The x-coordinate of the vertex is 2 and the y-coordinate is -10. The discriminant is 144.
Explanation:The quadratic function can be rearranged into the form ax² + bx + c = 0, where a = 2, b = -8, and c = -10. To find the x-coordinate of the vertex, we use the formula x = -b / (2a). Plugging in the values, we get x = -(-8) / (2*2) = 2. The y-coordinate of the vertex can be found by substituting the x-coordinate into the original function. Plugging in x = 2, we get f(2) = 2(2)² - 8(2) - 10 = -10.
The discriminant is calculated as b² - 4ac. Plugging in the values, we get (-8)² - 4(2)(-10) = 64 + 80 = 144.
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The price of bananas is $6.50 for 5 pounds. What is the price as a unit rate?
$6.50/1lb
$1.30/1lb
$1/30/3lb
$1.05/1lb
What is the volume of a right circular cone with a diameter of 21 centimeters and a height of 87 centimeters? Use 3.14 as an approximation for π. Round your answer to the nearest tenth.
A grab bag contains 8 football cards and 2 basketball cards. an experiment consists of taking one card out of the bag, replacing it, and then selecting another card. determine whether the events are independent or dependent. what is the probability of selecting a football card and then a basketball card? express your answer as a decimal.
Answer:
Independent - 0.16
Step-by-step explanation:
what is the reciprocal of 8-3i
The reciprocal of the complex number 8-3i is found by dividing its complex conjugate (8+3i) by the modulus squared of 8-3i, which is 73. The result is 8/73 + 3i/73.
Explanation:The reciprocal of a complex number is the complex conjugate of that number divided by the modulus squared of the original number. In the case of the complex number 8-3i, its complex conjugate is 8+3i. To find the reciprocal of 8-3i, you would divide this complex conjugate by the modulus squared of 8-3i.
First, calculate the modulus squared of 8-3i:
Modulus of 8-3i = sqrt(82 + (-3)2) = sqrt(64 + 9) = sqrt(73).Modulus squared = (sqrt(73))2 = 73.Then, divide the complex conjugate by this modulus squared to get the reciprocal:
Reciprocal of 8-3i = (8+3i) / 73 = 8/73 + 3i/73.
Given that jklm is a rhombus, find kjm.
a. 37°
c. 106°
b. 74°
d. 143°
Answer:
C.
Step-by-step explanation:
4/101.78 do long divison for this problem
How much money will you have at the end of one year if interest is compounded semiannually at 10% on a $600 deposit? A. $661.50 B. $662.00 C. $660.00 D. $659.50
Compound interest on a principal of $600.00 at a rate of 10% per year compounded twice per year over a period of one year results in an accumulated total of $661.50 (principal plus interest).
What is compound interest rate?Compound interest is computed as interest on the principle of an account plus any accrued interest.
Compound interest can be calculated using the following formula:
A = P(1 + r/n[tex])^{nt}[/tex]
,where x = compound interest
P = principal (the initial deposit or loan amount)
r = annual interest rate
n = the number of compounding periods per unit of time
t = the number of time units the money is invested or borrowed for
Given:
P = principal (the initial deposit amount) = $600
r = annual interest rate = 10%
n = the number of compounding periods per unit of time = 2
t = 1
First, convert R as a percent to r as a decimal
r = R/100
r = 10/100
r = 0.1 rate per year,
Then solve the equation for A
A = P(1 + r/n[tex])^{nt}[/tex]
A = 600.00(1 + 0.1/2[tex])^{(2)(1)}[/tex]
A = 600.00(1 + 0.05[tex])^{(2)}[/tex]
A = $661.50
Therefore, the amount is $661.50.
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If the probability of an event is 0.7 repeating, what are the odds against the event
Which of the following is not a way to represent the solution of the inequality 2(x − 1) less than or equal to 10? (1 point)
A. x less than or equal to 6
B. 6 greater than or equal to x
C. A number line with a closed circle on 6 and shading to the left
D. A number line with a closed circle on 6 and shading to the right
A and B are the same and C is proven wrong due to the equality sign lkeaving only D to be correct
There are 36 students on the bus. There are 2 times as many girls than boys on the bus. On your paper, write a system of liner equations and solve for the number of girls and boys on bus. How many girls are on the bus. A-12 B-24 C-17 D-19
Final answer:
To find the number of girls and boys on the bus, create a system of linear equations and solve for the variables. In this case, there are 12 boys and 24 girls on the bus.
Explanation:
To solve for the number of girls and boys on the bus:
Let G represent the number of girls and B represent the number of boys.
From the problem, G = 2B and G + B = 36.
Substitute G = 2B into the second equation to get 2B + B = 36, which gives B = 12. Therefore, there are 12 boys and 24 girls on the bus.
The x-intercept of the graph of f(x)= 3log(x-5)+2 is:
Answer: [tex]\frac{1}{e^{\frac{2}{3}}}+5[/tex] or 5.51
Step-by-step explanation:
The given function : [tex]f(x)= 3\log(x-5)+2[/tex]
We know that , the x-intercept is the point on graph( basically intersection of graph and x-axis) where y coordinate is zero.
I.e. for x-intercept of function , f(x) =0
i.e. [tex]0= 3\log(x-5)+2[/tex]
[tex]\Rightarrow\ \log(x-5)=\dfrac{-2}{3}[/tex]
Taking exponent on both sides , we get
[tex]x-5=e^{\frac{-2}{3}}\\\\\Rightarrow\ x=e^{\frac{-2}{3}}+5\ \ or\ \ x=\dfrac{1}{e^{\frac{2}{3}}}+5[/tex]
On simplification , [tex]\frac{1}{e^{\frac{2}{3}}}+5\approx5.51[/tex].
Hence , the x-intercept of the graph f(x)= [tex]\dfrac{1}{e^{\frac{2}{3}}}+5[/tex] or 5.51.
Answer:
10^-2/3 +5
Step-by-step explanation:
How would you convert the repeating, nonterminating decimal into a fraction? Explain the process as you solve the problem. 0.1515
Answer:
5/33
Step-by-step explanation:
x = 0.1515
100 x = 15.1515
100 x - x = 15.1515 - 0.1515
99 x = 15
x = 15 / 99 = 3 ∙ 5 / 3 ∙ 33 = 5 / 33
0.15165 = 5 / 33
find multiplicative inverse of 2+3i / 3-2i
Identify the function that best models the given data.
Answer: W(i) = 3.125x^2 − 14.5x + 208.5
Step-by-step explanation:
There are 4! (or 24) "words" that can be formed using each of the letters a, b, c and d once. if these "words" are alphabetized, which one is 17th?
A circle is drawn in the xy-coordinate plane. if there are n different points (x, y) on the circle such that xy = 0, then the possible values of n are
question is in the image
the polynomial (x - 2) is a factor of the polynomial 3x2 - 8x + 2.
First, let's factor 3x²-8x+2
Looking at wee can see that the first term is and the last term is where the coefficients are 3 and 2 respectively.
Now multiply the first coefficient 3 and the last coefficient 2 to get 6. Now what two numbers multiply to 6 and add to the middle coefficient -8? Let's list all of the factors of 6:
Factors of 6:
1,2,3,6
-1,-2,-3,-6 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 6
1*6
2*3
(-1)*(-6)
(-2)*(-3)
note: remember two negative numbers multiplied together make a positive number
Now, which of these pairs add to -8? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -8
None of these pairs of factors add to -8.
So the expression 3x²-8x+2 cannot be factored.
So (x - 2) is NOT a factor of 3x²-8x+2
So the statement is false
Answer:
B.false
Step-by-step explanation:
apexs
How many distinguishable 7 letter "words" can be formed using the letters in alabamaalabama?
Final answer:
The number of distinguishable 7-letter words that can be formed using the letters in alabamaalabama is 5040.
Explanation:
The number of distinguishable 7-letter words that can be formed using the letters in alabamaalabama can be calculated using permutations. In this case, we have 12 letters, but some of them are repeated. To calculate the total number of permutations, we need to divide the total number of permutations by the factorial of the number of times each repeated letter appears. The word alabamaalabama has 7 distinct letters, so there are no repeated letters in this case. Therefore, the number of distinguishable 7-letter words that can be formed is simply 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.
930 miles to travel with a car that gets 22 miles per gallon. How much will it cost to travel if gas costs 2.03 a gallon?
There are 150 marigold plants in a back yard. Each month, the number of marigold plants decreases by 15%. There are 125 sunflower plants in the back yard. Each month, 8 sunflower plants are removed. Part A: Write functions to represent the number of marigold plants and the number of sunflower plants in the back yard throughout the months. (4 points) Part B: How many marigold plants are in the back yard after 3 months? How many sunflower plants are in the back yard after the same number of months? (2 points) Part C: After approximately how many months is the number of marigold plants and the number of sunflower plants the same? Justify your answer mathematically. (4 points)
To solve this problem, let us first assign variables. Let us say that:
X = number of marigold plants
Y = number of sunflower plants
n = number of months
We can see that in the given problem, X is decreasing by a percentage, this means that we have to set-up a geometric equation while for Y the decrease is linear so we set-up an arithmetic equation.
Part A.
For marigold plants X, a geometric sequence has a general form of:
X = Xo * (1 + r)^n
where r = -15% = -0.15 (negative since it is decreasing)
Xo = the initial amount of marigold plants = 150
X = 150 * (1 – 0.15)^n
X = 150 (0.85)^n
For the sunflower plants Y, an arithmetic sequence has a general form of:
Y = Yo + d * n
where d = -8 and Yo = 125
Y = 125 – 8 n
Part B. For n = 3
X = 150 (0.85)^3 = 92.12 = 92
Y = 125 – 8 (3) = 101
Part C. From Part B we see that the two values are very far from each other when n = 3, therefore they must be similar when n < 3. So we try n = 2
X = 150 (0.85)^2 = 108.38 = 108
Y = 125 – 8 (2) = 109
Therefore the two plants have approximately similar amount after 2 months.
Question 3 (Essay Worth 10 points)
(03.06 MC)
Part A: Eveline rented a car at $180 for 4 days. If she rents the same car for 9 days, she has to pay a total rent of $325.
Write an equation in the standard form to represent the total rent (y) that Eveline has to pay for renting the car for x days. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
To which real number subset(s) do the following real numbers belong?
-4, -2, 1, 3, 5
A. whole numbers
B. natural numbers
C. integers and rational numbers
D. natural and irrational numbers
Find the value of X and Y. Show your work.
A company makes triangular plates for individual slices of pizza. For each plate, the base is 7 inches and the height is 12 inches. The area of the top of the plate is ____ inches squared.
Answer:
42 Inches squared ( hope that helps) ;)
The area of the top of the plate will be 42 inches squared.
What is the area of the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,
A = (1/2) × h·b
A company makes triangular plates for individual slices of pizza. For each plate, the base is 7 inches and the height is 12 inches.
Then the area of the triangle is given as,
Area = 1/2 x 12 x 7
Area = 6 x 7
Area = 42 square inches
The area of the top of the plate will be 42 inches squared.
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The diameter of a beach ball is 10 inches. How many cubic inches of air can the beach ball hold? Use 3.14 for pie . Round to the nearest tenth of a cubic inch
volume = 4/3 x PI x r^3
r = 10/2 =5
V = 4/3 x 3.14 x 5^3 = 523.333
523.3 cubic inches
How to algebraically find the limit of a function as x approaches infinity?
Well... One way you can do this is by testing a set of arrays and see the trend. If I chose to find what y1 is in (100, y1) and what y2 is in (101, y2), I would find the difference between y2 and y1. If y2 - y1 is positive, this means there is a positive relationship and y is also approaching POSITIVE infinity. A negative relation means that it is approaching NEGATIVE infinity. However, it could be approaching a single number like "4" for instance, and you just need to plug in the right number of data sets to make that educated guess.
Formula Example:
5 + 1 / (x + 1) will always approach 5 because "1 / (x + 1) will approach 0".
Hope this helps.
To algebraically find limit of a function as "x" approaches infinity, identify highest degree term, divide by "x", and evaluate the resulting expression.
To algebraically find the limit of a function as x approaches infinity, we can follow the below steps :
(i) Identify the highest degree term: Determine the term with the highest power of x in the function.
(ii) Ignore lower degree terms: If the highest degree term is dominant, ignore lower degree terms and constants.
(iii) Divide by x: Divide every term in the function by x raised to the power of the highest degree.
(iv) Evaluate the limit: Examine the resulting expression as x approaches infinity. If the expression tends to a finite value, that is the limit. If the expression diverges (goes to infinity or negative infinity), then the limit does not exist.
By simplifying the function and observing the behavior of the resulting expression, we can algebraically determine the limit of the function as x approaches infinity.
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The number of points awarded in each round of a game can be represented by f(x) = 2x, where x represents the number of the round.
What is x when f(x) = 16?
Answer:
x=4; in round 4, 16 points will be rewarded
f-7 over g equals h, sole for f
Suppose that f(x)=x^2 and g(x)= -4/5x^2 which statement best compares the graph of g(x) with the graph of f(x)
Answer: the graph of g(x) is the graph of f(x) compressed vertically
Step-by-step explanation: