The best approximation for the measure of angle ABC is 58.3° ⇒ 3rd answer
Step-by-step explanation:
Let us revise the trigonometry ratios in the right triangle ABC, where B is the right angle, AC is the hypotenuse, AB and BC are the legs of the triangle
The trigonometry ratios of the angle BAC, the opposite side to this angle is BC and the adjacent side to it is AB are
[tex]sin(BAC)=\frac{opposite}{hypotenuse}=\frac{BC}{AC}[/tex] [tex]cos(BAC)=\frac{adjacent}{hypotenuse}=\frac{AB}{AC}[/tex] [tex]tan(BAC)=\frac{opposite}{adjacent}=\frac{BC}{AB}[/tex]In Δ ABC
∵ ∠ BCA is a right angle
∴ The hypotenuse is AB
∵ The adjacent side to ∠ABC is BC
∵ AB = 20 centimeters
∵ BC = 10.5 centimeters
- Use cosine ratio to find the measure of the angle because you
have the adjacent side of the angle ABC and the hypotenuse
∵ m∠ABC is x
∵ [tex]cos(x)=\frac{BC}{AB}[/tex]
∴ [tex]cos(x)=\frac{10.5}{20}[/tex]
- To find x use the inverse of cos(x)
∵ [tex]x=cos^{-1}(\frac{10.5}{20})[/tex]
∴ x = 58.33°
∴ m∠ABC = 58.33°
The best approximation for the measure of angle ABC is 58.3°
Learn more:
You can learn more about the trigonometry ratios in brainly.com/question/4924817
#LearnwithBrainly
The best approximation for the measure of angle ABC is 31.7°.
To find the measure of angle ABC (x), we can use trigonometric ratios. Since angle BCA is a right angle, we can use the sine function, which relates the opposite side to the hypotenuse in a right-angled triangle.
Let's denote the sides of the triangle as follows:
BC is the opposite side to angle ABC, with a length of 10.5 cm.
AB is the hypotenuse, with a length of 20 cm.
AC is the adjacent side to angle ABC.
Using the sine function, we have:
[tex]\[ \sin(x) = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{BC}{AB} \][/tex]
[tex]\[ \sin(x) = \frac{10.5}{20} \][/tex]
[tex]\[ \sin(x) = 0.525 \][/tex]
Now, we need to find the angle whose sine is approximately 0.525. Using a calculator or trigonometric tables, we can approximate the angle x. The angle whose sine is approximately 0.525 is about 31.7°.
What is the simplified expression of 8 times y times 9
Answer:
72y
Step-by-step explanation:
Multiplication can be done in any order
8x9=72
72 times y is 72y
just 3 math problem show step by step
1 5x+y=-12
5x-7y=4
2. -5x+4y=-3
-9x-y=-30
3. -9x+6y=27
-x+3y=10
please help me out
Answer:
see attached picture please
Simplify. (x^4)^3
Write your answer without parentheses.
Answer:
x^12
Step-by-step explanation:
Jared made 12 3/4 cups of snack mix for cups of snack mix for a party. His guests are 2/3 of the mic. How much snack mix did his guests eat.
a. 4 5/12
b. 4 1/2
c. 8 1/2
d 12 5/7
Answer:
8 1 /2
For this we need to determine what
2 /3 of 12 3/4 is, so we multiply the fractions together.
PLEASE HELP ME PLEASE HELP PLEASE IF YOU HAVE A HEART! What do you know about yourself as a learner?
How can you use this information to help you succeed in math?
Answer:
Hope this helps!
Step-by-step explanation:
1. Do all of the homework. ...
2. Fight not to miss class. ...
3. Find a friend to be your study partner. ...
4. Establish a good relationship with the teacher. ...
5. Analyze and understand every mistake. ...
6. Get help fast. ...
7. Don't swallow your questions. ...
8. Basic skills are essential.
How many solutions does this system of equations have?
y = –2x + 3
y = –2x – 1
Answer:
Step-by-step explanation:
in y = mx + b form, the slope is in the m position and the y int is in the b position
y = -2x + 3.....slope is -2 and y int is 3
y = -2x - 1...slope is -2 and y int is - 1
same slope, different y int's....means parallel lines...NO SOLUTION
learn this...it helps
same slope, different y int's = no solution
different slopes, different y int's = 1 solution
same slope, same y int's = infinite solutions
Final answer:
The given system of equations represents two parallel lines with the same slope and different y-intercepts, implying there are no solutions where the lines intersect.
Explanation:
The system of equations provided is:
y = –2x + 3
y = –2x – 1
These two equations represent two separate lines. To determine the number of solutions to the system, we observe the slopes of the two lines. Both equations have the same slope of –2. Because they have the same slope but different y-intercepts, these two lines are parallel and will never intersect. Therefore, the system has no solutions.
Which expression are equivalent 10
Answer:
I believe the answer to this question is: B.
Answer: The first part is the 2nd & 4th.
The second part is the 1st & 3rd.
Step-by-step explanation:
Edge 2021
The measure of an angle is 135 degrees. What is the measure of its supplementary angle ?
Remember that if two angles are supplementary, then the sum of their measures is 180°. So if the measure of an angle is 135 degrees. What is the measure of its supplement?
If the measure of an angle is 135°,
then the measure of its supplement is 45°.
We can find the measure of its supplement by taking 180 minus the measure of the original angle which in this case is 180 - 135 or 45°.
Final answer:
The measure of the supplementary angle to a 135-degree angle is 45 degrees, calculated by subtracting 135 degrees from 180 degrees.
Explanation:
The measure of an angle is 135 degrees. Supplementary angles are two angles whose measures add up to 180 degrees. To find the measure of the supplementary angle, we subtract the given angle's measure from 180 degrees. Here's the calculation:
Identify the measure of the given angle (135 degrees).Subtract the measure of the given angle from 180 degrees: 180 degrees - 135 degrees = 45 degrees.The measure of the supplementary angle is therefore 45 degrees.There is a bag with 7 blue marbles and 4 orange marbles. You pull a marble out of the bag three times, without replacing the marble each time. What is the probability that you will pull out 3 blue marbles?
a. 0.64
b. 0.56
c. 0.27
d. 0.21.
Answer:
Answer D
Step-by-step explanation:
Answer:Option D
Step-by-step explanation:
mon Core Algebra I A-CR
The graph of f(x) = (x - h\ + k contains the points (-6, -2)
and (0, -2). The graph has a vertex at (h, -5). Describe
how to find the value of h. Then, explain how this value
translates the graph of the parent function.
Answer:
h = -3
The value h = -3 translates the graph of the parent function [tex]y=x^2[/tex] 3 units to the left.
Step-by-step explanation:
The graph of [tex]f(x)=(x-h)^2+k[/tex] contains the points (-6, -2) and (0, -2).
This is the equation of parabola in vertex form, where [tex](h,k)[/tex] are the coordinates of the vertex.
If the graph has a vertex at [tex](h,-5),[/tex] then [tex]k=-5.[/tex]
So, the equation of the parabola is
[tex]f(x)=(x-h)^2-5[/tex]
If the graph passes through the points (0,-2) and (-6,-2) (these two points lie on the same horizontal line y = -2), then the parabola vertical line of symmetry divides the segment between these points into two congruent segments. Hence, the equation of the line of symmetry is
[tex]x=\dfrac{0+(-6)}{2}=-3[/tex]
The vertex lies on the line of symmetry, so its x-coordinate is -3. Thus, (-3,-5) is the vertex.
The value h = -3 translates the graph of the parent function [tex]y=x^2[/tex] 3 units to the left.
Answer:
Sample Response: The absolute value function is symmetric. Since the points (–6, –2) and (0, –2) have the same output, the points are the same distance from the line of symmetry. Between –6 and 0 is the value of –3. So, the vertex must have an x-coordinate of –3, which is the value of h. This would translate the graph of the parent function 3 units to the left.
Twyla puts $1000 in a saving account that pays 4% interest, compounded monthly. How much money will in the account 11 years later if she makes no more deposits?
Answer:
$1551.57
Step-by-step explanation:
Each month, the account balance is multiplied by 1+.04/12, so after 132 months, it will be ...
$1000×(1 +.04/12)^132 ≈ $1551.57
The United States Postal Service charges a
"nonmachinable surcharge" for first-class mail
If the length of the envelope (parallel to the
address) divided by the height of the envelope
is less than 1.3 or more than 2.5. Charlene has
an envelope with a height of 3.5 inches. Write
a compound inequality to show the lengths in
inches for which Charlene will have to pay the
surcharge.
Graph the solutions.
Answer:
Step-by-step explanation:
1.3 < Length/3.5 < 2.5
4.55 < Length < 8.75
Graph:
|-----------------|
| |
| |
| |
| |
| |
| |
| 4.55 -------- 8.75 |
| |
| |
| |
| |
| |
| |
|-----------------|
12. Noah raised $54 to support the animal shelter, which is 60% of his fundraising goal.
a. Write an algebraic equation to represent the situation.
b. What is Noah's fundraising goal?
To represent the situation algebraically, we use the equation 54 = 0.60G, and solving it gives us Noah's fundraising goal of $90.
Let's represent Noah's fundraising goal as G. According to the problem, Noah has raised $54, which is 60% of his goal. This situation can be translated into the algebraic equation:
54 = 0.60GTo find Noah's fundraising goal (G), we can divide both sides of the equation by 0.60:
G = 54 ÷ 0.60G = $90Therefore, Noah's fundraising goal is $90.
A playground is in the shape of a square. If the perimeter of the playground is 40 feet, find the diagonal distance across the park. Leave your answer in radical form
The length of diagonal of park is √200 feet.
Step-by-step explanation:
Given,
Perimeter of square playground = 40 feet
Let,
a be the length of one side.
Perimeter = 4a
[tex]4a=40\\\\a=\frac{40}{4}\\\\a=10[/tex]
Length of one side of square is 10 feet.
A diagonal will form a right triangle, where,
Diagonal = c
a = 10
b = 10
Using pythagoras theorem
[tex]a^2+b^2=c^2\\(10)^2+(10)^2=c^2\\100+100=c^2\\200=c^2\\c^2=200[/tex]
Taking square root on both sides
[tex]\sqrt{c^2}=\sqrt{200}\\c=\sqrt{200}[/tex] feet
The length of diagonal of park is √200 feet.
Keywords: perimeter, square
Learn more about perimeter at:
brainly.com/question/9045597brainly.com/question/8955867#LearnwithBrainly
Answer:
10√2 (Simplest Radical Form)
Step-by-step explanation:
While Absor201 got √200, it is still not in simplest radical form. If you got this question from MathNation, then 10√2
What value of x is in the solution set of 2(3x - 1) = 4x - 6?
Answer:
x=-2
Step-by-step explanation:
[tex]2(3x - 1) = 6x - 2 = 4x - 6 \\ 2x = - 4 \\ x = - 2[/tex]
I will mark brainliest
Answer:
A) 2x+50
Step-by-step explanation:
First, let's make a variable for each person
Sam = x
Hector = h
Ted = t
Gina = g
We know that Hector has twice the amount hat Sam has so his equation is
h = 2x
We know that Ted has 100 more than Hector so his equation is
t = h + 100
Gina has 50 less than Ted to she has
g = t - 50
Since we need to find out how much Gina has using units of Sam the equation will be
g = 2x + 100 - 50 or simplified g = 2x + 50
Please help I will mark brainliest
Answer:
10
Step-by-step explanation:
The square length of hypotenuse is equal to two sides' length square added together
C = 10^2 + 7.5^2 = √156 approximately 12.5
The answer is 10 if needed to round to nearest tenth.
If 7 notepads cost $3.15, what is the unit price of the notepads?
Answer:
$0.45
Step-by-step explanation:
Unit price is basically the same as unit rate. Unit rate is the cost of one item.
So $3.15 divided by seven is point fourty-five.
Answer: 45 cents
Step-by-step explanation: Unit price means the cost per unit. In this case, the cost per notepad.
Since we know that it costs $3.15 for 7 notepads, to find the cost for 1 notepad, we need to divide 7 into $3.15 or 7 into 3.15.
I used long division wish I have shown in the image attached and ended up with .45 which means that each notepad costs 45 cents.
So the unit price for 7 notepads is 45 cents.
Which situation is best represented by the following equation?
40w + 12.50 = 492.50
A) Nicole paid $40 for self-defense classes. She paid a $12.50 registration fee and $492.50 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
B) Nicole paid $12.50 for self-defense classes. She paid a $492.50 registration fee and $40 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
C) Nicole paid $492.50 for self-defense classes. She paid a $40 registration fee and $12.50 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
D) Nicole paid $492.50 for self-defense classes. She paid a $12.50 registration fee and $40 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
Eliminate
Final answer:
The equation 40w + 12.50 = 492.50 best represents Nicole paying $40 per week for self-defense classes, plus a one-time registration fee of $12.50, totaling $492.50.
Explanation:
The situation best represented by the equation 40w + 12.50 = 492.50 is option A) Nicole paid $40 for self-defense classes. She paid a $12.50 registration fee and $492.50 for each week she was enrolled in the classes. Here, w represents the number of weeks Nicole was enrolled in self-defense classes. The equation can be understood as follows: $40 is multiplied by the number of weeks (w), and $12.50 is added for the registration fee, summing to a total of $492.50.
What is the answer to -2(3x+2)=2x+6
Answer:
x=-5/4
Step-by-step explanation:
-2(3x+2)=2x+6
-6x-4=2x+6
-6x-2x-4=6
-8x-4=6
-8x=6+4
-8x=10
x=10/-8
x=-10/8
simplify
x=-5/4
Savanah solved the equation 3 + 4|3 plus 4 StartAbsoluteValue StartFraction x Over 2 EndFraction plus 3 EndAbsoluteValue equals 11. + 3| = 11 for one solution. Her work is shown below:
Answer:
x=-2 OR x=-10 i.e.
Solution Set = {-2,-10}
Step-by-step explanation:
The equation described in words is typed and solved below:
[tex]3+4|\frac{x}{2}+3|=11 \\4|\frac{x}{2}+3|=11-3\\4|\frac{x}{2}+3|=8\\|\frac{x}{2}+3|=\frac{8}{4} \\|\frac{x}{2}+3|=2\\\frac{x}{2}+3=2 OR \frac{x}{2}+3=-2\\\frac{x}{2}=2-3 OR \frac{x}{2}=-2-3\\\frac{x}{2}=-1 OR \frac{x}{2}=-5\\x=-2ORx=-10\\[/tex]
Answer:
it is -10
Step-by-step explanation:
95-a (b+c) when a=9, b= 3, and c = 7.4
Step-by-step explanation:
95-a (b+c)
95-9 (3+7.4)
95-9×10.4
95-93.6
=1.4
Answer: 894.4
Step-by-step explanation:
95-9(3+7.4)
⬇️
95-9 (10.4)
⬇️
86(10.4)
⬇️
894.4
The Johnsons need to put up a fence, as shown in the picture. They have already measured two of the sides. Find the length of the missing side of the farmyard (round to two decimal places). A) 17.00 feet B) 27.00 feet C) 32.15 feet D) 46.77 feet
Answer:
D
Step-by-step explanation:
its D for sure
Answer:
d
Step-by-step explanation:
46.77 feet Use the Pythagorean theorem.
Hugo is saving for a new baseball
Answer:
Step-by-step explanation:
What's the question?
PROBABILITY DISTRIBUTIONS?? Do anyone know how to find probabilities??
Probability of more than 3 = 0.25
Solution:
Given table shows the pitches, frequency and probability of pitches.
P(x = 1) = 0.15, P(x = 2) = 0.2, P(x = 3) = 0.4, P(x = 4) = 0.15, P(x = 5) = 0.1
To find the probability that the pitcher will throw more than 3 pitches.
Probability of more than 3 pitches = P(x > 3)
= P(x = 4) + P(x = 5)
= 0.15 + 0.1
= 0.25
P(x > 3) = 0.25
Hence the probability that the pitcher will throw more than 3 pitches to a batter is 0.25.
Final answer:
Probability distributions are used to assess the likelihood of different outcomes in a given set of data. To find probabilities, you need to determine the type of probability distribution and use the appropriate formulas or tables.
Explanation:
Probability distributions are used to assess the likelihood of different outcomes in a given set of data. They can take different shapes depending on the nature of the population. One common type of probability distribution is the normal distribution, which represents a bell curve.
To find probabilities using a probability distribution, you can follow these steps:
Determine the type of probability distribution you are dealing with, such as binomial or normal.Identify the values or events for which you want to find probabilities.Use the appropriate formulas or tables to calculate the probabilities, considering factors such as mean and standard deviation.What is the LCM of 2 and 5?
Answer:
Step-by-step explanation:
10
Answer:
10Step-by-step explanation:
Since 2 and 5 are co-prime then
LCM(2 , 5) = 2×5 = 10
:)
Identify the x-intercept and y-intercept of a line with the equation -3x+6y=12 and use these points to graph the line below.
Answer:
x-intercept: -4
y-intercept: 2
Step-by-step explanation:
ax+by=c
divide c by a and then c by b
-3x+6y=12
X-intercept: 12/-3= -4
Y-intercept: 12/6=2
Answer:
Step-by-step explanation:
if ur gonna graph it, u should put it in y = mx + b form
-3x + 6y = 12
6y = 3x + 12
y = 3/6x + 12/6
y = 1/2x + 2
in y = mx + b form, the slope is in the m position, and the y int is in the b position.
y = mx + b
y = 1/2x + 2.....so ur slope (which will help u in graphing) is 1/2, and ur y intercept is 2 or (0,2) <===
u could also find ur y intercept by subbing in 0 for x and solving for y...in ur original equation.
to find ur x intercept, sub in 0 for y and solving for x
-3x + 6y = 12
-3x + 6(0) = 12
-3x = 12
x = -12/3
x = -4...so ur x int is -4 or (-4,0) <=====
The system of equations is graphed on the coordinate plane.
y=−12x−1y=14x−4
Enter the coordinates of the solution to the system of equations in the boxes.
(
,
)
A graph with a blue line passing through coordinates (0, -4) and (4, -3) and a red line passing through coordinates (0, -1) and (4, -3).
Answer:
Step-by-step explanation:
y = -12x - 1
y = 14x - 4
-12x - 1 = 14x - 4
-1 + 4 = 14x + 12x
3 = 26x
3/26 = x
y = 14x - 4
y = 14(3/26) - 4
y = 42/26 - 4
y = 42/26 - 104/26
y = - 62/26 reduces to - 31/13
solution : x = 3/26 and y = -31/13 or (3/26,-31/13)
Find the equation of the line normal to the curve of y=cos1/3x, where x=pi
Answer:
The equation of the line normal to the curve of y=cos1/3x, where x=pi is y= 2√3 x - 10.38
Step-by-step explanation:
The equation of the normal to the curve is
Y- y1 = - 1/m (x- x1)
Where m is the gradient.
See attached picture for the complete solution.
The equation of the line normal to the curve of y=cos(1/3)x, where x=pi, can be found by taking the negative reciprocal of the derivative of the curve at that point and using the point-slope form of a line.
Explanation:The equation of the line normal to the curve of y=cos(1/3)x at x=pi can be found by taking the negative reciprocal of the derivative of the curve at that point.
The derivative of cos(1/3)x is -sin(1/3)x*(1/3).
At x=pi, the derivative is -sin(pi/3). Taking the negative reciprocal of this gives the slope of the line normal to the curve
So the slope is 1/ tan(pi/3).
Now, we can use the point-slope form of a line to find the equation of the line.
The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope.
Plugging in the values, we get y - cos(pi/3) = (1/tan(pi/3))(x - pi).
Simplifying further will give us the equation of the line normal to the curve at x=pi.
A TUB USES 20 GALLONS. a shower uses 15 gallons. if 40 people take a bath instead of a shower, how much extra water is used?
Answer:
200 additional gallons of water are used when 40 people take a bath instead of a shower
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Amount of water used when we take a bath = 20 gallons
Amount of water used when we take a shower = 15 gallons
Number of people who wants to take a bath = 40
2. How much extra water is used?
Extra water is used = Number of people * (Amount of water used when we take a bath - Amount of water used when we take a shower)
Replacing with the real values, we have:
Extra water is used = 40 * (20 - 15)
Extra water is used = 40 * 5 = 200 gallons