The answer of the given question based on the triangle is , the length of ac rounded to 3 sf is 6.71.
The length of ac rounded to 3 sf is 6.71.
We can calculate the length of ac using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
This theorem is represented by the equation c² = a² + b²,
where c is the hypotenuse and a and b are the other two sides.
In the given problem, we know that angle CAB = 90°.
This means that triangle ABC is a right triangle.
Also, AB = 9.2, ∠ ABC = 49°.
Therefore, we can calculate the length of BC using the following trigonometric equation:
tan(∠ABC) = BC/AB
tan(49°) = BC/9.2
BC = 9.2 × tan(49°)
BC ≈ 10.92
Now, we can use the Pythagorean theorem to calculate the length of AC.
c² = a² + b²
c² = AB² + BC²
c² = (9.2)² + (10.92)²
c² ≈ 221.94
c ≈ √221.94
c ≈ 14.9 (rounded to two decimal places)
Thus, the length of ac rounded to 3 sf is 6.71.
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Can someone help me with this problem and show work please !
Answer: Length - 20, Width - 10
Step-by-step explanation:
First we will use the formula to find area:
Area = Length * Width --- However, since it's double the length we will do 2Length.
Area = 2x*x
Given Area = 200
Next we will solve to find Width:
[tex]2x^{2} =200[/tex]
Divide by 2:
[tex]x^{2} =100[/tex]
Take square root:
[tex]x=10[/tex]
Width = 10
Now we multiply 10 by 2, as length is twice it's width:
[tex]2*10=20[/tex]
Length = 20
Final answer: Width = 10, Length = 20
I hope this helps!
Which points lie on the graph of f(x) = -√-x?
□(-9,3)
□(-4,-2)
□ (-1, 1)
□(0,0)
□ (1,1)
□(2,-4)
□(9,3)
Answer:
(-4, -2).
(0, 0).
Step-by-step explanation:
Both coordinates will be negative or (0.0).
It's these followings:
□(-4,-2)
□(0,0)
Hope this helps!
1/2a+2/3b=50 when b=30?
The given equation is (1/2)a + (2/3) b = 50
and b = 30
Substituting the given value of b is above the equation we get
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow\left(\frac{1}{2}\right)a+\left(\frac{2}{3}\right)\times30=50 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow \left(\frac{1}{2}\right)a+20=50 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow\left(\frac{1}{2}\right)a=50-20=30 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow a = 30 \times 2 = 60 } \end{gathered}$}[/tex]
Therefore, a = 60 and b = 30 is a solution of the given equation.
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Find the length of the base.
Answer:
32
Step-by-step explanation:
The length of segment AB is the average of XY and WZ.
(22 + x)/2 = 27
22 + x = 54
x = 32
Evaluate the piecewise function at the indicated values from the domain:
ƒ(−1) = 1
ƒ(−1) = −1
ƒ(−1) = −2
ƒ(−1) = 0
The value of the piecewise function at the domain is f(-1) = 1
How to evaluate the piecewise function?The complete question is added as an attachment
At x = -1, the function is
f(x) = x^2
So, we have:
f(-1) = (-1)^2
Evaluate
f(-1) = 1
Hence, the value of the piecewise function at the domain is f(-1) = 1
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percentage of 67 of 98
The percentages of 67 of 98 is 68.36%
Percentages and fractionsFractions are written as a ratio of two integers. According to the question we are to determine the percentage of 67 that is 98.
Fraction of 67 of 98 = 67/98
Percentage = 67/98 * 100
Percentages = 6700/98
Percentages = 68.37%
Hence the percentages of 67 of 98 is 68.36%
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A linear expression does not have a squared variable.
it is true that a linear expression does not have a squared variable.
How to determine the true statement?The following are the forms of a linear expression
y = mx + c
Ax + By = C
x = a
Notice that none of the above expressions have a squared variable
This means that, a linear expression does not have a squared variable.
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Find AC please help trig is so hard
If the sum of the interior angle of a polygon is 1800 how many sides does it have
Answer: 12 sides
Step-by-step explanation:
The sum of the interior angles of a polygon is 180(n-2), where n is the number of sides
[tex]180(n-2)=1800\\\\n-2=10\\\\n=12[/tex]
If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)? On a coordinate plane, a straight line with a negative slope crosses the y-axis at (0, 5) and crosses the x-axis at (1, 0). On a coordinate plane, a parabola opens down. It goes through (negative 2, negative 4), has a vertex at (0, 5), and goes through (2, negative 2) On a coordinate plane, a parabola opens up. It goes through (negative 3, 7), has a vertex at (negative 1, 2), and goes through (0, 5). On a coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5) - edge21
Answer:
Can i have the graph? THis doesn't make sense
Step-by-step explanation:
The graph of (f+g)(x) is on the coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5).
What is the graph of a parabolic equation?The graph of a parabolic equation is a curved U-shape graph from where the domain, the range, x-intercept(s), and the y-intercept(s) can be determined.
Given that:
f(x) = -x² + 3x + 5
g(x) = x² + 2x
To find (f + g)(x), we have:
(f + g)(x) = (-x² + 3x + 5)+(x² + 2x)
(f + g)(x) = -x² + 3x + 5 +x² + 2x
(f + g)(x) = 3x + 2x + 5
(f + g)(x) = 5x + 5
Use the Slope-intercept form: We are to find the graph of y = 5x + 5
y = 5x + 5
Here:
Slope = 5 x-intercept = (-1, 0)y-intercept = (0,5)Therefore, we can conclude that on the coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5)
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The vectors are linearly independent if and only if?
The vectors are linearly independent if and only if k ≠ -11
How to solve the vectorIn mathematics, the definition of a vector is a quantity that is made up of both magnitude and also have direction. This type of quantity is not one that is considered based on its position. A very good example of such a quantity with magnitude and direction is acceleration.
Vectors are used to represent items such as position, velocity, physical quantities and others in mathematics and in physics.
In this question,
We have 2v - 3w
We have to multiply 2 by the values of v and multiply 3 with the values of w
this would produce
[2,6,8]-[6,6,12]
subtract w from v
= [-4, 0, -4]
We u as -1, 0 and 10+k
It is not possible to -1 = 10 + k
-11 = k
Hence we have to conclude that they are linearly independent if and only if k ≠ -11
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1. A committee of 3 men and 4 women is to be formed from 5 men and 6 women. If a particular woman is not to be included, how many different committees are possible
Step-by-step explanation:
Taking the men first: there are 5 ways to form a 4-man committee out of 5 men.
Taking the women now: There are 20 ways to form a 3-woman committee out of 6 women.
Each of the 5 possible male groups can be combined with any of the 20 possible female groups.
So: 100.
Find the maximum or minimum value of the product of two numbers whose difference is 14.
The maximum value of the product of two number whose difference is 14 is 49.
What is the maximum or minimum value of a function?The maximum or minimum value of a function is the highest or lowest value of that function.
How to determine the maximum or minimum of the product of two numbers?Let the numbers be x and y
Their product f(x,y) = xy
Since their difference is 14, x - y = 14
So, x = 14 - y
Substituting x into f(x,y), we have
f(x,y) = xy
= (14 - y)y
= 14y - y²
To find the maximum or minimum value of f(x,y) we differentiate it with respect to y and equate to zero.
So, f(x,y) = f(y) = 14y - y²
df(y)/dy = d(14y - y²)/dy
df(y)/dy = d(14y)/dy - dy²/dy
df(y)/dy = 14 - 2y
Equating to zero, we have
df(y)/dy = 0
14 - 2y = 0
14 = 2y
y = 14/2
y = 7
To determine if this gives a maximum or minimum for f(y) = f(x,y), we differentiate f'(y) again
So, df'(y)/dy = d(14 - 2y)/dy
= d14/dy + d(-2y)/dy
= 0 - 2
= -2 < 0.
Since f"(y) = -2 < 0, then y = 7 gives a maximum for f(x,y)
So, since y = 7,
x = 14 - y = 14 - 7 = 7
So, f(x,y) is maximum at x = 7 and y = 7
So, f(7,7) = 7 × 7
= 49
So, the maximum value of the product of two number whose difference is 14 is 49.
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A new Concept XI bicycle cost a bike shop $800. The shop set the original list price of the bicycle at a price greater than $800. During the shop’s 30th anniversary sale, every list price in the store was marked down 30%. The shop sold this bicycle during its anniversary sale. Given that the shop made a 40% profit on the sale of this bicycle, what was the bicycle’s original list price?
Based on the fact that the shop still made a 40% profit on the concept xi bicycle, the original listing price must have been $1,600.
what price was the bicycle originally listed at?assuming the list price is x, the formula would be:
800 x 1.40 = (x × 0.7)
solving gives:
1,120 = 0.7x
x = 1,120 / 0.7
= $1,600
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There are 15 players on a volleyball team. Only 6 players can be on the court for a game. How many different groups of players of 6 players can the coach make, if the position does not matter?
Using the combination formula, the coach can make 5,005 different groups.
The position does not matter, hence the combination formula is used.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 6 students are taken from a set of 15, hence the number of groups is:
[tex]C_{15,6} = \frac{15!}{6!9!} = 5005[/tex]
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You are driving from your house to your office. Currently, it is 7:10 a.m., and you are 12 miles from your office. If you travel at an average speed of 30 miles per hour, at what time should you arrive at your office
We would reach our office by 7:34 a.m.
How to find the time that we would take to travel from our house to the office?The average speed is given as 30 miles per hour.
Let us convert this into miles per minute.
30 miles/1 hour = 30 miles/60 minutes
= 0.5 miles per minute
The distance between the house and the office is 12 miles.
Therefore, we can find what it would take to reach the office by dividing the distance by the average speed:
Time taken = distance/average speed
= 12 miles/0.5 miles per minute
= 24 minutes
The time is given to be 7:10 a.m. Therefore we would reach our office by 7:34 a.m.
Therefore, we would reach our office by 7:34 a.m.
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When rolling a single number cube, what are the odds, in simplest form, in favor of rolling a 4 or a 5?
A. 1:1
B. 1:2
C. 1:3
D. 1:5
Answer:
C
Step-by-step explanation:
You have a total of 6 outcomes (1,2,3,4,5,6). That is your numerator. Out of those numbers, you only want 2 of them (4 or 5), so the fractions would be 2/6 or 1/3 which can also be written 1:3
What is the size of exterior angle of regular polygon which has interior angle of 120 degree?
Answer: 60 degrees
Step-by-step explanation:
An interior angle of a polygon and its corresponding exterior angle are supplementary (add to 180 degrees).
2. (4)1 point possible (graded, results hidden)Recall for Define the kernel function Write as a function of the dot product . To answer, let , and enter in terms of . z^2 submitted
The Kernel Function K (x,x') written as a function of the dot product x *x' is K (x, x') = Z². See the working below.
What is a Kernel Function?A kernel function is a way for taking input data and transforming it into the needed form of processing data.
The term "kernel" refers to a collection of mathematical functions used in Support Vector Machine to provide a window to alter data.
What is the solution deriving the expression given above?Given x = [x₁, x₂][tex]^{T}[/tex]
β(x) = [x²₁, √2 x₁ x₂, x²₂]
K (x₁, x') = β(x)[tex]^{T}[/tex] β(x')[tex]^{T}[/tex]
Hence, X' = [x₁, x₂][tex]^{T}[/tex]
→ β(x') = [x'²₁, √2 x'₁ x'₂, x'²₂]
K (x, x') = [x²₁, √2 x₁ x₂, x²₂][tex]^{T}[/tex] [x'²₁, √2 x'₁ x'₂, x'²₂]
K (x, x') = [x²₁, [x'²₁ + 2x₁ x₂ x'₁ x'₂ + x²₂ x'²₂
Because Z = x · x' (dot product of x·x')
= x₁ x'₁ + x₂x₂'
Expressing K (x,x') as a function of Z, we have
K (x₁, x') = x²₁ x'²₁ + 2x₁x₂ x'₁ x'² + x²₂ x'²₂
Simplified, we have
(x₁ x₁¹ + x₂x¹₂)² = Z²; and
[(a+b)² = a²+2ab+b₂] = z x₁x₁¹ + x₂x₁²
Therefore,
K (x, x¹) = Z²
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Answer this one please!
Solve the equation: √2 + 4 - 1 = 2
A) ±x= √5
B) ±x = √13
OC) x= 3
D) x = 5
Answer:
Step-by-step explanation:
1) Separate terms with roots from terms without roots.
[tex]x^2+4=\sqrt[\frac{1}{2} ]{4+1}[/tex]
2) Simplify 4 + 1 to 5.
[tex]x^2+4=\sqrt[\frac{1}{2} ]{5}[/tex]
3) Invert and multiply.
[tex]x^2+4=5^2[/tex]
4) Simplify [tex]5^2[/tex] to 25.
[tex]x^2+4=25[/tex]
5) Subtract 4 from both sides.
[tex]x^2=25-4[/tex]
6) Simplify 25 - 1 to 24.
[tex]x^2=21[/tex]
7) Take the square root of both sides.
[tex]x=\pm\sqrt{21}[/tex]
Answer:
A
Step-by-step explanation:
[tex]\sqrt{x^{2}+4}-1=2\\\sqrt{x^{2}+4}=3\\x^{2}+4=9\\x^{2}=5\\x=(plus/minus) \sqrt{5}[/tex]
60÷8 explained well and not in a decimal form
Answer: 15/2
Step-by-step explanation: if you fraction it, it'll be 60/8 so you can simplify it by 4. So 60÷4/8÷4 will be 15/2. So the answer is 15/2
Answer:
15/2 or 7 1/2.
Step-by-step explanation:
60 / 8 divide top and bottom by 4:-
= (60/4) / (8/4)
= 15/2.
The volume of a sphere is 500/3π cm3.
Work out the surface area of the sphere.
Give your answer in terms of π.
The answer is 100π cm².
Since we are given the volume, equate it to the formula of a sphere to find the radius.
500/3π = 4/3πr³r³ = 500/4r³ = 125r = 5 cmNow, substitute this in the formula to find surface area.
A = 4πr²A = 4π × (5)²A = 100π cm²Is x^25+1 polynomial function
Answer:
Step-by-step explanation:
yes I believe it is an quartic binomial
Answer:
yes
Step-by-step explanation:
If because it has two terms, it is a binomial, therefore it also qualifies as a polynomial.
Hope this helps
Is 1/11 a irrational number?
Answer:
No
Step-by-step explanation:
Am irrational number is a number that can't be expressed by a ratio (fraction). 1/11 is a fraction so it is rational, not irrational.
Find the circumference of a circle with diameter, d = 8.92m. give your answer rounded to 2 dp.
Answer:
Step-by-step explanation:
circumference is 2πr
r=d/2
r=4.46m
C=2π(4.46)=28.02
Identify the perimeter of a rectangle in which h = 8 ft and a = 144x ft^2. please help asap
Here, Given
h= 8ft
a=144 * ft^2
then,
A=L*H
144=L*8 or 144/8 =L
L=18
now, P=2(L+H)
P=2(18+8)
P=52m
Perimeter and area are two important and basic mathematical subjects. They help quantify the physical space and also provide a more advanced foundation of mathematics in algebra, trigonometry, and calculus. Perimeter is a measure of the distance around a shape, and area indicates how much area the shape covers.
The perimeter of a 2D shape is the distance around the shape. You can imagine wrapping a string around a triangle. The length of this cord is around the triangle. Or, if you're traveling outside the park, take a route that goes around the edge of the park.
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What is the value of the function at x=−2? y=−4 y equals negative 4 y = 0 y, = 0 y = 2 y = 2, y = 3
Based on the graph which models the function at x = -2 (see attachment), the corresponding y-value is y = 3.
What is a function?In Mathematics, a function can be defined as a mathematical expression which can be used to define and show the relationship that exist between two or more variables in a data set.
In this scenario, there are several values (points) on the given linear graph expressed as a coordinate (x, y). Hence, the x-values on the x-axis is directly proportional to the y-values on the x-axis.
By critically observing the graph which models the function at x = -2 (see attachment), we can logically deduce that the corresponding y-value is three (3).
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Answer:
Ik im late but yea
Step-by-step explanation:
I took the test :O
What number is represented by point B? A number line going from 1 to 2 with 5 equal spaces between 1 and 2. Point B is one mark to the left of 2. StartFraction 4 Over 5 EndFraction 1 and StartFraction 4 Over 5 EndFraction 1 and StartFraction 5 Over 4 EndFraction 2 and StartFraction 1 Over 5 EndFraction
Since A number line going from 1 to 2 with 5 equal spaces between 1 and 2the number represented by point B is 1⁴/₅
The question has to deal with proportion
What is proportion?Proportion is the measure of a variable or quantity relative to another.
How to calculate which number represents point B?Since A number line going from 1 to 2 with 5 equal spaces between 1 and 2, the measure of a sub-unit between 1 and 2 is
= 1/5
So, each sub-unit measure 1/5
Since point B is one mark to the left of 2, we have that point B is y = 2 - 1/5 = (10 - 1)/5
= 9/5
= 1⁴/₅
So, the number represented by point B is 1⁴/₅
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Geroge is bringing garonla bars and apples for his classmate at school apples cost 0.75 each qnd garonla bars cost 0.15 each geroge will bring 60 total items too school and spend a total of 21$ whixh system of equations best respesents the number of apples a and the number of garonla bars g?
The system of equations best represents the number of apples a and the number of garonia bars g be a+b=60, 0.75x+0.15y=21.
Given that cost of 1 apple is $0.75, cost of 1 gargonia bars be $0.15 ,total things are 60 and total money paid be $21.
Equation is relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+by=c. It may be a linear equation,quadratic equation, cubic equation.
Because we have been told that there are 60 total things and a represents the number of apples and g represents number of garonia represents the number of garonia bars.
a+b=60--------1
Money paid by consumers is cost per units*number of units
So,
0.75a+0.15b=21
Hence the system of equations best represent the number of apples and the number of garonua bars g are a+b=60, 0.75a+0.15b=21.
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