Answer:
Slope = 2
Step-by-step explanation:
Slope is the change in y/change in x. So (8-4)/4-2)=2.
Answer: Using the formula below you will get -4/-2 which is slope of 2
Step-by-step explanation:
So you would use the slope formula which is y_{2}- y_{1} / x_{2}-x_{1}
what's the answer to this?
(x+1)²=25
[tex](x+1)^2=25\\x+1=5 \vee x+1=-5\\x=4 \vee x=-6[/tex]
Which statement is true regarding the graphed functions?
Answer:
Option A) f(2)=0 and g(-2)=0
Step-by-step explanation:
we know that
The vertex of f(x) is equal to (2,0)
The vertex of g(x) is equal to (-2,0)
step 1
Find the value of f(x) and g(x) for x=2
Observing the graph
For x=2
f(2)=0 ----> the y-coordinate of the vertex
g(2) > 12
step 2
Find the value of f(x) and g(x) for x=-2
Observing the graph
For x=-2
f(-2)> 12
g(-2)=0 ----> the y-coordinate of the vertex
therefore
The statement that is true regarding the graphed functions is
f(2)=0 and g(-2)=0
if m + 1 is an an even integer which one of the following must be an odd integer ?
A : m - 1
B : 2m - 2
C : 2m + 1
D : 2m + 2
To find which expression must be an odd integer when m + 1 is even, we analyze each option using substitution. The only option that results in an odd integer is 2m + 1.
If m + 1 is an even integer, then m must be an odd integer. Let's analyze each option to see which one of them must be an odd integer:
(A) m - 1: Since m is odd, subtracting 1 from an odd number will result in an even number. Therefore, (A) m - 1 is not an odd integer.(B) 2m - 2: If we substitute an odd integer for m, we get (2 * odd) - 2, which simplifies to an even number. Thus, (B) 2m - 2 is not an odd integer.(C) 2m + 1: Substituting an odd integer for m gives (2 * odd) + 1, which simplifies to an odd number. Therefore, (C) 2m + 1 is an odd integer.(D) 2m + 2: If we substitute an odd integer for m, we have (2 * odd) + 2, which simplifies to an even number. Hence, (D) 2m + 2 is not an odd integer.Therefore, the answer is (C) 2m + 1 as it is the only option that must be an odd integer.
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Final answer:
Option C, which is 2m + 1, must be an odd integer if m + 1 is an even integer because adding 1 to any even integer results in an odd integer.
Explanation:
Given that m + 1 is an even integer, we can determine which of the other expressions would therefore be an odd integer. We know that any even integer can be written in the form 2k, where k is an integer, because even integers are multiples of 2. Similarly, odd integers can be written as 2k + 1, where k is also an integer.
Given the options:
A: m - 1, if m + 1 is even, then m is odd, and subtracting 1 from an odd number results in an even number, so this option is not correct.B: 2m - 2, this is clearly even because it is a multiple of 2 regardless of the value of m, so this option is not correct.C: 2m + 1, if m is odd (since m + 1 is even), this will result in an odd number, so this option is correct.D: 2m + 2, like option B, this is also clearly even, so this option is not correct.Therefore, the answer is C: 2m + 1.
If sin theta =7/25, use the Pythagorean identity to find cos theta
Answer:
[tex]\cos(\theta)=\pm \frac{24}{25}[/tex]
Step-by-step explanation:
I don't know where [tex]\theta[/tex] is so there is going to be two possibilities for cosine value, one being positive while the other is negative.
A Pythagorean Identity is [tex]\cos^2(\theta)+\sin^2(\theta)=1[/tex].
We are given [tex]\sin(\theta)=\frac{7}{25}[/tex].
So we are going to input [tex]\frac{7}{25}[/tex] for the [tex]sin(\theta)[/tex]:
[tex]\cos^2(\theta)+(\frac{7}{25})^2=1[/tex]
[tex]\cos^2(\theta)+\frac{49}{625}=1[/tex]
Subtract 49/625 on both sides:
[tex]\cos^2(\theta)=1-\frac{49}{625}[/tex]
Find a common denominator:
[tex]\cos^2(\theta)=\frac{625-49}{625}[/tex]
[tex]\cos^2(\theta)=\frac{576}{625}[/tex]
Square root both sides:
[tex]\cos(\theta)=\pm \sqrt{\frac{576}{625}}[/tex]
[tex]\cos(\theta)=\pm \frac{\sqrt{576}}{\sqrt{625}}[/tex]
[tex]\cos(\theta)=\pm \frac{24}{25}[/tex]
diameter of a circular garden pool is six feet. what is the area of the pool in algebra
For this case we have that by definition, the area of a circle is given by:
[tex]A = \pi * r ^ 2[/tex]
Where:
r: It is the radius of the circle
As data we have that[tex]r = 6 \ ft[/tex]
Then, replacing we have:
[tex]A = \pi * 6 ^ 2\\A = 36 \pi[/tex]
Taking [tex]\pi = 3.14[/tex]
A = 113.04
So, the pool area is [tex]113.04 \ ft ^ 2[/tex]
Answer:
[tex]113.04 \ ft ^ 2[/tex]
Answer:
9π ft²
Step-by-step explanation:
PLEASE HELP!!!
Eliminate the parameter. x = 5 cos t, y = 5 sin t. Answer must be a rectangular equation
Answer:
[tex]x^2+y^2=25[/tex]
Step-by-step explanation:
Recall the following Pythagorean Identity:
[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]
Let's solve the x equation for cos(t) and the y equation for sin(t).
After the solve we will plug into our above identity.
x=5cos(t)
Divide both sides by 5:
(x/5)=cos(t)
y=5sin(t)
Divide both sides by 5:
(y/5)=sin(t)
Now we are ready to plug into the identity:
[tex]\sin^2(t)+\cos^2(t)=1[/tex]
[tex](\frac{y}{5})^2+(\frac{x}{5})^2=1[/tex]
[tex]\frac{x^2}{5^2}+\frac{y^2}{5^2}=1[/tex]
Multiply both sides by 5^2:
[tex]x^2+y^2=5^2[/tex]
This is a circle with center (0,0) and radius 5.
All I did to get that was compare our rectangular equation we found to
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where (h,k) is the center and r is the radius of a circle.
The graph below shows the function f(x)=x-3/x^2-2x-3 which statement is true
Answer:
The correct option is A.
Step-by-step explanation:
Domain:
The expression in the denominator is x^2-2x-3
x² - 2x-3 ≠0
-3 = +1 -4
(x²-2x+1)-4 ≠0
(x²-2x+1)=(x-1)²
(x-1)² - (2)² ≠0
∴a²-b² =(a-b)(a+b)
(x-1-2)(x-1+2) ≠0
(x-3)(x+1) ≠0
x≠3 for all x≠ -1
So there is a hole at x=3 and an asymptote at x= -1, so Option B is wrong
Asymptote:
x-3/x^2-2x-3
We know that denominator is equal to (x-3)(x+1)
x-3/(x-3)(x+1)
x-3 will be cancelled out by x-3
1/x+1
We have asymptote at x=-1 and hole at x=3, therefore the correct option is A....
Answer:
Its A. I just passed the final exam with 5 minutes left of the SESSION.
Step-by-step explanation:
Use a calculator to evaluate 9 and the square root of three to the nearest ten thousandth. a. 27.1234 c. 44.9569 b. 6.7050 d. 5.1962 Please select the best answer from the choices provided
Answer:
Option D 5.1962
Step-by-step explanation:
we have
The number [tex]9[/tex] and the number [tex]\sqrt{3}[/tex]
I assume for the choices provided that the operation is calculate [tex]9[/tex] divided by [tex]\sqrt{3}[/tex]
so
[tex]\frac{9}{\sqrt{3}} =5.1962[/tex] (rounded to the nearest ten thousandth)
Answer:
C. 44.9569
Step-by-step explanation:
A hot air balloon is at a height of 2250 feet.It descends 150 feet each minute.Find its height after 6,8,and 10 minutes.
.Make a table to show the pattern of heights.
.Write an expression for the balloon height at m minutes.
Answer:
equation: y=-150m+2250
Height after:
6 Minutes: 1350 ft
8 Minutes: 1050 ft
10 Minutes: 750 ft
Step-by-step explanation:
We know that the hot air balloon has an initial height of 2250 ft, so that is our y-intercept (in the equation, y =mx+b, the y-intercept is b). Next you know that after every minute, the balloon goes down 150 ft. So that means -150 ft per minute. Now put it together, the equation is written as "y = 150m+2250" (since m is the required variable, that's what is written in the equation instead of x).
Next, to make a table, you need to determine what value goes in the left side, the x values (the independent variables) and what goes in the right side, the y values (the dependent variables). The two variables here are Height and Time. Time is not dependent on the height of the balloon-- the height depends on how much time has passed. So Time on the left and height on the right. Next just plug in the values 6, 8, and 10 into your equation. Your answer will be the output, aka the height of the hot air balloon after x minutes.
Your table should look something like this:
m y
6 1350
8 1050
10 750
Hope this helps :)
Find all solutions to the equation. (1 point) sin x = square root of three divided by two.
Answer:
x=pi/3 + 2pi*k
x=2pi/3+2pi*k
Step-by-step explanation:
sin(x)=sqrt(3)/2
This happens twice in the first rotation on our unit circle.
It happens in the first quadrant and in the second quadrant. Third and fourth quadrants are negative for sine.
So we are looking for when the y-coordinate on the unit circle is sqrt(3)/2.
This is at pi/3 and 2pi/3.
So we can get all the solutions by adding +2pi*k to both of those. This gives us a full rotation about the circle any number of k times. k is an integer.
So the solutions are
x=pi/3 + 2pi*k
x=2pi/3+2pi*k
An equation is formed of two equal expressions. The solution to the equation sin(x)=√3/2 is (π/3 ± 2πn), (2π/3 ± 2πn), where n is any natural number.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of sinx=√3/2 are,
sin(x) = √3/2
x = sin⁻¹ √3/2
x = (π/3 ± 2πn), (2π/3 ± 2πn)
Hence, the solution to the equation sin(x)=√3/2 is (π/3 ± 2πn), (2π/3 ± 2πn), where n is any natural number.
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SEE IMAGE! Two lines below intersect to form four angles, as shown. The measure of angle 2 is 114°. What is the sum of the measures of angles 1 and 3?
A) 66
B) 90
C) 114
D) 132
Write the Recursive rule for the geometric sequence
An=1072-1
8, 4, 2, 1, 1/2,...
[tex]\bf 8~~,~~\stackrel{8\cdot \frac{1}{2}}{4}~~,~~\stackrel{4\cdot \frac{1}{2}}{2}~~,~~\stackrel{2\cdot \frac{1}{2}}{1}~~,~~\stackrel{1\cdot \frac{1}{2}}{\cfrac{1}{2}} \\\\\\ a_n=\cfrac{1}{2}\cdot a_{n-1}\qquad \begin{cases} a_1=\textit{previous term}\\ a_n=\textit{current term}\\ a_1=\textit{first term}\\ \qquad 8 \end{cases}[/tex]
Solve for variable: 5z/8 – 1/3 = 2/5
Answer: z= .6
Step-by-step explanation:
Numerator: When you do 5•.6, you get 3, and then 3-1 equals 2.
Denominator: 8 - 3 = 5.
Therefore you get 2/5 which makes z = .6
A solid right pyramid has a hexagon all base with an area of 7.4 units the pyramid has a height of 6 units what is the volume of the pyramid
Answer:
14.8 units³
Step-by-step explanation:
The volume of a "pointed" solid, such as a cone or pyramid, is one-third the product of its base area and height:
V = (1/3)Bh
Filling in the given numbers and doing the arithmetic, we find the volume to be ...
V = (1/3)(7.4 units²)(6 units) = 14.8 units³
The volume of the pyramid is 14.8 cubic units.
Find the average rate of change for the given function from x = 1 to x = 2.
1) -2
2) -1/2
3) 1/2
4) 2
Answer:
2
Step-by-step explanation:
The average rate of change from x=1 to x=2 is the same as finding the slope of a line at x=1 and x=2.
So we are going to need to corresponding y coordinates.
What y corresponds to x=1? y=3
What y corresponds to x=2? y=5
So we have the ordered pairs (1,3) and (2,5).
Line the points up vertically and subtract vertically then put 2nd difference over 1st difference.
(2 , 5)
-(1 , 3)
-----------
1 2
The average rate of change is 2/1 or just 2.
Now since we were asked to find the average rate of change given the function was a line, it really didn't matter what two points you used on that line.
Answer: Fourth option
[tex]m=2[/tex]
Step-by-step explanation:
If we call m the average change rate of a function between [tex]x_1[/tex] and [tex]x_2[/tex], then, by definition:
[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
In this case the function is the line shown in the graph. Then we look for the values of [tex]y = f (x)[/tex] for [tex]x = 1[/tex] and [tex]x = 2[/tex]
When [tex]x=1[/tex] then [tex]f(x)=3[/tex]
When [tex]x=2[/tex] then [tex]f(x)=5[/tex]
Therefore
[tex]m=\frac{5-3}{2-1}[/tex]
[tex]m=\frac{2}{1}[/tex]
[tex]m=2[/tex]
Amir stands on a balcony and throws a ball to his dog, who is at ground level.
The ball's height (in meters above the ground), xxx seconds after Amir threw it, is modeled by
h(x)=-(x+1)(x-7)
How many seconds after being thrown will the ball reach its maximum height?
________ seconds
I know I literally just posted one a couple minutes ago but, please help me again T-T
Answer:
3 seconds
Step-by-step explanation:
The given equation describes a parabolic curve with zeros at x=-1 and x=7. The line of symmetry of the curve is halfway between the zeros, at ...
x = (-1 +7)/2 = 6/2 = 3
The maximum of the curve is on the line of symmetry. The ball will reach its maximum height 3 seconds after being thrown.
_____
Additional comment
The maximum height will be 16 meters.
The ball will reach its maximum height 3 seconds after being thrown.
Explanation:To find the time when the ball reaches its maximum height, we need to determine the vertex of the quadratic equation representing the ball's height. The equation h(x)=-(x+1)(x-7) can be rewritten in vertex form as h(x)=-x^2+6x-7. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation.
In this case, a = -1 and b = 6. Plugging these values into the formula, we get x = -6/-2 = 3. Therefore, the ball reaches its maximum height 3 seconds after being thrown.
What is the surface area of the right prism below?
Answer:
C. [tex]432\text{ units}^2[/tex]
Step-by-step explanation:
We have been given an image of a right prism. We are asked to find the surface area of our given prism.
The surface area of our given prism will be sum of area of two base right triangles and area of three rectangles.
[tex]SA=2B+Ph[/tex], where,
SA = Surface area,
B = Area of each base,
P = Perimeter of base,
h = Height of prism.
Let us find area of right base of prism.
[tex]B=\frac{1}{2}\times 6\times 8[/tex]
[tex]B=3\times 8[/tex]
[tex]B=24[/tex]
Perimeter of base will be [tex]6+8+10=24[/tex].
Upon substituting these values in surface area formula, we will get:
[tex]SA=2*24+24*16[/tex]
[tex]SA=24(2+16)[/tex]
[tex]SA=24(18)[/tex]
[tex]SA=432[/tex]
Therefore, the surface area of our given prism is 432 square units and option C is the correct choice.
A graph of quadratic function y = f(x) is shown below.
What is the solution set of the quadratic inequality f(x) ≥ 0?
Answer: it’s B 0
Step-by-step explanation:
In circle C, r = 32 units.
What is the area of circle C?
Answer:
A = 1024π units², A ≈ 3216.99 units²
Step-by-step explanation:
The equation of the area of a circle is A = πr², where A = area and r = radius.
Given that, we can plug in r as 32 units: A = π(32 un.)²
Simplifying that gives us A = 1024π units², or A ≈ 3216.99 units²
PLEASE URGENT
Carrie is finding the set of even numbers within the set of prime numbers.
Of the sets described, which is the universal set?
all real numbers
all integers
prime numbers
even numbers
Answer:
Prime Numbers
Step-by-step explanation:
Two sets are being considered in the given statement:
Set of even numbersSet of prime numbersA universal set is defined as such a set from which all the other subsets are taken for a given case. Or in other words, a universal set is such a set to which all the subsets belong and this universal set contains all the elements being studied/considered.
For the given case, set of Even Numbers is the subset which is being taken from the set of prime numbers. The set of prime numbers contains all the elements which we are considering for this very scenario.
Therefore, the set of prime numbers is the universal set.
Answer:
c
Step-by-step explanation:
What is the measure of angle COA?
140°
150°
160°
170°
Answer:160
Step-by-step explanation:
To solve the problem we must know the concept of the Center angle theorem. The measure of the center angle ∠AOC is 160°.
What is the central angle theorem?According to the central angle theorem, if an arc of a circle makes an angle with any point on the circumference of that circle then the measure of that angle is half the angle made by that arc at the center of the circle.
Given to us
∠ABC = 80°
As we already know the angle made by Arc AC at point B, therefore, the center angle made by ARC AC at the center will be twice of it. Therefore,
∠AOC = 2∠ABC
∠AOC = 2(80°)
∠AOC = 160°
Hence, the measure of the center angle ∠AOC is 160°.
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A right cylinder has a radius of 5 m and a height of 3 m. What is the volume of the cylinder?
Answer:
V = 75 pi m^3
or approximately
V =235.5 m^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
where r is the radius and h is the height
V = pi * 5^2 *3
V = 75 pi m^3
If we use 3.14 as an approximation for pi
V =235.5 m^3
Answer:
volume = 75(pi) m^3 (exactly)
volume = 235.6 m^3 (approximately)
Step-by-step explanation:
volume of cylinder = pi * radius^2 * height
volume = pi * (5 m)^2 * 3 m
volume = 75(pi) m^3 (exactly)
volume = 235.6 m^3 (approximately)
Ali, Ben and Joe sell 73 raffle tickets between them. Ben sells twice as many tickets as Ali, and Joe sells 8 more tickets than Ben. How many tickets does each person sell?
Answer:
Ali-13
Ben-26
Joe-34
Step-by-step explanation:
Ali-x
Ben-2x
Joe-2x+8
x+2x+2x+8=73
3x+2x+8=73
5x+8=73
5x=73-8
5x=65
x=65/5
=13
Ali sells 13 tickets
Ben sells 13×2
=26 tickets
Joe sells (13×2)+8
=34 tickets
Ali sells 13 tickets. Ben sells 26 tickets. Joe sells 34ctickets
How many tickets does each person sell?Let
Ali = x
Ben = 2x
Joe = 2x+8
⇒ x+2x+2x+8=73
⇒ 3x+2x+8=73
⇒ 5x+8=73
⇒ 5x=73-8
⇒ x=65/5
⇒ 13
Ali sells 13 tickets.
Ben sells 13×2
= 26 tickets.
Joe sells (13×2)+8
= 34 tickets.
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
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A number cube with the numbers 1 through 6 is rolled. What is the theoretical probability, as a decimal, of the number cube showing a 1? Round the decimal to the nearest hundredth.
Answer:
0.17
Step-by-step explanation:
The numbers are from 1 to 6 on each side.
The total sample space will be 6.
Denoted as:
n(S) = 6
There will be only one outcome as 1
So,
Let A be the event that the number is 1
Then,
n(A) = 1
[tex]P(A) = \frac{n(A)}{n(S)} \\=\frac{1}{6} =0.166[/tex]
Hence the theoretical probability of the number cube showing a 1 is 0.166 ..
Rounding off to the nearest hundred
0.17 ..
Which system of equations has only one solution?
Answer:
The answer is the last option, D.
Step-by-step explanation:
A function with one solution can be added and have a variable and a constant leftover. The variables in the other three options cancel each other out, so none of them have one solution. The first and third equations have no solutions, and the second has infinitely many solutions. The fourth option has only one variable cancel out and still has a constant on the other side of the equation. The fourth option is correct.
Write an equation: The sides of a rectangle are x and ( x - 4 ). The perimeter is 87
The perimeter of a rectangle, is all of the sides added up.
In a rectangle, there are two widths (right and left), and two lengths (up and down)
So:
Perimeter = 2 × width + 2 × length.
To get the equation we just substitute in the values that we are given:
length = (x)
width = (x - 4)
perimeter = 87
So just put these values into: perimeter = 2 × width + 2 × length:
87 = 2(x) + 2(x - 4)
_____________________________
Answer:
The equation is: 87 = 2(x) + 2(x - 4)
(note: this can be simplified down like so:
87 = 2x + 2x - 8
87 = 4x - 8
95 = 4x
23.75 = x
)
Find the area.
A. 19 ft²
B. 30 ft²
C. 31 ft²
D. 84 ft²
Answer: D. 84 ft^2
Step-by-step explanation: The area of a trapezoid is (a+b)/2 x h. A and B are the bases, and h is the height. Plug in the numbers.
(8+16)/2 x 7 = 84
Your answer would be 84 ft^2. D.
If sales tax is 6% and you buy a shirt for $25 how much do you owe?
Answer:
26.50
Step-by-step explanation:
First we need to calculate the sales tax
25 * 6%
Changing to decimal from
25 * .06
1.50
Then we add the tax to the cost of the shirt
25+1.50
26.50
We owe 26.50
The Reed High School basketball program earned $7,115.03 in profits over the current season. Based on game attendance, it is determined that the girls' basketball team will receive 7% of the profits, while the boys' basketball team will receive 11% of the profits. Which is the best estimate of how much more the boys' team will receive in profits than the girls' team?
A.
$770
B.
$490
C.
$280
D.
$1,260
Answer:
c. $280
Step-by-step explanation:
first you times the total profits by the percent that the girls get then the percent the boys get to find out how much of the profit the girls and boys basketball teams each get, then you subtract the profits the boys get by the profits the girls get to find out how much more the boys get than the girls.
7,115.03 x .07 = 498.0521
7,115.03 x .11 = 782.6533
782.6533 - 498.0521 = 284.6012
the boys receive 284.6012 more in profits than the girls
so c. $280 would be the best estimate of how much more the boys team will receive
Given the expression, , choose the correct horizontal asymptote. y=x^2-8x+3/x^2+3x+1 None y = 0 y = 1 y = -2
Answer:
y = 1
Step-by-step explanation:
Given function is:
[tex]\frac{x^2+8x+3}{x^2+3x+1}[/tex]
In order to find the horizontal asymptote, the coefficients of highest degree variable of numerator and denominator are divided.
In our case,
both the numerator and denominator have 1 as he co-efficient of x^2
So the horizontal asymptote is y = 1/1
Hence, third option y=1 s correct ..
Final answer:
The correct horizontal asymptote for the given rational expression is y = 1, found by comparing the degrees and leading coefficients of the numerator and denominator.
Explanation:
For the expression y = (x² - 8x + 3) / (x² + 3x + 1), the correct horizontal asymptote is determined by looking at the degrees of the polynomials in the numerator and the denominator. When the degrees are the same, the horizontal asymptote is found by dividing the leading coefficients. In this case, both polynomials are of degree 2, and the leading coefficients are both 1. Thus, the horizontal asymptote is y = 1.