(cos2A−cos2B)2+(sin2A+sin2B)2=4sin2(A+B)
Answer:
[tex] {( \cos2A - \cos2B) }^{2} + {( \sin2A + \sin2 B }^{2}\\ = ( - 2\cos2A \cos2B + { \cos {}^{2} 2A } + \cos {}^{2} 2B) + (2 \sin2A \sin2B + \sin {}^{2} 2A + \sin {}^{2} 2B)\\ \\ { = - 2( \sin2A + \sin 2 B - \cos2 A - \cos2B) }\\ \\ { = - 2( - 4 \sin( A + B) \cos(A + B) } \\ \\ = {\tt{double \: angle \: of \: sine}}\\ \\ { = 2 \times 2(2 \sin (A + B) \cos(A + B)) }\\ \\ { = 4 \sin2(A + B)}[/tex]
show the following equations on a number line. a) -16 < 4x _ x÷2
Step-by-step explanation:
-16(2)<4x(2)-x/2(2)
-32<8x-x
-32<7x
-32/7<7x/7
-32/7<x
-4.5714285714285714<x
~-4.56<x
So after drawing the number line, indicate it starting from negative 4.6 and pointing the arrow towards the right. Do not shade
John made this model to show \frac{4}{7}\times\frac{13}{9} 7 4 × 9 13 Using John's model, what is \frac{4}{7}\times\frac{13}{9} 7 4 × 9 13 ? You may use the scratchpad to show your work.
Answer:
[tex]\frac{4}{7}\times\frac{13}{9} = \frac{52}{63}[/tex]
Step-by-step explanation:
Given
See attachment for model
Required
Determine [tex]\frac{4}{7}\times\frac{13}{9}[/tex] from the model
The model is represented by:
[tex]\frac{4}{7}\times\frac{13}{9} = \frac{4}{7}\times\frac{9}{9} + \frac{4}{7}\times\frac{4}{9}[/tex]
To get: [tex]\frac{4}{7}\times\frac{9}{9}[/tex], we consider the first partition
The number of shaded box is 63 ---- this represents the denominator
The total boxes shaded at the bottom is 36 ---- this represents the numerator
So, we have:
[tex]\frac{4}{7}\times\frac{9}{9} = \frac{36}{63}[/tex]
To get: [tex]\frac{4}{7}\times\frac{9}{9}[/tex], we consider the first partition
The number of shaded box is 63 ---- this represents the denominator
The total boxes shaded at the bottom is 16 (do not count the gray boxes) ---- this represents the numerator
So, we have:
[tex]\frac{4}{7}\times\frac{4}{9} =\frac{16}{63}[/tex]
The equation becomes:
[tex]\frac{4}{7}\times\frac{13}{9} = \frac{4}{7}\times\frac{9}{9} + \frac{4}{7}\times\frac{4}{9}[/tex]
[tex]\frac{4}{7}\times\frac{13}{9} = \frac{36}{63} + \frac{16}{63}[/tex]
[tex]\frac{4}{7}\times\frac{13}{9} = \frac{36+16}{63}[/tex]
[tex]\frac{4}{7}\times\frac{13}{9} = \frac{52}{63}[/tex]
The equation of a linear function in point-slope form is y – y1 = m(x – x1). Harold correctly wrote the equation y = 3(x – 7) using a point and the slope. Which point did Harold use
Answer:
Coordinate of points = (7 , 0)
Step-by-step explanation:
Given:
Equation of slope;
y – y1 = m(x – x1)
Equation of slope;
y = 3(x – 7)
Find:
Coordinate of points
Computation:
By comparing
y - 0 = 3(x - 7)
So,
y1 = 0
m = 3
x1 = 7
Coordinate of points = (7 , 0)
Please help this is due today!!
Answer:
81 grams
Step-by-step explanation:
if you use the calculator by putting in 7 for t in the equation: 100(0.97)^7
then solve you get 80.79..... a big long decimal. round to the nearest whole number and you get 81
Please help me with this geometry question and show work
(3) 8
Step-by-step explanation:
Note that ∆ADE is similar to ∆ABC. As such, the ratios of their legs are equal. Also note that AD = AB + BD.
BC/AB = DE/AD
BC/10 = 12/(10 + 5) = 12/15 = 4/5
or
BC = 10(4/5) = 8
A telephone pole is 24 feet tall. A 26 foot guy wire is used to stabilize the pole. How far from the base of the telephone pole should the end of the guy wire be set?
Step-by-step explanation:
Let,
the telephone pole be AB
the wire be AC
therefore AB=24
AC=26
By using Pythagora's theorem
(AC)² =(AB)² + (BC)²
(26)² =(24)² + (BC)²
676 = 576 + (BC)²
(BC)²= 676 - 576
(BC)²=100
BC =✓100
BC. =10
Therefore, the base of the telephone pole is set 10m far
HOPE IT HELP YOUFour and two thirds add one and three fourths
Answer:
4 2/3 + 1 3/4 = 6 5/12
Consider the graph of the function f(x)=2x.
Which statement describes a key feature of
function g if g(x) = 2f(x)? Answers:
A. y-intercept at (0,2)
B. y-intercept at (2,0)
C. horizontal asymptote of y = -2
D. horizontal asymptote of y = 2
Given:
The parent function is:
[tex]f(x)=2^x[/tex]
The other function is:
[tex]g(x)=2f(x)[/tex]
To find:
The statement that describes a key feature of function g.
Solution:
We have,
[tex]f(x)=2^x[/tex]
[tex]g(x)=2f(x)[/tex]
Using these two functions, we get
[tex]g(x)=2(2)^x[/tex]
Putting [tex]x=0[/tex], we get
[tex]g(x)=2(2)^{(0)}[/tex]
[tex]g(x)=2(1)[/tex]
[tex]g(x)=2[/tex]
The y-intercept of the function g at (0,2). So, option A is correct and option B is incorrect.
We know that [tex]g(x)\to 0[/tex] as [tex]x\to -\infty[/tex] and it will never intersect the line [tex]y=0[/tex]. It means the horizontal asymptote of the function g is
Therefore, the correct option is A.
Answer:
A
Step-by-step explanation:
Bill is ten years older than his sister. If Bill was twenty-five years of age in 1983, in what year could he have been born?
Answer:
1968
Step-by-step explanation:
can someone help?? thanks and no links pls
Answer:
x = 10
Step-by-step explanation:
The angles are vertical angles and vertical angles are equal
8(x-1) = 6(x+2)
Distribute
8x-8 = 6x+12
Subtract 6x from each side
8x-8 -6x = 6x+12-6x
2x-8 = 12
Add 8 to each side
2x-8+8 = 12+8
2x=20
Divide by 2
2x/2 = 20/2
x = 10
Answer:
x must be 10
Step-by-step explanation:
The two angles shown are "vertical angles" and are thus equal.
So 8(x - 1) = 6(x + 2), or (after carrying out the indicated multiplication):
8x - 8 = 6x + 12, or
2x = 20
Then x must be 10.
Work out the volume of this cylinder. Give your answer rounded to the nearest whole number.
Answer:
31793 cm^3
Step-by-step explanation:
Equation
Volume = [tex]\pi[/tex] * r^2 * h
Givens
d = 2*r
d = 30
r = 15
h = 45
[tex]\pi[/tex] = 3.14
Solution
V = 3.14 * 15^2 * 45
V = 31793 rounded.
Help plzz
Question given below
There are 18 apples and a number of oranges in a box. The probability of choosing an
3
-
apple is
Find the total number of apples and oranges in the box.
3/7
Answer:
60 apples and oranges
Step-by-step explanation:
18/3/7 = 42
18/42 = 3/7
18+42 = 60
Use the Distance Formula and the Pythagorean Theorem to find the distance, to the nearest tenth, from T(2, –2) to W(–7, 3).
Answer:
10.3 units
Step-by-step explanation:
coordinate points are
T(2, -2) =(x1 , y1)
W(-7, 3) =(x2 , y2)
distance formula = [tex]\sqrt{(x2 -x1)^2 + (y2 -y1)^2}[/tex]
=[tex]\sqrt{(-7-2)^2 + {3-(-2)}^2[/tex]
=[tex]\sqrt{(-9)^2 + (3+2)^2[/tex]
=[tex]\sqrt{81 + 5^2[/tex]
=[tex]\sqrt{81 + 25[/tex]
=[tex]\sqrt{106[/tex]
=10.29563014
=10.3 (after converting it to the nearest tenth)
Find the total surface area of this prism where the cross section is an isosceles triangle 5cm, 13cm, 24cm, 10cm
Answer: 620 cm2
Step-by-step explanation:
The base of the prism is a rectangle with 24 cm x 10 cm, so the base area is: B = 24 * 10 = 240 cm2
The cross section is a triangle with base = 24 cm and height = 5 cm, so its area is: C = 24 * 5 / 2 = 60 cm2
The sides are rectangles with 10 cm x 13 cm, so their area is: D = 10 * 13 = 130 cm2
The total surface area is: S = B + 2C + 2D = 240 + 2*60 + 2*130 = 620 cm2
What is the distance between the following points?
Evaluate the following f(x) = x^2 - 6 for f(4)
Answer:
Just replace the variable "x" with "5":
f(5) = 2×5 + 4 = 14
Answer: f(5) = 14
Step-by-step explanation:
Guide Questions:
1. How students have age between 12 and 14?
2. How many 14-year-old grade 7 students do there?
Answer:
2. There are 5 students 14 years old 7 grade
What does "Time (s)" represent in the graph?
Time vs. Position of Battery Operated Car
the y-axis
O the dependent variable
O an inverse relationship
o the independent variable
sition (m)
Answer:
the independent variable
Step-by-step explanation:
tome is the independent variable
position is the dependent variable
In the given graph titled "Time vs. Position of Battery Operated Car," the "Time (s)" represents the independent variable.
The independent variable is typically plotted on the x-axis of a graph and represents the variable that is intentionally changed or controlled in an experiment or study.
In this case, the graph shows how the position of the battery-operated car changes over time, with time being the independent variable.
So the time represents the independent variable.
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ7
How do you write an equivalent logarithmic equation for e^4=x
Answer:
4 = ln x
Step-by-step explanation:
e^4=x
Take the natural log of each side
ln(e^4)=ln(x)
We know ln a^b = b ln a
4 ln e = ln x
ln (e) =1
4 = ln x
can someone PLEASE HELP me?? the answer has to be in simplest form and i keep getting it wrong. the ixl score needs to be at 68 and im only at 30. i really need this done please
explaining your answer to me will get you brainliest.
Answer: The formula for sector area is simple, multiply the central angle by the radius squared, and divide by 2: Sector Area = r² * α / 2. So you want to do that for every problem like this
Step-by-step explanation:s
=========================================================
Explanation:
Let's ignore the area of the shaded slice for now. Instead, we'll find the area of the full circle
We plug in the radius r = 1 to find that
A = pi*r^2
A = pi*1^2
A = pi
The exact area of that full circle is pi square meters. You can think of an actual pie (the baked pastry, not the constant) with this area as a way to help conceptualize things.
If we wanted the whole circle, then we'd say pi is the answer. However, we only want a slice of that circle. The fractional amount 66/360 represents the slice we want. This fraction reduces to 11/60 after you divide both parts by 6. If you were to cut the pizza up into 60 slices, then you would shade 11 of them in to represent the green area.
Multiply 11/60 with the area pi to get the final answer 11pi/60
This answer is exact in terms of pi
To get an approximate value, you could replace pi with 3.14 to get 11pi/60 = 11*3.14/60 = 0.57567 meaning the green shaded area is roughly 0.57567 square meters. Use more decimal digits of pi to get a more accurate shaded area.
Select the correct answer. 2 Jay stores hay in cubic stacks on his farm. If the length of each stack is 3 yard, what is the volume of hay in each stack? O A. cubic yard O B. cubic yard OC. cubic yard OD 8 cubic yard 27 Reset Next
Cubic stack would mean all the sides are the same length.
The length of the side is given as 3 yards.
Volume = 3^3 = 3 x 3 x 3 = 27
Volume = 27 cubic yards.
if $7000 is borrowed at the rate of 5% per annum for 3 years what is the simple interest
Answer:
$450
Step-by-step explanation:
Un polígono regular está inscrito en una circunferencia. ¿Qué medida del polígono es igual al radio de la circunferencia?
Answer:
La medida del polígono que es igual al radio de la circunferencia es el segmento de recta comprendido entre el centro geométrico del polígono y cualquiera de sus vértices, cuyo nombre es también radio.
Step-by-step explanation:
La medida del polígono que es igual al radio de la circunferencia es el segmento de recta comprendido entre el centro geométrico del polígono y cualquiera de sus vértices, cuyo nombre es también radio.
What is a two-column proof
Answer:
A two-column proof uses a table to present a logical argument and assigns each column to do one job, and then the two columns work in lock-step to take a reader from premise to conclusion.
Step-by-step explanation:
Basically in simple terms, one side is the statements, and the otherside is the reasoning
need help with this Q&A 4
Answer:
y=4x + 3/4
Step-by-step explanation:
A garden is 10m by 12m. A fence is put around the outside of the garden. The total length of the fence is
When the sun shines at a 60° angle to the ground, Talisa's shadow is 36 inches long.
Answer:
Talisa is 62 inches tall
Step-by-step explanation:
tan = opp/adj
tan60 = opp/36
36 * tan 60 = opp
use calculator
opp = 62.353829072479583
Rounded
Talisa is 62 inches tall
Answer:
Using the right triangle created by this situation, and the fact that the trig ratio tan(θ) = opposite/adjacent, we can say tan(60°) = h/36 or h = 36•tan(60°) = 62.354So, to the nearest inch, Talisas is 62 inches long.if you satisfied to my answer ,can you put brainliest in top of my name , and ur welcome
What is the interquartile range (IQR) of the data?
Answer:
15
Step-by-step explanation:
looks like quartile 3 is at 45
IQR is Q3-Q1 so 45-30 = 15