Recall the following identities,
• 1 + tan²(x) = sec²(x)
• sin(2x) = 2 sin(x) cos(x)
• sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
as well as the following properties of sine and cosine,
• cos(-x) = cos(x)
• sin(-x) = -sin(x)
Then we have
2 tan(π/4 - A) / (1 + tan²(π/4 - A)) = 2 tan(π/4 - A) / sec²(π/4 - A)
… = 2 tan(π/4 - A) cos²(π/4 - A)
… = 2 (sin(π/4 - A) / cos(π/4 - A)) cos²(π/4 - A)
… = 2 sin(π/4 - A) cos(π/4 - A)
… = sin(2 (π/4 - A))
… = sin(π/2 - 2A)
… = sin(π/2) cos(-2A) + cos(π/2) sin(-2A)
… = cos(2A)
as required.
The area of the triangle below is 10.6 square centimeters. What is the length of the
base?
4 cm
Answer:
6 cm
Step-by-step explanation:
The area of a triangle is [tex]\frac{bh}{2} = A[/tex], where b = base, h = height, and A = area. In this case, we're given the height as 4 cm and the area as 6 cm^2.
Let's plug in these values.
[tex]\frac{4b}{2} = 6[/tex]Now, let's solve this algebraically.
Step 1: Multiply both sides by 2.
[tex]\frac{4b}{2} * 2 = 6 * 2[/tex] [tex]4b = 12[/tex]Step 2: Divide both sides by 4.
[tex]\frac{4b}{4} = \frac{12}{4}[/tex] [tex]b = 3[/tex]Step 3: Check if solution is correct.
[tex]\frac{3*4}{2} = 6[/tex] [tex]\frac{12}{2} = 6[/tex] [tex]6 = 6[/tex]Therefore, the base is 6 cm. (but don't put the cm in the box because it's already there)
Have a lovely rest of your day/night, and good luck with your assignments! ♡
A delivery truck weighs 5.5 tons before it is loaded with packages. Once the delivery truck is full of x packages it weighs 6.1 tons.
Each package in the truck weighs 0.0075 tons.
How many packages are on the truck?
Enter your answer in the box
packages
Answer:
80 packages
Step-by-step explanation:
0.0075*80= 0.6 5.5 + 0.6= 6.1
correct answer only need urgent help
Answer:
Step-by-step explanation:
Use the formule V=4/3 *Pi*R^3
where R =10
so V=4/3*Pi*10^3
v= 4000Pi/3 =4188.7902
What is the solution for the equation 6x - 8 = 4x?
Ox= 0.8
Ox= 4
Ox= 8
Ox= 16
HELP ASAP
Dave is packing 23 sweaters into boxes.
Each box will hold 3 sweaters. How
many boxes will Dave fill? How many
boxes will he need? Explain.
Answer:
He will completely fill 7 boxes, although in that case, not all sweaters would be in. He needs 8 boxes so that all of the sweaters can fit- even if there's leftover space.
Step-by-step explanation:
23 / 3 = 7.6 ( 1s.f)
Answer:
Dave will fill 7 boxes, and will need 8 boxes.
Step-by-step explanation:
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Above is 23 sweaters, where 7 boxes will hold 3 sweaters and only one will hold 2 sweaters.
Given that y varies inversely as x, and y = 8 when x = 3, what is the value of y when x = 12?
Answer:
y = 2 when x =12
Step-by-step explanation:
y = k/x ..............as y varies inversely as x
8 = k/3
k = 8 * 3
k = 24
So,
y = k/x
y = 24/12
y = 2
Answer:
"y=32"
is the answer
Step-by-step explanation:
x=3 > y=8
x=3+3+3+3=12 then y=8+8+8+8=32
Can someone help me please
Answer:
x+54°=90° ( Given)
x=36°
x+y°=90°
y=90°-36°
y=54°
Hope this help!
PLEASE HELP FAST!!!!
What is the complete factorization of 5x2 - 11x - 12?
Answer:
(x-3)(5x+4)
plx give me a brainliest if its correct
2x² + 5x+2
Ac method??
Answer:
the answer is c
Step-by-step explanation:
Find the selling price is a store pays $12 for a book and the markup is 25%.
Answer:
$15
Step-by-step explanation:
use a calculator and type 25%x12 and you will get 3
so 3 is 25% of 12
add 12 and 3 together to get your answer. $15
Answer:
$15
Step-by-step explanation:
$12 + 25% = $15
Alice has 2 number cubes, labeled 1 to 6. If she rolls both number cubes what is the probability that she will get a sum of 11?
Using the probability concept, it is found that there is a 0.0556 = 5.56% probability that she will get a sum of 11.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem:
Two cubes, each with 6 outcomes are rolled, hence there is a total of 6² = 36 outcomes.Of those, in two of them, which are (5,6) and (6,5), a sum of 11 is obtained.Then:
[tex]p = \frac{2}{36} = \frac{1}{18} = 0.0556[/tex]
0.0556 = 5.56% probability that she will get a sum of 11.
You can learn more about the probability concept at https://brainly.com/question/15536019
please help me
math math math
Answer:A12/A6= A6
Step-by-step explanation:
Hi, can I get an answer ASAP? Thanks!
Answer:
X = 148
Step-by-step explanation:
Opposite angles are equal
Identify the terms and like terms in the expression -2n + 7n - r + 10r
To be able to buy a new computer, Salma decides to save for 4 years. She opens a savings account with $600. The account pays simple interest at an annual rate of 5%. She doesn't make any more deposits.
Answer:
5% of 600 is 30, then you multiply the 30 by the 4 years which gives you 120. then you add the original 600 with the 5 person from the four years which is 120 that comes to 720. so 720 is how much is in salma's account after 4 years.
The longest side of a triangle is 30 inches long. Two of the angles have measures of 45 and 79. Solve the triangle.
Answer:
Step-by-step explain
180 -(45+79) = 124
answer: 124
Find K' if the figure is reflected across the x-axis
Explanation:
Point K is located at (1, -4)
We use the rule that [tex](x,y) \to (x,-y)[/tex] when reflecting over the x axis.
The x coordinate stays the same, but the y coordinate flips from positive to negative or vice versa.
Therefore, K(1,-4) will move to K ' (1, 4)
Which series of transformations shows that pentagon A is congruent to pentagon B?
A.
Rotate pentagon A 90° clockwise about the origin, translate it 5 units down, and reflect it over the y-axis.
B.
Rotate pentagon A 90° clockwise about the point (4, 1), and reflect it over the y-axis.
C.
Translate pentagon A 5 units to the left, rotate it 90° clockwise about the origin, and reflect it over the x-axis.
D.
Translate pentagon A 5 units down, rotate it 90° clockwise about the point (5, 2), and reflect it over the y-axis.
Answer:
Its A i just did it
Step-by-step explanation:
Francisco needed to get his computer fixed. He took it to the repair
store. The technician at the store worked on the computer for 5 hours
and charged him $176 for parts. The total was $651. Write and solve an
equation which can be used to determine x, the cost of the labor per
hour.
Answer:
$95 per hour
Step-by-step explanation:
The total of charges is the sum of the cost of labor and the cost of parts. The cost of labor is the product of hours (5) and the cost per hour (x). Then the equation for total cost is ...
total cost = parts cost + hours cost
651 = 176 + 5x
475 = 5x . . . . . . . subtract 176
95 = x . . . . . . . . . divide by 5
The cost of labor per hour is $95.
What is X equal to? PS it’s not 180
Answer:
x=47
Step-by-step explanation:
all straight lines add up to 180°
we can work out x using this
we do:
180-86=94 to work out what 2x equals to
then we do
94/2=47 to find out what x equals to
x=47
hope this helps!
X - 5y=7
2x + 7y=-20
Substitution
Answer: (x,y) = (-3, -2)
Step-by-step explanation:
yb better
Write the prime factorization of 24. Order the factors from least to greatest ( for example, 2 x 2 x 3 x 5)
Answer:
2×2×2×3
Step-by-step explanation:
[tex]24 = 8 \times 3 \\ factorize8 \\ 8 = 2 \times 2 \times 2 \\ therefore \: the \: prime \: \\ factrization \\ \: is \\ \: 24 = 2 \times 2 \times 2 \times 3[/tex]
If I am correct please follow
What are the factors of 24?
What are factors?
A factor is a number or digit that a number is divisible by.
24 is divisible by
1, 2, 3, 4, 6, 12, 24.
Now, what about prime factors? Prime numbers are only divisible by 1 and themselves.
Thus, the prime factorization of 24 is
2*2*2*3
Hope you find it helpful.
Feel free to ask if you have any doubts.
-MistySparkles*
can anyone help? does anyone know the last answer? its 3.
Find all real zeros of the function algebraically -5(x^2+2x-4)
[tex]−5(²+2−4)[/tex]
[tex]−5²−10+20[/tex]
Solution :—
[tex]−5²−10+20[/tex]
Answer:
Step-by-step explanation:
-5(x² + 2x - 4) = -5x² - 10x + 20
a = -4 ; b = -10 ; c = 20
D = b² - 4ac = (-10)² - 4*(-4)*20
= 100 + 320 = 420
[tex]\sqrt{D}=\sqrt{2*2*3*5*7}=2\sqrt{105}\\\\x=\dfrac{-b+\sqrt{D}}{2a} \ ; x =\dfrac{-b-\sqrt{D}}{2a}\\\\\\x=\dfrac{10+2\sqrt{105}}{2*(-5)} \ ; \ x =\dfrac{10-2\sqrt{105}}{2*(-5)}\\\\\\x = \dfrac{2*(5+\sqrt{105})}{2*(-5)} ; \ x =\dfrac{2*(5-\sqrt{D})}{2*(-5)}\\\\\\x =\dfrac{5+\sqrt{105}}{-5} \ ; \ x=\dfrac{5-\sqrt{105}}{-5}\\\\\\x=\dfrac{-5-\sqrt{105}}{5} \ ; \ x =\dfrac{-5+\sqrt{105}}{5}[/tex]
Can you please help with number three
Answer:
AAA and SSA are not real theorems
Step-by-step explanation:
Side Side Angle is not a valid theorem because the unknown side could be located in two different places which would not prove the triangles congruent.
Angle Angle Angle is also not a valid theorem because all the angles might have congruent measures but that doesn't mean the sides will have the same measures therefore AAA cannot prove triangles congruent.
The rest are valid congruence theorems.
Which set of numbers form a right triangle?
a. 3.2, 1.3, 2
b. 4, 2.1, 5
C. 5, 13, 12
Step-by-step explanation:
Pythagoras must be true :
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), and it is always the longest of the 3 sides.
so, the sum of the squares of the 2 smaller numbers must be the square of the largest number.
1.3² + 2² = 1.69 + 4 = 5.69
that is NOT 3.2² = 10.24
so, this is NOT a right-angled triangle.
2.1² + 4² = 4.41 + 16 = 20.41
that is NOT 5² = 25
so, this is NOT a right-angled triangle.
5² + 12² = 25 + 144 = 169 = 13²
so, yes, this is a right-angled triangle.
I need this done :( please
#b
x+4y=-26--(1)x-4y=8--(2)Solve graphically
Solution is(-9,-4.25)#c
x+y=2--(1)-3x-y=5--(2)Solution is(-3.5,5.5)Both graphs attached
Answer:
Question b
[tex]\textsf{Equation 1:} \ \dfrac12x-2y=-13[/tex]
[tex]\textsf{Equation 2:} \ x-4y=8[/tex]
Multiply Equation 2 by two:
[tex]\implies \textsf{Equation 3:} \ x+4y=-26[/tex]
Subtract Equation 2 from Equation 3:
[tex]\begin{aligned}x-4y & =8\\- \ \ \ x+4y & =-26\\\cline{1-2}-8y & =34\end{aligned}[/tex]
Solve for y:
[tex]\implies -8y=34[/tex]
[tex]\implies y = -\dfrac{17}{4}[/tex]
Substitute found value of y into Equation 2 and solve for x:
[tex]\implies x-4\left(-\dfrac{17}{4}\right)=8[/tex]
[tex]\implies x+17=8[/tex]
[tex]\implies x=-9[/tex]
Question a
[tex]\textsf{Equation 1:} \ x+y=2[/tex]
[tex]\textsf{Equation 2:} \ -3x-y=5[/tex]
Add Equation 1 and Equation 2:
[tex]\begin{aligned}x+y & = 2\\+ \ \ \ -3x-y & =5\\\cline{1-2}-2x & = 7\end{aligned}[/tex]
Solve for x:
[tex]\implies -2x=7[/tex]
[tex]\implies x = -\dfrac{7}{2}[/tex]
Substitute found value of x into Equation 1 and solve for y:
[tex]\implies \left(-\dfrac{7}{2}\right)+y=2[/tex]
[tex]\implies y=\dfrac{11}{2}[/tex]
What is the answer to x and y
Answer:
y= 128, x=52
Step-by-step explanation:
The Sum of all the angles in a quadrilateral is 360.
y is 128 because both those angles are equal
the other 2 angles are also equal to each other.
360 - 128-128= 104
104/2 is 52
Answer:
Step-by-step explanation:
y = 128
x + y = 180 {Supplementary}
x + 128 = 180
x = 180 - 128
x = 52
Could anybody solve this by any chance? Thanks
Answer:
y=x÷20x19
Step-by-step explanation:
x÷20=5% then 5%x19=95% basically 5% off
