A waitress earned $73 for 6 hours of work. The total included $46 in tips. What was her hourly wage? (Show Work) ...?
what are the vertex focus and directrix of the parabola with the given equation
y=1/28(x-4)^2-5
The answer is:
vertex: (4,-5); focus: (4,2); directrix: y=-12
The vertex of the parabola is (4, -5), the focus is (4, 2), and the directrix is the line y = -12.
To determine the vertex, focus, and directrix of a parabola given by the equation y = {1{28}(x - 4)² - 5, we must first identify the standard form of a parabolic equation, which is y = a(x - h)² + k where (h, k) is the vertex of the parabola. In this case, we can see that the vertex (h, k) is (4, -5).
The focus of a parabola is a fixed point from which the distance to any point on the parabola is equal to the distance from that point to the directrix.
The directrix is a fixed straight line. The distance between the vertex and the focus, denoted as 4p, can be determined from the coefficient a in the standard form, where a = {1}/{4p} or p = {1}/{4a}. Thus, p = {1}/{4({1}/{28})} = 7. The focus is then at (h, k + p) = (4, -5 + 7) = (4, 2).
The directrix has the equation y = k - p, so it will be y = -5 - 7 = -12. The parabola opens upwards because the value of a is positive.
In summary, the vertex of the parabola is (4, -5), the focus is (4, 2), and the directrix is the line y = -12.
Which shows the conversion of 0.427 kg to pounds?
There are 2.2 pounds in 1 kilogram.
A.
0.427 kg × 2.2 lb/kg = 9.39 lb
B.
0.427 kg × 2.2 lb/kg = 0.939 lb
C.
0.427 kg + 2.2 lb/kg = 2.627 lb
D.
0.427 kg ÷ 2.2 lb/kg = 0.194 lb
To convert 0.427 kg to pounds, multiply 0.427 by 2.2, resulting in approximately 0.939 pounds. Thus, the correct answer is Option B.
To convert 0.427 kg to pounds, we use the given conversion factor: 1 kilogram (kg) = 2.2 pounds (lb). Here is the step-by-step explanation:
Write down the value to be converted: 0.427 kg.
Multiply by the conversion factor: 0.427 kg × 2.2 lb/kg.
Perform the multiplication: 0.427 × 2.2 = 0.9394 lb.
So, 0.427 kg is approximately 0.939 lb. Therefore, the correct answer is Option B.
If an object is dropped from a height of 144 feet, the function h(t)=-16t^2 +144 gives the height of the object after t seconds. When will the object hit the ground?
Determine the zeros of x^2 + 4x - 16 = -2x .
For the following system.
kx + y + z = 1
x + ky + z = 1
x+ y + kz = 1
Determine for what values of k the system has:
a) No solutions
b) One solution
c) A lot of solutions ...?
Okay, I really need help on this one. See attachment.
Carlos went out to a restaurant for dinner. he tipped 25% of his bill, which brought the sum of the dinner bill plus the tip to $45. how much was the original bill?
What is the simplified form of the quantity of x plus 8, all over 4 − the quantity of x plus 5, all over 4?
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
the simplified form of the quantity of x plus 8, all over 4 − the quantity of x plus 5, all over 4
[tex]\frac{x+8}{4} -\frac{x+5}{4}[/tex]
To simplify the expression , we check the denominator.
When the denominators are same then we subtract the numerators, we put denominator only once
[tex]\frac{x+8-(x+5)}{4}[/tex]
Multiply negative inside the parenthesis and combine like terms
[tex]\frac{x+8-x-5}{4}[/tex]
[tex]\frac{3}{4}[/tex]
Is 701. 5 = to 701. 50.
Final answer:
701.5 is equal to 701.50 because in decimals, trailing zeroes after the decimal point do not change the value of the number; they only indicate precision.
Explanation:
The question is about whether 701.5 is equal to 701.50. In mathematics, when comparing numbers with different numbers of decimal places, it's important to understand the significance of trailing zeroes in the decimal part.
A zero after the decimal point but at the end of a number (trailing zero) does not change the value of the number.
Therefore, 701.5 is exactly equal to 701.50
This is because the trailing zero in 701.50 does not add any value but merely serves as a placeholder, indicating precision to the hundredth place without changing the number's value.
There are 84 new houses being built in a neighborhood. Last month, 1/3 of them were sold. This month, 5/7 of the remaining houses were sold. How many houses are left to be sold?
The number of houses left to be sold is 9, calculated from the initial total and the proportions sold each month.
The number of houses left to be sold is 9.
Initially, 1/3 of the 84 new houses were sold, which is 84 × (1/3) = 28 houses sold.
There were 84 - 28 = 56 houses remaining.
From these remaining houses, 5/7 were sold this month, which equates to 56 × (5/7) = 40 houses sold. Thus, 56 - 40 = 16 houses are left to be sold.
The cost of producing pots is the initial investment, $175, plus $3.50 in materials per pot. Therefore, the function C(p) = 175 + 3.5p defines the cost, C, of producing a number of pots, p. To the nearest cent, how much will it cost to produce 125 pots? (Enter only the number without the dollar sign, such as 25.03 for twenty-five dollars and 3 cents.)
How many pots can be produced if the budget is limited to $450?
Apply the rules for order of operations to simplify 2+3-4+(5X4)
Divide and simplify.
(24a^3)/(35b^2) divided by (16a)/(14b^3)
A. (12a)/(35b)
B. (5a^2b)/(3)
C. (4a^2)/(5b)
D. (3a^2b)/(5)
2cos^2x+3cosx-2=0 ...?
A polynomial function has a zero at x=3 which of the follwing expressions must be one factor of the polynomial. A. x + 3 b. 3x C. x^3 D. x - 3 but could you explain how to do it so i can do it on my own! ...?
Answer: The correct option is (D) (x - 3).
Step-by-step explanation: Given that a polynomial function has a zero at x = 3.
We are to select the correct expression that must be a factor of the polynomial.
FACTOR THEOREM : The theorem states that if x = a is a zero of a polynomial p(x), then (x - a) will be a factor of the polynomial p(x).
In case of our given polynomial, since x = 3 is a zero of the polynomial, so by factor theorem, we can say that
(x - 3) is a factor of the given polynomial.
Thus, the required factor is (x - 3).
Option (D) is CORRECT.
What is 972 divided by 37?
To solve the inequality 9x > -4, the inequality sign must be reversed.
true or false?
Graph the function. Identify the vertex and axis of symmetry.
f(x)=-2x^2+2x-1
Answer:
Part A) The vertex is the point [tex](0.5,-0.5)[/tex]
Part B) The axis of symmetry is [tex]x=0.5[/tex]
Part C) The graph in the attached figure
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex of the parabola
and the axis of symmetry is equal to the x-coordinate of the vertex
so
[tex]x=h[/tex] -----> equation of the axis of symmetry
In this problem we have
[tex]f(x)=-2x^{2}+2x-1[/tex]
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]f(x)+1=-2x^{2}+2x[/tex]
Factor the leading coefficient
[tex]f(x)+1=-2(x^{2}-x)[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]f(x)+1-(1/2)=-2(x^{2}-x+(1/4))[/tex]
[tex]f(x)+(1/2)=-2(x^{2}-x+(1/4))[/tex]
Rewrite as perfect squares
[tex]f(x)+(1/2)=-2(x-(1/2))^{2}[/tex]
[tex]f(x)=-2(x-(1/2))^{2}-(1/2)[/tex] -----> equation in vertex form
The vertex of the parabola is the point [tex](0.5,-0.5)[/tex]
Is a vertical parabola open downward
The axis of symmetry is equal to
[tex]x=0.5[/tex]
see the attached figure to better understand the problem
For what intervals is f(x)=xe^-x concave down?
The function f(x) = xe⁻ˣ is concave down for intervals where the second derivative f''(x) is negative, which occurs when x > 0.
To determine the intervals where the function f(x) = xe⁻ˣ is concave down, we need to find the second derivative of the function and identify where it is negative. The first derivative of the function f'(x) = e⁻ˣ - xe⁻ˣ is obtained using the product rule. Then, we take the second derivative: f''(x) = -e⁻ˣ - e⁻ˣ + xe⁻ˣ = -2e⁻ˣ + xe⁻ˣ.
To find where the function is concave down, we need to find the intervals where f''(x) < 0. By analyzing the second derivative, we can see that the term -2e⁻ˣ is always negative, while the term xe⁻ˣ can be either positive or negative depending on the value of x.
For x > 0, the term xe⁻ˣ is positive, making f''(x) more negative, therefore, the function is concave down for x > 0.
Ralph is 3 times as old as Sara. In 6 years, Ralph will be only twice as old as Sara will be then. Find Ralph's age now. Ralph's age is _____. A)6 B)12 C)18 D)24
Answer:
C)18
Step-by-step explanation:
Let Sara present age = x years.
According to question Ralph present age =3x
Sara age after 6 years =x+6.
Ralph age after 6 years =3x+6.
After 6 years Ralph will be only twice as old as Sara will be then.
3x+6=2(x+6)
Solving for x:
3x+6=2x+12
3x-2x=12-6
x=6.
Ralph present age = 3x=3(6)= 18 years.
Option C.
In the drawing, six out of every 10 tickets are winning tickets. Of the winning tickets, one out of every three awards is a larger prize.
What is the probability that a ticket that is randomly chosen will award a larger prize?
Answer:
The probability that a ticket that is randomly chosen will award a larger prize is:
1/5=0.2
Step-by-step explanation:
Let A denote the event that the ticket is a winning ticket.
B denote the event that there is a larger prize.
A∩B denote the event that there is a larger prize on the winning ticket.
Let P denote the probability of an event.
Now according to the given information we have:
[tex]P(A)=\dfrac{6}{10}[/tex]
Also, [tex]P(B|A)=\dfrac{1}{3}[/tex]
Hence, we are asked to find: P(A∩B)
We know that:
[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}\\\\\\\dfrac{1}{3}=\dfrac{P(A\bigcap B)}{\dfrac{6}{10}}\\\\\\P(A\bigcap B)=\dfrac{1}{3}\times \dfrac{6}{10}\\\\P(A\bigcap B)=\dfrac{2}{10}=\dfrac{1}{5}=0.2[/tex]
The probability is:
1/5=0.2
The overall probability that a randomly chosen ticket will award a larger prize is 0.2, or 20%, obtained by multiplying the probability of drawing a winning ticket (0.6) with the probability of winning a larger prize if the ticket is a winner (0.333).
For the probability that a ticket randomly chosen will award a larger prize, given that 6 out of every 10 tickets are winners and of those, 1 out of every 3 is a larger prize.
First, we calculate the probability of drawing a winning ticket, which is 6/10 or 0.6.
Then we compute the probability of the winning ticket awarding a larger prize, which is 1/3 or approximately 0.333.
To find the overall probability of a randomly chosen ticket awarding a larger prize, we multiply these two probabilities together:
Overall probability = Probability of winning ticket×Probability of larger prize on winning ticket
Overall probability = 0.6 ×0.333
Overall probability ≈ 0.2
So, the probability that a ticket awards a larger prize is 0.2, or 20%.
81 is 37.5% of what number
Which of the expressions is rational?
Is the following definition of supplementary reversible? If yes, write it as a true biconditional .
Linear pairs of angles are supplementary.
A. The statement is not reversible
B. Yes, if angles form a linear pair, they are supplementary
C. Yes, angles form a linear pair if ( and only if ) they are supplementary
D. Yes, angles are supplementary if they form a linear pair
Factor completely 5x2 – 5x – 100
A)5(x + 4)(x – 5)
B)5(x – 2)(x + 10)
C)(5x + 20)(x – 5)
D)(5x – 10)(x + 10) ...?
Final answer:
The quadratic equation 5x² - 5x - 100 is factored completely by first taking out the greatest common factor of 5, and then finding two binomials that multiply to give the remaining quadratic. The correct factorization is 5(x - 5)(x + 4), which is option A.
Explanation:
To factor the quadratic equation 5x² − 5x − 100 completely, we need to find two binomials that, when multiplied together, will give us the original equation. First, we will factor out the greatest common factor (GCF), which is 5. This leaves us with:
5(x² − x − 20)
Now, we need to factor the quadratic expression inside the parentheses. The factors of −20 (the constant term) that add up to −1 (the coefficient of the middle term) are −5 and 4. Thus:
5(x − 5)(x + 4)
We can confirm that none of the other choices provide the correct factors:
Choice B does not give us the original middle term when expanded.Choice C is incorrect because it does not result in the original constant term when expanded.Choice D also doesn't give us the desired constant term.Therefore, the correct answer is 5(x − 5)(x + 4), which corresponds to option A.
The product of two numbers is 48, and one of the numbers is 12. find the other number.
compare and contrast the division property of equality and the division property of inequality.a.the two properties are exactly the same.b.the two properties are exactly the same when dividing by a positive number. for the division property of inequality, dividing by a negative number causes the relation symbol to change. dividing both sides of an equation by a negative number does not have an effect on the equal sign.c.the two properties are exactly the same when dividing by a negative number. for the division property of inequality, dividing by a positive number causes the relation symbol to change. dividing both sides of an equation by a positive number does not have an effect on the equal sign.d.the two properties are exactly the same when dividing by a positive number. for the division property of equality, dividing by a negative number causes the equal sign to change. dividing both sides of an inequality by a negative number does not have an effect on the relation symbol.
Wesley ran of a mile on saturday and of a mile on sunday how many miles did wesley run in all
What is the description of one-hundredth of 36?
Answer:
0.36
Step-by-step explanation:
One - hundredth =[tex]\frac{1}{100}[/tex]
one hundredth means we have to divide 1 by hundred.
When we divide one by hundred we get 0.01
To find one-hundredth of 36, than we have to multiply 36 by 0.01
After multiplying we get
36×0.01=0.36
OR
36×[tex]\frac{1}{100}[/tex]=0.36
Hence, the correct answer is 0.36
One-hundredth of 36 is 0.36.
To find one-hundredth of 36, we simply need to divide 36 by 100. Dividing by 100 means shifting the decimal point two places to the left. Therefore, one-hundredth of 36 is 0.36.
For example, if we have the number 36, we can represent this as 36/1 to show that we have 36 whole parts. When we want one-hundredth of these 36 parts, we are seeking 1 part out of every 100 parts. So, we would write this as (36/1)/ (100/1) which simplifies to 36/100. After simplification, we get 0.36 as the final answer.
This concept is similar to understanding that 1 cm is 1/100th of a meter. By using division or understanding fractions and decimal places, we can easily find one-hundredth of any given number.