Answers
When solving the quadratic equation x² + 4x + 3 = 0 we get:
x = -1 and x = -3 .
What is completing the squares?In mathematics, completing the square is a method for converting a quadratic expression of the form ax² + bx + c to the vertex form ,a(x + m)² + n.
The most common application of this method is to solve a quadratic equation by rearranging the expression obtained after completing the square: a(x + m)² + n, so that the left side is a perfect square trinomial.Here given an equation,
x² + 4x + 3 = 0
(x² + 4x +4) + (-4 + 3) =0
(x² + 4x + 4 ) = 1
(x + 2)² = 1
x + 2 = ±√1
x + 2 = ± 1
x + 1 = 0
x + 3 = 0
x = -1
x = -3
The answers are underlined.
By solving the equation x² + 4x + 3 = 0 we get x = -1 and x = -3.
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Related Questions
express your answer as a polynomial in Itandard form.
Answer:
f(x) = x + 5
g(x) = x² - 4x + 8
Find: g(f(x))
Answers
The answer to g(f(x)) expressed as a polynomial in Standard form is x² + 6x + 13.
What is the Composition of Functions?The composition of the functions f(x) and g(x), where g(x) acts first, is denoted by f(g(x)) or (fog)(x). A new function is created by combining two or more existing functions. The output of the function inside the parenthesis that is being composed becomes the input for the function outside of the parenthesis. i.e.,In f(g(x)), g(x) is the input to f(x).In g(f(x)), f(x) is the input to g(x).Given the composition of functions g(f(x)),
For which f(x) = x + 5, and g(x) = x² - 4x + 8.
Considering f(x) as input we substitute it in g(x) in place of x.
g(f(x)) = (x+5)²- 4(x+5) + 8
= x² + 25 + 10x - 4x -20 + 8
= x² + 6x + 13
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4.5 simplified into a fraction is?
Answers
4.5 = 45/10 Using GCF
9/2
The figure below can be used to prove the Pythagorean Theorem. Use the drop-down menusto complete the proof.aababClick the arrows to choose an answer from each menu.The expression Choose... represents the area of the figure as the sum of the area of theshaded triangles and the area of the white square.The equivalent expressions Choose...use the length of the figure torepresent the area.Setting two of these area expressions equal to each other and subtracting Choose...from both sides of the equation results in the Pythagorean Theorem, a? + b2 = c?.
Answers
2ab + c²
(a+b)² and a² + 2ab + b²
2ab
1) Examining that picture, we can state the following about that:
The shaded triangles area:
[tex]\frac{1}{2}ab\text{ +}\frac{1}{2}ab+\frac{1}{2}ab+\frac{1}{2}ab=2ab[/tex]Note that the area of the triangle is 1/2 the product of the base by its height.
The area of that white inner square is given by c² since the Area of a square is equal to the side length raised to the 2nd powe.
2) Then
The expression 2ab + c² represents the area...
The equivalent expressions (a+b)² and a² + 2ab + b² use the length of the figure (a square) raised to the 2nd power. As explained above.
For the last statement let's calculate it:
2ab + c² = (a+b)²
a² +2ab + b² = 2ab +c² Subtracting 2ab
a² +b² = c²
3) Hence, the answers are:
2ab + c²
(a+b)² and a² + 2ab + b²
2ab
The mean of 6 numbers is 12.
The numbers are in the ratio 1 : 1 : 1 : 1 : 2 : 3.
Find the range.
Answers
Answer:
range = 16
Step-by-step explanation:
The total of all the numbers = mean x number of values = 6 x 12 = 72
The ratio of the numbers is
1: 1: 1: 1:2 :3
The sum of the ratios is 9
So the numbers in the ratio of 1 must be 1/9 x 72 = 8
The number with a ratio of 2 must be 2 x 8 = 16
and finally the number with the ratio of 3 = 3 x = 24
The range of the numbers is 24-8 = 16
Which fraction divided by 3/6 is equal to -9/10?
A. -3/2
B. -9/20
C. 9/20
D. 9/40
Answers
Reasoning: -9/20 is equal to -9/10 when divided by 3/6
because it is equivalent
10. The value of a new car decreases by 15% each year. The value (D) of the car after t years could be modelled as D = 23000(1 - 0.15) a) Show that the cost of the new car was £23 000. b) What is the cost of the car after 6 years? c) If we drew a graph, what would be the equation of the asymptote? - I just need help with question c
Answers
Answer:
y = 0
Step-by-step explanation:
The function has a horizontal asymptote at y = 0 where y is the value of the car
[tex]\text{Since the equation for the value of the car is }[/tex] [tex]23000(1-0.15)^t[/tex]
As [tex]t \rightarrow \infty, \text{the term } (1-0.15)^t \rightarrow 0 \\[/tex]
This is because the term (1-0.15) is < 1 and a nˣ approaches 0 as x → ∞ since the values get smaller and smaller with increasing powers of x
So the equation for the horizontal asymptote is y = 0
Provided graph to illustrate
state if the triangles are similar. If so, how do you know they are similar and complete the similarity statement.ABC
Answers
Remember that
If two triangles are similar, then the ratio of their corresponding sides is proportional and their corresponding angles are congruent
Verify the proportionality between corresponding sides
so
[tex]\begin{gathered} \frac{AB}{AV}=\frac{AC}{AW} \\ substitute\text{ given values} \\ \frac{42}{27}=\frac{24}{16} \\ 1.561.5\text{ } \\ \end{gathered}[/tex]that means
The triangles are not similar
Option AUse synthetic division to determine whether or not (2 – 1) is a factor of (-32% – 2x² – 1).-- Quotient:help (formulas)- Remainder:help (numbers)- Is (2 – 1) is a factor of (-323 – 2x2 - 1)?Yes No
Answers
Answer:
Explanations:
From the question, we are to use synthetic division to divide x - 1 by the polynomial function -3x^3 - 2x^2 - 1
Next is to use the synthetic division to carry out the operation as shown below;
From the calculation above, we can conclude the following;
[tex]undefined[/tex]WILL GIVE BRAINLIEST
A customer at a shipping store is planning to send a package and is considering two options. The customer can send a package for $3, plus an additional $2 per pound. The cost, y, can be represented by the equation y = 3 + 2x, where x represents the amount of pounds of the package. Another option is that the customer can pay a one-time fee of $17 to send the box, represented by the equation y = 17.
Based on the graph of the system of equations, when will the cost of the two shipping options be the same?
A package that weighs 10 pounds will cost $17 for both options.
A package that weighs 7 pounds will cost $17 for both options.
A package that weighs 17 pounds will cost $31 for both options.
A package that weighs 17pounds will cost $37 for both options.
Answers
The cost of the two shipping options be the same when B. a package that weighs 7 pounds will cost $17 for both options.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The cost, y, can be represented by the equation: y = 3 + 2x,
x = the amount of pounds of the package
Another option is that the customer can pay a one-time fee of $17 to send the box, represented by the equation y = 17.
The equation will be equated together.This will be:
3 + 2x = 17
Collect like terms
2x = 17 - 3
2x = 14
Divide
x = 14 / 2
x = 7
The weight is 7 pounds.
In conclusion, the correct option is B.
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Hank has just purchased a small rectangular fish tank that holds 950.4 milliliters of water. The tank has a width of 8.8 cm and a height of 9 cm. what is the length of the fish tank?
Answers
We will investigate how to determine one of the indicator dimensions of a regular figure.
We have a rectangular fish tank which can be modeled as a cuboid. The indicator lengths of a cuboid or a rectangular fish tank are as such:
[tex]\begin{gathered} \text{Length ( L ) } \\ \text{Width ( w ) = 8.8 cm} \\ \text{Height ( h ) = 9 cm} \end{gathered}[/tex]One of the indicator lengths of the rectangular fish tank Length ( L ) is unknown. Howver, we are given the total amount of water that the fish tank can withold as follows:
[tex]\text{Water in fish tank = 950.4 mL}[/tex]We will use the conversion factor between milliLiters and centimeter cube as follows:
[tex]1\text{ mL }\to1cm^3[/tex]Therefore,
[tex]950.4\text{ mL }\to950.4cm^3[/tex]The amount of water a fish tank can hold is equivalent to the volume of the fish tank. We have modeled our rectangular fish tank as a cuboid. The volume ( V ) of a cuboid can be expressed in terms of its indicator dimensions as follows:
[tex]V\text{ = L}\cdot w\cdot h[/tex]We can use the above volume expression to determine one off our missing indicator dimension of length ( L ). We plug in the respective quantities and evaluate:
[tex]\begin{gathered} 950.4\text{ = L}\cdot(8.8\text{ ) }\cdot\text{ ( 9 )} \\ \\ L\text{ = }\frac{950.4}{8.8\cdot9}\text{ = }\frac{950.4}{79.2} \\ \\ L\text{ = 12 cm} \end{gathered}[/tex]Therefore, the length ( L ) of the fish tank must be:
[tex]12\text{ cm }\ldots\text{ Answer}[/tex]Simplify.10(15 + n)150 n150 + n150 + 10 n50 + n
Answers
The Solution:
Given:
[tex]10(15+n)[/tex]We are required to simplify.
[tex]\begin{gathered} 10(15+n) \\ 150+10n \end{gathered}[/tex]Therefore, the correct answer is:
[tex]undefined[/tex]Jennifer is making frendship braclets. She makes 4 with neon colors for every 3 she makes. If Jennifer made 16 bracelts with neon colors, how many did she make with pastel colors?
Answers
She made 12 bracelets with pastel colors
Here, we want to get the number of bracelets she made with pastel colors
From the question, we are told that for every 4 bracelets she makes with neon colors, she has 3 bracelets made with pastel colors
So the ratio of neon to pastel color bracelets is 4 to 3
For the 16 neon bracelets, let the number of pastel colored bracelets made be x
Thus, we have;
[tex]\begin{gathered} 4\colon3\text{ = 16:x} \\ \frac{4}{3}\text{ = }\frac{16}{x} \\ \\ 4\text{ }\times\text{ x = 16 }\times\text{ 3} \\ \\ 4x\text{ = 48} \\ \\ x\text{ = }\frac{48}{4} \\ \\ x\text{ = 12} \end{gathered}[/tex]Answer: 12
Step-by-step explanation:
find figure 0 for the tile pattern below. write a rule that will give the number of tiles in any figure, record the data for the first six tiles 0-5 in a table, and graph the data
Answers
Solution
for this case we can see that for
Figure 0 = 6 tiles
Figure 1 = 7 tiles
Figure 2 = 8 tiles
Figure 3= 9 tiles
Figure 4 = 10 tiles
Figure 5= 11 tiles
Then the table would be given by:
Figure number (x) 0 1 2 3 4 5 x
Number of tiles (y) 6 7 8 9 10 11 6+x
And the line should be like this:
El cargo por servicio de Julia en un salón de belleza fue de $72.60 antes de impuestos. La tasa del impuesto sobre las ventas era del 8%. Si agregó el 20% de la cantidad antes de impuestos como propina, ¿cuánto pagó por el servicio en el salón?
Answers
Answer:
20.36
Step-by-step explanation:
72.60 cuando se divide por 100 se obtiene 1% o 0.73x8=5.84
entonces 72.60/10=7.26x2=20% o 14.52
14.52+5.84=20.36
Abdul, Beckie, Cynthia and Douglas are making pancakes according to the recipe below:Which person can make the most pancakes?BeckieAbdulCynthiaDouglas
Answers
To make 12 pancakes we need 100 g flour, 2 eggs, 300 ml milk
Abdul has 175 g flour, 4 eggs and 500 g milk
The ration between Abdul's amount of each ingredient and the total needed to make 12 pancakes is: (175/100) = 1.75 flour, (4/2) = 2 eggs, (500/300) = 1.67 milk.
So, the total amount of pancakes that Abdul can make is determined by the amount of the less abundant ingredient (milk): 1.67*12 = 20 pancakes
Doing the same steps for Beckie, we got that her less abundant ingredient is milk, with a ratio of 400/300 = 1.33. Then, she can make 1.33*12 = 16 pancakes.
For Cynthia, her less abundant ingredient is flour, with a ratio of 150/100 1.5. Then, she can make 1.5*12 = 18 pancakes.
And for Douglas, his less avundant ingredient is egg, with a ratio of 3/2 = 1.5. Then, he can make 1.,5*12 = 18 pancakes.
Therefore, Abdul is the one who can make the most pancakes
Francesca leaves her home and Drive South 150 km. Then she drives West 70 km. At this point, she drives North 30 km. Finally, she drives east 20 km. How far is she from her home? Included diagram of her trip.
Answers
To find the distance between her home and her latest position:
According to the question, the diagram is,
Consider the right triangle,
AB=120 km
BC=50 km
To find AC:
Using Pythagoras theorem,
[tex]\begin{gathered} AC^2=AB^2+BC^2_{} \\ =120^2+50^2 \\ =14400+2500 \\ =16900 \\ =130\text{ km} \end{gathered}[/tex]Hence, the distance between the new position and her home is 130 km.
will you kindly please work the math expressionpls brake in detail numbers
Answers
We are given the expression below:
[tex]\lbrack44+(4\times7)\rbrack\div9-5[/tex]To find the solution to the expression, we would make use of PEDMAS to other our steps on finding the solution. PEDMAS implies
[tex]\begin{gathered} P-Parenthesis \\ E-Exponential \\ D-Division \\ M-Multiplication \\ A-Addition \\ S-Subtraction \\ \end{gathered}[/tex]The order of PEDMAS would then be utilized in finding the value in the question.
[tex]\begin{gathered} \lbrack44+(4\times7)\rbrack\div9-5 \\ =\lbrack44+28\rbrack\div9-5 \\ =72\div9-5 \\ =8-5 \\ =3 \end{gathered}[/tex]Therefore, the answer is
[tex]3[/tex]The right option is option C
The number of bank robberies that occur in Lagos is modeled to be Poisson distributed with mean of 1.8 per day. Find the probability of getting exactly three robberies in a day.
Answers
The Poisson distribution is a discrete distribution that calculates the likelihood that a certain number of events will occur within a certain amount of time.
The probability of getting exactly three robberies in a day is 0.1607.
What is meant by poison distribution?The Poisson distribution is a discrete probability distribution used in probability theory and statistics to express the likelihood that a given number of events will occur within a specified time or space interval if they occur at a known constant mean rate and regardless of the interval since the last event.
The Poisson distribution is a discrete distribution that calculates the likelihood that a certain number of events will occur within a certain amount of time.
In the poison distribution a discrete random variable X has the following probability mass function,
[tex]$P(X=x)=\frac{e^{-\lambda} \cdot \lambda^x}{x !}$[/tex], where [tex]$\lambda$[/tex] is the mean of the distribution and [tex]$x=0,1,2,3 \ldots \ldots$[/tex]
Given that [tex]$\lambda=1.8$[/tex]
The required probability, [tex]$P(X=3)=\frac{e^{-1.8} .(1.8)^3}{3 !}=0.1607$[/tex]
Therefore, the probability of getting exactly three robberies in a day is = 0.1607.
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What is the percent of 80 of 62
Answers
i need help fast as possible and explanation
Answers
Answer:
x>0
Step-by-step explanation:
any number less than or equal to zero does not give a negative solution and you need a negative solution so x must be greater than 0
also could u do brainliest?
Segment AB has endpoints A (-5, 7) and B (4, 4). The segment is reflected over the line y =4 to create endpoints A'B' and then rotated 90° CW to form points A"B". Find the location of A" and B".
Answers
A(-5,7)
B(4,4)
The segment is reflected over the line y =4
The line y=4 is a horizontal line, coordinate in x doesn't change after reflection.
To find coordinate y after reflection:
Find the distance of each point from y=4
Point A: (-5,7)[tex]\lvert7-4\rvert=3[/tex]As y=4 is below the point A, the point A' will have a coordinate y of: 4-3=1
Point A': (-5,1)Point B: (4,4)[tex]\lvert4-4\rvert=0[/tex]As point B is on line y=4 the point B' will have a coordinate y of 4-0:4
Point B': (4,4)_____________________________then rotated 90° CW:
Rule for a rotation 90º CW:
[tex]P(x,y)\rightarrow P^{\prime}(y,-x)[/tex]Then, you get the next coordinates for A'' and B'':
[tex]\begin{gathered} A^{\prime}(-5,1)\rightarrow A^{\doubleprime}(1,5) \\ B^{\prime}(4,4)\rightarrow B^{\doubleprime}(4,-4) \end{gathered}[/tex]17. You divide 5 1/2 cups of juice evenly among 6 glasses. How much juice is in each glass?
Answers
Answer:
11/12
Step-by-step explanation:
hopes this helps, I am sorry if I am wrong
5 1/2 ÷ 6
11/2 ÷ 6
11/2 × 1/6
11/12
2+1+What are thex-intercepts ofthis quadratic?2 B-2t(-1, [?]); ([ ], [ )-3-44- 5+57
Answers
The x intercepts of the quadratic function are the points where the graph of the parabola intersects with the x axis.
In the given graph, the parabola intersects the x axis at points with coordinates (-1, 0) and (3, 0).
Therefore, the x intercepts of the quadratic are:
(-1, 0) ; (3, 0).
The Cougars scored a total of 84 points in their basketball game last nightagainst the Bears. The Cougars made no one-point shots, and a total of38 two-point and three-point shots. Let x represent the number of two-pointshots and y represent the number of three-point shots.a. How many two-point shots did the Cougars make? How many three-pointshots did the Cougars make? Write and solve a system of equations that canbe used to solve this problem.
Answers
Step 1: Write out the values
For Cougars
Total Points = 84
Number of 1 point shot = 0
Number of 3 and 2 points shots = 38
Step 2: Write out the system of equations
[tex]x+y=38---------------------(1)[/tex]Since there are x number of two-point shots, then the total number of points from the two-point shots is 2x
Also, there are y number of three-point shots, then the total number of points from the three-point shots is 3y
Hence, the total number of points is 2x + 3y
Therefore,
[tex]2x+3y=84----------------(2)[/tex]Step 3: Solve the system of equation simultaneously
x + y = 38 ------ equation 1
2x + 3y = 84 ------ equation 2
Using the elimination method to eliminate x
Multiply equation 1 by 2 to get a new equation
2x + 2y = 76 ------ equation 3
Step 4: combine equation 2 and 3 and solve simultaneously
2x + 3y = 84------- equation 2
2x + 2y = 76 ------ equation 3
Subtract equation 3 from 2
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Given the definitions of f(x) and g(x) below, find the value of (gof)(-8).
f(x) = 2x + 12
g(x) = 2x² + 2x + 12
Answers
(g o f)(-8) = 36
For f(x) = 2x + 12 and g(x) = 2x² + 2x + 12 the value of (g o f)(-8) is 36.
Solution:Given that f(x) = 2x + 12, g(x) = 2x² + 2x + 12.
to locate (g o f) (-8),
To find (g o f)(-8), we must first find g(f(x)) and then substitute x = -8.
Find g(f(x)) by substituting f(x) into g. (x)
= g(f(x)) = 2( 2x +12)² + 2( 2x + 12) + 12
x = -8 so,
g( f( - 8) ) = 2( 2(-8) +12)² + 2( 2(-8) + 12) + 12
g( f( - 8) ) = 2( -16 +12)² + 2( -16 + 12) + 12
g( f( - 8) ) = 2(-4)² + 2( -4 ) + 12
g( f( - 8) ) = 2 x 16 -8 + 12
g( f( - 8) ) = 32 - 8 + 12
g( f( - 8) ) = 36
So (g o f)(-8) = 36
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determine if the following are rotations
Answers
Answer: D and C are the other rotations
Step-by-step explanation: A is mirrored
Robert has 3 more than twice the number of t-shirtsthat Brianne has. Robert has 19 shirts. How manyShirts does Brianne have?** 3x + 219X+ 5 = 16* 2 + 3 =19
Answers
1) Considering that we can call t-shirts "x" then we can write out the following equations to express this problem:
Robert: 2x +3
Brianne: x
2) Now, we can write out the following equation to find out how many t-shirts does Brianne have:
[tex]\begin{gathered} 2x+3=19 \\ 2x+3-3=19-3 \\ 2x=16 \\ \frac{2x}{2}=\frac{16}{2} \\ x=8 \end{gathered}[/tex]So that's the number of t-shirts Brianne has. And the equation used is:
[tex]2x+3=19[/tex]Domain: 100, 200,300, 425, 575
Range: 100, 25, 200, 50, 75
Is this a function? Why or why not
Answers
Reason:
There aren't any repeated items in the domain. Each x input goes to exactly one y output. This is why we have a function.
The y values can repeat, but the function wouldn't be one-to-one (i.e. injective).
Solve for x.Question options:A) 11 B) 13 C) 12 D) 10
Answers
Notice that triangles QRS and YRZ are similar, therefore:
[tex]\frac{YZ}{QS}=\frac{YR}{QR}=\frac{1}{2}\text{.}[/tex]Substituting YZ=x+2, QS=3x-8, and solving for x we get:
[tex]\begin{gathered} \frac{x+2}{3x-8}=\frac{1}{2}, \\ 2(x+2)=3x-8, \\ 2x+4=3x-8, \\ x=12. \end{gathered}[/tex]Answer: Option C).
Miguel mixes plant food with water to feed his plants. The instructions on the
plant food say to mix 1 teaspoon of plant food into every 4 cups of water.
b. How much plant food should Miguel add to 7 cups of water? Use a model to show your work
Answers
The plant food should Miguel add to 7 cups of water is 336 plant food
What is Algebra?
One of the many different mathematical disciplines is algebra. Algebra, a common thread that runs through nearly all of mathematics, is the study of mathematical symbols and the rules for using them in formulas.
To feed his plants, Miguel combines water and plant food. According to the directions on the plant food, you should add 1 teaspoon to every 4 cups of water. To demonstrate the relationship between cups of water (w) and teaspoons of plant food (f), create an equation.
48 teaspoons = 1 cup.
1 teaspoon = plants food
4 cups = water.
= 48 teaspoons x 4.
= 192 teaspoons
The formula is:
water in cups = w
Teaspoon of nourishment for plants equals f
The mixture = 192w + f
The relation between f and w is f = kw.
1 teaspoon = plant food
7 cups = water.
= 48teaspoon x 7
= 336teaspoon
The formula is:
water in cups = w
Teaspoon of nourishment for plants equals f
The mixture = 336w + f
Hence, 336 plant food should Miguel add to 7 cups of work
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