Step-by-step explanation:
2 things to remember :
1. the sum of all angles in a triangle is always 180°.
2. the law of sine
a/sin(A) = b/sin(B) = c/sin(C)
triangle 1 :
angle B = 180 - 62.2 - 43.8 = 74°.
a/sin(62.2) = 15.8/sin(74)
a = 15.8 × sin(62.2)/sin(74) = 14.53961961... in
c/sin(43.8) = 15.8/sin(74)
c = 15.8 × sin(43.8)/sin(74) = 11.37657122... in
triangle 2 :
14.9/sin(49) = 11.6/sin(A)
sin(A) = 11.6 × sin(49)/14.9 = 0.587559136...
angle A = 35.98398776...° ≈ 36°
angle C = 180 - 49 - 35.98398776... = 95.01601224...° ≈
≈ 95°
c/sin(95) = 14.9/sin(49)
c = 14.9 × sin(95)/sin(49) = 19.66708505...
newly weds triangle :
let's call the 2 sides a and b (25 m and 30 m).
the angle between them is 60°.
here we should use the extended Pythagoras for general triangles :
c² = a² + b² - 2×a×b×cos(C)
with c being the side opposite to the angle C.
so, we have in our case
c² = 25² + 30² - 2×25×30×cos(60) = 625 + 900 - 750 =
= 775
c = sqrt(775) = sqrt(25×31) = 5×sqrt(31) = 27.83882181... m
the area of the triangle we get via Heron's formula :
s = (a+b+c)/2 = (25+30+c)/2 = 41.41941091...
area = sqrt(s(s-a)(s-b)(s-c)) = sqrt(s(s-25)(s-30)(s-c)) =
= sqrt(105,468.75) = 324.7595264... m²
with Php 2000 per m² this would cost
324.7595264... × 2000 = Php 649,519.0528...
> Next question
Find the last term to make the trinomial into perfect square
x2 – 2x
Answer:
+ 1.
Step-by-step explanation:
That would be (-2/2)^2
= + 1.
x2 - 2x + 1 = (x - 1)(x - 1)
[tex]\text{If a quadratic expression is a perfect square, then}\\\\~~~~~~~\text{Discriminant = 0}\\\\\implies b^2 -4ac = 0\\\\\implies (-2)^2 -4 c = 0\\\\\implies 4-4c = 0\\\\\implies 4c = 4\\\\\implies c = 1 \\\\\text{Hence, the last term should be 1.}\\\\x^2 -2x +1 = (x-1)^2[/tex]
which inequality is represented by this graph?
Answer:
the answer is A for the shaded region
URGENT PLEASE HELP!!
Write the equation of the given line in slope-intercept form:
Answer:
y = -3x - 1
Step-by-step explanation:
The slope intercepts the y-axis at -1, and moves down 3 on the y for every one space right on the x-axis
on a piece of paper, graph:
Answer:
every public company is listed company true or false every public company is listed company true or false every public company is listed company true or false every public company is listed company true or false every public company is listed company true or false every public company is listed company true or false every public company is listed company true or false
Please help, image below. Thank you!
A radius extends from the center of the circle to the edge.
If J is the center of the circle, then possible radii are JK, JL, JM, and JN.
Of those options, JN is the only one listed as an answer choice.
Answer: Third option, JN
Hope this helps!
Which of the following could be the center of a circle that includes the points (-5, 2) and (-3, 6)?
A. (0, 2)
B. (0, -2)
C. (2, 2)
D. (2, 1)
The center of a circle that includes the points (-5, 2) and (-3, 6) could be (a) (0,2)
How to determine the center of the circle?The points are given as:
(-5, 2) and (-3, 6)
The equation of a circle is represented as:
[tex](x -a)^2 + (y - b)^2 = r^2[/tex]
Where:
Points = (x,y)Center = (a,b)Radius = rSubstitute both points in the above equation
[tex](-5 + a)^2 + (2 - b)^2 = r^2[/tex]
[tex](- 3+ a)^2 + (6 - b)^2 = r^2[/tex]
The radii are equal.
So, we have:
[tex](-5 + a)^2 + (2 - b)^2 = (- 3+ a)^2 + (6 - b)^2[/tex]
Expand the equations
[tex]25 -10a + a^2 + 4 - 4b + b^2 = 9 - 6a + a^2 + 36 - 12b + b^2[/tex]
Evaluate the like terms
[tex]25 -10a + 4 - 4b = 9 - 6a + 36 - 12b[/tex]
Collect like terms
6a -10a - 4b + 12b = 9 + 36 - 25 - 4
Evaluate
-4a + 8b = 16
Divide through by - 4
a - 2b = -4
Next, we test the options:
Option (a) (a,b) = (0,2)
Substitute these values in the equation
0 - 2*2 = -4
Evaluate
-4 = -4
Both sides of the equation are the same
Hence, the center of a circle that includes the points (-5, 2) and (-3, 6) could be (a) (0,2)
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Y=x^2 – 4x + 5 vertex form please
Answer:
Step-by-step explanation:
help me pleaseeeeeeeeeeeeeeeeeeeeeee
a. To solve for the greatest common factor (GCF), we can determine the prime factors of 6, which is 2 and 3. Then for the other number, we can do the exact same thing. The prime factors of 8 are 1, 2, and 4. When matching the all the prime factors together, we notice that 2 is in both the prime factors.
This means that the GCF of 6 and 8 is 2.
b. To factor the GCF of 6 and 8, we can use the prime factors of both 6 and 8. That means:
6 + 8 = 2 × (3 + 4).
14 = 14
House numbers along a street consist of two-digit numbers. Each house number is made up of non-zero digits, and no digit in a house number is repeated. Event A is defined as choosing 8 as the first digit, and event B is defined as choosing a number less than 6 as the second digit. If a house number along this street is picked at random, with each number being equally likely and no repeated digits in a number, what is P(A and B) expressed in the simplest form? A. 1/9 B. 5/72 C. 5/8 D. 2/3
The value of the probability P(A and B) is 5/72 if the house numbers along a street consist of two-digit numbers, option (B) is correct.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Total number of outcomes = 9×8 = 72
(because the total number of digits excluding 0)
Event A: choosing 8 as the first digit
Event B: choosing a number less than 6 as the second digit
Total favourable outcomes = 1×5 = 5
Because there are total 5 digits that are less than 6 {1, 2, 3, 4, 5}
Probability = 5/72
Thus, the value of the probability P(A and B) is 5/72 if the house numbers along a street consist of two-digit numbers option (B) is correct.
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Answer:
The answer is B I'm pretty sure.
Step-by-step explanation:
Time4Learning 2022 quiz
Sheriff Aniskin receives confidential information: the thief with the stolen accordion
has been traveling on a raft for 2 hour 40 minutes from Village Ivanovo toward
Village Sosnovka. Aniskin immediately leaves Sosnovka in a motorboat and travels
upstream toward the raft. Aniskin catches the thief 27 km from Sosnovka. Find the
speed of the raft if the speed of the motorboat in still water is 12 km/h and the
distance from Ivanovo to Sosnovka is 44 km.
The speed of the raft if the speed of the motorboat in still water is 3 km/h
What is speed?
Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
Let the speed of the raft (current) - r
Speed of motorboat - 12 km/h
The distance between villages - is 44 km
Let the time spent by Aniskin - t
The time the thief was in travel = 2 hr 40 min + t = 2 40/60 + t = 3/8 + t
The distance the thief traveled = 44 - 27 = 17 km
We have the following equations:
r(8/3 + t) = 17
(12 - r)t = 27
Simplify the equations:
r(8/3 + t) = 17 ⇒ rt + 8/3r = 17
(12 - r)t = 27 ⇒ 12t - rt = 27
Add up the equations and solve for r:
rt + 8/3r + 12t - rt = 44
8/3r + 12t = 44
r = 16.5 - 4.5t
Substitute r into the second equation:
(12 - 16.5 + 4.5t)t = 27
4.5t² - 4.5t = 27
9t² - 9t - 54 = 0
Solving we get
t = 3 h
Find r:
r = 16.5 - 4.5*3 = 3 km/h
Therefore the speed of the raft if the speed of the motorboat in still water is 3 km/h
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Paula is wallpapering a wall in her house. The wall is 14 ft x 8 ft with a
doorway that is 3 ft x 6 ft and a window that is 4 ft x 4 ft. How much
area does Paula need to wallpaper?
Answer:
78 ft^2
Step-by-step explanation:
14x8 - (3x6) + (4×4)
112 - (18+16)
= 78ft^2
Find the area of the figure below by first finding the areas of the rectangle and triangles.
Area of the rectangle:
Area of the triangle on the left:
Area of the triangle on the right:
Area of the figure:
a. The area of the rectangle: 16 units²
b. The area of the triangle on the left: 6 units²
c. Area of the triangle on the right: 10 units²
d. Area of the figure: 32 units²
What is the Area of a Rectangle and a Triangle?Area of a rectangle = (l)(w)Area of a triangle = 1/2bha. l = 4 units
w = 4 units
Area of the rectangle = (4)(4) = 16 units²
b. b = 3 units
h = 4 units
Area of the triangle on the left = 1/2(3)(4) = 6 units²
c. b = 5 units
h = 4 units
Area of the triangle on the right = 1/2(5)(4) = 10 units²
d. Area of the figure = 16 + 6 + 10 = 32 units²
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Answer:
a: 16
b: 6
c:10
d: 32
Step-by-step explanation:
explained already <3
solve by completing the square
Step-by-step explanation:
answer is in the picture above
NEED TO KNOW HOW TO GET ASNWER
The prep cook needs to make 115 sandwiches. Each sandwich contains 3 ounces of chicken salad. The chicken salad comes in a 32-ounce container. How many containers need to be purchased?
Answer:
you would need 11 containers but you would have some left over.
Step-by-step explanation:
A business serves 24 customers with 64 staff to maintain a strong ratio of staff to guests. How many staff members would be
needed if 229 customers are expected? Calculate to the nearest whole number.
Do not put units, only put the number value for your answer.
Answer:
611
Step-by-step explanation:
[tex]\frac{24 customers}{64 staff} = \frac{229 customers}{? staff}[/tex]
Solve for ? by cross multiplying and isolating ?staff.
You will get (64 x 229) / 24
Your answer will be ~ 611.
If the diameter of the circle is 14 units, calculate its area: then calculate its circumference
Answer:
Area: 153.86
Circumference: 43.96
Please help me. I need to find the limit. I WILL give you BRAINLIEST!
Answer:
-1
Step-by-step explanation:
The answer of this question is -1
calculate the value of:
1+3+5+....+43
As an event organizer, you are to host 120guests in a room of dimensions 18m long and 12m wide. You have rectangular tables which are 2m long and 0.75m wide. The number of guests allocated for the top table is 12 and the rest of the guests are on 3springs. NB: cover space is 0.6m i) Sketch the table plan arrangement. ii) Calculate the number of tables required for the top table. iii) Calculate the number of covers on each spring. iv) calculate the number of tables required for each spring. v) What is the purpose of leaving a gangway when arranging tables and chairs for an event?
The room, the tables and the guests are illustrations of rectangles and areas.
How many tables are required for the top table?This is calculated using:
Tables = Guest ÷ Guest per top table
So, we have:
Tables = 120 ÷ 12
Evaluate
Tables = 10
Hence, 10 tables are required for the top table
How many covers are on each spring?This is calculated using:
Covers = Number of spring ÷ Cover space
So, we have:
Covers = 3 ÷ 0.6
Evaluate
Covers = 5
Hence, 5 covers are required for each spring
How many tables are required for each spring?This is calculated using:
Tables = Tables for top table ÷ Spring
So, we have:
Tables = 10 ÷ 3
Evaluate
Tables = 3.33
Remove decimal
Tables = 3
Hence, 3 tables are required for each spring
What is the purpose of leaving a gangway when arranging tables and chairs for an event?This is done to allow passage for walkway
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can someone help me? no fake answers my other questions are also worth 50 points each btw
Step-by-step explanation:
Let's simplify step-by-step.
(6)(6)x−60x+900
=36x+−60x+900
Combine Like Terms:
=36x+−60x+900
=(36x+−60x)+(900)
=−24x+900
Answer:
=−24x+900
A line intersects the points (3,11) and (-9, -13). What is the slope of the line In simplest form?
Answer:
m = 2
Step-by-step explanation:
Write the slope formula
Substitute: m = - 13 - 11/ - 9 - 3
Calculate the sum or difference: m = -24 / - 9 - 3
Calculate the sum or difference: m = -24 /-12
Reduce the fraction: m = 2
Answer: m = 2
Answer: m = 2
Step-by-step explanation:
Slope formula = [tex]\frac{y2-y1}{x2-x1}[/tex]
plug in values
[tex]\frac{-13-11}{-9-3}[/tex]
simplify
[tex]\frac{-24}{-12}[/tex]=2
⇒M = 2
Rewrite this question to make it a statistical question:
How old am I?
Answer:
“How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students' ages.
Using the Data Set {125, 6, 133, 129, 125}, find the standard deviation:
What is the slope of the line that passes through the points(−8,2) and (-11, 3)? Write your answer in simplest form.
Answer: -1/3
Step-by-step explanation:
The formula is y2 - y1/ x2 - x1 . So the answer would be -1/3 bc 3 - 2 = 1 and -11 - (-8) = -3.
help me pleaseeeeeeeeeeeeeeeeee
Answer:
Step-by-step explanation:
Volume
V = w h l
V = 2*15*13
V = 390 ft^3
-------------------------
Surface area
SA = b*h
SA = 15*13
SA = 195
-------------------------
b) Surface area
C) Volume
please help please please help
Answer:
3:2
Step-by-step explanation:
PLS HELP QUICKLY
Data was collected at a pool. It showed that being older does not imply that a swimmer will stay for a shorter or longer amount of time. What is likely true?
There is no correlation between age and length of stay.
There is a correlation between age and length of stay. There may or may not be causation. Further studies would have to be done to determine this.
There is a correlation between age and length of stay. However, there is no causation. This is because there is likely an increase in the length of stay with a decrease in age.
The true statement is there is no correlation between age and length of stay.
What is correlation?
Correlation is a statistical measure used to measure the relationship that exists between two variables. For example, if the older a child is, the longer he would stay at the pool. it can be said that there is a positive correlation.
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A group of 18 students began raising money for a new community park. If each student reaches the goal of $980, how much will the
group raise toward the park project?
A $17,670
B $17.640
C $17,630 D$17,740
what is the area of a circle with 5cm radius
Answer:
Step-by-step explanation:
The formula to calculate the area of a circle is
[tex]A =\pi r^2[/tex]
This means that if [tex]r = 5 "cm"[/tex], the area is
[tex]A = 5^2\pi " cm"^2 = 25 \pi " cm"^2 =(estimation) 78.539816 " cm"^2[/tex]
Answer:
See below
Step-by-step explanation:
We are given that a circle has a radius of 5 cm
We want to find the area of this circle
The area of a circle is given as [tex]\pi r^{2}[/tex], where r is the radius
As stated above, the radius of this circle is 5; ergo, r =5
We can substitute 5 as r in the formula
A = [tex]\pi r^{2}[/tex]
A = [tex]\pi (5)^{2}[/tex]
Raise 5 to the 2nd power
A = π * 25
A = 25π cm²
If you need your answer in terms of pi (or as an exact answer), the answer would be 25π cm² (don't forget your units!)
However, if your system wants pi approximated, see below:
If your system wants pi to be used as 3.14, then multiply 25 by 3.14; 25 * 3.14 = 78.5 cm²
If your system wants pi to be used as 22/7, then multiply 25 by 22/7; 25 * 22/7 ≈ 78.57 cm²
what is the name of the first female mathematician?
Answer:
Hypatia was the first female mathmatican
Answer:
Hypatia, (born c. 355 ce—died March 415, Alexandria), mathematician, astronomer, and philosopher who lived in a very turbulent era in Alexandria's history. She is the earliest female mathematician of whose life and work reasonably detailed knowledge exists.
Step-by-step explanation: