Answer:
7740° / 45
Step-by-step explanation:
The sum of the interior angles is given by this formula: (n - 2) * 180°. So a regular 45-gon would have interior angles that add up to: (45 - 2) * 180°. = 43 * 180°. = 7740°. Now divide that by the 45 angles to find the measure of one interior angle
hope that helped :(
The measure of each exterior angle of a regular 45-gon is calculated using the formula: Exterior Angle = 360° / Number of Sides. Hence, each exterior angle of a 45-gon measures 8°.
Explanation:In mathematics, the measure of each exterior angle of a regular polygon can be found using the formula: Exterior Angle = 360° / Number of Sides. So, to find the measure of an exterior angle in a 45-sided shape, or 45-gon, you would perform the calculation: 360° / 45 = 8°.
This indicates that each exterior angle of a regular 45-gon measures 8 degrees. This is a key concept to remember when working with regular polygons, as it can be used to determine other characteristics of the shape such as the sum of the exterior angles, which in any polygon is always 360°.
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sorry but i need your help (again) :
given the quadratic function f(x)= 3x²- 6x + 1
express the quadratic function f(x) in the form a(x+p)²+q, where a, p and q are constants. determine whether f(x) has a maximum or minimum value and state the value.
Answer:
It's minimum value
and the value is :(1 , -2)
Answer:
see explanation
Step-by-step explanation:
Given
f(x) = 3x² - 6x + 1
To express in vertex form
f(x) = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Use the method of completing the square
The coefficient of the x² must be 1, so factor out 3
f(x) = 3(x² - 2x) + 1
add/subtract ( half the coefficient of the x- term )² to x² - 2x
f(x) = 3(x² + 2(- 1)x + 1 - 1) + 1
= 3(x - 1)² - 3 + 1
= 3(x - 1)² - 2 ← in vertex form
with vertex = (1, - 2)
To determine if vertex is a max/ min
• If a > 0 then minimum
• If a < 0 then maximum
here a = 3 > 0 ⇒ minimum at (1, - 2)
The minimum value is the y- coordinate of the vertex, that is
minimum value = - 2
In the diagram shown above, ABCD is a parallelogram. The ratio of the area of triangle AGB to the area of triangle CGE is 9:25. If CG=10 and GE=15 find AG.
Answer:
The answer should be A.
Answer: The Answer is A.) AG=6
Step-by-step explanation:
Maria solved an equation as shown below. What is the solution to Maria’s equation?
Answer:
[tex]x=19[/tex]
Step-by-step explanation:
We have the following equation
[tex]3(x+6)=5(x-4)[/tex]
Notice that in this equation the variable that we want to find is x.
Then the equation for the variable x must be solved
After applying the distributive property and simplifying the equation Maria obtained the following result
[tex]19=x[/tex]
This is the same as:
[tex]x=19[/tex]
That means that the value of x for which equality is met is [tex]x = 19[/tex]. Therefore the solution of the equation is [tex]x = 19[/tex]
10x +2y = 64
3x - 4y = -36
Use the elimination method to solve the system of equation. Choose the correct ordered pair
Answer:
x = 4, y = 12 → (4, 12)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}10x+2y=64&\text{multiply both sides by 2}\\3x-4y=-36\end{array}\right\\\underline{+\left\{\begin{array}{ccc}20x+4y=128\\3x-4y=-36\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad23x=92\qquad\text{divide both sides by 2}\\.\qquad x=4\\\\\text{put the value of x to the first equation:}\\\\10(4)+2y=64\\40+2y=64\qquad\text{subtract 40 from both sides}\\2y=24\qquad\text{divide both sides by 2}\\y=12[/tex]
The previous rectangular prism had a surface area of 254 square inches. If each dimension is doubled, how does the surface area change?
The surface area doubles.
The surface area triples.
The surface area increases by 4 times.
The surface area increases by 8 times.
Answer:
The surface area increases by 4 times
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
Let
z -----> the scale factor
x ----> the surface area of the new rectangular prism
y ---> the surface area of the original rectangular prism
so
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=2[/tex] ----> because is doubled
[tex]y=254\ in^{2}[/tex]
substitute and solve for x
[tex]2^{2}=\frac{x}{254}[/tex]
[tex]x=(4)254=1,016\ in^{2}[/tex] ----> surface area increases by 4 times.
Answer:
The surface area increases by four times.
Step-by-step explanation:
Which formula can be used to determine the total number of different eight-letter arrangements that can be formed using the letters in the word "CLIMBING"?
The word "climbing" has 8 letters, so there are [tex]8![/tex] permutations of all the letters.
Nevertheless, the letters are not unique: there are 2 I's. This means that, if we start from a given word and we exchange the positions of the two I's, we'd still get the same word. So, we have to divide the number of possible permutations by [tex]2![/tex], because for any given permutation there are two identical words, given by the interchange of the I's.
So, the number of possible words is
[tex]\dfrac{8!}{2!} = \dfrac{8\times7\times6\times5\times4\times3\times2}{2}=8\times7\times6\times5\times4\times3=40320[/tex]
Which is equivalent to sin-1(–0.4)? Round your answer to the nearest hundredth of a radian.
Answer:
-0.41 radians
Step-by-step explanation
(Credit goes to calculista)
let
A---> the angle
if sin A=-0.4
then
A=sin-1(-0.4)
using a calculator
A=-23.578°----> the angle A belong to the IV quadrant
convert to radians
if pi radians--]----> 180°
x--------> -23.578°
x=-23.578*pi/180----> x=-0.41 radians
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Answer:
C. –0.41
Step-by-step explanation:
What are the x-intercepts of the function f(x) = 2x^2 - 3x + 20?
There are two: -4 and -5/2
Steps
0 = (2x - 5)(x + 4) | FOIL (distribution)
2x = 5 | zero product rule
x = 5/2 <<<
x = -4 <<< | zero product rule again.
Solve the equation.
8(4-x) = 7x + 2
Answer:
x = 2.
Step-by-step explanation:
8(4-x) = 7x + 2
32 - 8x = 7x + 2
32 - 2 = 7x + 8x
15x = 30
x =2.
Ava wants to figure out the average speed she is driving. She starts checking her car’s clock at mile marker 0. It takes her 4 minutes to reach mile marker 3. When she reaches mile marker 6, she notes that 8 minutes total have passed since mile marker 0.
What is the average speed of the car in miles per minute?
mile(s) per minute
What is an equation of the line that represents n, the number of mile marker passed, as a function of t, time in minutes?
Answer:
0.75 mile(s) per minute
n-6=0.75(t-8)
hope this helps!!
Step-by-step explanation:
Answer:
0.75 miles per minute
Equation: n - 6 = 0.75(t - 8)
Step-by-step explanation:
took the test and got it right
.
What is the area of the irregular polygon shown below?
O
A. 65 sq. units
O
B. 49 sq. units
O
C. 105 sq. units
O
D. 35 sq. units
Answer:
Option B: 49 square units.
Step-by-step explanation:
The irregular polygon consists of a rhombus a square.
Area of rhombus = 0.5*(product of diagonals).
Area of square = length * length = l^2.
The diagonals of the rhombus measure 8 units and 6 units respectively. The diagram shows the length of half of the diagonals, so doubling both the lengths gives us the required lengths. The side of the square measures 5 units. Substituting all the information in the formula:
Total Area = Area of rhombus + Area of square.
Total Area = 0.5*8*6 + 5^2.
Total Area = 24 + 25
Total Area = 49 square units.
Therefore, Option B is the correct answer!!!
If x+y = z and y−z=x which of the following must be equal to z?
(A) 0 (B) x (C) y (D) −x (E) –y
ANSWER
(C) y
EXPLANATION
We have two equations:
The first one is
[tex]x + y = z...(1)[/tex]
The second equation is
[tex]y - z = x...(2)[/tex]
Let us make z the subject of this second equation:
[tex] \implies \: -x +y = z...(3)[/tex]
We now add equation (1) and (3) to get:
[tex](-x + x) + (y + y) = z + z[/tex]
We simplify to get:
[tex]0+2y= 2z[/tex]
[tex]2y= 2z[/tex]
Divide throu by 2.
[tex] \frac{2y}{2} = \frac{2z}{2} [/tex]
[tex]y= z[/tex]
[tex] \therefore \: z = y[/tex]
The correct answer is C
The equation of a linear function in point-slope form is y - y1 = m(x - Xt). Harold correctly wrote the equation y = 3(x -
7) using a point and the slope. Which point did Harold use?
When Harold wrote his equation, the point he used was (7,3).
When Harold wrote his equation, the point he used was (0, 7).
When Harold wrote his equation, the point he used was (7,0).
When Harold wrote his equation, the point he used was (3, 7).
Answer:
When Harold wrote his equation, the point he used was (7,0).
Step-by-step explanation:
we know that
The equation of a line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
where
(x1,y1) is the point
m is the slope
In this problem we have
[tex]y=3(x-7)[/tex]
therefore
the point is (x1,y1)=(7,0)
the slope is m=3
A credit union pays 5% annual interest, compounded daily, on savings deposits. Find the value after one year of $500 deposited in this account.
$525.64
$25.64
$20.40
$520.40
Step-by-step answer:
Given:
5% annual interest (APR)
compounded daily
Principal = 500
Solution:
Since it is compounded daily, we first calculate the
daily rate = 5% / 365 = 0.05/365
After one year,
future value
= 500 ( 1 + 0.05/365)^365
= 525.634 (to the tenth of a cent)
note: sometimes a year is considered to be rounded to 360 days, or 366 days for a leap year, but there is practically no difference in the results for this problem.
Final answer:
To calculate the future value of a $500 deposit with a 5% annual interest rate compounded daily for one year, we use the compound interest formula. The resulting amount is approximately $525.64.
Explanation:
To calculate the value of a $500 deposit in a credit union that pays 5% annual interest compounded daily, we will use the formula for compound interest:
A = P(1 + (r/n))^(nt)
Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money).
r = the annual interest rate (decimal).
n = the number of times that interest is compounded per year.
t = the time the money is invested or borrowed for, in years.
Using the given information:
P = $500
r = 5% or 0.05 (as a decimal)
n = 365 (since the interest is compounded daily)
t = 1 year
Substituting the values into the formula:
A = 500(1 + (0.05/365))^(365*1)
After calculating, we get:
A ≈ $525.64
Therefore, the value of the $500 deposit at the end of one year with daily compounding at a 5% annual interest rate is approximately $525.64.
1. There were 36,000 people at a horse race in Lexington, Kentucky. The day's
receipts were $250,000. The only two types of seats available were clubhouse
or grandstand seats. How many people paid $12.00 for clubhouse seats and
how many people paid $5.00 for grandstand seats? Only an algebraic solution
will earn credit. State what any variables represent by writing a "let statement”.
Answer:
10000 people paid $12.00 each for clubhouse seats and26000 people paid $5.00 each for grandstand seats.Step-by-step explanation:
The question is asking for a system of equations, which make explanations easy. :)
Define the variables. Setting [tex]x[/tex] to the number of clubhouse seats sold and [tex]y[/tex] to the number of grandstand seats sold will be sufficient. The "let statement[s]" will be:
Let [tex]x[/tex] be the number of clubhouse seats sold.Let [tex]y[/tex] be the number of grandstand seats sold.The number of equations shall be no less than the number of variables for the solution to be unique. There are two variables. It will take at least two equations to find a unique solution.
Everyone at the race need a seat. The number clubhouse seats plus the number of grandstand seats shall be the same as the number people at the race. There were 36,000 people. Therefore the first equation shall be:
[tex]x + y = 36000[/tex].
Every clubhouse seat will add $12.00 to the receipt. [tex]x[/tex] clubhouse seats will add $[tex]12\;x[/tex] to the receipt. Similarly, [tex]y[/tex] grandstand seats will add $[tex]5\;y[/tex] to the receipt. The two values shall add up to $250,000.
Drop the dollar sign to get the second equation:
[tex]12\;x +5\;y =250000[/tex].
Hence the system:
[tex]\displaystyle \left\{\begin{aligned}& x + y = 36000 && \textcircled{\raisebox{-0.9pt}1}\\ & 12\;x + 5\;y = 250000 && \textcircled{\raisebox{-0.9pt}2}\end{aligned} \phantom{\small credit for the raisebox hack: tex[dot]stackexchange[dot]com/questions/7032/good-way-to-make-textcircled-numbers}[/tex].
Solve this system.
The first non-zero coefficient in equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] is already one. That's the coefficient for [tex]x[/tex]. Use multiples of equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] to get rid of [tex]x[/tex] in other equations (equation [tex]\textcircled{\raisebox{-0.9pt}2}[/tex] in this case.)
[tex]-12[/tex] times equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] is
[tex]-12 \;x - 12\;y = -432000[/tex].
Add [tex]-12\times \textcircled{\raisebox{-0.9pt}1}[/tex] to [tex]\textcircled{\raisebox{-0.9pt}2}[/tex] to get:
[tex]0\;x + -7\;y = -182000[/tex].
Divide both sides by -7 to get:
[tex]y = 26000[/tex].
Add -1 times this equation to equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] to get:
[tex]x = 10000[/tex].
That is:
[tex]\displaystyle \left\{\begin{aligned}&x = 10000\\&y = 26000\end{aligned}[/tex].
In other words,
10000 clubhouse seats were sold, and26000 grandstand seats were sold.Which is the correct formula to calculate the volume of a cone?
Answer:
Multiply all the sides
Step-by-step explanation:
Multiply every side together and you should get your answer just make sure you put the right unit hope this helped :)
If f(x) =-x^2 +6 x-1 and g(x) =3x^2-4x-1 find ( f+g) (x)
[tex](f+g)(x)=-x^2+6x-1+3x^2-4x-1=2x^2+2x-2[/tex]
Answer: [tex](f+g)(x)=2x^2+2x-2[/tex]
Step-by-step explanation:
Given the function f(x), which is:
[tex]f(x)=-x^2 +6x-1[/tex]
And the function g(x), which is:
[tex]g(x) =3x^2-4x-1[/tex]
You can observe that [tex](f+g)(x)[/tex] indicates that you need to add the functions, then you know that:
[tex](f+g) (x)=(-x^2+6 x-1)+(3x^2-4x-1)[/tex]
Finally, to simplify it you must addthe like terms. Therefore, you get that [tex](f+g)(x)[/tex] is:
[tex](f+g)(x)=-x^2+6 x-1+3x^2-4x-1[/tex]
[tex](f+g)(x)=2x^2+2x-2[/tex]
Origami is the Japanese art of paper folding. The diagram below represents
an unfolded paper kabuto, a samurai warrior's helmet. Which of the following
are pairs of congruent segments?
Check all that apply.
Answer:
The correct options are B, C and D.
Step-by-step explanation:
It is given that the figure is a Japanese art of paper folding. It means the figure have many lines of symmetry (i.e., AK, IO, CM and NF).
From the figure it is clear that HV is larger than GW, so segment HV and GW are not pairs of congruent segments.
Therefore option A is incorrect.
[tex]\overline{IJ}\cong \overline{LM}[/tex] (AK is line of symmetry)
[tex]\overline{AB}\cong \overline{AP}[/tex] (AK is line of symmetry)
[tex]\overline{BC}\cong \overline{PO}[/tex] (AK is line of symmetry)
Therefore the correct options are B, C and D.
From the figure it is clear that PO is smaller than ON, so segment HV and GW are not pairs of congruent segments.
Therefore option E is incorrect.
Jack is organizing his shots he has 20 pair of socks there are seven pair of black socks eight pair of blue socks and the rest of the pair or white how many pair of socks are white
A fish tank is in the shape of a rectangular prism with dimensions 30 in. by 12 in. by 15 in. The tank is 90% filled with water.
How much water is in the tank?
Answer:
4860 in ^3
Step-by-step explanation:
First we find the volume of the tank
V = l*w*h
V = 30*12*15
V = 5400 in ^3
It is 90% full so we multiply by 90 %
5400 * 90%
5400 * .90
4860 in ^3
PLEASE HELP ME WITH THIS QUESTION ASAP!!!!
Answer:
137°Step-by-step explanation:
The pentagon RSTYZ is a regular polygon. Therefore all angles are congruent.
If m∠RST = 108°, then m∠STY = 108°.
We have the equation:
m∠UTY + m∠STY + m∠STU = 360°.
Substitute m∠STY = 108° and m∠UTY = 115°.
115° + 108° + m∠STU = 360°
223° + m∠STU = 360° subtract 223° from both sides
m∠STU = 137°
The slope of a line is
-1/5 and the y-intercept is 5. What is the equation of the line written in general form?
0x-51-25=0
0x-5y-5=0
X + 5y - 25 = 0
Answer:
Step-by-step explanation:
This is impossible to figure out because 0 = 0x, as defined by the Zero Property of Multiplication. I apologize.
Quiz 4: Solving Inequalities
Elijah wants to hire a painter and keep his total bill to at most $100. The painter charges a $60 flat fee to come to his house and then $15 per hour. Which inequality best
represents the situation if x represents the number of hours the painter works?
Answer:
[tex]15x+60\leq 100[/tex]
Step-by-step explanation:
Let
x -----> the number of hours that the painter works
we know that
The inequality that represented this situation is equal to
[tex]15x+60\leq 100[/tex]
solve for x
Subtract 60 both sides
[tex]15x\leq 100-60[/tex]
[tex]15x\leq 40[/tex]
Divide by 15 both sides
[tex]x\leq 40/15[/tex]
[tex]x\leq 2.67\ hours[/tex]
The maximum number of hours is 2
Which equation represents a line that passes through (5, 1) and has a slope of 1/2?
Oy-5= {(x-1)
Oy- z = 5(x-1)
O y-1 = {(x+5)
O y-1= 5(x-1)
Answer:
C
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = [tex]\frac{1}{2}[/tex] and (a, b) = (5, 1), so
y - 1 = [tex]\frac{1}{2}[/tex](x - 5)
The equation that represents a line that passes through (5, 1) and has a slope of 1/2 is; C: y - 1 = ¹/₂(x - 5)
What is the Equation of the Line?The formula for equation of a line in point- slope form is expressed as;
y - b = m(x - a)
where;
m is the slope of line
(a, b) is a coordinate point on the line
In this question, we are given;
m = 1/2 and (a, b) = (5, 1)
Thus equation of the line is;
y - 1 = ¹/₂(x - 5)
Read more about Equation of Line at; https://brainly.com/question/13763238
What is the third quartile, Q3, of the following distribution?
4,5, 33, 10, 12, 14, 34, 43, 21, 22, 21, 22, 44, 29, 16, 18, 20, 24, 26, 29
Answer:
The third quartile is:
[tex]Q_3=29[/tex]
Step-by-step explanation:
First organize the data from lowest to highest
4, 5, 10, 12, 14, 16, 18, 20, 21, 21, 22, 22, 24, 26, 29, 29, 33, 34, 43, 44
Notice that we have a quantity of n = 20 data
Use the following formula to calculate the third quartile [tex]Q_3[/tex]
For a set of n data organized in the form:
[tex]x_1, x_2, x_3, ..., x_n[/tex]
The third quartile is [tex]Q_3[/tex]:
[tex]Q_3=x_{\frac{3}{4}(n+1)}[/tex]
With n=20
[tex]Q_3=x_{\frac{3}{4}(20+1)}[/tex]
[tex]Q_3=x_{15.75}[/tex]
The third quartile is between [tex]x_{15}=29[/tex] and [tex]x_{16}=29[/tex]
Then
[tex]Q_3 =x_{15} + 0.75*(x_{16}- x_{15})[/tex]
[tex]Q_3 =29 + 0.75*(29- 29)\\\\Q_3 =29[/tex]
Answer:
29
Step-by-step explanation:
The temperature of an oven went from 280 to 350 what was the percent increase in temperature
Answer:
25% Increase
Step-by-step explanation:
[(350 - 280) / 280] × 100% = 0.25 × 100% = 25%
The function P(x) = 3x2 + 4x + 5,is dilated by the function I(x) = P(2x). Write the new function I(x).
Answer:
I(x) = 12x² + 8x + 5
Step-by-step explanation:
* Lets talk about the solution
- P(x) is a quadratic function represented graphically by a parabola
- The general form of the quadratic function is f(x) = ax² + bx + c,
where a is the coefficient of x² and b is the coefficient of x and c is
the y-intercept
- To find I(x) from P(x) change each x in P by 2x
∵ P(x) is dilated to I(x) by change x by 2x
∵ I(x) = P(2x)
∵ P(x) = 3x² + 4x + 5
∴ I(x) = 3(2x)² + 4(2x) + 5 ⇒ simplify
∵ (2x)² = (2)² × (x)² = 4 × x² = 4x²
∵ 4(2x) = 8x
∴ I(x) = 3(4x²) + 8x + 5
∵ 3(4x²) = 12x²
∴ I(x) = 12x² + 8x + 5
help me please with this question
Answer:
B
Step-by-step explanation:
Ratio of sides = a : b , then
Ratio of volumes = a³ : b³
Here the ratio of volumes = 27 : 729, hence
Ratio of sides = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{729}[/tex] = 3 : 9
Ratio of sides = 3 : 9 = 1 : 3 ← in simplest form
Hence sides of larger cube are 3 times sides of smaller cube → B
Evaluate a + 6 for a = 10?
6
16
60
What is the approximate value of 0, if cos 0=8/15 ?
Answer:
The approximate value of angle theta is [tex]57.8\°[/tex]
Step-by-step explanation:
we have that
[tex]cos(\theta)=8/15[/tex]
so
using a calculator
[tex]\theta=arccos(8/15)=57.8\°[/tex]
Answer:
for plato or edmentum its option A 50 degrees
Step-by-step explanation: