Answer:
c = 3.09375Step-by-step explanation:
Standard for of quadratic equation:
ax² + bx + c = 0We have
2x² - 5x + c = 0Sum of the roots
x₁ + x₂ = - b/a = -(-5)/2 = 2.5Product of the roots
x₁x₂ = c/a = c / 2We have:
x₁ - x₂ = 0.25The square of the above is:
(x₁ - x₂)² = (x₁ + x₂)² - 4x₁x₂Substitute known values and solve for c:
0.25² = (2.5)² - 4(c/2) 2c = 6.25 - 0.06252c = 6.1875c = 3.09375Answer:
c = 3.09375
Step-by-step explanation:
Factored form of a quadratic equation
[tex]y=a(x-r_1)(x-r_2)[/tex]
where:
a is the leading coefficient[tex]r_1[/tex] and [tex]r_2[/tex] are the rootsGiven quadratic:
[tex]2x^2-5x+c=0[/tex]
Therefore, the leading coefficient is:
[tex]\implies a=2[/tex]
Substitute the value of a into the formula:
[tex]\implies y=2(x-r_1)(x-r_2)[/tex]
Expand:
[tex]\implies y=2x^2-(2r_2+2r_1)x+2r_1r_2[/tex]
Compare the coefficients of x:
[tex]\implies -(2r_2+2r_1)=-5[/tex]
[tex]\implies 2r_2+2r_1=5[/tex]
[tex]\implies r_2+r_1=2.5[/tex]
If the difference between the roots is 0.25 then:
[tex]\implies r_2-r_1=0.25[/tex]
Add the two root equations to eliminate r₁:
[tex]\implies 2r_2=2.75[/tex]
[tex]\implies r_2=1.375[/tex]
Substitute the found value of r₂ into one of the root equations and solve for r₁:
[tex]\implies 1.375-r_1=0.25[/tex]
[tex]\implies r_1=1.375-0.25[/tex]
[tex]\implies r_1=1.125[/tex]
As c = 2r₁r₂ then:
[tex]\implies c=2(1.125)(1.375)[/tex]
[tex]\implies c=3.09375[/tex]
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In direct variation where y = kx, if y = 18 and x = 4, what is the value of x when y = 36 ?
Answer:
18/4x36/x
18x=4x36
18x=144
x=144/18
x=8
Answer:
x = 8
Step-by-step explanation:
Given
y = kx ← k is the constant of variation
To find k use the condition y = 18, x = 4 , then
18 = 4k ( divide both sides by 4 )
4.5 = k
y = 4.5x ← equation of variation
When y = 36, then
36 = 4.5x ( divide both sides by 4.5 )
8 = x
Cars enter a car wash at a mean rate of 4 cars per half an hour. What is the probability that, in any hour, exactly 4 cars will enter the car wash? Round your answer to four decimal places.
The probability that exactly 4 cars will enter the car wash in an hour is 0.195
What is the probability that, in any hour, exactly 4 cars will enter the car wash?Generally, This is a Poisson process, where the mean number of cars entering the car wash is 4 cars per hour. The probability of exactly 4 cars entering in an hour is given by the Poisson probability mass function:
P(X = 4) = (e^(-4) * 4^4) / 4!
where e is approximately 2.71828, and 4! is
4 * 3 * 2 * 1 = 24.
Plugging in the values, we get:
P(X = 4) = (2.71828^(-4) * 4^4) / 24
P(X = 4) =0.195
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Mark has 10 pens. Kate has 5 times as many pens as Mark.
Which equation below answers how many pens Kate has? (y = number of
Kate's pens)
10 = 5 x y
B
10 = 5 + y
c.
y = 5 x 10
D
y = 10 - 5
Answer:
The answer to this questions is A
A solution set always includes...
A. all the numbers that make the inequality false.
B. all the numbers that make the inequality true.
C. zero and infinity.
D. negative infinity.
Answer:
A
Step-by-step explanation:
i got the same answer and got ir right
Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answer:
C) {6+√43, 6-√43}
Step-by-step explanation:
Applying,
x = [-b±√(b²-4ac)]/2a.................... Equation 1
From the question,
Given: a = 1, b = -12, c = 7
Substitute these values into equation 1
x = [-(-12)±√(-12²+4×1×7)]/2×1
x = [12±√(144+28)]/2
x = [12±√172]/2
either,
x = (12-√172)/2
x = (12-2√43)2
x = (6+√43)
or
x = (12+√172)/2
x = (12+2√43)/2
x = (6+√43)
Hence,
The right answer is C). {6+√43, 6-√43}
Find the value of x. Round to the nearest tenth.
What is the product? 3a(8a - 6b)
24a² - 6b
24a² - 6ab
24a² - 18b²
24a² - 18ab
The product of expression is 24a² - 18ab.
What is Polynomial?A polynomial is a sort of algebraic expression in which all variable exponents are whole numbers. Variable exponents in any polynomial must be non-negative integers. A polynomial is made up of constants and variables, however we cannot divide polynomials by variables.
We have,
3a( 8a - 6b)
Now, multiplying the expression as
= 3a(8a) - 3a(6b)
= 24a² - 18ab
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What is the value of x? Solve for x. You may build and solve the equation on your Equation Mat. Or you may solve the equation algebraically (to the right). Of this -2x-2=3 (-x+2 )
Answer:
[tex] - 2x - 2 = 3( - x + 2) \\ - 2x - 2 = - 3x + 6 \\ - 2x + 3x = 6 + 2 \\ x = 8[/tex]
Clara baked a sheet cake with a length of 0.5 meters. She covered the cake in small 1 frosting polka dots that are the length of the cake. What is the approximate 100 length of a polka dot, in meters?
Answer:
kkuguftfhbnkmom ugvtvtv uvbuub
Frank earns an annual salary of $42,800. He pays 8% in total taxes. How much money will Frank pay in taxes each year?
Answer:
$3424
Step-by-step explanation:
42800 x .08
.08 = 8%
The table below shows the number of minutes played (x) by various basketball players and the number of rebounds (y) they had.
Scatter plot that has 2 through 20 for x and 1 through 10 for y.
a. Draw a scatter plot of the data. Label the axes.
b. Find an equation for a line of best fit.
c. Use your equation from part b above to predict how many rebounds a player would have if they played 30 minutes in the game.
I will give all my points to the first person that answers.
Answer:
A
Step-by-step explanation:
Question 3: Use the graph to fill in the blank with the correct number. f(3) =
10A
5
•
0
5
•
-5.
-10%
Your answer
Answer:
f(3) = 2
Step-by-step explanation:
See the attached graph. f(3) = ____ is asking us to find the value of the function, f, at the point x = 3. At x = 3, the value of y is 2.
What type of triangle is 70 70 40?
70-70-40 is an isosceles triangle.
The isosceles triangle has three acute angles, which means that the angles are less than 90°.The summation of three angles of an isosceles triangle is always 180°. In an isosceles triangle, if two sides are equal, then the angles opposite to the two sides correspond to each other and are also always equal.The two equal sides are defined as the legs and the third side is defined as the base of the triangle.The two angles opposite the legs are equal and are always acute, so the categorization of the triangle as acute, right, or obtuse depends only on the angles between its two legs.Read more about the isosceles triangle:
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What is the unknown fraction?
Answer:
47/100
Step-by-step explanation:
we will shift the 2/10 to the other side and change the sign to minus
PLS SOMEONE HELPP I NEED THIS ASAP
The rate of change for the graph, when x=0 and x=1 is 2 units.
What is average rate of change?
This expression represents the average rate of change of the function f(x) over the range a<=x<=b, is less than or equal to x, and is less than or equal to b -
[f(b)-f(a)]/b-a
The rate of change of graph is determined by the formula -
[f(b)-f(a)]/b-a
[f(1)-f(0)]/1-0
Here, in the graph it can be clearly seen that f(0)=-1 and f(1)=1.
Plugging in the values -
[1-(-1)]/1
(1+1)/1
2
Therefore, the rate of change is 2 units.
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Which of the following is correctly written in Standard Form?
Therefore , the solution to the given problem of equation comes out to be4x-3y = 6 as a standard equation in all the above options.
An equation's definitionAn equation is a representation of two identical variables in mathematics, one on either side of an equals sign. Common difficulties can be solved using equations. We frequently seek pre algebra help when faced with obstacles in real life. Lessons in pre-algebra cover the basics of mathematics.
Here,
Given : 4x-3y = 6
-4x + 2y =8
=> y = 4/5x + 4
=> 4/5x + 2y = 6
Thus ,
From the above following equations we get ,
4x-3y = 6
as a standard equation in all the above options.
Therefore , the solution to the given problem of equation comes out to be 4x-3y = 6 as a standard equation in all the above options.
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Molly bought a large basket of 60 apples.
When she got home, she found 4 rotten
ones. If she goes back and buys 200 more
apples, how many rotten apples would she
expect there to be?
Group of answer choices
20
24
13
8
Step-by-step explanation:
1. 60 apples
2. 60-4=56
3. 56+200=256
200/60
60/4
60+60=120
120+60=180
I think either 13.
Please answer quick! The question is in a file down below.
Answer:
perimeter= 9+9π cm
area= 40.5-10.125π cm²
Step-by-step explanation:
area of the square =9x9=81cm²
area of the two semicircles which have the same diameter =area of one circle
= (9÷2)²π =(81÷4)π
area of the whole shaded part = 81- (81÷4)π cm²
the area of each shaded part= (81-(81÷4)π)÷2
= 40.5-10.125π cm²
circumference of 2 semicircles= circumference of 1 circle = 2πr = 2x9xπ= 18π cm
then are perimeter of the whole shaded part = 18π+9+9= 18+18π cm
perimeter of each shaded part = (18+18π)÷2=
9+9π cm
3 times one number minus a second is 8 and the sum of the numbers is 12
Answer: 3x-y=8
Step-by-step explanation:
What is the domain and range of √ X 2?
The domain of √ X 2 is X ≥ 4. The range is all real numbers.
Here is the proof, In order for the square root to be defined, the radicand (the value inside the square root symbol) must be greater than or equal to zero. In this case, the radicand is X - 2, so we must have X - 2 ≥ 0, which is equivalent to X ≥ 4. Therefore, the domain of √ X - 2 is all values of X that are greater than or equal to 4. The range of √ X - 2 is all real numbers because the square root of any non-negative value is a real number.
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How do you find the sides of an isosceles triangle given the angles?
To find the sides of an isosceles triangle given the angles, use the Law of Cosines to calculate the length of each side.
An isosceles triangle has two angles and two sides that are both equal.. To find the sides, you will need to use the Sine Law. The Sine Law states that the ratio of the length of a side of a triangle to the sine of its opposite angle is equal for all sides and angles of the triangle.
For example, if you have the angles A and B, and you know that they are both equal (i.e. they are the angles of an isosceles triangle), then you can use the Sine Law to calculate the length of the sides:
Side AB = Side BC = (Side AC) x (Sin A / Sin B)
Where A and B are the angles of the triangle and Side AC is the known side length.
Once you have calculated the length of the two equal sides, you can then use the Pythagorean Theorem to calculate the length of the third side (the base).
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Sara had 222 dollars to spend on 9 books after buying then she had 15 dollars how much did each book cost
Answer:
each book cost=222-15=207/9=22.88 dollar
HELP ME PLEASE AND THANK YOUUU
Answer:
x=3 y=1
Step-by-step explanation:
-2/3x+3=2x-5
x=3
y=-2/3(3)+3
y=1
y=2(3)-5
y=1
anyone help please?
Answer:
The transformation is a reflection over the y axis
(PLEASE HELP)
Which expression is represented on the number line?
Answer:
F .0-(-8) I think so..........................
Answer:
F is represented on the number line
MATH HELP CALC
LOOK AT IMAGE
The right Riemann sum for the given function is 2.5.
Firstly, we must find the width of each of the subintervals Δx,
We know n = 4, a = 0, b = 2
∴ Δx = b - a / n
Δx = 2 - 0 / 4
Δx = 1/2
The width of each rectangle is 0.5
Next, we must find the locations of the right endpoints of the rectangles -
x1 = a + Δx(1) = 0.5
x2 = a + Δx(2) = 1
x3 = a + Δx(3) = 1.5
x4 = a + Δx(4) = 2
Now that we have the width of each rectangle, Δx = 0.5, and the right endpoints for the rectangles, x1 = 0.5, x2 = 1, x3 = 1.5, x4 = 2.
we can compute the right Riemann sum.
Computing the sum of the areas of the rectangles:
∑Δx f(x) = ∑ 0.5f(xi)
= 0.5 f(x1) + 0.5 f(x2) + 0.5 f(x3) + 0.5 f(x4)
= 0.5 (0.5) + 0.5 (1) + 0.5 (1.5) + 0.5 (2)
= 2.5
[tex]\int\limits^2_0 {x^{3} } \, dx[/tex] ≈ 2.5
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What does → mean in math?
â' in mathematics refers to the hexadecimal representation of the number 10.
What does hexadecimal notation provide for?In machine code and assembly programming languages, hexadecimal is widely utilised. It is frequently used to refer to memory addresses. It can be used to represent numbers kept in a CPU's registers or in main memory, as well as during the debugging phase of designing a computer programme.
How is the hexadecimal notation read?Although there are six more digits to consider, counting in hex is very similar to counting in decimal. When a digit position exceeds "F," you roll that place over to "0" and increase the digit to the left by 1. And once you've reached 1F16, move on to 2016 and keep churning the right-most
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6n = 21 what is the answer
Answer:
Decimal: n = 3.5
Fraction: n = 7/2
Step-by-step explanation:
6n = 21
n = 21/6
n = 7/2
n = 3.5
Answer:
3.15
Step-by-step explanation:
Divide 21 by 6
Jamila deposits $800 in an account that earns yearly simple interest at a rate of 2.65%. How much money is in the account after 3 years and 9 months?
Answer:
$821.2
Step-by-step explanation:
cause 2.65 percentage of 800 dollars is 800/100=8*2.65=21.2dollars.+800 =$821.2
im homeschooled and someone asked me if I was in school and I said "yes" and he asked if I was in "7th period" I literally dont know what that means :)
There is no 7th period, so no you aren't in 7th period.