Answers
The solutions to the given quadratic equation are as follows:
x = 1.10, x = 10.9.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
For this problem, the equation in item D is:
-x² + 12x - 12 = 0
x² - 12x + 12 = 0
Hence the coefficients are:
a = 1, b = -12, c = 12.
Then the solutions to the equation are found as follows:
Delta = (-12)² - 4 x 1 x 12 = 96x1 = 0.5(12 + sqrt(96)) = 10.9x2 = 0.5(12 - sqrt(96)) = 1.10The solutions are:
x = 1.10, x = 10.9.
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Related Questions
An airplane covers 3500 km in three hours. What would be the distance covered by the plane in 4.5 hours if it flies at the same constant speed. ( I need the proportion equation please help ASAP.)
Answers
Answer:
5,250 km
Step-by-step explanation:
[tex]\frac{hours}{miles}[/tex] = [tex]\frac{hours}{miles}[/tex]
[tex]\frac{3}{3500}[/tex] = [tex]\frac{4.5}{x}[/tex] Cross Multiply
3x = (4.5)(3500)
3x = 15750 Divide both sides of the equation by 3
x = 5,250
Need help! Someone please help!!!
Answers
Answer:
B. Ounces of water consumed compared with the number of same-size bottles dr*nk
Step-by-step explanation:
A constant rate of change means that the two values should be linear. Let's analyze why the other three options are wrong:
A. The distance between different airports can be very different (i.e the distance between Airport 1 and Airport 2 is 20 km and the distance between Airport 2 and Airport 3 is 500 km), meaning that the distance the airplane travels and the number of airports it visits are not linear.
C. Similar to A, the point scored in different quarters can be very different (i.e. 0 points scored in the 1st quarter, 35 points scored in the 2nd quarter, etc.)
D. Similarly, the number of fish in a pond can either be very large or very small, even if the volume of the pond stays the same
B is correct because the bottles are the same size, meaning that if you drink x bottles of 2-ounce bottles, you will always drink 2x ounces of water, no matter what, creating a linear function.
Solve the equation. Write the smaller value of x. x^2-4x-5=0
Answers
(x-5)(x+1) = 0
x = 5
x = -1
x = 5 OR x = -1
since it says write the smaller value, then i think the answer is -1.
write a solution system for the inequality 3x-2>10
Answers
Answer:
x>4
Step-by-step explanation:
3x - 2 >10 add 2 to both sides
3x > 12 Divide both sides by 3
x >4
Answer:
[tex]x > \bf 4[/tex]
Step-by-step explanation:
To find a solution to this inequality, we have to rearrange this equation to make [tex]x[/tex] its subject:
[tex]3x - 2 > 10[/tex]
⇒ [tex]3x - 2 + 2 > 10 + 2[/tex] [Add 2 to both sides]
⇒ [tex]3x > 12[/tex]
⇒ [tex]\frac{3x}{3} > \frac{12}{3}[/tex] [Divide both sides by 3]
⇒ [tex]x > \bf 4[/tex]
Latoya has a lot of doctor’s visits coming up, and her children all need vaccinations for the upcoming school year. which type of insurance would be most helpful to her in this situation?
Answers
Health insurance would be most helpful to Latoya.
What is Health insurance?Health insurance, often known as medical insurance in South Africa, is a type of insurance that covers all or part of the risk of a person incurring medical expenses. Risk, like other types of insurance, is shared among many people. An insurer can design a routine finance structure, such as a monthly premium or payroll tax, to provide the money to pay for the health care benefits stipulated in the insurance agreement by calculating the overall risk of health risk and health system expenses over the risk pool.The benefit is managed by a central institution, such as a government agency, a private company, or a non-profit organization.Therefore, health insurance would be most helpful to Latoya.
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give me some questions of grade 7
Answers
Q1: For 30 minutes, a person jogged 10 times along the perimeter of a rectangular field at 12 kilometers per hour. Find the square meters of the field if its length is twice its width.
Q2: A car is traveling at a speed of 75 kilometers per hour. In one minute, how many meters does the car travel?
Q3: What is the length of 2000 millimeters in inches? Round your answer to the nearest hundredth.
Hope this helps =)
Let S1 be the amount allowing 10% discount on the price of some goods and then adding 10% VAT. Let S2 be the amount adding 10% VAT and then allowing 10% discount. Which of the following is true? (i) S1 > S2 (ii) S1 < S2 (iii) S1 = S2 (iv) Cant be decided
Answers
Using decimal multipliers, the correct statement is given by:
(iii) S1 = S2.
What is a decimal multiplier?Increases of a% or decreases of a% re represented by decimal values, as follows:
The equivalent multiplier for an increase of a% is given by: [tex]\frac{100 + a}{100}[/tex]The equivalent multiplier for an decrease of a% is given by: [tex]\frac{100 - a}{100}[/tex]Hence, in the context of this problem:
An increase of 10% is represented by 1.1.A decrease of 10% is represented by 0.9.The options are given as follows:
S1 = 0.9 x 1.1 = 0.99.S2 = 1.1 x 0.9 = 0.99.They are equal, hence option (iii) is correct.
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Function a (b) relates the area of a trapeze with a given height of 14 and a base length of 5 with the length of its other base. it takes the other base value as input and returns the trapeze area as output. what equation below represents the inverse function b (a), which takes the trapeze area as input and returns the length of the other base as an output?
Answers
The function accepts the trapezoid's area as input and returns as output the length of the other base exists A(x)/7-5=x.
What is an area of a trapezoid?The function of the trapezoid area exists:
[tex]A(x)=(B+b)*h/2[/tex]
where B exists the bases
h stands the height.
Given a height of 14 and one base length of 5 with the length of its other base
With the given data:
h = 14B and b =5 and x (it may vary which one exists bigger)
So that function becomes:
[tex]$A(x)=(5+x)*14/2[/tex]
A(x) = (5 + x) [tex]*[/tex] 7
So if you want the inverse function, to find the value of x:
A(x) / 7 = 5 + x
A(x )/ 7 - 5 = x
Therefore, the function accepts the trapezoid's area as input and returns as output the length of the other base exists A(x)/7-5=x.
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Find the surface
7 in.
4 in.
4 in.
+
4 in.
5 in.
7 in.
5 in.
j
SA = [?]in.² please explain how you got it I’m stuck
Answers
And multiply 4,5,7,5
Hope this helps
In the 2020 presidential election, Indiana had 11 electoral votes. That was 29 votes fewer than the number of electoral votes in Texas. Write and solve an equation to find the number of electoral votes in Texas.
Answers
Answer:
40
Step-by-step explanation:
11+29=40
Answer:
B)0 to 21 electoral votes
Step-by-step explanation:
edge 2023
-6 - (2x + 7) = -2(x +6) -1
Answers
Answer:
Infinite solutions
Step-by-step explanation:
You can put in any number for x and the 2 sides of the equation will equal each other.
Answer:
The equation has not solution, both parts of the equation correspond to the same line.
Step-by-step explanation:
-6 -(2x+7) = -2(x+6) - 1
-6 -2x - 7 = (-2*x + (-2*6)) - 1
-6 - 2x - 7 = -2x - 12 - 1
-2x - 13 = -2x - 13
-2x = - 2x
find the value of n: [tex]3n (\frac{1}{4} ) = 16 \frac{1}{2}[/tex]
Answers
[tex]\boldsymbol{\sf{3n\left(\dfrac{1}{4}\right)=16\dfrac{1}{2} } }[/tex]
Multiply both sides of the equation by 4, the lowest common denominator of 4.2.
[tex]\boldsymbol{\sf{ 12n\times\left(\dfrac{1 }{4}\right)=2(16\times2+1) }}[/tex]
Multiply 12 and 1/4, because once multiplied, we get the following 12/4.
[tex]\boldsymbol{\sf{\dfrac{12}{4}n=2(16\times2+1) \ \ \longmapsto \ \ [Divide \ 12 \div 4.] }}[/tex]
[tex]\boldsymbol{\sf{3n=2(16\times2+1) \ \ \longmapsto \ \ [ Multiply \ 16\times 2] }}[/tex]
[tex]\boldsymbol{\sf{3n=2(32+1) \ \longmapsto \ \ [Add] }}[/tex]
[tex]\boldsymbol{\sf{3n=2\times33 \ \ \longmapsto \ \ [Multiply] }}[/tex]
[tex]\boldsymbol{\sf{3n=66}}[/tex]
Divide both sides by 3.
[tex]\boldsymbol{\sf{n=\dfrac{66}{3} \ \longmapsto \ \ [Split] } }[/tex]
[tex]\boxed{\boldsymbol{\sf{n=22}}}[/tex]
Once the exercise is solved, we find that the value of n is 22.
Use the method of undetermined coefficients to solve the given nonhomogeneous system. x' = −1 5 −1 1 x + sin(t) −2 cos(t)
Answers
It looks like the system is
[tex]x' = \begin{bmatrix} -1 & 5 \\ -1 & 1 \end{bmatrix} x + \begin{bmatrix} \sin(t) \\ -2 \cos(t) \end{bmatrix}[/tex]
Compute the eigenvalues of the coefficient matrix.
[tex]\begin{vmatrix} -1 - \lambda & 5 \\ -1 & 1 - \lambda \end{vmatrix} = \lambda^2 + 4 = 0 \implies \lambda = \pm2i[/tex]
For [tex]\lambda = 2i[/tex], the corresponding eigenvector is [tex]\eta=\begin{bmatrix}\eta_1&\eta_2\end{bmatrix}^\top[/tex] such that
[tex]\begin{bmatrix} -1 - 2i & 5 \\ -1 & 1 - 2i \end{bmatrix} \begin{bmatrix} \eta_1 \\ \eta_2 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix}[/tex]
Notice that the first row is 1 + 2i times the second row, so
[tex](1+2i) \eta_1 - 5\eta_2 = 0[/tex]
Let [tex]\eta_1 = 1-2i[/tex]; then [tex]\eta_2=1[/tex], so that
[tex]\begin{bmatrix} -1 & 5 \\ -1 & 1 \end{bmatrix} \begin{bmatrix} 1 - 2i \\ 1 \end{bmatrix} = 2i \begin{bmatrix} 1 - 2i \\ 1 \end{bmatrix}[/tex]
The eigenvector corresponding to [tex]\lambda=-2i[/tex] is the complex conjugate of [tex]\eta[/tex].
So, the characteristic solution to the homogeneous system is
[tex]x = C_1 e^{2it} \begin{bmatrix} 1 - 2i \\ 1 \end{bmatrix} + C_2 e^{-2it} \begin{bmatrix} 1 + 2i \\ 1 \end{bmatrix}[/tex]
The characteristic solution contains [tex]\cos(2t)[/tex] and [tex]\sin(2t)[/tex], both of which are linearly independent to [tex]\cos(t)[/tex] and [tex]\sin(t)[/tex]. So for the nonhomogeneous part, we consider the ansatz particular solution
[tex]x = \cos(t) \begin{bmatrix} a \\ b \end{bmatrix} + \sin(t) \begin{bmatrix} c \\ d \end{bmatrix}[/tex]
Differentiating this and substituting into the ODE system gives
[tex]-\sin(t) \begin{bmatrix} a \\ b \end{bmatrix} + \cos(t) \begin{bmatrix} c \\ d \end{bmatrix} = \begin{bmatrix} -1 & 5 \\ -1 & 1 \end{bmatrix} \left(\cos(t) \begin{bmatrix} a \\ b \end{bmatrix} + \sin(t) \begin{bmatrix} c \\ d \end{bmatrix}\right) + \begin{bmatrix} \sin(t) \\ -2 \cos(t) \end{bmatrix}[/tex]
[tex]\implies \begin{cases}a - 5c + d = 1 \\ b - c + d = 0 \\ 5a - b + c = 0 \\ a - b + d = -2 \end{cases} \implies a=\dfrac{11}{41}, b=\dfrac{38}{41}, c=-\dfrac{17}{41}, d=-\dfrac{55}{41}[/tex]
Then the general solution to the system is
[tex]x = C_1 e^{2it} \begin{bmatrix} 1 - 2i \\ 1 \end{bmatrix} + C_2 e^{-2it} \begin{bmatrix} 1 + 2i \\ 1 \end{bmatrix} + \dfrac1{41} \cos(t) \begin{bmatrix} 11 \\ 38 \end{bmatrix} - \dfrac1{41} \sin(t) \begin{bmatrix} 17 \\ 55 \end{bmatrix}[/tex]
PLEASE HELP ME ASAP! BEING TIMED
If the tens digit of a number is 4 times the units digit and the hundreds digit is twice the tens digit, is the number even or odd?
Answers
The number is 841
So we can see that the number is odd.
Is the number even or odd?
Here we have a 3-digit number that can be written as:
a*100 + b*10 + c
Here we know that:
"the tens digit of a number is 4 times the units digit"
b = 4*c
"the hundreds digit is twice the tens digit"
a = 2*b
Now, remember that a, b, and c, are numbers on the set {0, 1, ..., 8, 9}
And if we replace the first equation into the second, we get:
a = 2*(4*c) = 8*c
Now, the only value of c that we can use such that a is a single digit whole number is c = 1
(if c = 0, then our number is zero)
a = 8*1 = 8
b = 4*1 = 4
c = 1
The number is 841
So we can see that the number is odd.
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Could someone explain how to get the correct answer when trying to find the f(X) and g(X) on a graph like this? Thanks!
Answers
Answer:
f(3) = g (3)
Step-by-step explanation:
graphically, we notice that the graphs of f and g intersect
at the point of coordinates (3 , 0)
Then
f(3) = 6 = g(3)
Then
f(3) = g (3)
Let startfraction cosine (2 x) over cosine (x) sine (x) endfraction = 0 where 0° ≤ x ≤ 180°. what are the possible values for x?
Answers
45° only the possible values for x.
What is the meaning of trigonometric ratio?
Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.The given equation can be presented as follows;
[tex]\frac{cos (2 . x )}{cosine(x) + sin(x)} = 0[/tex]
We have that cos(2·x) = cos²(x) - sin²(x)
Also, we have, by the difference of two squares, the following relation;
cos²(x) - sin²(x) = (cos(x) - sin(x))(cos(x) + sin(x))
Therefore, the given equation can be written as follows;
[tex]\frac{cos (2 . x )}{cosine (x) + sin(x) } = \frac{(cos(x) - sin(x) * (cos(x) + sin(x)}{(cos(x) + sin(x))} = 0[/tex]
Crossing the common term, (cos(x) + sin(x)), in the numerator and the denominator, we have-
[tex]\frac{(cos(x) - sin (x) * (cos(x) + sin(x)}{(cos(x) + sin(x))} = cos (x) - sin(x) = 0[/tex]
From cos(x) - sin(x) = 0, we have;
Adding sin(x) to both sides of the equation
cos(x) - sin(x) + sin(x) = 0 + sin(x)
cos(x) = sin(x)
Therefore, the opposite leg and the adjacent leg of the right triangle formed with reference to the angle x are equal
∴ x = 90/2 = 45° only for 0° ≤ x ≤ 180°
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If a1=6 and a5=12, what does a3=?
Answers
a3=9
assuming the pattern is constant, a3 is right in the middle of a1 and a5 so the answer would be right in the middle of 6 and 12. the average of 6 and 12 is 9, so a3=9.
hope this helps!
Find two positive numbers whose product is 81 and whose sum is a minimum. (enter your answers as a comma-separated list. )
Answers
Answer: 18
Step-by-step explanation: the smallest two positive numbers whose product is 81 are 9 and 9. 9+9 is equal to 18.
PLEASE ANSWER QUICKLY
Answers
Answer:
3
Step-by-step explanation:
f(x) = 3x² - 2x + 1
f(x) = ax² + bx + c
a = 3
Which is the greatest fraction in this list? 1/2,3/4,5/8,11/16
Answers
Answer:
3/4
Step-by-step explanation:
multiply each fraction by 100 or you could find the LCM
If m ABD = 61, and m DBC = 59, then m ABC = ? PLS ASAP
Answers
Given that angle ABD and angle DBC are adjacent angle, the value of angle ABC is 120 degrees.
What is the value of angle ABC?Given the data in the question;
Angle ABD = 61°Angle DBC = 59°Angle ABC = ?Since angle ABD and angle DBC are adjacent angle, there addition will give us the value of angle ABC.
∠ABD + ∠DBC = ∠ABC
We substitute in the given values
61° + 59° = ∠ABC
∠ABC = 120°
Given that angle ABD and angle DBC are adjacent angle, the value of angle ABC is 120 degrees.
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The minor arc measures of circle Z are shown in the figure.
Circle Z is shown. Radii Z Y, Z X, Z W, Z V, Z U, and Z T are shown. The arc measure of Y X is 71 degrees, the arc measure of X W is 32 degrees, the arc measure of W V is 71 degrees, the arc measure of V U is 78 degrees, the arc measure of U T is 54 degrees, and the arc measure of T Y is 54 degrees.
Use the drop-down menus to complete each statement.
Angle UZT is congruent to angle
.
Angle VZW is congruent to angle
.
Answers
The completed statement are:
Angle UZT is congruent to angle TZY.Angle VZW is congruent to angle YZX.What is the angle about?Part A:
Angle UZT is congruent to angle TZY.
Using the image attached figure, we can see that:
∠UZT = 54°
∠TZY = 54°
Hence one can say that ∠TZY = ∠UZT are both congruent angles.
Part B:
Angle VZW is congruent to angle YZX.
Using the image attached attached, we can see that:
∠VZW = 71°
∠YZX = 71°
Hence, ∠YZX = ∠VZW are both regarded as congruent angles .
Therefore, The completed statement are:
Angle UZT is congruent to angle TZY.Angle VZW is congruent to angle YZX.Learn more about Angles from
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Answer: a, c
Step-by-step explanation:
1. Part A. Graph the following coordinates on the grid below.
(4, 3), (4,-5), (-2, 3), and (-2,-5)
Answers
Answer:
Step-by-step explanation:
a) start at the origin (0,0) then go 4 boxes to the right, 3 up
b) start at the origin (0,0) then go 4 boxes to the right, 5 down
c) start at the origin (0,0) then go 2 boxes to the left, 3 up
d) start at the origin (0,0) then go 2 boxes to the left, 5 down
Consider this equation.
Use the graph to find the approximate solutions to this equations
Answers
The equation be 2(x-2)-5=√x+3-1 then the graphical solution of the equations exists approximately x = 3 and x = 6.
What is the solution of the equation?The solution of an equation creates that equation true.
The equation of can be simplified, therefore:
2(x-2)-5=√x+3-1
simplifying the above equation, we get
2x -9 =√x+2
4 x²-37x + 79 = 0
The graphical solution of the equations exists at approximately x = 3 and
x = 6
In ending, the solution of an equation makes the equation true.
Therefore, the graphical solution of the equations exists approximately x = 3 and x = 6
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Solve for x: 12x2 – 6 (a2 + b2)x + 3a2b2 = 0
Answers
Answer:
x:12×2−6(a2+b2)x+3a2b2=0
Step-by-step explanation:
equation
Determine how much this home would cost to replace: 3,800 square feet at $102.00 per square foot
Answer: $
___
This is exactly what the questions look like, can’t find anything.
Answers
Hope it help you
Please mark me brainliest
The graph shows two lines, A and B:
A graph is shown with x and y axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 2, 6 with the ordered pair 5, 0. Another straight line labeled B joins the ordered pair 0, 2 with the ordered pair 6, 6.
Based on the graph, which statement is correct about the solution to the system of equations for lines A and B?
(3, 4) is the solution to both lines A and B.
(3, 4) is the solution to line A but not to line B.
(0, 2) is the solution to both lines A and B.
(0, 2) is the solution to line A but not to line B.
Answers
Answer:
Part A) The system has one solution
Part B) The solution is the point (4,4)
i believe
Pls help
Write the equation for a parabola with a focus at (-4,3) and a directrix at y=5
Answers
Answer:
y=(1/-4)(x+4)^2 +4
Step-by-step explanation:
Don't ask
The prices for different lengths of ribbon sold at a fabric store are shown in the table.
Which statement best justifies whether or not the relationship between the length and price represents a function?
Answers
the correct option is the last option, the table represents a function because no length of ribbon has more than one price.
What is a function?
A function is a relationship that maps elements from a set, the domain (set of the inputs), into elements from another set, the range (set of the outputs).
Such that each element of the domain can be mapped into only one element of the range.
If we look at the table, we can see that each input (length of ribbon) is mapped into only one output (price). Then we conclude that this table represents a function.
Then the correct option is the last option, the table represents a function because no length of ribbon has more than one price.
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Select the correct answer. a number is selected at random from the set {2, 3, 4, ... 10}. which event, by definition, covers the entire sample space of this experiment?
Answers
[tex]( \: 2 \: 3 \: 4 \: 5 \:6 \: 7 \:8 \: 9 \: 10 \: )[/tex]
[tex]Event \: P \\P:"choosing \: a \: natural \: number \: from \: 2 \: to \: 10 \: inclusive"[/tex]
