4. In the triangle ABC, angle A = 90° and
sec B = 2
a.Work out the size of angles B and C.
b.Find tan B.
c. Show that 1 + tan² B = sec² B.
Answers
Step-by-step explanation:
here the answers is it helpful
Related Questions
( this is my summer math homework, please help!)
Find the selling price of each item.
1. Original price of a bunny: $46.00
Text: 2%
2. Original price of a CD: $14.99
Tax: 2%
3. Original price of a CD: $16.50
Tax: 4%
4. Original price of a car: $19,500.00
Tax: 4%
Answers
Using proportions, the selling prices are given as follows:
1. $46.92.
2. $15.29.
3. $17.16.
4. $20,280.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
To find the selling prices, we have to multiply the original prices by either 1.02(2% sales tax) or 1.04(4% sales tax), hence they are given as follows:
1. 46 x 1.02 = $46.92.2. 14.99 x 1.02 = $15.29.3. 16.50 x 1.04 = $17.16.4. 19500 x 1.04 = $20,280.More can be learned about proportions at https://brainly.com/question/24372153
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in the number pattern below, in which row is 2007
1
2. 3.
4. 5. 6.
....
Answers
The number 2007 is in the 63rd row
How to determine the number of row?The pattern is given as
1
2 3
4 5 6
The sum of n natural numbers is:
Sum = 0.5n(n + 1)
Assume n = 62
Sum = 0.5 * 62 * (62 + 1)
Sum = 1953
Assume = 63
Sum = 0.5 * 63 * (63 + 1)
Sum = 2016
2007 is between 1953 and 2016
Since 2016 is greater than 1953, we can conclude that 2007 is in row 63
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Hi I need help with the question in the image. Step by step, thank you!
Answers
The exponential function is [tex]f(x) = 18(12)^{-x-4} + 2[/tex]
How to determine the equation?An exponential function is represented as:
y = b^x
Where b represents the base.
The base is given as:
b = 12
So, we have:
y = (12)^x
It is vertically compressed by a factor of 1/8.
So, we have:
y = 18(12)^x
When reflected across the y-axis, we have:
[tex]y = 18(12)^{-x}[/tex]
The horizontal asymptote is y = 2.
So, we have:
[tex]y = 18(12)^{-x} + 2[/tex]
It passes through the point (-3, 4).
So, we shift the function to the right by 4 units
[tex]y = 18(12)^{-x-4} + 2[/tex]
Express as a function
[tex]f(x) = 18(12)^{-x-4} + 2[/tex]
Hence, the exponential function is [tex]f(x) = 18(12)^{-x-4} + 2[/tex]
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If y is inversely proportional to z^4, when y = 16 and z = 3, then 16 = k/81
true or false
Answers
Answer: 65
Step-by-step explanation:
1 + 64 = 65
Complete the following chart (check picture below)
Answers
The following requires the submission of the details of the parabola related to the equations.
What is a Parabola?A parabola, simply defined, is a plane curve that is created by a point that is moving such that it's distance from a fixed locus is equal to it's distance from a line that is fixed.
What are the details for equation y = -2(x-5)² + 3?Vertex → (5,3)Axis of Symmetry → x = 5Direction of Opening → Opens downMax or Min → (5, 3)Y-intercept → 25/8What are the details for equation y = (x + 2)²Vertex → (-2, 0)Axis of Symmetry → x = -2Direction of Opening → Opens UpMax or Min - (-2, 0)Y-intercept → (0,-47)Learn more about Parabola at;
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Consider [tex]$\triangle ABC$ such that $BC = 3AC$ and $\angle A = \pi/6$[/tex]
What are [tex]\[12 \sin(\angle B), 12 \sin(\angle C)\][/tex] in that order?
Answers
The answer to the question is,
12 sin(∠B) = 2, 12 sin(∠C) = √3+√35
Sin rule is,
sin(A)/BC = sin(B)/AC = sin(C)/AB
sin(B) = (sin(A)×AC)/BC
sin(C) =(sin(B)×AB)/AC
To solve this question we apply sin rule,
Now we take
12 sin(∠B) =12 (sin(∠A)×AC)/BC
12 sin(∠B) =12 (sin(π/6)×(x/3x)) where ∠A =π/6 and AC=x, BC =3x
12 sin(∠B) =12 ((1/2)×(1/3))
12 sin(∠B) =12/6 = 2
12 sin(∠B) = 2
now we find the value of 12 sin(∠C)
12 sin(∠C) = 12(sin B)×(AB/BC)
now put the value of 12 sin(∠B) = 2
12 sin(∠C) = 2×(AB/BC)
12 sin(∠C) = (2/AC)×[AC×(cos(π/6))+BC×(cos B)]
12 sin(∠C) = 2×[cos(π/6)+(BC/AC)×(cos B)]
cos (π/6) = √3/2 and BC/AC =3
then
12 sin(∠C) = 2×[(√3/2)+3×(cos B)]
cos B= √1-sin²B
12 sin(∠C) = 2×[(√3/2)+3×√(1-sin²B)]
12 sin(∠B) = 2
sin B = 1/6
12 sin(∠C) = 2×[(√3/2)+3×√(1-(1/6)²]
12 sin(∠C) = 2×[(√3/2)+3×√1-(1/36)]
12 sin(∠C) = 2×[(√3/2)+3×√(36-1)/36]
12 sin(∠C) = 2×[(√3/2)+3×√(35/36)]
12 sin(∠C) = 2×[(√3/2)+(3/6)×√35]
12 sin(∠C) = 2×[(√3/2)+(1/2)×√35]
12 sin(∠C) = 2×[(1/2)(√3+√35)]
12 sin(∠C) = √3+√35
Hence the answer is,
12 sin(∠B) = 2, 12 sin(∠C) = √3+√35
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The number of cars parked in a car park increases from 50 to 73. what is the percentage increase?
Answers
73 is a 46% increase of 50.
What is percentage ?
A percentage is a relative value that represents the hundredth part of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given amount.
Percentage is defined as a specific part or amount out of a hundred. It is a fraction with the denominator 100 and is denoted by the symbol "percent."
The percent increase formula is as follows:
Percent increase = [(new value - original value)/original value] * 100.
Number of car parking (original value)=50
Number of car parking(new value)=73
The Percentage increase =[(73-50)/50]*100
= [(23)/50]*100
=.46*100
=46%
73 is a 46% increase of 50.
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Hi! Please help me find the slope of the line.
Answers
Answer:
3/2
Step-by-step explanation:
We can use the slope formula to find the slope of the line
m = ( y2-y1)/(x2-x1)
Using the points (0,-4) and (2,-1)
m = ( -1 - -4)/( 2 - 0)
= (-1+4)/ (2 -0)
= 3/2
y-intercept equation= y = 6/4x-4
Geometry)
Given the circle with center O and with m angle ROQ=144^o , find the measure of minor arc PR.
Answer choices…
72^o
216^o
36^o
18^o
(Picture is below) Thank you!
Answers
AMSWER :
Just remove the given angle from 180°
since , a straight line makes a angle of 180°
hence,
ROQ + ROP = 180°
144° + ROP = 180°
ROP = 180° - 144° = 36°
.
.
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Thé nth term rule for a sequence is 4n + 7 what is the 3rd term of this sequence?
Answers
Answer:
a₃ = 19
Step-by-step explanation:
to find the third term substitute n = 3 into the nth term rule
a₃ = 4(3) + 7 = 12 + 7 = 19
Answer:
a₃ = 19
Step-by-step explanation:
the relationship between any two terms of an arithmetic sequence (in our case the relationship between the 3rd term and nth term) gives us this equality :
[tex]a_n - a_3 = 4(n-3)[/tex]
Then
4n + 7 - a₃ = 4n - 12
Then
7 - a₃ = - 12
Then
7 + 12 = a₃
Then
a₃ = 19
What is the best first step in solving the equation 3+√6x=5?
O Subtract 3 from both sides.
O Find the cube of Vex.
O Cube both sides of the equation.
O Subtract 5 from both sides.
Answers
remember PEMDAS
parentheses
Exponents
Multiplication
Division
Addition
Subtraction
A correlation coefficient of 0.08 indicates strong positive correlation. Group startsTrue or False
Answers
Since the correlation coefficient has an absolute value that is less than 0.6, it is not a strong relationship, hence the statement is False.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.In this problem, the correlation coefficient is of 0.08, hence:
The coefficient is positive, hence the is a positive correlation.The coefficient is of 0.08, which is less than 0.6, hence the correlation is not strong.Thus, the given statement is False.
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State whether each of the following is an
open or closed question.
a) Why do you enjoy cooking?
b) What is your favourite fruit?
c) How tall are you?
d) Do you enjoy cooking?
e) What did you do on your holiday?
Answers
B is closed question
C is Closed question
D is open question
E is open question
What is the value of x
Could someone help me out here and show the work for this question? Thank and this is much appreciated
Answers
Answer:
[tex]\boxed{\boxed{\bf x = 7}}[/tex]
Step-by-step explanation:
[tex] \sf \cfrac{4x - 4}{20} = \cfrac{30}{25} [/tex]
[tex]\sf 4x - 4 = \cfrac{(20)(30)}{25} [/tex]
[tex]\sf 4x - 4 = \cfrac{600}{25} [/tex]
[tex]\sf 4x - 4 = 24[/tex]
[tex]\sf 4x = 24 + 4[/tex]
[tex]\sf \cfrac{4x}{4} = \cfrac{28}{4} [/tex]
[tex]\sf x = 7[/tex]
----------------------------------30 =25+ 1/5 of 25
4x-4 =20+1/5 of 20 (=24)
4x-4=24
4x=28
X=7
24/20= 1.2
30/25= 1.2
what is the midpoint of the line segment that joins -3/4 and 2 1/2
Answers
The mid point between the two points is at 13/8 .
What is a Line Segment ?A line segment is a line of fixed measure .
The line segment extends from (-3/4) to [tex]\rm 2 \dfrac{1}{2}[/tex]
i.e the line extends form -3/4 to 5/2
To find the mid point , the total distance needs to be determined
So the distance between the two point is
(5/2) + (3/4) = 13/8
The mid point is at half the distance of this
so it is at 13/8 from both the points
Any point at 13/8 distance from 5/2 towards (-3/4) will be
= (5/2) - (13/8)
= 7/8
So the mid point between the two points is at 13/8 .
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Abigail poured 8 x 10 milliliters of water into a beaker to use for an experiment. How is 8 x 10 written as a whole number?
Answers
Answer:
80?
hshsshjsjsjjsjajjsjsnnsnsnnw
Step-by-step explanation:
hhddussisusuis
Given that is the angle bisector of A, determine the length of x. (SHOW YOUR WORK PLEASE!!!)
Answers
The length of x will be 4 cm if is the angle bisector of A.
What is an angle bisector?A straight line that splits an angle in a triangle into two congruent angles is known as the angle bisector.
Given sides;
AB=12
AE=8
BD=6
DE=x
From the triangle angle bisector theorem;
[tex]\rm \frac{BD}{DE} = \frac{AB}{AE} \\\\ \frac{6}{x} =\frac{12}{8} \\\\ x=4[/tex]
Hence the length of x will be 4 cm.
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Which of the following demonstrates the correct first step in copying an angle?
Create a line that intersects the angle.
Draw a ray with one endpoint.
Create a point outside of the angle.
Swing an arc that intersects the angle's rays.
Answers
"Draw a ray with one endpoint" demonstrates the correct first step in copying an angle. This is further explained below.
What is the angle?In general, the distance (which is sometimes stated as a degree) that occurs between two crossing lines or surfaces at or near the point where they meet. This distance might be positive or negative.
The formation of an angle is caused by the conjunction of two rays at a single point in space. The split or 'opening' that can be seen between these two rays is referred to as a 'angle,' and the symbol denotes this particular angle. The degree is the standard unit of measurement for angles, and its values include things like 60 degrees and 90 degrees, amongst other possible combinations.
In conclusion, "Draw a ray with one terminal" illustrates the correct first step in duplicating an angle. This step shows how to replicate an angle.
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Determine the value of x.
घ
55°
yo
E
(11x + 4)º
Answers
Answer: 6
Step-by-step explanation:
Because [tex]\overline{DE} \cong \overline{EF}[/tex], [tex]y=55[/tex]. So, because angles in a triangle add to 180 degrees, [tex]11x+4=70 \longrightarrow x=6[/tex]
The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair. (1 point)
Function 1
graph of function f of x equals negative x squared plus 8 multiplied by x minus 15
Function 2
f(x) = −x2 + 2x − 3
Function 1 has the larger maximum at (1, 4).
Function 1 has the larger maximum at (4, 1).
Function 2 has the larger maximum at (1, −2).
Function 2 has the larger maximum at (−2, 1).
13.
Answers
Answer: Function 1 has the larger maximum at (4,1).
Step-by-step explanation:
The vertex of f(x) is at [tex]x=-\frac{2}{2(-1)}=1[/tex], and [tex]f(1)=-2[/tex].
For the graph, the maximum is obviously at (4,1).
So, Function 1 has the larger maximum at (4,1).
Complete the sentence below. if (3x2 22x 7) ÷(x 7) = 3x 1, then (x 7)( ) = . the check of the polynomial division problem shows that the product of two polynomials is a polynomial. this supports the fact that the property is satisfied for polynomial multiplication.
Answers
The full set is;
(x + 7) (3x + 1) = 3x² + 22x + 7
This question introduces the concept of polynomial long division.
This is what we are
Given: (3x² + 22x + 7) ÷ (x + 7) = 3x + 1
Now, from the concept of polynomial long division, we can see that:
if, f (x) ÷ g (x) = h (x),
This means that we can write:
f (x) = g (x) × h (x)
Applying the same concept to the question, we can also say:
(3x² + 22x + 7) ÷ (x + 7) = 3x + 1,
Next; (x + 7) (3x + 1) = 3x² + 22x + 7
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Knowing that sin 30° = 1, what is a?
OA. 3.5
OB. 14
OC. 12.12
OD. 7
30⁰
7
a
60⁰
Answers
Answer:
B
Step-by-step explanation:
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{a}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
a = 7 × 2 = 14
Find x
Help me please thank u
Answers
Step-by-step explanation:
ATTACHED IS THE SOLUTION!!!Pedro Fernández es gerente de Avon Chic, Pedro estaba interesado en las tasas de rendimiento de los últimos cinco años de dos diferentes fondos mutuos. Trujix, Inc., mostro un periodo de cinco años, tasas de rendimiento del 12; 10; 3; 9 y 11%, mientras que Fondo Corporation arrojo 13; 12:14:10 y 6%. Un cliente se acercó a Pedro y expreso su interés uno de estos fondos mutuos. ¿cuál debería escoger Pedro para su cliente?
Answers
Pedro Fernández should advice his client to go with the second mutual fund named as Fund Corporation. This is because, it showed an higher average return over the five-year period at an average of 11% beating Trujix Inc by 3%.
What is the calculation that supports the above?To get the better fund, Pedro must calculate a simple average of the interest rates of the various funds over the past 5 year period.
Trujix Inc 5-Year Average
(12 + 10+ 3 +9 + 11)/5
= 45/5
=9%
Fund Corporation 5-Year Average
(13 + 12 +14 + 10+ 6)/5
= 55/5
= 11%
Hence, the better investment is the one by Fund corporation.
Full Question
Pedro Fernández is a manager at Avon Chic, Pedro was interested in the rates of return for the last five years of two different mutual funds. Trujix, Inc., showed a five-year period, rates of return of 12; 10; 3; 9 and 11%, while Fund Corporation showed 13; 12:14:10 and 6%. A client approached Pedro and expressed his interest in one of these mutual funds. Which one should Pedro choose for his client?
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Calculate the angle of depression from the
top of the flag pole to point A.
Give your answer to 1 d.p.
A
31 feet
25 feet
Answers
The angle of depression from the top of the flag pole to point A is 36.2 degrees.
What is the angle of depression?From trigonometric ratio: cos(θ) = Adjacent / Hypotenuse
Given that;
Adjacent = 25ftHypotenuse = 31ftAngle of depression θ = ?cos(θ) = Adjacent / Hypotenuse
Cos(θ) = 25ft/31ft
Cos(θ) = 0.80645
θ = cos⁻¹( 0.80645 )
θ = 36.2°
Therefore, the angle of depression from the top of the flag pole to point A is 36.2 degrees.
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Elvira College has an enrollment of 1,000 students and is located in a small Midwestern town named Johnsonville. Johnsonville has a total population of 2,500 people. The nearest town is 20 miles away. Most of the residents shop locally, but they travel about once a month to the larger city and pick up the large-ticket items. Johnsonville has one fairly good-size supply store named Jameson's Grocery. The only other place in town where you might buy supplies is at the gas station/convenience store located on the edge of town. What competitive situation is Jameson's Grocery experiencing?
Answers
Since there are only two (2) sellers in the town with many buyers, the competitive situation which Jameson's Grocery is experiencing is an oligopoly.
What is an oligopoly?An oligopoly can be defined as a market structure which comprises a small number of business firms (sellers) that are offering identical (similar) products to many buyers, wherein none of the sellers can limit the significant influence of others.
In this scenario, we can infer and logically deduce that the competitive situation which Jameson's Grocery is experiencing is an oligopoly because there are only two (2) sellers in the town with many buyers (1,000 students).
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Rohan's salary 1200$ per month he spends 75% of it how does he spend in dollars?
Answers
Answer:900
Step-by-step explanation:
The coordinate grid shows points A through K. What point is a solution to the system of inequalities? y < −2x + 10 y < 1 over 2x − 2 coordinate grid with plotted ordered pairs, point A at negative 5, 4 point B at 4, 7 point C at negative 2, 7 point D at negative 7, 1 point E at 4, negative 2 point F at 1, negative 6 point G at negative 3, negative 10 point H at negative 4, negative 4 point I at 9, 3 point J at 7, negative 4 and point K at 2, 3 I B A F
Answers
The point that is a solution to the system of inequalities on the coordinates grid is A.
How to illustrate the information?It should be noted that form the information given, the expression is y < −2x + 10. In this case, draw the solid line y = -2x + 10.
Shade the region below the like for x = 5.
y = -2(5) + 10
= -10 + 10
= 0
For x= 0
y = -2(0) + 10
= 0 + 10
= (0, 10)
The diagram is attached.
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Abbot Tools is designing a new toolbox. The length of the toolbox will be three times its width, w, and the length of the diagonal of the top cover will be 30 inches.
Use this information to determine the length, l, of the box. Select the correct answer from the drop-down menu.
Answers
The length and width of the toolbox given the diagonal is 45 inches and 15 inches respectively.
TriangleWidth of the triangle = wLength of the triangle = 3wDiagonal = 30 inchesHypotenuse ² = opposite ² + adjacent ²
30² = w² + (3w²)
30² = 4w²
900 = 4w²
w² = 900/4
= 225
w = √225
w = 15
Therefore,
Width of the triangle = w
= 15 inches
Length of the triangle = 3w
= 3(15)
= 45 inches
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the answer the answer
Answers
Answer:
the answer
Step-by-step explanation:
Answer:
K?
Step-by-step explanation:
The answer of the answer is the answer.
Hope this helped :D