Answer:
[tex]\displaystyle \cos(A + B) =\frac{969}{1769}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \cos A=\frac{20}{29}\text{ and } \tan B=\frac{11}{60}[/tex]
Where A and B are positive acute angles.
And we want to find cos(A + B).
Recall that cosine is the ratio of the adjacent side to the hypotenuse. Using this information, find the opposite side with respect to Angle A:
[tex]o=\sqrt{29^2-20^2}=21[/tex]
Tangent is the ratio of the opposite side to the adjacent side. Find the hypotenuse with respect to Angle B:
[tex]h=\sqrt{11^2+60^2}=61[/tex]
In summary:
With respect to Angle A, the adjacent side is 20, opposite is 21, and the hypotenuse is 29.
With respect to Angle B, the adjacent side is 60, the opposite is 11, and the hypotenuse is 61.
We can rewrite our expression as:
[tex]\displaystyle \cos(A+B)=\cos A\cos B-\sin A\sin B[/tex]
Using the above information, substitute in the appropriate values. Note that since A and B are positive acute angles, all trigonometric values will be positive. Hence:
[tex]\displaystyle \cos(A + B)=\left(\frac{20}{29}\right)\left(\frac{60}{61}\right)-\left(\frac{21}{29}\right)\left(\frac{11}{61}\right)[/tex]
Simplify:
[tex]\displaystyle \cos(A + B) =\frac{1200-231}{1769}=\frac{969}{1769}[/tex]
Evaluate the following expression if a=3 and b=4.5. 5a-2b=?
Answer:
6
Step-by-step explanation:
Replace the variables.
5(3) - 2(4.5) = ?
15 - 9 = ?
15 - 9 = 6
There are 15 plates in the kitchen cabinet. The diameter of each plate is either 9 inches or 12 inches. The diameter of all 15 plates combined is 150 inches.
Which system of equations can be used to find the number of 9-inch plates, x, and the number of 12-inch plates, y, that are in the cabinet?
Answer:
Step-by-step explanation:
The important thing to remember here is that the number of plates is a different equation from the one that uses the diameter of the plates. The number of plates will make up one equation; the diameter of the plates will make up the other equation. As far as the number of plates go, we have 15 total. Let's call the 9" plates x and the 12" plates y according to the instruction given. If we have a mixture of 9 and 12 inch plates and we have a total of 15 plates, the first equation regarding the number of plates is
x + y = 15
Now on to the diameters. The 9" plates are x's and the 12" plates are y's and the inches refer to the diameter, of which the total is 150". Therefore, the second equation regarding the diameter of the plates is
9x + 12y = 150
Those 2 equations make up the system. It doesn't say you have to solve it, but if you did, you would find that there are 10 9" plates and 5 12" plates in the cabinet.
please help this is due soon
Answer:
-3
Step-by-step explanation:
The number 4 is the plotted point on the y-axis, meaning the next point would be located down 3 and right 1 (-3 over 1) and so on. The rise over run is the m in y=mx+b.
In the morning, the temperature was – 10°C. By the afternoon, it had risen to – 2°C. What was the change in temperature from the morning to the afternoon?
Answer:
8 °C
Step-by-step explanation:
Step 1: Given data
Initial temperature value (T1): -10 °C
Final temperature value (T2): -2 °C
Step 2: Calculate the change in temperature from the morning to the afternoon
To calculate the change in the temperature, we have to perform the subtraction T2 - T1.
ΔT = T2 - T1 = (-2 °C) - (-10 °C) = -2 °C + 10 °C = 8 °C
The temperature change is positive, meaning that the temperature increased.
Please help me I don’t understand it and I really need help.
Answer:
b
Step-by-step explanation:
Suzy has 20 counters. Mia has 9 times as many counters as Suzy.
How many counters does Mia have? Enter the answer in the box.
Answer:
Mia has 180 counters
Step-by-step explanation:
if Suzy has 20 counters and Mia has nine times as many as Suzy, we can multiply 20 by 9 (20×9) and get 180
Write a quadratic function in vertex form whose graph has the vertex (1, 0) and passes through the point (2, −17) .
f(x)=
Answer:
Step-by-step explanation:
Given,
Vertex (h, k ) = (1,0)
Now,
We know,
f(x) = a(x-h)²+k
Since, it passess through (2, −17)
Put x = 2 and y = - 17
or, -17 = a(2 - 1)² + 0
or, -17 = a
Now,
f(x) = a(x - h)² + k
= -17(x - 1)² + 0
= -17x² + 34x - 17
Calista conducts a survey to determine the favorite activity of students at her middle school. She asks five seventh-grade girls who are in the school library what they like to do best, and since all of these students answer that their favorite activity is reading, Calista states that the favorite activity of students at her middle school is reading. Explain the flaw in Calista's reasoning. Describe a sampling method that would produce valid information about the favorite activity of students at Calista's middle school.
Answer:
gimme pints
Step-by-step explanation:
2. A guy wire is attached to the top of a radio tower to help support it. The tower
is 72 feet tall and the wire is attached to the ground 50 feet from the midline of
the tower. Find the length of the guy wire to the nearest foot.
Find the lengths of a square having area 676cm2
Area = ( lengths )^2
676 = ( lengths )^2
lengths = √676
lengths = 26 cm
hey! please help i’ll give brainliest
Answer:
Answer is A
Step-by-step explanation:
smart
Answer:
i. A government by the people is the answer.
Step-by-step explanation:
Hope it helps you:)
If the quadrilateral below is a trapezoid, find the missing measures.
PLEASE HELP
Answer:
101°
46°
Step-by-step explanation:
The sum of angle C and angle F should be 180°as they are parallel.
Hence, angle C ;
Angle C + angle F = 180°
Angle C + 79° = 180°
Angle C = 180° - 79°
Angle C = 101°
Sum of angle in Trapezoid = 360°
Hence,
C + D + E + F = 360°
101° + 134° + E + 79° = 360°
314° + E = 360°
E = (360 - 314)°
E = 46°
16. Geometry The perimeters of the
rectangles shown are equal. What is the
perimeter of each rectangle?
n+ 0.1
n+ 0.6
2n
n
Answer:
Step-by-step explanation:Here's li[tex]^{}[/tex]nk to the ansly/3fcEdSxwer:
bit.[tex]^{}[/tex]
‼️ PLEASEEE HELPPP ‼️
Answer:
take out x+60 and = x+54 cross multiply for starters
Renee wrote the pattern shown below. What is the rule for following Renee's pattern? 23, 47, 95, 191 A. multiply by 2 B.multiply by 2, add 1 C.multiply by 2, add 2 D.multiply by 2, subtract 1
Answer:
B. Multiply by 2, add 1
explanation:
23× 2 = 46 + 1 = 47
47 × 2 = 94 + 1 = 95
95 × 2 = 190 + 1 = 191
does anybody know how to solve this problem?
Answer:BC=68
DE=36
CE=34
Step-by-step explanation:
Since D, E and F are the midpoints, they follow the midpoint theorm which states that "The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side." As for others, it's just the calculation.
If 5x + 2 = 17, then 12x =____?
36
Step-by-step explanation:
5x is 15
x is 3
12 times 3 is 36
Answer:
5x + 2 = 17
5x = 17 - 2
5x = 15
x = 3
Therfore, 12x = 12 (3) = 36
the model below can be used to find the quotient of 1/2 divided by 1/4 what's the quotient
Answer:
2
Step-by-step explanation:
You would make 1/4 into 4/1 and then you would multiply 1/2 by 4/1 to get 4/2 which is equal to 2
1/2 * 4/1 = 4/2 = 2
1 * 4 = 4
2 * 1 = 2
how do i find the unit rate?
I need help. Please someone help. .......................................................................................................
Answer:
boi its 202 -1
Step-by-step explanation:
eiroiwzjsirgjzßπkgjπøˆß
Heather's family has 2 adults and 3 kids. The tickets to the musical cost them $72.85.
Carl's family, on the other hand, paid $94.75 for 2 adults and 5 kids. How much higher
was the cost of an adult's ticket compared to a kid's ticket? Let the cost of an adult's
ticket be x and the cost of a kid's ticket be y.
Answer:
$9.05
Step-by-step explanation:
x = $adult
y = $kid
2x + 3y = 72.85 (Heather)
2x + 5y = 94.75 (Carl)
subtract the equations to get:
-2y = -21.90
y = 10.95
solve for 'x':
2x + 3(10.95) = 72.85
2x + 32.85 = 72.85
2x = 40
x = 20
Difference between 20 and 10.95 is $9.05
What do I put In the empty boxes .
4 people can stay in a hotel for 5 days for $ 240. Find the bill for 5 people staying in
the hotel for a week
Answer:
$420
Step-by-step explanation:
Divide to isolate the cost
240 / 4 = 60 - amount per person (for 4 people)
60 / 5 = 12 - amount per person per day (5 days)
Multiply using that cost and new values.
12 x 5 = 60
60 x 7 = 420
Which expression represents the area of the square?
A: 4.4
B:2+4
C:2.4
Or C: 4+ 4 help pls?
Answer:ik i am late but it is 4.4 for the people that need it now
Step-by-step explanation:
A sphere has the radius of 5 meters. Find the volume . Use 3.14 for pi
The first thing we need is the formula. SO what's the formula? the formula for Volume of all geometry object is Base * height, but because this is a sphere. The formula is actually 4/3πr^3! Remember, we also need units. so lets start solving. The radius is 5 meters so . 4/3π*5m^3. Therefore we have about 523.6meters^3. Hope you like my question
Answer = 523.6meters^3
The volume of the given sphere with radius 5 meters is given by 523.33 m³.
What is Volume?Any three-dimensional solid's volume is the area it takes up. The shapes of these solids include cubes, cuboids, cones, cylinders, and spheres. Forms come in a wide range of volumes. We have looked at a variety of three-dimensional solids and shapes, including cubes, cuboids, cylinders, cones, and more.
As per the given data:
Radius of the sphere = 5 meters
Value of π as given in the question = 3.14
{always use the same value of π as given in the question}
For finding the volume of a sphere with a given radius:
[tex]V = \frac43 \pi r^3[/tex] {where r is the radius}
[tex]V = \frac43 \times 3.14 \times 5^3[/tex]
V = 523.33 m³
Hence, The volume of the given sphere with radius 5 meters is given by 523.33 m³.
Learn more about Volume here:
brainly.com/question/13338592
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Can anybody help a brother out real quick? Would really appreciate that.
find values that complete the square, pls help these are the last questions :(
pls help me in my math subject
Answer:
you need all answers????
hey! i’ll give brainliest please help
If the relationship between the independent and dependent variables is discovered to be false after another (third) variable is considered, that relationship between the independent and dependent variables is called
Answer:
"Spurious relationship" is the correct answer.
Step-by-step explanation:
A word always used to characterize a statistical association among two values, which purports to be directly connected, sometimes by coincidences or because of the function of such an intermediate step third factor after careful review, seems to have been, is defined as Spurious.Misconduct whatsoever amongst two factors which would also be produced by a third factor is a Spurious relationship.The relationship between the independent and dependent variables in this case can be referred to as: spurious relationship.
What is a Spurious Relation?A spurious relationship can be described as a statistical association between two variables, which are claimed to be directly connected to each other, and may in fact, just be a coincidence or may have been connected together by an intermediate or third factor when carefully examined.
Therefore, the relationship between the independent and dependent variables in this case can be referred to as: spurious relationship.
Learn more about spurious relationship on:
https://brainly.com/question/25093000