Answers
Using the formula below
[tex]\begin{gathered} b^2-4ac \\ \text{Solving for the first option} \end{gathered}[/tex]For 2x²+4x+4, relataing it to the general form of a quadratic equation,
[tex]ax^2+bx+2=0[/tex]Where a, b, and c for the 2x²+4x+4 is given below,
[tex]\begin{gathered} a=2,b=4,c=4 \\ b^2-4ac=4^2-4(2\times4)=16-32=-16 \end{gathered}[/tex]Since b²-4ac is not supposed to be negative (i.e complex roots),
Answer is A
Related Questions
Using y= sin x OR y= cos x [Sinusoidal function] as the parent function, make your own transformations (5 units right, reflect on x axis, 2 units down, horizontal compression with factor 2). Then graph and state domain and range.
Answers
Using
[tex]y=\sin (x)[/tex]5 units right: Let's use the following rule:
[tex]\begin{gathered} y=f(x-5) \\ so\colon \\ y=\sin (x-5) \end{gathered}[/tex]Reflect on x-axis: Let's use the following rule:
[tex]\begin{gathered} y=-f(x) \\ so\colon \\ y=-\sin (x-5) \end{gathered}[/tex]2 units down: Let's use the following rule:
[tex]\begin{gathered} y=f(x)-2 \\ so\colon \\ y=-\sin (x-5)-2 \end{gathered}[/tex]Horizontal compression with factor 2: Let's use the following rule:
[tex]\begin{gathered} y=f(2x) \\ so\colon \\ y=-\sin (2x-5)-2 \end{gathered}[/tex]Let's graph the parent function, and the new function:
The blue graph is the parent function and the red graph is the new function after the transformations applied.
The domain and the range of the new function are:
[tex]\begin{gathered} D\colon\mleft\lbrace x\in\R\mright\rbrace_{\text{ }}or_{\text{ }}D\colon(-\infty,\infty) \\ R\colon\mleft\lbrace y\in\R\colon-3\le y\le-1\mright\rbrace_{\text{ }}or_{\text{ }}R\colon\lbrack-3,-1\rbrack \end{gathered}[/tex]Mrs. Thornton asked her students to draw a figure with a perimeter of 4x + 4. Shown below are 4 drawings madeby her students. (They are not drawn to scale.) Which one is NOT correct?А2x+11B2x2C.X + 4XDX+ 1X+ 1сdba
Answers
The perimeter is 4x+4
the formula of the perimeter of a rectangle is
[tex]P=2l+2w[/tex]for the first drawing
[tex]P=2(2x+1)+2(1)=4x+2+2=4x+4[/tex]It is correct
for the second drawing
[tex]P=2(2x)+2(2)=4x+4[/tex]It is correct
for the third drawing
[tex]P=2(x+4)+2x=2x+8+2x=4x+8[/tex]It is not correct
for the fourth drawing
[tex]P=2(x+1)+2(x+1)=2x+2+2x+2=4x+4[/tex]it is correct
As we can see the incorrect draw is C.
The distance d (in inches) that a beetle travels over time + (inseconds) is given by the function d (t) = 2t^3 . Find the averagespeed of the beetle from t1 = 0 second to t2 = 2 seconds.inches/second
Answers
Given distance,
[tex]d(t)=2t^3[/tex]Let v is the speed of the beetle.
It is given by
[tex]v=\frac{d(t)}{t}[/tex]Now,
[tex]\begin{gathered} v=\frac{2t^3}{t} \\ v=2t^2 \end{gathered}[/tex]At t = 0 sec.
[tex]\begin{gathered} v=2t^2 \\ v=2\times0 \\ v=0 \end{gathered}[/tex]At t = 2 sec.
[tex]\begin{gathered} v=2t^2 \\ v=2\times2^2 \\ v=8\text{ m/sec} \end{gathered}[/tex]So, the average speed of the beetle is 8 m/sec.
17. Write the equation of the line in slope-intercept form with the given information. 17. Passes through (-2, 6) with a slope of (-1/4)
Answers
Given:
Slope of line is m = -1/4 and passes through point (-2,6).
Explanation:
The general equation of line with slope m and passing through point (x_1,y_1) is,
[tex]y-y_1=m(x-x_1)[/tex]Determine the equation of line passing through point (-2,6) and have slope of -1/4.
[tex]\begin{gathered} y-6=-\frac{1}{4}(x-(-2)) \\ y-6=\frac{-1}{4}\cdot x-\frac{1}{4}\cdot2 \\ y=-\frac{x}{4}-\frac{1}{2}+6 \\ y=-\frac{x}{4}+\frac{11}{2} \end{gathered}[/tex]So equation of line is,
y = -x/4 + 11/2
how does you solve Vertices: (0,7), (0,-7) Co vertices: (2,0), (-2,0)
Answers
As according to given conditions let us draw these 4 points on the graph:
So the center is (0,0)
So the equation is:
[tex]\frac{(x-0)^2}{4}+\frac{(y-0)^2}{49}=1[/tex]7. On Friday, Stock 1 dropped 3/4 point and Stock 2 dropped 5/8 point. Based on this information, which statement is true? Stock 2 dropped more Stock 1 dropped more The stocks dropped the same amount O Both stocks sold at the same price Clear selection
Answers
Let's divide each fraction
[tex]\begin{gathered} \frac{3}{4}=0.75 \\ \frac{5}{8}=0.625 \end{gathered}[/tex]As you can observe, 3/4 is greater than 5/8.
Hence, Stock 1 dropped more.Find the distance between each pair of points using the distance formula - round to the nearest 10th
Answers
Explanation: Below we have the distance formula
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step 1: Now let's identify the values of the variable as follows
Step 2: Now we can substitute the values on the distance formula as follows
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(-4_{}-(-2))^2+(4_{}-0_{})^2} \\ d=\sqrt[]{(-4_{}+2)^2+(4_{}_{})^2} \\ d=\sqrt[]{(-2)^2+16^{}} \\ d=\sqrt[]{4^{}+16} \\ d=\sqrt[]{20} \\ d=4.472135955 \\ d\cong4.5 \end{gathered}[/tex]Final answer: So the distance between the pair of points rounded to the nearest tenth is 4.5
Scott borrowed $8000 at a rate of 19%, compounded annually. Assuming he makes no payments, how much will he owe after 8 years? Round your answer to the nearest cent
Answers
To answer this question we will use the following formula for compounded interest:
[tex]A=A_0(1+r)^t,[/tex]where A is the final amount, A₀ is the initial amount, r is the interest rate as a decimal number, and t is the number of times that the interest rate is applied.
Substituting A₀=8000, r=0.19, and t=8 we get:
[tex]A=8000(1+0.19)^8\text{.}[/tex]Simplifying the above result we get:
[tex]\begin{gathered} A=8000(1.19)^8, \\ A\approx32171.08 \end{gathered}[/tex]Answer: $32171.08.
I need some help please Find the inverse function of the given function.1. F(x)= x^2-4/2x^2
Answers
to solve this problem, we can follow some steps
step 1
replace f(x) with y
[tex]\begin{gathered} f(x)=\frac{x^2-4}{2x^2} \\ y=\frac{x^2-4}{2x^2} \end{gathered}[/tex]step 2
replace every x with a y and every y with an x
[tex]\begin{gathered} x=\frac{y^2-4}{2y^2} \\ \end{gathered}[/tex]step 3
solve for y
[tex]\begin{gathered} x=\frac{y^2-4}{2y^2} \\ \text{cross multiply both sides} \\ 2y^2\times x=y^2-4^{} \\ 2y^2x=y^2-4 \\ \text{collect like terms} \\ 2y^2x-y^2=-4 \\ \text{factorize y}^2 \\ y^2(2x-1)=-4 \\ \text{divide both sides by 2x - 1} \\ \frac{y^2(2x-1)}{(2x-1)}=-\frac{4}{(2x-1)} \\ y^2=-\frac{4}{2x-1} \\ \text{take the square root of both sides} \\ y=-\sqrt[]{\frac{4}{2x-1}} \end{gathered}[/tex]therefore the inverse of f(x) is
[tex]f^{-1}(x)=-\sqrt[]{\frac{4}{2x-1}}[/tex]find the values for A and B. explain of show your reasoning
Answers
Answer:
The value of a is 5, and b is 6.
Explanation:
The points on the line are (6,10), (a,8), (4,b) and (2,2).
• The slope of a straight line is always constant.
First, determine the slope using the points (6,10) and (2,2).
[tex]\begin{gathered} \text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{10-2}{6-2} \\ =\frac{8}{4} \\ =2 \end{gathered}[/tex]Next, using points (6,10) and (a,8):
[tex]\begin{gathered} m=\frac{10-8}{6-a} \\ 2=\frac{2}{6-a} \\ \text{Cross multiply} \\ 2(6-a)=2 \\ 12-2a=2 \\ -2a=2-12 \\ -2a=-10 \\ a=-\frac{10}{-2} \\ a=5 \end{gathered}[/tex]Next. using points (6,10) and (4,b):
[tex]\begin{gathered} m=\frac{10-b}{6-4} \\ 2=\frac{10-b}{2} \\ \text{Cross multiply} \\ 10-b=2\times2 \\ 10-b=4 \\ b=10-4 \\ b=6 \end{gathered}[/tex]The value of a is 5 and b is 6.
19. A wooden box has 20 cm on each edge. Find its volume.A. 875 cu. cmB. 8 000 cu. cmC. 8 875 cu. cm
Answers
Given:
Length of the edge of wooden box = 20 cm
Required:
The volume of wooden box.
Explanation:
The volume of cubical box is given as,
[tex]\begin{gathered} Volume\text{ = Edge}^3 \\ Volume\text{ = 20 cm }\times\text{ 20 cm }\times\text{ 20 cm} \\ Volume\text{ = 8000 cm}^3 \end{gathered}[/tex]Answer:
Thus the volume of the wooden box is 8000 cu. cm. The correct answer is option B.
a chemist has 30% and 60% Solutions of acid available how many liters of each solution should be mixed to obtain 120 liters of 34% acid solution
Answers
Answer:
104 litres of 30% solution and 16 litres of 60% solution.
Explanation:
Let us call x the litres of 30% solution and y the litres of 60% solution.
Now, we know that the end result is 120 litres of a solution; therefore, we have
[tex]x+y=120[/tex]Morover, we are also
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
The value of sin Ф will be [tex]2\sqrt{6} /5[/tex] .
What are trigonometric function?A right-angled triangle's angle can be related to side length ratios using trigonometric functions, which are real functions in mathematics. They are extensively employed in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more. The term "Circular" is another name for trigonometric functions. A triangle's angle functions can be used to define functions. It implies that these trig functions can be used to determine the relationship between a triangle's angles and sides. There are several trigonometric identities and formulas that show the relationship between the functions and aid in determining the triangle's angles. Here is an in-depth explanation of all these trigonometric functions and their formulas.
sin²Ф + cos²Ф = 1
sinФ = [tex]\sqrt{1 - 1/25}[/tex]
= [tex]2\sqrt{6} /5[/tex]
To know more about trigonometric function, visit:
brainly.com/question/26719838
#SPJ1
A certain college has been raising tuition every year since the year it opened. The function T = 12,000 (1+.03)* represents the tuition, T, after x years. If the college opened in the year 1990, what was the tuition in 2020?
Answers
Aline has a slope of -3/4 and a y-intercept of 5. Write an equation insiope-intercept for that could represent this situation."
Answers
Here, we want to write an equation in the slope-intercept form
Mathematically, we have this as;
[tex]y\text{ = mx + b}[/tex]b is the slope and m is the y-intercept
Thus, substituting the values we have in the question;
m = -3/4 and b = 5
Thus, we have the equation as;
[tex]y\text{ = -}\frac{3}{4}x\text{ + 5}[/tex]What’s 51,053 minus 12,947?
Answers
Answer:
The answer you're looking for would be 38,106.
Step-by-step explanation:
May I have Brainliest please? I am so close to getting my next ranking! I just need 3 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
- 12,947
—————
38106
10,720MasteryLook at the image below.4Course suRatios, rateArithmetic10Course cheTest yourthe skillsWhat is the area of the triangle?
Answers
The given triangle is not the regular drawing of a triangle. We need to identify the height and base.
From the diagram, the height = 10
base = 4
Substitute the values:
[tex]\begin{gathered} \text{Area of the triangle = }\frac{1}{2}\times\text{ 10}\times4 \\ \text{Area of the triangle = 20 units}^2 \end{gathered}[/tex]need help with the the association property etc
Answers
Line 1:
[tex](2+x)x[/tex]Line 2:
[tex]x(2+x)[/tex]Line 1 to Line 2 is:
Commutative property of Multiplication.
Line 3:
[tex]x(x+2)[/tex]Line 2 to Line 3 is:
Commutative property of Addition
-3x^2 – 24x – 13 = -13
Answers
oh,
if ace of 21 = 856 find ace 20 and ace of 22 given a common ratio of 1/4.
Answers
Answer:
[tex]a_{20}=214,a_{22}=3424[/tex]Explanation:
We are told that the common ratio between the numbers is 1/4, meaning each consquetive number is
Graph the solution set of each system of inequalities.19. 4x-y52x + 2y <6
Answers
The graph is given by:
The volume of the oceans and their seas is nearly 1.5 . 109 cubic kilometers. Write this number in Standard Form A:0.00000000015km³ B: 1,500,000,000km³ C: 0.0000000015km³ D: 15,000,000,000km³
Answers
Given data:
[tex]\text{1}.5\cdot10^9[/tex]the above number in standard form is.
1,500,000,000km³.
The answer is option c. 1,500,000,000km³
write 77.56 as a scientific notation
Answers
The scientific notation/standard form of 77.56 can be represented below
[tex]7.756\times10^1[/tex]The logic behind it is we shift the dot backward until it get to the last number. The number of step we took represent the exponential of 10.
*i will give you brainliest and 100 pts* Find the value of y. 3 cm 5 cm х 6 cm 2 cm 3cm. y = [?] cm Enter a decimal rounded to the nearest tenth. Enter
Answers
We have to use the secant theorem, which states
[tex](y+3)\cdot3=(9+2)\cdot2[/tex]Then, we solve for y
[tex]\begin{gathered} 3y+9=11\cdot2 \\ 3y=22-9 \\ y=\frac{13}{3}=4.3 \end{gathered}[/tex]Hence, y is equal to 4.3 cm.There are 110 calories per 177.4 grams of Cereal X. Find how many calories are in 246.5 grams of this cereal There are ? calories in 246.5 grams of this cereal ( round to the nearest whole number as needed )
Answers
We can solve this question by means of the rule of three, which can be stated as
[tex]\begin{gathered} 110\text{ calories ----------- 177.4 grams} \\ \text{ x ---------------- 246.5 grams} \end{gathered}[/tex]then by using cross-multiplication to calculate x, we have
[tex]x\cdot177.4\text{ grams=(110 calories)}\cdot(246.5\text{ grams)}[/tex]so, by dividing both sides by 117.4 grams, x is given as
[tex]\begin{gathered} x=\frac{\text{(110 calories)}\cdot(246.5\text{ grams)}}{177.4\text{ grams}} \\ x=152.54667\text{ calories} \end{gathered}[/tex]Therefore, by rounding this result to the nearest whole nuymber, there are 153 calories in 246.5 grams of cereal
The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90%pure fruit juice. The company is attempting to produce a fruit drink that contains 75% pure fruit juice. How many pints of each ofthe two existing types of drink must be used to make 170 pints of a mixture that is 75% pure fruit juice?First fruit drink:pintsХ5?Second fruit drink: pints
Answers
Let
x ----> number of pints of the First fruit drink
y ----> number of pints of the Second fruit drink
we have that
x+y=170 -------> x=170-y ----> equation A
65%=0.65
90%=0.90
75%=0.75
so
0.65x+0.90y=0.75(170) -----> equation B
Solve the system of equations
substitute equation A in equation B
0.65(170-y)+0.90y=0.75(170)
solve for y
110.5-0.65y+0.90y=
Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8, 9, 10}. Find a) A ∩ B ∩ C. b) A ∪ B ∪ C. c) (A ∪ B) ∩ C. d) (A ∩ B) ∪ C.
Answers
b) AuBuC = {0,1,2,3,4,5,6,7,8,9,10}
c) (AuB)nC ; (AuB) = {0,1,2,3,4,5,6,8,10}
:. (AuB)nC = {4,5,6,8,10}
d) (AnB)uC ; (AnB) = {0,2,4,6}
:. (AnB)uC = {0,2,4,5,6,7,8,9,10}
What is the slope of a line that goes through (2,6) and (4,12)?
Answers
Answer:
Slope = 3
Explanation:
To determine the slope of the line that goes through the given points: (2,6) and (4,12), we use the slope formula.
[tex]\text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}[/tex]Substituting the points, we have:
[tex]\begin{gathered} \text{Slope}=\frac{12-6}{4-2} \\ =\frac{6}{2} \\ =3 \end{gathered}[/tex]The slope of the line is 3.
what is the x intercept?
Answers
Answer:
x intercept is -2
Step-by-step explanation:
[4]How many solutions does the system of equations have?y = 7x-4y = 7x + 2 One Soluton Infinite Solutions No Solution
Answers
Given system of equations:
[tex]\begin{gathered} y\text{ = 7x - 4} \\ y\text{ = 7x + 2} \end{gathered}[/tex]Let us attempt to solve the equations
From equation 1:
[tex]y\text{ = 7x -4}[/tex]Substituting the expression for y into equation 2:
[tex]\begin{gathered} y\text{ = 7x + 2} \\ 7x\text{ -4 = 7x + 2} \\ \text{Collect like terms} \\ 7x\text{ - 7x = 2 + 4} \\ 0\text{ = 6} \end{gathered}[/tex]This imples that there is no solution to the system of equations.
We can plot the graph of the equations to better visualize and see that the lines don't intersect
The lines are parallel and do not intersect. Hence, there is no solution to the system of equations