Evaluate the following expression.
153^0
Which relationship is always true for the angles r, x, y, and z of triangle ABC?
x + z = y
180 degrees − x = r
x + y + z = 180 degrees
x + y + z = 90 degrees
Answer with explanation:
In the problem , given about triangle, four angles are given , r,x ,y and z.
→→One of the three, must be exterior angle of triangle ABC, and other three, must be interior angles of Δ ABC.
So, two properties of triangle that we will use in this problem
1. Angle sum property of triangle: the sum of three angles of triangle is 180°.
2.Exterior angle property: Exterior angle of a triangle is equal to sum of two interior opposite angles.
So, if x, y and z are interior angles , and r is exterior angle
then
Option 3: x + y + z = 180° is always true.
either, r= y + z
and ,r +x=180°
f(x) = sin(x^2 - 2)
find points of discontinuity, if any ...?
On a coordinate grid, both point (−4, −1) and (2, 6) point are reflected across the y-axis. what are the coordinates of the reflected points?
Simplify each expression:
12^log base 12 of 144
The simplification of the mathematical expression 12^log base 12 of 144 is 144, according to the properties of logarithms.
Explanation:To simplify 12^log base 12 of 144, you need to understand the definition of logarithms. A logarithms in base b of a number x is the power to which we have to raise b to get x. In other words, if y = log base b of x, then b^y = x.
Applying this to our example, since log base 12 of 144 is 2 (because 12^2 = 144), then 12^log base 12 of 144 = 12^2 = 144.
Therefore, the simplification of the expression 12^log base 12 of 144 is 144.
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To simplify the expression 12^log base 12 of 144, evaluate the logarithm, substitute the value back into the expression, and perform exponentiation.
Explanation:In essence, the logarithm with base 12 and argument 144 essentially asks, "To what power must 12 be raised to obtain 144?" The answer, as established, is 2. Consequently, when we raise 12 to the power of 2, we retrieve the original value of 144. This simplification showcases the inherent relationship between logarithms and exponentiation, providing a clearer understanding of the expression's evaluation.
To simplify the expression 12^log12(144), we need to evaluate the logarithm first. Since the base of the logarithm is the same as the base of the exponentiation, we can simplify it to just log(144). Using a calculator, we find that log(144) = 2.158. Now we can substitute this value back into the original expression: 12^2.158. Evaluating the exponentiation gives us the final answer: 205.08.
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48 is how many percent of 70
distance can be represented by absolute value.true or false.?
Mrs.ulrich has 3 times as many markers as colored pencils.the total number of markers and colored pencils is 84.how many markers does mrs.ulrich have
What is the factored form of the expression?
s^4 – 16
A. (s - 2)^2(s + 2)^2
B. (s - 2)(s + 2)
C. (s - i)(s + i)(s - 2)(s + 2)
D. (s - 2i)(s + 2i)(s - 2)(s + 2)
can someone help me please Write 243 in exponential form ...?
The exponential form of 243 is: 243 = 3⁵.
To write 243 in exponential form, you need to express it as a power of a base number.
The most common base used for this purpose is 3.
243 can be written as: 243 = 3⁵
Here's the reasoning:
[tex]\[ 3 \times 3 = 9 \][/tex]
[tex]\[ 9 \times 3 = 27 \][/tex]
[tex]\[ 27 \times 3 = 81 \][/tex]
[tex]\[ 81 \times 3 = 243 \][/tex]
So, 243 is 3 raised to the power of 5.
Therefore, 243 In exponential form is: [tex]\[ 243 = 3^5 \][/tex]
Solve -2.5n + 8.7 > 5.45.
n < 1.3
n > 1.3
n < -5.66
n > -5.66
Answer:
N < 1.3
Step-by-step explanation:
Go thank the answer above! :)
The formula for the area of a square can be written as A = s^2 and means “area equals side-squared”. Explain how the formula for the area of a square can be derived from the formula for the area of a rectangle.
The area of a square, represented as A = s², is derived from the formula for the area of a rectangle (A = w × h) where the width and height are equal in a square, hence the side (s) is squared (s × s).
The formula for the area of a square is derived from the area of a rectangle because a square is a special type of rectangle where all sides are equal.
The formula for the area of a rectangle is A = w × h, where w is the width and h is the height. In the case of a square, the width and height are the same, which we call the side length s. Therefore, the formula A = s imes s, or A = s², naturally follows for finding the area of a square.
To visualize this, consider placing a square on graph paper. Each side of the square touches the same number of squares on the graph paper because the sides are of equal length.
When you multiply the side length by itself, you are effectively counting the total number of squares inside the square, which gives the area in square units. This visual method confirms that the area of a square is indeed the side length squared.
A box contains 13 transistors, 3 of which are defective. if 3 are selected at random, find the probability that
a. All are defective
b. None are defective
a. Probability all defective: [tex]\( \frac{1}{286} \)[/tex]. b. Probability none defective: [tex]\( \frac{60}{143} \)[/tex].
To solve this problem, we can use the concept of probability.
a. Probability that all selected transistors are defective:
When selecting the first transistor, the probability of choosing a defective one is [tex]\( \frac{3}{13} \)[/tex], as there are 3 defective transistors out of 13 total.
After the first defective transistor is chosen, there are 2 defective transistors left out of 12 total transistors.
So, the probability of choosing a second defective transistor given that the first one was defective is [tex]\( \frac{2}{12} \).[/tex]
Similarly, for the third selection, the probability of choosing a defective transistor given that the first two were defective is [tex]\( \frac{1}{11} \)[/tex].
To find the probability that all three selected transistors are defective, we multiply the individual probabilities:
P(All defective) = [tex]\frac{3}{13} \times \frac{2}{12} \times \frac{1}{11}[/tex]
P(All defective) = [tex]\frac{3 \times 2 \times 1}{13 \times 12 \times 11}[/tex]
P(All defective) = [tex]\frac{6}{1716}[/tex]
P(All defective) = [tex]\frac{1}{286}[/tex]
So, the probability that all selected transistors are defective is [tex]\( \frac{1}{286} \).[/tex]
b. Probability that none of the selected transistors are defective:
This is essentially the complement of the event that all selected transistors are defective. Since there are 3 defective transistors out of 13, the remaining 10 transistors are not defective.
So, to find the probability that none are defective, we select 3 out of the 10 non-defective transistors.
P(None defective) = Number of ways to choose 3 non-defective transistors/Total number of ways to choose 3 transistors
P(None defective) = [tex]\frac{{\binom{10}{3}}}{{\binom{13}{3}}}[/tex]
P(None defective) = [tex]\frac{{120}}{{286}}[/tex]
P(None defective) = [tex]\frac{{60}}{{143}}[/tex]
So, the probability that none of the selected transistors are defective is [tex]\( \frac{{60}}{{143}} \).[/tex]
Which algebraic expression means “three more than a number squared”?
a) 2n+3
b) 2n-3
c) n^2+3
d) n^2-3
Option C is the correct anwser, Hope this helps :)
6375/10000 in simplest form
When you see a traffic light turn red, you apply the brakes until you come to a stop. Suppose your initial speed was 11.2 m/s, and you come to rest in 34.7 m. How much time does this take? Assume constant deceleration.
...?
The revenue from selling x shirts is r(x) = 11x.
The cost of buying x shirts is c(x) = 6x + 20.
The profit from selling x shirts is p(x) = r(x) – c(x).
What is p(x)?
A. p(x) = 5x + 20
B. p(x) = 17x + 20
C. p(x) = 17x – 20
D. p(x) = 5x – 20
HELP!!give me the correct answer!! thank you
Answer:
Correct answer is: D p(x)=5x-20: Apex
Step-by-step explanation:
The value of the profit function is equal to 5x - 20. The correct option is D.
Given that:
Revenue function: r(x) = 11x
Cost function: c(x) = 6x + 20
To find the profit function, we need to subtract the cost function from the revenue function:
p(x) = r(x) - c(x)
Substituting the given revenue and cost functions and calculated as:
p(x) = 11x - (6x + 20)
Simplifying above expression as:
p(x) = 11x - 6x - 20
Combining like terms as:
p(x) = 5x - 20
Therefore, the value of the profit function is equal to 5x - 20. The correct option is D.
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What is the value of x, when 10(x + 2) = 5(x + 8)?
The value of ( x ) is 4.
To find the value of ( x ) in the equation [tex]\( 10(x + 2) = 5(x + 8) \)[/tex], we'll follow these steps:
[tex]\[ 10(x + 2) = 5(x + 8) \][/tex]
[tex]\[ 10x + 20 = 5x + 40 \][/tex]
[tex]\[ 10x - 5x + 20 = 5x - 5x + 40 \][/tex]
[tex]\[ 5x + 20 = 40 \][/tex]
[tex]\[ 5x + 20 - 20 = 40 - 20 \][/tex]
[tex]\[ 5x = 20 \][/tex]
[tex]\[ \frac{5x}{5} = \frac{20}{5} \][/tex]
[tex]\[ x = 4 \][/tex]
Therefore, [tex]\( x = 4 \)[/tex] is the solution.
A company has tow electric motors consume varying amounts of power. The power consumed by each motor is a function of the time (t in minutes) for which it runs. The cost of power (in $) to run one motor is given by the function Ca(t)=t^2-2t+5. The cost of running the second motor is given by Cb(t)=3t+2. Which gives the total cost of running both motors?
C(t)=3t^3-6t^2+15t
C(t)=2t^2-4t+10
C(t)=t^2+t+7
C(t)=3t^3+6t^2-15t
Answer:
Option (c) is correct.
The total cost of running both motors is [tex]t^2+t+7[/tex]
Step-by-step explanation:
Given : The cost of power (in $) to run one motor is given by the function [tex]C_a(t)=t^2-2t+5[/tex] and The cost of running the second motor is given by [tex]C_b(t)=3t+2[/tex]
We have to find the total cost of running both motors.
Since we are given the cost to run each motors so, total cost will be the sum of running both motors.
Let C(t) be the total cost of running both motors.
[tex]C(t)=C_a(t)+C_b(t)[/tex]
Substitute,
[tex]C_a(t)=t^2-2t+5[/tex]
and [tex]C_b(t)=3t+2[/tex]
We get,
[tex]C(t)=t^2-2t+5+3t+2[/tex]
Simplify, we get,
[tex]C(t)=t^2+t+7[/tex]
Thus, The total cost of running both motors is [tex]t^2+t+7[/tex]
Find the product for 7 x 2/3
The word product is the answer to a multiplication problem.
7 x 2/3
7/1 x 2/3
(7 x 2)/(1 x 3)
Answer: 14/3
What is the value of the expression when a = 5 and b = 2?
a + 2b −3
6
9
11
24
A = bh/2
A' = b'h/2 + bh'/2
b' = (A' - bh'/2)(2/h) can someone explain this. its steps to the derivative of bh/2.
Answer:
To find A' they used the rule of multiplication, which is:
the derivative of a product of two terms is the first term times the derivative of the second term plus the second term times the derivative of the first.
To find b' they just isolated b'
Step-by-step explanation:
Franko's pizza is selling their pizzas 35% cheaper than usual. if a pizza normally costs $12.00, how much is it now?
Solve for x.
log6(2x + 3) = 3 ...?
The value of x that satisfies the original equation is 106.5. To solve the given logarithmic equation, convert it to its exponential form and simplify. Subtract 3 from both sides, and finally divide by 2 to find that x equals 106.5.
Explanation:To solve for x in the equation log6(2x + 3) = 3, we can convert the logarithmic equation into its exponential form. This means that we interpret the equation as 6 raised to the power of 3 equals 2x + 3:
63 = 2x + 3
The next step is to simplify. 6 to the power of 3 is 216:
216 = 2x + 3
We can now solve for x by first subtracting 3 from both sides:
216 - 3 = 2x
213 = 2x
And then dividing by 2:
x = 213 / 2
x = 106.5
Thus, the value of x that satisfies the original equation is 106.5.
(URGENT-15 Points) Can someone help me/check my answers for this? Thank you! For the first screenshot, my answers for 1-5 are: (1) 79.2 (2) 12.4 (3) 78 and 82 (4) 76 and 84 (5) 74 and 86. I am stuck on questions 6-8 (#8 is on the second screenshot at the top...). On the second screenshot, I'm not sure how to answer question (9) based on the dot-plot on the first screenshot. For (10), if it's asking for the mean of these numbers, I got 23.8. If it's just asking for the sum, I got 119. For 11-12, the means aren't the same because this mean (#10) is based on the random sample generated from the original number of grades, while the first mean (#2) was based on the total population of grades for the entire class. It would make sense that the second mean would be smaller than the first. I'm giving away 15 points to the person who can help me with this and check my answers! I'd really appreciate it! :)
jake goes to the grocery store and buys 3 apple, 2 cans of soup, and 1 box of cereal. the apples cost $0.89 each; the soup costs $2.98 per can; and the box of cereal costs $4.99.
Answer:
c=(3 x 0.89)+(2.98)+4.99
Step-by-step explanation:
What is the product of 1.5 and 2.8 is 4.2?
The product of 1.5 and 2.8 is correctly calculated as 4.2, in accordance with the rules of significant figures.
Explanation:The statement "1.5 and 2.8 is 4.2" seems to imply a multiplication between 1.5 and 2.8 resulting in 4.2. However, this is a misconception. The actual product of multiplying 1.5 by 2.8 is 4.2. To confirm this, you multiply the two numbers: 1.5 × 2.8 equals 4.2.
In significant figures, if the numbers 1.5 and 2.8 were part of a calculation with inexact numbers, the answer would be limited by the smallest number of significant figures present in the inexact numbers. In this case, as both 1.5 and 2.8 have two significant figures, the product is correctly expressed with two significant figures as 4.2.
Let f and g be two functions whose second derivatives are defined. Then (f · g) '' = f · g '' + f '' · g. true or false?
The statement (f · g)'' = f · g'' + f'' · g is false. The second derivative of a product of two functions is given by a different formula.
The statement (f · g)'' = f · g'' + f'' · g is false.
The second derivative of a product of two functions, f(x) and g(x), is given by (f · g)'' = f''g + 2f'g' + fg''.
To see why the given statement is false, consider the example where f(x) = x and g(x) = x^2. The left-hand side is 0, but the right-hand side is not zero, so the statement does not hold true.
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f the graph of y=ax+b/x+c has a horizontal asymptote y=2 and a vertical asymptote x=-3 then a+c=?
a)-3
b)-1
c)0
d)1
E)5 ...?
Answer: 5
Step-by-step explanation:
Lim x-> a (ax+b)/x+c = a you know that a=2
Since the limit of x ->-3 equals infinity, you know that x =3.
Thus a+c = 5
A computer uses 239 watts per hour. How many watts would it use if it is on for 8 days?
Answer:
29 watts
Step-by-step explanation:
239 ÷ 8 = 29.875