The coefficients of the given quadratic equation are:
a = -2b = 4c = -3What are the values of a, b, and c?
Here we want to find the coefficients for the following quadratic equation:
-2x^2 + 4x - 3 = 0
Now, the general quadratic equation is written as:
a*x^2 + b*x + c = 0
So the two equations are:
-2x^2 + 4x - 3 = 0
a*x^2 + b*x + c = 0
So c is the constant term, comparing this with the given quadratic equation, we can see that:
c = -3
b is on the linear term, ad we can see that:
b = 4
a is on the quadratic term, we can see that:
a = -2
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on the number line, the distance between x and y is greater than the distance between x and z. does z lie between x and y on the number line?
yes, z can lie between x and y but z can also lie on another side of x in Number lines.
With an example, define number line?
Number lines in mathematics are horizontal straight lines on which numbers are arranged in equal intervals.
A number line can be used to visualize all the numbers in a succession. The endpoints of this line go on forever.
What does the math number line mean?
A horizontal line with uniformly spaced numerical increments is called a number line. How the number on the line can be answered will depend on the numbers that are provided.
How a number is used—for example, to plot a point—depends on the question that goes with it.
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Find the inverse of f(x) = 2(x-2) ^2 +1
Find the inverse of y = ^3√x-3
Answer:
f^-1(x) = 2(x-2)^2 + 1
f^-1(x) = (x+3)^3
Step-by-step explanation:
The inverse of a function is found by switching the roles of the dependent and independent variables. In other words, we can find the inverse of a function by interchanging the x and y values in the equation. So, the inverse of the function f(x) = 2(x-2)^2 + 1 can be written as f^-1(x) = 2(x-2)^2 + 1.
1. To find the inverse function explicitly, we can use the following steps:
2. Replace f(x) with y in the original function to obtain y = 2(x-2)^2 + 1.
3. Solve for x in terms of y to obtain x = +/- sqrt((y-1)/2) + 2.
The inverse function f^-1(x) can then be written as f^-1(x) = +/- sqrt((x-1)/2) + 2.
Note that this inverse function is not a one-to-one function, because for some values of x (namely, x < 1), the function has two possible values of y (i.e. it has two solutions). Therefore, the inverse function is not a function in the strict mathematical sense, but it is still a useful concept in certain contexts.
To find the inverse of a function, we switch the roles of the dependent and independent variables, so the inverse function can be written as x = ^3√y-3.
1. To find the inverse function explicitly, we can use the following steps:
2. Replace y with x in the original function to obtain x = ^3√y-3.
3. Solve for y in terms of x to obtain y = (x+3)^3.
The inverse function can then be written as f^-1(x) = (x+3)^3.
Note that this inverse function is a one-to-one function, meaning that for every value of x, there is only one corresponding value of y. Therefore, the inverse function is a function in the strict mathematical sense.
need help! can't figure it out :/
Answer:
please tell me if you get the answer. I need it too!
What is the value of p in the equation 8p 2 = 4p - 10?
Answer:
Step-by-step explanation:
member c: works 7 hours per week at $7.25 per hour member d: works 9 hours per week at $6.35 per hour a. a and b b. a and c c. b and c d. b and d
Only member B and D will reach their goal.
Given;
Amount to be saved = $285
Total time to save money = 5 weeks
Now,
For member A:
Working hours = 8 per week
per hour earnings = $6.15
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hour
= 8 × 5 × 6.15
= $246
For member B:
Working hours = 10 per week
per hour earnings = $5.85
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hours
= 10 × 5 × 5.85
= $292.5
For member C:
Working hours = 7 per week
per hour earnings = $7.25
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hours
= 7 × 5 × $7.25
= $253.75
For member D:
Working hours = 9 per week
per hour earnings = $6.35
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hours
= 9 × 5 × $6.35
= $285.75
Since, the amount earned by member B and D is greater than the goal amount and the amount earned by member A and C is less than the goal amount
therefore,
Only member B and D will reach their goal
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Your question is incomplete. Please find the missing content below:
To be able to go on the band trip, four band members each get a part-time job. Each person has 5 weeks in which to save his or her money. Analyze the four individual plans below and decide which of the four people will reach his or her goal of saving $285? Member A: Works 8 hours per week at $6.15 per hour Member B: Works 10 hours per week at $5.85 per hour Member C: Works 7 hours per week at $7.25 per hour Member D: Works 9 hours per week at $6.35 per hour
Matthew Westhoven deposited $925 in a new regular savings account that earns 5.5% interest compounded semiannually for 1 year. What is the compound interest?
The compound interest received by Matthew Westhoven is $51.80
What is compound interest?The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You'll have $110.25 after the second year is over.
Given, the principal amount (P) = $925
Compound interest percentage (r) = 5.5% = 0.055
Time period (t) = 1
Since, it is semiannually compounded (n) = 2*t = 2
Amount (A) = P(1 + r/n)^nt
= 925(1 + 0.055/2)^2
= 925(1.0275)^2
= 925(1.056)
= 976.80
Thus, Interest amount (CI) = A - P
= $976.80 - $925
= $51.80
The compound interest received by Matthew Westhoven is $51.80
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Mrs. Boggs asked her students to create a cylinder to hold
chocolate candies using a standard piece of paper (8.5 inches by 11 inches.)
Some of the students made cylinders that were 11 inches tall, and others created cylinders that were 8.5 inches tall.
The students began discussing the amount of chocolate candies
that each person could store. Oliver said that each cylinder
would hold the same amount of chocolate candies because they used the same size paper. Anna disagreed.
Who is correct? Try it out with a piece of paper and then use the calculations on the next page to compare.
The cylinder made with a paper size of 8.5 inches by 11 inches is having more volume and thus contains more chocolate, so, the statement by Oliver is wrong.
What is cylinder?
A cylinder is a three-dimensional solid that maintains two parallel bases spaced at a set distance from one another. These bases often have a circular form (like a circle).
Given:
The size of the first paper = 8.5 inches by 11 inches,
The size of the second paper = 11 inches by 8 inches,
The width of the paper when folded becomes the circumference of the cylinder circle, so,
Circumference of the cylinder for the first case = 2 × π × r
11 = 2 × π × r,
r = 1.75 inches,
The volume of the cylinder for the first case = π × r² × h
The volume of the cylinder for the first case = π × (1.75)² × 8.5
The volume of the cylinder for the first case = 81.78 inches³
Calculate the volume for the second case,
Circumference of the cylinder for the second case = 2 × π × r,
8.5 = 2 × π × r
r = 1.35 inches
The volume of the cylinder for the second case = π × (1.35)² × 11
The volume of the cylinder for the first case = 63.24 inches³
As we know, the cylinder with a higher volume contains more chocolate.
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find X giving Brainly show work
Answer:
[tex]b = 6\sqrt{2}[/tex]
Step-by-step explanation:
Don't say giving brainiest for work, I will still help you.
Use the Pythagorean Theorem to solve:
[tex]a^2+b^2=c^2[/tex]
A and B refers to the legs, or the shorter sides. C refers to the hypotenuse, or the longest side.
Plug in what you know:
[tex](7)^2+b^2=(11)^2[/tex]
[tex]49 + b^2 = 121[/tex]
Subtract 49 on both sides.
[tex]49 - 49 + b^2 = 121-49[/tex]
[tex]b^2=72[/tex]
Find the square root of both sides.
[tex]\sqrt{b^2} = \sqrt{72}[/tex]
b = [tex]6\sqrt{2}[/tex]
I will give brainliest to whoever ANSWERS THESE 2 QUESTIONS
100 POINTS!!!
Answer:
2. 43 degrees
3. 35 degrees
Step-by-step explanation:
Srr the attached worksheet.
Find the lengths of segments AD and BD. Then check your answers using a different method.
Answer: BD = 5
Step-by-step explanation:
Using the Pythagorean theorem [tex]a^{2} + b^{2} =c^{2}[/tex] where c is the hypotenuse, we can solve for BD[tex]a^{2} +12^{2} =13^{2}[/tex]
[tex]a^{2} =13^{2}-12^{2}[/tex]
[tex]a = \sqrt{25}[/tex]
[tex]a = 5[/tex]
Therefore BD = 5
A right triangle is shown, where the horizontal leg has a measure of 48 centimeters (cm), and the hypotenuse has a measure of 73 cm.
Answer:
55
Step-by-step explanation:
Using the Pythagorean theorm:
a^2+b^2=c^2
48^2+b^2=73^2
b^2=73^2-48^2
b^2=3025
b=55
Pamela is 9 years younger than jiri. The sim of their ages is 49. What is jiri’s age ?
Answer: 40
Step-by-step explanation:
all you have to to is subtract
9 from 49 = 40
Answer:40
Step-by-step explanation:49-9=40
For what values of x, y, and z is this a parallelogram?
The values of x = 19.5, y= 17, and z=30.6 is not valid for the parallelogram.
What are the Properties of Angles of a Parallelogram?
A parallelogram is a quadrilateral with equal and parallel opposite sides. There are some special properties of a parallelogram that make it different from the other quadrilaterals.
The opposite angles of a parallelogram are congruent (equal). All the angles of a parallelogram add up to 360°. All the respective consecutive angles are supplementary.The consecutive angles are supplementary then,
5y + 7y - 24 = 180
12y = 180 + 24
12y = 204
y = 204/12
y = 17
The opposite angles of a parallelogram are congruent (equal) then,
5y = 4x + 7
5(17) = 4x + 7
85 = 4x + 7
85 -7 = 4x
4x = 78
x = 78/4 = 19.5
x = 19.5
the consecutive angles are supplementary, then
4x + 7 + 3z = 180
4(19.5) + 7 + 3z = 180
78 + 7 + 3z = 180
85 + 3z = 180
3z = 180 - 88
3z = 92
z = 92/3
z = 30.6
All the angles of a parallelogram add up to 360°, then:
4x + 7 + 3z + 5y +7y - 24 = 360
To check is this a parallelogram? put the values of x, y, and z in the above equation:
4(19.5) + 7 + 3(30.6) + 5(17) +7(17) - 24 = 360
356.8 ≠ 360
hence, the values of x = 19.5, y= 17, and z=30.6 is not valid for the parallelogram.
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The ratio of a to b is 4/7. If a is 16, find the value of b.
Answer:
B=28
Step-by-step explanation:
Graph the line that has a slope of -4/3 and includes the point ( -6,2)
The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.
Slope intercept form:The slope-intercept form a line is given by
y = mx + c,where m is the slope of a line and c is the y-intercept.
Here we use the Slope intercept form to find the line of the equation by using the equation we will draw the graph of the line
Here we have
Slope of line = -4/3
The point of the line
As we know y = mx + c is the line Here m is the slope of the line
From the given data, m = -4/3
=> y = (-4/3)x + c
=> 3y = -4x + 3c
Given that the point on the line is (-6, 2)
=> 3(2) = -4(-6) + 3c
=> 6 = 24 + 3c
=> 3c = 18
=> c = 6
Therefore,
The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.
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You mix 1 fourth cup of crisp wheat cereal with 1 1 half cups of crisp rice cereal. Find and interpret the value of the ratio of crisp wheat cereal to crisp rice cereal.
The amount of crisp wheat cereal is _____ the amount of crisp rice cereal
Response:
Answer:
The value of the ratio of crisp wheat cereal to crisp rice cereal is 1/4 to 1 1/2, which can be simplified to 1/4 to 3/2. This means that for every 4 parts of crisp wheat cereal, there are 3 parts of crisp rice cereal. The amount of crisp wheat cereal is therefore less than the amount of crisp rice cereal. Specifically, the amount of crisp wheat cereal is 1/4 * the amount of crisp rice cereal.
Step-by-step explanation:
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. Explanation is given.
What are angle bisectors?Lines that cross the angle under investigation are known as angle bisectors. To "bisect" is to split into two sections of equal size. Therefore, the bisected halves divide the considered angle in half.
According to the angle bisector theorem;
An angle bisector divides the opposing side of a triangle into two portions that are proportionate to the other two sides, according to the angle bisector theorem.
a point is equally far from both sides of an angle if it is on the angle's bisector.
According to the inverse of the angle bisector theorem, a point is on the angle's bisector if it is both in the interior of the angle and equally far from its sides.
The explanation with diagram is given in the image.
Therefore, If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
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Reduce to the standard form
1) -18/45
2) -3/-15
3)28/56
4)45/99
The fractions reduced to standard form are -2/5, 1/5, 1/2 and 5/11 for 1), 2), 3), and 4) respectively
How to reduce fractions to standard form?
To reduce a fraction to standard form, you need to divide both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD). The GCD is the largest number that can be evenly divided into both the numerator and the denominator.
Given:
1) -18/45
The GCD of 18 and 45 is 9. Thus:
-18/45 = -2/5
2) -3/-15
The GCD of 3 and 15 is 3. Thus:
-3/-15 = 1/5
3) 28/56
The GCD of 28 and 56 is 28. Thus:
28/56 = 1/2
4) 45/99
The GCD of 45 and 99 is 9. Thus:
45/99 = 5/11
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1)-6/15
2)1/5
3)1/2
4)5/11
1) -18/45
⇒-6/15
2)-3/-15
⇒-1/-5
⇒1/5
3)28/56
⇒4/8
⇒1/2
4)45/99
⇒15/33
⇒5/11
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a population of adult wildebeests in a certain region of africa have weights that are normally distributed with a standard deviation of 579 lbs. how large of a sample is needed to estimate the mean weight to within 135 lbs with a 99% confidence level?
Sample size 123 is needed to estimate the mean weight to within 135 lbs with a 99% confidence level
What is confidence interval?
In statistics, the probability that a population parameter will fall between a set of values for a predetermined percentage of the time is referred to as the confidence interval. Analysts frequently employ confidence ranges that include 95% or 99% of anticipated observations.
Z(α/2) at 99% confidence level = 2.576
λ = 579
margin of error = ( Z(α/2) * λ ) / √n = 135
(2.576 * 579) / √n = 135
On simplifying, n ≈ 123
So, sample size 123 is needed to estimate the mean weight to within 135 lbs with a 99% confidence level
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The side of a cube has a length of 4x³y6 cm. The volume of the cube can be found using
the formula V = S³. What is the volume of the cube in cubic centimeters?
PLEASE HELP
Answer:
find my dad
Step-by-step explanation:
A bakery used `25\%` less butter this month than last month.
The bakery used `240` kilograms of butter this month.
How much did it use last month?
In linear equation, The amount of butter used is an illustration of equivalent ratio.
The amount of butter used last month is 300kg.
What is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Because the bakery used 25% more last month, the amount they used is then calculated using
Amount = ( 1 + 25%) * last month
Substitute 240kg for Last Month
Amount = ( 1 + 0.25) * 240
Remove brackets
Amount = 1.25 * 240kg
= 300 kg
Hence, the amount of butter used last month is 300kg.
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What does 43,589 + 12,641 equal
Also, what does
63,274+ 97,047 and what does 41,805- 26,426 equal and my last question what does 82,004-11,534
Equal
Answer:
1st one is 160,321
2nd one is 15,379
3rd one is 70,470
Step-by-step explanation:
63,274+ 97,047 = 160,321
41,805- 26,426 = 15,379
82,004-11,534 = 70,470
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
The expressions in the table represent the number of canned goods collected by two homerooms during a charity food drive.
Homeroom Cans Collected
Mr. Juarez 8n−7
Ms. Wade 6n+3
Write an expression that shows the total number of cans collected by both homerooms.
Part B
The students in Mr. Juarez's homeroom collected more cans than students in Ms. Wade's homeroom. Write an expression that represents how many more cans were collected.
The expression that shows the total number of cans collected by both homerooms is 14n - 4
The expression for more cans collected is 8n - 7 > 6n + 3
The total number of cans collectedFrom the question, we have the following parameters that can be used in our computation:
Homeroom Cans Collected
Mr. Juarez 8n−7
Ms. Wade 6n+3
The total number of cans collected is calculated as
Cans collected = Mr. Juarez + Ms. Wade
Substitute the known values in the above equation, so, we have the following representation
Cans collected = 8n - 7 + 6n + 3
Evaluate the like terms
Cans collected = 14n - 4
How many more cans were collectedHere, we have
Mr. Juarez's homeroom collected more cans
This means that
Mr. Juarez > Ms. Wade
Substitute the known values in the above equation, so, we have the following representation
8n - 7 > 6n + 3
Hence, the expression is 8n - 7 > 6n + 3
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What is sin(60) in degrees?
Answer:
(sqrt3)/2
Step-by-step explanation:
Sin(x)=opposite/hypotenuse
30, 60, 90 right triangle.
ratio of sides are 1, sqrt3, and 2.
Locate the 60 degree angle on the triangle
The opposite side is sqrt3
The hypotenuse is 2
so its (sqrt3)/2
Answer:
√3/2 or 0.866
Step-by-step explanation:
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:
[tex]51.4^{\circ}[/tex]
Step-by-step explanation:
Since this is a right triangle, the cosine formula says
[tex]\cos(x) = \dfrac{5.3}{8.5}[/tex]
[tex]\longrightarrow cos(x) = 0.6235[/tex]
[tex]So\\\\x = \cos^{-1}(0.6235) = 51.4256^{\circ}[/tex]
Rounded to the nearest tenth this would be
[tex]51.4^{\circ}[/tex]
In a video game, a player follows a certain path that can be partially modeled by the functionf(x)=x(x−5)(x−3) . This function can be graphed on a coordinate plane.
The graph of the function f(x) = x(x - 5)(x - 3) is given by the image shown at the end of the answer.
How to draw the sketch of the graph?To draw the sketch of the graph, we need to consider these three following features:
The x-intercepts.The y-intercept.The end behavior.The function in this problem is defined as follows:
f(x) = x(x - 5)(x - 3).
From the factor theorem, the x-intercepts are taken from the linear factors, as follows:
x = 0.x - 5 = 0 -> x = 5.x - 3 = 0 -> x = 3.The y-intercept is the value of y when the graph of the function crosses the y-axis, that is, the value of y when x = 0, hence:
f(0) = 0(0 - 5)(0 -3) = 0.
In the problem, we have a cube function, hence:
At the left tail(negative infinity) it goes to negative infinity.At the right tail(positive infinity) it goes to positive infinity.More can be learned about functions at https://brainly.com/question/24808124
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Graph the function and analyze it for domain, range, continuity, increasing or decreaseing behavior, symmetry, boundedness,
extrema, asymptotes, and end behavior.
f(x)=3•e^2x
A graph is a collection of points and the connections between some subset of those points that may or may not be empty in mathematical terms.
What are the values of the terminologies of the graph ?The given function is f (x ) = [tex]3e^{2x}[/tex]
1. Domain :
The function has no undefined points or domain constraints . Therefore the domain is -∞ < x < ∞ .2.Range :
The range of the exponential function is of the form f(x) > kSince k = 0, f(x) > 03.Continuity:
The graph is a single, continuous curve (i.e. a curve that can be drawn in one movement without taking your pen off the paper). We can observe that the function is basically continuous.4.Behaviour that is either increasing or decreasing:
For any x in the domain, as x grows, f(x) shrinks. This indicates that the function behaves in a diminishing manner.5.Symmetry:
It is clear to see the graph of f(x) has no symmetry.6.Boundedness:
When we choose negative values, the graph of f(x) expands upward exponentially, showing that it is unbounded above.7.Extrema:
There are no extreme points for the function.8.Asymptotes:
This curve does not have any vertical asymptotes, despite the way it seems. Simply put, the curve's negative-x region is expanding so swiftly that it resembles an asymptote. For any x < 0, there is a value for f(x). However, a horizontal asymptote exists , y = 0.9.End behaviour :
As [tex]\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty[/tex] As,[tex]\:x\to \:-\infty \:,\:f\left(x\right)\to \:0[/tex]Refer image for graph.To learn more about Asymptotes , refer:
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What are the slope and Y intercepted of the relationship?
The slope of the equation 10x+5y-15=0 is -2 and the y-intercept is 3.
What is the slope-intercept form of the line?
The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y-intercept (0, b). In the formula, b represents the y value of the y-intercept point.
To find the slope of the equation, we need to put it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To do this, we can first divide both sides of the equation by 5 to get:
2x + y - 3 = 0
Then, we can add 3 to both sides to get:
y = -2x + 3
Now comparing the equation with y = mx + c, we can say that
the slope is -2 and the y-intercept is 3.
Hence, the slope of the equation 10x+5y-15=0 is -2 and the y-intercept is 3.
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Mikaela purchased a paddleboard originally priced at $699. If all merchandise was on sale for 40% off and the state tax rate is 7. 25%, what is the total amount that mikaela spent on the paddleboard?.
The total amount that Mikaela spent on the paddleboard will be $449.80.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths.
As per the given,
Original price = $699
The selling price = $699 - 40% of $699
⇒ $699 - 0.40 x $699 = $419.4
The state tax (assuming it applied to the selling price) will be as,
7.25% of $419.4 = (7.25/100) x 419.4 = $30.4065
Final amount = $419.4 + $30.4065 = $449.80
Hence "Mikaela will have spent $449.80 in total on the paddleboard".
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HELP PLEASEEEE ASAP
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $29,521. The variable costs will be $12 per book. The publisher will sell the finished product to bookstores at a price of $25.25 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
Answer:
2,228
Step-by-step explanation:
Each unit will make 13.25 in profit before incorporating the one time cost. This means that 29,521/13.25= the amount needed to break even.
