Answer:
The value of a is 63° and the value of b is 27°
Step-by-step explanation:
In the given figure
∵ OA, OB, and OC are radii of the circle O
→ The radii of a circle are equal
∴ OA = OB = OC
In Δ AOC
∵ OA = OC
∴ Δ AOC is an isosceles triangle
→ Base angles of the isosceles triangle are equal
∵ ∠OAC and ∠OCA are the base angles of the triangle
∴ m∠OAC = m∠OCA
∵ m∠OAC = a°
∴ m∠OCA = a°
→ The sum of angles in any triangle is 180°
∵ a° + a° + m∠AOC = 180°
∵ m∠AOC = 54°
∴ a° + a° + 54 = 180°
→ Add the like terms
∴ 2a° + 54 = 180°
→ Subtract 54 from both sides
∴ 2a° = 126°
→ Divide both sides by 2
∵ m∠OAC = m∠OCA = 126 ÷ 2
∴ a° = 63
∴ The value of a is 63°
In ΔBOC
∵ OB = OC
∴ Δ BOC is an isosceles triangle
→ Base angles of the isosceles triangle are equal
∵ ∠OBC and ∠OCB are the base angles of the triangle
∴ m∠OBC = m∠OCB
∵ m∠OBC = b°
∴ m∠OCB = b°
∵ ∠AOC is an exterior angle of ΔBOC at the vertex O
→ The measure of the exterior angle equals the sum of the measure
of the opposite interior angles to this vertex
∵ ∠OBC and ∠OCB are the opposite interior angle of ∠AOC
∴ m∠OBC + m∠OCB = m∠AOC
→ Substitute their measures
∵ b° + b° = 54°
→ Add the like terms
∴ 2b° = 54
→ Divide both sides by 2
∴ b° = 27
∴ The value of b is 27°
find f(-10) f(x)=7x-5
Answer:
f(-10) = -75Step-by-step explanation:
F(x) is simply another way of saying y. We are given the x value of -10. We can substitute this in for x and find y.
f(-10) = 7(-10) - 5
f(-10) = -70 - 5
f(-10) = -75
Answer:
Rewrite the equation in term of
x
and
y
.
f
(
x
)
=
2
x
2
−
7
x
+
5
Rewrite the equation in vertex form.
Tap for fewer steps...
Complete the square for
2
x
2
−
7
x
+
5
.
Tap for more steps...
2
(
x
−
7
4
)
2
−
9
8
Set
y
equal to the new right side.
y
=
2
(
x
−
7
4
)
2
−
9
8
Use the vertex form,
y
=
a
(
x
−
h
)
2
+
k
, to determine the values of
a
,
h
, and
k
.
a
=
2
h
=
7
4
k
=
−
9
8
Find the vertex
(
h
,
k
)
.
(
7
4
,
−
9
8
)
Step-by-step explanation:
A graduated cylinder is filled with 20ml of water. Then, an 8g marble is dropped into the cylinder, causing the volume to change to 24ml. What is the density of the marble?
Answer:
The density of the marble is 2,000 kg/m³
Step-by-step explanation:
The given parameters for finding the density of the marble are;
The volume of water in the graduated cylinder, v₁ = 20 ml
The mass of the marble dropped into the graduated cylinder, m = 8 g
The new volume of the cylinder after the 8 g marble is dropped into the cylinder, v₂ = 24 ml
Therefore, the volume of the marble, v = v₂ - v₁
Substituting the known values gives;
The volume of the marble, v = 24 ml - 20 ml = 4 ml
Density, ρ = Mass, m/(Volume, v), the units of density is kg/m³
Therefore, the density of the marble, [tex]\rho _{marble}[/tex], is given as follows;
[tex]\rho _{marble}[/tex] = m/v = (8 g)/(4 ml) = 2 g/ml
1 g/ml = 1 kg/l = 1,000 kg/m³
∴ [tex]\rho _{marble}[/tex] = 2 kg/l = 2,000 kg/m³.
Copy the expressions which are polynomials. Give reasons why the remaining are
not polynomials.
a)3x-2
b)p^2+1/p
c3y^2-2y/3+1
Answer: a and c are polynomials, b is not.
Step-by-step explanation:
A polynomial p(x) is written as:
p(x) = aₙ*xⁿ + ... + a₂*x² + a₁*x¹ + a₀*x⁰
where x is the variable, and the numbers aₙ, aₙ₋₁, ..., a₁, a₀ are the coefficients of the polynomial, such that aₙ is the leading coefficient, and the value of n (always a natural number) is the degree of the polynomial.
Notice that the powers need to be always natural numbers.
Now, let's analyze the options:
a) 3*x - 2
We can rewrite this as:
3*x¹ - 2*x⁰
Then this is a polynomial.
b) p² + 1/p (in this case the variable is p)
the second term can be written as:
1/p = p⁻¹
Then we have a term with a negative power of p, this means that this is not a polynomial.
c) 3*y² - 2*y/3 + 1
Same as in the first case, we can rewrite this as:
3*y² - (2/3)*y¹ + 1*y⁰
This is a polynomial.
Rico and nita solved the answer the same problem.Rico got 6/8 for an answer, and nita got 3/4.Which answer is corrext. Use the term equivalent fraction in your explanation
Answer:
Both are correct
Step-by-step explanation:
Rico got 6/8
Nita got 3/4
Equivalent fraction
2/2 x Nita point
2/2 x 3/4
6 / 8
So,
Nita point = Rico point
6/8 = 6/8
Answer:
Both are corre
Step-by-step explanation:
Jan 15, 8:40:40 AM
Determine if the following system of equations has no solutions, infinitely many
solutions or exactly one solution.
-6x + 5y = 7
30x – 25y = -35
One Solution
Infinitely Many Solutions
Submit Answer
O No Solutions
Which price is equivalent to $1.50 for 1 pound of apples?
A.. 6 pounds of apples for $9
B..8.5 pounds of apples for $9
C..9 pounds of apples for $9
D..13.5 pounds of apples for $9
Which answer choice describes y = -3x2 +7x - 2 accurately?
Answer:y = y = -7x
Step-by-step explanation: y - 14 = -7(x - (-2))
y - 14 = -7x - 14
Please help!! 20 points!!! I don’t know if is d....
find the value of the expression below x=2 3x
Help!!! What is the difference ? (x - 8)/(3x) - (3x)/(x ^ 2)
Answer:
Given that you're providing only a single term, asking for a difference doesn't make a lot of sense. I assume you're asking to have the expression simplified?
If so, then it can be reduced to (x - 17) / 3x
Step-by-step explanation:
You can simplify by multiplying both terms each by a different ratio that equals one, but also gives the terms common denominator. Multiplying the first one by x²/x² and the second by 3x/3x will do that for you.
After that you can group the terms into one fraction and simplify:
[tex]\frac{x - 8}{3x} - \frac{3x}{x^2} \\\\= \frac{x - 8}{3x}\times\frac{x^2}{x^2} - \frac{3x}{x^2} \times\frac{3x}{3x} \\\\= \frac{x^3 - 8x^2}{3x^3} - \frac{9x^2}{3x^3} \\\\= \frac{x^3 - 8x^2 - 9x^2}{3x^3} \\\\= \frac{x - 8 - 9}{3x}\\\\= \frac{x - 17}{3x}\\[/tex]
Answer:
The difference of [tex]\frac{x-8}{3x}-\frac{3x}{x^2}[/tex] is [tex]\mathbf{\frac{x-17}{3x}}[/tex]
Step-by-step explanation:
We need to find the difference: [tex]\frac{x-8}{3x}-\frac{3x}{x^2}[/tex]
Simplifying to find the difference:
[tex]\frac{x-8}{3x}-\frac{3x}{x^2}[/tex]
x is common in both 3x and x^2 so, we can cancel it out and we get:
[tex]=\frac{x-8}{3x}-\frac{3x}{x(x)}\\=\frac{x-8}{3x}-\frac{3}{x}[/tex]
Now, taking LCM of 3x and x we get 3x, We will multiply 3x with both terms and then solve we get:
[tex]=\frac{x-8-3(3)}{3x}\\=\frac{x-8-9}{3x}\\=\frac{x-17}{3x}[/tex]
It cannot be further simplified, so we get [tex]\frac{x-17}{3x}[/tex] as answer.
So, The difference of [tex]\frac{x-8}{3x}-\frac{3x}{x^2}[/tex] is [tex]\mathbf{\frac{x-17}{3x}}[/tex]
Pls help and show workings due ASAP
please help will mark brainliest
Answer:
[tex]m\angle N=57^{\circ}[/tex]
Step-by-step explanation:
From the isosceles-base theorem, the measure of the angles adjacent to the pair of congruent sides of the triangle are equal. Since the problem declares [tex]LM\cong LN[/tex], the remaining unknown angles are equal ([tex]m\angle N=m\angle M[/tex]). The sum of the interior angles of a triangle always add up to [tex]180^{\circ}$[/tex].
Therefore:
[tex]m\angle N\cdot 2+66=180,\\m\angle N\cdot 2=114,\\m\angle N=\fbox{$57^{\circ}$}[/tex] .
Answer:
LMN is rectangle in L so LMN= 180° ; ML=66°;N=? N= 180°- 66°=114=114/2= 57° so N=57°
Step-by-step explanation:
When the angle at the top is close to 0 °, the two of the base get less than 180 °, or less than 90 ° for each. If the angle at the top is 60 °, the other two are: 180 - 60 = 120 °, and each is: 120/2 = 60 °.
2. 4x + 5y = -30
Slope-standard form
A cherry pie has a 16 inch diameter. What is its approximate area? Round to the nearest hundredth. (Use 3.14 for π)
Answer:
200
Step-by-step explanation:
Formula to find the area: πr²
First, find the radius: 16 ÷ 2 = 8
The radius is 8. So...
= 3.14 (8²)
= 3.14 × 64
= 200.96
Rounded to the nearest hundredth: 200
Answer:
200.96
Step-by-step explanation:
A=3.14r^2(formula for area of a circle)
r=16/2=8
r=8
A=3.14*8^2=200.96
A store advertises 15% off an item that regularly sells for $300
what is the price of the item?
For this problem, we're finding the percent of 300. To do that we:
1. Multiply 300 by 15.
300 x 15 = 4500
2. Divide 4500 by 100. (% = 100)
4500 / 100 = 45
Therefore, the unit price is 45. But we're not done. We need to subtract 45 by 300.
300 - 45 = 255
Now, our answer is 255 and the unit price is 45.
Let me know of any questions!
Please answer as soon as possible.
Determine whether the quantities in each table represent a proportional relationship. If yes put the constant rate otherwise put no
Answer:
There is not a proportional relationship
Step-by-step explanation:
The first and second hour the pay is $9.50/hour, but in the third hour the pay is $11/hour. Then in the fourth hour it changes again to $10/hourIf there was a proportional relationship there would need to be a constant rate of change in pay.
Answer:
Yes, the proportional relationship is 9.50
Step-by-step explanation:
In the graph that you have attached this picture with, hours x 9.50 = pay.
Hope this helps :D
food delilah has 4 1/2 pies to divide equally among 9 people. how much would each person get
Answer:
4.5/9 = 0.5
half a pie each
Which shows how much water drips the faucet hour each
Answer:
2.5 ounces drip from the faucet per hour.
Step-by-step explanation:
You can figure this out by dividing the amount of water (7.5) by the hours (3).
7.5/3 = 2.5
To check your work you can do the same for the other combinations.
10/4=2.5, 12.5/5=2.5....
I hope this helped :)
f(x) = 2x^2-10x+13
Find f(-4)
Answer:
85
Step-by-step explanation:
2(-4)^2=32
-10(-4)=40
32+40+13=85
y = 2x + 4.6
m = ____ b = ____
fill in the blank !!!
Answer:
m = 2, b = 4.6
Step-by-step explanation:
The slope intercept formula is y = mx + b, So you can substitute for the values given.
3x² ×2x³
help please
Hope you have a good day!〜
Also please tell me if I'm wrong or not...
Also also if I'm right can I please have Brainliest?
.
plz help, I need help
Answer:
Answer is A
Step-by-step explanation:
because 2 × $11.50 is for adult tickets
$8 × 4 is for childrens tickets
and the equation would represent the total cost
An English book consists of two sections, literature and grammar, in a ratio of 3:2. How much of each type of content will be needed to make a book of 150 pages?
Answer:
For Literature = 90 pages
For Grammar = 60 pages
Step-by-step explanation:
An English book consists of two sections, literature and grammar, in a ratio of 3:2. How much of each type of content will be needed to make a book of 150 pages?
Literature : Grammar
3 : 2
Total number of Proportion = 3 + 2 = 5
For Literature
= 3/5 × 150 pages
= 90 pages
For Grammar
= 2/5 × 150 pages
= 60 pages
The sum of two numbers is 120. Three times
their difference is 48. What are the numbers?
TERS A.5(C) A.1(A), A1(B)
F. 16, 120
G 36, 52
H 52,68
J 68, 84
Pleasss help thank you :)
Answer:
The answer is 68 and 52
Step-by-step explanation:
x + y = 120
3(x - y ) = 48
We have 3x + 3y = 360
and 3x - 3y = 48
Adding we have the following:
6x = 408
x = 68
y = 120-48 = 52
Hi! during this pandemic it's kind of hard to learn math over the screen. no one is willing to help since my teachers are busy and my mom is confused. I Don't have friends to go to who could help me..So i'm hoping someone here could help! ...!!i cropped it so you could see better..Thanks!
Answer:
a) c=33.5
I'll try my best to explain and help you out here! online school sucks, I hope you get the hang of it soon!
Step-by-step explanation:
Simplify both sides of the equation.
c(5)=(35.5)(5)−10
5c=177.5+−10
5c=(177.5 + −10) (Combine Like Terms)
5c=167.5
Divide both sides by 5.
5c/5 = 167.5/5
c=33.5
I'm not entirely sure about the second question but I'll try to figure it out and let you know!
If it takes eight men ten hours to build a wall, how long would it take four men?
Answer:
20 bc if 8 men took 10 hours then 4 men would take double the time
Answer:
ha ha is it math question seriously or riddle if riddle the wall is already built by men they non time is taken by men.
IF YOU DO ALL THREE AND U ANSWER THEM CORRECTLY ILL GIVE YOU 50+ POINTS
❤️
Answer:
30 on the first one 5x6=30, the 2nd one is 5 and the 3 one is 10 chickens
Answer:
1. Zack has 6 times more seeds than Ben, if Ben has 5 seeds, just multiply how many seeds Ben has by 6, which means Zack planted 30 seeds (This can be written Z=B*6, where Z is how many seeds Zack has, and B is how many seeds Ben has)
2. If there are a total of 40 cards divided into 8 groups of students, that means that each group got 5 card (40 ÷ 8 = 5)
3. If each chicken has 2 wings, and she has a total of 20 wings, that means that she bought a total of 10 chickens (20 ÷ 2 = 10)
What is the domain and range?
Answer:
The domain D = {0, 1, 2, 3, 4, 5}
The range R = {3, 4}
Step-by-step explanation:
Given the ordered pairs or points on the graph
{(0, 4), (1, 4), (2, 4), (3, 3), (4, 3), (5, 3)}
We know that the domain of the function is the set of input or arguments for which the function is real and defined.
In other words,
Domain refers to all the possible sets of input values on the x-axis.It means the set of all the x-coordinates of the given points or ordered pairs on a graph will be the domain.
Thus,
The domain D = {0, 1, 2, 3, 4, 5}
Determining the range:
We also know that range is the set of values of the dependent variable for which a function is defined.
In other words,
Range refers to all the possible sets of output values on the y-axis.It means the set of all the y-coordinates of the given points or ordered pairs on a graph will be the range.
Thus,
The range R = {3, 4}
Note: Please note that the duplicated elements in the range are written only once.
Find the average rate of change
f(x)=x^2−6x+8 when x2=1 and x1=3
Answer:
Average rate of change for given function is: -2
Step-by-step explanation:
Given function is:
[tex]f(x)=x^2-6x+8\\x_12= 1\\x_1 = 3[/tex]
In order to find the rate of change, we have to find the value of function on x1 and x2
So,
[tex]f(x_1) = (3)^2-6(3)+8 = 9-18+8 = -1\\f(x_2) = (1)^2-6(1)+8 = 1-6+8 = 3[/tex]
The formula for finding the rate of change is:
[tex]Rate\ of\ change = \frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
Putting the values, we get
[tex]=\frac{3-(-1)}{1-3}\\=\frac{3+1}{-2}\\=\frac{4}{-2}\\= -2[/tex]
Hence,
Average rate of change for given function is: -2
Answer:
Average rate of change for given function is: -2
Step-by-step explanation:
Sammie read at the rate of 25 pages per hour. Alex read at the rate of 1/2 of a pages per minute. Who was reading faster? By how many pages per hour faster?
Answer:
Alex is reading faster by 5 more pages per hour.
Step-by-step explanation:
Alex's rate of reading is 1/2 pages per minute, or 1 page every 2 minutes. To convert his rate to pages per hour, we can divide 60 (minutes in an hour) by 2 (minutes it takes Alex to read a page) which is equal to 30 (pages read in an hour). Therefore, Alex is reading at 30 pages an hour and reading 5 more pages an hour than Sammie.