, student, and adult. Ticket sales for two movies are shown in the table.
Ticket Type
Child Student Adult Total
Movie Title The Ransom 12 38 70 100
Space Force 34 42 56 132
Total 46 80 126 232
What proportion of tickets sold were adult tickets?
0.4310
0.5431
0.5556
0.7000
Answer:
(b) 0.5431
Step-by-step explanation:
The proportion of adult tickets sold is the ratio of the total number of adult tickets sold to the total number of tickets sold. Those totals are found on the bottom line of the table.
__
proportion = (adult tickets)/(total tickets) = 126/232 ≈ 0.5431
Approximately 0.5431 of the tickets sold were adult tickets.
Answer:
B) 0.5431
Step-by-step explanation:
edge 2023
Sum of 1/(1*2*3) + 1/(2*3*4) +....+1/(18*19*20)
Answer: 189/760
Step-by-step explanation:
The series can be represented in sigma notation as:
[tex]\sum^{18}_{n=1} \frac{1}{n(n+1)(n+2)}[/tex]
We can perform partial fraction decomposition as follows:
[tex]\frac{1}{n(n+1)(n+2)}=\frac{A}{n}+\frac{B}{n+1}+\frac{C}{n+2}\\\\ \implies 1=A(n+1)(n+2)+B(n)(n+2)+C(n)(n+1)[/tex]
If n = 0, then [tex]1=A(0+1)(0+2) \implies A=\frac{1}{2}[/tex]
If n = -1, then [tex]1=B(-1)(-1+2) \longrightarrow B=-1[/tex]
If n = -2, then [tex]1=C(-2)(-2+1) \longrightarrow C=\frac{1}{2}[/tex]
This means the series can be expressed as:
[tex]\sum^{k}_{n=1} \left(\frac{1}{2n}-\frac{1}{n+1}+\frac{1}{2(n+2)} \right)=\frac{k(k+3)}{4(k+1)(k+2)}[/tex]
Substituting in k=18,
[tex]\frac{18(21)}{4(19)(20}=\boxed{\frac{189}{760}}[/tex]
find the missing values in this sequence; -6;...;3...;15.
Answer:
Maybe 9 and 12 ?
Step-by-step explanation:
-6 + 9 = 3
then 3 + 9 = 12
then 12 + 3 = 15
each term is the sum of the two that are before it
Multiply (3a³-6b³) (4a² + 5b²)
Answer:
[tex]12a^5+15a^3b^2-24b^3a^2-30b^5[/tex]
Step-by-step explanation:
(3a³-6b³) (4a² + 5b²) -> Simplify not Multiply
Expand (3a³-6b³) (4a² + 5b²) using the FOIL Method.
Apply the distributive property.
[tex]3a^3(4a^2+5b^2)-6b^3(4a^2+5b^2)[/tex]
[tex]3a^3(4a^2)+3a^3(5b^2)-6b^3(4a^2+5b^2)[/tex]
[tex]3a^3(4a^2)+3a^3(5b^2)-6b^3(4a^2)-6b^3(5b^2)[/tex]
Simplify each term.
Rewrite using the commutative property of multiplication.
[tex]3*4a^3a^2+3a^3(5b^2)-6b^3(4a^2)-6b^3(5b^2)[/tex]
↓
[tex]12a^5+15a^3b^2-24b^3a^2-30b^5[/tex]
Equation Simplified.
---------------------------------------------------------------------------------------
Hope this helped!
b) 1/16 + 3/64 + 9/256 + 27/1024 ....
The sum of the geometric series will be 1/4. And the sum of the series will be the negative 0.13.
The complete question is attached below.
What is the sum of the geometric series?Let a be the first term and r be the common ratio. Then the sum of the geometric series will be
S = a / (1 – r) if r < 1
S = a / (r – 1) if r > 1
The series is given below.
1/16 + 3/64 + 9/256 + 27/1024 ....
Then we have
a = 1/16
r = (3/64) / (1/16) = 3/4
Then the sum of the series will be
S = (1/16) / [1 – (3/4)]
S = (1/16) / (1/4)
S = 1/4
Let [tex]\rm S = (-0.13)^m[/tex], where m = 1
Then the value of S will be
S = (-0.13)¹
S = -0.13
Hence, the sum of the series will be the negative 0.13.
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What is the equation of the line that has a slope of -4 and passes through the point (2,3)?
Answer:
The answer is y = -4x+11
yo
24
yx
SECTION B
(a) Identity element;
(b) Inverse of 3 and -5 under *
Range y
[30 marks]
Answer all the questions in this section. All questions carry equal marks.
1. A binary operation is defined on the set of real numbers, R, by x + y = x + y + 10.
Find the:
The inverse of 3 and _ 5
Answer:
Sorry I don't know the answer
Help me with this please and thank you!! :)
Answer:
Step-by-step explanation:
[tex]A \cap C[/tex] denotes the set of elements in both A and C, which is [tex]\{20, 24, 28\}[/tex].[tex]B^{C}[/tex] denotes the complement of set B, which is the set of all elements that are in the universal set that are not in set B. In this case, this set is [tex]\{3, 4, 5, 6, 8, 11, 13, 16, 17, 19, 20, 22, 23, 24, 25, 26, 27, 28\}[/tex]Consider the matrix [tex]A_{4x4}, det(A) = -2[/tex]
Show that the following is true or false:
[tex]det(adj(2A^{-1}) =-2^{9}[/tex]
We found a counterexample, so the statement is false.
Is the statement true?
Let's use the matrix:
[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]
This is a 4x4 matrix with determinant equal to -2.
The inverse matrix is:
[tex]\left[\begin{array}{cccc}1/2&0&0&0\\0&-1&0&0\\0&0&-1&0\\ 0&0&0&-1 \end{array}\right][/tex]
If we multiply it by 2, we get:
[tex]\left[\begin{array}{cccc}1&0&0&0\\0&-2&0&0\\0&0&-2&0\\ 0&0&0&-2 \end{array}\right][/tex]
The adjoint of that is the original matrix, actually:
[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]
Which we already know, has a determinant of -2.
So the statement is false, as we found a counterexample.
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−3x(4x² − 81) (x² + 64) = 0
Answer: [tex]x=0,x=-\frac{9}{2}, x=\frac{9}{2}[/tex]
Step-by-step explanation:
[tex]-3x(4x^2-81)(x^2+64)=0\\[/tex]
multiply the terms together
[tex]-12x^5-525x^3+15552x=0[/tex]
factor left side of the equation
[tex]3x(-x^2-64)(2x+9)(2x-9)=0[/tex]
set factors equal to 0
[tex]x=0,x=-\frac{9}{2}, x=\frac{9}{2}[/tex]
Which statement is true about this equation Y=-3x2+4x+-11
Answer:
For plato users, the answer would be letter C.
Step-by-step explanation:
A.
It represents neither a relation nor a function.
B.
It represents a relation only.
C.
It represents both a relation and a function.
D.
It represents a function only.
This equation represents both a relation and a function.
Took the test, hope this helps!
Step-by-step explanation:
Evaluate iint S sqrt 1+x^ 2 +y^ 2 dS where S is the helicoid: r(u, v) = u * cos (v) * i + u * sin (v) * j + vk with 0 <= u <= 1, 0 <= v <= 2pi
Given the parameterization
[tex]\vec r(u,v) = u\cos(v) \, \vec\imath + u\sin(v) \,\vec\jmath + v \,\vec k[/tex]
take the normal vector to be
[tex]\vec n = \dfrac{\partial\vec r}{\partial u} \times \dfrac{\partial \vec r}{\partial v} = \sin(v) \,\vec\imath - \cos(v) \,\vec\jmath - u \,\vec k[/tex]
(The order of partial derivatives in the cross product doesn't matter since this a scalar line integral.)
Compute the magnitude of the normal vector.
[tex]\|\vec n\| = \sqrt{\sin^2(v) + (-\cos(v))^2 + (-u)^2} = \sqrt{1+u^2}[/tex]
so that the area element reduces to
[tex]dS = \|\vec n\| \, du\,du = \sqrt{1+u^2}\,du\,du[/tex]
Evaluate the integrand at [tex]\vec r[/tex] to get
[tex]\sqrt{1 + (u\cos(v))^2 + (u\sin(v))^2} = \sqrt{1 + u^2}[/tex]
The surface integral reduces to
[tex]\displaystyle \iint_S \sqrt{1+x^2+y^2} \, dS = \int_0^{2\pi} \int_0^1 (1+u^2) \, du \, dv = 2\pi \int_0^1 (1+u^2) \, du = \boxed{\frac{8\pi}3}[/tex]
Look at the attachment! This is algebra. 10 points!
If x∆y = 3x - y², then
5∆1 = 3×5 - 1² = 15 - 1 = 14
and
14∆6 = 3×14 - 6² = 42 - 36 = 6
So (5∆1)∆6 = 6.
How would you multiply 4x 2
—
3
( 4 x 2 by 3 (fractions))
Answer:
8/3
Step-by-step explanation:
4 x 2 = 8, so (4 × 2)/2 = 8/3.
We can describe 3x- 2 as an expression. How can we describe the parts of the expression that the arrows point to? 3x- 2
Step-by-step explanation:
3x - 2 is formatted in the formula y = mx + c
To substitute for 3x - 2
y = 3x -2
Help me with this question please!!!
Question 1
We want to choose a white marble, then a black marble.
The probability of choosing a white marble is 9/(9+7+8)=9/24.The probability of choosing a black marble is 8/(9+7+8)=8/24.Multiplying these probabilities, we get (9/24)(8/24) = 1/8.
Question 2
For the guess to be less than 6, they have to choose 1, 2, 3, 4, or 5.Thus, the probability is 5/10 = 1/2.
Question 3
The probability of choosing a yellow marble is 7/(7+8+9)=7/24.The probability of choosing a green marble after is 9/(6+8+9)=9/23. [Note that the 7 yellow marbles is now 6 since we are assuming a yellow marble was drawn beforehand]Multiplying these probabilities, we get (7/24)(9/23) = 21/184.
Which numbers below are odd?
A. 4271
B. 7966
C. 787
D. 288
E. 8113
F. 985
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
-10
10- (2, 10)
(0, 0)
10
The equation of the line with points (2,10) and (0,0) is: y = 5x.
How to Find the Equation of a Line?The line given has two points which are stated as:
(2,10) and (0,0).
Find the slope(m):
Slope (m) = change in y / change in x = (10 - 0)/(2 - 0)
Slope (m) = 10/2
Slope (m) = 5
The y-intercept (b) = 0
Substitute m = 5 and b = 0 into y = mx + b
y = 5x + 0
y = 5x
The equation of the line is: y = 5x.
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One leg of a 90-45-45 triangle is 5. What are the sides of the hypotenuse and the other leg?
Answer:
5√2, 5
Step-by-step explanation:
in a 90 45 45 triangle, each leg is the same legnth
the hypotenuse of a 90 45 45 triangle is x√2
x being the measure of the leg
6x -8=16 solve equation
Answer:
x = 4
Step-by-step explanation:
6x - 8 = 16 (add 8 to both sides)
6x = 24 (divide by 6 on both sides)
x = 4
Brainliest, please :)
Step-by-step explanation:
6x=16+8
6x=24
6x/6=24/6
x=4
so the answer is 4
Write a linear equation in slope-intercept form using a slope and a given point. If a line has a slope of short dash 2 and goes through the point open parentheses 1 comma short dash 3 close parentheses, then the equation for the line in slope-intercept form is ______________. a.) y equals short dash 2 x minus 1 b.) y equals short dash 2 x plus 1 c.) y equals 2 x minus 5 d.) y equals 2 x plus 5
y equals short dash 2 x minus 1
In other words, y = -2x - 1 is the equation
=========================================================
Explanation:
Slope = m = -2
Point on the line is (x,y) = (1, -3)
Use these three items to find the y intercept b
y = mx+b
-3 = -2*1 + b
-3 = -2 + b
-3+2 = b
-1 = b
b = -1
The slope intercept form of y = mx+b turns into y = -2x-1 after plugging m = -2 and b = -1
For any real number c, √² =
A. ²
B. cl
C. 1
D. C
Answer:
answer D ( if i interpreted your question correctly )
Step-by-step explanation:
Sqrt (c^2) = √(c^2) = C
Which statements are true about the ordered pair (-1,-4) and the system of equations? x-y=3 and 7x-y=-3
Answer:
when (-1, -4) is substituted into the first equation it's true
when (-1, -4) is substituted into the second equation it's true
the ordered pair (-1, -4) is a solution to the systems of equation
Step-by-step explanation:
original equation
x-y=3
multiply both sides by 7
7x-7y = 21
add 7y to both sides
7x=7y + 21
substitute into second equation
(7y+21)-y=-3
simplify
6y+21=-3
subtract 21 from both sides
6y=-24
y=-4
substitute y into original equation
x-(-4) = 3
cancel out negative signs
x+4=3
subtract -4 from both sides
x=-1
