Quadrilateral ABCD is inscribed in circle O.
What is m∠C?
Enter your answer in the box.
____°
Please show how to solve this question. Thanks again.
Answers
To solve this question we will have to make use of one of the properties of the inscribed quadrilateral. That property is: "Opposite angles in any quadrilateral inscribed in a circle are supplements of each other".
Thus, as we can see from the diagram given, [tex] \angle B+\angle D=180^{\circ} [/tex]
[tex] (2x+3)+(4x+3)=180^{\circ} [/tex]
[tex] \therefore 6x+6=180^{\circ} [/tex]
[tex] 6x=174^{\circ} [/tex]
[tex] \therefore x=\frac{174^{\circ}}{6} =28^{\circ} [/tex]
Thus, now that we know the value of x, we can easily find the value of the [tex] \angle C [/tex] because we know that:
[tex] \angle C=2x+1 [/tex]
[tex] \therefore \angle C=2(29^{\circ})+1=59^{\circ} [/tex]
Thus, [tex] \boldsymbol{59^{\circ}} [/tex] is the correct answer.
Related Questions
every day Josie bakery bakes muffins and bagels. the ratio of m7ffins to bagels is always the same. the table shows data about what Josie bakery bakes 3 days of the week. How many bagels did Josie bakery bakes on wednesday
Answers
x = (300*165)/180 = 275
Ivan earns $8 each time he walks his neighbors dog.he already walked his neighbors dog 5 times.how many more times does he need to walk the dog to earn enough money to buy a game that costs $88
Answers
Answer:
6 more times
Step-by-step explanation:
A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 1 cm more than the shorter leg and the hypotenuse 2 cm more than the shorter leg. how long should the sides of the triangle be?
Answers
The sides should be 3 cm, 4 cm, 5 cm.
Three times a number added four times the number equals 84 find the number
Answers
3x+4x=84
7x=84
7x/7=84/7
x=12
The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.
V(t)=24,500(0.95^t)
Find the initial value of the car and the value after 13 years.
Round answers to the nearest dollar as necessary.
Answers
24,500*(0.95^0) =
24,500*1 = 24,500
Hence, the initial value is £24,500
The value after 13 years means t equals 13. Therefore
24,500*(0.95^13) =
12,576.88
Hence, the value after 13 years is about £12,577
What is the ratio of CDs & DVDs
Answers
B. 1:4
C. 1:2
D. 1:5
Philip is going on a 400040004000-kilometer road trip with three friends. The car consumes 666 liters of gas per 100100100 kilometers, and gas costs \$1.50$1.50dollar sign, 1, point, 50 per liter. If Philip and his friends want to split the cost of gas evenly, how much should they each pay?
Answers
In total, this will cost 240*1.5=360$. He has 3 friends, so they are 4 in total. Everyone will have to pay 360/4=90$
First, we will calculate how much it consumes per kilometer:
[tex]g_{ckm}=6/100=0.06\frac{l}{km}[/tex]
The total consumption for the whole trip would be:
[tex]g_t=L\cdot g_{ckm}=0.06\cdot 4000=240 l[/tex]
To get the total cost of the gas we multiply the total gas consumed by its cost:
[tex]C_t=g_t\cdot1.5=360\$[/tex]
So, each passenger must pay $90.
-7(3x+5) use Distributive property to solve
Answers
= ( - 7 )(3x + 5)
= ( - 7 )(3x) + ( - 7)(5)
Answer: = - 21x - 35
Describe the graph of a system of linear equations that has infinite solutions.
Answers
The explicit rule for a sequence is an=9(−5)n−1 .
What is recursive rule for the sequence?
an=5−(an−1),a1=9
an=−9(an−1),a1=5
an=9−(an−1),a1=5
an=−5(an−1),a1=9
Answers
The recursive rule is a(n) = -5*a(n-1); a(1) = 9
The first term is 9. Each new term is found by multiplying the previous term by -5
We can see this when we raise -5 to a whole number power. Eg: 9(-5)^3 = 9*(-5)*(-5)*(-5)
Answer: Choice D
Answer:
Option 4th is correct.
[tex]a_n = -5 \cdot a_{n-1}[/tex] , [tex]a_1 = 9[/tex]
Step-by-step explanation
The explicit sequence of the geometric sequence is given by:
[tex]a_n = a_1r^{n-1}[/tex] ....[1]
where,
r is the common ratio
n is the number of terms
[tex]a_1[/tex] is the first term
As per the statement:
The explicit rule for a sequence is:
[tex]a_n=9(-5)^{n-1}[/tex]
On comparing [1] we have;
[tex]a_1 = 9[/tex] and r= -5
Recursive formula for the geometric sequence is given by:
[tex]a_n = r \cdot a_{n-1}[/tex] for [tex]n\geq 2[/tex]
Substitute the given values we have;
[tex]a_n = -5 \cdot a_{n-1}[/tex]
Therefore, the recursive rule for the sequence is, [tex]a_n = -5 \cdot a_{n-1}[/tex] , [tex]a_1 = 9[/tex]
Censorship was established in the Bill of Rights. True or false! First answer will be marked brainliest!
Answers
Answer:
make the other brainliest but its false
Step-by-step explanation:
HELP!!...................
Answers
r = x^2 +5x + 14 = 5^2 +5(5) +14 = 25 +25 +14 = 64
c = x^2-4x +5 = 5^2-4(5) + 5 = 25-20 +5 = 10
r- c = 64-10 = 54
so the store will have a profit of 54,000 after it's 5th month
Answer is C
Warren wants to build a rectangular enclosure for his animals. one side of the pen will be against the barn, so he needs no fence on that side. the other three sides will be enclosed with wire fencing. if warren has 500 feet of fencing, you can find the dimensions that maximize the area of the enclosure.
a.let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). write an function for the area a of the enclosure in terms of w . (hint first write two equations with w and l and
a. solve for l in one equation and substitute for l in the other). a ( w ) = 1/2w
b.what width w would maximize the area? w = ft
c.what is the maximum area? a = square feet
Answers
a = lw
a) l = 500 -2w
.. a = (500 -2w)*w
b) The zeros of the above equation are w=0, w=250. The vertex of this quadratic is on the line of symmetry, halftway between the zeros, at w=125 ft.
c) a = (500 -2*125)*125 = 31,250 . . . . square feet
Let's solve this step by step.
a. We begin by establishing the relationship between the width (w) and the length (l) using the total amount of fencing available (500 feet). Since one side of the pen is against the barn, we only need to fence the other three sides. Thus, the total amount of fencing used will be for two widths and one length, or \(2w + l\).
Setting up the equation for total fencing, we get:
\[2w + l = 500\]
Now, to express \(l\) in terms of \(w\), we solve for \(l\):
\[l = 500 - 2w\]
Next, we can write the function for the area \(A\) of the enclosure in terms of \(w\). Since area is \(width \times length\), we substitute our expression for \(l\):
\[A(w) = w \cdot l\]
\[A(w) = w \cdot (500 - 2w)\]
\[A(w) = 500w - 2w^2\]
This is the function that expresses \(A\) in terms of \(w\).
b. To find the width \(w\) that maximizes the area, we take the derivative of \(A(w)\) with respect to \(w\) and set it equal to zero to find the critical points.
\[A'(w) = \frac{d}{dw}(500w - 2w^2)\]
\[A'(w) = 500 - 4w\]
Setting \(A'(w)\) equal to zero and solving for \(w\):
\[500 - 4w = 0\]
\[-4w = -500\]
\[w = \frac{500}{4}\]
\[w = 125\]
The width that maximizes the area of the enclosure is 125 feet.
c. Now let’s find the maximum area by substituting \(w = 125\) back into the area function \(A(w)\):
\[A(125) = 500 \cdot 125 - 2 \cdot 125^2\]
\[A(125) = 62500 - 2 \cdot 15625\]
\[A(125) = 62500 - 31250\]
\[A(125) = 31250\]
The maximum area that Warren can enclose is 31,250 square feet.
Triangle ABC was dilated and translated to form similar triangle A'B'C'.
What is the scale factor of the dilation?
A. 1/5
B. 2/5
C. 5/2
D. 5/1
Answers
On this exercise is asked to find the scale factor by which the triangle ABC was
dilated to produce the triangle A'B'C'.
Dilation is define by the rule (x,y)-- (kx, ky) where k represents the scale factor.
As can be see on the picture the dilation produce was an enlargement meaning that the image is larger that the preimage.
Of this form you can discard the choices A and B as possible solutions.
Lets try 5/2 as the possible scale factor:
(x,y)-- (kx, ky)
A(0,2)--(5/2(0),5/2(2))=A'(0,5)
B(2,2)--(5/2(2),5/2(2))=B'(5,5)
C(2,0)--(5/2(2),5/2(0))=C'(5,0)
Lets try 5/1 or 5 as the scale factor:
A(0,2)--(5(0),5(2))=A'(0,10)
B(2,2)--(5(2),5(2))=B'(10,10)
C(2,0)--(5(2),5(0))=C'(10,0)
As said at the beginning of the question the triangle was not only dilated.
After a dilation and a translation, the scale factor of the dilation is letter C or 5/2.
correct answer is 5/2
A 2-digit number is one more than 6 times the sum of its digits. If the digits are reversed, the new number is 9 less than the original number. Find the original number
Answers
hope this helps<3
:)
I WILL GIVE BRAINLIEST FOR Correct Answer
A plane is located at C on the diagram. There are two towers located at A and B. The distance between the towers is 7,600 feet, and the angles of elevation are given.
EXPLAIN YOUR ANSWER
a. Find BC, the distance from Tower 2 to the plane, to the nearest foot.
b. Find CD, the height of the plane from the ground, to the nearest foot.
Answers
Answer:
a. 15052.1ft b. 6122ft
Step-by-step explanation:
Jim runs a food cart and during a business outdoor Festival he sold $8470 worth of food he sells hot dogs for $2.50 and steak sandwiches for $10 if he sold a total of 985 items that they how many of each item did he sell?
Answers
x: hot dogs
y: steak sandwiches
We write the following system of equations:
2.50x + 10y = 8470
x + y = 985
Resolving graphically we have:
x = 184
y = 801
Note: see attached image for the solution.
Answer:
He sold:
hot dogs = 184
steak sandwiches = 801
Can someone help me please, how to add this? Thank you!
Answers
Choice B) [tex]9.9 \angle \underline{76.10^{\circ}}[/tex]
============================================
Explanation:
The given vectors in polar form are
(17,60)
(8,220)
by polar form I mean (r,theta) where
r = magnitude
theta = angle
Convert the polar form (r,theta) = (17,60) to component form
x = r*cos(theta)
x = 17*cos(60)
x = 8.5
y = r*sin(theta)
y = 17*sin(60)
y = 14.72243186
The component form of the first vector is (x,y) = (8.5, 14.72243186)
Do the same for the second vector
x = r*cos(theta)
x = 8*cos(220)
x = -6.1283555
y = r*sin(theta)
y = 8*sin(220)
y = -5.1423009
The component form of the second vector is (x,y) = (-6.1283555, -5.1423009)
Now we add the vectors. Add up the corresponding components
(8.5, 14.72243186)+(-6.1283555, -5.1423009)
(8.5+(-6.1283555) , 14.72243186+(-5.1423009))
(2.3716445, 9.58013096)
So,
(x,y) = (2.3716445, 9.58013096)
is the component form of the resultant vector. Its the vector we get after adding the two original vectors
The last step is to convert this back to polar form
r = sqrt(x^2+y^2)
r = sqrt(2.3716445^2+9.58013096^2)
r = 9.869326564
which is roughly 9.9
theta = arctan(y/x)
theta = arctan(9.58013096/2.3716445)
theta = 76.09548164
which rounds to 76.10
So we end up with (r,theta) = (9.9, 76.10) pointing to choice B as the answer
You deposit $1500 in an account that pays 7% annual interest. Find the balance after 2 years when the interest is compounded daily.
Answers
The balance after 2 years when the interest is compounded daily is
$1,725.39.
What is Compound Interest?The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Given:
P= $1500
R= 7%
T = 2 years
Now, using
A = P[tex](1 + r/n)^{nt[/tex]
A = 1,500.00[tex](1 + 0.07/365)^{(365)(2)[/tex]
A = 1,500.00[tex](1 + 0.00019178082191781)^{(730)[/tex]
A = $1,725.39
Hence, the balance is $1,725.39.
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using these complex zeros (1,1,-1/2,2+i,2-i) factor f(x)=-2x^5 +11x^4 -22x^3 +14x^2 +4x -5
Answers
[tex]\bf (x^2-2x+1)(2x+1)~[(x-2)^2-(i)^2] \\\\\\ (x^2-2x+1)(2x+1)~[(x^2-4x+4)-(-1)] \\\\\\ (x^2-2x+1)(2x+1)~[(x^2-4x+4)+1] \\\\\\ (x^2-2x+1)(2x+1)~[x^2-4x+5] \\\\\\ (x^2-2x+1)(2x+1)(x^2-4x+5)[/tex]
of course, you can always use (x-1)(x-1)(2x+1)(x²-4x+5) as well.
For a school group, a skating rink charges a flat fee of $50 for skates for the students to use the skating rink.
•For 40 Students the skating rink charges 180.
•For 75 students, the skating rink charges 293.75
Which question represents the amount the skating rink charges for x students?
A)y=3.25x+35
B)y=3.25x+ 50
C)y=4.50x+ 35
D) y=4.50x+ 50
Answers
That fixed part is given by the fee for skates, which is $50.
The variable part depends on the quantity of students which is called 'x'. For this part, you are provided with a couple of points where the linear function passes by, they are: A(40,180) and B(75,293.75).
So, first thing to do is getting the slope:
[tex]m= \dfrac{293.75-180}{75-40} = \dfrac{113.75}{35} \\ \\ m=3.25[/tex]
Linear function structure is:
[tex]y=mx+b[/tex]
Where b is the y-intercept, which in this case is the fixed part, 50.
Finally, the function is:
[tex]y=3.25x+50[/tex]
Attached picture shows its graph.
What is the measure of angle x, help
Answers
x = 180 - 73 - 72 = 35
x = 35 degrees
=73
x=180-72-73
=35°
Simplify these algebraic expressions: 12x + 3 − 4x + 7, 8 − 7x − 13 + 2x, −3x − 18 + 5x − 2
Answers
8-7x-13+2x=-5-5x
-3x-18+5x-2=-16x-2
The simplified expressions are:
12x + 3 − 4x + 7 = 8x + 10
8 − 7x − 13 + 2x = −5x − 5
−3x − 18 + 5x − 2 = 2x − 20
What is an expression?A term is a single mathematical phrase. It might consist of only one variable—a letter—one number—positive or negative—or several variables multiplied but never added or subtracted. A number is placed in front of some nouns that have variables. Coefficients are numbers that come before phrases.
To simplify each expression, we combine like terms:
Expression 1:
12x + 3 − 4x + 7 = (12x − 4x) + (3 + 7)
12x + 3 − 4x + 7 = 8x + 10
Expression 2:
8 − 7x − 13 + 2x = (−7x + 2x) + (8 − 13) = −5x − 5
Expression 3:
−3x − 18 + 5x − 2 = (−3x + 5x) + (−18 − 2) = 2x − 20.
Therefore, the simplified expressions are:
12x + 3 − 4x + 7 = 8x + 10
8 − 7x − 13 + 2x = −5x − 5
−3x − 18 + 5x − 2 = 2x − 20
To learn more about the expression;
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PLEASE HELP ME ON THIS QUESTION
THX
~BRAINLIEST AVAILABLE TO CORRECT ANSWER
Answers
x=-2→g(-2)=-f(-2)-2=-(-1)-2=1-2→g(-2)=-1
x=-1→g(-1)=-f(-1)-2=-(1)-2=-1-2→g(-1)=-3
x=0→g(0)=-f(0)-2=-(3)-2=-3-2→g(0)=-5
x=1→g(1)=-f(1)-2=-(5)-2=-5-2→g(1)=-7
x -2 -1 0 1
g(x) -1 -3 -5 -7
f(x)={(-2,-1),(-1,1),(0,3),(1,5)}
Need to find g(x)=-f(x)-2
First step is to find f(x) in analytical form.
The slope-intercept form would be convenient because we can find both the slope and y-intercept.
In a typical linear function
f(x)=mx+c
m= slope, can be found by (y2-y1)/(x2-x1)
c= y-intercept [value of y when x=0]
So here, taking points (0,3),(1,5)
m=(5-3)/(1-0)=2
c=3 [y-value when x=0]
=>
f(x)=2x+3
=>
g(x)
=-f(x)-2 [given]
=-(2x+3)-2 [don't forget the parentheses]
=-2x-3-2
=-2x-5
Finally
g(-2)=-2(-2)-5=4-5=-1
g(-1)=-2(-1)-5=2-5=-3
g(0)=-2(0)-5=0-5=-5
g(1)=-2(1)-5=-2-5=-7
...
when the solutions to each of the two equations below are graphed in the xy coordinate plane, the graphs of the solutions intersect at two places. Write the y-coordinate of the points of intersection in the boxes below in order from smallest to largest. y=2x and y=x^2-3
Answers
Since both of these equations have y isolated, we can set them equal to each other:
2x=x²-3
We want all of the variables on one side, so subtract 2x:
2x-2x = x²-3-2x
0=x²-3-2x
Write the quadratic in standard form:
0=x²-2x-3
This is easily factorable, as there are factors of -3 that will sum to -2. -3(1)=-3 and -3+1=-2:
0=(x-3)(x+1)
Using the zero product property we know that either x-3=0 or x+1=0; therefore x=3 or x=-1.
Substituting this into the first equation (it is simpler):
y=2(3) = 6
y=2(-1)=-2
Therefore the coordinates are (3, 6) and (-1, -2).
Answer:
Step-by-step explanation:
From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.
⇒ -3,
⇒ 0.59,
⇒ 3.41
△ABC∼△DEF , △ABC has a height of 20 inches, and △DEF has a height of 24 inches. What is the ratio of the area of △ABC to the area of △DEF ? Enter your answer, in simplest form, in the boxes. :
Answers
h1---------------> height of △ABC
b1---------------> base of △ABC
h2--------------->height of △DEF
b2---------------> base of △DEF
we know that
h1=20 in
h2=24 in
Since they are similar, their bases must be in the same proportion:
h1/b1=h2/b2------> 20/b1=24/b2-----------> 24b1=20b2
b1=20b2/24-------------> equation 1
Area of △ABC=b1*h1/2
Area of △DEF=b2*h2/2
Let
r------>[the ratio of the area of △ABC to the area of △DEF]
r=[b1*h1/2]/[b2*h2/2]------> [b1*h1]/[b2*h2]
r=[20b1]/[24b2]---------------> equation 2
I substitute 1 in 2
r=[20(20b2/24)]/[24b2]--------> r=20²/24²-------> r=0.6944
the answer is
the ratio of the area of △ABC to the area of △DEF is 0.69
Ben bought a desk for $249.99. The sales tax rate was 6.25%. How much did Ben pay for the desk? Round your answer to the nearest cent. (1 point)
$15.62
$187.49
$265.61
$406.23
Just tell me if its A,B,C, or D.
Answers
So C
The Price for Desk after tax is $265.614.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
Ben bought a desk for $249.99.
Tax rate = 6.25%
So, the price for desk after tax
= 249.99 + 249.99 x 6.25%
= 249.99 + 249.99 x 0.0625
= 249.99 +15.62
= $265.614
Hence, the Price for Desk after tax is $265.614.
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What would be the side length of the smallest square plate on which a 40-cm chopstick can fit along a diagonal without any overhang? (Correct answer will get reward)
Answers
The side length of the smallest square plate required to fit a 40-cm chopstick along its diagonal without any overhang is approximately 28.284 cm.
To find the side length of the smallest square plate in which a 40-cm chopstick can fit along a diagonal without any overhang, we can use the Pythagorean theorem. The diagonal of a square is the hypotenuse of a right-angled triangle formed by two sides of the square. Since the sides of the square are equal, if one side is s, then the diagonal d can be calculated using the equation d = s√2, where √2 is the square root of 2 (approximately 1.4142).
Therefore, to fit a 40-cm chopstick along the diagonal:
Let d = 40 cm.
Use the equation s√2 = 40 cm to find s, the side of the square.
s = 40 cm / √2.
s ≈ 28.284 cm when rounded to three decimal places.
So, the side length of the smallest square plate on which a 40-cm chopstick can fit along a diagonal without any overhang is approximately 28.284 cm.
Solve 2x^3-5x^2-11x-4=0
Answers
x = {-1, -0.5, 4}
The factorization will be
.. (2x+1)(x +1)(x -4) = 0
An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 4 cm long. A second side of the triangle is 7.4 cm long. Find the longest and shortest possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter. Question 3 options: 11.1 cm, 4.9 cm 44.4 cm, 3.2 cm 44.4 cm, 11.1 cm 24 cm, 4.9 cm
Answers
7.4/x=6/4
When we clear "x", we obtain:
6x=(7.4)(4)
x=(7.4)(4)/6
x=4.9 cm (This is the shortest possible length of the third side of the triangle)
Let's find the longest possible length:
4/6=7.4/x
When we clear the "x", we have:
4x=(7.4)(6)
x=(7.4)(6)/4
x=11.1 cm (This is the longest possible length of the third side of the triangle)
Answer:
11.1 cm, 4.9 cm