The standard form of the equation is:
[tex]x=8y^2-16y-7[/tex]
Step-by-step explanation:We know that the standard form of a quadratic equation is given by the expression:
[tex]x=ay^2+by+c[/tex]
where a,b and c are real numbers.
and a≠0
Here we are given the vertex form of the equation of a parabola by:
[tex]x=8(y-1)^2-15[/tex]
Now, on expanding the parentheses term by using the formula:
[tex](a-b)^2=a^2+b^2-2ab[/tex]
Here a=y and b= 1
Hence, we have:
[tex]x=8(y^2+1-2y)-15\\\\i.e.\\\\x=8\times y^2+8\times 1-2y\times 8-15\\\\i.e.\\\\x=8y^2+8-16y-15\\\\i.e.\\\\x=8y^2-16y+8-15[/tex]
( Since, in the last step we combined the constant term i.e. 8 and -15 )
Hence, we get the standard form of the equation as:
[tex]x=8y^2-16y-7[/tex]
What compound inequality has all real numbers that are less than than -3 or greater than or equal to 5?
Answer:
less than -3 and greater than 5
Step-by-step explanation:
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
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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12 out of 142 people standing in line for tickets were going to see the movie in theater
a. if there were a total of 1704 tickets sold, predict how many people were going to see the movie in theater a?
List at least three (3) characteristics of carbon that make it a unique element.
Answer: Carbon occurs as a solid, liquid, and gas.
Carbon is found everywhere.
Carbon is versatile and easily combines with other elements.
Carbon bonds with other elements to form macromolecules.
Graph y≤1−3x .
Number graph x axis ranging from negative one to five, and y axis ranging from negative four to two. A solid line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded below the line.
A graph with y axis ranging from negative 4 to 2 and x axis ranging from negative 1 to 4. A dotted line with arrows at both ends passing through the y axis at one and the x axis at point 3. The graph is shaded above the line.
Number graph with y axis ranging from negative 4 to 2, and x axis ranging from negative 2 to 6. A solid line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded above the line.
Number graph with x axis ranging from negative one to five, and y axis ranging from negative four to two. A dotted line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded below the line.
To graph the inequality y ≤ 1 - 3x, we can start by graphing the equation y = 1 - 3x. The graph should be a solid line passing through the y-axis at 1 and the x-axis at 1/3. The shaded region below the line represents the solution set.
Explanation:The given inequality is y ≤ 1 - 3x. To graph this inequality, we can start by graphing the equation y = 1 - 3x. This equation represents a line with a y-intercept of 1 and a slope of -3. We can plot the y-intercept at (0, 1) and use the slope to find additional points on the line.
For example, if we increase x by 1, y will decrease by 3. So, when x = 1, y = -2. By connecting these points and extending the line, we can have a line passing through the y-axis at 1 and the x-axis at 1/3.
To graph the inequality y ≤ 1 - 3x, we shade the region below the line because any point in this region will satisfy the inequality.
Therefore, the graph should be a solid line with arrows at both ends, passing through the y-axis at 1 and the x-axis at 1/3, and the region below the line shaded.
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The _______ represents the expected proportion of intervals that will contain the parameter if a large number of different samples of size n is obtained. it is denoted _______.
The concept referred to in the question is the 'confidence interval', which represents the estimated range that will contain the parameter in the event of obtaining a large quantity of different samples of size n. The denoted term '____' is the standard error (SE), which describes the standard deviation of these sample means distribution. As the number of samples increases, according to the central limit theorem, these sample sums or means tend towards a normal distribution.
Explanation:The portion of the question, 'The _______ represents the expected proportion of intervals that will contain the parameter if a large number of different samples of size n is obtained...' refers to the confidence interval. The confidence interval is a range of values, derived from statistical analysis, that is likely to contain the parameter of interest. For instance, a 0.95 confidence interval stands for a 95% probability that the population parameter will fall within this range.
The second fill-in-the-blank part of the question, 'it is denoted _______.' refers to the standard error. The standard error denoted as SE or rarely s.e., represents the standard deviation of the sampling distribution of the mean or in simpler words, it highlights how much our sample mean might differ from the actual population mean.
As the number of different samples (n) gets larger, the sampling distribution of the sum, ΣX, or the mean, X, tends towards the normal distribution, according to the central limit theorem. This feature is harnessed in diverse areas such as probability theory and statistics.
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Your friend has $90 when he goes to the fair. he spends $5 to enter the fair and $15 on food. rides at the fair cost $1.50 per ride. which function can be used to determine how much money he has left over after x rides? (1 point)
Complete the following theorem.
If two angles in a triangle are congruent to two angles in another triangle, then the ______________ angles are also congruent.
The temperature fell from 0 degrees to 6 3/5 degrees below 0 in 2 1/5 hours. what was the temperature change per hour?
divide 6 3/5 by 2 1/5
6 3/5 = 33/5
2 1/5 = 11/5
33/5 / 11/5 = 3
the temperature dropped 3 degrees per hour
Use laws of sine to answer
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.
What's the relationship between compound interest and exponential growth?
Final answer:
Compound interest and exponential growth both involve the concept of compounding, where growth is based on previous amounts. Compound interest refers to interest earned on past interest, causing savings to grow over time. Similarly, compound growth rates result in exponential growth.
Explanation:
The relationship between compound interest and exponential growth is that they both involve the concept of compounding, where the growth or increase is based on previous amounts. Compound interest refers to the interest earned on past interest, causing the total amount of financial savings to grow over time. Similarly, compound growth rates mean that the rate of growth is multiplied by a base that includes past growth, resulting in an exponential growth curve.
For example, if you have $1,000 in a bank account with a compound interest rate of 5% per year, the interest earned each year is added to the principal amount and becomes part of the new base for calculating future interest. As a result, the amount of money in the account grows exponentially over time. This relationship can also be seen in other areas, such as population growth or economic growth rates.
What is the inverse of the function f(x) = 2x - 10?
Answer:
[tex]f^{-1}(x)=\frac{x+10}{2}[/tex]
Step-by-step explanation:
We ate asked to find the inverse of the given function [tex]f(x)=2x-10[/tex].
To find the inverse of function, first of all we will replace [tex]f(x)=y[/tex] and then interchange x and y values as shown below:
[tex]y=2x-10[/tex]
Inter-change x and y variables:
[tex]x=2y-10[/tex]
Solve for y using opposite operations:
[tex]x+10=2y-10+10[/tex]
[tex]x+10=2y[/tex]
Switch sides:
[tex]2y=x+10[/tex]
Divide both sides by 2:
[tex]\frac{2y}{2}=\frac{x+10}{2}[/tex]
[tex]y=\frac{x+10}{2}[/tex]
We will inverse function notation [tex]f^{-1}(x)[/tex] to write the inverse function as:
[tex]f^{-1}(x)=\frac{x+10}{2}[/tex]
Therefore, our required inverse function would be [tex]f^{-1}(x)=\frac{x+10}{2}[/tex].
Solve the inequality: -1+4y < 31
-1 +4y < 31
add 1 to each side:
4y < 32
divide both sides by 4
y<32/4
y<8
Use the vertical line test to determine whether the relation is a function ((-6,-2)
Why do you flip the inequality sign when dividing by a negative number?
Create an expression, to equal 13, using any grouping of addition, subtraction, multiplication, and division. You must use all the basic operations at least once (addition, subtraction, multiplication, and division) and you must use at least one set of parentheses.
Answer:
Step-by-step explanation:
(5x2)+3
=13
This how you work the problem:
(5x2)+3 (5x2=10) 10+3=13. :)
I NEED HELP QUICK, PLEASE!
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
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?
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:
There are three pieces of pizza how many 1/4 pieces of pizza can be sliced from the 3 pieces
answer to #10 and #13. can’t figure out how to use interval notation to write domain and range for graphs.
Vicky ran 5⁄14 of a mile and walked 1⁄7 of a mile. how much further did vicky run than walk?
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:
Correct & best answer ill get brainliest.
1 cubic meter of concrete has a wight of 2400 kg. 15% of the concrete is water. The rest of the ingredients are cerment, sand and stone. The weights are in a ratio of 1:2:5. Work out the weight of cement, sand and stone in the 1 cubic meter of concrete
Help me please i have a test coming up
Answer:
Step-by-step explanation:
2400 × 0.15 = 360
2400 - 360 = 2040
2040 × 1/8 = 255 kg of Cement
2040 × 2/8 = 510 kg of Sand
2040 × 5/8 = 1275 kg of Stone
To check if it is right
255 + 510 + 1275 = 2040 kg
1 cubic meter of concrete the weight of water is 360 Kg, the weight of cement is 255 Kg, the weight of sand is 510 Kg and the weight of stone is 1275 Kg and this can be determine by forming the linear equation in one variable.
Given :
1 cubic meter of concrete has a wight of 2400 kg.15% of the concrete is water.The rest of the ingredients are cement, sand and stone. The weights are in a ratio of 1:2:5.The weight of the water in the concrete will be:
[tex]= 2400\times \dfrac{15}{100}[/tex]
= 360 Kg
Let x be the weight in Kg. Then the combine weight of stone, cement and sand will be:
[tex]8x = 2400 - 360[/tex]
8x = 2040
x = 255 Kg
Then the weight of the cement will be = 255 Kg.
The weight of the sand will be = [tex]\rm 255\times 2 = 510\; Kg[/tex].
The weight of the stone will be = [tex]\rm 255\times 5 = 1275\; Kg[/tex].
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Which expression represents the phrase "one third the sum of 12 and a number"?
A.) 1/3+12+x
B.) 1/3(12+x)
C.) 1/3x+12
D.) 1/3(12)+x
The expression that represents the phrase 'one third the sum of 12 and a number' is B.) 1/3(12+x).
To represent the phrase "one third the sum of 12 and a number", we can break it down into two parts:
1. The sum of 12 and a number
2. One third of that sum
The expression for the sum of 12 and a number is (12 + x). Then, one third of that sum is [tex]\(\frac{1}{3}(12 + x)\).[/tex]
So, the correct expression is:
[tex]B.) \(\frac{1}{3}(12 + x)\)[/tex]
Name the property of equality that justifies this statement if p=q then p+s=q+s
Answer:
Addition property of equality that justifies this statement if p=q then p+s=q+s
Step-by-step explanation:
Addition property of equality states that you add the same number to both sides of an equation.
For example
If a = b then;
a+c = b+c
As per the statement:
if p=q
then;
p+s=q+s
⇒Addition property of equality justifies this statement.
Solve for x and y. What is m