Answer:
cos(θ - φ) is -240/289
Step-by-step explanation:
The given parameters are;
The location of θ = Quadrant III
The location of φ = Quadrant I
cos(θ) = -8/17
cos(φ) = 15/17
By trigonometric identities, we have;
cos(θ - φ) = cos(θ)·cos(φ) - sin(θ)·sin(φ)
Given that 'θ' is in quadrant III, we have;
sin(θ) is negative
By Pythagoras' theorem, we have;
∴ sin(θ) = -√(17²- 8²)/17 = -15/17
Whereby 'φ' is in quadrant I, by Pythagoras' theorem, we have;
sin(φ) = √(17² - 15²)/17 = 8/17
∴ cos(θ - φ) = (-8/17) × (15/17) + (-15/17) × (8/17) = -240/289 = -0.83044982699
Carla wants to save $55.50 to buy a new video game. Carla babysits her niece once a week and earns the same amount of money each week. After every time she babysits she donates $2 from the money she earned to the local food bank. Carla calculates that it will take her 6 weeks to save enough to buy her video game. Write and solve an equation to determine how much money Carla earns per week.
Answer:
$11.25
Step-by-step explanation:
55.50 divided by 6 = 9.25
9.25 + 2 = 11.25
O There were 9 bags of
candy donated for the
neighborhood party.
Each bag contained
245 pieces. How much
candy did they have
for the party?
Today i will walk 3 miles per hour to school, which is 1.5 miles away how many hours would this trip take
Answer: 30 minutes so 1/2 hour
Step-by-step explanation:
Because 3 miles = 1 hour
1.5 times 2 = 3
divide 2 on both sides
Answer:
2 hours
Step-by-step explanation:
divide3 by 1.5 and that is how long it will take you
Consider the following pair of equations:
y = −2x + 8
y = x − 1
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.
Answer:
y = -2x + 8
x = 3
y = x - 1
y = 2
Step-by-step explanation:
if 2x + y = 8 and x - y = 1
you can solve using substitution, elimination, matrix etc.
You will find that x = 3 and y = 2
Hope this helped.
MARKING BRAINLIEST TO FIRST PERSON WHO IS CORRECT!
I need help with #13
Answer:
True
False
False
Step-by-step explanation:
Find all the missing sides and angles of this triangle,
А
7
B
70°
The measurement of angle A
A A=
The length of side BC
The length of side AC-
Answer:
See solutions below
Step-by-step explanation:
From the given diagram;
AC = opposite
AB = 7 = hypotenuse
Angle of elevation = 70 degrees
Using SOH CAH TOA
Sin theta = opp/hyp
Sin theta = AC/AB
Sin 70 = AC/7
AC = 7sin70
AC = 7(0.9397)
AC = 6.58
Similarly
tan 70 = AC/BC
tan 70 = 6.58/BC
BC = 6.58/tan70
BC = 6.58/2.7475
BC = 2.39
tan m<A = BC/AC
tanm<A = 2.39/6.58
tan m<A = 0.3632
m<A = 19.96degrees
Simplify the expression: 5(x + 2) > 50
Answer:
x >8
Step-by-step explanation:
Answer:
x > 8
Step-by-step explanation:
Solving an algebraic inequality is the same as solving an algebraic equation. One uses the technnique of inverse operations to undo every step in the expression to get the answer. The only difference is that with an inequality, one must remember to flip the inequality sign when dividing or multiplying by a negative. This rule does not apply to the given inequality.
5(x + 2) > 50
/5 /5
x + 2 > 10
-2 -2
x > 8
simplify this number 27:81
Answer:
I believe the simplified form of this ratio is 1:3
*The common factor to both numbers is 27.
27÷27=1 and 81÷27=3
So, that's where the 1:3 came from
PLSSS HELP IF YOU KNOW THISS:))
Please help me I know it's A but I don't know why.
Answer:
Maybe try explaining that if you narrow it down and simplify the numbers by dividing them by 8 or somewhere around there.
Find the measure of the exterior angle.
The diameter of a circle is 6 kilometers. What is the area?
d=6 km
Give the exact answer in simplest form.
square kilometers
Answer:
28.27 rounded orrrr 28.27433388 not rounded.
Step-by-step explanation:
area of circle=πr^2
radius=3 km
3^2=9
9*π
Step-by-step explanation:
Area of a circle = πr²
Radius (r) =1/2 Diameter
=60/2
=30km
Area = π x (30)²
= π x 900
= 2027km²
Marlene went shopping and bought a bunch of candy for her swim team. She bought packs of Skittles for $1.50 each and packs of M&Ms for $2 each. She spent a total of $39 and bought 24 items. How many of each item did she buy?
Answer:
18 Skittles
6 M&Ms
Step-by-step explanation:
Set up an equation:
Variable x = number of skittles
Variable y = number of M&Ms
1.50x + 2y = 39
x + y = 24
In the second equation, isolate a variable:
x = 24 - y
Substitute the value of x for 24 - y in the first equation:
1.50(24 - y) + 2y = 39
Use distributive property
36 - 1.5y + 2y = 39
Combine like terms
36 + 0.5y = 39
Isolate variable y:
0.5y = 3
y = 6
Substitute the value of y for 6 in the second equation:
x + 6 = 24
Isolate variable x:
x = 18
Plug these values into any equation of your choice to see if these values are correct (I'll do both equations just to prove it):
1.50(18) + 2(6) = 39
27 + 12 = 39
39 = 39
Correct
x + y = 24
18 + 6 = 24
24 = 24
Correct
hi please help i’ll give brainliest
Answer:
Ellipse. It is irregular at some points.
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
What is the vertex of f(x) = -2|x + 1| + 2?
Answer:
(-1,2) i think
Step-by-step explanation:
Please help ASAP last question. Number 6
If 19,000=19% Then 100,000=100%
100,000-900=99,100
Answer: $99,100 was his salary last year
please help, is it x = 6, y = 6, y = x, or y = 2?
01:08:55
B
O
B
А
A'
2
D
C
ci
D'
Х
6
8
10
2
O x = 6
O y = 6
O y = x
O y=2
The equation for the line of reflection is x = 6
What is reflection?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
For example, 3x + 5 = 15.
Given that, a graph, we need to find the equation of the reflection of the polygon graphed,
We can see, all the vertices on the polygon are being mirrored across the line x = 6.
So, we can say the line of reflection is x = 6.
Hence, the equation for the line of reflection is x = 6
Learn more about equations, click;
https://brainly.com/question/29657983
#SPJ7
Find the slope will give brainliest if it is correct.
Answer:
I cannot see pictures, so I will explain how to find slope, so you can do it on your own.
Step-by-step explanation:
Find 2 coordinates on the line.
Ex: (2,3) and (4,6)
Subtract the y-coords and x-coords from each other and divide.
6-3 = 3
4-2 = 2
3/2
So the example slope is 3/2.
The 3 represents the rise, and 2 represents the run.
---
hope it helps
Solve the following system of equations using addiction
Answer:
3x+y=13
+2x-y=12
SOlve it like what you would normally do
3x+2x=5x
y+(-y)=0
13+12=25
Basically
5x+0=25
Bring down all appropiate signs
Now solve that
5x=25
x=5
Now to find “y”
Plug in The “x”
3*5=15
15+y=13 now solve that and you’d get -2
If you plug it into the other one, it would be the same thing
2*5=10
10-y=12
-y=2
y= -2
x=5
y= -2
help me find the answer please
Answer:
A x<1125
Step-by-step explanation:
Part C
Calculate the ratio of the lengths of the two line segments formed on each transversal. You will have two sets of calculations. Round your answers to the hundredths place. What do you notice about the ratios of the lengths for each transversal? How do they compare?
Answer:
Line segment PM = 4.2 length
ML = 6.2
ON = 3
NK = 2
Step-by-step explanation:
Just got it on plato your welcome:)
The segments formed by each transversals and the three parallel lines are
proportional according to the three parallel lines theorem.
The observations are;
The parallel lines divide the transversals in equal proportions, such that the ratio of the lengths of each transversal are equal.[tex]\displaystyle \mathrm{ Ratio \ of \ the \ segments ;\ }\frac{\overline{CB}}{\overline{AB}} = \frac{\overline{EF}}{\overline{DE}}[/tex]Reasons:
The question is a four part question
Let the equations of the parallel lines be as follows;
Line, x; y = x
Line, y; y = x + 1
Line z; y = x + 2
The points at which transversal 1 intersect the lines x, y, and z, are;
A(0.4, 0.4), B(0.6, 1.6), and C(0.8, 2.8)
The length of segment [tex]\overline{AB}[/tex] = √((0.6 - 0.4)² + (1.6 - 0.4)²) = 0.2·√(37)
The length of segment [tex]\mathbf{\overline{CB}}[/tex] = √((0.8 - 0.6)² + (2.8 - 1.6)²) = 0.2·√(37)
The ratio of the lengths of the segment formed by transversal 1 is therefore;
[tex]\sqrt{x} \displaystyle Ratio \ of \ the \ length \ of \ the \ segments = \mathbf{\frac{\overline{CB}}{\overline{AB}}} =\frac{2 \cdot \sqrt{37} }{2 \cdot \sqrt{37} } = 1[/tex]
The points at which transversal 2 intersect the lines x, y, and z, are;
D(1.1, 3.1), E(1.3, 2.3), and F(1.5, 1.5)
The length of segment [tex]\overline{DE}[/tex] = √((1.3 - 1.1)² + (2.3 - 3.1)²) = 0.2·√(17)
The length of segment [tex]\overline{EF}[/tex] = √((1.5 - 1.3)² + (1.5 - 2.3)²) = 0.2·√(17)
[tex]\sqrt{x} \displaystyle Ratio \ of \ the \ length \ of \ the \ segments = \mathbf{\frac{\overline{EF}}{\overline{DE}}} =\frac{0.2 \cdot \sqrt{17} }{0.2 \cdot \sqrt{17} } = 1[/tex]
Therefore;
[tex]\displaystyle \frac{\overline{CB}}{\overline{AB}} = \frac{\overline{EF}}{\overline{DE}} = 1[/tex]Which gives;
The proportion with which the parallel lines divide the transversals are equal.The ratio of the lengths for each transversal are equal.The the comparison can also be made with the triangle proportionality theorem.
Learn more about triangle proportionality theorem here:
https://brainly.com/question/8160153
Paul uses a coordinate plane to design his model town layout. Paul moves the market 2 units left and 3 units down. He says the ordered pair for the new location of the market is (0, 6). Explain Paul's mistake and write the correct ordered pair for the new location of the market.
Answer:
(1,5) because, before it was at (3,8) and
3 – 2 = 1
8 – 3 = 5
For further explanation:
(3,8) / (2,3) = (1,5)
2 for 2 units left and 3 for 3 units down
11. Dave is building a doghouse that is a scale model of his shed in the farm yard, One of
the windows on the shed is 117 cm wide and 130 cm high. On the doghouse the window
is 9 cm wide,
a) What is the scale factor Dave is using to build the doghouse?
a.
2 mar
b) How high is the window in the scale model?
Answer:
a) 1/13 (or 13 depending on the factor is being applied to the dog house or applied to the shed. If its being applied to the shed like 117 * scale factor it is 1/13)
b) 10
Step-by-step explanation:
The scale factor is 13 and the height of the dog house is 10 cm.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object.
Given that, Dave is building a doghouse that is a scale model of his shed in the farmyard, One of the windows on the shed is 117 cm wide and 130 cm high. On the doghouse the window is 9 cm wide,
a) Since, the scale factor = ratio of original scale to scale of the model.
Therefore,
Scale factor = 117 / 9 = 13
b) Since, the scale factor is 13 and the original scale of the window high is 130 cm.
Therefore, height of the doghouse = 130 / 13 = 10 cm
Hence, the scale factor is 13 and height of the dog house is 10 cm.
Learn more about scales, click;
https://brainly.com/question/1287267
#SPJ2
What is the answer to this question?
Answer:
C is the answer also can I have brian list
Step-by-step explanation:
PLEASE HELP ASAP!! WILL GIVE BRANLIEST!!!
Answer:
Brand A
Step-by-step explanation:
The volume (V) of a cone is calculated as
V = [tex]\frac{1}{3}[/tex]πr²h ( r is the radius and h the height )
Brand A
V = [tex]\frac{1}{3}[/tex]π × 6² × 15 = [tex]\frac{1}{3}[/tex]π × 36 × 15 = π × 12 × 15 = 180π in³
Brand B
V = [tex]\frac{1}{3}[/tex]π × 5² × 18 = π × 25 × 6 = 150π in³
Brand A have the largest volume
Max is mixing oil and gas for his moped. He uses 3.75 liters of gas and 1.5 liters of oil. How many liters of gas are used per liter of oil?
Answer:
2.5 liters of gas is used with per liter of oil
Step-by-step explanation:
Max is missing oil and gas for his moped.
Amount of gas used = 3.75 liters
Amount of oil required = 1.5 liters
Ratio in which gas and oil are mixed = [tex]\frac{3.75}{1.5}[/tex]
= [tex]\frac{2.5}{1}[/tex]
That means if he uses 1 liter of oil then the gas required for the mixture = 2.5 liters
Therefore, 2.5 liters of gas is used per liter of oil.
What is the solution to this system
Answer:
Sorry, I was on my phone. Its (2,3)
Step-by-step explanation:
Answer:
(2,3) is the answer
Step-by-step explanation:
Solve the stimultanious equations
Answer:
x = -1 /2= -0.5 y = 15 /10= 1.5
does anybody know the answer?
Answer:
y+48=90
y= 90-48
y= 42
Step-by-step explanation:
ok
by using the property
sum of two opposite interior angles of triangle is equal to exterior angle
In OK, which arc is a major arc?
G
H
74
K
A GEI
C FJG
D IJF
B HIJ
Answer:
D
i thank
Step-by-step explanation:
