The values of c such that the function f is continuous are: c = -2.79 and c = 1.79
The function is given as:
[tex]f(x) = \left\{ \begin{array}{lcl} {5} - x^{2}, & & x \le c \\ x, & & x > c \end{array}\right.[/tex]
For the function to be continuous, then the following must be true
[tex]5 - x^2 = x[/tex]
Substitute c for x
[tex]5 - c^2 = c[/tex]
Express as a quadratic function
[tex]c^2 + c - 5 = 0[/tex]
Using a graphing calculator, the values of c are:
c = -2.79 and c = 1.79
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Which pair of non-congruent figures must be similar? two squares two parallelograms (not rectangles) two right triangles two isosceles triangles (not equilateral)
The amount of carbon-14 present in animal bones t years after the animal's death is given by P(t)= -0.00012097t. How old is an ivory tusk that has lost 34% of its carbon-14?
I believe the equation you gave is wrong because the standard form of equation for C-14 decay is in the form of:
A = Ao e^-kt
So I think the right form of equation is (correct me if I’m wrong):
P(t) = Po e^(-0.00012097t)
Where,
Po = initial value of C-14 at t = 0
t = time elapsed
Since it is given that:
P = (1 – 0.34) Po
P = 0.66 Po
Therefore, t is:
0.66 Po = Po e^(-0.00012097 t)
0.66 = e^(-0.00012097 t)
taking ln of both side:
ln 0. 66 = -0.00012097 t
t = - ln 0. 66 / 0.00012097
t = 3,434.86 years
Therefore the ivory tusk is about 3,435 years old.
The probability that you will win a game is 0.18. if you play the game 504 times, what is the most likely number of wins?
Find the length of the third Angelou a triangle given that the first two angels are 35 and 70 show your work
angles in a triangle = 180 degrees
70 +35 = 105 degrees
180-105 = 75 degrees
3rd angle = 75 degrees
Solve the equation by graphing. x^2+14x+45=0 First, graph the associated parabola by plotting the vertex and four additional points, two on each side of the vertex. Then, use the graph to give the solution(s) to the equation. If there is more than one solution, separate them with commas.
Points:
Solution(s):
What's 10⁄12 written as a fraction in simplest form?
A. 5⁄6
B. 10⁄6
C. 3⁄5
D. 5⁄12
If 4 1/2 = 2, 8 1/3 = 2, and 16 1/4 = 2, then for what value of x would x 1/5 = 2?
2
4
24
32
what is e/4 + 2f-3 when e =12 andf =1/2
Factor of x^3-x^2-24x-36
Which number is greater? 0 -1 -25 -50?
The perimeter of a rectangle is 56 feet. Describe the the possible lengths of a side if the area of the rectangle is not to exceed 132 square ft
The possible lengths of sides of the rectangle will be [tex](6,22)[/tex] or [tex](22,6)[/tex] .
What is area ?Area is the space which is occupied by any [tex]2D[/tex] surface.
Area of rectangle [tex]=Length\ *\ Breadth[/tex]
Perimeter of rectangle [tex]=2(Length\ +\ Breadth)[/tex]
We have,
Perimeter of rectangle [tex]=56[/tex] feet
Area of rectangle [tex]=132[/tex] squared feet
Let,
Length of rectangle [tex]=x[/tex]
Breadth of rectangle [tex]=y[/tex]
So,
Perimeter of rectangle [tex]=2(Length\ +\ Breadth)[/tex]
[tex]56=2(x+y)[/tex]
[tex]28=(x+y)[/tex]
⇒ [tex]x=28-y[/tex] [tex]........(i)[/tex]
Now,
Area of rectangle [tex]=Length\ *\ Breadth[/tex]
[tex]132=x\ *\ y[/tex] [tex]........(ii)[/tex]
Now substitute value of [tex]x[/tex] in [tex](ii)[/tex],
[tex]132=(28-y)y[/tex]
[tex]132=28y-y^2[/tex]
⇒[tex]y^2-28y+132=0[/tex]
Now using Middle term split method;
[tex]y^2-28y+132=0[/tex]
[tex]y^2-22y-6y+132=0[/tex]
[tex]y(y-22)-6(y-22)=0[/tex]
[tex](y-6)(y-22)=0[/tex]
⇒
[tex](y-6)=0[/tex]
⇒ [tex]y=6[/tex]
[tex](y-22)=0[/tex]
⇒ [tex]y=22[/tex]
So,
Now if we take [tex]y=6[/tex], then
[tex]x=28-6[/tex]
[tex]x=22[/tex]
And,
if we take [tex]y=22[/tex], then
[tex]x=28-22[/tex]
[tex]x=6[/tex]
So, the possible lengths of sides of the rectangle are [tex](6,22)[/tex] or [tex](22,6)[/tex] .
Hence, we can say that he possible lengths of sides of the rectangle are [tex](6,22)[/tex] or [tex](22,6)[/tex] .
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How many different committees can be formed from 10 teachers and 41 students if the committee consists of 2 teachers and 2 students?
A psychologist claims that less than 5.8 percent of the population suffers from professional problems due to extreme shyness. Express the null hypothesis and the alternative hypothesis in symbolic form. Use p, the true percentage of the population that suffers from extreme shyness. Select one: a. H0: p = 5.8% H1: p < 5.8% b. H0: p > 5.8% H1: p ≤ 5.8% c. H0: p < 5.8% H1: p ≥ 5.8% d. H0: p = 5.8% H1: p > 5.8%
Answer:
Step-by-step explanation:
Using 8(-20) in a real world situation
If 52/x is a positive integer, how many integer values are possible for x?
There are a total of 6 integer values that are possible for x: 1, 2, 4, 13, 26, and 52.
What is the quotient?If 52/x is a positive integer, it means that 52 is divisible by x, and x is a factor of 52. In other words, x must be a positive divisor of 52.
The positive divisors of 52 are: 1, 2, 4, 13, 26, and 52.
Thus;
52/1 = 52 (a positive integer)
52/2 = 26 (a positive integer)
52/4 = 13 (a positive integer)
52/13 = 4 (a positive integer)
52/26 = 2 (a positive integer)
52/52 = 1 (a positive integer)
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Which question is not a good survey question?
a) Don’t you agree that the financial crisis is essentially over?
b) On average, how many hours do you sleep per day?
c) What is your opinion of educational funding this year?
d) Are you happy with the availability of electronic products in your state?
Answer:
See image
Step-by-step explanation:
Plato
"let v = r 2 with the usual addition and scalar multiplication defined by k(u1, u2) = (ku1, 0). determine which of the five axioms of vector spaces involving scalar multiplication v satisfies and which fail. for the ones it satisfies, prove that it satisfies the axiom. for those that fail, show that it fails with a counterexample."
Let (-7, -4) be a point on the terminal side of theta. Find the exact values of Sin, CSC and COT
What is the greatest number of triangular sections, each with a base of 5 inches and a height of 8 inches, that can be cut from a rectangular piece of paper measuring 30 inches by 40 inches?
What is the median of the data set given below? 19, 22, 46, 24, 37, 16, 19, 33
An ellipse has vertices along the major axis at (0, 8) and (0, –2). The foci of the ellipse are located at (0, 7) and (0, –1). What are the values of a, b, h, and k, given the equation below? (y-k)^2/a^2+(x+h)^2/b^2=1
Answer: The values for a, b, h, and k are a = 5, b = 3, h = 0, k = -3.
Step-by-step explanation: In this problem, we know ellipse has vertices along the major axis at (0, 8) and (0, -2). The foci of the ellipse are located at (0, 7) and (0, -1). We are asked to determine the values of a, b, h, and k.
We were also then provided with the equation for vertical eclipse:
[tex]\frac{(x-h)^2}{b^2} + \frac{(y -k)^2}{a^2}[/tex]
Before we begin, we need to first define our values for a, b, h, and k.
a - distance to vertices from the centerb - distance to co-vertices from the center(h, k) - represents the center of the eclipseThe first step, we need to determine the center of the eclipse. We can use the midpoint formula to determine the midpoint between the vertices along the major axis: (0, 8) and (0, -2).
[tex]M = (\frac{x_{1} +x_{2} }{2} , \frac{y_{1} + y_{2} }{2} )[/tex]
[tex]M = (\frac{0 + 0}{2} , \frac{-2 + 8}{2} )\\M = (0, 3)[/tex]
We now know that our center (h, k) is (0, 3). Which means our values for h and k are 0 and 3. Next, we have to determine our values for a and b. Considering the center of our eclipse is not at the center, we can use one of our vertices to determine our value for a.
[tex]V_{1}[/tex] = (h, k±a)
(0, 8) = (0, 3±a)
3 ± a = 8
±a = 5
Now, we know that a = 5. For us to get b, we need to use this formula: [tex]c^2 = a^2 - b^2[/tex]. Let's rewrite this formula, so we can focus on getting our b-value.
[tex]c^2 - a^2 = -b^2[/tex]
For us to use this formula, we need to determine our c value. To find our c-value, we have use of our foci points: (h, k±c). C is the units away/further from the center towards our foci points.
(0, 3±c) = (0, 7)
3 + c = 7
7 - 3 = c
4 = c
Now, we know that our value for c is 4. Now, let's plug into the formula.
[tex](4)^2 - (5)^2 = -b^2\\16 - 25 = -b^2\\\frac{-9}{-1} = \frac{-b^2}{-1} \\\sqrt{b^2} = \sqrt{9} \\b = 3[/tex]
Our value for b is 3. If we put into our eclipse formula:
[tex]\frac{(x-0)^2}{3^2} + \frac{(y -(-3))^2}{5^2}[/tex]
Jane is one of 50 students to take a standardized math test that includes 100 multiple choice questions. If she has the highest score of any student with a raw score of 87, what is her percentile score?
Two cars that are 150 miles apart start driving toward each other on parallel roads. The average speed of the first car is 60 miles per hour. The average speed of the second car is 55 miles per hour. Which equation can be used to determine t, the time it takes for the two cars to pass each other?
60t – 55t = 0
60t + 55t = 1
60t + 55t = 150
60t – 55t = 150
The equation that can be used to determine t, the time it takes for the two cars to pass each other is:
60t + 55t = 150
Option C is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
The equation that can be used to determine t, the time it takes for the two cars to pass each other is:
60t + 55t = 150
Here,
60t represents the distance covered by the first car in time t, and 55t represents the distance covered by the second car in time t.
When they meet, the sum of their distances would be equal to the total distance between them, which is 150 miles.
Therefore,
We can add their distances and set them equal to 150 miles to solve for t.
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M(5, 7) is the midpoint of rs The coordinates of S are (6, 9). What are the coordinates of R?
(5.5, 8)
(7, 11)
(10, 14)
(4, 5)
An isosceles triangle has a base with length 15 inches and two congruent sides with lengths of 15 inches each. Find the height of the triangle. (Round your answer to the nearest tenth of an inch.)
Final answer:
By using the Pythagorean theorem on one of the right triangles formed by dividing the isosceles triangle, we find the height to be approximately 13.0 inches when rounded to the nearest tenth.
Explanation:
To find the height of an isosceles triangle with a base of 15 inches and congruent sides each 15 inches, we can use the Pythagorean theorem or note that the triangle can be split into two right triangles by a height dropping from the vertex opposite the base to the midpoint of the base.
The midpoint will divide the 15-inch base into two segments, each 7.5 inches. The height of the isosceles triangle is the same as the height of the right triangle.
Using the Pythagorean theorem (a² + b² = c²), we can find the height (h) knowing that the hypotenuse (c) is one of the congruent sides (15 inches) and one leg (a, half of the base) is 7.5 inches:
h² + (7.5 inches)² = (15 inches)²
h² + 56.25 inches sup>2 = 225 inches²
h² = 225 inches² - 56.25 inches²
h² = 168.75 inches²
h = sqrt{168.75 inches²}
h approx 12.99 inches, which rounds to 13.0 inches to the nearest tenth.
Therefore, the height of the isosceles triangle rounds to 13.0 inches.
Find an ordered pair (x , y) that is a solution to the equation
what is the answer to 11 over 7 in improper fractions
Guess the value of the limit (correct to six decimal places). (if an answer does not exist, enter dne.) lim hâ0 (4 + h)5 â 1024 h
If, on average, Bob can make a sale to every 3rd person that comes into his store, how many people must come into Bob�s store if he wanted to make approximately fifteen (15) sales?
a,(-a)^2=a^2 This is true or false?