5(x2 + 4x + 4) = 7 + 20 quadratic equation by completing the square The correct statement is 5(x2 + 4x + 4) = 7 + 20.
What distinguishes a quadratic equation?A quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero. A parabola is a curve that represents the graph of a quadratic function. Parabolas can have openings that are upward or downward, different "widths" or "steepnesses," but they all share the same fundamental "U" shape.
Describe the fundamental quadratic equation?Quadratic equations are the degree two, one-variable polynomial equations of the form f(x) = ax2 + bx + c = 0, where a, b, c, and an are all divisible by R and an is equal to zero. It is the quadratic equation's general form, with 'a' standing for the leading coefficient and 'c' standing for the absolute term of f. (x).
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Classify the given angle.
right angle
obtuse angle
acute angle
straight angle
Answer: Acute Angle
Step-by-step explanation: It is less than 90 degrees (right angle) so it is an acute angle
Answer:
Step-by-step explanation:
Acute Angle 100% Correct!!
Ayuda, me gustaría su ayuda con mi tarea
Answer:
1.) x = 1, 2/3
2.) x = -3±[tex]\sqrt{6}[/tex]
3.) x = [tex]\frac{4+/-\sqrt{37} }{3}[/tex] or x = −3.36092084, 0.69425417
Step-by-step explanation:
These are quadratic equations so we use the quadratic formula method.
Use the quadratic formula by taking:
[tex]ax^{2}+bx^{2} +c=0[/tex]
1.) a = 3, b = -5, c = 2
2.) a = 1, b = 6, c = 3
3.) a = -3, b = -8, c = 7
Then, substitute into the quadratic formula:
(Check the picture provided for the quadratic formula)
A small technology company started offering shares of stock to investors in 1987. At that time, the price of one share of stock was $0.39. Since then, the company has experienced rapid growth. Twenty-two years later, the price of a single share of stock has risen to over $110. One scatterplot shown summarizes the number of years since the initial stock offering in 1987 and the price of the stock, while the other compares years since 1987 to the log of stock price.
Based on these scatterplots, what type of model is most appropriate for summarizing the relationship between year and stock price?
A linear model is appropriate because the scatterplot of the transformed data is roughly linear.
An exponential model is appropriate because the scatterplot of time and log price is increasing.
An exponential model could be appropriate because the scatterplot of log height versus log weight is roughly linear. The next step is to look at the residual plot.
A power model is appropriate because the scatterplot of time and price shows a curved relationship.
PLS HURRY
These scatterplots show that model type A is best suited to summarize the relationship between year and stock price. The scatterplot of the processed data is nearly linear, so a linear model is suitable.
What is linear model ?These scatterplots show that model type A is best suited to summarize the relationship between year and stock price. The scatterplot of the processed data is nearly linear, so a linear model is suitable.
A linear model is applicable if we can create a linear equation based on the connection between the independent and dependent variables (because there is no constant rate of change).
Otherwise, we can simulate the relationship using an exponential model.
An exponential model is:When the rate of increase representing the relationship between the year and stock price is proportional or constant, we utilize the exponential model.
By determining whether the ratio of the dependent values is the same, one can choose to describe the connection as an exponential equation.
As a result, even though the time and price scatterplot is curved, a linear model is adequate.
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What is the perimeter of triangle mno
Answer:
[tex]\huge{\boxed{82.8\text{ units}}}[/tex]
Step-by-step explanation:
Because the triangles have all of the same angles, similarity can be proven via AAA.
Now that ΔJKL ~ ΔMNO, the sides must be proportional.
Because the sides are proportional, the following equation can be made:
[tex]\frac{24}{20}=\frac{x}{22}[/tex]
Via cross-multiplication, the equation simplifies to:
20x = 24 * 22
20x = 528
x = 26.4
Now, because perimeter is simple the sum of all sides, the perimeter of ΔMNO is simply 32.4 + 24 + 26.4, or 82.8.
Hope it helps :) and let me know if you want me to elaborate.
the number of cells in a specimen of bacteria doubles every hour. what type of function best represents the growth of the bacteria?
An example of an exponential function is the growth of bacteria. the growth of the bacteria is by exponential growth in the number of cells in a specimen of bacteria doubles every hour.
Some bacteria double her size every hour. Starting with 1 bacterium, every hour he doubles, after x hours he doubles as bacterium. This can be written as f(x) = 2x.
Bacteria replicate by binary fission, the process by which one bacterium divides into two. Bacteria therefore multiply in number by a geometric progression, doubling the population with each generation. The binary fission is the actual multiplication procedure of the cells division where cells grows fastly and further divided itself into other groups or colony.
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A cyclist rides her bike at a speed of 18 miles per hour. What is this speed in kilometers per hour? How many kilometers will the cyclist travel in 5 hours? In your
computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
Speed: Distance traveled in 5 hours:
The speed in kilometres per hour is 28.8 km/hr.
The distance in kilometres the cyclist will travel in 5 hours is 144 km.
How to find speed and distance?A cyclist rides her bike at a speed of 18 miles per hour. The speed in kilometres per hour an be calculated as follows;
1 miles = 1.6 km
18 miles = ?
cross multiply
distance in km = 18 × 1.6
distance in km = 28.8 km
Therefore, the speed in kilometres per hour is 28.8.
The kilometres the cyclist will travel in 5 hours can be calculated as follows;
speed = distance / time
28.8 = d / 5
cross multiply
distance travelled in km = 28.8 × 5
Therefore,
distance travelled in km = 144 km
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A rectangular fish tank has width w inches, length w + 8 inches, and height 18 - w inches. All dimensions are greater than 6 inches. The volume of the tank is 1440 cubic inches. Find the length, width, and height of the fish a. width: 12 in., length: 20 in., height: 6 in. b. width: 10 in., length: 18 in., height: 8 in. C width: 10 in., length: 8 in., height: 18 in. d. width: 12 in., length: 18 in., height: 8 in.
Answer:
To find the dimensions of the fish tank, we can set up the equation:
(width) * (length) * (height) = 1440 cubic inches
Substituting the given expressions for the dimensions of the tank, we get:
(w) * (w + 8) * (18 - w) = 1440
This is a quadratic equation in w, and we can solve it using the quadratic formula:
w = (-(w + 8) +/- sqrt((w + 8)^2 - 4*(18 - w)11440)) / (2*1)
This simplifies to:
w = (-(w + 8) +/- sqrt(w^2 + 16w + 64 - 72w + 5760)) / 2
= (-(w + 8) +/- sqrt(w^2 - 56w + 5760)) / 2
We can further simplify this equation by factoring:
w = (-(w + 8) +/- sqrt((w - 40)(w - 144))) / 2
We can then solve for w by setting each factor equal to zero:
w - 40 = 0 => w = 40
w - 144 = 0 => w = 144
Since the width of the fish tank must be greater than 6 inches, the only valid solution for w is 40 inches. Substituting this value back into the equation for the volume of the tank, we find that the length of the tank is 48 inches (w + 8 = 40 + 8 = 48) and the height of the tank is 12 inches (18 - w = 18 - 40 = 12).
Therefore, the dimensions of the fish tank are:
width: 40 inches
length: 48 inches
height: 12 inches
The correct answer is therefore (a) width: 12 in., length: 20 in., height: 6 in.
Step-by-step explanation:
Unit 3 Lesson 8 Cumulative Practice Problems
1. This is an invalid proof that all isosceles triangles are similar. Explain which step is
invalid and why.
1. Draw 2 isosceles triangles ABC and DEF where AC = BC and DF = EF.
2. Dilate triangle ABC to a new triangle A'B'C using center C and scale factor de so
that A'C = B'C = DF = EF.
3. Translate by directed line segment CF to take A'B'C to a new triangle A"B" F.
Since translation preserves distance, A" F = A'C= DF and B" F = BC = EF.
4. Since A" F = DF, we can rotate using center F to take A" to D.
5. Since B" F = EF, we can rotate using center F to take B" to E.
6. We have now established a sequence of dilations, translations, and rotations that
takes A to D, B to E, and C to F, so the triangles are similar.
Answer:
Step-by-step explanation:
Let ABC be an isosceles triangle with lateral sides AB and AC, a base of BC, and medians of AC and AB, respectively, at BD and CE.
In △ACE and △ABD ,
AB≅AC lateral sides of isosceles triangle
∠A≅∠A common angle
AE≅AD half segments of equal lateral sides
As a result, ACE ≅ABD according to the side angle side theorem. as a result, median BD is consistent with median CE.
If any two figures can be positioned exactly over one another, the congruence between them can be seen. The relationship between two figures is referred to as their congruence, and is expressed using the word "congruence".
In other terms, two geometric figures are said to be congruent if they can be superimposed on one another.
All figures, including triangles, quadrilaterals, and other shapes, have this feature. Along with figures, line segments and angles that have the same measure are also said to be congruent. To comprehend what congruent figures represent, look at the following figure.
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If g(x)=x^2+6 and f(x)=2x-4, find g(f(x))
The value of the function g(f(x)) is 2x² - 8x + 11.
What is function?
In the composition of functions, we completely swap out one function for another. The function f with g has the notation (fg)(x)=f(g(x)) and is read as f of g of x. It signifies that the function g(x) is substituted for every instance of an x in the function f.The combination of two functions is frequently referred to as a "function of a function," and g*f is sometimes represented as g.f.g(x) = x² + 6
f(x) = 2x - 4
g(f(x)) = (2x-4)² + 6
= 4x² - 16x + 16 + 6
= 4x² - 16x + 22
= 2x² - 8x + 11
Hence, the value of the function g(f(x)) is 2x² - 8x + 11.
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Given the system below,
9x+3y=-18
y=x+7
What is the ordered pair for the intersection
)?
Answer:
(-3.25,3.75)
Step-by-step explanation:
Thuis can be answered with either of two approaches: Graphing and Matematical. We'll do both:
Graphing
Graph both equations. It is helpful to use a free online graphing utility: DESMOS.
The attached graph reveals the intersection of the lines at point (-3.25, 3.75).
Matematical
Solve the equations be using substitution. Rearrange either equation to isolate one of the two variables (x or y).
Lets use the second, since y is already isolated, making the task simple and fast. But the other equation could also be used, if desired.
y=x+7
Now use this expression of y in the other equation:
9x+3y=-18
9x+3(x+7)=-18
9x +3x +21 = -18
12x = -39
x = -(39/12)
x = -3 - (3/12)
x = -3.25
Now use x= -3.25 in either equation tand solve for y:
y=x+7
y=(-3.25)+7
y = 3.75
The solution to this series of equations is (-3.25,3.75)
surveys, if not done correctly, can lead to seriously biased samples. which is not a bias due to the sampling plan?
Volunteer/voluntary response bias, also known as self-selection bias, occurs when research participants exert control over the decision to engage in the study.
What is Probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let's look at a straightforward application.
Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.
There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.
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A bank features a savings account that has an annual percentage rate of r=3.5% with interest compounded quarterly. Althea deposits $3,500 into the account.
What values should be used P, r, and n?
How much money will Althea have in the account in 8 years? Round to the nearest penny.
Althea will have a $4625.32 compound amount in the account in 8 years.
What is compound interest?
The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. Compound interest is computed as interest on the initial principal plus any accrued interest from prior periods.
Given,
Principal (P) = $3,500
rate of interest (r) =3.5% = 0.035
for compounded quarterly (n) = 4
time (t) = 8 years
The compound amount is given by
[tex]A = P(1+\frac{r}{n})^{nt}\\A = 3500(1+\frac{0.035}{4})^{4*8}[/tex]
A = 4625.32
Hence, Althea will have $4625.32 in the account in 8 years.
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What value of w makes the equation 3(−4w−5)=−7(5+w) true?
4 is the value of w which makes the equation true.
What is an equation?
There are many different ways to define an equation. A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.There are three main types of equations depending on the degree. More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.A quadratic equation must have at least one variable with an exponent of 2.A third-order equation is a cubic equation. Cubic equations need the exponentiation of at least one variable.It is given that,
3(−4w−5)=−7(5+w)
by solving the equation,
-12w-15=-35-7w
12w-7w=35-15
5w=20
w=20/5
∴w=4
Hence, 4 is the value of w which makes the equation true.
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ABC has vertices at a(11,6), B(5,6), and (5,17).
The correct statements regarding the congruent triangles are given as follows:
Triangle ABC and triangle MNO are congruent by a sequence of rotations and translations.Triangle JKL and triangle ABC are congruent by a single rotation.What are congruent triangles?Congruent triangles are triangles in which the outer side lengths have the same measure.
Then the triangles ABC and triangle MNO are congruent by a sequence of rotations and translations, as both are right triangles.
Triangle JKL and triangle ABC are congruent by a single rotation, as the distances between the vertices of each triangle are equal.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Hello, can someone help me out with these two questions please!?!?!?
Answer: No solution
Step-by-step explanation:
3(2x + 3) - 3x = 9 + 3x
6x + 3 - 3x = 9 + 3x - 3x
6x + 3 - 6x = 9
3 = 9
No solution
a study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. it was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 2.75 days with an approximately normal distribution. (a) find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places.
Therefore, the probability that their hospital stay is from 5 to 6 days is 0.03310 .
What exactly is probability?Probability deals with calculating or making estimates of how probable or "possible" an event is to occur. To convey the probability of an event occurring, words like "certainly," "impossible," or "likely" might be employed. Probabilities are always represented in mathematics as fractional, decimals, or percentages, with values that range from 0 to 1.
Here,
Given:
Mean, μ =7.37 days
Standard Deviation, σ = 2.75 days
Given: hospital stays are distributed in a bell-shaped manner, which is a typical distribution.
Formula:
Z = [tex]\frac{x-u}{\alpha }[/tex]
a) P( 5 to 6 days are spent in the hospital.)
P(5≤x≤6)
=>P([tex]\frac{5-7.37}{2.75}[/tex] ≤x≤ [tex]\frac{6-7.37}{2.75}[/tex])
=>P(-0.861≤x≤-0.498)
=>P(Z≤-0.498) - P(Z<-0.861)
=>0.034 - 0.001 = 0.03310
=> P(5≤x≤6) =3.3%
Therefore the probability that their hospital stay is from 5 to 6 days is 3.3%.
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2. Multiply the polynomials (4a³-5a - 3) and (2a² - 7a+ 3). Simplify the answer. Show your work.
Can the answer be given by hand please
Answer:
Step-by-step explanation:
A builder need 2,964 nail to finih a project. If the nail come in package of 52, how many package hould the builder purchae?
Number of nails to finish the project by buying are required = 2964 units
1 package of nails contains per unit = 52 units
To find the no. of packages we have to simply divide the total no. of nails required by the total of no. of nails of unit given in the one package of nails.
So,
Number of package required to the builder
= Total number of nails required to buy by the builder / no. of nails provided per package
=2964/52
=57 packages
Therefore, No. of packages required by the builder to buy to complete the project
=57 packages needed.
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Answer: 57
Step-by-step explanation:
Just plug it into a calculator.
2964/52 = 57
He needs to buy 57 packages
fraction find the missing number 1/2 of 30= 1/4=
The missing number in the equation 1/2 of 30 = 1/4 is 60
How to determine the missing number?From the question, we have the following parameters that can be used in our computation:
1/2 of 30 = 1/4
This equation can be properly expressed as
1/2 of 30 = 1/4 of __
Represent the blank with a variable x
So, we have the following representation
1/2 of 30 = 1/4 of x
Express as products
1/2 * 30 = 1/4 * x
Multiply both sides by 4
This gives
x = 4 * 1/2 * 30
Evaluate
x = 60
Hence, the missing number is 60
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The perimeter of a rectangle i 104m the length i 7m more than twice the width. What are the dimenion of the rectangle
Size will be 37 L x 15 W.
What is perimeter?Perimeter is the distance around the edge of a shape. Discover how to calculate a shape's perimeter by adding its side lengths.
Finding the dimension is required, if the perimeter is 104 meters and the length is 7 meters longer than twice the breadth.
Let L be the length and W be the width
L = 7 + 2*W
P = 2(L + W) ; 104 = 2(7 + 2W + W) ; 104 = 2(7 + 3W) ;
104 = 14 + 6W
6*W = 90 ;
W = 15 L = 37
Hence the dimension is 37*15
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Need help with this, Plot the points that represent the profit you can expect to earn each month, for each business, on a single xy-plane. You can create your plot by hand or you can use Desmos to help you. HINT: Use a different, single color for each business to help you keep track of your points
A value of lawn care is negetive because the profits are decreasing after month-3. So it is sloping downards. Had the profits been raising the a-value would have been positive.
Based on the plot the profits of each month can be found out using a qudratic function?
The lawn care business shows diminishing returns after month 3 . So it is not a viable business to conitnue for the long term. Based on the projections around month 8 profit becomes -$14.44. This is loss.
The other two businesses are profitable. The show upward growing trend as the months progress. Following table shows projected earnings for 1 year based on the equations showed in the graph.
3. A quadratic funtion can be used to represent the profits. The equation is given in the plots
4. A value of lawn care is negetive because the profits are decreasing after month-3. So it is sloping downards. Had the profits been raising the a-value would have been positive.
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Select the statement that correctly describes the
solution to this system of equations,
18x-2y=-4
4x-y=-2
There is exactly one solution at (2.0),
There is no solution,
There is exactly one solution at (0-2).
There are infinitely many solutions.
HELP ASAP
The solution of the equations 18x - 2y = -4 and 4x - y = -2 is (0,-2). Hence option c is the correct option.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given pair of equations is
18x - 2y = -4 ....(i)
4x - y = -2 .....(ii)
To solve the equation apply elimination method.
Multiply equation (ii) by 2 and subtract it from (i):
18x - 2y = -4
8x - 2y = -4
(-) (+) (+)
_________
10x = 0
x = 0
Putting x = 0 equation (ii)
0 - y = -2
y = 2
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Consider the system of equations
5x+3y=30
−5x−2y=−25
Part A: Solve the system. Show your work.
Part B: Use the solution to your equation to find the value of x – y. Show your work.
x−y =
What will happen to the graph of the line y = -54x + 3 if you change -54 to 54?
Imagine Math
Calcula el número si 30 menos el triple del número es cuatro veces la diferencia del triple del número más 10
Answer:Calcula el número si 30 menos el triple del número es cuatro veces la diferencia del triple del número más 10
Step-by-step explanation:
Will mark as brainiest. Please help more points!
The total area of the two shaded faces of the cuboid below is = 112[tex]cm^{2}[/tex]
Since the two shaded faces of the cuboid shown are adjutant to each other and are of the same dimensions so according to the calculations -
Let us consider only one side of the shaded portion-
The length of the shaded part = 8cm
The width of the shaded portion = 7cm
So it appears that due to the uneven measure of length and breath this is a rectangle, so the area of a rectangle
= [ length (l) x width(w) ]
= 8cm x 7cm
= 56[tex]cm^{2}[/tex]
Since the question asks the total area of both sides so because both the shaded sides are equal then total area = 56 x 2 = 112 [tex]cm^{2}[/tex]
Therefore, the total area of the shaded faces of the cuboid = 112[tex]cm^{2}[/tex]
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What is an equation of the line that passes through the point (4,1) and is perpendicular to the line 2x-y=4
Answer: [tex]y-1=-\frac{1}{2}(x-4)[/tex]
Step-by-step explanation:
The equation of the given line can be rearranged as [tex]y=2x-4[/tex].
Perpendicular lines have slopes that are negative reciprocals, so the slope of the line we need to find is -1/2.
Using point-slope form, the equation is [tex]y-1=-\frac{1}{2}(x-4)[/tex].
Which product is represented by the model?
A. 0.05×0.04=0.002
B. 5×0.4=2
C. 0.5×0.4=0.2
D. 0.5×0.04=0.02
The value of inserting area of an array is 0.02
What is meant by area ?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
The region that an object's shape defines as its area. The amount of space occupied by a figure or any other two-dimensional geometric shape in a plane is known as its area.
Given:
5 column (hundred grid) = 5/100 = 0.05
4 row (hundred grid) = 4/100 = 0.04
Find:
Area equation
Computation:
Area equation = 0.05 x 0.04
0.05 x 0.04 = 0.002
Therefore the value of inserting area of an array is 0.02
The complete question is : Which product is represented by the model? A hundred grid model shows 5 columns shaded and 4 rows shaded. The intersecting area is an array that is 5 by 4. A. 0 . 05 × 0 . 04 = 0 . 002 B. 5 × 0 . 4 = 2 C. 0 . 5 × 0 . 4 = 0 . 2 D. 0 . 5 × 0 . 04 = 0 . 02
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(25 points)
Which inequality is represented by this number line?
Answer:
C
Step-by-step explanation:
Pick point 7 and sub into the equations
eq 1 not equal to 10
eq 2 not equal to 12
eq 3 is equal to 15
eq 4 not equal to 18
Now sub in the value of -3 into equation 3 Yes equal to 15
so answer is eq 3
numbers greater than 7 and less than -3 are also true ....
is x^4+2x^3-x^2+7x+11 a quintic binomial
On solving the provide question, we got that - [tex]x^4+2x^3-x^2+7x+11[/tex] is not a quintic binomial
What is quintic polynomial?A mathematical word raised to the fifth power of the independent variable. B. Or 5th order polynomial in the form of 5th order or 5th order for 5th order (not equivalent).
What is an example of a quintic polynomial?A polynomial of degree 5. Examples: x5 – x3 + x, y5 + y4 + y3 + y2 + y + 1, and 42a3b2.
[tex]x^4+2x^3-x^2+7x+11[/tex] is not a quintic binomial
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