Good evening ,
Answer:
Circle 0 , 4 , 16
Step-by-step explanation:
→ 0 = 0²
→ 4 = 2²
→ 16 = 4²
:)
A rocket was launched into the air from a platform above ground. The height, in feet, of the rocket above the ground t seconds after being thrown can be determined by the expression -16t^2 + 64t + 80. What does the 80 in the expression represent
Answer:
80 is the height of the platform
the rocket didnt launch from the ground so u need to add it in
Answer:
The rocket was launched from a platform 80 feet above the ground.
Step-by-step explanation:
The + 80 is where it starts
a _____ angle has the same measure as its arc.
Answer:
central
Step-by-step explanation:
greetings the correct answer is central odyssey ware
Square root of one hundred and twenty three
Input the expression x +9/2
Answer:um where is the constant
Step-by-step explanation:
The expression 'x + 9/2' involves adding a variable 'x' to the fraction 9/2. In an example situation, if you substitute x with the number 5, the result would be 9.5. Remember, x can represent any number.
Explanation:The expression you provided is x + 9/2. In mathematics, this is an algebraic expression which comprises of a variable x and a fraction 9/2. It means that you're adding the x variable to the fraction 9/2. For example, if you were to substitute x with a number, let's say 5, the answer would then be 5 + 9/2 = 9.5. It's important to remember that variables can represent any number, and in this case, the variable is x.
Learn more about Algebraic Expression here:
https://brainly.com/question/34192827
#SPJ3
EUREKA MATH kATRINA HAS 23 STICKERS AND JENNIFER HAS 9. HOW MANYMORE STICKERS DOES JENNIFER NEED TO HAVE AS MANY AS KATRINA?
Answer:
14
Step-by-step explanation:
23 - 9 = 14
Answer:
14
Step-by-step explanation:
23-9=14
Fifteen less than eight times a number (n) is twenty seven in equation form
Answer:
x = -4/5 = -0.800
Step-by-step explanation:
Pull out like factors :
-12 - 15x = -3 • (5x + 4)
Solve :
-3 = 0
Solve :
5x+4 = 0
5x = -4
x = -4/5 = -0.800
Which point is on the line y = -2x + 3?
(-2,-1)
(3, -3)
(3, 3)
(-3,-9)
Answer:
Hence (3, -3) is on the given line y = -2x + 3
Step-by-step explanation:
For a point on the Line, It must Satisfy the Equation of a line
Therefore for
[tex]y=-2x+3[/tex]
For (-2,-1)
Substitute x = - 2 and y = -1 in above equation
Left Hand Side = y
= -1
Right Hand Side = -2 × (-2) +3
= 4 +3
= 7
Left Hand Side ≠ Right Hand Side
Not Satisfied
Hence (-2,-1) is NOT on the given line
For (3, -3)
Substitute x = 3 and y = -3 in above equation
Left Hand Side = y
= -3
Right Hand Side = -2 × (3) +3
= -6 +3
= -3
Left Hand Side = Right Hand Side
Satisfied
Hence (3, -3) is on the given line y = -2x + 3
For (3, 3)
Substitute x = 3 and y = 3 in above equation
Left Hand Side = y
= 3
Right Hand Side = -2 × (3) +3
= -6 +3
= -3
Left Hand Side ≠ Right Hand Side
Not Satisfied
Hence (3,3) is NOT on the given line
For (-3,-9)
Substitute x = -3 and y = -9 in above equation
Left Hand Side = y
= -9
Right Hand Side = -2 × (-3) +3
= 6 +3
= 9
Left Hand Side ≠ Right Hand Side
Not Satisfied
Hence (-3,-9) is NOT on the given line
Only the point (3, -3) lies on the line y = -2x + 3. None of the other points satisfy the equation.
To determine which point lies on the line y = -2x + 3, we need to substitute the coordinates of each point into the equation:
(-2, -1): Substitute x = -2 into y = -2x + 3:
y = -2(-2) + 3 = 4 + 3 = 7. Since y = -1, this point does not lie on the line.
(3, -3): Substitute x = 3 into y = -2x + 3:
y = -2(3) + 3 = -6 + 3 = -3. Since y = -3, this point lies on the line.
(3, 3): Substitute x = 3 into y = -2x + 3:
y = -2(3) + 3 = -6 + 3 = -3. Since y = 3, this point does not lie on the line.
(-3, -9): Substitute x = -3 into y = -2x + 3:
y = -2(-3) + 3 = 6 + 3 = 9. Since y = -9, this point does not lie on the line.
The only point that satisfies the equation is (3, -3).
Complete question:
Which point is on the line y = -2x + 3?
A. (-2,-1)
B. (3, -3)
C. (3, 3)
D. (-3,-9)
Which of these strategies would eliminate a variable in the system of equations?
2x-5y=13
-3x+2y=13
Answer:
B
Step-by-step explanation:
2x-5y=13.........(1) × 3
-3x+2y=13.......(2) × 2
6x - 15y = 39
-6x + 4y = 26
Adding
6x - 6x - 15y + 4y = 13 + 13
Answer:
Step-by-step explanation:
2x - 5y = 13
-3x + 2y = 13
multiply the top equation by 3 and the bottom one by 2, then add <==
watch...
2x - 5y = 13.....multiply by 3
-3x + 2y = 13....multiply by 2
-----------------
6x - 15y = 39 (result of multiplying by 3)
-6x + 4y = 26 (result of multiplying by 2)
-----------------add
- 11y = 65.....notice how out x terms were eliminated :)
The cube root of 0.000004913 is
Answer:
[tex]\sqrt[3]{0.000004913}=0.017[/tex]
Step-by-step explanation:
Cubic Root
The cubic root of a number N is M, if
[tex]M^3=N[/tex]
It's usually tedious to manually compute cubic roots, but if we use some basic algebra concepts, the job is easily done.
Let's compute
[tex]M=\sqrt[3]{0.000004913}[/tex]
The argument can be expressed in scientific notation as
[tex]0.000004913= 4913\ 10^{-9}[/tex]
The power of 10 has an exact cubic root since the exponent is a multiple of 3. To find the cubic root of the mantissa, we note it's the triple product of 17, i.e.
[tex]4913=17*17*17=17^3[/tex]
Thus our number is
[tex]M=\sqrt[3]{17^3\ 10^{-9}}=17\ 10^{-3}=0.017[/tex]
We have then
[tex]\boxed{\sqrt[3]{0.000004913}=0.017}[/tex]
Find the third side in simplest radical form:
Answer:
[tex]\sqrt{10}[/tex]
Step-by-step explanation:
Since this is a right triangle then we can apply the Pythagorean theorem
look at the photo below for the details.
:)
Use the calculator for these calculations. Round
your answer to the nearest thousandth, if
necessary: 18•(27+26/3)
Answer:
378
Step-by-step explanation:
First: Start with the parentheses
Meaning to add 27 + 36 then divide by 3.
Second: You should have 21 afterwards,
when you have this number you can use the number
outside of the parentheses a.k.a (21 x 18)
Third: You should get the answer "378" unless you do something wrong.
To calculate the expression 18•(27+26/3), follow the order of operations: division, addition, and then multiplication. The result is approximately 642.006.
Explanation:To calculate the expression 18•(27+26/3), we need to follow the order of operations. First, we perform the division 26/3 which gives us 8.66666... (rounded to the nearest thousandth, this is 8.667). Next, we add 27 and 8.667 which equals 35.667. Finally, we multiply 18 by 35.667 to get the final result of 642.006 (rounded to the nearest thousandth, this is 642.006).
Learn more about Mathematics here:https://brainly.com/question/26854035
#SPJ2
What is the quotient when the decimal number 10 and 6/10 is divided by four hundredths
A) 265
B) 265.2
C) 26.25
D) 26.52
Answer:
Step-by-step explanation:
10 and 6/10 = 10.6
4 hundredths = 4/100 = 0.04
10.6 / 0.04 = 265 <==
I WILL GIVE BRAINLIEST
Answer:
[tex] - 10 \div 9 = \frac{ - 10}{9} [/tex]
[tex]10 \div ( - 9) = \frac{10}{ - 9} [/tex]
[tex] - ( - 10 \div ( - 9)) = - (10 \div 9) = - \frac{10}{9} [/tex]
[tex] - \frac{10}{9} = \frac{10}{ - 9} = - \frac{10}{9} [/tex]
A and B are the correct choices.
In Connecticut, there is a tax charge of $0.84 on a $14 dinner bill. Find the tax rate in
Connecticut. (Tax rates are based on cents per one dollar.)
What is the equation to solve this?
Explanation: Calculation of the general sales taxes of Connecticut State for 2019 ... combined rates mentioned above are the results of Connecticut state rate (6.35%). There is no county sale tax for Connecticut. There is no city sale tax for the Connecticut cities. ... The Connecticut's tax rate may change depending of the type of purchase.
Answer:
0.84+1.00=1.84 +14=15.
A hamster runs at a speed of 17 centimeters per second in a wheel of radius 10 centimeters angular velocity and how fast will the wheel spin in revolutions per minute
Answer:
3.229 revolutions per minute
Step-by-step explanation:
The angular velocity of an object is the rate at which it rotates around a fixed axis. In this case, the hamster wheel is rotating.
To find the angular velocity of the wheel, we need to convert the linear velocity of the hamster into angular velocity.
The linear velocity of the hamster is given as 17 centimeters per second. This means that for every second, the hamster moves 17 centimeters along the circumference of the wheel.
To find the angular velocity, we need to find the distance traveled along the circumference of the wheel in one revolution. The circumference of a circle is given by the formula C = 2πr, where r is the radius of the wheel.
In this case, the radius of the wheel is 10 centimeters. So, the circumference of the wheel is C = 2π(10) = 20π centimeters.
Since the hamster runs at a speed of 17 centimeters per second, in one revolution of the wheel, it covers a distance of 20π centimeters.
Now, we can find the angular velocity by dividing the linear velocity by the distance traveled in one revolution.
Angular velocity = linear velocity / distance traveled in one revolution
Angular velocity = 17 centimeters per second / (20π centimeters per revolution)
Simplifying the expression, we get:
Angular velocity = 17 / (20π) revolutions per second
To convert the angular velocity from revolutions per second to revolutions per minute, we need to multiply it by 60 (since there are 60 seconds in a minute).
Angular velocity in revolutions per minute = (17 / (20π)) * 60
Calculating the value, we get:
Angular velocity in revolutions per minute ≈ 3.229 revolutions per minute
Therefore, the wheel will s
AI-generated answer
The angular velocity of an object is the rate at which it rotates around a fixed axis. In this case, the hamster wheel is rotating.
To find the angular velocity of the wheel, we need to convert the linear velocity of the hamster into angular velocity.
The linear velocity of the hamster is given as 17 centimeters per second. This means that for every second, the hamster moves 17 centimeters along the circumference of the wheel.
To find the angular velocity, we need to find the distance traveled along the circumference of the wheel in one revolution. The circumference of a circle is given by the formula C = 2πr, where r is the radius of the wheel.
In this case, the radius of the wheel is 10 centimeters. So, the circumference of the wheel is C = 2π(10) = 20π centimeters.
Since the hamster runs at a speed of 17 centimeters per second, in one revolution of the wheel, it covers a distance of 20π centimeters.
Now, we can find the angular velocity by dividing the linear velocity by the distance traveled in one revolution.
Angular velocity = linear velocity / distance traveled in one revolution
Angular velocity = 17 centimeters per second / (20π centimeters per revolution)
Simplifying the expression, we get:
Angular velocity = 17 / (20π) revolutions per second
To convert the angular velocity from revolutions per second to revolutions per minute, we need to multiply it by 60 (since there are 60 seconds in a minute).
Angular velocity in revolutions per minute = (17 / (20π)) * 60
Calculating the value, we get:
Angular velocity in revolutions per minute ≈ 3.229 revolutions per minute
Therefore, the wheel will spin at a rate of approximately 3.229 revolutions per minute.
What is the measure of AC?
Answer:
AC = 52.8
Step-by-step explanation:
33/20 = 1.65
12*1.65 = 19.8
BA = 19.8
CB + BA = AC
33 + 19.8 = 52.8
Answer:
AC = 52.8
Step-by-step explanation:
Since BE is parallel to CD and intersects the 2 sides of the triangle then it divides those sides proportionally, that is
[tex]\frac{BC}{AB}[/tex] = [tex]\frac{DE}{AE}[/tex], substituting values
[tex]\frac{33}{AB }[/tex] = [tex]\frac{20}{12}[/tex] ( cross- multiply )
20AB = 396 ( divide both sides by 20 )
AB = 19.8
Thus
AC = AB + BC = 19.8 + 33 = 52.8
Two communications companies offer calling
plans. With Company X, it costs 35¢ to connect
and then 5¢ for each minute. With Company Y,
it costs 15¢ to connect and then 4¢ for each
minute.
Write and simplify an expression that represents
how much more Company X charges than
Company Y, in cents, for n minutes.
Answer:
(20 + n)¢
Step-by-step explanation:
With Company X, it costs 35¢ to connect and then 5¢ for each minute.
So, for n minutes of calling the company X charges, C(x) = (35 + 5n)¢
Again, With Company Y, it costs 15¢ to connect and then 4¢ for each minute.
So, for n minutes of calling the company Y charges, C(y) = (15 + 4n)¢.
Therefore, the company Y charges for n minutes of calling less than company X is [(35 + 5n) - (15 + 4n)]¢ = (20 + n)¢ (Answer)
To find how much more Company X charges than Company Y for n minutes, subtract the cost of Company Y from the cost of Company X. The expression to represent the difference in charges is 0.2 + 0.01n.
Explanation:To find how much more Company X charges than Company Y, we need to subtract the cost of Company Y from the cost of Company X for n minutes.
Let's denote the cost of Company X as CX and the cost of Company Y as CY.
For Company X, the cost is $0.35 to connect and $0.05 for each minute. So, the cost of CX for n minutes is given by CX = 0.35 + 0.05n.
Similarly, for Company Y, the cost is $0.15 to connect and $0.04 for each minute. So, the cost of CY for n minutes is given by CY = 0.15 + 0.04n.
To find the difference in charges, we subtract CY from CX:
Company X charges (CX - CY) = (0.35 + 0.05n) - (0.15 + 0.04n) = 0.2 + 0.01n
7x + 3x + 5 - 2x + 7. Select all that are equivalent.
a. 2x + 6
b. 10X + 12 - 2x
c. 12x + 12
d. 8x + 12
Answer:
d 8x+12
Step-by-step explanation:
7x+3x+5-2x+7
combine 7x+3x-2x=8x
and 5+7=12
8x+12
Answer:
Step-by-step explanation:
7x+3x-2x=8x
5+7=12
8x+12
The main story has 150 times as many pages as the prologue there is 750 pages in all how many pages in the main story
There are approximately 745 pages in main story
Solution:
Let "x" be the number of pages in main story
Let "y" be the number of pages in prologue
Given that there are 750 pages in all
Therefore,
number of pages in main story + number of pages in prologue = 750
x + y = 750 ---------- eqn 1
The main story has 150 times as many pages as the prologue
Therefore, a equation is framed as:
number of pages in main story = 150(number of pages in prologue)
x = 150y ----------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 2 in eqn 1
150y + y = 750
151y = 750
y = 4.967
Substitute y = 4.967 in eqn 2
x = 150(4.967)
x = 745.05
Thus there are approximately 745 pages in main story
W
13. one-third the sum of eleven and p
We can model the statement "one-third the sum of eleven and [p]" as y = (1/3)(11 + p)
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have one-third the sum of eleven and [p].
We can model the given question as -
y = (1/3)(11 + p)
Therefore, we can model the statement "one-third the sum of eleven and [p]" as y = (1/3)(11 + p)
To solve more questions on Equation Modelling, visit the link below -
brainly.com/question/14441381
#SPJ5
Evaluate the expression when m=6 and n=33.
n-5m=
2x-7 divided by 6x squared -37x+56
Answer:
the 6.192# melebulated by 59 and devide it by 597 your answere is 64
Step-by-step explanation:
Is the square root of 25/35 rational or irrational
The square root of 25/35, which simplifies down to the square root of 5/7 is an irrational number because the decimal form of the square root doesn't terminate or repeat.
Explanation:The question is asking about the nature of the square root of the fraction 25/35. To solve it, we first simplify the fraction to its lowest terms, which is 5/7. The square root of 5/7 is a decimal that doesn't terminate or repeat, which means that it is an irrational number. In contrast, 25/35 rational refers to numbers that can be expressed as a ratio of two integers, which the square root of 5/7 cannot be.
Learn more about Square Root here:https://brainly.com/question/1540542
#SPJ2
(3-20i)-(14+6i)-(8-2i)
Because there are parentheses we distribute the negative signs:
3 - 20i + (-14) - 6i + (-8) + 2i
Next combine like terms:
3 + (-14) + (-8) and -20i - 6i + 2i
-19 -24i
simplify this please
Answer:
[tex]\frac{12q^{\frac{7}{3}}}{p^{3}}[/tex]
Step-by-step explanation:
Here are some rules you need to simplify this expression:
Distribute exponents: When you raise an exponent to another exponent, you multiply the exponents together. This includes exponents that are fractions. [tex](a^{x})^{n} = a^{xn}[/tex]
Negative exponent rule: When an exponent is negative, you can make it positive by making the base a fraction. When the number is apart of a bigger fraction, you can move it to the other side (top/bottom). [tex]a^{-x} = \frac{1}{a^{x}}[/tex], and to help with this question: [tex]\frac{a^{-x}b}{1} = \frac{b}{a^{x}}[/tex].
Multiplying exponents with same base: When exponential numbers have the same base, you can combine them by adding their exponents together. [tex](a^{x})(a^{y}) = a^{x+y}[/tex]
Dividing exponents with same base: When exponential numbers have the same base, you can combine them by subtracting the exponents. [tex]\frac{a^{x}}{a^{y}} = a^{x-y}[/tex]
Fractional exponents as a radical: When a number has an exponent that is a fraction, the numerator can remain the exponent, and the denominator becomes the index (example, index here ∛ is 3). [tex]a^{\frac{m}{n}} = \sqrt[n]{a^{m}} = (\sqrt[n]{a})^{m}[/tex]
[tex]\frac{(8p^{-6} q^{3})^{2/3}}{(27p^{3}q)^{-1/3}}[/tex] Distribute exponent
[tex]=\frac{8^{(2/3)}p^{(-6*2/3)}q^{(3*2/3)}}{27^{(-1/3)}p^{(3*-1/3)}q^{(-1/3)}}[/tex] Simplify each exponent by multiplying
[tex]=\frac{8^{(2/3)}p^{(-4)}q^{(2)}}{27^{(-1/3)}p^{(-1)}q^{(-1/3)}}[/tex] Negative exponent rule
[tex]=\frac{8^{(2/3)}q^{(2)}27^{(1/3)}p^{(1)}q^{(1/3)}}{p^{(4)}}[/tex] Combine the like terms in the numerator with the base "q"
[tex]=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)}q^{(1/3)}}{p^{(4)}}[/tex] Rearranged for you to see the like terms
[tex]=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)+(1/3)}}{p^{(4)}}[/tex] Multiplying exponents with same base
[tex]=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(7/3)}}{p^{(4)}}[/tex] 2 + 1/3 = 7/3
[tex]=\frac{\sqrt[3]{8^{2}}\sqrt[3]{27}p\sqrt[3]{q^{7}}}{p^{4}}[/tex] Fractional exponents as radical form
[tex]=\frac{(\sqrt[3]{64})(3)(p)(q^{\frac{7}{3}})}{p^{4}}[/tex] Simplified cubes. Wrote brackets to lessen confusion. Notice the radical of a variable can't be simplified.
[tex]=\frac{(4)(3)(p)(q^{\frac{7}{3}})}{p^{4}}[/tex] Multiply 4 and 3
[tex]=\frac{12pq^{\frac{7}{3}}}{p^{4}}[/tex] Dividing exponents with same base
[tex]=12p^{(1-4)}q^{\frac{7}{3}}[/tex] Subtract the exponent of 'p'
[tex]=12p^{(-3)}q^{\frac{7}{3}}[/tex] Negative exponent rule
[tex]=\frac{12q^{\frac{7}{3}}}{p^{3}}[/tex] Final answer
Here is a version in pen if the steps are hard to see.
round 2.7364 to the nearest thousandths
Answer:
2.736
Step-by-step explanation:
5 it more --> round up
4 or less --> leave it how it is
Answer:
i think its 2.74
Step-by-step explanation:
A wave has a frequency of 6.1 x 1014 Hz and a speed of 3.00 x 108 m/s. Use
the wavelength equation to calculate the wavelength.
O A. 4.9x107m
B. 2.77 x 104 m
O
C. 1.83 x 1023 m
O D. 9.91 x 108 m
SUBMIT
Answer:
(A) [tex]4.9\times 10^{-7}\ m[/tex]
Step-by-step explanation:
Given:
Frequency of the wave (f) = [tex]6.1\times 10^{14}\ Hz[/tex]
Speed of the wave (v) = [tex]3.00\times 10^8\ m/s[/tex]
The wavelength equation of the wave is given as:
[tex]\lambda=\dfrac{v}{f}[/tex]
Here, [tex]\lambda \to wave\ wavelength[/tex]
Now, plug in the given values and simplify.
[tex]\lambda=\frac{3\times 10^8}{6.1\times 10^{14}}\\\\\lambda=4.9\times 10^{-7}\ m[/tex]
Therefore, the wavelength of the wave is option (A) [tex]4.9\times 10^{-7}\ m[/tex]
A moose population is growing exponentially following the pattern in the table shown below. Assuming that the pattern continues, what will be the population of moose after 12 years? Show all your work! Round your answer to the nearest whole number. (5 points)
Time (year) Population
0 40
1 62
2 96
3 149
4 231
Answer:
The population of moose after 12 years will be 7,692
Step-by-step explanation:
we know that
In this problem we have a exponential function of the form
[tex]y=a(b^x)[/tex]
where
y ----> population of moose
x ----> the time in years
a is the y-intercept or initial value
b is the base of the exponential function
we have
[tex]a=40[/tex] ----> the y-intercept is given in the table (value of y when the value of x is equal to zero)
substitute
[tex]y=40(b^x)[/tex]
Find the value of b
For x=1, y=62
substitute in the equation
[tex]62=40(b^1)\\b=62/40\\b=1.55[/tex]
therefore
[tex]y=40(1.55^x)[/tex]
What will be the population of moose after 12 years?
For x=12 years
substitute in the exponential equation
[tex]y=40(1.55^{12})[/tex]
[tex]y=7,692[/tex]
For the function f defined by f(x)=3x2−2x+5 find f(−x),−f(x) , and −f(−x).
Step-by-step explanation:
[tex]f(x)=3x^2-2x+5\\\\f(-x)=\text{substitute (-x) instead x in f(x)}\\\\f(-x)=3(-x)^2-2(-x)+5=3x^2+2x+5\\\\-f(x)=-(3x^2-2x+5)=-3x^2-(-2x)-5=-3x^2+2x-5\\\\-f(-x)=-(3x^2+2x+5)=-3x^2-2x-5[/tex]
The answers are:
[tex]\begin{aligned}& f(-x)=3 x^2+2 x+5 \\& -f(x)=-3 x^2+2 x-5 \\& -f(-x)=-3 x^2-2 x-5\end{aligned}[/tex]
Let's find f(−x), −f(x), and −f(−x) for the given function [tex]f(x)=3 x^2-2 x+5[/tex].
f(−x):
Replace x with −x in the function:
[tex]f(-x)=3(-x)^2-2(-x)+5[/tex]
Simplify this expression:
[tex]f(-x)=3 x^2+2 x+5[/tex]
−f(x):
Multiply the entire function f(x) by −1:
[tex]-f(x)=-\left(3 x^2-2 x+5\right)[/tex]
Distribute the negative sign:
[tex]-f(x)=-3 x^2+2 x-5[/tex]
−f(−x):
Replace x with −x in the function f(x) and then multiply the whole expression by −1:
[tex]-f(-x)=-\left(3(-x)^2-2(-x)+5\right)[/tex]
Simplify this expression:
[tex]-f(-x)=-\left(3 x^2+2 x+5\right)[/tex]
Distribute the negative sign:
[tex]-f(-x)=-3 x^2-2 x-5[/tex]
Question:
For the function f defined by [tex]f(x)=3 x^2-2 x+5[/tex] find f(−x),−f(x) , and −f(−x).
9 cm
3 cm
AB is parallel to DC.
AD = 9 cm, DC = 3 cm. Angle BCD = 35°
Angle ABD = 90°
Calculate the size of angle BAD.
Give your answer correct to one decimal place.
Answer:
∴ ∠BAD = [tex]sin^{-1}[/tex](0.2044) = 11.8°
Step-by-step explanation:
i) AD = 9 cm
ii) DC = 3 cm
iii) ∠BCD = 35°
iv) Since AB is parallel to DC and ∠ABD = 90° then we can conclude that ∠BDC = 90°.
v) [tex]\frac{BD}{DC} = \frac{BD}{3\hspace{0.1cm}cm} = tan(35)[/tex] = 0.6128 ∴ BD = 3 [tex]\times[/tex] 0.6128 = 1.84 cm
vi) ∴ sin(∠ BAD ) = [tex]\frac{BD}{AD}[/tex] ⇒ sin(∠ BAD ) = [tex]\frac{1.84}{9}[/tex] = 0.2044
∴ ∠BAD = [tex]sin^{-1}[/tex](0.2044) = 11.8°
Answer:
Step-by-step explanation: