Answers
[tex]x^2+4x-7=x^2+4x+4-11=(x+2)^2-11[/tex]
Related Questions
What are the coordinates of the vertex of the function f(x) = x2 − 12x + 5?
(6, 31)
(−6, 31)
(6, −31)
(−6, −31)
Answers
Answer: (6, -31)
Explanation: See attachment
2.) The quotient of 3 and y
Answers
Answer:
3 ÷ y
Step-by-step explanation:
Quotient refers to the division of two values, in this case 3 and y.
Answer:
3/y
Step-by-step explanation:
Encontrar los valores de x,y,z
Answers
The value of the angles x,y, and z is 73 degrees,88 degrees, and 55 degrees.
We have given that,
Two overlapping triangles
Here we have the angle Z and 52
What is the sum of the angle in a triangle?The sum of the all angle in a triangle is 180 degrees.
Therefore we have
The Z+43+52+40=180
Z+125=180
Z=55
Therefore in a triangle degree 52 degrees and 40 degree
y+52+40=180
y+92=180
y=180-92
y=88 degrees
For the angle x, we have
x+15+40+52=180
x+107=180
x=180-107
x=73
The value of the angles x,y, and z is 73 degrees,88 degrees, and 55 degrees.
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A polynomial f(x) has the given zeros of 7-1, and-3
Part A: Using the Factor Theorem, determine the polynomial f (x) in expanded form Show all necessary calculations (3 points)
Part B: Divide the polynomial f (x) by (x²-x-2) to create a rational function g(x) in simplest factored form. Determine g(x) and find its slant asymptote (4 points)
Part C: List all locations and types of discontinuities of the function g(x) (3 points)
Answers
The polynomial f(x) in expanded form is [tex]f(x) = x^3 - 3x^2 - 25x - 21[/tex]
The polynomial f(x)The polynomial zeros are given as:
x = 7, x = -1 and x = -3
Rewrite as:
x - 7 = 0, x + 1 = 0 and x + 3 = 0
Multiply the zeros
f(x) = (x - 7)(x + 1)(x + 3)
Expand
[tex]f(x) = (x - 7)(x^2 + 4x + 3)[/tex]
Further, expand
[tex]f(x) = x^3 + 4x^2 - 7x^2 + 3x - 28x - 21[/tex]
Evaluate
[tex]f(x) = x^3 - 3x^2 - 25x - 21[/tex]
Hence, the polynomial f(x) in expanded form is [tex]f(x) = x^3 - 3x^2 - 25x - 21[/tex]
Rational function g(x)We have:
[tex]g(x) = \frac{f(x)}{x^2 - x- 2}[/tex]
This gives
[tex]g(x) = \frac{x^3 - 3x^2 - 25x - 21}{x^2 - x- 2}[/tex]
Expand the numerator
[tex]g(x) = \frac{x^3 - x^2 - 2x^2 - 2x + 2x - 25x + 4 - 25}{x^2 - x - 2}[/tex]
Rewrite as:
[tex]g(x) = \frac{x^3 - x^2 - 2x - 2x^2 + 2x + 4 - 25x - 25}{x^2 - x - 2}[/tex]
Factorize
[tex]g(x) = \frac{(x - 2)(x^2 - x- 2) - 25x - 25}{x^2 - x- 2}[/tex]
Evaluate the quotient
[tex]g(x) = x - 2 - \frac{25x + 25}{x^2 - x- 2}[/tex]
The slant asymptote is the quotient i.e. x - 2
Hence, the slant asymptote of the function g(x) is x - 2
The discontinuities of g(x)In (b), we have:
[tex]g(x) = \frac{x^3 - 3x^2 - 25x - 21}{x^2 - x- 2}[/tex]
Set the denominator to 0
[tex]x^2 - x - 2 = 0[/tex]
Expand
[tex]x^2 + x - 2x - 2 = 0[/tex]
Factorize
x(x + 1) - 2(x + 1) = 0
Factor our x + 1
(x - 2)(x + 1) = 0
Solve for x
x = 2 or x = -1
2 is greater than -1.
So, the discontinuities and their types are:
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If the line segment joining the points A(4, − 5) and B(4, 5) is divided by the point P such that AP/PB = 2/5. find the co-ordinates of P.
Answers
Answer:
Step-by-step explanation:
0P=OA+AP
=OA+2/5(AB)
=(4,-5)+2/5(0,10)
=(4,-5)+(0,4)
=(4,-1)
therefore P(4,-1)
Please i need it for now PLSSSS
Answers
The measure of the other side of a quadrilateral is [tex]3\sqrt{13}[/tex] cm.
In the given quadrilateral one side is unknown we need to find the unknown side.
By dividing the given quadrilateral into a rectangle and a triangle we can find the other side.
What is Pythagoras theorem?The Pythagoras theorem states that if a triangle is right-angled, then the square of the hypotenuse is equal to the sum of the squares of the other two sides. That is, [tex]c^{2}=a^{2}+b^{2}[/tex].
Now, [tex]x^{2} =9^{2}+6^{2}=81+36=17[/tex]
⇒[tex]x=\sqrt{13 \times 9} =3\sqrt{13}[/tex]
Therefore, the measure of the other side of a quadrilateral is [tex]3\sqrt{13}[/tex] cm.
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Directions:
Sarah is going to the movies and she has $10 to spend on snacks. Smoothies are $3
and candy bars are $1 each. She will be spending all of the $10.
Budget: $10
Smoothies: $3
Candy bars: $1
Draw a line graph that represents the budget constraints and possible purchasing
options that Sarah has with her $10.
Answers
The attached graph represents the graph of the equation 3x + y = 10
How to determine the line graph?The given parameters are:
Budget: $10Smoothies: $3Candy bars: $1Represent the number of smoothies with x and the number of candy bears with y.
So, the equation is:
3x + 1y = 10
This gives
3x + y = 10
Next, we plot the graph of the above equation
See attachment for the graph of 3x + y = 10
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The line equation 3x + y = 10 represents the budget constraints and possible purchasing options that Sarah has with her $10, and the graph is shown in the picture.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
Sarah is going to the movies, and she has $10 to spend on snacks. Smoothies are $3 and candy bars are $1 each. She will be spending all of the $10.
Let's suppose the number of smoothies is x and the number of candy bars is y:
Then, we can frame a linear equation in one variable:
3x + y = 10
Drawing the above the line on the coordinate plane:
Thus, the line equation 3x + y = 10 represents the budget constraints and possible purchasing options that Sarah has with her $10, and the graph is shown in the picture.
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The expression for the nth term of a sequence is 4n+6
What are the first three terms in the sequence? Give your answers in
order.
Answers
Answer:
10, 14, 18
Step-by-step explanation:
We know that the nth term is '4n+6', so we just have to plug in whichever number we want for n, where n is the nth term in the sequence. The first term would be 4 * 1 + 6 = 10, the second term would be 4 * 2 + 6 = 14, and finally the third term would be 4 * 3 + 6 = 18. Therefore, your answer should be 10, 14, 18.
Need help (pic included)
Answers
Answer:
(-4,-2)
x=-4
y=-2
Step-by-step explanation:
-3x-4y=20
3(x-10y=16)=3x-30y=48
The reason I multiplied 3 to the second equation is for when we add the equations together the x will cancel out.
-3x-4y=20
+ 3x-30y=48
-34y=68
Divide -34 from both sides.
y=-2
To find x you need to plug in -2 for y into one of the equations.
x-10y=16
x-10(-2)=16
Remember a negative times a negative equals a positive.
x+20=16
Subtract 20 from both sides.
x=-4
Hope this helps!
If not, I am sorry.
HELP PLEASE!!!!!!!!!!!!!!!!!!!
Answers
Answer:
D.) x - 4
Step-by-step explanation:
This is a graph of an exponential/quadratic function. There general structure looks like this:
ax² + bx + c
Generally, when finding the zeros these functions, you are told to factor the equation. Once you have factored the equation, you can set the factors equal to zero to find the points where the function touches the x-intercept.
That being said, you can determine the factors without having the entire equation by identifying the zeros on the function. On this graph, there is a zero at (4,0). This means that one of the factors must have been "x - 4". You can check your work by setting the factor equal to zero.
x - 4 = 0
x = 4
find x ratio y... help please, i have a test tomorrow.
thanks
Answers
Answer:
27/4
Step-by-step explanation:
added in the picture
(05.06)
Which of the following points lie in the solution set to the following system of
inequalities? (1 point)
y<-3x+3
y
O (1.-5)
O (1.5)
O (5.1)
0 (-1.5)
Answers
What is the length of the missing side of this triangle?
A
2
B
10
C
50
D
100
the top is 26 bottom is 24 left side is the missing side
Answers
Answer:
The answer is B=10 and the top is called hypothenus
Answer:
x = 10
Step-by-step explanation:
The given is a right triangle, in right triangles the sum of square value of two legs (base and height) is equal to square value of hypotenuse.
Now, know the value of base and hypotenuse are 24 and 26
let x represent the missing side:
26^2 = x^2 + 24^2
676 = x^2 + 576 subtract 576 from both sides
100 = x^2 find the root of both sides
10 = x this is the length of the missing side
(2x²+3)(3x-2)-3x(x²-4)
Answers
Answer:
3x^3-4x^2+12x-6
Step-by-step explanation:
i hope this is right<3
If f(x) = -x-2, what is f¹(x)?
Answers
Answer:
f¯¹(x) =9x+18, for the pictorial(image) question what is the send question is it asking derivative or inverse If it is inverse f¯¹(x)=-x-2 as it isOr if it is derivative f'(x)=-1Step-by-step explanation:
For the image question f(x)=1/9x-2,f¯¹(x)=?f(x)=1/9x-2............giveny=1/9x-2................swapping f(x) by y to Easily writex=1/9y-2................interchanging x and y1/9y-2=x................changeling side of equation 9(1/9y-2)=(x)9.......multiplying both sides by 9 to override the fraction on the right side y-18=9xy=9x-18.................Return to where it weref¯¹(x)=9x+18..........swap back f¯¹(x) in the yFor the question f(x)=-x-2,f¯¹(x)=?following the ☝️ arrangement y=-x-2x=-y-2-y-2=x-y=x+2y=-x-2f¯¹(x)=-x-2A classroom monitors chicken eggs in various temperatures. The table shows the class's recorded results. Using the data in the table, a conclusion is made by calculating probabilities related to a randomly selected egg.
(see attachment for table)
Based on the information, which statement about the eggs is correct?
Given the egg has _______, the egg was kept warmer than room temperature.
answer choices for blank: hatched, not hatched
Answers
Given the egg has hatched, the egg was kept warmer than room temperature.
Given:Cool Room temperature Warm Total
Hatched 5 16 21 42
Unhatched 18 10 4 32
Total 23 26 25 74
To fill the blank we need to analyse the temperature carefully if see the table then cool hatched eggs are 5 , unhatched cool eggs are 18, eggs on room temperature and hatched are 16, eggs on room temperature and unhatched are 10, warm hatched eggs are 21 and warm unhatched eggs
So we can notice that hatched eggs are more in room temperature.
Hence hatched eggs are more in room temperature.
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Answer:
Given the egg has hatched the egg was kept warmer than room temperature.
Hope this helped!
can someone please help mee
Answers
Answer:
0,5 b
Step-by-step explanation:
Two number cubes are rolled for two separate events:
Event A is the event that the sum of numbers on both cubes is less than 10.
Event B is the event that the sum of numbers on both cubes is a multiple of 3.
Find the conditional probability of B given that A occurs first.
Answers
Answer:
You are right...........
Which step in the construction of copying a line segment ensures that the new line segment has the same length as the original line segment
Answers
Now out of these points, steps 5 and 6 are the main steps that ensure that the copied line segment is exactly the same as the original segment.
The steps to copy a line segment are given below:
1. Let's start with a line segment AB that we have to copy.
2. Now mark a point C. Below or above AB, which will be one endpoint of the new line segment.
3. Now, put the compass tip on point A of the line segment AB.
4. Spread the compass up to point B, so that the compass width is equal to the length of AB.
5. Without changing the compass width, now place the compass tip on point C that you made in step 2.
6. Now, draw an arc roughly without changing the compass settings. Mark that point D. This will form the new line segment.
7. Draw a line from C to D.
Now out of these points, steps 5 and 6 are the main steps that ensure that the copied line segment is exactly the same as the original segment.
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find the probability of at least 6 failures in 7 trials of a binomial experiment in which the probability of success in any one trial is 9%.
p=____%
Answers
The probability of at least 6 failures in 7 trials of a binomial experiment in which the probability of success in any one trial is 9% will be 0.000343311 %
What is the probability?Probability is synonymous with possibility. It is concerned with the occurrence of a random event.
Probability can only have a value between 0 and 1. Its simple notion is that something is very likely to occur. It is the proportion of favorable events to the total number of events.
No of failure,n = 7
No of trials,x≥6
A binomial probability is represented as;
[tex]\rm P(x) = nC_x p^z(1-p)^{n-r}[/tex]
Substitute the given data;
[tex]P(x \geq 6) = 7C_6 \times 9^6 \times 91-9)^{7-6} +7C_7 (9)^7+(1-9)^{(7-7)}[/tex]
[tex]\rm P(x \geq 6) = 0.000000343311 \\\\ P(x \geq6)=0.000343311 \%[/tex]
Hence,the probability of at least 6 failures in 7 trials of a binomial experiment in which the probability of success in any one trial is 9% will be 0.000343311 %
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Simplify
21x^6 y^5
14x^2y^9
Answers
Answer:
[tex]\frac{3x^{4} }{2y^{4} }[/tex]
Step-by-step explanation:
Factor out 7 from top and bottom :
[tex]\frac{7(3x^6y^5)}{7(2x^2y^9)}[/tex]
Divide top and bottom by 7 :
[tex]\frac{3x^6y^5}{2x^2y^9}[/tex]
Simplify :
[tex]\frac{x^6}{x^4}=x^{2}[/tex]
Simplify :
[tex]\frac{y^5}{y^9} = y^{-4} = \frac{1}{y^{4} }[/tex]
Collect everything together :
[tex]\frac{3x^{4} }{2y^{4} }[/tex]
Hope this helped and have a good day
In the diagram below, triangle lmn is congruent to cba. What is the length of segment ln?
Answers
Answer:
this is step by step explenation
see more...
Rotate the given triangle 90 degrees
CLOCKWISE about the origin.
0
0
07
0
-
-3 -4
0 -3
[?]
Answers
The value is [tex]\left[\begin{array}{ccc}0&3&4\\0&7&-1\end{array}\right][/tex]
what is clockwise and counterclockwise?Clockwise Rotations (CW) mimic the path of a clock's hands.
Negative numbers are used to represent these rotations. Counterclockwise rotations (CCW) follow the path of a clock's hands in the opposite direction.
Now, rotating 90 degree clockwise we get
[tex]\left[\begin{array}{ccc}0&3&4\\0&7&-1\end{array}\right][/tex]
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)In the figure below, lines m and n are parallel:
Two parallel lines are shown crossed by a transversal. The angles are labeled with number 1-8. The angles on line m where the line is crossed by the transversal are 1, 2, 4, and 3 in clockwise order from top left. The angles on line n where the line is crossed by the transversal are 5, 6, 8, and 7 in clockwise order from top left.
In the diagram shown, ∠6 measures 97 degrees. What is the measure of ∠5?
83 degrees
90 degrees
97 degrees
180 degrees
Answers
Based on the linear pair theorem, the measure of angle 5 is: A. 83 degrees.
What is the Linear Pair Theorem?The linear pair theorem states that if two angles are on a straight line, the sum of their measures equals 180 degrees.
∠5 and ∠6 are a linear pair. Therefore:
m∠5 = 180 - m∠6
m∠5 = 180 - 97
m∠5 = 83°
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Answer:83 degrees
Step-by-step explanation:topG
Deon has bought 18 pounds of dog food. He feeds his dog
Write your answer in simplest form.
2|3
pounds for each meal. For how many meals will the food last?
Answers
Answer:
6 to 9 meals
Step-by-step explanation:
9 If he feeds 2 pounds per meal. 18÷2 =9
6 if he feeds 3 pounds per meal. 18÷3=6
Maite's rent increased by 6%. The increase was $97.8. What was the original amount of Maite's rent? Please show me how to solve it as well please
Answers
Answer:
1630
Step-by-step explanation:
In words you are looking for 6% of what number is 97.80, turn that into an Algebra equation .06x = 97.80 so x = 97.80/.06 so x = 1630
sam and jose mowed 2/3 of the yard. jose mowed 3/4of that amount. whta part of the yard did jose mow?
Answers
Answer:
09
Step-by-step explanation:
34
square root of x plus 8 end root minus 6 equals x
Answers
Answer:
Squaring both the sides, we get a quadratic and solving it, we find that the possible values of x are -7 and -4.
Step-by-step explanation:
The expression can be written as √(x+8) - 6 = x. Take 6 on the other side and square both the sides.
[√(x + 8)]² = (x + 6)²
x + 8 = x² + 12x + 36
x² + 11x + 28 = 0
x² + 7x + 4x + 28 = 0
(x + 7)(x + 4) = 0
x = -7 and x = -4
The possible values of x are -7 and -4.
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The amount of weight a truck can hold is limited to 1200 pounds. If you weigh 165 pounds and each brick weighs 3 pounds, how many bricks, b, can you
haul?
Answers
Answer:
max weight truck can hold = 1200 pounds
your weight. 165 pounds
1200 - 165
1035 pounds left
3 pounds --- 1 brick
1035 --- ?
1035 / 3
345 can haulYou can haul 345 bricks in the truck.
How many bricks, b, can you haul?An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4.
From the given information, we have:
The amount of weight a truck can hold is limited to 1200 pounds.
You weigh 165 pounds and each brick weighs 3 pounds.
Number of bricks you can haul, b.
Thus, we can say:
Your weight + (Weight of each brick * Number of bricks) ≤ Total weight capacity of the truck
165 + (3 * b) ≤ 1200
3b ≤ 1200 - 165
3b ≤ 1035
b ≤ 1035/3
b ≤ 345
Therefore, you can haul 345 bricks in the truck.
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The sum of three times a first number and twice a second number is 14. If the second number is subtracted from twice the first number, the result is 7. Find the numbers. The sum of three times a first number and twice a second number is 14. If the second number is subtracted from twice the first number , the result is 7 . Find the numbers . Or as points
Answers
Step-by-Step Explanation:
Let the First Number be ‘x’
Let the Second Number be ‘y’
Framing 2 Equations :-
=> 3x + 2y = 14 (Eq. 1)
=> 2x - y = 7 (Eq. 2)
Multiplying Eq. 2 by 2 :-
=> 4x - 2y = 14 (Eq. 3)
Adding Eq. 1 and Eq. 3 we get :-
7x = 14 + 14
7x = 28
x = 28/7
=> x = 4
Therefore, x = 4
Substitute value of ‘x’ in Eq. 1 :-
3x + 2y = 14
3(4) + 2y = 14
12 + 2y = 14
2y = 14 - 12
2y = 2
y = 2/2
=> y = 1
Therefore, y = 1
Hence,
First Number = 4
Second Number = 1
