1. In the figure given below, < ABC and < BDC are right angles; If AB-5cm, AD = 3cm and BD = 4cm (3 points) find BC and DC ?
Answers
In the given figure, the length of BC is 6.66 cm and the length of DC is 5.33 cm
TrigonometryFrom the question, we are to determine the length of BC and DC
Considering the diagram,
First, we will determine the measure of angle A
Using SOH CAH TOA
We can write that
[tex]sin A = \frac{4}{5}[/tex]
sin A = 0.8
∴ A = sin⁻¹(0.8)
A = 53.13°
Now, we will determine the measure of angle C
∠A + ∠ABC + ∠C = 180° (Sum of angles in a triangle)
53.13° + 90° + ∠C = 180°
∠C = 180° - 90° - 53.13°
∠C = 36.87°
Also,
Using SOH CAH TOA
[tex]tan C = \frac{BD}{DC}[/tex]
[tex]tan36.87 ^\circ=\frac{4}{DC}[/tex]
[tex]0.7500 = \frac{4}{DC}[/tex]
[tex]DC = \frac{4}{0.75}[/tex]
DC = 5.33 cm
By the Pythagorean theorem,
/BC/² = /BD/² + /DC/²
/BC/² = 4² + 5.33²
/BC/² = 16 + 28.4089
/BC/² = 44.4089
/BC/ = √44.4089
/BC/ = 6.66 cm
Hence, the length of BC is 6.66 cm and the length of DC is 5.33 cm
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Related Questions
Which operations can be applied to a matrix in the process of Gauss-Jordan elimination?
replacing a row with twice that row
replacing a row with the sum of that row and another row
replacing a row with three times another row
swapping rows
replacing a row with the absolute values of that row
Answers
Operations that can be applied to a matrix in the process of Gauss-Jordan elimination are options 1,2 and 4.
What is gauss Jordan's elimination?Gauss-Jordan Elimination is a matrix-based technique for solving linear equations or determining a matrix's inverse.
When using Gauss Jordan elimination, the following operations may be carried out on a matrix:
1. Replacing a row with twice that row
2. Replacing a row with the sum of that row and another row
3. Swapping row
The optional row(or column) procedures that can be employed are:
1. Alternate any two rows (or columns)
2. Scalar multiples of one row (column) are added or subtracted from another row (column) occurs when a row is substituted with the sum of another row and that row.
3. Multiply any row (or column) fully by a nonzero scalar, as seen below by substituting a row with two rows.
Hence, Gauss-Jordan elimination includes options 1,2, and 4.
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3 lines are shown. A line with points T, R, W intersects with a line with points S, R, V at point R. Another line extends from point R to point U in between angle V R W.
Which pair of angles are vertical angles?
Answers
Answer:
∠TRV and ∠WRS or ∠TRS and ∠WRV
Step-by-step explanation:
Vertical angles are angles that share a vertex and have sides that are opposite rays. That is, the opposites of the rays that form one of the angles are the rays that form the other angle.
__
Where lines cross, two pairs of vertical angles are formed. In your diagram, those pairs are ...
∠TRV and ∠WRS . . . . one vertical angle pair
∠TRS and ∠WRV . . . . another vertical angle pair
_____
Additional comment
In this diagram, the ray RU is of no consequence with respect to any vertical angles. It can be ignored.
The vertical angles will each have one red ray and one blue ray as sides. These rays have end point R. No sides are shared.
What is the equation for this graph?
Answers
Answer:
hmm try multiplying every number at the top and then put them all together
then divide the answer u got and u have ur answer :)
Step-by-step explanation:
what would i put in, in the blanks? please help, i don’t get this
Answers
Answer:
Parent function
[tex]f(x)=\log_2(x)[/tex]
Since we cannot take logs of zero or negative numbers, the domain is [tex](0, \infty)[/tex] and there is a vertical asymptote at [tex]x=0[/tex].
There are no horizontal asymptotes and the range is [tex](- \infty,\infty)[/tex].
The end behaviors of the parent function are:
[tex]\textsf{As } x \rightarrow 0^+, f(x) \rightarrow - \infty[/tex]
[tex]\textsf{As } x \rightarrow \infty, f(x) \rightarrow \infty[/tex]
To determine the attributes of the given function, compare the given function with the parent function.
Given function
[tex]f(x)=- \log_2(x)+5[/tex]
The given function is reflected in the x-axis. Therefore, the end behaviors are a reflection of those of the parent function:
[tex]\textsf{As } x \rightarrow 0^+, f(x) \rightarrow \infty[/tex]
[tex]\textsf{As } x \rightarrow \infty, f(x) \rightarrow - \infty[/tex]
As the given function is translated vertically (5 units up) only, the domain, range and asymptote will not change, since the function has not been translated horizontally.
[tex]\textsf{Domain}: \quad (0, \infty)[/tex]
[tex]\textsf{Range}: \quad (- \infty, \infty)[/tex]
[tex]\textsf{Asymptote}: \quad x=0[/tex]
Conclusion
The function f(x) is a [tex]\boxed{\sf logarithmic}}[/tex] function with a [tex]\boxed{\sf vertical}}[/tex] asymptote of [tex]\boxed{x = 0}[/tex].
The range of the function is [tex]\boxed{(- \infty, \infty)}[/tex], and it is [tex]\boxed{\sf decreasing}[/tex] on its domain of [tex]\boxed{(0, \infty)}[/tex].
The end behavior on the LEFT side is as [tex]\boxed{x \rightarrow 0^+}[/tex], [tex]\boxed{f(x) \rightarrow \infty}[/tex], and the end behavior of the RIGHT side is [tex]\boxed{x \rightarrow \infty}[/tex], [tex]\boxed{f(x) \rightarrow -\infty}[/tex].
Assuming that there are no hidden cubes, what is the front orthographic view of the diagram?
Answers
Answer:
the visible number of cubes is 7
Step-by-step explanation:
Assuming that there are no hidden cubes, the # of visible cubes is 7
If $3700 is invested at a rate of 2.4% that is compounded annually, how much will it be worth after 4 years?
Answers
The amount the money will be worth in 4 years is $4072.41
Compound interestThe formula for calculating the compound interest is expressed as;
A = P(1+r/n)^nt
Given the following
P = $3700
rate r = 2.4% = 0.024
n =12
t = 4 years
Substitute
A = 3700(1+0.024/12)^12(4)
A = 3700(10.024/12)^48
A = 3700(1.10065)
A= 4072.41
Hence the amount the money will be worth in 4 years is $4072.41
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please help i’ll give brainliest
Answers
The missing length in triangle A given the similarity between the two triangles is 18.67
Solving triangles using ratioTriangle A is similar to triangle B
Triangle A:
Side 1 = (x + 2)Side 2 = 14Triangle B:
Side 1 = 8Side 2 = 6Ratio of side 1 to side 2 of the triangles respectively
(x + 2) : 8 = 14 : 6
(x + 2) / 8 = 14/6
cross product(x + 2) × 6 = 8 × 14
6x + 12 = 112
6x = 112 - 12
6x = 100
x = 100/6
x = 16.67
Therefore, Triangle A:
Side 1 = (x + 2)
= 16.67 + 2
= 18.67
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What is the slope of the line graphed below?
(-2,2)
(3, 1)
Answers
Answer:
-1/5
Step-by-step explanation:
To find the slope, the formula is y2-y1/x2-x1
1-2/3-(-2) = -1/5
Answer:
‐1/5Step-by-step explanation:
hope this helps!!!!
Find the sum of the first 7 terms of the following series, to the nearest integer. 150,60,24...
Answers
Answer:
250
Step-by-step explanation:
The sum of the terms of a geometric series is given by the formula ...
Sn = a1×(1 -r^n)/(1 -r)
sum of n terms for first term a1 and common ratio r.
__
series sumThe given series has first term a1 = 150, and common ratio r = 60/150 = 2/5. Putting these values into the formula gives a sum of 7 terms that is ...
S7 = 150×(1 -(2/5)^7)/(1 -2/5) = 150((77997/78125)/(3/5))
S7 = 150×(25999/15625) = 249.5904
Rounded to the nearest integer, the sum of the first 7 terms is 250.
Which linear inequality is graphed in the figure
Answers
Answer:
A) y < 1/3x - 2
Step-by-step explanation:
a store owner wishes to make a new tea with a unique flavor by mixing black tea and oolong tea. if he has 35 pounds of oolong tea that sells for 2.40 per pound, how much black tea worth 1.80 per pound must he mix with it so that he can sell the final mixture for 2.10 per pound
Answers
35 pounds of black tea is needed to be mixed to get the final mixture for 2.10 per pound
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of black tea worth 1.80 per pound to be mixed to get the final mixture for 2.10 per pound, hence:
2.4(35) + 1.8(x) = 2.1(x + 35)
x = 35 pounds
35 pounds of black tea is needed to be mixed to get the final mixture for 2.10 per pound
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(2.01)A polygon is shown on the graph:
If the polygon is translated 3 units down and 4 units left, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates.
Answers
Answer:
see picture for the coordinates
A’ = -2,-4
B’ = -3,-7
C’ = -1,-8
D’ = 1,-6
Step-by-step explanation:
add the translation coordinates to the original to get new coordinates
Answer:
Given translation:
4 units left3 units downTherefore,
To translate a point 4 units left, subtract 4 units from the x-value. To translate a point 3 units down, subtract 3 units from the y-value.⇒ (x, y) → (x - 4, y - 3)
Calculations
A (2, -1) ⇒ (2 - 4, -1 - 3) = A' (-2, -4)
B (1, -4) ⇒ (1 - 4, -4 - 3) = B' (-3, -7)
C (3, -5) ⇒ (3 - 4, -5 - 3) = C' (-1, -8)
D (5, -3) ⇒ (5 - 4, -3 - 3) = D' (1, -6)
Therefore, the new coordinates using prime notation are:
A' (-2, -4)B' (-3, -7)C' (-1, -8)D' (1, -6)Multi choice choose the rule for the table year 8 level maths
Answers
Answer:
second option, x + 2y = 3
Step-by-step explanation:
The slope intercept form is y = mx + b
y = y coordinate
m = slope
x = x coordinate
b = y intercept
The y - intercept is when x = 0
In the table its shown that (0, 3), y = 3 so b = 3
The slope (gradient) is a number that describes both the direction and the steepness of the line.
slope = rise / run = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
(x_1, y_1) = coordinates of first point in the line
(x_2, y_2) = coordinates of second point in the line
x is increasing by 1 (run)
y is decreasing by 2 (rise)
rise / run = -2 / 1 = -2
so the slope is -2
our slope intercept equation is, y = -2x + 3
Choice:
Some choice are in standard form so we need to convert to slope intercept
y = x + 3 is already in the correct form2x + y = 3 becomes y = -2x + 3subtract 2x from both sides, 2x - 2x + y = 3 - 2x
x + 2y = 3 becomes y = -1/2x - 3/2subtract x from both sides, x - x + 2y = 3 - x becomes 2y = 3 - x
divided both sides by 2, 2y / 2 = (3 - x) / 2
x - y = 0 becomes y = xsubtract x from both sides, x - x - y = 0 - x than switch signs
which option matches?!
THE SECOND ONE
30 points!!!
The dot plot below shows the hourly rate of some babysitters in a city:
A number line is shown from 1 dollar to 7 dollars in increments of 1 dollar for each tick mark. The horizontal axis label is Dollar per hour. There are 2 dots above 4 dollars, 3 dots above 5 dollars, 3 dots above 6 dollars, and 2 dots above 7 dollars. The title of the line plot is Babysitting Rates.
Which statement best describes the shape of the data?
A. It is symmetric and has no gaps.
B. It is not symmetric and has a peak at $7.00.
C. It is a cluster from $1.00 to $7.00 and has no gaps.
D. It is a cluster from $1.00 to $7.00 and has a peak at $6.00.
Answers
From the given choices, the answer is option A: It is symmetric and has no gaps.
How can we describe a number line?A number line is shown from 1 dollar to 7 dollars in increments of 1 dollar for each tick mark.
The horizontal axis label is Dollar per hour.
There are 2 dots above 4 dollars, 3 dots above 5 dollars, 3 dots above 6 dollars, and 2 dots above 7 dollars.
The title of the line plot is Babysitting Rates.
A dot plot is the same as a histogram but it uses dots instead of bars.
The dot plot as described by the problem is shown in the picture.
A bell shape is drawn for symmetrical data.
From the given choices, the answer is option A: It is symmetric and has no gaps.
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A ladder is resting against a wall. The top of the ladder touches the wall at a height of 9 ft. Find the length of the ladder if the length is 3 ft more than its distance from the wall.
Answers
Answer:15
Step-by-step explanation:
A ladder is resting against a wall.The top of the ladder touches the wall at a height of 9 feet.Find the length of the ladder if the length is 3 feet more than its distance from the wall.
Let the distance of the ladder from the wall be x
The length of the ladder = x+3
The ladder touches the wall at a vertical height of 9 feet.
(x+3)^2 = x^2 + 9^2 ( using the pythagoras theorem
x^2 + 6x+ 9 = x^2 + 81
x^2- x^2 +6x = 81-9
6x= 72
x= 12
Therefore the length of the ladder will be x+3 = 12 + 3 =15 Answer.
How many and what type of solutions does 5x^2-2x+6 have?
1 rational solution
2 rational solutions
2 irrational solutions
2 nonreal solution
Answers
Answer:
D) 2 nonreal solutionStep-by-step explanation:
GivenQuadratic trinomial
5x² - 2x + 6In order to determine what kind of roots it has, we need to find the value of the discriminant:
[tex]D= b^2-4ac[/tex][tex]D = (-2)^2-4*5*6 =4-120 =-116[/tex]Since the discriminant is negative, its square root is an imaginary number, hence there is no real solution.
Correct answer choice is D.
What is the domain of the function graphed below?
OA.{x\x = −2,1}
OB. (x | x-2,-1, 1)
OC. {x|x-1,}
OD. {x|x-1, 1}
Answers
From the graph, the domain of the function will be {x| x = −2,1}. Then the correct option is D.
What is an asymptote?An asymptote is a line that constantly reaches a given curve but does not touch at an infinite distance.
From the graph, the domain of the function will be
The function is not defined for x = 2 and x = -1.
Then the domain will be
{x| x = −2,1}
Then the correct option is D.
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Taub went shopping for a new video game because of a sale. The price on the tag was $26, but Taub paid $23.40 before tax. Find the percent discount.
Answers
Answer:
10%
Step-by-step explanation:
(26-23.40)/26x100%
Answer:
10%
Step-by-step explanation:
what is 250/100 as a whole number?
Answers
Answer:
Unless im being completely braindead right now there isn't a whole number that works with this. When simplified its 5/2 or 2.5 but because it isn't an actual whole number (like 2, 4 and 6) they don't count.
Answer:
between two whole numbers 2 and 3 or just 3.
Step-by-step explanation:
The answer to 250/100 would be 2.5 but that is a decimal and not a whole number. You couod round 2.5 to 3 to make it a whole nunber or you say that it is in between two whole nunbers which are 2 and 3 if you are allowed to. (since 2.5 alone is not a whole number)
There are 8 metal boxes of gold. Each box holds 625 pounds of gold. How many pounds of gold are in the 8 boxes?
pounds of gold
You may use the scratchpad or scratch paper to show your work.
Answers
Answer:
5000 lbs
Step-by-step explanation:
if there ae 8 boxes and each one has the weight of 625 you will need to ultiply 8 by 625 and that will be 5000 pounds
The graph of the fourth-degree polynomial function f (x) is shown in the coordinate plane below. Based on the graph, which of the following are linear factors of f (x). Select all that apply. A. (x - 2) B. (x - 3) C. (x + 2) D. (x - 5) E. (x + 1)
Answers
The linear factors of the function are the x-intercepts which are (x + 5), (x + 2), (x - 1) and (x - 6)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the graph of the function. The linear factors of the function are the x-intercepts which are (x + 5), (x + 2), (x - 1) and (x - 6)
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work out 4x10^8 x 5 x 10^-6 give your answer in standard form
Answers
Answer:
2 × 10³
Step-by-step explanation:
a number expressed in standard form is
a × [tex]10^{n}[/tex]
where 1 ≤ a < 10 and n is an integer
4 ×[tex]10^{8}[/tex] × 5 × [tex]10^{-6}[/tex]
= 4 × 5 × [tex]10^{8}[/tex] × [tex]10^{-6}[/tex]
= 20 × [tex]10^{(8-6)}[/tex]
= 20 × 10²
= 2 × [tex]10^{1}[/tex] × [tex]10^{2}[/tex]
= 2 × [tex]10^{(1+2)}[/tex]
= 2 × 10³
Answer:
[tex]2.0 \times {10}^{3} [/tex]
is correct ans
100 POINTS AND BRAINLIST
Answers
The answer could be c
Because the title of the table says the dollar sales and how much it's increasing so my answer is c
Hope I helped!
TheOneAndOnlyLara~
Answer:
C.
Step-by-step explanation:
Hope it helped!
I need help asap please? and this is for the math question? what is the missing angle?
Answers
Answer:
the missing angle or the exterior angle is 120
Step-by-step explanation:
180-60=120
Answer:
90 degrees.
Step-by-step explanation:
The square symbol at the unlabeled angle means 90 degrees. Also, a triangle's interior angles equal 180. We already have 30 and 60, so 30+60=90. Now, subtract this from 180. 180-90=90. The answer is 90 degrees.
Hope this helps!
help with addition for child 324+423
Answers
Answer:
747
Step-by-step explanation:
Have a great day!!
Step-by-step explanation:
the answer for this is 747
A. Median
B. Perpendicular bisector
C. Angle bisector
D.altitude
Answers
Answer:
I belive c angle bisector
Find equivalent expressions of 3+2x−9−4x+11+5x−x.
Answers
The equivalent expression of the given expressions is 2x + 5.
What are Expressions?Expressions are statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The given expression is,
3 + 2x - 9 - 4x + 11 + 5x - x
There are like terms in the expression, which can be operated together.
Write terms with variables together and the constants together.
3 + 2x - 9 - 4x + 11 + 5x - x
= (2x - 4x + 5x - x) + (3 - 9 + 11)
= 2x + 5
Hence the given expression can be simplified to 2x + 5.
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Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a
viable solution if x represents the number of days that a library book is late and y represents the total fee?
Answers
Answer:
y=0.30x
Step-by-step explanation:
because the amount of money (the fee) will keep increasing with the multiplication of the amount of days
Grayson is preheating his oven before using it to bake. The initial temperature of the oven is 65° and the temperature will increase at a rate of 15° per minute after being turned on. What is the temperature of the oven 6 minutes after being turned on? What is the temperature of the oven tt minutes after being turned on?
Answers
Answer:
155 Degrees
Step-by-step :
(Time x Rate of Temp) + Initial Temp = Final Temperature
Ex. (6 * 15) + 65 = 155 Degrees
Answer:
The temperature of the oven 6 minutes after being turned on is 155°
The temperature of the oven t minutes after being turned on is 15t + 65
Step-by-step explanation:
y=mx + b
y = y coordinate
m = slope
x = x coordinate
b = y intercept
The y intercept is when x = 0, so the initial temperature
b = 65°
The slope is increase at a rate of per minute after being turned on.
m = 15°
The y coordinate will represent the temperature of the oven after a certain amount of minutes after being turned on
y
The x coordinate will represent the amount of minutes after the oven being turn on
x = t
combine:
What is the temperature of the oven tt minutes after being turned on?
y = 15t + 65
What is the temperature of the oven 6 minutes after being turned on?
t = 6 minutes
y = 15t + 65
y = 15(6) + 65
y = 90 + 65
y = 155
AND WELCOME TO BRAINLY!
Twenty Three more than a number is 68 . what is the number
Answers
Answer:
the answer is 45.
Step-by-step explanation:
45 + 23 = 68.