Answer:
Angle A = 98.1°
Angle B = 59.5°
Angle C = 22.4°
Step-by-step explanation:
When given vertices (x1,y1) ,(x2,y2), we would be using the formula:
√(x2 - x1)² + (y2 - y1)²
ABC has vertices A(-1,6), B(2,10) and C(7,-2)
Side AB = A(-1,6), B(2,10)
√(x2 - x1)² + (y2 - y1)²
= √(2-(-1))² + (10 - 6)²
= √(3² + 4²)
= √9+16
= √25
= 5
Side BC = B(2,10), C(7,-2)
√(x2 - x1)² + (y2 - y1)²
√(7-2)² + (-2 - 10)²
= √5² +(-12)²
= √(25 + 144)
= √169
= 13
Side AC = A(-1,6), C(7,-2)
√(x2 - x1)² + (y2 - y1)²
√(7-(-1))² + (-2 - 6)²
= √6² +(-8)²
= √(64 + 64)
= √128
= 11.314
To find the measure of each angle we would be using the cosine rule
Where
a² = b² + c² - 2bc × Cos A
b² = a² + c² - 2ac × Cos B
c² = a² + b² - 2ab × Cos C
Sketching a triangle we find out that
Side AB = c = 5
Side AC = b = 11.314
Side BC = a = 13
Hence
1) for Side BC = a
a² = b² + c² - 2bc × Cos A
Cos A = b² + c² - a²/ 2bc
Cos A = 11.314² + 5² -13²/(2 × 11.313 × 5)
A = arc cos[(11.314² + 5² -13²)/(2 × 11.313 × 5)]
A = 98.13°
To the nearest tenth = 98.1°
2) for Side AC = b
b² = a² + c² - 2ac × Cos B
Cos B = a² + c² - b²/ 2ac
Cos B = 13² + 5² - 11.314/2 × 13 × 5
B = arc cos[ (13² + 5² - 11.314)/(2 × 13 × 5)]
B = 59.49°
To the nearest tenth = 59.5°
3) for Side AB = c
c² = a² + b² - 2ab × Cos C
Cos C = a² + b² - c²/ 2ab
Cos C = 13² + 11.314² - 5²/ 2 × 13 × 11.314
C = arc cos[(13² + 11.314² - 5²)/ (2 × 13 × 11.314)]
C = 22.38°
To the nearest tenth = 22.4°
Sara wanted to gather data about the cost of local gyms in her area. She plotted the data and determined that the average gym costs consist of a one-time registration fee and a monthly fee modeled by the equation y = 10x + 30. Identify and interpret the y-intercept in this model.
Answer:
y-intercept is 30
Step-by-step explanation:
Given the model [tex]y = 10x + 30.[/tex] comparing this model to the equation of a straight lines we can get the y- intercept
[tex]y = 10x + 30\\\y= mx+c[/tex]
The y- intercept is 30 which is the constant factor and it describes to us about the one-time registration fee of $30.
The y-intercept in this model for the average gym costs is 30.
What is the y-intercept?In a linear equation, the y-intercept can be interpreted as the constant. It is the value that does not change with the number of months a person goes to the gym. The y-intercept can also be referred to as the fixed cost. In this question, the y-intercept is 30.
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Find the surface area
Answer:
143 yards squared.
Step-by-step explanation:
According to the diagram, there are 6 sides: two trapezoids, and 4 rectangles.
To find the area of a trapezoid, you need to calculate using the formula shown below.
The height of each trapezoid is 3.5 yards. The b1 of each trapezoid is 3 yards. The b2 of each trapezoid is 7 yards.
So, the area of a single trapezoid is [3.5(3 + 7)] / 2 = (3.5 * 10) / 2 = 35 / 2 = 17.5 yards squared.
The area of two trapezoids will be 17.5 * 2 = 35 yards squared.
To find the area of a rectangle, do base times height.
There are, apparently, three types of rectangles in the diagram. All four rectangles have a width of 6 yards. One rectangle has a length of 3 yards, two rectangles have lengths of 4 yards, and one rectangle has a length of 7 yards.
So, the total areas of the rectangles are: (3 * 6) + 2(4 * 6) + (7 * 6) = 18 + 2 * 24 + 42 = 18 + 48 + 42 = 108 yards squared.
So, the total surface area of the figure is 35 + 108 = 143 yards squared.
Hope this helps!
when you sample 3000 people is this a census or a sample?
Answer:
participants (random sampling) will determine the population to which we ... In other words, they had obtained a census rather than a sample. ... population characteristics from a relatively small representative sample of 2,000 to 3,000 people.
Answer: I'm Pretty sure its census
Step-by-step explanation: have a great day
Definition: A set of points that form a line are called a ___ pattern.
Answer:
linear
Step-by-step explanation:
linear pattern
Answer:
a linear pattern
Step-by-step explanation:
A mother is 30 years older than her son. Fifteen years ago the son was 1/3 of
his mother's age. How old is each now?
Answer: The son is 30 and the mother is 60
Step-by-step explanation:
Mother's age = m
Son's age = s
m = s + 30
m-15 = 3(s - 15)
m - 15 = 3s - 45
m = 3s - 30
(Substitution)
s + 30 = 3s - 30
2s = 60
s = 30
m = 60
Hope it helps <3
Trick question---
Just kidding I think that 15 years ago his mother was 45
he was 15 and now he is 30 and she is 60.
literally sat here thinking that 30 is ruled out, and 60 would be 20 but then she'd be too old, suddenly it clicked, if you said he'd be half her age now, it'd be to easy, because half her age now would be 30 and it'd give the answer straight away.
You or your teacher has a big percentage of the brain used. I respect.
Write the functions by the graphs
F(x)=
G(x)=
H(x)=
Answer:
f(x) = |x|
g(x) = |x| - 2
h(x) = |x| + 3
Step-by-step explanation:
All the functions graphed represent the absolute value functions.
Since function g(x) passes through (0, 0) and (1, 1),
Let the equation of a line passing through these points is,
y = mx + b
Slope of the line passing through these points 'm' = [tex]\frac{\text{Rise}}{\text{Run}}=\frac{1-0}{1-0}[/tex]
m = 1
y-intercept of the line 'b' = 0
Therefore, equation of the line will be,
y = x
And the function representing the two lines (both are the mirror images) joining at the origin will be,
f(x) = |x|
When the parent function is shifted 3 units up, the new function will be
h(x) = |x| + 3
When the parent function is shifted 2 units down,
g(x) = |x| - 2
A parachutist's rate during a free fall reaches 198 feet per second. What is this rate in meters per second? At this rate, how many meters will the parachutist fall during 5 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.
Answer:
300 feet
Step-by-step explanation:
If we were using feet the expression would be 198x, where x is feet per second
Since they are asking in meters we need to convert feet to meters
When you do that you get 60
Now the expression is 60x
When you plug 5 into the equation it is 300
Jackie exchanges 8 Kappa coins for 3 Gamma coins. Lana wants to exchange
32 Kappa coins. How many Gamma coins will she receive?
O 7
O 11
O12
O 40
Answer:
12
Step-by-step explanation:
8/3=2.66666666667
1 kappa coin=2.66666666667 gamma coins
32/2.66666666667=12
Answer:
12 gamma coins
Step-by-step explanation:
We can use a ratio to solve
8 kappa 32 kappa
------------------ = ----------------
3 gamma x gamma
Using cross products
8x = 3*32
Divide each side by 8
8x/8 = 32 *3/ 8
x = 32/8 *3
x = 12 coins
Solve the inequality 9(x - 3) < 4(x + 10).
Answer:
The solution is the area x < 67/5
Step-by-step explanation:
Perform the indicated multiplication. We get:
9x - 27 < 4x + 40
Combining like terms results in:
5x < 67
Then the solution is the area x < 67/5
Answer:
Step-by-step explanation:
9(x - 3) < 4(x + 10)
9x - 27 < 4x + 40
-4x -4x
5x -27 < 40
+27 +27
5x < 67
/5 /5
x < 13.4
or
67/5
PLEASE HELP WITH THIS(INORDER FOR ME TO GIVE YOU A BRIANLIST,EXPLAIN HOW U GOT IT)(will give brainlist and thanks)(Find the perimeter)
Answer:
13x+10
Step-by-step explanation:
Answer:
7x+10 cm
Step-by-step explanation:
To find the perimeter add up all the sides
There are 5 sides
3x+5+2x+2x+5
Combine like terms
3x+2x+2x +5+5
7x+10
The perimeter is 7x+10
Figure B is a scaled copy of Figure A. What is the scale factor from Figure A to Figure B?
Answer:
1/3
Step-by-step explanation:
figure a to figure b is a reduction so we do the smaller side divided by the bigger side (use the similar sides on the figures)
5/15 = 1/3
or you could do 11/33 = 1/3
ronaldo likes to display a section of soft drinks next to the register at the lunch counter at which he works. Each day, he chooses 4 soft drinks from the 7 different soft drinks that the lunch counter sells and decides the order in which he wants to display them. For any one day, how many different arrangements of soft drinks can ronaldo display?
Answer:
35 different Arrangements
Step-by-step explanation:
To solve this question, we would be using the Combination formula because is from the question, we are told that Ronaldo CHOOSES 4 soft drinks from 7 different soft drinks
Combination Formula = C(n,r) = nCr
= n!/r! (n - r)!
n = 7
r = 4
7C4 = 7!/4! (7 - 4)!
7C4 = 7!/4! 3!
7C4 = 7 × 6 × 5 × 4 × 3 × 2 × 1/(4 × 3 × 2 × 1) × (3 × 2 × 1)
7C4 = 35
Therefore, Ronaldo can display 35 different arrangements of soft drinks
Please help me find volume of prism
Answer:
216 yds
Step-by-step explanation:
Each are multiplied together by length, width, and height. 6 x 6 x 6 equals 216. So your answer is 216 yards.
Answer:
216 [tex]yd^3[/tex]
Step-by-step explanation:
Recall the formula for the volume of a prism:
[tex]Vol=W\,*\,D\,*\,H[/tex]
where W represents the prism's width, D its depth, and H its height.
In your case the prim is in fact a cube because the three dimensions above are equal (all of them are 6 yards)
Then the volume of this prism is:
[tex]Vol=W\,*\,D\,*\,H\\Vol= 6\,yd\,*\,6\,yd\,\,*\,6\,yd\,\\Vol= 216\,\,yd^3[/tex]
a simple closed figure formed by three or more segement is called a
Answer:
Step-by-A simple, closed plane figure formed by three or more line segments meeting only at their endpoints is called a polygon. step explanation:
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Featured snippet from the web
A simple, closed plane figure formed by three or more line segments meeting only at their endpoints is called a polygon. Polygons are named according to the number of sides. A regular polygon has all sides congruent and all angles congruent
Answer:
Polygon
Step-by-step explanation:
a simple closed figure formed by three or more segement is called a Polygon. Polygons are named according to the number of sides. A regular polygon has all sides congruent and all angles congruent.
Hope this helps!
The endpoints of CD¯¯¯¯¯¯¯¯ are C(−8,−6) and D(−4, 10). The coordinates of the midpoint M of CD¯¯¯¯¯¯¯¯ are ( , ).
Answer:
m(-6,2)
Step-by-step explanation:
m=(-8+-4/2,-6+10/2)
=(-12/2,4/2)
=(-6,2)
The coordinates of the midpoint M of CD of the line segment CD with endpoints, C(−8,−6) and D(−4, 10), are (-6,2).
What is midpoint?For a line segment, mid-point is the middle point of it which divides the line segment into the two equal parts.
The formula to find the midpoint using the coordinates of the line is,
[tex]m=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
Here, (x1,y1) and (x2,y2) are the coordinates of the endpoints of the line.
The endpoints of CD are C(−8,−6) and D(−4, 10). To find the coordinates of the midpoint M, put the values in the above formula as,
[tex]m=\left(\dfrac{-8+(-4)}{2},\dfrac{-6+10}{2}\right)\\m=\left(\dfrac{-12}{2},\dfrac{4}{2}\right)\\m=\left(-6,2)[/tex]
Thus, the coordinates of the midpoint M of CD of the line segment CD with endpoints, C(−8,−6) and D(−4, 10), are (-6,2).
Learn more about midpoint here:
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Write an
explicit formula for
then
th
an.
term of the sequence 45, 15,5. ....
Answer:
The sequence above is a geometric sequence
For an nth in a geometric sequence
[tex]u(n) = a {r}^{n - 1} [/tex]
where n is the number of terms
a is the first term
r is the common ratio
From the question
a = 45
r = 15 / 45
The explicit formula for the sequence is
U(n) = 45(1/3)^n-1
Hope this helps you
Which sum or difference is modeled by the algebra tiles?
Answer:
option 4
Step-by-step explanation:
(2x - 3) - (-3x + 4)
= 2x - 3 +3x - 4 {remove parenthesis by bringing in th (-) sign}
= 2x + 3x - 3 - 4 {add the like term}
= 5x - 7
What is the y-intercept of the line that passes through (-6,2) and (4,-2) ?
2
5
22
5
No lo a los alusta
2
5
22
5
Answer:
Step-by-step explanation:
Slope (m) =
ΔY
ΔX
=
-2
5
= -0.4
θ =
arctan( ΔY ) + 360°
ΔX
= 338.19859051365°
ΔX = 4 – -6 = 10
ΔY = -2 – 2 = -4
Distance (d) = √ΔX2 + ΔY2 = √116 = 10.770329614269
Equation of the line:
y = -0.4x – 0.4
or
y =
- 2 x
5
– 2
5
When x=0, y = -0.4
When y=0, x = -1
Answer:
Step-by-step explanation:
Slope (m) =
ΔY
ΔX
=
-2
5
= -0.4
θ =
arctan( ΔY ) + 360°
ΔX
= 338.19859051365°
ΔX = 4 – -6 = 10
ΔY = -2 – 2 = -4
Distance (d) = √ΔX2 + ΔY2 = √116 = 10.770329614269
Equation of the line:
y = -0.4x – 0.4
or
y =
- 2 x
5
– 2
5
When x=0, y = -0.4
When y=0, x = -1
pls help me with my homework
Answer:
Any number larger than 10 units (in my example, 30 units)
Step-by-step explanation:
A scaled copy of a shape means that all the angles are the same and that it is basically the same shape that has been made bigger or smaller but still with the same proportions.
Note: If the scale factor is greater than 1, it means that Iria's scaled copy will be larger than this triangle.
Step 1.
Choose any number larger than 1 (as we aren't given the actual number she chose). To make things easy, I will choose the number 3 as it's a small number and it's a whole number (not a fraction or decimal).
Step 2.
Take the number you chose before (in my case, 3) and multiply it with the base length of the triangle in the diagram.
10 x 3 = 30 units
Note: Since the scale factor could be any number larger than 1, the base length can be any number larger than 10.
I hope this helps! :)
Bluey
Three of the angles of a quadrilateral are 530, 1270 and 720. What is the size of the 4th angle?
Answer:
108
Step-by-step explanation:
There is 360° in a quadrilateral so:
53°+127°+72°=252°
360-252=180
Answer: 108°
Answer:
108
Step-by-step explanation:
Vicki currently earns $35.00 an hour at her job. Thanks to her hard work, her boss is going to give her a 15% raise. How much will she earn each hour after the raise?
Answer:
$40.25 per hour
Step-by-step explanation:
If you multiply 35 by 15% you get 5.25. You can either add this on, or you can multiply by 1.15 instead of .15.
PLEASE HELP!! Question with picture is below
Answer:
It honestly does not matter, but I'd choose the ring because I feel like it is more pleasant to look at.
Step-by-step explanation:
We need to find the area of both shapes to compare:
3/4 of a circle:
A = 6^2pi
= 36pi
36pi(0.75) = 27pi
Ring:
A = 36pi
A2 = 3^2pi = 9pi
36pi-9pi = 27pi
As you can see, the two areas are the same.
Hope this helped! :)
Answer:
27
Step-by-step explanation:
HELP ASAPPPPP!
What is the value of Fraction 1 over 2x3 + 3.4y when x = 2 and y = 5?
18
20
21
37
(p.s if its easy im in 5th grade dont judge)
Answer:
can you please make the question more clear!
Step-by-step explanation:
i am guessing you are asking if 1/ (2·2) (3+(3.4·5))=
1/ 4+17+3
1/24?
If a>b, then the solution Problem is in the picture and answers choices in pictures too
And please show process
Answer: B
Step-by-step explanation:
Given that a is greater than b.
Let a = 7 and b = 5
If x < a and x <= b
Let us analyse the inequality graphically
The broken line represents less than, while the thick line represents greater than or equal to
Shading downward means less than.
From the graph, we can conclude that x is less than a. That is,
X < a
Find the attached file for more information.
Please help!! You want to distribute 7 candies to 4 kids. If every kid must receive at least one candy, in how many ways can you do this?
Answer: 20ways
Step-by-step explanation:
Number of candies = 7
Number of kids = 4
Since each kid must receive at least one candy ;
Therefore number of candies left to ration is
7 - 4 = 3 candies ; among 4 kids.
To share 'n' identical object among 'r' number of individuals can be expressed in the form :
[n+(r-1)Cr-1]
n = 3 ; r = 4
[3+(4-1)C4-1] = 6C3
Recall: nCr = n! / (n-r)!r!
6C3 = 6!/(6-3)!3!
6C3 = 6!/3!3!
= (6 * 5 * 4) / (3 * 2 * 1)
= 120 / 6
= 20ways
which is not an equation of the line going through (3, -6) and (1,2)
FIND THE MISSING LENGTH INDICATED
Answer:
25 units.
Step-by-step explanation:
The first thing we need to do is find the hypotenuse of the triangle with side lengths 12 and 16. 12^2 + 16^2 = 144 + 256 = 400. sqrt(400) = 20. So, the hypotenuse of that triangle is 20 units.
Because the smaller length of the smaller triangle bisects the largest triangle's right angle, the two triangles are similar, with the side length 12 corresponding to the smaller side length of the larger triangle, the side length 16 corresponding to the 20 unit side, and the 20 unit hypotenuse corresponding to x.
Now that we know the triangles are similar, we can construct a proportion...
[tex]\frac{16}{20} =\frac{20}{x}[/tex]
That means that 4/5 = 20/x
1/5 = 5/x
x = 25
Hope this helps!
The sum of two numbers is 264. One number ends with a zero. If this zero is erased, you get the second number. Find these numbers.
Answer:
240 is the number with a zero and 24 is the number with no zero
Step-by-step explanation:
240 + 24 equals 264 . 240 has a zero take away the zero and you get the second number
A Shopkeeper
made 20% profil selling
becycle at the labelled price . he
would gain only Rs 150 when 5% discount was
allowed! What
was the
cost price of that
bicycle
Answer:
The cost of bicycle is Rs1000
Step-by-step explanation:
Let x be the cost of bicycle
Total profit gained by the shopkeeper by selling at labelled price = 20%
Suppose he sell the bicycles at at 5% discount
Which means that the total profit he learn after discount will be:
20% -5% = 15%
The shopkeeper earns a profit of 15% if he sells at discount.
Profit gained by shopkeeper is:
15% of x = 15/100 · x
15% of x = 0.15x
Thus the profit gained will be 0.15x. As profit gained is equal to 150, we can say that
0.15x = 150
x = 1000
The cost of bicycle is Rs1000
10
8
6
4
-10 8
.6 4.
4
6
8
10
4
-6
8
-10
14. How many solutions does the system contain?
O A. Two
B. One
C. Zero
D. Three
Answer:
c
Step-by-step explanation: