Answers
• External point D (vertex outside of the circle) creates two secant segments (DR and DB).
• Using the exterior angle theorem: angleD= (1/2) RB - EC. This becomes 5x-10 = (13x+7-60°)/2.
• Now solve for x
multiply both sides by 2
10x-20=13x+7-60°
Add/subtract like terms to isolate variable on one side
60° = 3x+27
Subtract 27 from both sides
33=3x
divide both sides by 3 to get variable x alone, and: 11 = x.
• x = 11.
• Plug this x value back into the expression representing arc RB
13(11)+7 = 150.
• mRB=150°.
• check: 5(11)-10=45°. Plug all known values into the exterior angle theorem to see if true; 45° = (1/2)*(150° - 60°)
45°=45°
[true]
Answer:
150°
Step-by-step explanation:
A secant is a straight line that intersects a circle at two points.
The circle shows two secants RD and BD that intersect at one exterior point D, so we can use the Intersecting Secants Theorem to solve.
Intersecting Secants Theorem
If two secant segments are drawn to the circle from one exterior point, the measure of the angle formed by the two lines is half of the (positive) difference of the measures of the intercepted arcs.
[tex]\implies \angle RDB = \dfrac{1}{2}\left(\overset{\frown}{RB}-\overset{\frown}{EC}\right)[/tex]
[tex]\implies 5x-10=\dfrac{1}{2}(13x+7-60^{\circ})[/tex]
[tex]\implies 2(5x-10)=13x-53[/tex]
[tex]\implies 10x-20=13x-53[/tex]
[tex]\implies -3x=-33[/tex]
[tex]\implies x=11[/tex]
To find the measure of [tex]\overset{\frown}{RB}[/tex], substitute the found value of x into the expression for the arc:
[tex]\implies \overset{\frown}{RB}=13x+7[/tex]
[tex]\implies \overset{\frown}{RB}=13(11)+7[/tex]
[tex]\implies \overset{\frown}{RB}=143+7[/tex]
[tex]\implies \overset{\frown}{RB}=150^{\circ}[/tex]
Therefore, the measure of arc RB is 150°.
Learn more about intersecting secants here:
https://brainly.com/question/27934565
Related Questions
Investments increase exponentially by
about 26% every 3 years. If you made a
$2,000 investment, how much money
would you have after 45 years?
Future Amount = $[?]
Hint: Future Amount = (1 + r)
Į(1
←time
periods
initial growth
Answers
Answer:
29
Step-by-step explanation:
if you calculate the mathimatical equipment to the $2,000 it'll be better
50 people sponsor Paula and she raises a total of $180.65 for charity. 28 people sponsor Kate and she raises a total of $135.60 for charity. 45 people sponsor Sam and he raises a total of $169.25 for charity.
How much money is raised altogether by three of them?
$_____________
Answers
Answer:
485.5
Step-by-step explanation:
180.65+135.60+169.25
If there are 3500 students in a school and 3/7 of them
are majoring in business, how many of them are majoring in business?
Answers
Answer:
1500
Step-by-step explanation:
3/7 of 3500
=3/7 × 3500
=150
Find the sum of all the even
numbers between 23 and 29.
Answers
Answer:
78
Step-by-step explanation:
even numbers are numbers that end in 0, 2, 4, 6, or 8. these numbers can be considered even because they would evenly split between a group of 2
the "sum" of a group of numbers is the numbers added together
So, the numbers between 23 and 29:
23, 24, 25, 26, 27, 28, 29
(even numbers are in bold)
if we add these numbers together,
{1} {carry the 1 from the 18 in the one's place}
24
26
+ 28
______
78
So the sum of all the even numbers between 23 and 29 is 78.
hope this helps!!
consider the quadratic function f(x)= x^2 -8x-4 what is the value of the leading coefficient
Answers
The leading coefficient of the quadratic equation f(x)= x² – 8x – 4 will be 1.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The quadratic function, of vertex (h, k), is given by:
y = a(x – h)² + k
where a is the leading coefficient.
Then we have the quadratic equation given below.
f(x)= x² – 8x – 4
f(x)= x² – 8x + 16 – 16 – 4
f(x)= (x – 4)² – 20
Then the leading coefficient will be 1.
More about the quadratic equation link is given below.
https://brainly.com/question/2263981
#SPJ1
Solve the following inequality: ALGEBRA 1
Answers
Answer:
[tex]m > 5[/tex]
Step-by-step explanation:
[tex] \frac{m + 4}{3} > 3 \\ \frac{m + 4}{3} \times 3 > 3 \times 3 \\ m + 4 > 9 \\ m + 4 - 4 > 9 - 4 \\ m > 5[/tex]
pleeeeeeeeeeeease hellllllllp meeeeeee the circle has a center of 0.its raduis is 3 cm,and the central angle A measures 100.what is the area of the shaded region? give exact anwsers in term of pi .please hurry dont worry I have permission to post this for anybody who decides to report me again
Answers
Answer:
2.5 pi
Step-by-step explanation:
Comment
If you were trying to get the area of a whole circle, you would use
Area = pi r^2
You have to modify the formula to show that just part of the circle has an area that you are interested in.
The new formula is
Area = (theta/360) pi r^2
Givens
r = 30 cm
theta = 100
Solution
Area = (100 / 360) * pi * r^2 Substitute the givens into this formula
Area = (5 / 18) * pi * 3^2 Expand
Area = (5 / 18) * pi * 9 Cancel 9 into 18
Area = 5/2 * pi
Area = 2.5 * pi
Solve the system of equations by graphing.
y = x − 6
3x − 3y = 18
Answers
X = 6
Y = (-6)
How does supply and demand affect consumers?
Answers
Supply and demand can help consumers make informed decisions about their purchases, anticipate price fluctuations, and stay up to date with market trends.
We have to give that,
To find supply and demand affect on consumers.
Supply and demand have a significant impact on consumers.
When the demand for a product or service is high and the supply is limited, it can lead to higher prices.
On the other hand, when there is high supply and low demand, prices tend to be lower.
For consumers, this means that when the demand for a product is high, they may have to pay more or face limited availability.
Conversely, when the demand is low, consumers may find discounted prices or special promotions.
Supply and demand dynamics also influence the choices available to consumers.
For example, if the demand for a particular type of product increases, companies may introduce new variations or brands to meet consumer preferences.
This can lead to a broader range of options for consumers to choose from.
In summary, understanding supply and demand can help consumers make informed decisions about their purchases, anticipate price fluctuations, and stay up to date with market trends.
To learn more about supply visit:
https://brainly.com/question/1222851
#SPJ6
In the equation 3y = 21, what is the next step in the equation solving sequence
Answers
Answer:
divide both sides by 3
Step-by-step explanation:
Solving the equation means to have y alone on the left side equaling a number.
Since the variable y is being multiplied by 3, the next step is to do the opposite operation to "multiplying by 3" which is "dividing by 3." Since the rule in algebra is that you must do the same operation to both sides of an equation, the next step is:
divide both sides by 3
Give the following number in Base 16
NO LINKS!!!
Answers
Answer:
[tex]\large{\boxed{35_{10} = \sf 23_{16}}}[/tex]
Explanation:
[tex]\sf Given : 35_{10}[/tex]
Compute:
35 ÷ 16 = 2.1875 = 2R3
2 ÷ 16 = 0.125 = 0R2
Jot down the remainders:
3 ↑2 ↑======
[tex]\sf Answer : \ 35_{10} = 23_{16}[/tex]
[tex]\hrulefill[/tex]
Let's look at another example: [tex]\sf 325_{10} = [?]_{16}[/tex]
Compute:
325 ÷ 16 = 20.3125 = 20R5
20 ÷ 16 = 1.25 = 1R4
1 ÷ 16 = 0.0625 = 0R1
Jot down remainders:
5 ↑4 ↑1 ↑=====
[tex]\sf 325_{10} = [145]_{16}[/tex]
[tex]\hrulefill[/tex]
Another example: [tex]\sf 500_{10} = [?]_{15}[/tex]
Compute:
500 ÷ 15 = 33.33... = 33R5
33 ÷ 15 = 2.2 = 2R3
2 ÷ 15 = 0.13... = 0R2
Jot down remainders:
5 ↑3 ↑2 ↑=====
[tex]\sf 500_{10} = [235]_{15}[/tex]
This is general conversation of decimal integer to hexadecimal integer
Let's check
(35)_10This is in decimal form
We know the ways to convert decimal into other forms like
Binary—»Divide by 2Octal—»Divide by 8Hexadecimal —»Divide by 16For third way
35/16=2(2)_16 is one part
Next
35%16=33 is not divisible by 16
i.e
3%16=0Hence
other part is (3)_16
Add (not general addition)
The final answer is
(23)_16The triangles in the diagram below are similar. Find the distance across Clarence Lake. ( Figure may not be drawn to scale)
Answers
Answer: 40 km
Step-by-step explanation:
As corresponding sides of similar triangles are proportional, if we let the distance across Clarence lake be x,
[tex]\frac{x}{8}=\frac{15}{3}\\\\\frac{x}{8}=5\\\\x=\boxed{40 \text{ km}}[/tex]
PLEASE HELP ASAP PLEASEEEEEEE PLEASEEEEEEEEE EASY 20 POINTS
Answers
The transformation of a function may involve any change. The function with the graph are given below.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)Right shift by c units: y=f(x-c)(same output, but c units late)Vertical shift:
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k \times f(x)Horizontal stretch by a factor k: y = f\left(\dfrac{x}{k}\right)The real graph of the function is f(x)=x², now if the graph of the given function can be found by using the transformation rule as shown above. The function with the graph are given below.
Learn more about Transforming functions:
https://brainly.com/question/17006186
#SPJ1
List five rational numbers between:
−4
7
and
1
2
Answers
5 rational number between -47 and 12 are {-46, -45, -44, -43, -42}
How to find the rational numbers?
Remember that any integer is also a rational number.
So, if we want to find 5 rational numbers between -47 and 12, we can just find 5 integers between these two numbers.
To do that, we can just add 1 to the lowest bound, we will et:
-47 + 1 = -46
-45 + 1 = -45
-44 + 1 = -44
-43 + 1= -43
-43 + 1 = -42
So 5 rational number between -47 and 12 are {-46, -45, -44, -43, -42}
If you want to learn more about rational numbers:
https://brainly.com/question/12088221
#SPJ1
5=1 2/3x how do I solve for x?
Answers
You'll first Cross multiply: 5× 3x
that'll give you 15x.
15x=12(12 is a numerical constant).
Divide both sides by the the coefficient of X .That is 15x/15= 12/15
Therefore the answer is 12/15= x
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathsf{5 = 1 \dfrac{2}{3}x}[/tex]
[tex]\mathsf{1 \dfrac{2}{3}x = 5}[/tex]
[tex]\mathsf{\dfrac{1\times3 + 2}{3}x= 5}[/tex]
[tex]\mathsf{\dfrac{3 + 2}{3}x = 5}[/tex]
[tex]\mathsf{\dfrac{5}{3}x = 5}[/tex]
[tex]\large\text{MULTIPLY }\rm{\dfrac{3}{5}}\large\text{ to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{3}{5}\times\dfrac{5}{3}x = \dfrac{3}{5}\times5}[/tex]
[tex]\large\text{SIMPLIFY IT!}[/tex]
[tex]\mathsf{x = \dfrac{3}{5}\times5}[/tex]
[tex]\mathsf{x = \dfrac{3}{5}\times\dfrac{5}{1}}[/tex]
[tex]\mathsf{x = \dfrac{3\times5}{5\times1}}[/tex]
[tex]\mathsf{x = \dfrac{15}{5}}[/tex]
[tex]\mathsf{x = \dfrac{15\div5}{5\div5}}[/tex]
[tex]\mathsf{x = \dfrac{3}{1}}[/tex]
[tex]\mathsf{x = 3\div1}[/tex]
[tex]\mathsf{x = 3}[/tex]
[tex]\huge\text{Therefore, your answer: \boxed{\mathsf{x = 3}}}\huge\checkmark[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Need help with Math (Quadratic)
Answers
Answer:
f(x) = 2(x -3)² +5 or f(x) = 2x² -12x +23
Step-by-step explanation:
The equation of a quadratic is easily written in vertex form when the coordinates of the vertex are given. Here, the point one horizontal unit from the vertex is 2 vertical units higher, indicating the vertical scale factor is +2.
__
vertex formThe vertex form equation for a parabola is ...
f(x) = a(x -h)² +k . . . . . . vertex (h, k); vertical scale factor 'a'
equationFor vertex (h, k) = (3, 5) and vertical scale factor a=2, the vertex form equation of the parabola is ...
f(x) = 2(x -3)² +5 . . . . . vertex form equation
Expanded to standard form, this is ...
f(x) = 2(x² -6x +9) +5
f(x) = 2x² -12x +23 . . . . . standard form equation
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
Answer:
–6x + 15 < 10 – 5x
An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Step-by-step explanation:
When you break down -6x + 15 < 10 - 5x, you get x > 5.
Because x is GREATER than 5, when making a number line, there is an open circle on 5 and a bold line pointing to the right.
Which of the following would best be solved using completing the square?
2x^2 + 15x = 6
x^2 = 36
x^3 - 3x^2 + 4x - 12 = 0
x^2 - x - 20 = 0
Answers
Answer:
2x^2 +15x = 6
Step-by-step explanation:
the form of this equation makes it easier to use the completing the square method
Sarah has a solid wooden cube with a length of 4/5 centimeter. From each of its 8 corners, she cuts out a smaller cube with a length of 1/5 centimeter. What is the volume of the block after cutting out the smaller cubes?
Answers
The volume of the block after cutting out the smaller cubes is [tex]\frac{63}{125}[/tex] cubic units.
Given that, Sarah has a solid wooden cube with a length of 4/5 centimetres. From each of its 8 corners, she cuts out a smaller cube with a length of 1/5 centimetre.
We need to find the volume of the block after cutting out the smaller cubes.
What is the volume of a cube?The volume of a cube is defined as the total space enclosed by the cube in a three-dimensional space. The formula to find the volume of a cube is a³, where a=edge of a cube.
Now, the volume of a solid wooden cube with a length of 4/5 centimetre
[tex]=(\frac{4}{5} )^{3} =\frac{4}{5} \times \frac{4}{5}\times \frac{4}{5}=\frac{64}{125}[/tex] cubic units.
The volume of a smaller cube with a length of 1/5 centimetre
[tex]=(\frac{1}{5} )^{3} =\frac{1}{5} \times \frac{1}{5}\times \frac{1}{5}=\frac{1}{125}[/tex] cubic units.
The volume of the block after cutting out the smaller cubes[tex]=\frac{64}{125}-\frac{1}{125}=\frac{63}{125}[/tex]
Therefore, the volume of the block after cutting out the smaller cubes is [tex]\frac{63}{125}[/tex] cubic units.
To learn more about the volume of a cube visit:
https://brainly.com/question/27770332.
#SPJ1
Answer:
the answer is 64/125 <3
Complete the recursive formula of the geometric sequence 56, -28, 14, -7,....
Answers
Step-by-step explanation:
each term in the sequence is half of the value of the previous term, and in the opposite sign.
therfore, the quotient between terms is (-2)
so, to get one term from the previous term, we multiply by 1/(-2), so:
d(n) = d(n-1) × 1/(-2)
the first term is 56 so d(1)=56
Answer:
56 and -1/2
Step-by-step explanation:
khan
need help with this please
Answers
Answer:
no lo sé no lo sé
Step-by-step explanation:
solo se que nada se
Find the sum.
([tex](-54x^{5}+35x^{3}-61)+(5x^{5}-69x^{3}-7)=[/tex]
Answers
Answer:
125250
Step-by-step explanation:
I just askeked and it gave me the answere
Answer: [tex]-49x^{5} - 34x^{3} - 68[/tex] or [tex]49x^{5} + 34x^{3} + 68[/tex]
Step-by-step explanation:
Since both groups have the same variables and exponents, just align them and add.
[tex]-54x^{5}+5x^{5} = - 49x^{5}[/tex]
[tex]35x^{3} - 69x^{3} = -34x^{3}[/tex]
- 61 - 7 = - 68
[tex]-49x^{5} - 34x^{3} - 68[/tex]
Given: m∠ELG = 124°
Prove: x = 28
3 lines are shown. A line with points D, L, G intersects a line with points E, L, H at point L. Another line extends from point L to point F between angle E L G. Angle D L E is (2 x) degrees.
Answers
Answer:
By using opposite angles of two intersecting straight lines are congruent we proved that x = 28°
Step-by-step explanation:
Opposite angles of two intersecting straight lines are congruent
Therefore ∠DLE = ∠GLH
Here ∠DLE = 2x = ∠GLH
Sum of all angles on a straight line is 180°
Therefore ∠ELG + ∠GLH = 180°
Given that ∠ELG = 124°
124° + ∠GLH = 180°
124° + 2x = 180°
2x = 180° - 124°
2x = 56°
x = 28°
hence proved that x = 28°
Learn more about congruent angles here - https://brainly.ph/question/15035628
#SPJ10
Lesson Posttes
Which of the following composition of transformations would create an image that is congruent to its original
image?
Answers
A translation 2 units to the left followed by dilation by 1/2.
The correct option is (B).
What is congruency?It states that that two triangles are said to be congruent if they are copies of each other and when superposed, they cover each other exactly.
The complete question is:
Which of the following composition of transformations would create an
image that is not congruent to its original image?
A rotation of 45° followed by a reflection across the x-axis
A translation 2 units to the left followed by dilation by 1/2
A reflection across the y-axis followed by a rotation of 60°
A rotation of 135º followed by a translation of 4 units to the right.
After a translation of 2 units to the left followed by dilation by 1/2 the image will not be congruent to its original image.
All other options are reflection and rotation, which not fit into the situation.
Learn more about congruency here:
https://brainly.com/question/7888063
#SPJ1
Need some help ASAP and work shown. Ps; If you answer I’ll mark you brainliest.
Answers
Answer:
h ≈ 37 ft
Step-by-step explanation:
let x be the height of the tree from the viewers eye level
using the tangent ratio, then
tan24° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{72}[/tex] ( multiply both sides by 72 )
72 × tan24° = x
then
height of tree = x + 5 = 72tan24° + 5 ≈ 37 ft ( to the nearest foot )
Answer:
37ft
Step-by-step explanation:
It can be considered as a right angle triangle. The height of the tree is equal to the product of tan(24°) and the distance between the man and tree+5 Therefore
⇒h=tan(24°)*72+5⇒h≈32ft+5⇒h≈37In conclusion
The height of the tree is 37ft
The school play sold $550 in tickets one night. The number of $8 adult tickets was 10 less than twice the number of $5 child tickets. How many tickets were sold for the adults vs the child tickets?
Answers
Answer:
This is my answer↓:
Step-by-step explanation:
He school play sold $550 in tickets one night.
The number of $8 adult tickets was 10 less than twice the number of
$5 child tickets.
How many of each ticket were sold
Let say child ticket sold = x
Adult tickets was 10 less than twice the number of child tickets.
=> Adult ticket sold = 2x - 10
Child ticket sold = x
$5 child tickets price
=> Revenue = 5x $
Adult ticket sold = 2x - 10
$8 Adult tickets price
=> Revenue = 8(2x - 10) =16x - 80 $
5x + 16x - 80 = 550
=> 21x = 630
=> x = 30
Child ticket sold = 30
Adult ticket sold = 50
Total ticket sold = 80
Mark as brainlist, thanks me, and rate. Hope it helps!!!
Can anyone help me???
Answers
Answer:
principal (p)=$1300
Interest (I) =$28.67
Time( T) = 1 year
R=?
we have,
R = I*100/T*R
What is the square root of -1? Complex numbers
Answers
Answer:
The square root of -1 is i
Step-by-step explanation:
"i" is the imaginary unit and represents the value of sqrt -1
Add. State the sum in simplest form.
Answers
Answer:
[tex] \frac{ {3x}^{2} }{x + 5} + \frac{15x}{x + 5} [/tex]
[tex] \frac{3 {x}^{2} + 15x}{x + 5 } [/tex]
3x ( x + 5) /( x + 5).
3x, X is not equal to (-5)What is the solution to -¾x+2<_-7
Answers
Answer:
[tex]x\geq 12[/tex]
Step-by-step explanation:
[tex]-3/4x + 2 \leq -7\\-3/4x \leq -9\\x \geq 12[/tex]