The measure of the line AC is 15√3/2
The measure of the line BC is 15/2
What is a Triangle?Triangle ABC is the display style for a triangle with vertices A, B, and C.
In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces.
One of the internal angles of a right triangle (also known as a right-angled triangle) measures 90 degrees (a right angle). The hypotenuse, the triangle's longest side, is the side that faces the right angle. The triangle's other two sides are referred to as its legs, Right triangles follow the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs of a right triangle (a2 + b2 = c2). Special right triangles have extra characteristics that simplify computations involving them. The 3-4-5 right triangle is one of the two most well-known.
Sin 60⁰=x/15
√3/2=x/15
x=15√3/2
The measure of the line AC is 15√3/2
Cos 60⁰= y/15
1/2=y/15
y=15/2
The measure of the line BC is 15/2
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Help me out with this
The derivative of the function f(x) = Sin⁻¹(3x) is f'(x) = 3/√(1-9x²) , the correct option is (c) .
In the question ,
a function is given as
f(x) = Sin⁻¹(3x) , we need to find the derivative .
we know that the derivative of Sin⁻¹(x) is equal to 1/√(1 - x²) .
So , on differentiating both sides with respect to "x" .
we get
f'(x) = d/dx (Sin⁻¹(3x))
= 1/√1-(3x)² × d/dx (3x)
= 1/√(1 - 9x²) × 3
On simplifying further ,
we get
= 3/√(1 - 9x²)
Therefore ,the derivative of the function is 3/√(1-9x²) , the correct option is (c) .
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I’m stuck on this question I’ve tried this question so many times and I just don’t understand so I need help please
Answer:
see explanation
Step-by-step explanation:
(a)
parallel line segments are indicated by arrows on the segments pointing in the same direction.
from the diagram EA and DC are parallel lines.
(b)
equal lines are indicated by a dash through the lines.
from the diagram AB and BC are equal.
(c)
perpendicular lines are at right angles (90° ) to each other, usually indicated by a small box between them.
from the diagram AE and CD are perpendicular to DE
45 POINTS!!!!! WILL GOVE BRAINLYEST!!
Answer:
20 units
Step-by-step explanation:
we find the side lengths by looking at the coordinates and just counting up
Sides are 6,4,6,4
So we just add
6+4+6+4
10+10
20
Hopes this helps please mark brainliest
Answer: Your answer is 20 units, because the height is 6 units, and the length is 4 units, so we then multiply by 2 for both numbers, then add them together, having a sum of 20 units.
Hope that helps.
5. The diagram shows a rectangular field ABCD has a path of uniform width around it. AB and BC are 6m and 4 m respectively. Given that area PQRS is twice the area of ABCD. Find the length of PQ and QR.
Tthe length of PQ and QR. is 6 and 8 m
Area of rectangular field ABCD is = 4m x 6m = 24m2
Area of rectangular field PQRS (ABCD with uniform path) = (4 + x)(6 + x)
= 24 + 4x + 6x + x²
48 = 24 + 10x + x²
x² + 10x - 24 = 0
x² + 12x - 2x - 24
x(x + 12) - 2(x + 12)
(x - 2)(x + 12) = 0
x - 2 = 0
x = 2
PQ = 4 + 2 = 6
QR = 6 + 2 = 8
Therefore, the length of PQ and QR. is 6 and 8 m
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Find the quotient and remainder using synthetic division for
x³ + 7x² + 12x + 5
x+2
The quotient is
The quotient will be x² + 5x + 2 and the remainder will be 1.
Synthetic division method is a method used to divide polynomials. It is used to divide polynomial with a linear factor whose leading coefficient is 1.
We will factorize x³ + 7x² + 12x + 5 by x + 2 using synthetic division method.
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Ben starts walking along a path at 3 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 6 mi/h. How long (in hours) will it be before Amanda catches up to Ben?
It would take Amanda 2.25 hours to catch up with Ben
Speed is the ratio of distance to time. It is given by:
Speed = distance/time
Given that Ben covers a distance d at time t, hence:
3 = d/t
d = 3t
Since Amanda leaves One and a half hours (1.5) after Ben leaves, hence Time = t - 1.5
5 = d/(t - 1.5)
d = 5t - 7.5
Since they catch up, hence:
3t = 5t - 7.5
2t = 7.5
t = 3.75 hours
Time for Amanda = t - 1.5 = 3.75 - 1.5 = 2.25 hours
Hence it would take Amanda 2.25 hours to catch up with Ben.
Determine the value of each expression. |-2-8|-|−5|
Answer:
5
Step-by-step explanation:
:)
Answer:5
Step-by-step explanation:|-10|-|-5|
10-5
5
How many solutions does the equation a+b+c+d=15 have?
The equation a+b+c+d=15 has infinite many solutions
How to determine the number of solutions?From the question, the equation is given as
a+b+c+d = 15
From the above representation of the equation, we can see that:
The equation is a linear equationAlso, the equation has 4 variablesWhen a linear equation that has more than one variable is given, the number of solutions cannot be quantified i.e. infinite number of solutions
Hence, the equation has infinite number of solutions
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Solve the system by back substitution.
- 2x - 4y - z- 3w = -5
-2y - 12z - 4w = - 16
5z +5w=10
4w =12
Answer:
y=8 x=-19.5
Step-by-step explanation:
Start from the bottom equation and work your way upSolve the fourth equation for w-5w=-15-5w/(-5)=-15/(-5)w = 3 Then use that value of w to plug into the third equation. Notice we're going backwards or up the chain of equations. After w is replaced, solve for zz+w = 2z+3 = 2z+3-3 = 2-3z = -1 Now use z = -1 and w = 3 to plug into the second equation. Solve for y-2y-12z-4w = -16-2y-12(-1)-4(3) = -16-2y+12-12 = -16-2y = -16-2y/(-2) = -16/(-2)y = 8
Use y = 8, z = -1, w = 3 to plug into the first equation. Solve for x:
2x+4y+z+3w=12x+4(8)+(-1)+3(3)=12x+32-1+9=12x+40=12x+40-40=1-402x=-392x/2=-39/2x = -39/2 The value of x as a fraction is x = -39/2The value of x in decimal form is x = -19.5
stu took a test. There were 60 questions. He answered 35 correctly. What grade did Stu make
Answer:
58%
Step-by-step explanation:
35/60=0.58333=58/100=58%
Write a quadratic function f whose zeros are 7 and -5.
Answer:
f(x) = x² -2x -35
Step-by-step explanation:
You want a quadratic function that has zeros 7 and -5.
FactorsEach zero (p) gives rise to a factor (x-p). The zeros 7 and -5 mean the quadratic has factors (x-7) and (x-(-5)).
f(x) = (x -7)(x +5)
f(x) = x² -2x -35
__
Additional comment
You may notice that the coefficient of the linear term is the opposite of the sum of the zeros. The constant term is the product of the zeros. Knowing this, we can write the quadratic without any concern for the factors.
sum: 7-5 = 2
product: (7)(-5) = -35
quadratic: f(x) = x² -2x -35
what is the rate of acceleration of a bycycle if it went from a complete stop to 15 meters per second in 5 seconds ILL MAKE U BRAINLIEST
The rate of acceleration of a bicycle. if it went from a complete stop to 15 meters per second in 5 seconds is
How to calculate the rate of accelerationacceleration is solved using the formula
a = (v - u) / t
definition of variables
final velocity = v
initial velocity = u
time taken = t
form the question we have that
v = 15 meters per seconds
u = 0 (bicycle went from complete stop)
t = 5 seconds
a = (15 - 0) / 5
a = 15 /5
a = 3 meters per seconds squared
The bicycle is travelling at an acceleration of 3 meters per seconds squared
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The amount $3.80 of 4% of what price?
A club with fourteen members is to choose three officers: president, vice-president, and secretary-treasurer. If each
office is to be held by one person and no person can hold more than one office, in how many ways can those offices
be filled?
ways
There can be 2184 ways in which three posts can be selected using permutation.
What is permutation?
An arrangement of things in a specific order is referred to as a permutation. In this arrangement, the components or components of sets are arranged in a linear or sequential order.
Main Body:
Total members =14
total posts =3
As one person can not hold more than 1 post ,
total ways are = ¹⁴P₃
Therefore total ways = 14!/11!
= (14*13*12*11!)/11!
= 14*13*12
= 2184 ways
Hence answer is 2184 ways to select 3 members out of 14.
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calculate the distance between two points a(-9,-10) and b(0,-10)
Answer:
The distance between two points on a 2D coordinate plane can be found using the following distance formula. d = √ (x2 - x1)2 + (y2 - y1)2. where (x 1, y 1) and (x 2, y 2) are the coordinates
Step-by-step explanation:
What is 8370dividedby62
If A = (6,7,8,11) and B = {(7,6,7,9), list the elements of A U B.
The elements of AUB is {6, 7, 8, 9, 11} when A = {6,7,8,11} and B = {7,6,7,9}.
According to the question,
We have the following information:
A = {6,7,8,11} and B = {7,6,7,9}
Now, we know that the elements of AUB means that all the elements which are there in both sets but the elements are not supposed to be repeated.
(Please that AUB can also be found using Venn diagram and questions are asked where the question has to be solved by making Venn diagram and representing all the elements in it.)
So, we have the following expression:
AUB = {6,7,8,9,11}
(Now, note that numbers however repeated in sets are not repeated here.)
Hence, the elements of AUB is {6, 7, 8, 9, 11} when A = {6,7,8,11} and B = {7,6,7,9}.
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Leg A of a right triangle is 12 inches long, and the hypotenuse, C, is 13 inches long. How long is the other leg, B?
The Helping Hands Student Club set a goal to raise $4,000 by the end of the school year for a project. After 3 months, it reaches 42% of its goal. How much was raised during the first 3 months?
During the first 3 months students club has raised fund of $1680.
Given that, The Helping Hands Student Club set a goal to raise $4,000 by the end of the school year for a project.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
After 3 months, it reaches 42% of its goal.
The fund raised during the first 3 months is
42% of 4000
= 42/100 × 4000
= 42×40
= $1680
Therefore, during the first 3 months students club has raised fund of $1680.
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Answer:
$1,680
Step-by-step explanation:
NEED HELP ASAP WILL GIVE BRAINLIEST!
3Fill blanks
1. _ 2. _<6ab+3b/3a+1<_
Answer:
Step-by-step explanation:
What is the domain of the function y=√x+6-7?
O x2-7
O x2-6
O x26
Ox27
The domain of the function is [ - 6 , ∞ ]
A radical function is the one provided.
It should be noted that a radical function can only be specified for values that will result in the radicand being larger than or equal to zero.
As a result, either the radicand of the provided function must be larger than or equal to zero, or:
Thus we can write it as
x + 6 ≥ 0
subtract 6 from both LHS and RHS
x + 6 - 6 ≥ 0 - 6
x ≥ - 6
Therefore the domain of the function is [ - 6 , ∞ ]
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Given p(x)=x+7/3, if p(x)=13 find x
x = 32
Step-by-step explanation:
[tex]{ \tt{p(x) = \frac{x + 7}{3} }}[/tex]
If p(x) = 13, then
[tex]{ \tt{13 = \frac{x + 7}{3}}} [/tex]
[tex]{ \tt{13 \times 3 = x + 7}}[/tex]
[tex]{ \tt{39 = x + 7}}[/tex]
[tex]{ \tt{39 - 7 = x}}[/tex]
[tex]{ \red{ \boxed{ \blue{ \sf{x = 32}}}}}[/tex]
The formula for distance is expressed as d = rt, where d is distance, r is the rate, and t is time.
How long would it take a car to travel 348 miles if it is traveling at a rate of 60 miles per hour?
hours
Answer:
5.8 hours
Step-by-step explanation:
First, you just plug it the given information.
Turn the equation to t=d/r by dividing the rate by both sides.
Plug it in 348miles/ 60 miles per hour
It'll take 5.8 hours for the car to travel 348 miles at the rate of 60 miles per hour.
In Exercises 27-30, give the measure of the angle in radians and
degrees. Give exact answers whenever possible.
sin¹ (0.5)
The measure of the angle for the given trigonometric function is 30°.
Given that, [tex]sin^{-1}(0.5)[/tex].
What are trigonometric angles?Trigonometric angles are the angles in a right-angled triangle using which different trigonometric functions can be represented. Some standard angles used in trigonometry are 0º, 30º, 45º, 60º, 90º.
Trigonometry angle can be expressed in terms of trigonometric ratios as,
θ = [tex]sin^{-1[/tex] (Perpendicular/Hypotenuse)
θ =[tex]sin^{-1[/tex] (0.5)
= [tex]sin^{-1[/tex] (1/2)
= 30°
Therefore, the measure of the angle for the given trigonometric function is 30°.
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The odds in favor of an event occurring are given. Compute the probability of the event occurring. (Enter the probability as a fraction.) 8 to 9
The probability expression when converted from odd's expression is 8/17
How to determine the probability?From the question, we have the following odd parameters
Odd = 8 to 9
To start with, we need to express the odd as ratio
So, we have the following representation
Odds ratio = 8 : 9
Solving further, we need to express the ratio as fraction
So, we have the following representation
Odds fraction = 8/9
To convert the above odd's expression to probability expression, we make use of the following equation
This is represented as
P = Odds/(Odds + 1)
Substitute the known values in the above equation
So, we have the following equation
P = (8/9)/(8/9 + 1)
Evaluate the sum
This gives
P = (8/9)/(17/9)
Express the quotient as product
P = (8/9) * (9/17)
Evaluate
P = 8/17
Hence, the probability is 8/17
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Solve for x
20=.694(x+150)*2
Answer: x = -135.59
Step-by-step explanation:
20 = 0.694(x + 150)(2)
Step 1: Simplify both sides of the equation.
20 = 0.694 (x + 150)(2)
20 = 1.388x + 208.2 (use the distributive property)
20 = 1.388x + 208.2
Step 2: Flip the equation.
1.388x + 208.2 = 20
Step 3: Subtract 208.2 from both sides of the equation.
1.388x + 208.2 − 208.2 = 20 − 208.2
1.388x = −188.2
Step 4: Divide both sides by 1.388.
1.388x/1.388 = −188.2/1.388
x = −135.590778
Optional: Simplify
x = -135.59
26³ +5=2(3)³ +5 7
please help me solve this lol
Answer:
(simplify 26³)
26³ = 17,576
= 17,576 + 5 = 3³+57
(simplify 3³)
3³ = 27
= 17,581 = 27+57
= 17,581 ≠ 84
b) How many more squares need to be shaded so that 70% of the grid is shaded?
The percentage of shaded grid is 45% and the number of squares is 5.
How to find the percentage of shaded grid?a. Percentage of shaded grid
The total number of shaded and unshaded grid is 20 while the total number of shaded area is 9 now let find the percentage of the shaded grid.
Percentage of shaded grid = Shaded grid /Total grid
Percentage of shaded grid = 9/20 × 100
Percentage of shaded grid = 45%
b. Number of squares to be shaded
Number of squares = 20 grid × (70% - 45%)
Number of squares = 20 grid × 25%
Number of squares = 5 squares
Therefore the percentage is 45% .
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there are 121 boys and 116 girls signed up for a trip to an amusement park the leader first makes groups of nine students each and then assigns any remaining students to make some groups of 10 students how many groups of 10 students will there be explained and how many groups of nine students will there be explained
By using addition, subtraction, multiplication and division of integers,
it can be calculated that
There are 3 groups of 9 and 21 groups of 10
What is addition, subtraction, multiplication and division of integers?
Addition of integers is used to find the sum total of two or more integers.
Subtraction of integers is used find the difference between two integers.
Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers.
Division is the process in which the value of single unit can be calculated from the value of multiple unit
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
Here, addition, subtraction, multiplication and division of integers will be used
Total number of boys = 121
Total number of girls = 116
Total number of students = 121 + 116 = 237
Now,
The leader first makes groups of nine students each and then assigns any remaining students to make some groups of 10 students
So the group of 9 is to be made in such a way that on multiplying the number by 9, unit digit of 7 is obtained
So the number is 3 as 9 [tex]\times[/tex] 3 = 27
Remaining number of students = 237 - 21 = 210
They will enter into a group of 10
Number of group of 10 = 210[tex]\div[/tex] 10 = 21
There are 3 groups of 9 and 21 groups of 10
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Use graphing to find the solutions to the system of equations.
- x² + y = 1
-x + y = 2
The solution to the equation using graph is x= -0.62 or x = 1.62.
What is equation?
A mathematical equation may be a formula that uses the equals sign to represent the equality of two expressions.
Main Body:
For [tex]-x^{2} +y = 1[/tex]
We make y the subject to obtain
[tex]y = x^{2} +1[/tex]
We can easily graph this function, because we just have to transform the graph [tex]y = x^{2}[/tex] of by shifting the intercept up to 1.
As for the straight line, -x +y = 2
We find the intercepts as follows,
When y = 0 , x = -2
When x = 0 , y = 2
We plot the points (-2,0) and (0,2).
We now draw the two graphs on the same graph sheet. The intersection of the two graphs gives the solution to be
x= -0.62 or x= 1.62
See graph
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