O is the centre of the circle, EF is a tangent, angle BCE = 28°, angle ACD = 31°
Line AB = line AC
Write down the size of
a) angle BAC
b) angle ABC
c) angle ADC
d) angle COB
Answers
Answer
a. 28˚
b. 76˚
c. 104˚
d. 56˚
Step-by-step explanation
Given,
∠BCE=28° ∠ACD=31° & line AB=AC .
According To the Question,
a. the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.(Alternate Segment Theorem) Thus, ∠BAC=28°b. We Know The Sum Of All Angles in a triangle is 180˚, 180°-∠CAB(28°)=152° and ΔABC is an isosceles triangle, So 152°/2=76˚
thus , ∠ABC=76° .
c. We know the Sum of all angles in a triangle is 180° and opposite angles in a cyclic quadrilateral(ABCD) add up to 180˚,Thus, ∠ACD + ∠ACB = 31° + 76° ⇔ 107°
Now, ∠DCB + ∠DAB = 180°(Cyclic Quadrilateral opposite angle)
∠DAB = 180° - 107° ⇔ 73°
& We Know, ∠DAC+∠CAB=∠DAB ⇔ ∠DAC = 73° - 28° ⇔ 45°
Now, In Triangle ADC Sum of angles in a triangle is 180°
∠ADC = 180° - (31° + 45°) ⇔ 104˚
d. ∠COB = 28°×2 ⇔ 56˚ , because With the Same Arc(CB) The Angle at circumference are half of the angle at the centre
For Diagram, Please Find in Attachment
Related Questions
Over what interval is the function in this graph constant?
Answers
Answer:
[tex]\text{A. }1\leq x \leq6[/tex]
Step-by-step explanation:
A constant intervals occurs when the function is neither increasing or decreasing. In the graph, we see this occurs from [tex]x=1[/tex] to [tex]x=6[/tex]. Therefore, the interval in which the graph is constant is [tex]\boxed{\text{A. }1\leq x \leq6}[/tex]
the equation of a straight line is given as 3x+y=7. the slope of this line is
Answers
Answer:
The slope is -3 and the y intercept is 7
Step-by-step explanation:
3x+y = 7
We can write the equation in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = -3x+7
The slope is -3 and the y intercept is 7
Need help quick easy problem to solve pls help!
Answers
Answer:
C
Step-by-step explanation:
12b + 30f = 240
7b + 10f = 125
Multiply the second equation by -3
12b + 30f = 240
-21b -30f = -375
Add up the two equations
-9b = -135
b = $15
Substitute this value in one of the two equations
12 * 15 + 30f = 240
180 + 30f = 240
30 f = 60
f = $2
please help me which of the following is the quotient of the rational expressions shown below
Answers
Answer is C
✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔
PQ and QR are 2 sides of a regular 12-sided polygon. PR is a diagonal of the polygon. Work out the size of angle PRQ. You must show your working.
Answers
Answer:
15°
Step-by-step explanation:
A regular polygon is a polygon in which all the sides and angles of the polygon are equal to each other.
A regular 12-sided polygon is a polygon with 12 equal sides and angles.
The sum of interior angles of a polygon is given as:
sum = (2n - 4)90; where n is the number of sides of the polygon
For a 12 sided polygon:
Sum of interior angles = (2 * 12 - 4)90 = (24 - 4)90 = 20 * 90 = 1800°
Therefore since all the angles are equal, each angle = 1800° / 12 = 150°
Therefore in the question, ∠PQR = 150° (angle of a 12 sided polygon), ∠PRQ = ∠QPR = x
Therefore in triangle PQR:
∠PQR + ∠PRQ + ∠QPR = 180°
150 + x + x = 180
150 + 2x = 180
2x = 30
x = 15°
∠PRQ = 15°
What is the equation of the following line written in slope-intercept form?
Answers
Answer:
C
Step-by-step explanation:
y=-7x-11
Need help of this!! Domain and range!!
Answers
Answer:
its the first one
Step-by-step explanation:
Solve the problem.
An initial investment of $930 is appreciated for 19 years in an account that earns
6% interest, compounded continuously. Find the amount of money in the
account at the end of the period.
$1275.35
$22,067.28
$12,424,545.93
$2907.89
Answers
Answer:
$2907.89
General Formulas and Concepts:
Symbols
e (Euler's number) ≈ 2.71828Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra i
Compounded Continuously Formula: [tex]\displaystyle A = Pe^{rt}[/tex]
P is principle amountr is ratet is timeStep-by-step explanation:
Step 1: Define
Identify variables
P = 930
t = 19
r = 6% = 0.06
Step 2: Find Interest
Substitute in variables [Compounded Continuously Formula]: [tex]\displaystyle A = 930e^{19 \cdot 0.06}[/tex][Exponents] Multiply: [tex]\displaystyle A = 930e^{1.14}[/tex]Evaluate exponents: [tex]\displaystyle A = 930(3.12677)[/tex]Multiply: [tex]\displaystyle A = 2907.89[/tex]The ratio of goldfish to gallons of water is 7 to 2. How many goldfish can you get if you have 16 gallons of water? __________ and How many gallons of water do you need to keep 28 fish? ____________.
Answers
Answer: 56, 8
Step-by-step explanation:
Given
The ratio of goldfish to gallons of water is 7:2
If there is 16 gallons of water. For x goldfish, We can write
[tex]\Rightarrow \dfrac{7}{2}=\dfrac{x}{16}\\\\\Rightarrow x=7\times8\\\Rightarrow x=56[/tex]
If there are 28 fish, for y gallons of water we can write
[tex]\Rightarrow \dfrac{7}{2}=\dfrac{28}{y}\\\\\Rightarrow y=2\times 4\\\Rightarrow y=8\ \text{gallons}[/tex]
if (x+y , 2x-3) = (5,3) find the value of x and y. plz answer ASAP!!!
Answers
Answer:
x=3
y=0
Step-by-step explanation:
2x-3=3
2x=6
x=3
x+y=3
3+y=3
y=0
Answer:
ans: x= 3 and y= 2
Step-by-step explanation:
equating corresponding order pair,
x + y = 5 and
2x-3 = 3
so x=6/2 I.e
x= 3
putting x in
x + y = 5
y = 5- 3
y = 2
choose the equation of the line that is parrarel to the y axis
Answers
If the grain pile has a diameter of 60 feet and a height of 13 feet, what is the volume of the grain pile?
Answers
Answer:
36,738
Step-by-step explanation:
The first step is to calculate the radius
= 60/2
= 30
Therefore the volume can be calculated as follows
= πr^2h
= 3.142 × 30^2 × 13
= 3.14× 900×13
= 36,738 cubit feet
Hence the volume of the grain pile is 36,738 cubic feet
−2(4y+1)=−8y−2??
Does it have one solution, no solution, or infinite?
Answers
Step-by-step explanation:
−2(4y+1)=−8y−2
4y+1=4y+1
infinite solutions
Answer:
Infinitely many solutions
Step-by-step explanation:
-2(4y+1)=−8y−2
=> -2(4y)-2(1)= -8y-2
=> -8y-2=-8y-2
=> Infinitely many solutions as x from both sides get cancelled
PLZZ HELPPP
Which matrix equation can be used to solve the system?
x+y=21
5x+4y=20
Answers
Answer:
[tex]X= \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \left[\begin{array}{ccc}21\\20\\\end{array}\right] \\[/tex]
Step-by-step explanation:
Given the simultaneous equation
x+y=21
5x+4y=20
To write in matrix form, it must be in the form AX= b
X = A⁻¹b
A⁻¹ is the inverse of matrix A
A is a 2by2 matrix
X is the variables
b is a column matrix
The expression will therefore be written as;
[tex]A=\left[\begin{array}{ccc}1&1\\5&4\\\end{array}\right] \\\\|A| = 1(4)- 5(1)\\|A| = 4-5\\|A| = -1\\A^{-1} = -\left[\begin{array}{ccc}4&-1\\-5&1\\\end{array}\right] \\\\A^{-1} = \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \\[/tex]
Hence the required product matrix that represent X is;
[tex]X= \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \left[\begin{array}{ccc}21\\20\\\end{array}\right] \\[/tex]
help pleaseee and thank you
Answers
Answer:
-2x-11=0
1) Add 11 to both sides
Dividde both sides by - 2
X= _11/2
Drcimal form: - 5.5
You get 11 points if you answer a.s.a.p
Answers
Answer:
Have you got it now?
Step-by-step explanation:
PLEAAASE HELP!!! WILL GIVE BRAINLIEST!!!!!!
Answers
Answer:
Compared to a standard cosine function, the graph has a phase shift of [tex]5\pi/6[/tex] to the right, and compared to a sine function it has a phase of shift of [tex]\pi/6[/tex] to the right.
Step-by-step explanation:
The standard cosine function [tex]y=\cos x[/tex] has its maximum (vertex of the interval concave down) intersect with the y-axis. In this case, that part is shifted [tex]\frac{5\pi}{6}[/tex] to the right.
The standard sine function [tex]y=\sin x[/tex] has the point where it crosses its midline intersect with the x-axis. In this case, that part is shifted [tex]\frac{\pi}{6}[/tex] to the right.
Determine where the PHD Mathematicians live.
The Mathematicians who live within the enclosure made by
the parabola
y = x2 +2x-3
and the line
y = -x + 1
have all earned their PHD in Mathematics. The following mathematicians live at the following coordinates:
Annie Easley:
Benjamin Banneker:
Fan Chung
Joan Clarke
A (-3,5)
B (6, 5)
C (5,5)
D(-1,-3)
Sophie Germain
Elbert Frank Fox:
Emmy Noether
Jama Musse Jama:
E (3,6) David Blackwell:
F (-2,-2) Mary Somerville:
G (-1,-4) Grace Hopper:
H(-6,8) Nalini Joshi
I (-1, -1)
J (3,-2)
K(-1,-2)
L (0, -1)
a) Plot the points given above on the grid. *Label each point with the given letter
b) Graph the line
y = -x + 1
Slope=__: y-intercept=
c) Factor and then find the x-intercepts.
y=x2+2x-3
Answers
Answer:
the answer to A,B,C
Step-by-step explanation:
all the points are on the graph
all answers
b) slope -1
intercept 1
c)(x+3)(x-1)
intercepts (-3,0),(1,0)
vertex (-1,-4)
If a + b = 5 and a - b = 9, what is a^2+b^2?
Answers
Answer:
=53
Step-by-step explanation:
a=5-b &. a=9+b
combine
5-b=9+b
-4=2b
b= -2
thus, a=7
(-2)^2 + (7)^2
4+49
=53
Answer : 3²+2²=13.
Step-by-step:
Ok …according to the question
a+b=5–(1)considering it as eqn 1
a-b=9—(2)considering it as eqn 2
Substracting eqn 2 from eqn 1 we get
2b=4
b=4/2
b=2
Now substituting this value of b in eqn 1 we get
a+2=5
So a=5–2
a=3
So a=3and b=2
What will be the remainder when 6x + 4x4 - 27x³
- 7x² + 27x + 3/2 is divided by (2x² – 3)?
Answers
Answer: The remainder is 0.
Step-by-step explanation:
We are given:
Dividend polynomial = [tex]6x^5+4x^4-27x^3-7x^2+27x+\frac{3}{2}[/tex]
Divisor polynomial = [tex]2x^2-3[/tex]
We divide the dividend by the divisor using the long division method.
In this method, the final answer written in the bottom is considered as remainder and the uppermost polynomial is considered as the quotient.
The long division of the two polynomials is attached in the image below.
From the image, we can say that the remainder of the two is 0
i have no idea what to do can someone pls help me quick
Answers
**PLEASE HELP**The frequency table below represents the 30 best battling averages for a semi pro baseball league. Which ranges of battling averages were least common among the players
Answers
The lower the frequency the least common the average.
There are two frequencies that are 1, which would be the least common.
The answer is C. 0.320-0.329 and 0.360 -0.369
Answer:
option C
Step-by-step explanation:
option c is contains the two batting averages which have a frequency of 1, this means that they both only occurred once which is the least amount of times any of the batting averages has occurred.
Find the lengths of the missing pieces of the triangle. (Picture attached). Thank you!!
Answers
Step-by-step explanation:
my answer is in the image above
Answer:
I've attached the Answer here
Which points are solutions to the system of inequalities shown below?
Check all that apply.
y>x
y> 2
X>4
A. (6,4)
B. (4,2)
C. (8,1)
D. (9,-2)
E. (9, 10)
F. (5,6)
Answers
Answer:
F
Step-by-step explanation:
y should be greater than x and greater than 2.
x should be greater than 4 but less than y
There are 1,281 souvenir paperweights that need to be packed in boxes. Each box will hold 15
paperweights. How many boxes will be needed?
Answers
Answer:
86 boxes
Step-by-step explanation:
Devon needs to come up with ordered pairs that make up the line for this linear equation 3y - 3x =
12? Which ones would work?
Answers
Answer:
Step-by-step explanation:
The given linear equation can be reduced, ending up as
y - x = 4 or y = x + 4
If we choose our own x values, we can calculate the corresponding y value in each case:
x y = x + 4 ordered pairs
0 4 (0, 4)
1 5 (1, 5)
3 7 (3, 7)
-2 2 (-2, 2)
In a standard deck of cards, there are 26 different red cards. How many possible combinations of 5 red cards
are there from those 26 cards?
Answers
Step-by-step explanation:
It doesn't matter what order they are drawn in, so youi have a combination problem
26C5
My calculator gives the answer directly,
It is 65780
THIS IS TO HELP OTHER PEOPLE IF THEY FIND THIS QUESTION THIS QUESTION IS ALREADY CORRECT
What is the value of this expression?
[(3+5)⋅2−5]⋅3
Enter your answer in the box.
Answers
Based on these results, express the probability that the next customer will pay with something other than a credit card as a fraction in simplest form.
Answers
Answer: 99/130
Payment made by any method except credit card is 95+4=99 and altogether there is three payment method including a credit card which sums up to 130.
So the probability is 99/130.
help me..........
only 23...
Answers
Question 23
Recall that a kite in geometry is any four sided figure where we have two different pairs of adjacent sides that are the same length.
We're told that PS = 4.5 and RS = 6. So this isn't an adjacent pair of congruent sides. But we can say that PS and PQ are one pair of adjacent congruent sides. That makes PQ to be 4.5 cm long.
Similarly, RS = RQ = 6 is the other pair of adjacent congruent sides. Notice that triangle PQR reflects over line PR to get triangle PSR.
See the diagram below.