Answer:
Triangle
Step-by-step explanation:
A regular polygon of n sides has interior angles of:
a = 180 (n-2) / n
Given a = 60:
60 = 180 (n-2) / n
n = 3 (n-2)
n = 3n - 6
6 = 2n
n = 3
The polygon has three sides, so it's a triangle.
A regular polygon with each angle measuring 60° is an equilateral triangle.
A regular polygon is a polygon with all sides and angles equal. To find the type of polygon where each angle measures 60°, we use the formula for the measure of each interior angle of a regular polygon, which is (n-2) x 180° / n, where n is the number of sides.
Let's solve for n:
Set the angle measure formula to 60°: (n-2) x 180° / n = 60°
Multiply both sides by n to clear the fraction: (n-2) x 180° = 60n
Distribute 180°: 180n - 360° = 60n
Move the terms involving n to one side: 180n - 60n = 360°
Simplify: 120n = 360°
Divide both sides by 120: n = 3
Therefore, a regular polygon with each angle measuring 60° is an equilateral triangle.
Problem
At full speed, Hal travels 600 miles in 2 hours
with the wind. The same distance against
the wind takes 3 hours.
What's the maximum speed of Hal's airplane
in still air? What's the speed of the wind?
Answer:
The maximum speed of Hal's airplane in still air is:
[tex]v= 250\ miles/h[/tex]
The speed of the wind
[tex]c = 50\ miles/h[/tex]
Step-by-step explanation:
Remember that the velocity v equals the distance d between time t.
[tex]v=\frac{d}{t}[/tex] and [tex]t*v=d[/tex]
The distance that Hal travels when traveling with the wind is:
[tex](2\ hours)(v + c) = 600[/tex] miles
Where v is the speed of Hal and c is the wind speed.
The distance when traveling against the wind is:
[tex](3\ hours)(v-c) = 600[/tex] miles
Now we solve the first equation for v
[tex](2)(v + c) = 600[/tex]
[tex]2v + 2c = 600[/tex]
[tex]2v= 600-2c[/tex]
[tex]v= 300-c[/tex]
Now we substitute the value of v in the second equation and solve for c
[tex]3((300-c)-c) = 600[/tex]
[tex]3(300-2c) = 600[/tex]
[tex]900-6c = 600[/tex]
[tex]-6c = 600-900[/tex]
[tex]-6c = -300[/tex]
[tex]6c = 300[/tex]
[tex]c = 50\ miles/h[/tex]
Then:
[tex]v= 300-(50)[/tex]
[tex]v= 250\ miles/h[/tex]
The maximum speed of Hal's airplane in still air is:
[tex]v= 250\ miles/h[/tex]
The speed of the wind
[tex]c = 50\ miles/h[/tex]
Which function is shown in the graph below?
Answer:b
Step-by-step explanation: you graph each answer choice and see which one looks like the graph
Answer: The correct option is
(B) [tex]y=\left(\dfrac{1}{2}\right)^{x-3}+1.[/tex]
Step-by-step explanation: We are given to select the function that is shown in the graph.
From the graph, we know that
if the function is represented by y = f(x), then f(0) = 9. That is, the value of y at x = 0 is 9.
Option (A) : Here, the given function is
[tex]y=\left(\dfrac{1}{2}\right)^{x+3}-1.[/tex]
So, at x = 0, the value of y is given by
[tex]y(x=0)=\left(\dfrac{1}{2}\right)^{0+3}-1=\dfrac{1}{8}-1=-\dfrac{7}{8}\neq 9.[/tex]
So, this option is not correct.
Option (B) : Here, the given function is
[tex]y=\left(\dfrac{1}{2}\right)^{x-3}+1.[/tex]
So, at x = 0, the value of y is given by
[tex]y(x=0)=\left(\dfrac{1}{2}\right)^{0-3}+1=\left(\dfrac{1}{8}\right)^{-1}+1=8+1=9.[/tex]
So, this option is CORRECT.
Option (C) : Here, the given function is
[tex]y=\left(\dfrac{1}{2}\right)^{x-1}+3.[/tex]
So, at x = 0, the value of y is given by
[tex]y(x=0)=\left(\dfrac{1}{2}\right)^{0-1}+3=2+3=5\neq 9.[/tex]
So, this option is not correct.
Option (D) : Here, the given function is
[tex]y=\left(\dfrac{1}{2}\right)^{x+1}-3.[/tex]
So, at x = 0, the value of y is given by
[tex]y(x=0)=\left(\dfrac{1}{2}\right)^{0+1}-3=\dfrac{1}{2}-3=-\dfrac{5}{2}\neq 9.[/tex]
So, this option is not correct.
Thus, (B) is the correct option.
What is the simplest form of 3square root 27a3b7
Answer:
= [tex]3ab^{\frac{2}{3} }[/tex]
Step-by-step explanation:
∛(27 a³ [tex]b^{7}[/tex])
= ∛27 · ∛a³ · ∛b³ · ∛b³ · ∛b
= 3 · a · b · b ∛b
= 3ab² [tex]b^{\frac{1}{3} }[/tex]
or
= [tex]3ab^{\frac{2}{3} }[/tex]
How many vertical asymptotes does the graph of this function have f(x)=3/(x-11)(x+4)
Answer:
2
Step-by-step explanation:
The function is given as [tex]f(x)=\frac{3}{(x-11)(x+4)}[/tex]
Vertical asymptotes occur when the denominator is set to 0.
Thus,
(x-11)(x+4) = 0
x = 11 or x = -4
Hence, there are 2 vertical asymptotes
Answer: 2
Step-by-step explanation:
A P E X
how do I solve y^4-13y^2+36=0
Answer:
The roots are {-3, -2, 2, 3}.
Step-by-step explanation:
The trick here is to represent y² by some other letter, such as x. If we do that, then y^4-13y^2+36=0 becomes x² - 13x + 36 = 0.
Recognize that the factors -4 and -9 of 36 sum up to 13. Thus,
x² - 13x + 36 = 0 is equivalent to (x - 4)(x - 9) = 0, and x = 4 or x = 9.
Recall that x = y².
When x = 4: y² = 4, and so y = ±2.
When x = 9, y² = 9, and so y = ±3.
The roots are {-3, -2, 2, 3}.
The roots of the bi-quadratic equation y⁴ - 13y² + 36 = 0 are,
- 2, 2, -3, 3.
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
Given, y⁴ - 13y² + 36 = 0.
This a bi-quadratic polynomial.
Let, x = y².
Therefore,
x² - 13x + 36 = 0.
x² - 4x - 9x + 36 = 0.
x(x - 4) - 9(x - 4) = 0.
(x - 4)(x - 9) = 0.
x = 4 Or x = 9.
Now,
For x = 4 ⇒ y² = 4 ⇒ y = ± 2.
For x = 9 ⇒ y² = 9 ⇒ y = ± 3.
So, The roots of the biquadratic equation are - 2, 2, -3, 3.
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Write the expression in complete factored form.
2p(n + 9) + q(n + 9) =
Answer:
(n+9) (2p+q)
Step-by-step explanation:
2p(n + 9) + q(n + 9) =
Factor out the term (n+9)
(n+9) (2p+q)
This is completely factor
Which two- way table contains the same information as the venn diagram?
Answer: C
Step-by-step explanation:
20 people have a dog: 8 are yes dog/yes cat & 12 are yes dog/no cat
17 people have no dog: 10 are no dog/yes cat & 7 are no dog/no cat
[tex]\begin{array}{c|c|c|c}\underline{\qquad \qquad}&\underline{Cat}&\underline{No\ Cat}&\underline{TOTAL}\\Dog&8&12&20\\\underline{\ No\ Dog\ }&\underline{\ 10\ }&\underline{\quad 7\quad }&\underline{\quad 17\quad }\\TOTAL&18&19&37\end{array}[/tex]
which function is odd check all that apply
a. y=sin x
b. y=csc x
c. y=cot x
d. y=sec x
Answer:
a) y = sin x
b) y = csc x
c) y = cot x
Step-by-step explanation:
only d is even
Type the correct answer in each box. Use numerals instead of words.
You reflect triangle PQR, with coordinates P(-4, -4), Q(-1, -3), and R(-3, -1), across the x-axis, across the y-axis, and across the x-axis again to form triangle P′Q′R′.
After these reflections, the coordinates of P′ will be (,
Answer:
After these reflections, the coordinates of P′ will be (4 , -4)
Step-by-step explanation:
* Lets revise some transformation
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
* Lets solve the problem
- The triangle PQR with coordinates P(-4, -4), Q(-1, -3), and R(-3, -1)
- The triangle is reflected across the x-axis
∵ Δ PQR is reflected across the x-axis
∴ All y-coordinates of the vertices P, Q , R reversed their signs
∴ The new points will be (-4 , 4) , (-1 , 3) , (-3 , 1)
- The new vertices will reflected across the y-axis
∴ All x-coordinates of the new vertices reversed their signs
∴ The new points will be (4 , 4) , (1 , 3) , (3 , 1)
- The new vertices will reflected across the x-axis to form Δ P'Q'R'
∴ All y-coordinates of the new vertices reversed their signs
∴ P' = (4 , -4) , Q' = (1 , -3) , R' = (3 , -1)
* After these reflections, the coordinates of P′ will be (4 , -4)
Final answer:
After reflecting triangle PQR across the x-axis, then the y-axis, and the x-axis again, point P' will have coordinates (4, -4).
Explanation:
Reflecting a triangle across an axis involves flipping the triangle over that axis. Each reflection inverses the corresponding coordinate (x or y) of each vertex of the triangle, while the other coordinate remains the same. Starting with the first reflection across the x-axis, the y-coordinate of each point negates, but the x-coordinate remains unchanged. The second reflection is across the y-axis, which negates the x-coordinate and keeps the y-coordinate (already negated from the first reflection) the same. The third reflection across the x-axis negates the y-coordinate again, effectively returning it to its original value before the first reflection. So for point P(-4, -4), after these reflections, the new coordinates for P' will be (4, -4).
whats the difference of 2 times d minus 3
a.2
b.1 c.4
d.3
e.0
Answer:
2(d - 3) is the equation. You cannot solve for d. You can only simplify it
How do you answer a, b and c, answers and also how you worked it out
We can either convert to standard form first or convert to a common multiplier, kinda like a common denominator. The latter makes more sense if they wanted the result in scientific notation, but let's do it that way anyway.
a)
4.5 × 10⁴ + 3.8 × 10³ = 45 × 10³ + 3.8 × 10³ = 48.8× 10³ = 48,800
Answer: 48,800
b)
4.5 × 10⁴ - 3.8 × 10³ = 45 × 10³ - 3.8 × 10³ = 41.2× 10³ = 41,200
Answer: 41,200
c)
7.2 × 10⁻³ + 6.3 × 10⁻² = 7.2 × 10⁻³ + 63 × 10⁻³ = 70.2 × 10⁻³
= 7.02 × 10⁻² = 0.0702
Answer: 0.0702
The function y = x^2 - 4x + 5 approximates the height, y, of a bird, and its
horizontal distance, x, as it flies from one fence post to another. All distances
are in feet. Complete the square to find and interpret the extreme value
(vertex).
Select two answers: one extreme value and one interpretation.
Height (feet)
Distance (feet)
Answer:
Option C and option D
Step-by-step explanation:
we have that
[tex]y=x^{2}-4x+5[/tex]
This is the equation of a vertical parabola open upward
The vertex is a minimum
Convert the equation into vertex form
Complete the square
[tex]y-5=x^{2}-4x[/tex]
[tex]y-5+4=x^{2}-4x+4[/tex]
[tex]y-1=x^{2}-4x+4[/tex]
[tex]y-1=(x-2)^{2}[/tex]
[tex]y=(x-2)^{2}+1[/tex] ----> equation of the parabola in vertex form
The vertex is the point (2,1)
therefore
when the bird is 2 feet away from the first fence post, it reaches its minimum height of 1 foot
Answer: C and D
Step-by-step explanation:
which expression is equivalent to...
Answer:
C
Step-by-step explanation:
Use exponents property:
[tex]\dfrac{x^a}{x^b}=x^{a-b}[/tex]
1. Note that
[tex]\dfrac{x^7}{x^{11}}=x^{7-11}=x^{-4}=\dfrac{1}{x^4}[/tex]
and
[tex]\dfrac{y^6}{y^8}=y^{6-8}=y^{-2}=\dfrac{1}{y^2}[/tex]
2. Now
[tex]\sqrt{\dfrac{55x^7y^6}{11x^{11}y^8}}=\sqrt{\dfrac{5}{x^4y^2}}=\dfrac{\sqrt{5}}{\sqrt{x^4}\sqrt{y^2}}=\dfrac{\sqrt{5}}{x^2y}[/tex]
because [tex]x>0,\ y>0[/tex]
40 points?With explanation
Answer:
46°
Step-by-step explanation:
Alternate angles from 46° and alternate angles are equal
The sum of the numerator and the denominator of
a fraction is 4 more than twice the numerator. If 3
is added to each of the numerator and denominator,
their ratio becomes 2 : 3. Find the fraction.
Step-by-step explanation:
(1)
Let the numerator be x and denominator be y. A/Q x + y = 4 + 2x → - x + y = 4
(2)
multiplying each term by 2, 2x-2y= -8
(3)
Also, (x+3) / (y+3) = 2 / 3 → 3x - 2y = -3
Subtracting (2) from (3) → x = 5 and by putting this in (1) we can get y=9. Hence, the fraction is 5 / 9
Answer:
[tex]\frac{5}{9}[/tex]
Step-by-step explanation:
let the fraction be [tex]\frac{x}{y}[/tex], then
x + y = 2x + 4 ( subtract x from both sides )
y = x + 4 → (1)
If 3 is added to numerator and denominator, then
[tex]\frac{x+3}{y+3}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )
3(x + 3) = 2(y + 3) ← distribute both sides
3x + 9 = 2y + 6 ← substitute y = x + 4
3x + 9 = 2(x + 4) + 6
3x + 9 = 2x + 8 + 6 = 2x + 14 ( subtract 2x from both sides )
x + 9 = 14 ( subtract 9 from both sides )
x = 5
Substitute x = 5 into (1)
y = 5 + 4 = 9
Hence the original fraction is [tex]\frac{5}{9}[/tex]
How to write (3+4i)+(8+2i) as a complex number in standard form
Answer:
Answer is 11+6i
Step-by-step explanation:
You just have to add imaginary part together and the real part. The answer will be 11+6i
Answer: 11+6i
Step-by-step explanation:
Find the area of the hexagon to the nearest tenth.
One of the solutions to x2 - 2x – 15 = 0 is x = -3. What is the other solution?
Ox=-5
Ox= -1
0 x=1
x = 5
Answer:
x=5
Step-by-step explanation:
Factoring x2 - 2x – 15 we get
(x+3)(x-5) so x+3=0 and x-5=0 or x=-3 and x=5
Answer:
x=5
Step-by-step explanation:
x^2 - 2x – 15 = 0
Factor
What 2 numbers multiply to -15 and add to -2
-5*3 = -15
-5+3 = -2
(x-5) (x+3) = 0
Using the zero product property
(x-5) =0 x+3 =0
x-5+5 =0+5 x+3-3 = 0-3
x=5 x=-3
pLeAsE HeLp
What is the domain of y=logx?
All real numbers less than 0
All real numbers greater than 0
All real numbers not equal to 0
All real numbers
Answer:all real number greater than 0
Step-by-step explanation:
Firstly if you input any number equal to 0 or less than 0 you will not find the defined range...
You cant use o or any negetive number as domain in the term of log or ln type math..
But if u put any value more than 0 you can find all real number as range
Such as, log(0.001)=-3
log(1)=0
log(120)=2.07
So the domain is all real number above o...but the range is all real number including 0 and negetive number..
The domain of y=logx is all real numbers greater than 0.
So, firstly we input any number equal to 0 or less than 0 then we will not find the defined range.We can't use 0 or any negative number as the domain in the term of log or in type mths.But if we put any value more than 0 then we will find that all are real numbers as a range such example given below[tex]log(0.001)=-3[/tex][tex]log1=0[/tex][tex]log120=2.07[/tex]So, the domain is all real numbers above 0But the range is all real numbers including 0 and negative numbers.Hence, option b is the correct answer.
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Which of the following is a classified as a binomial? A. 3x^3 -6x^2-x B. 6x^3-6x^2+x-1 C. 3x^3-6x D. 6x^3
Answer: C
Step-by-step explanation:
Binomial have only two terms.
A) 3x²-6x²-+x has three terms
B) 6x³-6x²+x-1 has four terms
C) 3x³-6x has two terms
D) 6x³ has only one term
WHAT IS ANOTHER WAY TO WRITE 6%
Answer:
3/50 or 0.06
Step-by-step explanation:
6/100=3/50
6/100=0.06
Answer:
0.06
Step-by-step explanation:
Which is the graph of x-y=1?
Answer:
In graph
Step-by-step explanation:
First put it in Slope -Intercept form.
then graph the y- intercept first.
After that it's rise over run so think 1/1
up 1 over one.
Answer:
CCCCCCCCCCCCC
Step-by-step explanation:
If f(x)=2x^2+1, what is f(x) when x=3?
Answer:
19
Step-by-step explanation:
Plug in x = 3 into the function
f(x)=2x^2+1
f(x)=2(3)^2+1
f(x)=18+1
f(x)=19
The answer is:
f(3) = 19
Work/explanation:
To evaluate this function, plug in 3 for x:
[tex]\sf{f(x)=2x^2+1}[/tex]
[tex]\sf{f(3)=2(3)^2+1}[/tex]
[tex]\sf{f(3)=2\times9+1}[/tex]
Then, according to PEMDAS, we multiply:
[tex]\sf{f(3)=18+1}[/tex]
[tex]\sf{f(3)=19}[/tex]
Therefore, when x = 3, the function evaluates to 19.
y=3x^2 + 7 + m have two intercepts ?
Answer:
In general, quadratic equations have two x-intercepts. But sometimes it happens that a quadratic eqution has one x-intercept or no interepts. That's why we should fully analyze this equation:
Given the following equation: y=3x^2 + 7 + m
If y=0, then:
3x^2 + 7 + m = 0 ⇒ x^2 = (-m-7)/3
Then [tex]x =[/tex]± [tex]\sqrt{\frac{-m-7}{3}}[/tex]
Given that we can take the square root of a negative number, the only way this equation has two x-intercepts is if m<-7.
Summarizing:
The equation: y=3x^2 + 7 + m has two x-intercepts only if m is less than -7. If m equals -7, the equation has only one x-intercept, and finally, if m is greater than -7, the equation has NO x-intercepts.
20 POINTS
WILL MARK BRAINLIEST
The last two pictures are to question two.
Answer:
The total surface area of the solid is 702 cm² ⇒ answer B
The true statements are m∠WYX = 46° and m∠YWX = 63° ⇒ 1st and 2nd answers
Step-by-step explanation:
* Lets explain the solid figure
- It has one rectangular base of dimensions 10 cm and 14 cm
- It has 4 rectangular side faces , two of dimensions 6 cm and 10 cm
and another two of dimensions 6 cm and 14 cm
- It has 4 triangular faces , two of base 10 cm and height 12 cm and
another two of base 14 cm and height 11 cm
- The total surface area of the solid is the sum of the area of the 9 faces
* Lets find the area of all the faces
# Area of the base
∵ The base is a rectangle
∵ Area of the rectangle = length × width
∵ Length = 14 cm and width = 10 cm
∴ Area of the base = 14 × 10 = 140 cm²
# Area of the four rectangular faces
∵ Length = 10 cm and width = 6 cm
∴ The area of the face with dimensions 10 , 6 = 10 × 6 = 60 cm²
∵ Length = 14 cm and width = 6 cm
∴ The area of the face with dimensions 14 , 6 = 14 × 6 = 84 cm²
# Area of the four triangular faces
∵ Area of a triangle = 1/2 × base × height
∵ The base = 10 cm and the height = 12 cm
∴ The area of the face = 1/2 × 10 × 12 = 60 cm²
∵ The base = 14 cm and the height = 11 cm
∴ The area of the face = 1/2 × 14 × 11 = 77 cm²
∵ The total surface area of the solid = the sum of the areas of 9 faces
∴ TSA = 140 + 2 × 60 + 2 × 84 + 2 × 60 + 2 × 77
∴ TSA = 140 + 120 + 168 + 120 + 154 = 702 cm²
* The total surface area of the solid is 702 cm²
* Lets solve the 2nd part
- WXY is a scalene triangle
- m∠WXY is 71°
- The two sides of the triangle WY and XY exceeded
- The ray WY and the ray XY intersect each other at point Y and
formed vertically opposite angles with measure 46°
∵ Ray WY intersect ray XY at point Y
∴ m∠WYX = 46°
- In Δ WYX
∵ m∠WXY = 71° ⇒ given
∵ m∠WYX = 46° ⇒ proved
∵ The sum of the measures of the interior angles of a triangle is 180°
∴ m∠YWX + m∠WXY + m∠WYX = 180°
∴ m∠YWX + 71° + 46° = 180
∴ m∠YWX + 117° = 180° ⇒ subtract 117 from both sides
∴ m∠YWX = 63°
Lets check the true statements
# m∠WYX = 46° ⇒ true
# m∠YWX = 63° ⇒ true
# m∠WXY = 46° ⇒ not true
# m∠YWX = 46° ⇒ not true
# m∠WYX = 134° ⇒ not true
* The true statements are m∠WYX = 46° and m∠YWX = 63°
Which relation is a function?
Can Sb help please
A relation is a function if you associate exactly one output for every input. This means that, when you choose a value for x, there must be only one correspondent value for y. This only happens in the top-right parabola.
What is the range of the exponential function shown below? F(x) = 11 • (1/3)x
Answer:
[tex](0, \infty)[/tex]
Step-by-step explanation:
By definition all the exponential functions of the form
[tex]f (x) = a (b) ^ x[/tex]
Where a is the main coefficient and b is the base they have range [tex](0, \infty)[/tex]
Whenever [tex]a> 0[/tex] and b> 0.
In this case the function is:
[tex]f (x) = 11(\frac{1}{3}) ^ x[/tex]
Note that for this function [tex]a = 11> 0[/tex] and [tex]b =\frac{1}{3}>0[/tex]
Therefor the range is: [tex](0, \infty)[/tex]
How do you work out 15 divided by 25
Answer:
Step-by-step explanation:
15/25. Divide both sides by a common number which is 5 3/5 is the final answer.
The result of the given mathematical expression is [tex]\frac{3}{5}[/tex] or 0.6.
What is a mathematical expression?"A mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context."
Given mathematical expression is
= (15 ÷ 25)
[tex]= \frac{15}{25}\\= \frac{3}{5}\\= 0.6[/tex]
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which function has the same y-intercept as the function. y=2/3x-3
A. 2/3x +3y=-3
B.-2/3x+3y=6
C. 6x-7y=21
D. x+4y=12
Answer:
C. 6x - 7y = 21
Step-by-step explanation:
y=2/3 x - 3, y-intercept = -3
A. 2/3 x + 3y = -3
3y = -2/3 x - 3
y = -2x - 1; y-intercept = -1
B.-2/3 x + 3y = 6
3y = 2/3 x + 6
y = 2x + 2; y-intercept = 2
C. 6x-7y=21
7y = 6x - 21
y = 6/7 x - 3; y-intercept = -3
D. x+4y = 12
4y = -x +12
y = -1/4 + 3; y-intercept = 3
Answer is C. 6x - 7y = 21
the line passing through point (0, 0) and parallel to the line whose equation is 3x + 2y - 6 = 0
Answer: y= -3/2x
Explanation:
3x+ 2y- 6
→ 2y= -3x+ 6
→ y= -3/2x+ 3
Parallel to y= ax+ b is to have the same slope (ax) and have a different y- intercept.
For this equation, y= -3/2x + 3, it is y= -3/2x because the line has to pass through point (0,0).