Use the graphing calculator to graph the quadratic function y = x2 − 5x − 36. Which value is a solution of 0 = x2 − 5x − 36?
Answer:
B) −4
Step-by-step explanation:
Help?
The coordinates of the vertices of a polygon are (−2, −2) , (−2, 3) , (2, 4) , (3, 1) , and (0, −2) .
What is the perimeter of the polygon?
Enter your answer as a decimal, rounded to the nearest tenth of a unit, in the box.
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A hair salon charges a fixed rate of $25.00 for a haircut and then an additional $15 for any other services. Write a function to model the cost of services there and then determine how many services you had if you were charged $115
A) f(x) = 15x + 25; f(6) = 115
B) f(x) = 25x + 15; f(6) = 165
C) f(x) = 15x + 25; f(6) = 125
D) f(x) = 15x + 25; f(115) = 1750
A) f(x) = 15x + 25; f(6) = 115
What are the factors of the function graphed below?
The diagram shows triangle KLM. Which term describes point N?
Answer:
C. Circumcenter.
Step-by-step explanation:
We have been given an image of a triangle KLM and we are asked to choose the term that describes point N.
We can see that point N is the point where perpendicular bisector of our given triangle are intersecting.
Since the point where the perpendicular bisectors of a triangle intersect is called circumcenter, therefore, point N is the circumcenter of our given triangle KLM nad option C is the correct choice.
Geraldine is picking a four-digit password by using the digits 0 through 9. She can use each digit only once. How many different passwords are possible?
0-9 = 10 numbers
1st digit can be 1 0f 10
2nd digit can be 1 of 9
3rd digit can be 1 of 8
4th digit can be 1 of 7
10 * 9 *8*7 = 5040 different combinations
The number of different possible passwords are possible
Given that each digit can be used once, then:
The first digit can be any of the 10 digitsThe second digit can be any of the remaining 9 digitsThe third digit can be any of the remaining 8 digitsThe fourth digit can be any of the remaining 7 digitsSo, the number of passwords is:
n = 10 * 9 * 8 * 7
Evaluate the products
n = 5040
Hence, there are 5040 different possible passwords
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Consider that 1 in=2.54 cm. if 1559 cm is converted to inches, how many significant figures should be in the answer
To convert 1559 cm to inches, divide by 2.54, and the result should be reported with the same number of significant figures as the given measurement, which is four. Thus, 1559 cm is equal to 613.8 inches.
Explanation:To convert 1559 cm to inches using the conversion factor 1 inch = 2.54 cm, we divide 1559 by 2.54. The number 1559 has four significant figures because all non-zero digits are considered significant. Since the conversion factor 2.54 cm per inch is exact and does not limit the number of significant figures, the result should also be reported with four significant figures.
The calculation would be as follows:
1559 cm ÷ 2.54 cm/in = 613.7795 inchesTo match the number of significant figures in 1559, we round the result to four significant figures.So, 1559 cm is equal to 613.8 inches when converted and properly rounded.
how can you interpret the independent or conditional probability of two events
1. Independent probability of A and B occurring together (drawing a red queen): [tex]\( \frac{1}{26} \)[/tex]
2. Conditional probability of A given B (drawing a red card given that a queen was drawn): [tex]\( \frac{1}{2} \)[/tex]
- Independent probability: This is the probability of two events occurring together, assuming that one event's occurrence does not affect the other. Mathematically, if A and B are independent events, then [tex]\( P(A \cap B) = P(A) \times P(B) \).[/tex]
- Conditional probability: This is the probability of an event occurring given that another event has already occurred. Mathematically, if A and B are events with[tex]\( P(B) > 0 \)[/tex], then the conditional probability of A given B is [tex]\( P(A|B) = \frac{P(A \cap B)}{P(B)} \).[/tex]
Let's illustrate these concepts with an example:
Suppose we have a deck of cards (52 cards total), and we're interested in two events:
A: Drawing a red card
B: Drawing a queen
First, let's find the independent probabilities:
1. Probability of A (drawing a red card):
- There are 26 red cards out of 52 total cards, so [tex]\( P(A) = \frac{26}{52} = \frac{1}{2} \).[/tex]
2. Probability of B (drawing a queen):
- There are 4 queens out of 52 total cards, so[tex]\( P(B) = \frac{4}{52} = \frac{1}{13} \).[/tex]
Now, let's find the probability of both events occurring together (A and B):
3. Probability of A and B (drawing a red queen):
- There are 2 red queens (hearts and diamonds) out of 52 total cards, so [tex]\( P(A \cap B) = \frac{2}{52} = \frac{1}{26} \).[/tex]
For independent events,[tex]\( P(A \cap B) = P(A) \times P(B) \):[/tex]
[tex]\[ \frac{1}{26} = \frac{1}{2} \times \frac{1}{13} \][/tex]
Now, let's find the conditional probability of A given B:
[tex]\[ P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{1}{26}}{\frac{1}{13}} = \frac{1}{2} \][/tex]
1. Independent probability of A and B occurring together (drawing a red queen): [tex]\( \frac{1}{26} \)[/tex]
2. Conditional probability of A given B (drawing a red card given that a queen was drawn): [tex]\( \frac{1}{2} \)[/tex]
In summary, we first calculated the independent probabilities of A and B, then found the probability of A and B occurring together, and finally calculated the conditional probability of A given B using the given formulas and calculations.v
complete question
how can you interpret the independent or conditional probability of two events
At the bookstore checkout, you watch as the register rings up your purchases and coupons.
The prices were as follows:
$1.85
$8.56
$6.30
$2.73
$5.25
$4.09
$7.95
– $0.85 (coupon)
– $2.10 (coupon)
The register gives your total bill as $41.44. Estimate the total amount of the bill, by rounding
each value to the nearest dollar, and use your answer to determine whether the total on the register is reasonable.
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Ellen has $75 in her savings account. She deposits $25 every week. Her father also deposits $35 into the account every time Ellen mows the lawn. Her savings account balance can be shown with the following expression:
75 + 25w + 35m
Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points)
Part B: If Ellen saves for 8 weeks and mows the lawn 2 times, how much will she have in her account? Show your work to receive full credit. (4 points)
Part C: If Ellen had $95 in her savings account, would the coefficient, variable, or constant in the expression change? Why? (3 points)
Multiply -2x^(-3) y (5yx^(5)+8xy-4y^(2) x(2) ).
Final answer:
The original equation, after multiplication and simplification, results in -10x^2y^2 - 16y^2 + 8x^-1y^3. This process demonstrates the use of the distributive property and exponent rules in algebra.
Explanation:
The question requires us to multiply -2x-3y by (5yx5+8xy-4y2x2). Proceed by applying the distributive property, which involves multiplying each term inside the parentheses by -2x-3y. Here are the steps:
Multiply -2x-3y by 5yx5 to get -10x2y2.
Multiply -2x-3y by 8xy to get -16y2.
Multiply -2x-3y by -4y2x2 to get 8x-1y3.
Therefore, the final result of the multiplication is -10x2y2 - 16y2 + 8x-1y3.
The result is [tex]\[ -10yx^2 - 16y^2x^{-2} + 8x^{-1}y^3 \][/tex].
To multiply [tex]\(-2x^{-3} y\) by \(5yx^5 + 8xy - 4y^2x^2\)[/tex], we distribute [tex]\(-2x^{-3} y\)[/tex] to each term inside the parentheses.
[tex]\[ -2x^{-3} y (5yx^5) + (-2x^{-3} y)(8xy) + (-2x^{-3} y)(-4y^2x^2) \][/tex]
Simplify each term:
[tex]\[ = -10yx^2 + (-16)x^{-2}y^2x + 8x^{-1}y^3 \][/tex]
[tex]\[ = -10yx^2 - \frac{16y^2}{x^2} + 8x^{-1}y^3 \][/tex]
[tex]\[ = -10yx^2 - 16y^2x^{-2} + 8x^{-1}y^3 \][/tex]
Thus, the final result of the multiplication is [tex]\[ -10yx^2 - 16y^2x^{-2} + 8x^{-1}y^3 \][/tex].
This expression cannot be further simplified, as it represents the result of multiplying each term in the first expression by each term in the second expression and then combining like terms.
Therefore, the correct option is B. [tex]\[ -10yx^2 - 16y^2x^{-2} + 8x^{-1}y^3 \][/tex].
Complete Question:
The function f(x) is shown in the graph.
What is the equation for f(x)?
Enter your answer in the box.
Find all angles θ between 0° and 180° satisfying the given equation. round your answer to one decimal place. (enter your answers as a comma-separated list.) sin(θ) = 3 4
We are given the equation:
sin θ = 3 / 4
To find for the value of θ, simply compute using the calculator:
θ = sin^-1 (3 / 4)
θ = 48.60° = θ1
To find for the other value, subtract the answer from 180°, so:
θ2 = 180° - 48.60°
θ2 = 131.40°
So the angles are 48.60° and 131.40°
The angles θ for which sin(θ) equals 3/4 between 0° and 180° are approximately 48.6° and 131.4°.
Explanation:The student's question relates to the topic of trigonometry. Specifically, finding the angles θ for which the sine equals 3/4. To answer this, in the first quadrant, we can use the arcsin function to get θ = arcsin(3/4). Using a calculator, θ ≈ 48.6°. In the second quadrant, the sine is still positive, so θ = 180° - arcsin(3/4) ≈ 131.4°. Thus, the solution is 48.6°, 131.4°. It's worth noting that using a calculator's arcsin function usually gives a result in the first quadrant (0° - 90°) so we have to calculate the second quadrant angle ourselves.
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There are three pieces of pizza how many 1/4 pieces of pizza can be sliced from the 3 pieces
A(n) __________ transformation preserves the size and shape of an object's original image; the image is congruent to the pre-image.
A. dilation
B. isometric
C. scale
D. non-isometric
The correct transformation that preserves the size and shape of an object, resulting in congruent images, is an isometric transformation. Examples include translation, rotation, and reflection, all of which maintain the object's proportions and dimensions.
A transformation that preserves the size and shape of an object's original image, such that the image is congruent to the pre-image, is known as an isometric transformation. This transformation includes operations like translation (a shift from one place to another), rotation (turning around a center), and reflection (flipping over a line). All these transformations keep the object's dimensions and proportions unchanged. The key property of isometric transformations is that they maintain congruency and preserve distances and angles.
An example of an isometric transformation is when a square is rotated 90 degrees around its center. The square's shape and size remain the same, even though its orientation has changed. This contrasts with dilation, which changes the size of the object, and affine transformations, which can alter both shape and size, such as through stretching or skewing. The correct answer to the student's question is B. isometric.
Every day a factory produces 5000 light bulbs, of which 2500 are type 1 and 2500 are type 2. if a sample of 40 light bulbs is selected at random on a particular day, and examined for defects, what is the approximate probability that this sample contains at least 18 light bulbs of each type?
Don't Put a Bad Words on your answer and you get a warning and report.
One of the rows in the table has an error and does not have the same ratio as the other rows.
Conversion Chart
Feet
Inches
Row 1
3
36
Row 2
6
72
Row 3
7
94
Row 4
9
108
Which explains how to correct the error in the table?
A.Row 1 should show 3 feet is equivalent to 32 inches.
B.Row 2 should show 6 feet is equivalent to 66 inches.
C.Row 3 should show 7 feet is equivalent to 84 inches.
D.Row 4 should show 9 feet is equivalent to 104 inches.
Luis deposited $500 into his bank account. He now has $4732. Write and solve an equation to find how much was in his account before the deposit.
if the population of state is 1,821,000 decreasing by 0.2% every year what will the population be in 5 years PLEASE PLEASE HELP
Answer:
1,802,862.
Step-by-step explanation:
We have been given that the population of state is 1,821,000 decreasing by 0.2% every year. We are asked to find the population of state after 5 years.
We will use exponential decay function to solve our given problem.
[tex]y=a\cdot b^x[/tex], where,
y = Amount left after x years,
a = Initial amount,
b = For decay b is in form (1-r) where r represents decay rate in decimal form.
x = Number of years.
Let us convert our given rate in decimal form.
[tex]0.2\%=\frac{0.2}{100}=0.002[/tex]
Upon substituting our given values in above formula we will get,
[tex]y=1,821,000 \cdot(1-0.002)^5[/tex]
[tex]y=1,821,000 \cdot(0.998)^5[/tex]
[tex]y=1,821,000 \cdot 0.990039920079968[/tex]
[tex]y=1,802,862.69[/tex]
Since we can not have 0.69 of a person, therefore, we will round down our answer.
[tex]y=1,802,862.69\approx 1,802,862[/tex]
Therefore, the population of state after 5 years will be 1,802,862.
Vicky ran 5⁄14 of a mile and walked 1⁄7 of a mile. how much further did vicky run than walk?
McDonald's has sold more than a billion hamburgers. If it were possible to eat a hamburger every minute of everyday (day and night) without stopping, how many years would it take to eat a billion hamburgers?
1. Find the zeros of the function.
f(x) = 9x2 + 6x - 8 (2 points)
a) -2 and 4
b) Negative two divided by three. and Four divided by three.
c) Two divided by three. and Negative four divided by three.
d) 2 and -4
2. Find the zeros of the function.
f(x) = 9x3 - 45x2 + 36x (2 points)
a) 0, 1, and 4
b) -1 and -4
c) 1 and 4
d) 0, -1, and -4
3. Find the zeros of the polynomial function and state the multiplicity of each.
f(x) = 4(x + 7)2(x - 7)3 (2 points)
a) 4, multiplicity 1; -7, multiplicity 3; 7, multiplicity 3
b) -7, multiplicity 3; 7, multiplicity 2
c) 4, multiplicity 1; 7, multiplicity 1; -7, multiplicity 1
d) -7, multiplicity 2; 7, multiplicity 3
4. Find a cubic function with the given zeros. (2 points)
Square root of five. , - Square root of five. , -7
a) f(x) = x3 - 7x2 - 5x - 35
b) f(x) = x3 + 7 x2 - 5x + 35
c) f(x) = x3 + 7x2 - 5x - 35
d) f(x) = x3 + 7x2 + 5x - 35
5. Expand the following using either the Binomial Theorem or Pascal's Triangle. You must show your work for credit.
(2x + 4)3
solve the given problem 7y-84=2y+61
Mariya is solving the quadratic equation by completing the square.
4x2 – 20x + 3 = 0
4x2 – 20x = –3
A(x2 – 5x) = –3
What is the value of A?
Answer:
The value of A is 4.
Step-by-step explanation:
Consider the provided quadratic equation.
[tex]4x^2-20x+3=0[/tex]
Subtract 3 from both sides.
[tex]4x^2-20x+3-3=-3[/tex]
[tex]4x^2-20x=-3[/tex]
Now take 4 common from the left side of the above equation.
[tex]4(x^2-5x)=-3[/tex]
Compare the above equation with [tex]A(x^2 - 5x) = -3[/tex]
By the comparison it is clear the value of A is 4.
Hence, the value of A is 4.
If angle a and angle b are complements and m angle a=36 degrees, what is angle b
Complementary angles add up to 90 degrees. Angle b can be found by subtracting the measure of angle a from 90 degrees.
Explanation:The question states that angle a and angle b are complements, and that the measure of angle a is 36 degrees. In mathematics, complementary angles are two angles whose measures add up to 90 degrees. So, if angle a is 36 degrees, angle b can be found by subtracting 36 from 90, which gives us 54 degrees. Therefore, angle b is 54 degrees.
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suppose m < ABC = 110. what is m < DBC
The measurement of ∠y = ∠DBC will be 40°.
What is Angle ?
In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Given is ∠ABC = 110°
Let ∠ABD = x , ∠DBC = y, ∠CBE = z
∠ABD + ∠DBC + ∠CBE = 180°
x + y + z = 180°
and
∠ABD + ∠DBC = 110°
x + y = 110°
Then -
z = 180° - (x + y)
z = 180 - 110
z = 70°
Since DB and EC are equally inclined -
x = z = 70°
Then -
x + y = 110°
y = 110° - 70°
y = 40°
Therefore, the measurement of ∠y = ∠DBC will be 40°.
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answer to #10 and #13. can’t figure out how to use interval notation to write domain and range for graphs.
Find both unit rates.
$27 for 4 hours of work
A.
$6.75 per hour and 0.15 hours per dollar
B.
$108 per hour and 6.75 hours per dollar
C.
$6.75 per hour and 108 hours per dollar
D.
$0.15 per hour and 6.75 hours per dollar
$27 / 4 = 6.75 dollars per hour
4 / 24 = 0.148 = 0.15 hours per dollar
Answer is A
The quotient of a number r and 7 is no more than 18. I cant find the equation part or the inequality
Answer:
The inequality would be r/7 ≤ 18 and the solution would be r ≤ 126
Step-by-step explanation:
We start by writing the inequality
r/7 ≤ 18
We know to use division between r and 7 since it asks for the quotient and we know to use a ≤ sign since it says "is no more than"
To solve, simply multiply both sides by 7
r ≤ 126
The inequality will be r/7 ≤ 18
Since it's a quotient, we'll need to divide the expression and this will be:
= r/7 ≤ 18
Now the value of r will be gotten thus:
r/7 ≤ 18
Cross multiply.
r ≤ 18 × 7
r ≤ 126
Therefore, this mean that the value of r will be 126 or numbers lower than 126
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