An equation in the form ax2+bx+c=0 is solved by the quadratic formula. The solution to the equation is shown below.x=−7±√ "572" What are the values of a, b, and c in the quadratic equation?
A: a= 1, b= -7, c = -2
B: a = 1, b= 7, c = -2
C: a = 2, b = -7, c = -1
D: a = 2, b = 7, c = -1
Question has errors in typing that 572 should be √57/2
Because if it's 572 then 2a=1 so
a=1/2Also
-7=1/2bb=-7(2)b=-14c also comes different
If it's like what I said
then
2a=2a=1and
-b=-7b=7By putting values
c=-2Option B can be correct
Answer:
B: a = 1, b= 7, c = -2
Step-by-step explanation:
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
Given:
[tex]x=\dfrac{-7\pm\sqrt{57}}{2}[/tex]
Comparing the terms of the given x-value with those of the quadratic formula:
[tex]\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}=\dfrac{-7\pm\sqrt{57}}{2}[/tex]
Therefore:
[tex]2a=2 \implies a=1[/tex][tex]b = 7[/tex][tex]b^2-4ac=57[/tex]Using the found values of a and b to solve for c:
[tex]\implies b^2-4ac=57[/tex]
[tex]\implies (7)^2-4(1)c=57[/tex]
[tex]\implies 49-4c=57[/tex]
[tex]\implies -4c=57-49[/tex]
[tex]\implies -4c=8[/tex]
[tex]\implies c=-2[/tex]
In summary: a = 1, b = 7, c = -2
[tex]\implies x^2+7x-2=0[/tex]
Therefore, option B is the correct solution.
please help me out :(
Answer:
The correct answer is B.
Step-by-step explanation:
Pay per month depends on hours of training, so hours of training is the domain, and pay per month is the range.
What is the standard deviation of the data? Round to the nearest whole number.
65
75
100
130
Rounded to the nearest whole number, the standard deviation of the data is 29.
How do we calculate the standard deviation of data?The following notations and formulas will be used in these calculations:
Mean = (sum of the values) / n
Variance = ((Σ(x - mean)^2) / (n - 1)
Standard deviation = Variance^0.5
Where:
n = number of values = 4
x = each value
Therefore, we have:
Mean = (65 + 75 + 100 + 130) / 4 = 92.50
Variance = ((65-92.5-)^2 + (75-92.50)^2 + (100-92.50)^2 + (130-92.50)^2) / (4-1) = 2,525 / 3 = 841.666666666667
Standard deviation = Variance^0.50 = 841.666666666667^0.5 = 29.011491975882
Rounding to the nearest whole number, we have:
Standard deviation = 29
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Answer:
The answer is C. 100
Step-by-step explanation:
A force F, of 25 newtons pulls at an angle of 20° above due east
A force F₂ of 35 newtons pulls at an angle of 55° below due west
Find the magnitude and direction of the resultant force
A force F, of 25 newtons pulls at an angle of 20° above due east
A force F₂ of 35 newtons pulls at an angle of 55° below due west
Find the magnitude and direction of the resultant force
14 What are the solutions to the equation 3(x − 4)² = 27?
(1) 1 and 7
(3) 4 ± √24
(2) −1 and -7
(4) − 4 ± √24
Answer:
(1) 1 and 7
Step-by-step explanation:
Hello!
We can solve by isolating the variable.
Solve3(x - 4)² = 27There are two solutions, 1 and 7.
The answer is option 1: x = 7, x = 1.
The angle by which turns clockwise about point b to coincide with is degrees. if from point b, a point e is drawn directly opposite point c so that b, e, and c are on the same straight line, the angle by which turns counterclockwise to coincide with is degrees.
The first drop-down menu answer is 63.9 And the second drop-down menu answer is 116.1
The complete question is as given below:-
The angle by which turns clockwise about point B to coincide with is degrees. If from point B, a point E is drawn directly opposite point C so that B, E, and C are on the same straight line, the angle by which turns counterclockwise to coincide with is degrees.
What is an angle?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
I have attached the figure for this problem and there are two questions for this problem. The first is the angle needed for AB to turn to coincide with BC.
Simply, get add the measures of the angles ABD and DBC. So,
33.3 + 30.6 = 63.6 degrees
The second question is the angle needed for AB to turn to coincide with EB. Angle EBA is complementary with angle ABC. So,
180 - 63.6 = 116.4 degrees
Therefore for first drop-down menu answer is 63.9 And the second drop-down menu answer is 116.1
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Answer:
90
Step-by-step explanation:
90
Solve for x. 3x/−8=−2/14
Answer:
4.14
Step-by-step explanation:
3x : -2
-8 14
cross multiply
3x × 14 : -2 × 8
42 + 14x : -16
42+ 16 : 14x
58 : 14x
58 : x
14
4.14 : x
In a city park, three walking paths form triangle ABC. The length AB is 800 meters, the length BC is 900 meters, and the length AC is 850 meters. Which angle of this triangle has the greatest measure?
Answer:
Step-by-step explanation:
angle c
The angle of the triangle with the greatest measure is ∠A
What is a triangle?A triangle is a polygon with three sides and three angles.
Analysis:
For the triangle, ABC the angle facing the side with the greatest measure is the angle with the greatest measure. From the given information side BC is the side with the greatest measure and the angle facing it is ∠A.
In conclusion, the angle with the greatest measure is ∠A
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solve 2(4x-3) = 5(2x-5)
Answer:
x = 19/2 or 9.5
Step-by-step explanation:
Hello!
We can distribute the parenthesis and solve.
Solve2(4x - 3) = 5(2x - 5)2(4x) - 2(3) = 5(2x) - 5(5)8x - 6 = 10x - 25Move all x terms to one side and integer terms to the other
8x - 6 = 10x - 25-6 + 25 = 10x - 8x19 = 2xx = 19/2x = 9.5In triangle ABC, m∠A=47∘ and m∠B=70∘. What is the measure of angle C?
Answer:
63
Step-by-step explanation:
Answer:
63
Step-by-step explanation:
A water sprinkler sends water out in a circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is452.16 square feet? Use 3.14 for .
We need radius
Let that be r
πr²=452.163.14r²=452.16r²=144r=√144r=12ftAnswer:
12 feet
Step-by-step explanation:
It asks how many feet away from the sprinkler can water be spread. Therefore, in this scenario, we require the radius.
Area of a circle :
Area (circle) = πr²
Solving :
⇒ 452.16 = 3.14 × r²
⇒ r² = 452.16 ÷ 3.14
⇒ r = √144
⇒ r = 12 feet
Which of the following represents y > 2x - 3?
Answer: Choice A
The two characteristics here are:
The boundary line is a dashed line. This visually indicates to the reader "points on the boundary do NOT count as solutions". Think of the boundary as an electric fence you cannot touch, but can get closer and closer to. We aren't including boundary points directly because of the lack of "or equal to". The shading is above the boundary, due to the "greater than" sign. This only works if we have y isolated.The graph of choice B is [tex]y \le 2x-3[/tex] since we have a solid line and shading below the solid line. This time points on the boundary are part of the solution set.
The length of a rectangle is four times the width. The perimeter of the rectangle is 45 inches. Write a system of equations that represents this problem. What is the area of the rectangle
Step-by-step explanation:
2×length + 2×width = 45
length = 4×width
now, we are using the second equation (a variable identity) in the first equation
2×4×width + 2×width = 45
8×width + 2×width = 45
10×width = 45
width = 45/10 = 4.5 in
length = 4×width = 4×4.5 = 18 in
the area of the rectangle is
length × width = 18 × 4.5 = 81 in²
If a plumber chargers a call out fee of $85 plus $72 per hour how much would it cost for 3 hours?
Show working out pls
Answer:
$301
Step-by-step explanation:
Charge for 1 hour = $ 72
To find the cost for 3 hours, multiply hourly rate ($72) by 3
Charge for 3 hours = 72 * 3 = $ 216
Now, to find the total cost, add the charge for 3 hours and the fixed rate.
Total cost = fixed rate + charge for 3 hours
= 85 + 216
= $ 301
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. X = t5 1, y = t6 t; t = −1
The equation of the tangent to the curve at the point corresponding to the given value of the parameter will be x + y = c.
How to calculate the tangent of the parameter curves at a point?The curves are given below.
x = t⁵ + 1 and y = t⁶ + t
Then differentiate the functions with respect to t, then we have
[tex]\rm \dfrac{dx}{dt} = 5t^4\\[/tex] ...1
and
[tex]\rm \dfrac{dy}{dt} = 6t^5 + 1[/tex] ...2
Divide equation 2 by equation 1, then we have
[tex]\rm \dfrac{\dfrac{dy}{dt} }{\dfrac{dx}{dt} } = \dfrac{dy}{dx} = \dfrac{6t^5 + 1}{5t^4}[/tex]
Then the slope of the equation at t = −1, then we have
dy/dx = [6(-1)⁵ + 1]/[5(-1)⁴]
dy/dx = (-6+1)/5
dy/dx = -5/5
dy/dx = -1
Then the equation of the tangent line will be
y = -x + c
x + y = c
Where c is a constant.
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ramon ate at a restaurant and gave the server a $4 tip the tip was 20% of the cost of the meal how much was the meal
Answer:
The meal was $20
Step-by-step explanation:
20%= 1/5
1/5=4/? ---> one converts to four by multiplying it by 4 so you should do the the same with the denominator which is five.
5×4= 20
Graph the function f(x) = 5(0.21)x.
Answer: A
Step-by-step explanation: BIG BRAIN
PLEASE HELP ASAP CANT MOVE ON
What is the scale factor of LaTeX: \triangle ABC\:to\:\triangle DEC? Be sure to simplify your answer!
answers:
2/7
10/21
3/14
5/14
Answer:
[tex]\frac{2}{7}[/tex]
Step-by-step explanation:
Triangle ABC is similar to triangle DEC, because all angles in one triangle are equal to angles in the other triangle.
That means that corresponding sides have the same ratio. Side AB and side DE are corresponding sides. Since there are no unknowns we can calculate the ratio (scale factor).
Since we are looking for scale factor of triangle DEC to triangle ABC, we put side AB (which is in triangle ABC) in the numerator.
[tex]\text{scale factor} = \frac{\text{AB}}{\text{DE}} = \frac{6}{21} = \frac{2}{7}[/tex]
I've marked corresponding sides and angles in the attached picture.
multiply (x^2 - 5x)(2x^2 + x - 3)
Answer:
[tex]\textbf{C.}~2x^4 -9x^3-8x^2 +15x[/tex]
Step-by-step explanation:
[tex]~~~~(x^2 -5x)(2x^2 +x-3)\\\\=2x^4+x^3 -3x^2 -10x^3 -5x^2 +15x\\\\=2x^4 -9x^3-8x^2 +15x[/tex]
Enzymatic browning, the darkening of cut fruit when exposed to the air, can be lessened by
a. cooking the fruit
b.dipping the fruit in a juice rich in vitamin c
c. freezing the fruit
d.dipping the fruit in chocolate
( geometry) Find the area of a regular hexagon whose sides are 22.6 cm, and whose apothem is 19.6 cm.
Answer:
1328.88 cm^2
Step-by-step explanation:
Area = 6 * 1/2 * 22.6 * 19.6
= 1328.88 cm^2
6x-2=8x-8 please i forgot how you do this
Answer:
x = 3
Step-by-step explanation:
6x - 2 = 8x - 8 ( subtract 8x from both sides )
- 2x - 2 = - 8 ( add 2 to both sides )
- 2x = - 6 ( divide both sides by - 2 )
x = 3
Answer:
x=3
Step-by-step explanation:
4 x 12 = 6 x n 4
6
8
12
Answer:
2 I believe
Step-by-step explanation:
you do 4x12 then divide it by 6x4 then it would be n equals 2
whats equlvlent to 3√6
Answer:
Important: 3
6
looks like a fraction, but it is actually an improper fraction.
There is an infinity number of equivalent fractions to 3
6
.
To find an equivalent fraction to 3
6
, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:
By dividing the original fraction by 3, we get:
3 ÷ 3
6 ÷ 3
= 1
2
By multiplying the original fraction by 2, we get:
3 × 2
6 × 2
= 6
12
Step-by-step explanation:
The lengths of the diagonals of a parallelogram are 10 feet and 16 feet. If one side of the parallelogram measures 4 feet, to the nearest hundredth of a degree, find the measure of the acute angle formed by the intersection of the diagonals.
Answer: 24.15
Step-by-step explanation:
A new pizza restaurant uses paid advertisement to increase pizza sales on Mondays. The table below is a record of the restaurant’s sales each Monday for the first quarter (13 weeks) of the paid advertisement.
Part A: Create a scatter plot to represent the data in the table. Then, draw the line of best fit, going through the points representing weeks 5 and 13. Be sure to label each axis, as well as to include the proper titles for the scatter plot.
Part B: Use the total sales for weeks 5 and 13 to write an equation for the line of best fit. In your final answer, include all of your calculations.
Part C: In terms of the slope of the equation for the lines of best, fit explain whether or not you think the paid advertisement is responsible for the restaurant's increase or decrease in pizza sales during the first quarter. Use complete senteneces in your answer.
Part D: Assuming that the pizza restaurant wishes to continue the paid advertisement for an additional quater, use the equation for the line of best fit to predict the restaurant's sales for the Monday of the 20th week.
A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.
What is a line of best fit?A line of best fit is also referred to as a trendline and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any correlation between a data.
Part B.By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that an equation for the line of best fit is given by:
y = 22.214x + 291.27
Part C.Since the slope of the equation for the line of best fit is positive, the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.
Part D.Next, we would predict the restaurant's sales for the Monday of the 20th week as follows:
y = 22.214x + 291.27
y = 22.214(20) + 291.27
y = 444.28 + 291.27
y = $735.55.
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Question 10 of 20
Which polynomial shows the difference of (4x² + 3x - 2) and (x²+2x+4)?
OA. 3x²+x-8
B. 3x²+x+2
OC. 3x² + 5x+2
OD. 3x²+x-6
Answer:
D.3x²+x-6
Step-by-step explanation:
4x²-x²+3x-2x-2-4
3x²+x-6
1. the prices for 6 different jerseys are
$98, $85, $34, $79, $85, and $92.
what is the outlier in the data set?
Answer:
Step-by-step explanation:
8
Mary measured the heights of two different plants every day. Plant A was 1 inch tall when
Mary began her measuring, and it grew 0.5 inch per day. Plant B was 3 inches tall, and it grew
0.25 inch per day. On which day were plant A and plant B the same height?
A day 5
B.
day 8
C. day 12
D.
day 16
The heights of plant A and plant B will be equal on the day 8.
How to find the heights of the trees?The height of the tree can be found as follows:
The equation for plant A can be described as follows:
y = 1 + 0.5x
where
x = number of days
y = height
The equation for plant B can be described as follows:
y = 3 + 0.25x
Therefore, for the height to be equal
1 + 0.5x = 3 + 0.25x
1 - 3 = 0.25x - 0.5x
-2 = -0.25x
x = 2 / 0.25
x = 8 days
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determine whether sec x -tanxsinx=cosx is a possible identity
[tex]\text{L.H.S}\\\\\sec x - \tan x \sin x\\\\\\=\dfrac{1}{\cos x}- \dfrac{\sin x }{ \cos x } \cdot \sin x\\\\\\=\dfrac 1{\cos x} - \dfrac{\sin^2 x}{\cos x}\\\\\\=\dfrac{1- \sin^2 x}{\cos x}\\\\\\=\dfrac{\cos^2 x}{\cos x}~~~~~~~~~~~~~;[\sin^2 x + \cos^2 x = 1]\\\\\\=\cos x\\\\\\=\text{R.H.S}\\\\\text{Since both sides are equal, the given equation is an identity.}[/tex]