Answer:
40° or 100°.
Step-by-step explanation:
If Angle ABD = 70° and Angle CBD = 30° Angle ABC can be 70° + 30° or 70° - 30°.
angle ABC measures 100 degrees.
To find the measure of angle ABC, we can use the fact that the sum of the angles in a triangle is 180 degrees.
In triangle ABC , we have angle ABD measuring 70 degrees and angle CBD measuring 30 degrees.
Since angle ABD and angle CBD are adjacent angles, they add up to form angle ABC.
Therefore, we can calculate angle ABC as follows:
m ∠ ABC = m ∠ ABD + m ∠ CBD
m ∠ ABC = 70° + 30°
m ∠ ABC = 100 degrees
Thus, angle ABC measures 100 degrees.
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please someone help me to prove this...
Answer: see proof below
Step-by-step explanation:
Use the following Power Reducing Identities:
[tex]\cos^2 A = \dfrac{1}{2}(1 + \cos 2A)\\\\\sin^2 A = \dfrac{1}{2}(1 - \cos 2A)[/tex]
Use the following Product to Sum Identity:
[tex]\cos A\cdot \cos B=\dfrac{1}{2}\bigg[\cos(A+B)+\cos(A-B)\bigg][/tex]
Proof LHS → RHS
[tex]\text{LHS:}\qquad \qquad \qquad \cos^2\beta\cdot \sin^4\beta\\.\qquad \qquad \qquad =\cos^2\beta\cdot \sin^2\beta\cdot \sin^2 \beta[/tex]
[tex]\text{Power Reducing:}\qquad \dfrac{1}{2}\bigg(1+\cos 2\beta\bigg)\dfrac{1}{2}\bigg(1-\cos 2\beta\bigg)\dfrac{1}{2}\bigg(1-\cos 2\beta\bigg)\\\\\\.\qquad \qquad \qquad \quad =\dfrac{1}{8}(1+\cos 2\beta)(1-\cos 2\beta)(1-\cos 2\beta)[/tex]
[tex]\text{Expand:}\qquad \qquad \dfrac{1}{8}\bigg(1-\cos 2\beta-\cos^2 2\beta+\cos^3 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{8}\bigg(1-\cos 2\beta-\cos^2 2\beta+\cos^2 2\beta \cdot \cos \2\beta\bigg)[/tex]
[tex]\text{Power Reducing:}\qquad \dfrac{1}{8}\bigg(1-\cos 2\beta -\dfrac{1}{2}(1+\cos 4\beta)+\dfrac{1}{2}(1+\cos 4\beta)\cos 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{16}\bigg(2-2\cos 2\beta -1-\cos 4\beta +\cos 2\beta +\cos 4\beta \cdot \cos 2\beta \bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{16}\bigg(1-\cos 2\beta -\cos 4\beta+\cos 4\beta \cdot \cos 2\beta \bigg)[/tex]
[tex]\text{Product to Sum:}\quad \dfrac{1}{16}\bigg(1-\cos 2\beta -\cos 4\beta +\dfrac{1}{2}[\cos(4\beta+2\beta)+\cos (4\beta-2\beta)]\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{32}\bigg(2-2\cos 2\beta -2\cos 4\beta +\cos 6\beta +\cos 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)[/tex]
[tex]\text{LHS=RHS:}\\ \dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)=\dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)[/tex]
If m 8 =22, m 7=31, and m EAD=102 find m 9
S is the answer
Step-by-step explanation:
Let 3+4+8+9+13+14+18+___ 40 terms=S
To solve the equation X - 62 = 123, you would ?
Evaluate f(x)=12 for the function f(x)=5(x-3)+17
Answer:
x = 5
Step-by-step explanation:
We are given the function;
f(x) = 5(x-3) + 17
And f(x) = 12
Thus;
5(x-3) + 17 = 12
Expanding the bracket gives;
5x - 15 + 17 = 12
5x + 2 = 12
5x = 12 - 2
5x = 10
x = 10/2
x = 5
Thus,for f(x) = 12, x has to be 5
what is the constant for -9x^3+12p+6
A constant is any numbers in an equation that don't have any variable connected to it.
-9x^3 and 12p are not constants since they are connected to variables.
6 is a constant because its not connected to any variable.
Best of Luck!
the perimiter of a parallelogram is 72 meters the width of the paralleogram is 4 meters less than its length. find the length and width of the parallelogram.
Answer:
length = 20 m
width = 16m
Step-by-step explanation:
It is 60 Celsius on the crust of a volcano. What is this number in Kelvin?
Answer:
333.15 Kelvin (K)
Step-by-step explanation:
When you convert from Celsius to Kelvin, you add 273.15
60 C + 273.15 = 333.15 K
So, that is the answer. Hope this helps!
Answer:
333.15 Kelvin (333 rounded)
Step-by-step explanation:
You must add 273.15.
60 + 273.15 = 333.15.
The answer is 333.15 (333 rounded.)
The perimeter of the rectangle and the triangle shown are the same. Write an equation to represent this situation, and solve for x. Then, find the perimeter of each shape.
Answer:
Step-by-step explanation:
Perimeter of a polygon = Sum of all sides of the polygon
Perimeter of the given rectangle = 2[(5x - 2) + (3x - 0.5)]
= 2[8x - 2.5]
= (16x - 5)
Perimeter of the given triangle = (2x + 3) + (2x + 3) + (10x - 5)
= 14x + 1
Since perimeter of the rectangle and triangle are same, equation will be
(16x - 5) = (14x + 1)
16x - 14x = 5 + 1
2x = 6
x = 3
Perimeter = (16x - 5)
= 48 - 5
= 43 units
Donalita ate 5 out of every 7 candies in a jar. If she ate 25 candies, what fraction represents the number of candies she ate over the total number of candies?
Answer:
25/35
Step-by-step explanation:
5 times 7 equals 35 and that means that this is the denominator because that is our total amount.
5 times 5 equals 25 and that makes it the numerator because that is what is being taken out of 5 jars
Hopefully this helps you :)
How do you right coordinates?
Answer: You write the latitude first, followed by a comma, and then the longitude.
Step-by-step explanation:
21(2−x)+12x=44
What does X=
Answer:
x= -2/9
Step-by-step explanation:
42-21x+12x=44
-21x+12x=44-42
-9x=2
x= -2/9
-8+9·2÷-3 math please answer quick please
Answer:
Exact form: [tex]-11.06[/tex]
Decimal form: [tex]-11.066667[/tex]
Step-by-step explanation:
[tex]-8+9.2[/tex] ÷ [tex]-3[/tex]
Let's simplify. We will have to change [tex]9.2[/tex] and [tex]-3[/tex] a draction
[tex]-8+\frac{9.2}{-3}[/tex]
This equals
Exact form: [tex]-11.06[/tex]
Decimal form: [tex]-11.066667[/tex]
Hope this helps!
A camping group began with 240 pounds of food and each day consumed about 12 pounds after how many days did they have 180 pounds left does anyone know step by step ?
Answer:
Five days
Step-by-step explanation:
First, we have to find out how much food they ate:
240 - 180 = 60
Now, we have to find out the number of days they would take to eat 60 pounds of food. We can do that by dividing:
60/12 = 5
They took five days to have 180 pounds leftover.
in geometry why do we use 3.14 rather than 3.14159??
Answer:
3.14 is the simplified version (approximate) to π
A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building. What are the dimensions of this rectangular room in the actual building? Group of answer choices
======================================================
The blueprints say that 1 inch represents 10 feet. This means we can form the equation below
1 inch = 10 feet
Of course 10 feet is much larger than 1 inch, so they cannot be actually equal to one another, but it helps tie together the two quantities. And it also allows us to multiply both sides by 3 to get
3 inches = 30 feet
So 3 inches on paper means we have 30 feet in real life.
Similarly,
1 inch = 10 feet
5.5 inches = 55 feet (multiply both sides by 5.5)
The 3 inch by 5.5 inch rectangle on paper corresponds to a 30 feet by 55 feet rectangle in real life.
----------------
In short, you multiply each given dimension by 10
3 inches goes to 3*30 = 30 feet
5.5 inches goes to 5.5*10 = 55 feet
HELP WILL GIVE BRAILEST AND WILL GIVE 50 POINTS!!!!! (also please tell me how you did it!) Simplify and Solve: 12x + 8 < 116
Answer:
Step-by-step explanation:
1. isolate the variable subtract both sides by 8 (12x+8-8<116-8)
2. Divide both sides by twelve (12x/12<116-8/12)
3. Simplify (x<108/12)
4. Answer (x<9)
=12x+8−8<116−8
=12x<108
Step 2: Divide both sides by 12.[tex] \frac{12x}{12} < \frac{108}{12} [/tex]
Answerx<9
i need help finding the range
Answer:
I think it's -1, 4. But i'm not a 100% sure.
Step-by-step explanation:
Answer:
To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.
Step-by-step explanation:
This is how you solve for Range; I can't view the image on my chromebook.
If it takes 10 seconds to hear thunder when lightning is 4 miles away, determine how far away the lightning is when it takes 6 seconds to hear the thunder. miles
Answer:
2.4 miles.
Step-by-step explanation:
10sec = 4 miles.......what abt.....
6 sec = ??
cross multiply:
6sec × 4miles ÷ 10 sec= 2.4miles
Write an equation in point-slope form for a line that passes through the given set of points.
(-2, - 4) and (1, 8)
First off, we need the slope
[tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{8-(-4)}{1-(-2)}[/tex]
That leaves you with
12/3 = 4
point-slope form: y-y1 = m ( x - x1)
So...
y - (-4) = 4 ( x - (-2))
y + 4 = 4 (x + 2)
y + 4 = 4x + 8
Now subtract 4 from both sides of the equation
y = 4x +4
unit rate 232 miles in 4 hours
Answer:
58 miles per hour
Step-by-step explanation:
leave a heart please :D
5. Find the base of the triangle if its area is 48 sq. in and its height is 16 in. 10 points none of the options 9 in O 12 in 6 in
Answer:
The answer is 6 inStep-by-step explanation:
Area of a triangle is given by
[tex] A = \frac{1}{2} bh[/tex]
where b is the base
h is the height
From the question
A = 48 sq. in
h = 16 in.
Substitute the values into the above formula and solve for the base
That's
[tex]48 = \frac{1}{2} 16b \\ 48 = 8b \\ \frac{8b}{8} = \frac{48}{8} [/tex]
We have the final answer as
6 inHope this helps you
I just need no. a please help me to prove this.
Answer: see proof below
Step-by-step explanation:
Given: A + B + C = π and cos A = cos B · cos C
scratchwork:
A + B + C = π
A = π - (B + C)
cos A = cos [π - (B + C)] Apply cos
= - cos (B + C) Simplify
= -(cos B · cos C - sin B · sin C) Sum Identity
= sin B · sin C - cos B · cos C Simplify
cos B · cos C = sin B · sin C - cos B · cos C Substitution
2cos B · cos C = sin B · sin C Addition
[tex]2=\dfrac{\sin B\cdot \sin C}{\cos B \cdot \cos C}[/tex] Division
2 = tan B · tan C
[tex]\text{Use the Sum Identity:}\quad \tan(B+C)=\dfrac{\tan B+\tan C}{1-\tan B\cdot \tan C}[/tex]
Proof LHS → RHS
Given: A + B + C = π
Subtraction: A = π - (B + C)
Apply tan: tan A = tan(π - (B + C))
Simplify: = - tan (B + C)
[tex]\text{Sum Identity:}\qquad \qquad \qquad =-\bigg(\dfrac{\tan B+\tan C}{1-\tan B\cdot \tan C}\bigg)[/tex]
Substitution: = -(tan B + tan C)/(1 - 2)
Simplify: = -(tan B + tan C)/-1
= tan B + tan C
LHS = RHS: tan B + tan C = tan B + tan C [tex]\checkmark[/tex]
The world's largest ocean, the Pacific ocean, has an area of about 200,000,000 km^(2) , which can be written as 2 x 10 ^(n) km^(2). What is n?
Answer:
n = 8
Step-by-step explanation:
:)
please answer this quick
I need help
Answer:
No, it is not a magic square.
Step-by-step explanation:
A magic square is when whatever way you add it from, it is always the same answer (the magic sum). As you can clearly tell, it doesn't add up to the same number.
. Denise has multiplied (2r – 3)(2r + 3) to get 4r2 – 9. After looking at her work, Hyder says her solution must be incorrect because multiplying two binomials will always produce a trinomial. Which student is correct? Explain the error to the incorrect student. HELP ME PLEASE NEED IT IN TIME THANKS.
Answer:
Answer:
The answer is 4r² – 9
Denise answer is correct.
Step-by-step explanation:
One of the methods of solving the given equation [(2r – 3)(2r + 3)] is the FOIL method
Using the FOIL method (Used for multiplying binomials)
F stands for first
O stands for outer
I stands for inner
L stands for last
In this method, it means we will first multiply the first terms followed by multiplying the outer term, then multiplying the inner terms and finally, the last terms.
So, for the equation (2r – 3)(2r + 3)
First : (2r)(2r) = 4r²
Outer : (2r)(+3) = 6r
Inner : (–3)(2r) = – 6r
Last : (–3)(+3) = – 9
Adding the results we get
4r² + 6r – 6r – 9 (+6r and – 6r cancels out)
= 4r² – 9
∴ (2r – 3)(2r + 3) = 4r² – 9
Hence, Denise answer is correct
what is 3,393 divided by 13
Answer:
261
I hope this helps!
The ratio of “D”s to “A”s in the school was 6 to 19. If there were 872 As in the school this term, how many Ds were there?
Answer:
The amount of D's there were is 275.4
Step-by-step explanation:
D : A
6 : 19
D : 872
Cross multiply 872 and 6
6*872 = 5232
Then divide the total by 19
5232/19 = 275.4 (simplified)
About how many ants would it take to wrap around the earth
Answer:
Ten billion
Step-by-step explanation:
There would around 16×10⁻¹⁰ ants to wrap around the earth.
What is circumference?Circumference is the distance around a circle., basically it is the perimeter of the circle.
Given that, an average sized ant is about 4×10⁻³ meter long the circumference of the earth is about 4×10⁻⁷ meters, we are asked to find the number of ants that would it take to wrap around earth,
To find the same, we will multiply the size of ants to the circumference of the earth,
So, 4×10⁻³ × 4×10⁻⁷
= 16×10⁻¹⁰
Hence, there would around 16×10⁻¹⁰ ants to wrap around the earth.
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Multi-Step: <ABD and <BDE are supplementary. Find the measures of both angles.
28. m<ABD = (12x - 12)° , m<BDE = (3x + 48)°
Answer:
get it helps me with lI do not know the answer
Step-by-step explanation:
sorry
What is 4/q as a decimal
Answer:
what is the value of q?
Step-by-step explanation: