17680 cm2
Using the formula V=W*H*L. The area can be divided by two since it is a right triangle. That gives you the height and length which is 85. 9.5*85*85
A survey asked people of different ages whether they get their news by reading the paper. What is the probability that a person surveyed is under and does not get the news by reading the paper?
Answer: I believe it is A
Step-by-step explanation:
In this table, you have to look at multiple things in the table. So you have to look at where it says Under 40 and that don't read the paper. So according to what I learned with this, you would have to do 36/40 and then get 0.9 which would be in percent form: 90 %.
I would recommend looking at another person's response also, before you submit this question. But hope this helps!
The probability that a person surveyed is under and does not get the news by reading the paper is A; 90%.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
So,
P(a person is under 40 and doesn't get the news by reading the paper)
= 36/40
= 0.90
= 90 %
Hence, option A is correct.
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Brayden is simplifying the expression 4n – (n – 3)2. He begins by distributing the negative to the terms inside the parentheses. What should he have done instead?
ANSWER
Brayden should have expanded the parenthesis first.
EXPLANATION
The expression Brayden is trying to simplify is
[tex]4n - {( n - 2)}^{2} [/tex]
To simplify this expression, the first thing to do is to expand the perfect square to obtain:
[tex]4n - {( n}^{2} - 4n + 4)[/tex]
We can now distribute the negative to the terms in the parenthesis.
[tex]4n - { n}^{2} + 4n - 4[/tex]
Answer:
He should have simplified [tex](n-3)^2[/tex] first then distribute the negative sign.
Step-by-step explanation:
Given that Brayden is simplifying the expression [tex]4n-(n-3)^2[/tex]. He begins by distributing the negative to the terms inside the parentheses. Which is basically the wrong step for the given problem.
Now we need to find about what should he have done instead.
According to order of operations, we should begin with exponent first.
So that means he should have simplified [tex](n-3)^2[/tex] first then distribute the negative sign.
PLEASE HELP! Will mark!!
Answer:
90
Step-by-step explanation:
A right triangle is a triangle that has a right angle. A right angle is an angle that is 90 degrees.
A 90 degree angle. That’s the answer .
Write the summation that represents the series 15 + 18 + 21 + 24. What is the explicit formula for the series shown?
Answer:
Summation: [tex]\sum_{n=1}^4(3n+12)[/tex]
Explicit formula: [tex]a_n=3n+12[/tex]
Step-by-step explanation:
The given series is 15 + 18 + 21 + 24.
The first term of this series is [tex]a_1=15[/tex].
The common difference is [tex]d=18-15=3[/tex]
The explicit formula is given by: [tex]a_n=a_1+d(n-1)[/tex].
We plug in the known values to get:
[tex]a_n=15+3(n-1)[/tex]
[tex]a_n=15+3n-3[/tex]
The explicit formula is [tex]a_n=3n+12[/tex]
The summation that represents the series is: [tex]\sum_{n=1}^4(3n+12)[/tex]
Answer:
3 12
Step-by-step explanation:
If m<13=m<15=m<7, what conclusions can you make about lines a, b, c, and d?
Answer:
option D
Lines a and b are parallel and lines c and d are parallel.
Step-by-step explanation:
Given in the question four lines a , b, c, d.
Prove oneIf two parallel lines (a,b) are cut by a transversal(d), then corresponding angles m<7 and m<15 are congruent.
They are know as corresponding angles.
Hence lines a and b are parallel.
Prove twoIf two parallel lines (c,d) are cut by a transversal(d), then corresponding angles m<13 and m<15 are congruent.
They are know as corresponding angles
Hence lines c and d are parallel
What is the value of x to the nearest tenth?
ANSWER
9.7 units
EXPLANATION
According to the Pythagoras Theorem, the square of the hypotenuse is equal to the sum of the squares of the two shorter legs
[tex] {x}^{2} + {7}^{2} = {12}^{2} [/tex]
This implies that,
[tex] {x}^{2} + 49= 144[/tex]
Group similar terms,
[tex] {x}^{2} = 144 - 49[/tex]
[tex] {x}^{2} = 95[/tex]
[tex]x = \sqrt{95} [/tex]
[tex]x = 9.7 \: units[/tex]
to the nearest tenth.
Jolie bought 3.75 pounds of turkey at the deli. About how many pounds of turkey did Jolie buy?
Answer:
4 pounds
Step-by-step explanation:
"About" means that you are rounding. Most of the time, when you are rounding food, you generally round to the next whole number. In this case, it is 3.75, so you round to 4.
Jolie bought ~4 pounds of turkey.
The reason you round up, is because you can have less than amount, but generally not more. Also, food's weight can change depending on temperature, heat, how it is at the moment (cooked, non-cooked, mashed, processed, unprocessed, etc.).
~
Marie ordered 12 pairs of shoes that were on sale. 7 out of the 12 shoes arrived on time.
What percent of shoes did not arrive on time? Round your answer off to the nearest tenths
place.
Answer:
41.7 % to the nearest tenth.
Step-by-step explanation:
5 out of did not arrive on time.
As a percentage this is 5*100 / 12
= 41.7 % .
How many 4-letter passords can be made using the letters A thought Z if...
a) Repetition of letters is allowed?
b) Repetition of letters is not allowed?
Final answer:
The number of 4-letter passwords using the letters A-Z with repetition allowed is 456,976, while without repetition it's 358,800.
Explanation:
When calculating the number of 4-letter passwords that can be made using the letters A through Z, two scenarios are considered: one where repetition of letters is allowed, and one where it is not allowed.
Scenario a) Repetition of letters is allowed
For each position in the 4-letter password, there are 26 possibilities (since there are 26 letters in the alphabet). Because repetition is permitted, each of the four positions can be filled by any of the 26 letters. Thus, the total number of possible passwords can be found by multiplying the number of choices for each position: 26 x 26 x 26 x 26 = 456,976.
Scenario b) Repetition of letters is not allowed
When repetition of letters is not allowed, the number of choices decreases for each subsequent position in the password. The first position can be filled by any of the 26 letters, the second can be filled by 25 remaining letters (since one letter has been used), the third position by the 24 remaining letters, and the fourth by 23 remaining letters. Thus, the calculation would be: 26 x 25 x 24 x 23 = 358,800.
What angle corresponds to angle AFG?
Look at the image below :)
In case you didn't know, corresponding angles are equal to each other and are on the same side of the traversal
Therefore the answer is angle CGH
Hope this helped!
Answer:
∠CGHStep-by-step explanation:
When two lines are crossed by another line, the angles in matching corners are called corresponding angles.
When the two lines are parallel Corresponding Angles are equal.
∠AFG and ∠CGH are corresponding angles.
The lines AB and CD are parallel, therefore m∠AFG = m∠CGH.
∠CGH and ∠DGH are supplementary angles.
Therefore m∠CGH + m∠DGH = 180°
Substitute m∠DGH = 54°:
m∠CGH + 54° = 180° subtract 54° from both sides
m∠CGH = 126°
Therefore m∠AFG = 126°.
Write an equation of the line that is perpendicular to y = 1 2 x + 3 and passes through the point (10, -5). A) y = -2x + 15 B) y = 2x - 15 C) y = -2x - 5 D) y = - 1 2 x
Answer:
[tex]\large\boxed{A)\ y=-2x+15}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ y=\dfrac{1}{2}x+3\to m_1=\dfrac{1}{2}.\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-2.\\\\\text{The equation of the searched line:}\ y=-2x+b.\\\\\text{The line passes through }(10,\ -5).[/tex]
[tex]\text{Put the coordinates of the point to the equation.}\ x=10,\ y=-5:\\\\-5=-2(10)+b\\\\-5=-20+b\qquad\text{add 20 to both sides}\\\\b=15[/tex]
Answer to this please ?
Answer:
45°
Step-by-step explanation:
Each corner of a square is a right angle. That is 90° which divided by 2 equals 45°
Write a sequence of transformation that maps quadrilateral ABCD onto quadrilateral A. B. C. D IN THE PICTURE
Answer:
The sequence of transformation is reflected across the y-axis and translated 2 units down
Step-by-step explanation:
Lets revise some transformation
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
- If point (x , y) translate h units to the right
∴ Its image is (x + h , y)
- If point (x , y) translate h units to the left
∴ Its image is (x - h , y)
- If point (x , y) translate k units up
∴ Its image is (x , y + k)
- If point (x , y) translate k units down
∴ Its image is (x , y - k)
* Now lets solve the problem
∵ The vertices of figure ABCD are:
A (-1 , 3) , B (1 , 0) , C (2 , 3) , D (1 , 4)
∵ The vertices of figure A"B"C"D" are:
A" (1 , 1) , B" (-1 , -2) , C" (-2 , 1) , D" (-1 , 2)
* Lets compare between ABCD and A"B"C"D"
∵ All x-coordinates has opposite signs
-1 ⇒ 1 , 1 ⇒ -1 , 2 ⇒ -2 , 1 ⇒ -1
∴ The ABCD is reflected across the y-axis
∵ All y-coordinates subtracted by 2
3 ⇒ 1 , 0 ⇒ -2 , 3 ⇒ 1 , 4 ⇒ 2
∴ The ABCD is translated 2 units down
* The sequence of transformation is reflected across the y-axis
and translated 2 units down
Simplify and then evaluate the equation
when x= 3.
-5(x – 5) + 2x = [?]
Answer:
-3x+25
16
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
-5(3 - 5) + 2(3) =
-5(-2) + 2(3)
10 + 6 =
16
29. Find the area of a regular hexagon with apothem of 6 inches.
Answer:
124.7 in²
Step-by-step explanation:
A hexagon consists of six equilateral triangles, each of side a, and we can divide each of them into two right triangles.
So, we can calculate the area of one right triangle and multiply by 12.
The formula for the area of one triangle is
A = ½bh
Step 1. Calculate the length of the side a
Per the Pythagorean Theorem,
[tex]\begin{array}{rcl}h^{2} + \left(\dfrac{a}{2}\right)^{2} & = & a^{2} \\\\6^{2} + \dfrac{a^{2}}{4} & = & a^{2}\\\\36 & = &\dfrac{3a^{2}}{4}\\\\144 & = & 3a^{2}\\\\\end{array}\\\\[/tex]
[tex]\begin{array}{rcl}a^{2} & = & \dfrac{144}{3}\\\\a & = & \dfrac{12}{\sqrt{3}}\\\\a & = & \dfrac{12\sqrt{3}}{3}\\\\a & = & 4\sqrt{3}\\\\\end{array}[/tex]
2.Calculate the area of a small triangle
The base of a small triangle is
b = ½a = ½ × 4√3 = 2√3
The area of one small triangle is
A = ½ bh = ½× 2√3 × 6 = 6√3 in²
3. Calculate the area of the hexagon
A = 12 × 6√3 = 72√3 = 124.7 in²
To find the area of a regular hexagon, use the formula A = (1/2) x Perimeter x Apothem, find the side length with the apothem, calculate the perimeter, and then apply the values to the formula.
Explanation:To find the area of a regular hexagon with an apothem of 6 inches, you can use the formula for the area of a regular polygon, which is A = (1/2) x Perimeter x Apothem. A regular hexagon can be split into six equilateral triangles, which means each side of the hexagon is equal in length. Since the apothem corresponds to the height of each of these triangle components, you can use the fact that in an equilateral triangle, the ratio of the side to the apothem is √3:1 to find the side length. Once the side length (s) is known, you can find the perimeter (P) of the hexagon by multiplying the side length by six. Then, plug the perimeter and the apothem into the formula to calculate the area.
Step 1: Calculate the side length (s).
s = apothem * √3 = 6 inches * √3Step 2: Calculate the Perimeter (P).
P = s * 6Step 3: Calculate the area (A).
A = (1/2) * P * apothemDad is 4 times as old as his son Jim. In 10 years, Dad's age will be 20 years more than twice Jim's age. How old is Jim?
Answer:
Jim is 5, Dad is 20
Step-by-step explanation:
Since dad is 4 times as old as Jim that means 5 x 4=20 and in ten years Jim will be 15 and Dad will be 30 and 15 x 2 is 30.
Hope this helps!
Which expressions are equivalent to 24x+30?
•6(4x+5)
•(12x+15)+(12x+15)
•2(12x+30)
•(10x+5)+(2x+10)+(10x+5)+(2x+10)
•(12x+10)+(12x+10)+(12x+10)
Answer:
the answer to that is the very first response.
Step-by-step explanation:
you see, 6(4x+5) is equal to saying (6•4x) + (6•5). hope this helped!
It’s the first answer choice, the second answer choice, and the forth one.
Please help.
Solve 5x + 7 > 17.
Answer:
[tex]\large\boxed{\{x\ |\ x>2\}}[/tex]
Step-by-step explanation:
[tex]5x+7>17\qquad\text{subtract 7 from both sides}\\\\5x+7-7>17-7\\\\5x>10\qquad\text{divide both sides by 5}\\\\\dfrac{5x}{5}>\dfrac{10}{5}\\\\x>2[/tex]
PLEASE HELP ME PLEASE I BEG YOU
A subscription-based website sends out email reminders to 15,000 customers whose subscriptions are due to be renewed, inviting them to renew at a discount. After the email is sent, the number of customers whose subscriptions are due to be renewed decreases at a rate that compounds hourly, for a per-day decrease of 14.4%. The number of such customers after n days is given by the expression below.
15,000(1-0.144/24)∧24n
What does (1-0.144/24) represent?
A. the change per hour in the number of customers whose subscriptions are due to be renewed
B. the number of customers whose subscriptions are still due to be renewed after one day
C. the initial number of customers whose subscriptions are due to be renewed
D. the decay rate, which reveals the hourly rate of change in the number of customers whose subscriptions are due to be renewed
Answer:
I think it's B.
Step-by-step explanation:
Because the equation is 1 - 0.144/24 should represent the amount of emails to be answered after one day.
Answer:
D. The decay rate, which reveals the hourly rate of change in the number of customers whose subscriptions are due to be renewed.
Step-by-step explanation:
An exponential decay function is,
[tex]f(x)=a(1-r)^x[/tex]
Where, a is initial value,
r is rate of change per period,
x is the number of periods,
(1-r) is decay factor that shows the periodic rate of change in the initial value.
Given expression that represents the number of such customers after n days is,
[tex]15,000(1-\frac{0.144}{24})^{24n}[/tex]
By comparing,
15,000 is the initial number of customers who are due to be renewed,
[tex]\frac{0.144}{24}[/tex] is the change per hour in the number of customers,
24n is the total number of hours,
[tex](1-\frac{0.144}{24})[/tex] is the decay factor or decay rate that reveals the hourly rate of change in the number of customers,
Hence, option 'D' is correct.
How do I describe the shape of a histogram?
Answer:
distribution of numerical data. It is an estimate of the probability distribution of a continuous variable it is different then a bar graph
Step-by-step explanation:
Please need help with this
For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut point with the "y" axis
[tex]m = \frac {y2-y1} {x2-x1}[/tex]
Then, we have the points:
[tex](x1, y1): (- 6, -3)\\(x2, y2) :( 6, -7)[/tex]
Substituting:
[tex]m = \frac {-7 - (- 3)} {6 - (- 6)}\\m = \frac {-7 + 3} {6 + 6}\\m = \frac {-4} {12}\\m = - \frac {1} {3}[/tex]
Thus, the equation is:
[tex]y = - \frac {1} {3} x + b[/tex]
We substitute a point to find the cut point:
[tex]-7 = - \frac {1} {3} (6) + b\\-7 = -2 + b\\b = -7 + 2\\b = -5[/tex]
Finally the equation is:
[tex]y = - \frac {1} {3} x-5[/tex]
ANswer:
[tex]y = - \frac {1} {3} x-5[/tex]
Look at the given triangles.
triangles
The blue triangle is a right triangle. The vertical leg is labeled with the expression 4 x plus 2. The horizontal leg is labeled with the expression 5 x minus 4. The hypotenuse is labeled with the expression 7 x plus 7.
The red triangle is a right triangle. The vertical leg is labeled with the expression x plus 3. The horizontal leg is labeled with the expression x plus 7. The hypotenuse is labeled with the expression 2 x minus 5.
a. Write an expression in simplest form for the perimeter of each triangle.
b. Write another expression in simplest form that shows the difference between the perimeter of the larger triangle and the perimeter of the smaller triangle.
c. Find the perimeter for each triangle when x = 3
Answer:
a. blue 16x + 5
a. red 4x + 5
b. 12x
c. blue 53
c. red 17
Step-by-step explanation:
a.
The perimeter of a polygon is the sum of the lengths of the sides of the polygon.
Blue triangle:
side lengths: 4x + 2, 5x - 4, 7x + 7
perimeter = 4x + 2 + 5x - 4 + 7x + 7 = 16x + 5
Red triangle:
side lengths: x + 3, x + 7, 2x - 5
perimeter = x + 3 + x + 7 + 2x - 5 = 4x + 5
b.
We subtract the perimeter of the red triangle from the perimeter of the blue triangle.
16x + 5 - (4x + 5) =
= 16x + 5 - 4x - 5
= 12x
c.
Blue triangle:
perimeter = 16x + 5 = 16(3) + 5 = 48 + 5 = 53
Red triangle:
perimeter = 4x + 5 = 4(3) + 5 = 12 + 5 = 17
Eli has 8 black pens and 5 in his desk drawer. He also has 3 yellow highlighters, 4 green highlighters, and 5 pink highlighters in his pencil case. If he chooses one pen and one highlighter without looking, what is the probability that he will get a blue pen and he will not get a yellow highlighter?
5/52
6/13
2/13
15/52
Answer:
The answer is 15/52. (Please make me as brainliest (: )
The probability that he will get a blue pen, and he will not get a yellow highlighter is 15/52 option fourth is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
We have:
Eli has 8 black pens and 5 in his desk drawer. He also has 3 yellow highlighters, 4 green highlighters, and 5 pink highlighters in his pencil case.
Total pens = 8+5 = 13
The probability of choosing the blue pen = 5/13
Total highlighter = 3+4+5 = 12
The probability of choosing yellow highlighter = 3/12 = 1/4
The probability of not choosing yellow highlighter = 1 - (1/4) = 3/4
The probability that he will get a blue pen, and he will not get a yellow highlighter:
= (5/13)(3/4)
= 15/52
Thus, the probability that he will get a blue pen, and he will not get a yellow highlighter is 15/52 option fourth is correct.
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Hi, I am taking a test and really need help...... This is worth 19 points please help!!!
(02.07 HC)
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.
A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to w is marked as o, and the other two angles inside the triangle are marked as m and n.
Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle)
Step 2: m∠p − m∠o = 90 degrees (alternate interior angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p
In which step did the student first make a mistake and how can it be corrected?
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)
Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)
Answer:
Step-by-step explanation:
I believe the correct option would be the 1st option because I just took the test and I got this correct! Hope this helps :)
if esther deposited $50 at the end of each month into an account with no interest, how much money would she have saved by the end of 12 months?
Answer:
$600
Step-by-step explanation 50 dollars every month for 12 months you would do 12 *50 and it gives you 600
Answer:
By the end of 12 months, Esther would have $600.
Step-by-step explanation:
As Esther deposits $50 each month in her account, and the account does not produce interests, it is just an addition of money each time she puts $50 in it. That money won't increase until she puts another $50 at the end of the following month. Therefore, by the end of twelve months, she would have $600 (50 x 12 = 600).
The pressure, P, of a gas varies inversely with its volume, V. Pressure is measured in units of Pa. Suppose that a particular amount of gas is initially at pressure of 84 PA at a volume of 51 L. If the volume is expanded to 153 L, what will the new pressure be?
A.) 495 Pa
B.) 153 Pa
C.) 17 Pa
D.) 28 Pa
Answer:
Option D.) 28 Pa
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
In this problem
[tex]P*V=k[/tex]
step 1
Find the value of k
For [tex]P=84\ Pa,V=51\ L[/tex]
substitute and solve for k
[tex]k=84*51=4,284[/tex]
step 2
If the volume is expanded to 153 L, what will the new pressure be?
we have
The equation is equal to
[tex]P*V=4,284[/tex]
For [tex]V=153\ L[/tex]
substitute
[tex]P*153=4,284[/tex]
[tex]P=4,284/153[/tex]
[tex]P=28\ Pa[/tex]
How do you write an equation for the line of best fit?
Answer:
A line of best fit (or "trend" line) is a straight line that best represents the data on a scatter plot.
This line may pass through some of the points, none of the points, or all of the points.
Step-by-step explanation:
1. Prepare a scatter plot of the data on graph paper.
2. Using a strand of spaghetti, position the spaghetti so that the plotted points are as close to the strand as possible.
3. Find two points that you think will be on the "best-fit" line.
4. We are choosing the points (9, 260) and (30, 530).
You may choose different points.
5. Calculate the slope of the line through your two points (rounded to three decimal places).
[tex]\frac{530-260}{30-9} =\frac{270}{21} =12.857[/tex]
6. Write the equation of the line.
[tex]y-y_{1} m(x-x_{1} )\\y-260=12.857(x-9)\\y=12.857(x-9)+260[/tex]
7. This equation can now be used to predict information that was not plotted in the scatter plot.
Question: Predict the total calories based upon 22 grams of fat.
y=12.857(22-9)+260
y=12.857(13)+260
y=427.141
ANS: 427.141 calories
The equation for the line of best fit is written as ŷ = a + bx, where 'a' is the y-intercept and 'b' is the slope determined by minimizing the sum of squared errors (SSE). You substitute various x-values to calculate the resulting y-values, then plot these points to visualize the line of best fit. The correlation coefficient 'r' and coefficient of determination 'r²' are used to measure the goodness of fit.
Explanation:To write an equation for the line of best fit, or the least-squares regression line, you would use the formula ŷ = a + bx, where 'a' is the y-intercept and 'b' is the slope of the line. Generally, 'b' is determined by minimizing the sum of the squared differences between the observed (actual) and predicted values of y, also known as the sum of squared errors (SSE). To do this, you would typically use statistical techniques or software that perform these calculations. Let's consider an example, the equation of the best-fit line is ŷ = -173.51 + 4.83x. Here, -173.51 is the value of 'a', and 4.83 is the value of 'b'.
While working with any specific equation, you can create a table of values by substituting different values for 'x' and calculating the resulting values for 'y'. You then plot these points and draw a line through them to visualize the line of best fit. The correlation coefficient 'r' and coefficient of determination 'r²' are also used to measure the goodness of fit of the regression line.
Remember, while your sample data might give you a best-fit line for your sample, testing the significance of the correlation coefficient is needed to confirm the suitability of this line for the overall population.
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What is the answer I really don’t know what it is
Answer:
Step-by-step explanation:
Use Pythagoras theorem
a = √ 8² + 5² = 9.4
b = √ 17² - 12² = 12.0
Answer: a=9.4 b=12.0
Step-by-step explanation:
Prove that cos 3A = cos (2A+A)
cos 3A = 4 cos³A – 3cosA..... Where from the cos A ....does sin A * cos A give cos A??
Cos 3A = cos (2A +A)
Cos 2A cos A - Sin2A sinA
(2cos²A-1)cosA-(2sinA cos A) sinA
2cos³A - cos A - 2 sin²A cos A
2 cos³A-cos A - 2(1-cos²A)cos A
2 cos³A - cos A - 2cos A + 2 cos³A
Cos3A = 4cos³A-3cos A
Not sure what the question is, but I guess it's to prove that
[tex]\cos3A=4\cos^3A-3\cos A[/tex]
Expand the left side as
[tex]\cos3A=\cos(2A+A)=\cos2A\cos A-\sin2A\sin A[/tex]
and use the double angle identities to write
[tex]\cos3A=(\cos^2A-\sin^2A)\cos A-2\sin^2A\cos A[/tex]
[tex]\cos3A=\cos^3A-3\sin^2A\cos A[/tex]
Recall the Pythagorean identity:
[tex]\cos3A=\cos^3A-3(1-\cos^2A)\cos A[/tex]
[tex]\cos3A=\cos^3A-3\cos A+3\cos^3A[/tex]
[tex]\implies\cos3A=4\cos^3A-3\cos A[/tex]
as required.
Given: m∠ABC = m∠CBD
Prove: BC bisects ∠ABD.
Justify the steps in the flowchart proof
a.
1)definition of congruent
2)definition of bisect
3)given
4)reflexive property
b.
1)definition of congruent
2)definition of bisect
3)given
4)reflexive property
c.
1)definition of congruent
2)definition of bisect
3)given
4)reflexive property
Answer:
(a) Option 3
(b) Option 1
(c) Option 2
Step-by-step explanation:
Given information: m∠ABC = m∠CBD
Prove: BC bisects ∠ABD.
Proof:
[tex]m\angle ABC=m\angle CBD[/tex] (Given)
Definition of congruent: Two angles are congruent if their measures are equal.
[tex]\angle ABC\cong \angle CBD[/tex] (Definition of bisect)
Definition of bisect: If a line divides an angle in two equal parts, then the line is called angle bisector.
BC bisects ∠ABD (Definition of bisect)
Hence proved.
An angle bisector divides the angle into two equal parts. The justification of each step of the flowchart is as follows
Given Definition of congruent Definition of bisectFrom the question, we are given that:
[tex]\angle ABC =\angle CBD[/tex]
This represents the first step of the flowchart.
So, the justification is (3) Given
From the figure, we have that:
[tex]\angle ABC \cong \angle CBD[/tex]
This represents the second step of the flowchart.
[tex]\cong[/tex] mean congruent
So, the justification is (1) Definition of congruent
Lastly:
Line BC bisects [tex]\angle ABC[/tex].
This represents the third step of the flowchart.
So, the justification is (2) Definition of bisect
Because line BC divides [tex]\angle ABC[/tex] into two equal halves.
Read more about bisections at:
https://brainly.com/question/2866798